C ALGORITHM 656, COLLECTED ALGORITHMS FROM ACM. C THIS WORK PUBLISHED IN TRANSACTIONS ON MATHEMATICAL SOFTWARE, C VOL. 14, NO. 1, P.18. * ************************************************************************ * * File of the REAL Level-2 BLAS. * =========================================== * * SUBROUTINE SGEMV ( TRANS, M, N, ALPHA, A, LDA, X, INCX, * $ BETA, Y, INCY ) * * SUBROUTINE SGBMV ( TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX, * $ BETA, Y, INCY ) * * SUBROUTINE SSYMV ( UPLO, N, ALPHA, A, LDA, X, INCX, * $ BETA, Y, INCY ) * * SUBROUTINE SSBMV ( UPLO, N, K, ALPHA, A, LDA, X, INCX, * $ BETA, Y, INCY ) * * SUBROUTINE SSPMV ( UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY ) * * SUBROUTINE STRMV ( UPLO, TRANS, DIAG, N, A, LDA, X, INCX ) * * SUBROUTINE STBMV ( UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX ) * * SUBROUTINE STPMV ( UPLO, TRANS, DIAG, N, AP, X, INCX ) * * SUBROUTINE STRSV ( UPLO, TRANS, DIAG, N, A, LDA, X, INCX ) * * SUBROUTINE STBSV ( UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX ) * * SUBROUTINE STPSV ( UPLO, TRANS, DIAG, N, AP, X, INCX ) * * SUBROUTINE SGER ( M, N, ALPHA, X, INCX, Y, INCY, A, LDA ) * * SUBROUTINE SSYR ( UPLO, N, ALPHA, X, INCX, A, LDA ) * * SUBROUTINE SSPR ( UPLO, N, ALPHA, X, INCX, AP ) * * SUBROUTINE SSYR2 ( UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA ) * * SUBROUTINE SSPR2 ( UPLO, N, ALPHA, X, INCX, Y, INCY, AP ) * * See: * * Dongarra J. J., Du Croz J. J., Hammarling S. and Hanson R. J.. * An extended set of Fortran Basic Linear Algebra Subprograms. * * Technical Memoranda Nos. 41 (revision 3) and 81, Mathematics * and Computer Science Division, Argonne National Laboratory, * 9700 South Cass Avenue, Argonne, Illinois 60439, US. * * Or * * NAG Technical Reports TR3/87 and TR4/87, Numerical Algorithms * Group Ltd., NAG Central Office, 256 Banbury Road, Oxford * OX2 7DE, UK, and Numerical Algorithms Group Inc., 1101 31st * Street, Suite 100, Downers Grove, Illinois 60515-1263, USA. * ************************************************************************ * SUBROUTINE SGEMV ( TRANS, M, N, ALPHA, A, LDA, X, INCX, $ BETA, Y, INCY ) * .. Scalar Arguments .. REAL ALPHA, BETA INTEGER INCX, INCY, LDA, M, N CHARACTER*1 TRANS * .. Array Arguments .. REAL A( LDA, * ), X( * ), Y( * ) * .. * * Purpose * ======= * * SGEMV performs one of the matrix-vector operations * * y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, * * where alpha and beta are scalars, x and y are vectors and A is an * m by n matrix. * * Parameters * ========== * * TRANS - CHARACTER*1. * On entry, TRANS specifies the operation to be performed as * follows: * * TRANS = 'N' or 'n' y := alpha*A*x + beta*y. * * TRANS = 'T' or 't' y := alpha*A'*x + beta*y. * * TRANS = 'C' or 'c' y := alpha*A'*x + beta*y. * * Unchanged on exit. * * M - INTEGER. * On entry, M specifies the number of rows of the matrix A. * M must be at least zero. * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the number of columns of the matrix A. * N must be at least zero. * Unchanged on exit. * * ALPHA - REAL . * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * A - REAL array of DIMENSION ( LDA, n ). * Before entry, the leading m by n part of the array A must * contain the matrix of coefficients. * Unchanged on exit. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * max( 1, m ). * Unchanged on exit. * * X - REAL array of DIMENSION at least * ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' * and at least * ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. * Before entry, the incremented array X must contain the * vector x. * Unchanged on exit. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * BETA - REAL . * On entry, BETA specifies the scalar beta. When BETA is * supplied as zero then Y need not be set on input. * Unchanged on exit. * * Y - REAL array of DIMENSION at least * ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' * and at least * ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. * Before entry with BETA non-zero, the incremented array Y * must contain the vector y. On exit, Y is overwritten by the * updated vector y. * * INCY - INTEGER. * On entry, INCY specifies the increment for the elements of * Y. INCY must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. REAL ONE , ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) * .. Local Scalars .. REAL TEMP INTEGER I, INFO, IX, IY, J, JX, JY, KX, KY, LENX, LENY * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( TRANS, 'N' ).AND. $ .NOT.LSAME( TRANS, 'T' ).AND. $ .NOT.LSAME( TRANS, 'C' ) )THEN INFO = 1 ELSE IF( M.LT.0 )THEN INFO = 2 ELSE IF( N.LT.0 )THEN INFO = 3 ELSE IF( LDA.LT.MAX( 1, M ) )THEN INFO = 6 ELSE IF( INCX.EQ.0 )THEN INFO = 8 ELSE IF( INCY.EQ.0 )THEN INFO = 11 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'SGEMV ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( M.EQ.0 ).OR.( N.EQ.0 ).OR. $ ( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) ) $ RETURN * * Set LENX and LENY, the lengths of the vectors x and y, and set * up the start points in X and Y. * IF( LSAME( TRANS, 'N' ) )THEN LENX = N LENY = M ELSE LENX = M LENY = N END IF IF( INCX.GT.0 )THEN KX = 1 ELSE KX = 1 - ( LENX - 1 )*INCX END IF IF( INCY.GT.0 )THEN KY = 1 ELSE KY = 1 - ( LENY - 1 )*INCY END IF * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through A. * * First form y := beta*y. * IF( BETA.NE.ONE )THEN IF( INCY.EQ.1 )THEN IF( BETA.EQ.ZERO )THEN DO 10, I = 1, LENY Y( I ) = ZERO 10 CONTINUE ELSE DO 20, I = 1, LENY Y( I ) = BETA*Y( I ) 20 CONTINUE END IF ELSE IY = KY IF( BETA.EQ.ZERO )THEN DO 30, I = 1, LENY Y( IY ) = ZERO IY = IY + INCY 30 CONTINUE ELSE DO 40, I = 1, LENY Y( IY ) = BETA*Y( IY ) IY = IY + INCY 40 CONTINUE END IF END IF END IF IF( ALPHA.EQ.ZERO ) $ RETURN IF( LSAME( TRANS, 'N' ) )THEN * * Form y := alpha*A*x + y. * JX = KX IF( INCY.EQ.1 )THEN DO 60, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = ALPHA*X( JX ) DO 50, I = 1, M Y( I ) = Y( I ) + TEMP*A( I, J ) 50 CONTINUE END IF JX = JX + INCX 60 CONTINUE ELSE DO 80, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = ALPHA*X( JX ) IY = KY DO 70, I = 1, M Y( IY ) = Y( IY ) + TEMP*A( I, J ) IY = IY + INCY 70 CONTINUE END IF JX = JX + INCX 80 CONTINUE END IF ELSE * * Form y := alpha*A'*x + y. * JY = KY IF( INCX.EQ.1 )THEN DO 100, J = 1, N TEMP = ZERO DO 90, I = 1, M TEMP = TEMP + A( I, J )*X( I ) 90 CONTINUE Y( JY ) = Y( JY ) + ALPHA*TEMP JY = JY + INCY 100 CONTINUE ELSE DO 120, J = 1, N TEMP = ZERO IX = KX DO 110, I = 1, M TEMP = TEMP + A( I, J )*X( IX ) IX = IX + INCX 110 CONTINUE Y( JY ) = Y( JY ) + ALPHA*TEMP JY = JY + INCY 120 CONTINUE END IF END IF * RETURN * * End of SGEMV . * END * ************************************************************************ * SUBROUTINE SGBMV ( TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX, $ BETA, Y, INCY ) * .. Scalar Arguments .. REAL ALPHA, BETA INTEGER INCX, INCY, KL, KU, LDA, M, N CHARACTER*1 TRANS * .. Array Arguments .. REAL A( LDA, * ), X( * ), Y( * ) * .. * * Purpose * ======= * * SGBMV performs one of the matrix-vector operations * * y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, * * where alpha and beta are scalars, x and y are vectors and A is an * m by n band matrix, with kl sub-diagonals and ku super-diagonals. * * Parameters * ========== * * TRANS - CHARACTER*1. * On entry, TRANS specifies the operation to be performed as * follows: * * TRANS = 'N' or 'n' y := alpha*A*x + beta*y. * * TRANS = 'T' or 't' y := alpha*A'*x + beta*y. * * TRANS = 'C' or 'c' y := alpha*A'*x + beta*y. * * Unchanged on exit. * * M - INTEGER. * On entry, M specifies the number of rows of the matrix A. * M must be at least zero. * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the number of columns of the matrix A. * N must be at least zero. * Unchanged on exit. * * KL - INTEGER. * On entry, KL specifies the number of sub-diagonals of the * matrix A. KL must satisfy 0 .le. KL. * Unchanged on exit. * * KU - INTEGER. * On entry, KU specifies the number of super-diagonals of the * matrix A. KU must satisfy 0 .le. KU. * Unchanged on exit. * * ALPHA - REAL . * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * A - REAL array of DIMENSION ( LDA, n ). * Before entry, the leading ( kl + ku + 1 ) by n part of the * array A must contain the matrix of coefficients, supplied * column by column, with the leading diagonal of the matrix in * row ( ku + 1 ) of the array, the first super-diagonal * starting at position 2 in row ku, the first sub-diagonal * starting at position 1 in row ( ku + 2 ), and so on. * Elements in the array A that do not correspond to elements * in the band matrix (such as the top left ku by ku triangle) * are not referenced. * The following program segment will transfer a band matrix * from conventional full matrix storage to band storage: * * DO 20, J = 1, N * K = KU + 1 - J * DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL ) * A( K + I, J ) = matrix( I, J ) * 10 CONTINUE * 20 CONTINUE * * Unchanged on exit. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * ( kl + ku + 1 ). * Unchanged on exit. * * X - REAL array of DIMENSION at least * ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' * and at least * ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. * Before entry, the incremented array X must contain the * vector x. * Unchanged on exit. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * BETA - REAL . * On entry, BETA specifies the scalar beta. When BETA is * supplied as zero then Y need not be set on input. * Unchanged on exit. * * Y - REAL array of DIMENSION at least * ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' * and at least * ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. * Before entry, the incremented array Y must contain the * vector y. On exit, Y is overwritten by the updated vector y. * * INCY - INTEGER. * On entry, INCY specifies the increment for the elements of * Y. INCY must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * .. Parameters .. REAL ONE , ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) * .. Local Scalars .. REAL TEMP INTEGER I, INFO, IX, IY, J, JX, JY, K, KUP1, KX, KY, $ LENX, LENY * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( TRANS, 'N' ).AND. $ .NOT.LSAME( TRANS, 'T' ).AND. $ .NOT.LSAME( TRANS, 'C' ) )THEN INFO = 1 ELSE IF( M.LT.0 )THEN INFO = 2 ELSE IF( N.LT.0 )THEN INFO = 3 ELSE IF( KL.LT.0 )THEN INFO = 4 ELSE IF( KU.LT.0 )THEN INFO = 5 ELSE IF( LDA.LT.( KL + KU + 1 ) )THEN INFO = 8 ELSE IF( INCX.EQ.0 )THEN INFO = 10 ELSE IF( INCY.EQ.0 )THEN INFO = 13 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'SGBMV ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( M.EQ.0 ).OR.( N.EQ.0 ).OR. $ ( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) ) $ RETURN * * Set LENX and LENY, the lengths of the vectors x and y, and set * up the start points in X and Y. * IF( LSAME( TRANS, 'N' ) )THEN LENX = N LENY = M ELSE LENX = M LENY = N END IF IF( INCX.GT.0 )THEN KX = 1 ELSE KX = 1 - ( LENX - 1 )*INCX END IF IF( INCY.GT.0 )THEN KY = 1 ELSE KY = 1 - ( LENY - 1 )*INCY END IF * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through the band part of A. * * First form y := beta*y. * IF( BETA.NE.ONE )THEN IF( INCY.EQ.1 )THEN IF( BETA.EQ.ZERO )THEN DO 10, I = 1, LENY Y( I ) = ZERO 10 CONTINUE ELSE DO 20, I = 1, LENY Y( I ) = BETA*Y( I ) 20 CONTINUE END IF ELSE IY = KY IF( BETA.EQ.ZERO )THEN DO 30, I = 1, LENY Y( IY ) = ZERO IY = IY + INCY 30 CONTINUE ELSE DO 40, I = 1, LENY Y( IY ) = BETA*Y( IY ) IY = IY + INCY 40 CONTINUE END IF END IF END IF IF( ALPHA.EQ.ZERO ) $ RETURN KUP1 = KU + 1 IF( LSAME( TRANS, 'N' ) )THEN * * Form y := alpha*A*x + y. * JX = KX IF( INCY.EQ.1 )THEN DO 60, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = ALPHA*X( JX ) K = KUP1 - J DO 50, I = MAX( 1, J - KU ), MIN( M, J + KL ) Y( I ) = Y( I ) + TEMP*A( K + I, J ) 50 CONTINUE END IF JX = JX + INCX 60 CONTINUE ELSE DO 80, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = ALPHA*X( JX ) IY = KY K = KUP1 - J DO 70, I = MAX( 1, J - KU ), MIN( M, J + KL ) Y( IY ) = Y( IY ) + TEMP*A( K + I, J ) IY = IY + INCY 70 CONTINUE END IF JX = JX + INCX IF( J.GT.KU ) $ KY = KY + INCY 80 CONTINUE END IF ELSE * * Form y := alpha*A'*x + y. * JY = KY IF( INCX.EQ.1 )THEN DO 100, J = 1, N TEMP = ZERO K = KUP1 - J DO 90, I = MAX( 1, J - KU ), MIN( M, J + KL ) TEMP = TEMP + A( K + I, J )*X( I ) 90 CONTINUE Y( JY ) = Y( JY ) + ALPHA*TEMP JY = JY + INCY 100 CONTINUE ELSE DO 120, J = 1, N TEMP = ZERO IX = KX K = KUP1 - J DO 110, I = MAX( 1, J - KU ), MIN( M, J + KL ) TEMP = TEMP + A( K + I, J )*X( IX ) IX = IX + INCX 110 CONTINUE Y( JY ) = Y( JY ) + ALPHA*TEMP JY = JY + INCY IF( J.GT.KU ) $ KX = KX + INCX 120 CONTINUE END IF END IF * RETURN * * End of SGBMV . * END * ************************************************************************ * SUBROUTINE SSYMV ( UPLO, N, ALPHA, A, LDA, X, INCX, $ BETA, Y, INCY ) * .. Scalar Arguments .. REAL ALPHA, BETA INTEGER INCX, INCY, LDA, N CHARACTER*1 UPLO * .. Array Arguments .. REAL A( LDA, * ), X( * ), Y( * ) * .. * * Purpose * ======= * * SSYMV performs the matrix-vector operation * * y := alpha*A*x + beta*y, * * where alpha and beta are scalars, x and y are n element vectors and * A is an n by n symmetric matrix. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the upper or lower * triangular part of the array A is to be referenced as * follows: * * UPLO = 'U' or 'u' Only the upper triangular part of A * is to be referenced. * * UPLO = 'L' or 'l' Only the lower triangular part of A * is to be referenced. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * ALPHA - REAL . * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * A - REAL array of DIMENSION ( LDA, n ). * Before entry with UPLO = 'U' or 'u', the leading n by n * upper triangular part of the array A must contain the upper * triangular part of the symmetric matrix and the strictly * lower triangular part of A is not referenced. * Before entry with UPLO = 'L' or 'l', the leading n by n * lower triangular part of the array A must contain the lower * triangular part of the symmetric matrix and the strictly * upper triangular part of A is not referenced. * Unchanged on exit. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * max( 1, n ). * Unchanged on exit. * * X - REAL array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element vector x. * Unchanged on exit. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * BETA - REAL . * On entry, BETA specifies the scalar beta. When BETA is * supplied as zero then Y need not be set on input. * Unchanged on exit. * * Y - REAL array of dimension at least * ( 1 + ( n - 1 )*abs( INCY ) ). * Before entry, the incremented array Y must contain the n * element vector y. On exit, Y is overwritten by the updated * vector y. * * INCY - INTEGER. * On entry, INCY specifies the increment for the elements of * Y. INCY must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. REAL ONE , ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) * .. Local Scalars .. REAL TEMP1, TEMP2 INTEGER I, INFO, IX, IY, J, JX, JY, KX, KY * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO, 'U' ).AND. $ .NOT.LSAME( UPLO, 'L' ) )THEN INFO = 1 ELSE IF( N.LT.0 )THEN INFO = 2 ELSE IF( LDA.LT.MAX( 1, N ) )THEN INFO = 5 ELSE IF( INCX.EQ.0 )THEN INFO = 7 ELSE IF( INCY.EQ.0 )THEN INFO = 10 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'SSYMV ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( N.EQ.0 ).OR.( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) ) $ RETURN * * Set up the start points in X and Y. * IF( INCX.GT.0 )THEN KX = 1 ELSE KX = 1 - ( N - 1 )*INCX END IF IF( INCY.GT.0 )THEN KY = 1 ELSE KY = 1 - ( N - 1 )*INCY END IF * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through the triangular part * of A. * * First form y := beta*y. * IF( BETA.NE.ONE )THEN IF( INCY.EQ.1 )THEN IF( BETA.EQ.ZERO )THEN DO 10, I = 1, N Y( I ) = ZERO 10 CONTINUE ELSE DO 20, I = 1, N Y( I ) = BETA*Y( I ) 20 CONTINUE END IF ELSE IY = KY IF( BETA.EQ.ZERO )THEN DO 30, I = 1, N Y( IY ) = ZERO IY = IY + INCY 30 CONTINUE ELSE DO 40, I = 1, N Y( IY ) = BETA*Y( IY ) IY = IY + INCY 40 CONTINUE END IF END IF END IF IF( ALPHA.EQ.ZERO ) $ RETURN IF( LSAME( UPLO, 'U' ) )THEN * * Form y when A is stored in upper triangle. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 60, J = 1, N TEMP1 = ALPHA*X( J ) TEMP2 = ZERO DO 50, I = 1, J - 1 Y( I ) = Y( I ) + TEMP1*A( I, J ) TEMP2 = TEMP2 + A( I, J )*X( I ) 50 CONTINUE Y( J ) = Y( J ) + TEMP1*A( J, J ) + ALPHA*TEMP2 60 CONTINUE ELSE JX = KX JY = KY DO 80, J = 1, N TEMP1 = ALPHA*X( JX ) TEMP2 = ZERO IX = KX IY = KY DO 70, I = 1, J - 1 Y( IY ) = Y( IY ) + TEMP1*A( I, J ) TEMP2 = TEMP2 + A( I, J )*X( IX ) IX = IX + INCX IY = IY + INCY 70 CONTINUE Y( JY ) = Y( JY ) + TEMP1*A( J, J ) + ALPHA*TEMP2 JX = JX + INCX JY = JY + INCY 80 CONTINUE END IF ELSE * * Form y when A is stored in lower triangle. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 100, J = 1, N TEMP1 = ALPHA*X( J ) TEMP2 = ZERO Y( J ) = Y( J ) + TEMP1*A( J, J ) DO 90, I = J + 1, N Y( I ) = Y( I ) + TEMP1*A( I, J ) TEMP2 = TEMP2 + A( I, J )*X( I ) 90 CONTINUE Y( J ) = Y( J ) + ALPHA*TEMP2 100 CONTINUE ELSE JX = KX JY = KY DO 120, J = 1, N TEMP1 = ALPHA*X( JX ) TEMP2 = ZERO Y( JY ) = Y( JY ) + TEMP1*A( J, J ) IX = JX IY = JY DO 110, I = J + 1, N IX = IX + INCX IY = IY + INCY Y( IY ) = Y( IY ) + TEMP1*A( I, J ) TEMP2 = TEMP2 + A( I, J )*X( IX ) 110 CONTINUE Y( JY ) = Y( JY ) + ALPHA*TEMP2 JX = JX + INCX JY = JY + INCY 120 CONTINUE END IF END IF * RETURN * * End of SSYMV . * END * ************************************************************************ * SUBROUTINE SSBMV ( UPLO, N, K, ALPHA, A, LDA, X, INCX, $ BETA, Y, INCY ) * .. Scalar Arguments .. REAL ALPHA, BETA INTEGER INCX, INCY, K, LDA, N CHARACTER*1 UPLO * .. Array Arguments .. REAL A( LDA, * ), X( * ), Y( * ) * .. * * Purpose * ======= * * SSBMV performs the matrix-vector operation * * y := alpha*A*x + beta*y, * * where alpha and beta are scalars, x and y are n element vectors and * A is an n by n symmetric band matrix, with k super-diagonals. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the upper or lower * triangular part of the band matrix A is being supplied as * follows: * * UPLO = 'U' or 'u' The upper triangular part of A is * being supplied. * * UPLO = 'L' or 'l' The lower triangular part of A is * being supplied. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * K - INTEGER. * On entry, K specifies the number of super-diagonals of the * matrix A. K must satisfy 0 .le. K. * Unchanged on exit. * * ALPHA - REAL . * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * A - REAL array of DIMENSION ( LDA, n ). * Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) * by n part of the array A must contain the upper triangular * band part of the symmetric matrix, supplied column by * column, with the leading diagonal of the matrix in row * ( k + 1 ) of the array, the first super-diagonal starting at * position 2 in row k, and so on. The top left k by k triangle * of the array A is not referenced. * The following program segment will transfer the upper * triangular part of a symmetric band matrix from conventional * full matrix storage to band storage: * * DO 20, J = 1, N * M = K + 1 - J * DO 10, I = MAX( 1, J - K ), J * A( M + I, J ) = matrix( I, J ) * 10 CONTINUE * 20 CONTINUE * * Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) * by n part of the array A must contain the lower triangular * band part of the symmetric matrix, supplied column by * column, with the leading diagonal of the matrix in row 1 of * the array, the first sub-diagonal starting at position 1 in * row 2, and so on. The bottom right k by k triangle of the * array A is not referenced. * The following program segment will transfer the lower * triangular part of a symmetric band matrix from conventional * full matrix storage to band storage: * * DO 20, J = 1, N * M = 1 - J * DO 10, I = J, MIN( N, J + K ) * A( M + I, J ) = matrix( I, J ) * 10 CONTINUE * 20 CONTINUE * * Unchanged on exit. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * ( k + 1 ). * Unchanged on exit. * * X - REAL array of DIMENSION at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the * vector x. * Unchanged on exit. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * BETA - REAL . * On entry, BETA specifies the scalar beta. * Unchanged on exit. * * Y - REAL array of DIMENSION at least * ( 1 + ( n - 1 )*abs( INCY ) ). * Before entry, the incremented array Y must contain the * vector y. On exit, Y is overwritten by the updated vector y. * * INCY - INTEGER. * On entry, INCY specifies the increment for the elements of * Y. INCY must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. REAL ONE , ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) * .. Local Scalars .. REAL TEMP1, TEMP2 INTEGER I, INFO, IX, IY, J, JX, JY, KPLUS1, KX, KY, L * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO, 'U' ).AND. $ .NOT.LSAME( UPLO, 'L' ) )THEN INFO = 1 ELSE IF( N.LT.0 )THEN INFO = 2 ELSE IF( K.LT.0 )THEN INFO = 3 ELSE IF( LDA.LT.( K + 1 ) )THEN INFO = 6 ELSE IF( INCX.EQ.0 )THEN INFO = 8 ELSE IF( INCY.EQ.0 )THEN INFO = 11 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'SSBMV ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( N.EQ.0 ).OR.( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) ) $ RETURN * * Set up the start points in X and Y. * IF( INCX.GT.0 )THEN KX = 1 ELSE KX = 1 - ( N - 1 )*INCX END IF IF( INCY.GT.0 )THEN KY = 1 ELSE KY = 1 - ( N - 1 )*INCY END IF * * Start the operations. In this version the elements of the array A * are accessed sequentially with one pass through A. * * First form y := beta*y. * IF( BETA.NE.ONE )THEN IF( INCY.EQ.1 )THEN IF( BETA.EQ.ZERO )THEN DO 10, I = 1, N Y( I ) = ZERO 10 CONTINUE ELSE DO 20, I = 1, N Y( I ) = BETA*Y( I ) 20 CONTINUE END IF ELSE IY = KY IF( BETA.EQ.ZERO )THEN DO 30, I = 1, N Y( IY ) = ZERO IY = IY + INCY 30 CONTINUE ELSE DO 40, I = 1, N Y( IY ) = BETA*Y( IY ) IY = IY + INCY 40 CONTINUE END IF END IF END IF IF( ALPHA.EQ.ZERO ) $ RETURN IF( LSAME( UPLO, 'U' ) )THEN * * Form y when upper triangle of A is stored. * KPLUS1 = K + 1 IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 60, J = 1, N TEMP1 = ALPHA*X( J ) TEMP2 = ZERO L = KPLUS1 - J DO 50, I = MAX( 1, J - K ), J - 1 Y( I ) = Y( I ) + TEMP1*A( L + I, J ) TEMP2 = TEMP2 + A( L + I, J )*X( I ) 50 CONTINUE Y( J ) = Y( J ) + TEMP1*A( KPLUS1, J ) + ALPHA*TEMP2 60 CONTINUE ELSE JX = KX JY = KY DO 80, J = 1, N TEMP1 = ALPHA*X( JX ) TEMP2 = ZERO IX = KX IY = KY L = KPLUS1 - J DO 70, I = MAX( 1, J - K ), J - 1 Y( IY ) = Y( IY ) + TEMP1*A( L + I, J ) TEMP2 = TEMP2 + A( L + I, J )*X( IX ) IX = IX + INCX IY = IY + INCY 70 CONTINUE Y( JY ) = Y( JY ) + TEMP1*A( KPLUS1, J ) + ALPHA*TEMP2 JX = JX + INCX JY = JY + INCY IF( J.GT.K )THEN KX = KX + INCX KY = KY + INCY END IF 80 CONTINUE END IF ELSE * * Form y when lower triangle of A is stored. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 100, J = 1, N TEMP1 = ALPHA*X( J ) TEMP2 = ZERO Y( J ) = Y( J ) + TEMP1*A( 1, J ) L = 1 - J DO 90, I = J + 1, MIN( N, J + K ) Y( I ) = Y( I ) + TEMP1*A( L + I, J ) TEMP2 = TEMP2 + A( L + I, J )*X( I ) 90 CONTINUE Y( J ) = Y( J ) + ALPHA*TEMP2 100 CONTINUE ELSE JX = KX JY = KY DO 120, J = 1, N TEMP1 = ALPHA*X( JX ) TEMP2 = ZERO Y( JY ) = Y( JY ) + TEMP1*A( 1, J ) L = 1 - J IX = JX IY = JY DO 110, I = J + 1, MIN( N, J + K ) IX = IX + INCX IY = IY + INCY Y( IY ) = Y( IY ) + TEMP1*A( L + I, J ) TEMP2 = TEMP2 + A( L + I, J )*X( IX ) 110 CONTINUE Y( JY ) = Y( JY ) + ALPHA*TEMP2 JX = JX + INCX JY = JY + INCY 120 CONTINUE END IF END IF * RETURN * * End of SSBMV . * END * ************************************************************************ * SUBROUTINE SSPMV ( UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY ) * .. Scalar Arguments .. REAL ALPHA, BETA INTEGER INCX, INCY, N CHARACTER*1 UPLO * .. Array Arguments .. REAL AP( * ), X( * ), Y( * ) * .. * * Purpose * ======= * * SSPMV performs the matrix-vector operation * * y := alpha*A*x + beta*y, * * where alpha and beta are scalars, x and y are n element vectors and * A is an n by n symmetric matrix, supplied in packed form. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the upper or lower * triangular part of the matrix A is supplied in the packed * array AP as follows: * * UPLO = 'U' or 'u' The upper triangular part of A is * supplied in AP. * * UPLO = 'L' or 'l' The lower triangular part of A is * supplied in AP. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * ALPHA - REAL . * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * AP - REAL array of DIMENSION at least * ( ( n*( n + 1 ) )/2 ). * Before entry with UPLO = 'U' or 'u', the array AP must * contain the upper triangular part of the symmetric matrix * packed sequentially, column by column, so that AP( 1 ) * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) * and a( 2, 2 ) respectively, and so on. * Before entry with UPLO = 'L' or 'l', the array AP must * contain the lower triangular part of the symmetric matrix * packed sequentially, column by column, so that AP( 1 ) * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) * and a( 3, 1 ) respectively, and so on. * Unchanged on exit. * * X - REAL array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element vector x. * Unchanged on exit. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * BETA - REAL . * On entry, BETA specifies the scalar beta. When BETA is * supplied as zero then Y need not be set on input. * Unchanged on exit. * * Y - REAL array of dimension at least * ( 1 + ( n - 1 )*abs( INCY ) ). * Before entry, the incremented array Y must contain the n * element vector y. On exit, Y is overwritten by the updated * vector y. * * INCY - INTEGER. * On entry, INCY specifies the increment for the elements of * Y. INCY must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. REAL ONE , ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) * .. Local Scalars .. REAL TEMP1, TEMP2 INTEGER I, INFO, IX, IY, J, JX, JY, K, KK, KX, KY * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO, 'U' ).AND. $ .NOT.LSAME( UPLO, 'L' ) )THEN INFO = 1 ELSE IF( N.LT.0 )THEN INFO = 2 ELSE IF( INCX.EQ.0 )THEN INFO = 6 ELSE IF( INCY.EQ.0 )THEN INFO = 9 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'SSPMV ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( N.EQ.0 ).OR.( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) ) $ RETURN * * Set up the start points in X and Y. * IF( INCX.GT.0 )THEN KX = 1 ELSE KX = 1 - ( N - 1 )*INCX END IF IF( INCY.GT.0 )THEN KY = 1 ELSE KY = 1 - ( N - 1 )*INCY END IF * * Start the operations. In this version the elements of the array AP * are accessed sequentially with one pass through AP. * * First form y := beta*y. * IF( BETA.NE.ONE )THEN IF( INCY.EQ.1 )THEN IF( BETA.EQ.ZERO )THEN DO 10, I = 1, N Y( I ) = ZERO 10 CONTINUE ELSE DO 20, I = 1, N Y( I ) = BETA*Y( I ) 20 CONTINUE END IF ELSE IY = KY IF( BETA.EQ.ZERO )THEN DO 30, I = 1, N Y( IY ) = ZERO IY = IY + INCY 30 CONTINUE ELSE DO 40, I = 1, N Y( IY ) = BETA*Y( IY ) IY = IY + INCY 40 CONTINUE END IF END IF END IF IF( ALPHA.EQ.ZERO ) $ RETURN KK = 1 IF( LSAME( UPLO, 'U' ) )THEN * * Form y when AP contains the upper triangle. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 60, J = 1, N TEMP1 = ALPHA*X( J ) TEMP2 = ZERO K = KK DO 50, I = 1, J - 1 Y( I ) = Y( I ) + TEMP1*AP( K ) TEMP2 = TEMP2 + AP( K )*X( I ) K = K + 1 50 CONTINUE Y( J ) = Y( J ) + TEMP1*AP( KK + J - 1 ) + ALPHA*TEMP2 KK = KK + J 60 CONTINUE ELSE JX = KX JY = KY DO 80, J = 1, N TEMP1 = ALPHA*X( JX ) TEMP2 = ZERO IX = KX IY = KY DO 70, K = KK, KK + J - 2 Y( IY ) = Y( IY ) + TEMP1*AP( K ) TEMP2 = TEMP2 + AP( K )*X( IX ) IX = IX + INCX IY = IY + INCY 70 CONTINUE Y( JY ) = Y( JY ) + TEMP1*AP( KK + J - 1 ) + ALPHA*TEMP2 JX = JX + INCX JY = JY + INCY KK = KK + J 80 CONTINUE END IF ELSE * * Form y when AP contains the lower triangle. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 100, J = 1, N TEMP1 = ALPHA*X( J ) TEMP2 = ZERO Y( J ) = Y( J ) + TEMP1*AP( KK ) K = KK + 1 DO 90, I = J + 1, N Y( I ) = Y( I ) + TEMP1*AP( K ) TEMP2 = TEMP2 + AP( K )*X( I ) K = K + 1 90 CONTINUE Y( J ) = Y( J ) + ALPHA*TEMP2 KK = KK + ( N - J + 1 ) 100 CONTINUE ELSE JX = KX JY = KY DO 120, J = 1, N TEMP1 = ALPHA*X( JX ) TEMP2 = ZERO Y( JY ) = Y( JY ) + TEMP1*AP( KK ) IX = JX IY = JY DO 110, K = KK + 1, KK + N - J IX = IX + INCX IY = IY + INCY Y( IY ) = Y( IY ) + TEMP1*AP( K ) TEMP2 = TEMP2 + AP( K )*X( IX ) 110 CONTINUE Y( JY ) = Y( JY ) + ALPHA*TEMP2 JX = JX + INCX JY = JY + INCY KK = KK + ( N - J + 1 ) 120 CONTINUE END IF END IF * RETURN * * End of SSPMV . * END * ************************************************************************ * SUBROUTINE STRMV ( UPLO, TRANS, DIAG, N, A, LDA, X, INCX ) * .. Scalar Arguments .. INTEGER INCX, LDA, N CHARACTER*1 DIAG, TRANS, UPLO * .. Array Arguments .. REAL A( LDA, * ), X( * ) * .. * * Purpose * ======= * * STRMV performs one of the matrix-vector operations * * x := A*x, or x := A'*x, * * where x is an n element vector and A is an n by n unit, or non-unit, * upper or lower triangular matrix. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the matrix is an upper or * lower triangular matrix as follows: * * UPLO = 'U' or 'u' A is an upper triangular matrix. * * UPLO = 'L' or 'l' A is a lower triangular matrix. * * Unchanged on exit. * * TRANS - CHARACTER*1. * On entry, TRANS specifies the operation to be performed as * follows: * * TRANS = 'N' or 'n' x := A*x. * * TRANS = 'T' or 't' x := A'*x. * * TRANS = 'C' or 'c' x := A'*x. * * Unchanged on exit. * * DIAG - CHARACTER*1. * On entry, DIAG specifies whether or not A is unit * triangular as follows: * * DIAG = 'U' or 'u' A is assumed to be unit triangular. * * DIAG = 'N' or 'n' A is not assumed to be unit * triangular. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * A - REAL array of DIMENSION ( LDA, n ). * Before entry with UPLO = 'U' or 'u', the leading n by n * upper triangular part of the array A must contain the upper * triangular matrix and the strictly lower triangular part of * A is not referenced. * Before entry with UPLO = 'L' or 'l', the leading n by n * lower triangular part of the array A must contain the lower * triangular matrix and the strictly upper triangular part of * A is not referenced. * Note that when DIAG = 'U' or 'u', the diagonal elements of * A are not referenced either, but are assumed to be unity. * Unchanged on exit. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * max( 1, n ). * Unchanged on exit. * * X - REAL array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element vector x. On exit, X is overwritten with the * tranformed vector x. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. REAL ZERO PARAMETER ( ZERO = 0.0E+0 ) * .. Local Scalars .. REAL TEMP INTEGER I, INFO, IX, J, JX, KX LOGICAL NOUNIT * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO , 'U' ).AND. $ .NOT.LSAME( UPLO , 'L' ) )THEN INFO = 1 ELSE IF( .NOT.LSAME( TRANS, 'N' ).AND. $ .NOT.LSAME( TRANS, 'T' ).AND. $ .NOT.LSAME( TRANS, 'C' ) )THEN INFO = 2 ELSE IF( .NOT.LSAME( DIAG , 'U' ).AND. $ .NOT.LSAME( DIAG , 'N' ) )THEN INFO = 3 ELSE IF( N.LT.0 )THEN INFO = 4 ELSE IF( LDA.LT.MAX( 1, N ) )THEN INFO = 6 ELSE IF( INCX.EQ.0 )THEN INFO = 8 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'STRMV ', INFO ) RETURN END IF * * Quick return if possible. * IF( N.EQ.0 ) $ RETURN * NOUNIT = LSAME( DIAG, 'N' ) * * Set up the start point in X if the increment is not unity. This * will be ( N - 1 )*INCX too small for descending loops. * IF( INCX.LE.0 )THEN KX = 1 - ( N - 1 )*INCX ELSE IF( INCX.NE.1 )THEN KX = 1 END IF * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through A. * IF( LSAME( TRANS, 'N' ) )THEN * * Form x := A*x. * IF( LSAME( UPLO, 'U' ) )THEN IF( INCX.EQ.1 )THEN DO 20, J = 1, N IF( X( J ).NE.ZERO )THEN TEMP = X( J ) DO 10, I = 1, J - 1 X( I ) = X( I ) + TEMP*A( I, J ) 10 CONTINUE IF( NOUNIT ) $ X( J ) = X( J )*A( J, J ) END IF 20 CONTINUE ELSE JX = KX DO 40, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = X( JX ) IX = KX DO 30, I = 1, J - 1 X( IX ) = X( IX ) + TEMP*A( I, J ) IX = IX + INCX 30 CONTINUE IF( NOUNIT ) $ X( JX ) = X( JX )*A( J, J ) END IF JX = JX + INCX 40 CONTINUE END IF ELSE IF( INCX.EQ.1 )THEN DO 60, J = N, 1, -1 IF( X( J ).NE.ZERO )THEN TEMP = X( J ) DO 50, I = N, J + 1, -1 X( I ) = X( I ) + TEMP*A( I, J ) 50 CONTINUE IF( NOUNIT ) $ X( J ) = X( J )*A( J, J ) END IF 60 CONTINUE ELSE KX = KX + ( N - 1 )*INCX JX = KX DO 80, J = N, 1, -1 IF( X( JX ).NE.ZERO )THEN TEMP = X( JX ) IX = KX DO 70, I = N, J + 1, -1 X( IX ) = X( IX ) + TEMP*A( I, J ) IX = IX - INCX 70 CONTINUE IF( NOUNIT ) $ X( JX ) = X( JX )*A( J, J ) END IF JX = JX - INCX 80 CONTINUE END IF END IF ELSE * * Form x := A'*x. * IF( LSAME( UPLO, 'U' ) )THEN IF( INCX.EQ.1 )THEN DO 100, J = N, 1, -1 TEMP = X( J ) IF( NOUNIT ) $ TEMP = TEMP*A( J, J ) DO 90, I = J - 1, 1, -1 TEMP = TEMP + A( I, J )*X( I ) 90 CONTINUE X( J ) = TEMP 100 CONTINUE ELSE JX = KX + ( N - 1 )*INCX DO 120, J = N, 1, -1 TEMP = X( JX ) IX = JX IF( NOUNIT ) $ TEMP = TEMP*A( J, J ) DO 110, I = J - 1, 1, -1 IX = IX - INCX TEMP = TEMP + A( I, J )*X( IX ) 110 CONTINUE X( JX ) = TEMP JX = JX - INCX 120 CONTINUE END IF ELSE IF( INCX.EQ.1 )THEN DO 140, J = 1, N TEMP = X( J ) IF( NOUNIT ) $ TEMP = TEMP*A( J, J ) DO 130, I = J + 1, N TEMP = TEMP + A( I, J )*X( I ) 130 CONTINUE X( J ) = TEMP 140 CONTINUE ELSE JX = KX DO 160, J = 1, N TEMP = X( JX ) IX = JX IF( NOUNIT ) $ TEMP = TEMP*A( J, J ) DO 150, I = J + 1, N IX = IX + INCX TEMP = TEMP + A( I, J )*X( IX ) 150 CONTINUE X( JX ) = TEMP JX = JX + INCX 160 CONTINUE END IF END IF END IF * RETURN * * End of STRMV . * END * ************************************************************************ * SUBROUTINE STBMV ( UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX ) * .. Scalar Arguments .. INTEGER INCX, K, LDA, N CHARACTER*1 DIAG, TRANS, UPLO * .. Array Arguments .. REAL A( LDA, * ), X( * ) * .. * * Purpose * ======= * * STBMV performs one of the matrix-vector operations * * x := A*x, or x := A'*x, * * where x is an n element vector and A is an n by n unit, or non-unit, * upper or lower triangular band matrix, with ( k + 1 ) diagonals. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the matrix is an upper or * lower triangular matrix as follows: * * UPLO = 'U' or 'u' A is an upper triangular matrix. * * UPLO = 'L' or 'l' A is a lower triangular matrix. * * Unchanged on exit. * * TRANS - CHARACTER*1. * On entry, TRANS specifies the operation to be performed as * follows: * * TRANS = 'N' or 'n' x := A*x. * * TRANS = 'T' or 't' x := A'*x. * * TRANS = 'C' or 'c' x := A'*x. * * Unchanged on exit. * * DIAG - CHARACTER*1. * On entry, DIAG specifies whether or not A is unit * triangular as follows: * * DIAG = 'U' or 'u' A is assumed to be unit triangular. * * DIAG = 'N' or 'n' A is not assumed to be unit * triangular. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * K - INTEGER. * On entry with UPLO = 'U' or 'u', K specifies the number of * super-diagonals of the matrix A. * On entry with UPLO = 'L' or 'l', K specifies the number of * sub-diagonals of the matrix A. * K must satisfy 0 .le. K. * Unchanged on exit. * * A - REAL array of DIMENSION ( LDA, n ). * Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) * by n part of the array A must contain the upper triangular * band part of the matrix of coefficients, supplied column by * column, with the leading diagonal of the matrix in row * ( k + 1 ) of the array, the first super-diagonal starting at * position 2 in row k, and so on. The top left k by k triangle * of the array A is not referenced. * The following program segment will transfer an upper * triangular band matrix from conventional full matrix storage * to band storage: * * DO 20, J = 1, N * M = K + 1 - J * DO 10, I = MAX( 1, J - K ), J * A( M + I, J ) = matrix( I, J ) * 10 CONTINUE * 20 CONTINUE * * Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) * by n part of the array A must contain the lower triangular * band part of the matrix of coefficients, supplied column by * column, with the leading diagonal of the matrix in row 1 of * the array, the first sub-diagonal starting at position 1 in * row 2, and so on. The bottom right k by k triangle of the * array A is not referenced. * The following program segment will transfer a lower * triangular band matrix from conventional full matrix storage * to band storage: * * DO 20, J = 1, N * M = 1 - J * DO 10, I = J, MIN( N, J + K ) * A( M + I, J ) = matrix( I, J ) * 10 CONTINUE * 20 CONTINUE * * Note that when DIAG = 'U' or 'u' the elements of the array A * corresponding to the diagonal elements of the matrix are not * referenced, but are assumed to be unity. * Unchanged on exit. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * ( k + 1 ). * Unchanged on exit. * * X - REAL array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element vector x. On exit, X is overwritten with the * tranformed vector x. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. REAL ZERO PARAMETER ( ZERO = 0.0E+0 ) * .. Local Scalars .. REAL TEMP INTEGER I, INFO, IX, J, JX, KPLUS1, KX, L LOGICAL NOUNIT * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO , 'U' ).AND. $ .NOT.LSAME( UPLO , 'L' ) )THEN INFO = 1 ELSE IF( .NOT.LSAME( TRANS, 'N' ).AND. $ .NOT.LSAME( TRANS, 'T' ).AND. $ .NOT.LSAME( TRANS, 'C' ) )THEN INFO = 2 ELSE IF( .NOT.LSAME( DIAG , 'U' ).AND. $ .NOT.LSAME( DIAG , 'N' ) )THEN INFO = 3 ELSE IF( N.LT.0 )THEN INFO = 4 ELSE IF( K.LT.0 )THEN INFO = 5 ELSE IF( LDA.LT.( K + 1 ) )THEN INFO = 7 ELSE IF( INCX.EQ.0 )THEN INFO = 9 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'STBMV ', INFO ) RETURN END IF * * Quick return if possible. * IF( N.EQ.0 ) $ RETURN * NOUNIT = LSAME( DIAG, 'N' ) * * Set up the start point in X if the increment is not unity. This * will be ( N - 1 )*INCX too small for descending loops. * IF( INCX.LE.0 )THEN KX = 1 - ( N - 1 )*INCX ELSE IF( INCX.NE.1 )THEN KX = 1 END IF * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through A. * IF( LSAME( TRANS, 'N' ) )THEN * * Form x := A*x. * IF( LSAME( UPLO, 'U' ) )THEN KPLUS1 = K + 1 IF( INCX.EQ.1 )THEN DO 20, J = 1, N IF( X( J ).NE.ZERO )THEN TEMP = X( J ) L = KPLUS1 - J DO 10, I = MAX( 1, J - K ), J - 1 X( I ) = X( I ) + TEMP*A( L + I, J ) 10 CONTINUE IF( NOUNIT ) $ X( J ) = X( J )*A( KPLUS1, J ) END IF 20 CONTINUE ELSE JX = KX DO 40, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = X( JX ) IX = KX L = KPLUS1 - J DO 30, I = MAX( 1, J - K ), J - 1 X( IX ) = X( IX ) + TEMP*A( L + I, J ) IX = IX + INCX 30 CONTINUE IF( NOUNIT ) $ X( JX ) = X( JX )*A( KPLUS1, J ) END IF JX = JX + INCX IF( J.GT.K ) $ KX = KX + INCX 40 CONTINUE END IF ELSE IF( INCX.EQ.1 )THEN DO 60, J = N, 1, -1 IF( X( J ).NE.ZERO )THEN TEMP = X( J ) L = 1 - J DO 50, I = MIN( N, J + K ), J + 1, -1 X( I ) = X( I ) + TEMP*A( L + I, J ) 50 CONTINUE IF( NOUNIT ) $ X( J ) = X( J )*A( 1, J ) END IF 60 CONTINUE ELSE KX = KX + ( N - 1 )*INCX JX = KX DO 80, J = N, 1, -1 IF( X( JX ).NE.ZERO )THEN TEMP = X( JX ) IX = KX L = 1 - J DO 70, I = MIN( N, J + K ), J + 1, -1 X( IX ) = X( IX ) + TEMP*A( L + I, J ) IX = IX - INCX 70 CONTINUE IF( NOUNIT ) $ X( JX ) = X( JX )*A( 1, J ) END IF JX = JX - INCX IF( ( N - J ).GE.K ) $ KX = KX - INCX 80 CONTINUE END IF END IF ELSE * * Form x := A'*x. * IF( LSAME( UPLO, 'U' ) )THEN KPLUS1 = K + 1 IF( INCX.EQ.1 )THEN DO 100, J = N, 1, -1 TEMP = X( J ) L = KPLUS1 - J IF( NOUNIT ) $ TEMP = TEMP*A( KPLUS1, J ) DO 90, I = J - 1, MAX( 1, J - K ), -1 TEMP = TEMP + A( L + I, J )*X( I ) 90 CONTINUE X( J ) = TEMP 100 CONTINUE ELSE KX = KX + ( N - 1 )*INCX JX = KX DO 120, J = N, 1, -1 TEMP = X( JX ) KX = KX - INCX IX = KX L = KPLUS1 - J IF( NOUNIT ) $ TEMP = TEMP*A( KPLUS1, J ) DO 110, I = J - 1, MAX( 1, J - K ), -1 TEMP = TEMP + A( L + I, J )*X( IX ) IX = IX - INCX 110 CONTINUE X( JX ) = TEMP JX = JX - INCX 120 CONTINUE END IF ELSE IF( INCX.EQ.1 )THEN DO 140, J = 1, N TEMP = X( J ) L = 1 - J IF( NOUNIT ) $ TEMP = TEMP*A( 1, J ) DO 130, I = J + 1, MIN( N, J + K ) TEMP = TEMP + A( L + I, J )*X( I ) 130 CONTINUE X( J ) = TEMP 140 CONTINUE ELSE JX = KX DO 160, J = 1, N TEMP = X( JX ) KX = KX + INCX IX = KX L = 1 - J IF( NOUNIT ) $ TEMP = TEMP*A( 1, J ) DO 150, I = J + 1, MIN( N, J + K ) TEMP = TEMP + A( L + I, J )*X( IX ) IX = IX + INCX 150 CONTINUE X( JX ) = TEMP JX = JX + INCX 160 CONTINUE END IF END IF END IF * RETURN * * End of STBMV . * END * ************************************************************************ * SUBROUTINE STPMV ( UPLO, TRANS, DIAG, N, AP, X, INCX ) * .. Scalar Arguments .. INTEGER INCX, N CHARACTER*1 DIAG, TRANS, UPLO * .. Array Arguments .. REAL AP( * ), X( * ) * .. * * Purpose * ======= * * STPMV performs one of the matrix-vector operations * * x := A*x, or x := A'*x, * * where x is an n element vector and A is an n by n unit, or non-unit, * upper or lower triangular matrix, supplied in packed form. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the matrix is an upper or * lower triangular matrix as follows: * * UPLO = 'U' or 'u' A is an upper triangular matrix. * * UPLO = 'L' or 'l' A is a lower triangular matrix. * * Unchanged on exit. * * TRANS - CHARACTER*1. * On entry, TRANS specifies the operation to be performed as * follows: * * TRANS = 'N' or 'n' x := A*x. * * TRANS = 'T' or 't' x := A'*x. * * TRANS = 'C' or 'c' x := A'*x. * * Unchanged on exit. * * DIAG - CHARACTER*1. * On entry, DIAG specifies whether or not A is unit * triangular as follows: * * DIAG = 'U' or 'u' A is assumed to be unit triangular. * * DIAG = 'N' or 'n' A is not assumed to be unit * triangular. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * AP - REAL array of DIMENSION at least * ( ( n*( n + 1 ) )/2 ). * Before entry with UPLO = 'U' or 'u', the array AP must * contain the upper triangular matrix packed sequentially, * column by column, so that AP( 1 ) contains a( 1, 1 ), * AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) * respectively, and so on. * Before entry with UPLO = 'L' or 'l', the array AP must * contain the lower triangular matrix packed sequentially, * column by column, so that AP( 1 ) contains a( 1, 1 ), * AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) * respectively, and so on. * Note that when DIAG = 'U' or 'u', the diagonal elements of * A are not referenced, but are assumed to be unity. * Unchanged on exit. * * X - REAL array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element vector x. On exit, X is overwritten with the * tranformed vector x. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. REAL ZERO PARAMETER ( ZERO = 0.0E+0 ) * .. Local Scalars .. REAL TEMP INTEGER I, INFO, IX, J, JX, K, KK, KX LOGICAL NOUNIT * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO , 'U' ).AND. $ .NOT.LSAME( UPLO , 'L' ) )THEN INFO = 1 ELSE IF( .NOT.LSAME( TRANS, 'N' ).AND. $ .NOT.LSAME( TRANS, 'T' ).AND. $ .NOT.LSAME( TRANS, 'C' ) )THEN INFO = 2 ELSE IF( .NOT.LSAME( DIAG , 'U' ).AND. $ .NOT.LSAME( DIAG , 'N' ) )THEN INFO = 3 ELSE IF( N.LT.0 )THEN INFO = 4 ELSE IF( INCX.EQ.0 )THEN INFO = 7 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'STPMV ', INFO ) RETURN END IF * * Quick return if possible. * IF( N.EQ.0 ) $ RETURN * NOUNIT = LSAME( DIAG, 'N' ) * * Set up the start point in X if the increment is not unity. This * will be ( N - 1 )*INCX too small for descending loops. * IF( INCX.LE.0 )THEN KX = 1 - ( N - 1 )*INCX ELSE IF( INCX.NE.1 )THEN KX = 1 END IF * * Start the operations. In this version the elements of AP are * accessed sequentially with one pass through AP. * IF( LSAME( TRANS, 'N' ) )THEN * * Form x:= A*x. * IF( LSAME( UPLO, 'U' ) )THEN KK =1 IF( INCX.EQ.1 )THEN DO 20, J = 1, N IF( X( J ).NE.ZERO )THEN TEMP = X( J ) K = KK DO 10, I = 1, J - 1 X( I ) = X( I ) + TEMP*AP( K ) K = K + 1 10 CONTINUE IF( NOUNIT ) $ X( J ) = X( J )*AP( KK + J - 1 ) END IF KK = KK + J 20 CONTINUE ELSE JX = KX DO 40, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = X( JX ) IX = KX DO 30, K = KK, KK + J - 2 X( IX ) = X( IX ) + TEMP*AP( K ) IX = IX + INCX 30 CONTINUE IF( NOUNIT ) $ X( JX ) = X( JX )*AP( KK + J - 1 ) END IF JX = JX + INCX KK = KK + J 40 CONTINUE END IF ELSE KK = ( N*( N + 1 ) )/2 IF( INCX.EQ.1 )THEN DO 60, J = N, 1, -1 IF( X( J ).NE.ZERO )THEN TEMP = X( J ) K = KK DO 50, I = N, J + 1, -1 X( I ) = X( I ) + TEMP*AP( K ) K = K - 1 50 CONTINUE IF( NOUNIT ) $ X( J ) = X( J )*AP( KK - N + J ) END IF KK = KK - ( N - J + 1 ) 60 CONTINUE ELSE KX = KX + ( N - 1 )*INCX JX = KX DO 80, J = N, 1, -1 IF( X( JX ).NE.ZERO )THEN TEMP = X( JX ) IX = KX DO 70, K = KK, KK - ( N - ( J + 1 ) ), -1 X( IX ) = X( IX ) + TEMP*AP( K ) IX = IX - INCX 70 CONTINUE IF( NOUNIT ) $ X( JX ) = X( JX )*AP( KK - N + J ) END IF JX = JX - INCX KK = KK - ( N - J + 1 ) 80 CONTINUE END IF END IF ELSE * * Form x := A'*x. * IF( LSAME( UPLO, 'U' ) )THEN KK = ( N*( N + 1 ) )/2 IF( INCX.EQ.1 )THEN DO 100, J = N, 1, -1 TEMP = X( J ) IF( NOUNIT ) $ TEMP = TEMP*AP( KK ) K = KK - 1 DO 90, I = J - 1, 1, -1 TEMP = TEMP + AP( K )*X( I ) K = K - 1 90 CONTINUE X( J ) = TEMP KK = KK - J 100 CONTINUE ELSE JX = KX + ( N - 1 )*INCX DO 120, J = N, 1, -1 TEMP = X( JX ) IX = JX IF( NOUNIT ) $ TEMP = TEMP*AP( KK ) DO 110, K = KK - 1, KK - J + 1, -1 IX = IX - INCX TEMP = TEMP + AP( K )*X( IX ) 110 CONTINUE X( JX ) = TEMP JX = JX - INCX KK = KK - J 120 CONTINUE END IF ELSE KK = 1 IF( INCX.EQ.1 )THEN DO 140, J = 1, N TEMP = X( J ) IF( NOUNIT ) $ TEMP = TEMP*AP( KK ) K = KK + 1 DO 130, I = J + 1, N TEMP = TEMP + AP( K )*X( I ) K = K + 1 130 CONTINUE X( J ) = TEMP KK = KK + ( N - J + 1 ) 140 CONTINUE ELSE JX = KX DO 160, J = 1, N TEMP = X( JX ) IX = JX IF( NOUNIT ) $ TEMP = TEMP*AP( KK ) DO 150, K = KK + 1, KK + N - J IX = IX + INCX TEMP = TEMP + AP( K )*X( IX ) 150 CONTINUE X( JX ) = TEMP JX = JX + INCX KK = KK + ( N - J + 1 ) 160 CONTINUE END IF END IF END IF * RETURN * * End of STPMV . * END * ************************************************************************ * SUBROUTINE STRSV ( UPLO, TRANS, DIAG, N, A, LDA, X, INCX ) * .. Scalar Arguments .. INTEGER INCX, LDA, N CHARACTER*1 DIAG, TRANS, UPLO * .. Array Arguments .. REAL A( LDA, * ), X( * ) * .. * * Purpose * ======= * * STRSV solves one of the systems of equations * * A*x = b, or A'*x = b, * * where b and x are n element vectors and A is an n by n unit, or * non-unit, upper or lower triangular matrix. * * No test for singularity or near-singularity is included in this * routine. Such tests must be performed before calling this routine. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the matrix is an upper or * lower triangular matrix as follows: * * UPLO = 'U' or 'u' A is an upper triangular matrix. * * UPLO = 'L' or 'l' A is a lower triangular matrix. * * Unchanged on exit. * * TRANS - CHARACTER*1. * On entry, TRANS specifies the equations to be solved as * follows: * * TRANS = 'N' or 'n' A*x = b. * * TRANS = 'T' or 't' A'*x = b. * * TRANS = 'C' or 'c' A'*x = b. * * Unchanged on exit. * * DIAG - CHARACTER*1. * On entry, DIAG specifies whether or not A is unit * triangular as follows: * * DIAG = 'U' or 'u' A is assumed to be unit triangular. * * DIAG = 'N' or 'n' A is not assumed to be unit * triangular. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * A - REAL array of DIMENSION ( LDA, n ). * Before entry with UPLO = 'U' or 'u', the leading n by n * upper triangular part of the array A must contain the upper * triangular matrix and the strictly lower triangular part of * A is not referenced. * Before entry with UPLO = 'L' or 'l', the leading n by n * lower triangular part of the array A must contain the lower * triangular matrix and the strictly upper triangular part of * A is not referenced. * Note that when DIAG = 'U' or 'u', the diagonal elements of * A are not referenced either, but are assumed to be unity. * Unchanged on exit. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * max( 1, n ). * Unchanged on exit. * * X - REAL array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element right-hand side vector b. On exit, X is overwritten * with the solution vector x. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. REAL ZERO PARAMETER ( ZERO = 0.0E+0 ) * .. Local Scalars .. REAL TEMP INTEGER I, INFO, IX, J, JX, KX LOGICAL NOUNIT * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO , 'U' ).AND. $ .NOT.LSAME( UPLO , 'L' ) )THEN INFO = 1 ELSE IF( .NOT.LSAME( TRANS, 'N' ).AND. $ .NOT.LSAME( TRANS, 'T' ).AND. $ .NOT.LSAME( TRANS, 'C' ) )THEN INFO = 2 ELSE IF( .NOT.LSAME( DIAG , 'U' ).AND. $ .NOT.LSAME( DIAG , 'N' ) )THEN INFO = 3 ELSE IF( N.LT.0 )THEN INFO = 4 ELSE IF( LDA.LT.MAX( 1, N ) )THEN INFO = 6 ELSE IF( INCX.EQ.0 )THEN INFO = 8 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'STRSV ', INFO ) RETURN END IF * * Quick return if possible. * IF( N.EQ.0 ) $ RETURN * NOUNIT = LSAME( DIAG, 'N' ) * * Set up the start point in X if the increment is not unity. This * will be ( N - 1 )*INCX too small for descending loops. * IF( INCX.LE.0 )THEN KX = 1 - ( N - 1 )*INCX ELSE IF( INCX.NE.1 )THEN KX = 1 END IF * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through A. * IF( LSAME( TRANS, 'N' ) )THEN * * Form x := inv( A )*x. * IF( LSAME( UPLO, 'U' ) )THEN IF( INCX.EQ.1 )THEN DO 20, J = N, 1, -1 IF( X( J ).NE.ZERO )THEN IF( NOUNIT ) $ X( J ) = X( J )/A( J, J ) TEMP = X( J ) DO 10, I = J - 1, 1, -1 X( I ) = X( I ) - TEMP*A( I, J ) 10 CONTINUE END IF 20 CONTINUE ELSE JX = KX + ( N - 1 )*INCX DO 40, J = N, 1, -1 IF( X( JX ).NE.ZERO )THEN IF( NOUNIT ) $ X( JX ) = X( JX )/A( J, J ) TEMP = X( JX ) IX = JX DO 30, I = J - 1, 1, -1 IX = IX - INCX X( IX ) = X( IX ) - TEMP*A( I, J ) 30 CONTINUE END IF JX = JX - INCX 40 CONTINUE END IF ELSE IF( INCX.EQ.1 )THEN DO 60, J = 1, N IF( X( J ).NE.ZERO )THEN IF( NOUNIT ) $ X( J ) = X( J )/A( J, J ) TEMP = X( J ) DO 50, I = J + 1, N X( I ) = X( I ) - TEMP*A( I, J ) 50 CONTINUE END IF 60 CONTINUE ELSE JX = KX DO 80, J = 1, N IF( X( JX ).NE.ZERO )THEN IF( NOUNIT ) $ X( JX ) = X( JX )/A( J, J ) TEMP = X( JX ) IX = JX DO 70, I = J + 1, N IX = IX + INCX X( IX ) = X( IX ) - TEMP*A( I, J ) 70 CONTINUE END IF JX = JX + INCX 80 CONTINUE END IF END IF ELSE * * Form x := inv( A' )*x. * IF( LSAME( UPLO, 'U' ) )THEN IF( INCX.EQ.1 )THEN DO 100, J = 1, N TEMP = X( J ) DO 90, I = 1, J - 1 TEMP = TEMP - A( I, J )*X( I ) 90 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/A( J, J ) X( J ) = TEMP 100 CONTINUE ELSE JX = KX DO 120, J = 1, N TEMP = X( JX ) IX = KX DO 110, I = 1, J - 1 TEMP = TEMP - A( I, J )*X( IX ) IX = IX + INCX 110 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/A( J, J ) X( JX ) = TEMP JX = JX + INCX 120 CONTINUE END IF ELSE IF( INCX.EQ.1 )THEN DO 140, J = N, 1, -1 TEMP = X( J ) DO 130, I = N, J + 1, -1 TEMP = TEMP - A( I, J )*X( I ) 130 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/A( J, J ) X( J ) = TEMP 140 CONTINUE ELSE KX = KX + ( N - 1 )*INCX JX = KX DO 160, J = N, 1, -1 TEMP = X( JX ) IX = KX DO 150, I = N, J + 1, -1 TEMP = TEMP - A( I, J )*X( IX ) IX = IX - INCX 150 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/A( J, J ) X( JX ) = TEMP JX = JX - INCX 160 CONTINUE END IF END IF END IF * RETURN * * End of STRSV . * END * ************************************************************************ * SUBROUTINE STBSV ( UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX ) * .. Scalar Arguments .. INTEGER INCX, K, LDA, N CHARACTER*1 DIAG, TRANS, UPLO * .. Array Arguments .. REAL A( LDA, * ), X( * ) * .. * * Purpose * ======= * * STBSV solves one of the systems of equations * * A*x = b, or A'*x = b, * * where b and x are n element vectors and A is an n by n unit, or * non-unit, upper or lower triangular band matrix, with ( k + 1 ) * diagonals. * * No test for singularity or near-singularity is included in this * routine. Such tests must be performed before calling this routine. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the matrix is an upper or * lower triangular matrix as follows: * * UPLO = 'U' or 'u' A is an upper triangular matrix. * * UPLO = 'L' or 'l' A is a lower triangular matrix. * * Unchanged on exit. * * TRANS - CHARACTER*1. * On entry, TRANS specifies the equations to be solved as * follows: * * TRANS = 'N' or 'n' A*x = b. * * TRANS = 'T' or 't' A'*x = b. * * TRANS = 'C' or 'c' A'*x = b. * * Unchanged on exit. * * DIAG - CHARACTER*1. * On entry, DIAG specifies whether or not A is unit * triangular as follows: * * DIAG = 'U' or 'u' A is assumed to be unit triangular. * * DIAG = 'N' or 'n' A is not assumed to be unit * triangular. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * K - INTEGER. * On entry with UPLO = 'U' or 'u', K specifies the number of * super-diagonals of the matrix A. * On entry with UPLO = 'L' or 'l', K specifies the number of * sub-diagonals of the matrix A. * K must satisfy 0 .le. K. * Unchanged on exit. * * A - REAL array of DIMENSION ( LDA, n ). * Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) * by n part of the array A must contain the upper triangular * band part of the matrix of coefficients, supplied column by * column, with the leading diagonal of the matrix in row * ( k + 1 ) of the array, the first super-diagonal starting at * position 2 in row k, and so on. The top left k by k triangle * of the array A is not referenced. * The following program segment will transfer an upper * triangular band matrix from conventional full matrix storage * to band storage: * * DO 20, J = 1, N * M = K + 1 - J * DO 10, I = MAX( 1, J - K ), J * A( M + I, J ) = matrix( I, J ) * 10 CONTINUE * 20 CONTINUE * * Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) * by n part of the array A must contain the lower triangular * band part of the matrix of coefficients, supplied column by * column, with the leading diagonal of the matrix in row 1 of * the array, the first sub-diagonal starting at position 1 in * row 2, and so on. The bottom right k by k triangle of the * array A is not referenced. * The following program segment will transfer a lower * triangular band matrix from conventional full matrix storage * to band storage: * * DO 20, J = 1, N * M = 1 - J * DO 10, I = J, MIN( N, J + K ) * A( M + I, J ) = matrix( I, J ) * 10 CONTINUE * 20 CONTINUE * * Note that when DIAG = 'U' or 'u' the elements of the array A * corresponding to the diagonal elements of the matrix are not * referenced, but are assumed to be unity. * Unchanged on exit. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * ( k + 1 ). * Unchanged on exit. * * X - REAL array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element right-hand side vector b. On exit, X is overwritten * with the solution vector x. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. REAL ZERO PARAMETER ( ZERO = 0.0E+0 ) * .. Local Scalars .. REAL TEMP INTEGER I, INFO, IX, J, JX, KPLUS1, KX, L LOGICAL NOUNIT * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO , 'U' ).AND. $ .NOT.LSAME( UPLO , 'L' ) )THEN INFO = 1 ELSE IF( .NOT.LSAME( TRANS, 'N' ).AND. $ .NOT.LSAME( TRANS, 'T' ).AND. $ .NOT.LSAME( TRANS, 'C' ) )THEN INFO = 2 ELSE IF( .NOT.LSAME( DIAG , 'U' ).AND. $ .NOT.LSAME( DIAG , 'N' ) )THEN INFO = 3 ELSE IF( N.LT.0 )THEN INFO = 4 ELSE IF( K.LT.0 )THEN INFO = 5 ELSE IF( LDA.LT.( K + 1 ) )THEN INFO = 7 ELSE IF( INCX.EQ.0 )THEN INFO = 9 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'STBSV ', INFO ) RETURN END IF * * Quick return if possible. * IF( N.EQ.0 ) $ RETURN * NOUNIT = LSAME( DIAG, 'N' ) * * Set up the start point in X if the increment is not unity. This * will be ( N - 1 )*INCX too small for descending loops. * IF( INCX.LE.0 )THEN KX = 1 - ( N - 1 )*INCX ELSE IF( INCX.NE.1 )THEN KX = 1 END IF * * Start the operations. In this version the elements of A are * accessed by sequentially with one pass through A. * IF( LSAME( TRANS, 'N' ) )THEN * * Form x := inv( A )*x. * IF( LSAME( UPLO, 'U' ) )THEN KPLUS1 = K + 1 IF( INCX.EQ.1 )THEN DO 20, J = N, 1, -1 IF( X( J ).NE.ZERO )THEN L = KPLUS1 - J IF( NOUNIT ) $ X( J ) = X( J )/A( KPLUS1, J ) TEMP = X( J ) DO 10, I = J - 1, MAX( 1, J - K ), -1 X( I ) = X( I ) - TEMP*A( L + I, J ) 10 CONTINUE END IF 20 CONTINUE ELSE KX = KX + ( N - 1 )*INCX JX = KX DO 40, J = N, 1, -1 KX = KX - INCX IF( X( JX ).NE.ZERO )THEN IX = KX L = KPLUS1 - J IF( NOUNIT ) $ X( JX ) = X( JX )/A( KPLUS1, J ) TEMP = X( JX ) DO 30, I = J - 1, MAX( 1, J - K ), -1 X( IX ) = X( IX ) - TEMP*A( L + I, J ) IX = IX - INCX 30 CONTINUE END IF JX = JX - INCX 40 CONTINUE END IF ELSE IF( INCX.EQ.1 )THEN DO 60, J = 1, N IF( X( J ).NE.ZERO )THEN L = 1 - J IF( NOUNIT ) $ X( J ) = X( J )/A( 1, J ) TEMP = X( J ) DO 50, I = J + 1, MIN( N, J + K ) X( I ) = X( I ) - TEMP*A( L + I, J ) 50 CONTINUE END IF 60 CONTINUE ELSE JX = KX DO 80, J = 1, N KX = KX + INCX IF( X( JX ).NE.ZERO )THEN IX = KX L = 1 - J IF( NOUNIT ) $ X( JX ) = X( JX )/A( 1, J ) TEMP = X( JX ) DO 70, I = J + 1, MIN( N, J + K ) X( IX ) = X( IX ) - TEMP*A( L + I, J ) IX = IX + INCX 70 CONTINUE END IF JX = JX + INCX 80 CONTINUE END IF END IF ELSE * * Form x := inv( A')*x. * IF( LSAME( UPLO, 'U' ) )THEN KPLUS1 = K + 1 IF( INCX.EQ.1 )THEN DO 100, J = 1, N TEMP = X( J ) L = KPLUS1 - J DO 90, I = MAX( 1, J - K ), J - 1 TEMP = TEMP - A( L + I, J )*X( I ) 90 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/A( KPLUS1, J ) X( J ) = TEMP 100 CONTINUE ELSE JX = KX DO 120, J = 1, N TEMP = X( JX ) IX = KX L = KPLUS1 - J DO 110, I = MAX( 1, J - K ), J - 1 TEMP = TEMP - A( L + I, J )*X( IX ) IX = IX + INCX 110 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/A( KPLUS1, J ) X( JX ) = TEMP JX = JX + INCX IF( J.GT.K ) $ KX = KX + INCX 120 CONTINUE END IF ELSE IF( INCX.EQ.1 )THEN DO 140, J = N, 1, -1 TEMP = X( J ) L = 1 - J DO 130, I = MIN( N, J + K ), J + 1, -1 TEMP = TEMP - A( L + I, J )*X( I ) 130 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/A( 1, J ) X( J ) = TEMP 140 CONTINUE ELSE KX = KX + ( N - 1 )*INCX JX = KX DO 160, J = N, 1, -1 TEMP = X( JX ) IX = KX L = 1 - J DO 150, I = MIN( N, J + K ), J + 1, -1 TEMP = TEMP - A( L + I, J )*X( IX ) IX = IX - INCX 150 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/A( 1, J ) X( JX ) = TEMP JX = JX - INCX IF( ( N - J ).GE.K ) $ KX = KX - INCX 160 CONTINUE END IF END IF END IF * RETURN * * End of STBSV . * END * ************************************************************************ * SUBROUTINE STPSV ( UPLO, TRANS, DIAG, N, AP, X, INCX ) * .. Scalar Arguments .. INTEGER INCX, N CHARACTER*1 DIAG, TRANS, UPLO * .. Array Arguments .. REAL AP( * ), X( * ) * .. * * Purpose * ======= * * STPSV solves one of the systems of equations * * A*x = b, or A'*x = b, * * where b and x are n element vectors and A is an n by n unit, or * non-unit, upper or lower triangular matrix, supplied in packed form. * * No test for singularity or near-singularity is included in this * routine. Such tests must be performed before calling this routine. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the matrix is an upper or * lower triangular matrix as follows: * * UPLO = 'U' or 'u' A is an upper triangular matrix. * * UPLO = 'L' or 'l' A is a lower triangular matrix. * * Unchanged on exit. * * TRANS - CHARACTER*1. * On entry, TRANS specifies the equations to be solved as * follows: * * TRANS = 'N' or 'n' A*x = b. * * TRANS = 'T' or 't' A'*x = b. * * TRANS = 'C' or 'c' A'*x = b. * * Unchanged on exit. * * DIAG - CHARACTER*1. * On entry, DIAG specifies whether or not A is unit * triangular as follows: * * DIAG = 'U' or 'u' A is assumed to be unit triangular. * * DIAG = 'N' or 'n' A is not assumed to be unit * triangular. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * AP - REAL array of DIMENSION at least * ( ( n*( n + 1 ) )/2 ). * Before entry with UPLO = 'U' or 'u', the array AP must * contain the upper triangular matrix packed sequentially, * column by column, so that AP( 1 ) contains a( 1, 1 ), * AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) * respectively, and so on. * Before entry with UPLO = 'L' or 'l', the array AP must * contain the lower triangular matrix packed sequentially, * column by column, so that AP( 1 ) contains a( 1, 1 ), * AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) * respectively, and so on. * Note that when DIAG = 'U' or 'u', the diagonal elements of * A are not referenced, but are assumed to be unity. * Unchanged on exit. * * X - REAL array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element right-hand side vector b. On exit, X is overwritten * with the solution vector x. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. REAL ZERO PARAMETER ( ZERO = 0.0E+0 ) * .. Local Scalars .. REAL TEMP INTEGER I, INFO, IX, J, JX, K, KK, KX LOGICAL NOUNIT * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO , 'U' ).AND. $ .NOT.LSAME( UPLO , 'L' ) )THEN INFO = 1 ELSE IF( .NOT.LSAME( TRANS, 'N' ).AND. $ .NOT.LSAME( TRANS, 'T' ).AND. $ .NOT.LSAME( TRANS, 'C' ) )THEN INFO = 2 ELSE IF( .NOT.LSAME( DIAG , 'U' ).AND. $ .NOT.LSAME( DIAG , 'N' ) )THEN INFO = 3 ELSE IF( N.LT.0 )THEN INFO = 4 ELSE IF( INCX.EQ.0 )THEN INFO = 7 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'STPSV ', INFO ) RETURN END IF * * Quick return if possible. * IF( N.EQ.0 ) $ RETURN * NOUNIT = LSAME( DIAG, 'N' ) * * Set up the start point in X if the increment is not unity. This * will be ( N - 1 )*INCX too small for descending loops. * IF( INCX.LE.0 )THEN KX = 1 - ( N - 1 )*INCX ELSE IF( INCX.NE.1 )THEN KX = 1 END IF * * Start the operations. In this version the elements of AP are * accessed sequentially with one pass through AP. * IF( LSAME( TRANS, 'N' ) )THEN * * Form x := inv( A )*x. * IF( LSAME( UPLO, 'U' ) )THEN KK = ( N*( N + 1 ) )/2 IF( INCX.EQ.1 )THEN DO 20, J = N, 1, -1 IF( X( J ).NE.ZERO )THEN IF( NOUNIT ) $ X( J ) = X( J )/AP( KK ) TEMP = X( J ) K = KK - 1 DO 10, I = J - 1, 1, -1 X( I ) = X( I ) - TEMP*AP( K ) K = K - 1 10 CONTINUE END IF KK = KK - J 20 CONTINUE ELSE JX = KX + ( N - 1 )*INCX DO 40, J = N, 1, -1 IF( X( JX ).NE.ZERO )THEN IF( NOUNIT ) $ X( JX ) = X( JX )/AP( KK ) TEMP = X( JX ) IX = JX DO 30, K = KK - 1, KK - J + 1, -1 IX = IX - INCX X( IX ) = X( IX ) - TEMP*AP( K ) 30 CONTINUE END IF JX = JX - INCX KK = KK - J 40 CONTINUE END IF ELSE KK = 1 IF( INCX.EQ.1 )THEN DO 60, J = 1, N IF( X( J ).NE.ZERO )THEN IF( NOUNIT ) $ X( J ) = X( J )/AP( KK ) TEMP = X( J ) K = KK + 1 DO 50, I = J + 1, N X( I ) = X( I ) - TEMP*AP( K ) K = K + 1 50 CONTINUE END IF KK = KK + ( N - J + 1 ) 60 CONTINUE ELSE JX = KX DO 80, J = 1, N IF( X( JX ).NE.ZERO )THEN IF( NOUNIT ) $ X( JX ) = X( JX )/AP( KK ) TEMP = X( JX ) IX = JX DO 70, K = KK + 1, KK + N - J IX = IX + INCX X( IX ) = X( IX ) - TEMP*AP( K ) 70 CONTINUE END IF JX = JX + INCX KK = KK + ( N - J + 1 ) 80 CONTINUE END IF END IF ELSE * * Form x := inv( A' )*x. * IF( LSAME( UPLO, 'U' ) )THEN KK = 1 IF( INCX.EQ.1 )THEN DO 100, J = 1, N TEMP = X( J ) K = KK DO 90, I = 1, J - 1 TEMP = TEMP - AP( K )*X( I ) K = K + 1 90 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/AP( KK + J - 1 ) X( J ) = TEMP KK = KK + J 100 CONTINUE ELSE JX = KX DO 120, J = 1, N TEMP = X( JX ) IX = KX DO 110, K = KK, KK + J - 2 TEMP = TEMP - AP( K )*X( IX ) IX = IX + INCX 110 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/AP( KK + J - 1 ) X( JX ) = TEMP JX = JX + INCX KK = KK + J 120 CONTINUE END IF ELSE KK = ( N*( N + 1 ) )/2 IF( INCX.EQ.1 )THEN DO 140, J = N, 1, -1 TEMP = X( J ) K = KK DO 130, I = N, J + 1, -1 TEMP = TEMP - AP( K )*X( I ) K = K - 1 130 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/AP( KK - N + J ) X( J ) = TEMP KK = KK - ( N - J + 1 ) 140 CONTINUE ELSE KX = KX + ( N - 1 )*INCX JX = KX DO 160, J = N, 1, -1 TEMP = X( JX ) IX = KX DO 150, K = KK, KK - ( N - ( J + 1 ) ), -1 TEMP = TEMP - AP( K )*X( IX ) IX = IX - INCX 150 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/AP( KK - N + J ) X( JX ) = TEMP JX = JX - INCX KK = KK - (N - J + 1 ) 160 CONTINUE END IF END IF END IF * RETURN * * End of STPSV . * END * ************************************************************************ * SUBROUTINE SGER ( M, N, ALPHA, X, INCX, Y, INCY, A, LDA ) * .. Scalar Arguments .. REAL ALPHA INTEGER INCX, INCY, LDA, M, N * .. Array Arguments .. REAL A( LDA, * ), X( * ), Y( * ) * .. * * Purpose * ======= * * SGER performs the rank 1 operation * * A := alpha*x*y' + A, * * where alpha is a scalar, x is an m element vector, y is an n element * vector and A is an m by n matrix. * * Parameters * ========== * * M - INTEGER. * On entry, M specifies the number of rows of the matrix A. * M must be at least zero. * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the number of columns of the matrix A. * N must be at least zero. * Unchanged on exit. * * ALPHA - REAL . * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * X - REAL array of dimension at least * ( 1 + ( m - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the m * element vector x. * Unchanged on exit. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * Y - REAL array of dimension at least * ( 1 + ( n - 1 )*abs( INCY ) ). * Before entry, the incremented array Y must contain the n * element vector y. * Unchanged on exit. * * INCY - INTEGER. * On entry, INCY specifies the increment for the elements of * Y. INCY must not be zero. * Unchanged on exit. * * A - REAL array of DIMENSION ( LDA, n ). * Before entry, the leading m by n part of the array A must * contain the matrix of coefficients. On exit, A is * overwritten by the updated matrix. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * max( 1, m ). * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. REAL ZERO PARAMETER ( ZERO = 0.0E+0 ) * .. Local Scalars .. REAL TEMP INTEGER I, INFO, IX, J, JY, KX * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( M.LT.0 )THEN INFO = 1 ELSE IF( N.LT.0 )THEN INFO = 2 ELSE IF( INCX.EQ.0 )THEN INFO = 5 ELSE IF( INCY.EQ.0 )THEN INFO = 7 ELSE IF( LDA.LT.MAX( 1, M ) )THEN INFO = 9 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'SGER ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( M.EQ.0 ).OR.( N.EQ.0 ).OR.( ALPHA.EQ.ZERO ) ) $ RETURN * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through A. * IF( INCY.GT.0 )THEN JY = 1 ELSE JY = 1 - ( N - 1 )*INCY END IF IF( INCX.EQ.1 )THEN DO 20, J = 1, N IF( Y( JY ).NE.ZERO )THEN TEMP = ALPHA*Y( JY ) DO 10, I = 1, M A( I, J ) = A( I, J ) + X( I )*TEMP 10 CONTINUE END IF JY = JY + INCY 20 CONTINUE ELSE IF( INCX.GT.0 )THEN KX = 1 ELSE KX = 1 - ( M - 1 )*INCX END IF DO 40, J = 1, N IF( Y( JY ).NE.ZERO )THEN TEMP = ALPHA*Y( JY ) IX = KX DO 30, I = 1, M A( I, J ) = A( I, J ) + X( IX )*TEMP IX = IX + INCX 30 CONTINUE END IF JY = JY + INCY 40 CONTINUE END IF * RETURN * * End of SGER . * END * ************************************************************************ * SUBROUTINE SSYR ( UPLO, N, ALPHA, X, INCX, A, LDA ) * .. Scalar Arguments .. REAL ALPHA INTEGER INCX, LDA, N CHARACTER*1 UPLO * .. Array Arguments .. REAL A( LDA, * ), X( * ) * .. * * Purpose * ======= * * SSYR performs the symmetric rank 1 operation * * A := alpha*x*x' + A, * * where alpha is a real scalar, x is an n element vector and A is an * n by n symmetric matrix. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the upper or lower * triangular part of the array A is to be referenced as * follows: * * UPLO = 'U' or 'u' Only the upper triangular part of A * is to be referenced. * * UPLO = 'L' or 'l' Only the lower triangular part of A * is to be referenced. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * ALPHA - REAL . * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * X - REAL array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element vector x. * Unchanged on exit. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * A - REAL array of DIMENSION ( LDA, n ). * Before entry with UPLO = 'U' or 'u', the leading n by n * upper triangular part of the array A must contain the upper * triangular part of the symmetric matrix and the strictly * lower triangular part of A is not referenced. On exit, the * upper triangular part of the array A is overwritten by the * upper triangular part of the updated matrix. * Before entry with UPLO = 'L' or 'l', the leading n by n * lower triangular part of the array A must contain the lower * triangular part of the symmetric matrix and the strictly * upper triangular part of A is not referenced. On exit, the * lower triangular part of the array A is overwritten by the * lower triangular part of the updated matrix. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * max( 1, n ). * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. REAL ZERO PARAMETER ( ZERO = 0.0E+0 ) * .. Local Scalars .. REAL TEMP INTEGER I, INFO, IX, J, JX, KX * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO, 'U' ).AND. $ .NOT.LSAME( UPLO, 'L' ) )THEN INFO = 1 ELSE IF( N.LT.0 )THEN INFO = 2 ELSE IF( INCX.EQ.0 )THEN INFO = 5 ELSE IF( LDA.LT.MAX( 1, N ) )THEN INFO = 7 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'SSYR ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( N.EQ.0 ).OR.( ALPHA.EQ.ZERO ) ) $ RETURN * * Set the start point in X if the increment is not unity. * IF( INCX.LE.0 )THEN KX = 1 - ( N - 1 )*INCX ELSE IF( INCX.NE.1 )THEN KX = 1 END IF * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through the triangular part * of A. * IF( LSAME( UPLO, 'U' ) )THEN * * Form A when A is stored in upper triangle. * IF( INCX.EQ.1 )THEN DO 20, J = 1, N IF( X( J ).NE.ZERO )THEN TEMP = ALPHA*X( J ) DO 10, I = 1, J A( I, J ) = A( I, J ) + X( I )*TEMP 10 CONTINUE END IF 20 CONTINUE ELSE JX = KX DO 40, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = ALPHA*X( JX ) IX = KX DO 30, I = 1, J A( I, J ) = A( I, J ) + X( IX )*TEMP IX = IX + INCX 30 CONTINUE END IF JX = JX + INCX 40 CONTINUE END IF ELSE * * Form A when A is stored in lower triangle. * IF( INCX.EQ.1 )THEN DO 60, J = 1, N IF( X( J ).NE.ZERO )THEN TEMP = ALPHA*X( J ) DO 50, I = J, N A( I, J ) = A( I, J ) + X( I )*TEMP 50 CONTINUE END IF 60 CONTINUE ELSE JX = KX DO 80, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = ALPHA*X( JX ) IX = JX DO 70, I = J, N A( I, J ) = A( I, J ) + X( IX )*TEMP IX = IX + INCX 70 CONTINUE END IF JX = JX + INCX 80 CONTINUE END IF END IF * RETURN * * End of SSYR . * END * ************************************************************************ * SUBROUTINE SSPR ( UPLO, N, ALPHA, X, INCX, AP ) * .. Scalar Arguments .. REAL ALPHA INTEGER INCX, N CHARACTER*1 UPLO * .. Array Arguments .. REAL AP( * ), X( * ) * .. * * Purpose * ======= * * SSPR performs the symmetric rank 1 operation * * A := alpha*x*x' + A, * * where alpha is a real scalar, x is an n element vector and A is an * n by n symmetric matrix, supplied in packed form. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the upper or lower * triangular part of the matrix A is supplied in the packed * array AP as follows: * * UPLO = 'U' or 'u' The upper triangular part of A is * supplied in AP. * * UPLO = 'L' or 'l' The lower triangular part of A is * supplied in AP. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * ALPHA - REAL . * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * X - REAL array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element vector x. * Unchanged on exit. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * AP - REAL array of DIMENSION at least * ( ( n*( n + 1 ) )/2 ). * Before entry with UPLO = 'U' or 'u', the array AP must * contain the upper triangular part of the symmetric matrix * packed sequentially, column by column, so that AP( 1 ) * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) * and a( 2, 2 ) respectively, and so on. On exit, the array * AP is overwritten by the upper triangular part of the * updated matrix. * Before entry with UPLO = 'L' or 'l', the array AP must * contain the lower triangular part of the symmetric matrix * packed sequentially, column by column, so that AP( 1 ) * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) * and a( 3, 1 ) respectively, and so on. On exit, the array * AP is overwritten by the lower triangular part of the * updated matrix. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. REAL ZERO PARAMETER ( ZERO = 0.0E+0 ) * .. Local Scalars .. REAL TEMP INTEGER I, INFO, IX, J, JX, K, KK, KX * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO, 'U' ).AND. $ .NOT.LSAME( UPLO, 'L' ) )THEN INFO = 1 ELSE IF( N.LT.0 )THEN INFO = 2 ELSE IF( INCX.EQ.0 )THEN INFO = 5 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'SSPR ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( N.EQ.0 ).OR.( ALPHA.EQ.ZERO ) ) $ RETURN * * Set the start point in X if the increment is not unity. * IF( INCX.LE.0 )THEN KX = 1 - ( N - 1 )*INCX ELSE IF( INCX.NE.1 )THEN KX = 1 END IF * * Start the operations. In this version the elements of the array AP * are accessed sequentially with one pass through AP. * KK = 1 IF( LSAME( UPLO, 'U' ) )THEN * * Form A when upper triangle is stored in AP. * IF( INCX.EQ.1 )THEN DO 20, J = 1, N IF( X( J ).NE.ZERO )THEN TEMP = ALPHA*X( J ) K = KK DO 10, I = 1, J AP( K ) = AP( K ) + X( I )*TEMP K = K + 1 10 CONTINUE END IF KK = KK + J 20 CONTINUE ELSE JX = KX DO 40, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = ALPHA*X( JX ) IX = KX DO 30, K = KK, KK + J - 1 AP( K ) = AP( K ) + X( IX )*TEMP IX = IX + INCX 30 CONTINUE END IF JX = JX + INCX KK = KK + J 40 CONTINUE END IF ELSE * * Form A when lower triangle is stored in AP. * IF( INCX.EQ.1 )THEN DO 60, J = 1, N IF( X( J ).NE.ZERO )THEN TEMP = ALPHA*X( J ) K = KK DO 50, I = J, N AP( K ) = AP( K ) + X( I )*TEMP K = K + 1 50 CONTINUE END IF KK = KK + N - J + 1 60 CONTINUE ELSE JX = KX DO 80, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = ALPHA*X( JX ) IX = JX DO 70, K = KK, KK + N - J AP( K ) = AP( K ) + X( IX )*TEMP IX = IX + INCX 70 CONTINUE END IF JX = JX + INCX KK = KK + N - J + 1 80 CONTINUE END IF END IF * RETURN * * End of SSPR . * END * ************************************************************************ * SUBROUTINE SSYR2 ( UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA ) * .. Scalar Arguments .. REAL ALPHA INTEGER INCX, INCY, LDA, N CHARACTER*1 UPLO * .. Array Arguments .. REAL A( LDA, * ), X( * ), Y( * ) * .. * * Purpose * ======= * * SSYR2 performs the symmetric rank 2 operation * * A := alpha*x*y' + alpha*y*x' + A, * * where alpha is a scalar, x and y are n element vectors and A is an n * by n symmetric matrix. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the upper or lower * triangular part of the array A is to be referenced as * follows: * * UPLO = 'U' or 'u' Only the upper triangular part of A * is to be referenced. * * UPLO = 'L' or 'l' Only the lower triangular part of A * is to be referenced. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * ALPHA - REAL . * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * X - REAL array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element vector x. * Unchanged on exit. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * Y - REAL array of dimension at least * ( 1 + ( n - 1 )*abs( INCY ) ). * Before entry, the incremented array Y must contain the n * element vector y. * Unchanged on exit. * * INCY - INTEGER. * On entry, INCY specifies the increment for the elements of * Y. INCY must not be zero. * Unchanged on exit. * * A - REAL array of DIMENSION ( LDA, n ). * Before entry with UPLO = 'U' or 'u', the leading n by n * upper triangular part of the array A must contain the upper * triangular part of the symmetric matrix and the strictly * lower triangular part of A is not referenced. On exit, the * upper triangular part of the array A is overwritten by the * upper triangular part of the updated matrix. * Before entry with UPLO = 'L' or 'l', the leading n by n * lower triangular part of the array A must contain the lower * triangular part of the symmetric matrix and the strictly * upper triangular part of A is not referenced. On exit, the * lower triangular part of the array A is overwritten by the * lower triangular part of the updated matrix. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * max( 1, n ). * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. REAL ZERO PARAMETER ( ZERO = 0.0E+0 ) * .. Local Scalars .. REAL TEMP1, TEMP2 INTEGER I, INFO, IX, IY, J, JX, JY, KX, KY * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO, 'U' ).AND. $ .NOT.LSAME( UPLO, 'L' ) )THEN INFO = 1 ELSE IF( N.LT.0 )THEN INFO = 2 ELSE IF( INCX.EQ.0 )THEN INFO = 5 ELSE IF( INCY.EQ.0 )THEN INFO = 7 ELSE IF( LDA.LT.MAX( 1, N ) )THEN INFO = 9 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'SSYR2 ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( N.EQ.0 ).OR.( ALPHA.EQ.ZERO ) ) $ RETURN * * Set up the start points in X and Y if the increments are not both * unity. * IF( ( INCX.NE.1 ).OR.( INCY.NE.1 ) )THEN IF( INCX.GT.0 )THEN KX = 1 ELSE KX = 1 - ( N - 1 )*INCX END IF IF( INCY.GT.0 )THEN KY = 1 ELSE KY = 1 - ( N - 1 )*INCY END IF JX = KX JY = KY END IF * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through the triangular part * of A. * IF( LSAME( UPLO, 'U' ) )THEN * * Form A when A is stored in the upper triangle. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 20, J = 1, N IF( ( X( J ).NE.ZERO ).OR.( Y( J ).NE.ZERO ) )THEN TEMP1 = ALPHA*Y( J ) TEMP2 = ALPHA*X( J ) DO 10, I = 1, J A( I, J ) = A( I, J ) + X( I )*TEMP1 + Y( I )*TEMP2 10 CONTINUE END IF 20 CONTINUE ELSE DO 40, J = 1, N IF( ( X( JX ).NE.ZERO ).OR.( Y( JY ).NE.ZERO ) )THEN TEMP1 = ALPHA*Y( JY ) TEMP2 = ALPHA*X( JX ) IX = KX IY = KY DO 30, I = 1, J A( I, J ) = A( I, J ) + X( IX )*TEMP1 $ + Y( IY )*TEMP2 IX = IX + INCX IY = IY + INCY 30 CONTINUE END IF JX = JX + INCX JY = JY + INCY 40 CONTINUE END IF ELSE * * Form A when A is stored in the lower triangle. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 60, J = 1, N IF( ( X( J ).NE.ZERO ).OR.( Y( J ).NE.ZERO ) )THEN TEMP1 = ALPHA*Y( J ) TEMP2 = ALPHA*X( J ) DO 50, I = J, N A( I, J ) = A( I, J ) + X( I )*TEMP1 + Y( I )*TEMP2 50 CONTINUE END IF 60 CONTINUE ELSE DO 80, J = 1, N IF( ( X( JX ).NE.ZERO ).OR.( Y( JY ).NE.ZERO ) )THEN TEMP1 = ALPHA*Y( JY ) TEMP2 = ALPHA*X( JX ) IX = JX IY = JY DO 70, I = J, N A( I, J ) = A( I, J ) + X( IX )*TEMP1 $ + Y( IY )*TEMP2 IX = IX + INCX IY = IY + INCY 70 CONTINUE END IF JX = JX + INCX JY = JY + INCY 80 CONTINUE END IF END IF * RETURN * * End of SSYR2 . * END * ************************************************************************ * SUBROUTINE SSPR2 ( UPLO, N, ALPHA, X, INCX, Y, INCY, AP ) * .. Scalar Arguments .. REAL ALPHA INTEGER INCX, INCY, N CHARACTER*1 UPLO * .. Array Arguments .. REAL AP( * ), X( * ), Y( * ) * .. * * Purpose * ======= * * SSPR2 performs the symmetric rank 2 operation * * A := alpha*x*y' + alpha*y*x' + A, * * where alpha is a scalar, x and y are n element vectors and A is an * n by n symmetric matrix, supplied in packed form. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the upper or lower * triangular part of the matrix A is supplied in the packed * array AP as follows: * * UPLO = 'U' or 'u' The upper triangular part of A is * supplied in AP. * * UPLO = 'L' or 'l' The lower triangular part of A is * supplied in AP. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * ALPHA - REAL . * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * X - REAL array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element vector x. * Unchanged on exit. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * Y - REAL array of dimension at least * ( 1 + ( n - 1 )*abs( INCY ) ). * Before entry, the incremented array Y must contain the n * element vector y. * Unchanged on exit. * * INCY - INTEGER. * On entry, INCY specifies the increment for the elements of * Y. INCY must not be zero. * Unchanged on exit. * * AP - REAL array of DIMENSION at least * ( ( n*( n + 1 ) )/2 ). * Before entry with UPLO = 'U' or 'u', the array AP must * contain the upper triangular part of the symmetric matrix * packed sequentially, column by column, so that AP( 1 ) * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) * and a( 2, 2 ) respectively, and so on. On exit, the array * AP is overwritten by the upper triangular part of the * updated matrix. * Before entry with UPLO = 'L' or 'l', the array AP must * contain the lower triangular part of the symmetric matrix * packed sequentially, column by column, so that AP( 1 ) * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) * and a( 3, 1 ) respectively, and so on. On exit, the array * AP is overwritten by the lower triangular part of the * updated matrix. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. REAL ZERO PARAMETER ( ZERO = 0.0E+0 ) * .. Local Scalars .. REAL TEMP1, TEMP2 INTEGER I, INFO, IX, IY, J, JX, JY, K, KK, KX, KY * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO, 'U' ).AND. $ .NOT.LSAME( UPLO, 'L' ) )THEN INFO = 1 ELSE IF( N.LT.0 )THEN INFO = 2 ELSE IF( INCX.EQ.0 )THEN INFO = 5 ELSE IF( INCY.EQ.0 )THEN INFO = 7 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'SSPR2 ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( N.EQ.0 ).OR.( ALPHA.EQ.ZERO ) ) $ RETURN * * Set up the start points in X and Y if the increments are not both * unity. * IF( ( INCX.NE.1 ).OR.( INCY.NE.1 ) )THEN IF( INCX.GT.0 )THEN KX = 1 ELSE KX = 1 - ( N - 1 )*INCX END IF IF( INCY.GT.0 )THEN KY = 1 ELSE KY = 1 - ( N - 1 )*INCY END IF JX = KX JY = KY END IF * * Start the operations. In this version the elements of the array AP * are accessed sequentially with one pass through AP. * KK = 1 IF( LSAME( UPLO, 'U' ) )THEN * * Form A when upper triangle is stored in AP. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 20, J = 1, N IF( ( X( J ).NE.ZERO ).OR.( Y( J ).NE.ZERO ) )THEN TEMP1 = ALPHA*Y( J ) TEMP2 = ALPHA*X( J ) K = KK DO 10, I = 1, J AP( K ) = AP( K ) + X( I )*TEMP1 + Y( I )*TEMP2 K = K + 1 10 CONTINUE END IF KK = KK + J 20 CONTINUE ELSE DO 40, J = 1, N IF( ( X( JX ).NE.ZERO ).OR.( Y( JY ).NE.ZERO ) )THEN TEMP1 = ALPHA*Y( JY ) TEMP2 = ALPHA*X( JX ) IX = KX IY = KY DO 30, K = KK, KK + J - 1 AP( K ) = AP( K ) + X( IX )*TEMP1 + Y( IY )*TEMP2 IX = IX + INCX IY = IY + INCY 30 CONTINUE END IF JX = JX + INCX JY = JY + INCY KK = KK + J 40 CONTINUE END IF ELSE * * Form A when lower triangle is stored in AP. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 60, J = 1, N IF( ( X( J ).NE.ZERO ).OR.( Y( J ).NE.ZERO ) )THEN TEMP1 = ALPHA*Y( J ) TEMP2 = ALPHA*X( J ) K = KK DO 50, I = J, N AP( K ) = AP( K ) + X( I )*TEMP1 + Y( I )*TEMP2 K = K + 1 50 CONTINUE END IF KK = KK + N - J + 1 60 CONTINUE ELSE DO 80, J = 1, N IF( ( X( JX ).NE.ZERO ).OR.( Y( JY ).NE.ZERO ) )THEN TEMP1 = ALPHA*Y( JY ) TEMP2 = ALPHA*X( JX ) IX = JX IY = JY DO 70, K = KK, KK + N - J AP( K ) = AP( K ) + X( IX )*TEMP1 + Y( IY )*TEMP2 IX = IX + INCX IY = IY + INCY 70 CONTINUE END IF JX = JX + INCX JY = JY + INCY KK = KK + N - J + 1 80 CONTINUE END IF END IF * RETURN * * End of SSPR2 . * END LOGICAL FUNCTION LSAME ( CA, CB ) * .. Scalar Arguments .. CHARACTER*1 CA, CB * .. * * Purpose * ======= * * LSAME tests if CA is the same letter as CB regardless of case. * CB is assumed to be an upper case letter. LSAME returns .TRUE. if * CA is either the same as CB or the equivalent lower case letter. * * N.B. This version of the routine is only correct for ASCII code. * Installers must modify the routine for other character-codes. * * For EBCDIC systems the constant IOFF must be changed to -64. * For CDC systems using 6-12 bit representations, the system- * specific code in comments must be activated. * * Parameters * ========== * * CA - CHARACTER*1 * CB - CHARACTER*1 * On entry, CA and CB specify characters to be compared. * Unchanged on exit. * * * Auxiliary routine for Level 2 Blas. * * -- Written on 20-July-1986 * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, Nag Central Office. * * .. Parameters .. INTEGER IOFF PARAMETER ( IOFF=32 ) * .. Intrinsic Functions .. INTRINSIC ICHAR * .. Executable Statements .. * * Test if the characters are equal * LSAME = CA .EQ. CB * * Now test for equivalence * IF ( .NOT.LSAME ) THEN LSAME = ICHAR(CA) - IOFF .EQ. ICHAR(CB) END IF * RETURN * * The following comments contain code for CDC systems using 6-12 bit * representations. * * .. Parameters .. * INTEGER ICIRFX * PARAMETER ( ICIRFX=62 ) * .. Scalar Arguments .. * CHARACTER*1 CB * .. Array Arguments .. * CHARACTER*1 CA(*) * .. Local Scalars .. * INTEGER IVAL * .. Intrinsic Functions .. * INTRINSIC ICHAR, CHAR * .. Executable Statements .. * * See if the first character in string CA equals string CB. * * LSAME = CA(1) .EQ. CB .AND. CA(1) .NE. CHAR(ICIRFX) * * IF (LSAME) RETURN * * The characters are not identical. Now check them for equivalence. * Look for the 'escape' character, circumflex, followed by the * letter. * * IVAL = ICHAR(CA(2)) * IF (IVAL.GE.ICHAR('A') .AND. IVAL.LE.ICHAR('Z')) THEN * LSAME = CA(1) .EQ. CHAR(ICIRFX) .AND. CA(2) .EQ. CB * END IF * * RETURN * * End of LSAME. * END SUBROUTINE XERBLA ( SRNAME, INFO ) * .. Scalar Arguments .. INTEGER INFO CHARACTER*6 SRNAME * .. * * Purpose * ======= * * XERBLA is an error handler for the Level 2 BLAS routines. * * It is called by the Level 2 BLAS routines if an input parameter is * invalid. * * Installers should consider modifying the STOP statement in order to * call system-specific exception-handling facilities. * * Parameters * ========== * * SRNAME - CHARACTER*6. * On entry, SRNAME specifies the name of the routine which * called XERBLA. * * INFO - INTEGER. * On entry, INFO specifies the position of the invalid * parameter in the parameter-list of the calling routine. * * * Auxiliary routine for Level 2 Blas. * * Written on 20-July-1986. * * .. Executable Statements .. * WRITE (*,99999) SRNAME, INFO * STOP * 99999 FORMAT ( ' ** On entry to ', A6, ' parameter number ', I2, $ ' had an illegal value' ) * * End of XERBLA. * END * ************************************************************************ * * File of the COMPLEX Level-2 BLAS. * ========================================== * * SUBROUTINE CGEMV ( TRANS, M, N, ALPHA, A, LDA, X, INCX, * $ BETA, Y, INCY ) * * SUBROUTINE CGBMV ( TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX, * $ BETA, Y, INCY ) * * SUBROUTINE CHEMV ( UPLO, N, ALPHA, A, LDA, X, INCX, * $ BETA, Y, INCY ) * * SUBROUTINE CHBMV ( UPLO, N, K, ALPHA, A, LDA, X, INCX, * $ BETA, Y, INCY ) * * SUBROUTINE CHPMV ( UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY ) * * SUBROUTINE CTRMV ( UPLO, TRANS, DIAG, N, A, LDA, X, INCX ) * * SUBROUTINE CTBMV ( UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX ) * * SUBROUTINE CTPMV ( UPLO, TRANS, DIAG, N, AP, X, INCX ) * * SUBROUTINE CTRSV ( UPLO, TRANS, DIAG, N, A, LDA, X, INCX ) * * SUBROUTINE CTBSV ( UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX ) * * SUBROUTINE CTPSV ( UPLO, TRANS, DIAG, N, AP, X, INCX ) * * SUBROUTINE CGERU ( M, N, ALPHA, X, INCX, Y, INCY, A, LDA ) * * SUBROUTINE CGERC ( M, N, ALPHA, X, INCX, Y, INCY, A, LDA ) * * SUBROUTINE CHER ( UPLO, N, ALPHA, X, INCX, A, LDA ) * * SUBROUTINE CHPR ( UPLO, N, ALPHA, X, INCX, AP ) * * SUBROUTINE CHER2 ( UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA ) * * SUBROUTINE CHPR2 ( UPLO, N, ALPHA, X, INCX, Y, INCY, AP ) * * See: * * Dongarra J. J., Du Croz J. J., Hammarling S. and Hanson R. J.. * An extended set of Fortran Basic Linear Algebra Subprograms. * * Technical Memoranda Nos. 41 (revision 3) and 81, Mathematics * and Computer Science Division, Argonne National Laboratory, * 9700 South Cass Avenue, Argonne, Illinois 60439, US. * * Or * * NAG Technical Reports TR3/87 and TR4/87, Numerical Algorithms * Group Ltd., NAG Central Office, 256 Banbury Road, Oxford * OX2 7DE, UK, and Numerical Algorithms Group Inc., 1101 31st * Street, Suite 100, Downers Grove, Illinois 60515-1263, USA. * ************************************************************************ * SUBROUTINE CGEMV ( TRANS, M, N, ALPHA, A, LDA, X, INCX, $ BETA, Y, INCY ) * .. Scalar Arguments .. COMPLEX ALPHA, BETA INTEGER INCX, INCY, LDA, M, N CHARACTER*1 TRANS * .. Array Arguments .. COMPLEX A( LDA, * ), X( * ), Y( * ) * .. * * Purpose * ======= * * CGEMV performs one of the matrix-vector operations * * y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, or * * y := alpha*conjg( A' )*x + beta*y, * * where alpha and beta are scalars, x and y are vectors and A is an * m by n matrix. * * Parameters * ========== * * TRANS - CHARACTER*1. * On entry, TRANS specifies the operation to be performed as * follows: * * TRANS = 'N' or 'n' y := alpha*A*x + beta*y. * * TRANS = 'T' or 't' y := alpha*A'*x + beta*y. * * TRANS = 'C' or 'c' y := alpha*conjg( A' )*x + beta*y. * * Unchanged on exit. * * M - INTEGER. * On entry, M specifies the number of rows of the matrix A. * M must be at least zero. * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the number of columns of the matrix A. * N must be at least zero. * Unchanged on exit. * * ALPHA - COMPLEX . * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * A - COMPLEX array of DIMENSION ( LDA, n ). * Before entry, the leading m by n part of the array A must * contain the matrix of coefficients. * Unchanged on exit. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * max( 1, m ). * Unchanged on exit. * * X - COMPLEX array of DIMENSION at least * ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' * and at least * ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. * Before entry, the incremented array X must contain the * vector x. * Unchanged on exit. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * BETA - COMPLEX . * On entry, BETA specifies the scalar beta. When BETA is * supplied as zero then Y need not be set on input. * Unchanged on exit. * * Y - COMPLEX array of DIMENSION at least * ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' * and at least * ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. * Before entry with BETA non-zero, the incremented array Y * must contain the vector y. On exit, Y is overwritten by the * updated vector y. * * INCY - INTEGER. * On entry, INCY specifies the increment for the elements of * Y. INCY must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. COMPLEX ONE PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ) ) COMPLEX ZERO PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) ) * .. Local Scalars .. COMPLEX TEMP INTEGER I, INFO, IX, IY, J, JX, JY, KX, KY, LENX, LENY LOGICAL NOCONJ * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC CONJG, MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( TRANS, 'N' ).AND. $ .NOT.LSAME( TRANS, 'T' ).AND. $ .NOT.LSAME( TRANS, 'C' ) )THEN INFO = 1 ELSE IF( M.LT.0 )THEN INFO = 2 ELSE IF( N.LT.0 )THEN INFO = 3 ELSE IF( LDA.LT.MAX( 1, M ) )THEN INFO = 6 ELSE IF( INCX.EQ.0 )THEN INFO = 8 ELSE IF( INCY.EQ.0 )THEN INFO = 11 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'CGEMV ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( M.EQ.0 ).OR.( N.EQ.0 ).OR. $ ( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) ) $ RETURN * NOCONJ = LSAME( TRANS, 'T' ) * * Set LENX and LENY, the lengths of the vectors x and y, and set * up the start points in X and Y. * IF( LSAME( TRANS, 'N' ) )THEN LENX = N LENY = M ELSE LENX = M LENY = N END IF IF( INCX.GT.0 )THEN KX = 1 ELSE KX = 1 - ( LENX - 1 )*INCX END IF IF( INCY.GT.0 )THEN KY = 1 ELSE KY = 1 - ( LENY - 1 )*INCY END IF * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through A. * * First form y := beta*y. * IF( BETA.NE.ONE )THEN IF( INCY.EQ.1 )THEN IF( BETA.EQ.ZERO )THEN DO 10, I = 1, LENY Y( I ) = ZERO 10 CONTINUE ELSE DO 20, I = 1, LENY Y( I ) = BETA*Y( I ) 20 CONTINUE END IF ELSE IY = KY IF( BETA.EQ.ZERO )THEN DO 30, I = 1, LENY Y( IY ) = ZERO IY = IY + INCY 30 CONTINUE ELSE DO 40, I = 1, LENY Y( IY ) = BETA*Y( IY ) IY = IY + INCY 40 CONTINUE END IF END IF END IF IF( ALPHA.EQ.ZERO ) $ RETURN IF( LSAME( TRANS, 'N' ) )THEN * * Form y := alpha*A*x + y. * JX = KX IF( INCY.EQ.1 )THEN DO 60, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = ALPHA*X( JX ) DO 50, I = 1, M Y( I ) = Y( I ) + TEMP*A( I, J ) 50 CONTINUE END IF JX = JX + INCX 60 CONTINUE ELSE DO 80, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = ALPHA*X( JX ) IY = KY DO 70, I = 1, M Y( IY ) = Y( IY ) + TEMP*A( I, J ) IY = IY + INCY 70 CONTINUE END IF JX = JX + INCX 80 CONTINUE END IF ELSE * * Form y := alpha*A'*x + y or y := alpha*conjg( A' )*x + y. * JY = KY IF( INCX.EQ.1 )THEN DO 110, J = 1, N TEMP = ZERO IF( NOCONJ )THEN DO 90, I = 1, M TEMP = TEMP + A( I, J )*X( I ) 90 CONTINUE ELSE DO 100, I = 1, M TEMP = TEMP + CONJG( A( I, J ) )*X( I ) 100 CONTINUE END IF Y( JY ) = Y( JY ) + ALPHA*TEMP JY = JY + INCY 110 CONTINUE ELSE DO 140, J = 1, N TEMP = ZERO IX = KX IF( NOCONJ )THEN DO 120, I = 1, M TEMP = TEMP + A( I, J )*X( IX ) IX = IX + INCX 120 CONTINUE ELSE DO 130, I = 1, M TEMP = TEMP + CONJG( A( I, J ) )*X( IX ) IX = IX + INCX 130 CONTINUE END IF Y( JY ) = Y( JY ) + ALPHA*TEMP JY = JY + INCY 140 CONTINUE END IF END IF * RETURN * * End of CGEMV . * END * ************************************************************************ * SUBROUTINE CGBMV ( TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX, $ BETA, Y, INCY ) * .. Scalar Arguments .. COMPLEX ALPHA, BETA INTEGER INCX, INCY, KL, KU, LDA, M, N CHARACTER*1 TRANS * .. Array Arguments .. COMPLEX A( LDA, * ), X( * ), Y( * ) * .. * * Purpose * ======= * * CGBMV performs one of the matrix-vector operations * * y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, or * * y := alpha*conjg( A' )*x + beta*y, * * where alpha and beta are scalars, x and y are vectors and A is an * m by n band matrix, with kl sub-diagonals and ku super-diagonals. * * Parameters * ========== * * TRANS - CHARACTER*1. * On entry, TRANS specifies the operation to be performed as * follows: * * TRANS = 'N' or 'n' y := alpha*A*x + beta*y. * * TRANS = 'T' or 't' y := alpha*A'*x + beta*y. * * TRANS = 'C' or 'c' y := alpha*conjg( A' )*x + beta*y. * * Unchanged on exit. * * M - INTEGER. * On entry, M specifies the number of rows of the matrix A. * M must be at least zero. * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the number of columns of the matrix A. * N must be at least zero. * Unchanged on exit. * * KL - INTEGER. * On entry, KL specifies the number of sub-diagonals of the * matrix A. KL must satisfy 0 .le. KL. * Unchanged on exit. * * KU - INTEGER. * On entry, KU specifies the number of super-diagonals of the * matrix A. KU must satisfy 0 .le. KU. * Unchanged on exit. * * ALPHA - COMPLEX . * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * A - COMPLEX array of DIMENSION ( LDA, n ). * Before entry, the leading ( kl + ku + 1 ) by n part of the * array A must contain the matrix of coefficients, supplied * column by column, with the leading diagonal of the matrix in * row ( ku + 1 ) of the array, the first super-diagonal * starting at position 2 in row ku, the first sub-diagonal * starting at position 1 in row ( ku + 2 ), and so on. * Elements in the array A that do not correspond to elements * in the band matrix (such as the top left ku by ku triangle) * are not referenced. * The following program segment will transfer a band matrix * from conventional full matrix storage to band storage: * * DO 20, J = 1, N * K = KU + 1 - J * DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL ) * A( K + I, J ) = matrix( I, J ) * 10 CONTINUE * 20 CONTINUE * * Unchanged on exit. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * ( kl + ku + 1 ). * Unchanged on exit. * * X - COMPLEX array of DIMENSION at least * ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' * and at least * ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. * Before entry, the incremented array X must contain the * vector x. * Unchanged on exit. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * BETA - COMPLEX . * On entry, BETA specifies the scalar beta. When BETA is * supplied as zero then Y need not be set on input. * Unchanged on exit. * * Y - COMPLEX array of DIMENSION at least * ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' * and at least * ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. * Before entry, the incremented array Y must contain the * vector y. On exit, Y is overwritten by the updated vector y. * * * INCY - INTEGER. * On entry, INCY specifies the increment for the elements of * Y. INCY must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. COMPLEX ONE PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ) ) COMPLEX ZERO PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) ) * .. Local Scalars .. COMPLEX TEMP INTEGER I, INFO, IX, IY, J, JX, JY, K, KUP1, KX, KY, $ LENX, LENY LOGICAL NOCONJ * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC CONJG, MAX, MIN * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( TRANS, 'N' ).AND. $ .NOT.LSAME( TRANS, 'T' ).AND. $ .NOT.LSAME( TRANS, 'C' ) )THEN INFO = 1 ELSE IF( M.LT.0 )THEN INFO = 2 ELSE IF( N.LT.0 )THEN INFO = 3 ELSE IF( KL.LT.0 )THEN INFO = 4 ELSE IF( KU.LT.0 )THEN INFO = 5 ELSE IF( LDA.LT.( KL + KU + 1 ) )THEN INFO = 8 ELSE IF( INCX.EQ.0 )THEN INFO = 10 ELSE IF( INCY.EQ.0 )THEN INFO = 13 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'CGBMV ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( M.EQ.0 ).OR.( N.EQ.0 ).OR. $ ( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) ) $ RETURN * NOCONJ = LSAME( TRANS, 'T' ) * * Set LENX and LENY, the lengths of the vectors x and y, and set * up the start points in X and Y. * IF( LSAME( TRANS, 'N' ) )THEN LENX = N LENY = M ELSE LENX = M LENY = N END IF IF( INCX.GT.0 )THEN KX = 1 ELSE KX = 1 - ( LENX - 1 )*INCX END IF IF( INCY.GT.0 )THEN KY = 1 ELSE KY = 1 - ( LENY - 1 )*INCY END IF * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through the band part of A. * * First form y := beta*y. * IF( BETA.NE.ONE )THEN IF( INCY.EQ.1 )THEN IF( BETA.EQ.ZERO )THEN DO 10, I = 1, LENY Y( I ) = ZERO 10 CONTINUE ELSE DO 20, I = 1, LENY Y( I ) = BETA*Y( I ) 20 CONTINUE END IF ELSE IY = KY IF( BETA.EQ.ZERO )THEN DO 30, I = 1, LENY Y( IY ) = ZERO IY = IY + INCY 30 CONTINUE ELSE DO 40, I = 1, LENY Y( IY ) = BETA*Y( IY ) IY = IY + INCY 40 CONTINUE END IF END IF END IF IF( ALPHA.EQ.ZERO ) $ RETURN KUP1 = KU + 1 IF( LSAME( TRANS, 'N' ) )THEN * * Form y := alpha*A*x + y. * JX = KX IF( INCY.EQ.1 )THEN DO 60, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = ALPHA*X( JX ) K = KUP1 - J DO 50, I = MAX( 1, J - KU ), MIN( M, J + KL ) Y( I ) = Y( I ) + TEMP*A( K + I, J ) 50 CONTINUE END IF JX = JX + INCX 60 CONTINUE ELSE DO 80, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = ALPHA*X( JX ) IY = KY K = KUP1 - J DO 70, I = MAX( 1, J - KU ), MIN( M, J + KL ) Y( IY ) = Y( IY ) + TEMP*A( K + I, J ) IY = IY + INCY 70 CONTINUE END IF JX = JX + INCX IF( J.GT.KU ) $ KY = KY + INCY 80 CONTINUE END IF ELSE * * Form y := alpha*A'*x + y or y := alpha*conjg( A' )*x + y. * JY = KY IF( INCX.EQ.1 )THEN DO 110, J = 1, N TEMP = ZERO K = KUP1 - J IF( NOCONJ )THEN DO 90, I = MAX( 1, J - KU ), MIN( M, J + KL ) TEMP = TEMP + A( K + I, J )*X( I ) 90 CONTINUE ELSE DO 100, I = MAX( 1, J - KU ), MIN( M, J + KL ) TEMP = TEMP + CONJG( A( K + I, J ) )*X( I ) 100 CONTINUE END IF Y( JY ) = Y( JY ) + ALPHA*TEMP JY = JY + INCY 110 CONTINUE ELSE DO 140, J = 1, N TEMP = ZERO IX = KX K = KUP1 - J IF( NOCONJ )THEN DO 120, I = MAX( 1, J - KU ), MIN( M, J + KL ) TEMP = TEMP + A( K + I, J )*X( IX ) IX = IX + INCX 120 CONTINUE ELSE DO 130, I = MAX( 1, J - KU ), MIN( M, J + KL ) TEMP = TEMP + CONJG( A( K + I, J ) )*X( IX ) IX = IX + INCX 130 CONTINUE END IF Y( JY ) = Y( JY ) + ALPHA*TEMP JY = JY + INCY IF( J.GT.KU ) $ KX = KX + INCX 140 CONTINUE END IF END IF * RETURN * * End of CGBMV . * END * ************************************************************************ * SUBROUTINE CHEMV ( UPLO, N, ALPHA, A, LDA, X, INCX, $ BETA, Y, INCY ) * .. Scalar Arguments .. COMPLEX ALPHA, BETA INTEGER INCX, INCY, LDA, N CHARACTER*1 UPLO * .. Array Arguments .. COMPLEX A( LDA, * ), X( * ), Y( * ) * .. * * Purpose * ======= * * CHEMV performs the matrix-vector operation * * y := alpha*A*x + beta*y, * * where alpha and beta are scalars, x and y are n element vectors and * A is an n by n hermitian matrix. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the upper or lower * triangular part of the array A is to be referenced as * follows: * * UPLO = 'U' or 'u' Only the upper triangular part of A * is to be referenced. * * UPLO = 'L' or 'l' Only the lower triangular part of A * is to be referenced. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * ALPHA - COMPLEX . * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * A - COMPLEX array of DIMENSION ( LDA, n ). * Before entry with UPLO = 'U' or 'u', the leading n by n * upper triangular part of the array A must contain the upper * triangular part of the hermitian matrix and the strictly * lower triangular part of A is not referenced. * Before entry with UPLO = 'L' or 'l', the leading n by n * lower triangular part of the array A must contain the lower * triangular part of the hermitian matrix and the strictly * upper triangular part of A is not referenced. * Note that the imaginary parts of the diagonal elements need * not be set and are assumed to be zero. * Unchanged on exit. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * max( 1, n ). * Unchanged on exit. * * X - COMPLEX array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element vector x. * Unchanged on exit. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * BETA - COMPLEX . * On entry, BETA specifies the scalar beta. When BETA is * supplied as zero then Y need not be set on input. * Unchanged on exit. * * Y - COMPLEX array of dimension at least * ( 1 + ( n - 1 )*abs( INCY ) ). * Before entry, the incremented array Y must contain the n * element vector y. On exit, Y is overwritten by the updated * vector y. * * INCY - INTEGER. * On entry, INCY specifies the increment for the elements of * Y. INCY must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. COMPLEX ONE PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ) ) COMPLEX ZERO PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) ) * .. Local Scalars .. COMPLEX TEMP1, TEMP2 INTEGER I, INFO, IX, IY, J, JX, JY, KX, KY * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC CONJG, MAX, REAL * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO, 'U' ).AND. $ .NOT.LSAME( UPLO, 'L' ) )THEN INFO = 1 ELSE IF( N.LT.0 )THEN INFO = 2 ELSE IF( LDA.LT.MAX( 1, N ) )THEN INFO = 5 ELSE IF( INCX.EQ.0 )THEN INFO = 7 ELSE IF( INCY.EQ.0 )THEN INFO = 10 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'CHEMV ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( N.EQ.0 ).OR.( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) ) $ RETURN * * Set up the start points in X and Y. * IF( INCX.GT.0 )THEN KX = 1 ELSE KX = 1 - ( N - 1 )*INCX END IF IF( INCY.GT.0 )THEN KY = 1 ELSE KY = 1 - ( N - 1 )*INCY END IF * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through the triangular part * of A. * * First form y := beta*y. * IF( BETA.NE.ONE )THEN IF( INCY.EQ.1 )THEN IF( BETA.EQ.ZERO )THEN DO 10, I = 1, N Y( I ) = ZERO 10 CONTINUE ELSE DO 20, I = 1, N Y( I ) = BETA*Y( I ) 20 CONTINUE END IF ELSE IY = KY IF( BETA.EQ.ZERO )THEN DO 30, I = 1, N Y( IY ) = ZERO IY = IY + INCY 30 CONTINUE ELSE DO 40, I = 1, N Y( IY ) = BETA*Y( IY ) IY = IY + INCY 40 CONTINUE END IF END IF END IF IF( ALPHA.EQ.ZERO ) $ RETURN IF( LSAME( UPLO, 'U' ) )THEN * * Form y when A is stored in upper triangle. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 60, J = 1, N TEMP1 = ALPHA*X( J ) TEMP2 = ZERO DO 50, I = 1, J - 1 Y( I ) = Y( I ) + TEMP1*A( I, J ) TEMP2 = TEMP2 + CONJG( A( I, J ) )*X( I ) 50 CONTINUE Y( J ) = Y( J ) + TEMP1*REAL( A( J, J ) ) + ALPHA*TEMP2 60 CONTINUE ELSE JX = KX JY = KY DO 80, J = 1, N TEMP1 = ALPHA*X( JX ) TEMP2 = ZERO IX = KX IY = KY DO 70, I = 1, J - 1 Y( IY ) = Y( IY ) + TEMP1*A( I, J ) TEMP2 = TEMP2 + CONJG( A( I, J ) )*X( IX ) IX = IX + INCX IY = IY + INCY 70 CONTINUE Y( JY ) = Y( JY ) + TEMP1*REAL( A( J, J ) ) + ALPHA*TEMP2 JX = JX + INCX JY = JY + INCY 80 CONTINUE END IF ELSE * * Form y when A is stored in lower triangle. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 100, J = 1, N TEMP1 = ALPHA*X( J ) TEMP2 = ZERO Y( J ) = Y( J ) + TEMP1*REAL( A( J, J ) ) DO 90, I = J + 1, N Y( I ) = Y( I ) + TEMP1*A( I, J ) TEMP2 = TEMP2 + CONJG( A( I, J ) )*X( I ) 90 CONTINUE Y( J ) = Y( J ) + ALPHA*TEMP2 100 CONTINUE ELSE JX = KX JY = KY DO 120, J = 1, N TEMP1 = ALPHA*X( JX ) TEMP2 = ZERO Y( JY ) = Y( JY ) + TEMP1*REAL( A( J, J ) ) IX = JX IY = JY DO 110, I = J + 1, N IX = IX + INCX IY = IY + INCY Y( IY ) = Y( IY ) + TEMP1*A( I, J ) TEMP2 = TEMP2 + CONJG( A( I, J ) )*X( IX ) 110 CONTINUE Y( JY ) = Y( JY ) + ALPHA*TEMP2 JX = JX + INCX JY = JY + INCY 120 CONTINUE END IF END IF * RETURN * * End of CHEMV . * END * ************************************************************************ * SUBROUTINE CHBMV ( UPLO, N, K, ALPHA, A, LDA, X, INCX, $ BETA, Y, INCY ) * .. Scalar Arguments .. COMPLEX ALPHA, BETA INTEGER INCX, INCY, K, LDA, N CHARACTER*1 UPLO * .. Array Arguments .. COMPLEX A( LDA, * ), X( * ), Y( * ) * .. * * Purpose * ======= * * CHBMV performs the matrix-vector operation * * y := alpha*A*x + beta*y, * * where alpha and beta are scalars, x and y are n element vectors and * A is an n by n hermitian band matrix, with k super-diagonals. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the upper or lower * triangular part of the band matrix A is being supplied as * follows: * * UPLO = 'U' or 'u' The upper triangular part of A is * being supplied. * * UPLO = 'L' or 'l' The lower triangular part of A is * being supplied. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * K - INTEGER. * On entry, K specifies the number of super-diagonals of the * matrix A. K must satisfy 0 .le. K. * Unchanged on exit. * * ALPHA - COMPLEX . * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * A - COMPLEX array of DIMENSION ( LDA, n ). * Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) * by n part of the array A must contain the upper triangular * band part of the hermitian matrix, supplied column by * column, with the leading diagonal of the matrix in row * ( k + 1 ) of the array, the first super-diagonal starting at * position 2 in row k, and so on. The top left k by k triangle * of the array A is not referenced. * The following program segment will transfer the upper * triangular part of a hermitian band matrix from conventional * full matrix storage to band storage: * * DO 20, J = 1, N * M = K + 1 - J * DO 10, I = MAX( 1, J - K ), J * A( M + I, J ) = matrix( I, J ) * 10 CONTINUE * 20 CONTINUE * * Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) * by n part of the array A must contain the lower triangular * band part of the hermitian matrix, supplied column by * column, with the leading diagonal of the matrix in row 1 of * the array, the first sub-diagonal starting at position 1 in * row 2, and so on. The bottom right k by k triangle of the * array A is not referenced. * The following program segment will transfer the lower * triangular part of a hermitian band matrix from conventional * full matrix storage to band storage: * * DO 20, J = 1, N * M = 1 - J * DO 10, I = J, MIN( N, J + K ) * A( M + I, J ) = matrix( I, J ) * 10 CONTINUE * 20 CONTINUE * * Note that the imaginary parts of the diagonal elements need * not be set and are assumed to be zero. * Unchanged on exit. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * ( k + 1 ). * Unchanged on exit. * * X - COMPLEX array of DIMENSION at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the * vector x. * Unchanged on exit. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * BETA - COMPLEX . * On entry, BETA specifies the scalar beta. * Unchanged on exit. * * Y - COMPLEX array of DIMENSION at least * ( 1 + ( n - 1 )*abs( INCY ) ). * Before entry, the incremented array Y must contain the * vector y. On exit, Y is overwritten by the updated vector y. * * INCY - INTEGER. * On entry, INCY specifies the increment for the elements of * Y. INCY must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. COMPLEX ONE PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ) ) COMPLEX ZERO PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) ) * .. Local Scalars .. COMPLEX TEMP1, TEMP2 INTEGER I, INFO, IX, IY, J, JX, JY, KPLUS1, KX, KY, L * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC CONJG, MAX, MIN, REAL * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO, 'U' ).AND. $ .NOT.LSAME( UPLO, 'L' ) )THEN INFO = 1 ELSE IF( N.LT.0 )THEN INFO = 2 ELSE IF( K.LT.0 )THEN INFO = 3 ELSE IF( LDA.LT.( K + 1 ) )THEN INFO = 6 ELSE IF( INCX.EQ.0 )THEN INFO = 8 ELSE IF( INCY.EQ.0 )THEN INFO = 11 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'CHBMV ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( N.EQ.0 ).OR.( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) ) $ RETURN * * Set up the start points in X and Y. * IF( INCX.GT.0 )THEN KX = 1 ELSE KX = 1 - ( N - 1 )*INCX END IF IF( INCY.GT.0 )THEN KY = 1 ELSE KY = 1 - ( N - 1 )*INCY END IF * * Start the operations. In this version the elements of the array A * are accessed sequentially with one pass through A. * * First form y := beta*y. * IF( BETA.NE.ONE )THEN IF( INCY.EQ.1 )THEN IF( BETA.EQ.ZERO )THEN DO 10, I = 1, N Y( I ) = ZERO 10 CONTINUE ELSE DO 20, I = 1, N Y( I ) = BETA*Y( I ) 20 CONTINUE END IF ELSE IY = KY IF( BETA.EQ.ZERO )THEN DO 30, I = 1, N Y( IY ) = ZERO IY = IY + INCY 30 CONTINUE ELSE DO 40, I = 1, N Y( IY ) = BETA*Y( IY ) IY = IY + INCY 40 CONTINUE END IF END IF END IF IF( ALPHA.EQ.ZERO ) $ RETURN IF( LSAME( UPLO, 'U' ) )THEN * * Form y when upper triangle of A is stored. * KPLUS1 = K + 1 IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 60, J = 1, N TEMP1 = ALPHA*X( J ) TEMP2 = ZERO L = KPLUS1 - J DO 50, I = MAX( 1, J - K ), J - 1 Y( I ) = Y( I ) + TEMP1*A( L + I, J ) TEMP2 = TEMP2 + CONJG( A( L + I, J ) )*X( I ) 50 CONTINUE Y( J ) = Y( J ) + TEMP1*REAL( A( KPLUS1, J ) ) $ + ALPHA*TEMP2 60 CONTINUE ELSE JX = KX JY = KY DO 80, J = 1, N TEMP1 = ALPHA*X( JX ) TEMP2 = ZERO IX = KX IY = KY L = KPLUS1 - J DO 70, I = MAX( 1, J - K ), J - 1 Y( IY ) = Y( IY ) + TEMP1*A( L + I, J ) TEMP2 = TEMP2 + CONJG( A( L + I, J ) )*X( IX ) IX = IX + INCX IY = IY + INCY 70 CONTINUE Y( JY ) = Y( JY ) + TEMP1*REAL( A( KPLUS1, J ) ) $ + ALPHA*TEMP2 JX = JX + INCX JY = JY + INCY IF( J.GT.K )THEN KX = KX + INCX KY = KY + INCY END IF 80 CONTINUE END IF ELSE * * Form y when lower triangle of A is stored. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 100, J = 1, N TEMP1 = ALPHA*X( J ) TEMP2 = ZERO Y( J ) = Y( J ) + TEMP1*REAL( A( 1, J ) ) L = 1 - J DO 90, I = J + 1, MIN( N, J + K ) Y( I ) = Y( I ) + TEMP1*A( L + I, J ) TEMP2 = TEMP2 + CONJG( A( L + I, J ) )*X( I ) 90 CONTINUE Y( J ) = Y( J ) + ALPHA*TEMP2 100 CONTINUE ELSE JX = KX JY = KY DO 120, J = 1, N TEMP1 = ALPHA*X( JX ) TEMP2 = ZERO Y( JY ) = Y( JY ) + TEMP1*REAL( A( 1, J ) ) L = 1 - J IX = JX IY = JY DO 110, I = J + 1, MIN( N, J + K ) IX = IX + INCX IY = IY + INCY Y( IY ) = Y( IY ) + TEMP1*A( L + I, J ) TEMP2 = TEMP2 + CONJG( A( L + I, J ) )*X( IX ) 110 CONTINUE Y( JY ) = Y( JY ) + ALPHA*TEMP2 JX = JX + INCX JY = JY + INCY 120 CONTINUE END IF END IF * RETURN * * End of CHBMV . * END * ************************************************************************ * SUBROUTINE CHPMV ( UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY ) * .. Scalar Arguments .. COMPLEX ALPHA, BETA INTEGER INCX, INCY, N CHARACTER*1 UPLO * .. Array Arguments .. COMPLEX AP( * ), X( * ), Y( * ) * .. * * Purpose * ======= * * CHPMV performs the matrix-vector operation * * y := alpha*A*x + beta*y, * * where alpha and beta are scalars, x and y are n element vectors and * A is an n by n hermitian matrix, supplied in packed form. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the upper or lower * triangular part of the matrix A is supplied in the packed * array AP as follows: * * UPLO = 'U' or 'u' The upper triangular part of A is * supplied in AP. * * UPLO = 'L' or 'l' The lower triangular part of A is * supplied in AP. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * ALPHA - COMPLEX . * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * AP - COMPLEX array of DIMENSION at least * ( ( n*( n + 1 ) )/2 ). * Before entry with UPLO = 'U' or 'u', the array AP must * contain the upper triangular part of the hermitian matrix * packed sequentially, column by column, so that AP( 1 ) * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) * and a( 2, 2 ) respectively, and so on. * Before entry with UPLO = 'L' or 'l', the array AP must * contain the lower triangular part of the hermitian matrix * packed sequentially, column by column, so that AP( 1 ) * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) * and a( 3, 1 ) respectively, and so on. * Note that the imaginary parts of the diagonal elements need * not be set and are assumed to be zero. * Unchanged on exit. * * X - COMPLEX array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element vector x. * Unchanged on exit. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * BETA - COMPLEX . * On entry, BETA specifies the scalar beta. When BETA is * supplied as zero then Y need not be set on input. * Unchanged on exit. * * Y - COMPLEX array of dimension at least * ( 1 + ( n - 1 )*abs( INCY ) ). * Before entry, the incremented array Y must contain the n * element vector y. On exit, Y is overwritten by the updated * vector y. * * INCY - INTEGER. * On entry, INCY specifies the increment for the elements of * Y. INCY must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. COMPLEX ONE PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ) ) COMPLEX ZERO PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) ) * .. Local Scalars .. COMPLEX TEMP1, TEMP2 INTEGER I, INFO, IX, IY, J, JX, JY, K, KK, KX, KY * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC CONJG, REAL * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO, 'U' ).AND. $ .NOT.LSAME( UPLO, 'L' ) )THEN INFO = 1 ELSE IF( N.LT.0 )THEN INFO = 2 ELSE IF( INCX.EQ.0 )THEN INFO = 6 ELSE IF( INCY.EQ.0 )THEN INFO = 9 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'CHPMV ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( N.EQ.0 ).OR.( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) ) $ RETURN * * Set up the start points in X and Y. * IF( INCX.GT.0 )THEN KX = 1 ELSE KX = 1 - ( N - 1 )*INCX END IF IF( INCY.GT.0 )THEN KY = 1 ELSE KY = 1 - ( N - 1 )*INCY END IF * * Start the operations. In this version the elements of the array AP * are accessed sequentially with one pass through AP. * * First form y := beta*y. * IF( BETA.NE.ONE )THEN IF( INCY.EQ.1 )THEN IF( BETA.EQ.ZERO )THEN DO 10, I = 1, N Y( I ) = ZERO 10 CONTINUE ELSE DO 20, I = 1, N Y( I ) = BETA*Y( I ) 20 CONTINUE END IF ELSE IY = KY IF( BETA.EQ.ZERO )THEN DO 30, I = 1, N Y( IY ) = ZERO IY = IY + INCY 30 CONTINUE ELSE DO 40, I = 1, N Y( IY ) = BETA*Y( IY ) IY = IY + INCY 40 CONTINUE END IF END IF END IF IF( ALPHA.EQ.ZERO ) $ RETURN KK = 1 IF( LSAME( UPLO, 'U' ) )THEN * * Form y when AP contains the upper triangle. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 60, J = 1, N TEMP1 = ALPHA*X( J ) TEMP2 = ZERO K = KK DO 50, I = 1, J - 1 Y( I ) = Y( I ) + TEMP1*AP( K ) TEMP2 = TEMP2 + CONJG( AP( K ) )*X( I ) K = K + 1 50 CONTINUE Y( J ) = Y( J ) + TEMP1*REAL( AP( KK + J - 1 ) ) $ + ALPHA*TEMP2 KK = KK + J 60 CONTINUE ELSE JX = KX JY = KY DO 80, J = 1, N TEMP1 = ALPHA*X( JX ) TEMP2 = ZERO IX = KX IY = KY DO 70, K = KK, KK + J - 2 Y( IY ) = Y( IY ) + TEMP1*AP( K ) TEMP2 = TEMP2 + CONJG( AP( K ) )*X( IX ) IX = IX + INCX IY = IY + INCY 70 CONTINUE Y( JY ) = Y( JY ) + TEMP1*REAL( AP( KK + J - 1 ) ) $ + ALPHA*TEMP2 JX = JX + INCX JY = JY + INCY KK = KK + J 80 CONTINUE END IF ELSE * * Form y when AP contains the lower triangle. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 100, J = 1, N TEMP1 = ALPHA*X( J ) TEMP2 = ZERO Y( J ) = Y( J ) + TEMP1*REAL( AP( KK ) ) K = KK + 1 DO 90, I = J + 1, N Y( I ) = Y( I ) + TEMP1*AP( K ) TEMP2 = TEMP2 + CONJG( AP( K ) )*X( I ) K = K + 1 90 CONTINUE Y( J ) = Y( J ) + ALPHA*TEMP2 KK = KK + ( N - J + 1 ) 100 CONTINUE ELSE JX = KX JY = KY DO 120, J = 1, N TEMP1 = ALPHA*X( JX ) TEMP2 = ZERO Y( JY ) = Y( JY ) + TEMP1*REAL( AP( KK ) ) IX = JX IY = JY DO 110, K = KK + 1, KK + N - J IX = IX + INCX IY = IY + INCY Y( IY ) = Y( IY ) + TEMP1*AP( K ) TEMP2 = TEMP2 + CONJG( AP( K ) )*X( IX ) 110 CONTINUE Y( JY ) = Y( JY ) + ALPHA*TEMP2 JX = JX + INCX JY = JY + INCY KK = KK + ( N - J + 1 ) 120 CONTINUE END IF END IF * RETURN * * End of CHPMV . * END * ************************************************************************ * SUBROUTINE CTRMV ( UPLO, TRANS, DIAG, N, A, LDA, X, INCX ) * .. Scalar Arguments .. INTEGER INCX, LDA, N CHARACTER*1 DIAG, TRANS, UPLO * .. Array Arguments .. COMPLEX A( LDA, * ), X( * ) * .. * * Purpose * ======= * * CTRMV performs one of the matrix-vector operations * * x := A*x, or x := A'*x, or x := conjg( A' )*x, * * where x is an n element vector and A is an n by n unit, or non-unit, * upper or lower triangular matrix. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the matrix is an upper or * lower triangular matrix as follows: * * UPLO = 'U' or 'u' A is an upper triangular matrix. * * UPLO = 'L' or 'l' A is a lower triangular matrix. * * Unchanged on exit. * * TRANS - CHARACTER*1. * On entry, TRANS specifies the operation to be performed as * follows: * * TRANS = 'N' or 'n' x := A*x. * * TRANS = 'T' or 't' x := A'*x. * * TRANS = 'C' or 'c' x := conjg( A' )*x. * * Unchanged on exit. * * DIAG - CHARACTER*1. * On entry, DIAG specifies whether or not A is unit * triangular as follows: * * DIAG = 'U' or 'u' A is assumed to be unit triangular. * * DIAG = 'N' or 'n' A is not assumed to be unit * triangular. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * A - COMPLEX array of DIMENSION ( LDA, n ). * Before entry with UPLO = 'U' or 'u', the leading n by n * upper triangular part of the array A must contain the upper * triangular matrix and the strictly lower triangular part of * A is not referenced. * Before entry with UPLO = 'L' or 'l', the leading n by n * lower triangular part of the array A must contain the lower * triangular matrix and the strictly upper triangular part of * A is not referenced. * Note that when DIAG = 'U' or 'u', the diagonal elements of * A are not referenced either, but are assumed to be unity. * Unchanged on exit. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * max( 1, n ). * Unchanged on exit. * * X - COMPLEX array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element vector x. On exit, X is overwritten with the * tranformed vector x. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. COMPLEX ZERO PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) ) * .. Local Scalars .. COMPLEX TEMP INTEGER I, INFO, IX, J, JX, KX LOGICAL NOCONJ, NOUNIT * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC CONJG, MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO , 'U' ).AND. $ .NOT.LSAME( UPLO , 'L' ) )THEN INFO = 1 ELSE IF( .NOT.LSAME( TRANS, 'N' ).AND. $ .NOT.LSAME( TRANS, 'T' ).AND. $ .NOT.LSAME( TRANS, 'C' ) )THEN INFO = 2 ELSE IF( .NOT.LSAME( DIAG , 'U' ).AND. $ .NOT.LSAME( DIAG , 'N' ) )THEN INFO = 3 ELSE IF( N.LT.0 )THEN INFO = 4 ELSE IF( LDA.LT.MAX( 1, N ) )THEN INFO = 6 ELSE IF( INCX.EQ.0 )THEN INFO = 8 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'CTRMV ', INFO ) RETURN END IF * * Quick return if possible. * IF( N.EQ.0 ) $ RETURN * NOCONJ = LSAME( TRANS, 'T' ) NOUNIT = LSAME( DIAG , 'N' ) * * Set up the start point in X if the increment is not unity. This * will be ( N - 1 )*INCX too small for descending loops. * IF( INCX.LE.0 )THEN KX = 1 - ( N - 1 )*INCX ELSE IF( INCX.NE.1 )THEN KX = 1 END IF * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through A. * IF( LSAME( TRANS, 'N' ) )THEN * * Form x := A*x. * IF( LSAME( UPLO, 'U' ) )THEN IF( INCX.EQ.1 )THEN DO 20, J = 1, N IF( X( J ).NE.ZERO )THEN TEMP = X( J ) DO 10, I = 1, J - 1 X( I ) = X( I ) + TEMP*A( I, J ) 10 CONTINUE IF( NOUNIT ) $ X( J ) = X( J )*A( J, J ) END IF 20 CONTINUE ELSE JX = KX DO 40, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = X( JX ) IX = KX DO 30, I = 1, J - 1 X( IX ) = X( IX ) + TEMP*A( I, J ) IX = IX + INCX 30 CONTINUE IF( NOUNIT ) $ X( JX ) = X( JX )*A( J, J ) END IF JX = JX + INCX 40 CONTINUE END IF ELSE IF( INCX.EQ.1 )THEN DO 60, J = N, 1, -1 IF( X( J ).NE.ZERO )THEN TEMP = X( J ) DO 50, I = N, J + 1, -1 X( I ) = X( I ) + TEMP*A( I, J ) 50 CONTINUE IF( NOUNIT ) $ X( J ) = X( J )*A( J, J ) END IF 60 CONTINUE ELSE KX = KX + ( N - 1 )*INCX JX = KX DO 80, J = N, 1, -1 IF( X( JX ).NE.ZERO )THEN TEMP = X( JX ) IX = KX DO 70, I = N, J + 1, -1 X( IX ) = X( IX ) + TEMP*A( I, J ) IX = IX - INCX 70 CONTINUE IF( NOUNIT ) $ X( JX ) = X( JX )*A( J, J ) END IF JX = JX - INCX 80 CONTINUE END IF END IF ELSE * * Form x := A'*x or x := conjg( A' )*x. * IF( LSAME( UPLO, 'U' ) )THEN IF( INCX.EQ.1 )THEN DO 110, J = N, 1, -1 TEMP = X( J ) IF( NOCONJ )THEN IF( NOUNIT ) $ TEMP = TEMP*A( J, J ) DO 90, I = J - 1, 1, -1 TEMP = TEMP + A( I, J )*X( I ) 90 CONTINUE ELSE IF( NOUNIT ) $ TEMP = TEMP*CONJG( A( J, J ) ) DO 100, I = J - 1, 1, -1 TEMP = TEMP + CONJG( A( I, J ) )*X( I ) 100 CONTINUE END IF X( J ) = TEMP 110 CONTINUE ELSE JX = KX + ( N - 1 )*INCX DO 140, J = N, 1, -1 TEMP = X( JX ) IX = JX IF( NOCONJ )THEN IF( NOUNIT ) $ TEMP = TEMP*A( J, J ) DO 120, I = J - 1, 1, -1 IX = IX - INCX TEMP = TEMP + A( I, J )*X( IX ) 120 CONTINUE ELSE IF( NOUNIT ) $ TEMP = TEMP*CONJG( A( J, J ) ) DO 130, I = J - 1, 1, -1 IX = IX - INCX TEMP = TEMP + CONJG( A( I, J ) )*X( IX ) 130 CONTINUE END IF X( JX ) = TEMP JX = JX - INCX 140 CONTINUE END IF ELSE IF( INCX.EQ.1 )THEN DO 170, J = 1, N TEMP = X( J ) IF( NOCONJ )THEN IF( NOUNIT ) $ TEMP = TEMP*A( J, J ) DO 150, I = J + 1, N TEMP = TEMP + A( I, J )*X( I ) 150 CONTINUE ELSE IF( NOUNIT ) $ TEMP = TEMP*CONJG( A( J, J ) ) DO 160, I = J + 1, N TEMP = TEMP + CONJG( A( I, J ) )*X( I ) 160 CONTINUE END IF X( J ) = TEMP 170 CONTINUE ELSE JX = KX DO 200, J = 1, N TEMP = X( JX ) IX = JX IF( NOCONJ )THEN IF( NOUNIT ) $ TEMP = TEMP*A( J, J ) DO 180, I = J + 1, N IX = IX + INCX TEMP = TEMP + A( I, J )*X( IX ) 180 CONTINUE ELSE IF( NOUNIT ) $ TEMP = TEMP*CONJG( A( J, J ) ) DO 190, I = J + 1, N IX = IX + INCX TEMP = TEMP + CONJG( A( I, J ) )*X( IX ) 190 CONTINUE END IF X( JX ) = TEMP JX = JX + INCX 200 CONTINUE END IF END IF END IF * RETURN * * End of CTRMV . * END * ************************************************************************ * SUBROUTINE CTBMV ( UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX ) * .. Scalar Arguments .. INTEGER INCX, K, LDA, N CHARACTER*1 DIAG, TRANS, UPLO * .. Array Arguments .. COMPLEX A( LDA, * ), X( * ) * .. * * Purpose * ======= * * CTBMV performs one of the matrix-vector operations * * x := A*x, or x := A'*x, or x := conjg( A' )*x, * * where x is an n element vector and A is an n by n unit, or non-unit, * upper or lower triangular band matrix, with ( k + 1 ) diagonals. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the matrix is an upper or * lower triangular matrix as follows: * * UPLO = 'U' or 'u' A is an upper triangular matrix. * * UPLO = 'L' or 'l' A is a lower triangular matrix. * * Unchanged on exit. * * TRANS - CHARACTER*1. * On entry, TRANS specifies the operation to be performed as * follows: * * TRANS = 'N' or 'n' x := A*x. * * TRANS = 'T' or 't' x := A'*x. * * TRANS = 'C' or 'c' x := conjg( A' )*x. * * Unchanged on exit. * * DIAG - CHARACTER*1. * On entry, DIAG specifies whether or not A is unit * triangular as follows: * * DIAG = 'U' or 'u' A is assumed to be unit triangular. * * DIAG = 'N' or 'n' A is not assumed to be unit * triangular. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * K - INTEGER. * On entry with UPLO = 'U' or 'u', K specifies the number of * super-diagonals of the matrix A. * On entry with UPLO = 'L' or 'l', K specifies the number of * sub-diagonals of the matrix A. * K must satisfy 0 .le. K. * Unchanged on exit. * * A - COMPLEX array of DIMENSION ( LDA, n ). * Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) * by n part of the array A must contain the upper triangular * band part of the matrix of coefficients, supplied column by * column, with the leading diagonal of the matrix in row * ( k + 1 ) of the array, the first super-diagonal starting at * position 2 in row k, and so on. The top left k by k triangle * of the array A is not referenced. * The following program segment will transfer an upper * triangular band matrix from conventional full matrix storage * to band storage: * * DO 20, J = 1, N * M = K + 1 - J * DO 10, I = MAX( 1, J - K ), J * A( M + I, J ) = matrix( I, J ) * 10 CONTINUE * 20 CONTINUE * * Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) * by n part of the array A must contain the lower triangular * band part of the matrix of coefficients, supplied column by * column, with the leading diagonal of the matrix in row 1 of * the array, the first sub-diagonal starting at position 1 in * row 2, and so on. The bottom right k by k triangle of the * array A is not referenced. * The following program segment will transfer a lower * triangular band matrix from conventional full matrix storage * to band storage: * * DO 20, J = 1, N * M = 1 - J * DO 10, I = J, MIN( N, J + K ) * A( M + I, J ) = matrix( I, J ) * 10 CONTINUE * 20 CONTINUE * * Note that when DIAG = 'U' or 'u' the elements of the array A * corresponding to the diagonal elements of the matrix are not * referenced, but are assumed to be unity. * Unchanged on exit. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * ( k + 1 ). * Unchanged on exit. * * X - COMPLEX array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element vector x. On exit, X is overwritten with the * tranformed vector x. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. COMPLEX ZERO PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) ) * .. Local Scalars .. COMPLEX TEMP INTEGER I, INFO, IX, J, JX, KPLUS1, KX, L LOGICAL NOCONJ, NOUNIT * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC CONJG, MAX, MIN * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO , 'U' ).AND. $ .NOT.LSAME( UPLO , 'L' ) )THEN INFO = 1 ELSE IF( .NOT.LSAME( TRANS, 'N' ).AND. $ .NOT.LSAME( TRANS, 'T' ).AND. $ .NOT.LSAME( TRANS, 'C' ) )THEN INFO = 2 ELSE IF( .NOT.LSAME( DIAG , 'U' ).AND. $ .NOT.LSAME( DIAG , 'N' ) )THEN INFO = 3 ELSE IF( N.LT.0 )THEN INFO = 4 ELSE IF( K.LT.0 )THEN INFO = 5 ELSE IF( LDA.LT.( K + 1 ) )THEN INFO = 7 ELSE IF( INCX.EQ.0 )THEN INFO = 9 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'CTBMV ', INFO ) RETURN END IF * * Quick return if possible. * IF( N.EQ.0 ) $ RETURN * NOCONJ = LSAME( TRANS, 'T' ) NOUNIT = LSAME( DIAG , 'N' ) * * Set up the start point in X if the increment is not unity. This * will be ( N - 1 )*INCX too small for descending loops. * IF( INCX.LE.0 )THEN KX = 1 - ( N - 1 )*INCX ELSE IF( INCX.NE.1 )THEN KX = 1 END IF * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through A. * IF( LSAME( TRANS, 'N' ) )THEN * * Form x := A*x. * IF( LSAME( UPLO, 'U' ) )THEN KPLUS1 = K + 1 IF( INCX.EQ.1 )THEN DO 20, J = 1, N IF( X( J ).NE.ZERO )THEN TEMP = X( J ) L = KPLUS1 - J DO 10, I = MAX( 1, J - K ), J - 1 X( I ) = X( I ) + TEMP*A( L + I, J ) 10 CONTINUE IF( NOUNIT ) $ X( J ) = X( J )*A( KPLUS1, J ) END IF 20 CONTINUE ELSE JX = KX DO 40, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = X( JX ) IX = KX L = KPLUS1 - J DO 30, I = MAX( 1, J - K ), J - 1 X( IX ) = X( IX ) + TEMP*A( L + I, J ) IX = IX + INCX 30 CONTINUE IF( NOUNIT ) $ X( JX ) = X( JX )*A( KPLUS1, J ) END IF JX = JX + INCX IF( J.GT.K ) $ KX = KX + INCX 40 CONTINUE END IF ELSE IF( INCX.EQ.1 )THEN DO 60, J = N, 1, -1 IF( X( J ).NE.ZERO )THEN TEMP = X( J ) L = 1 - J DO 50, I = MIN( N, J + K ), J + 1, -1 X( I ) = X( I ) + TEMP*A( L + I, J ) 50 CONTINUE IF( NOUNIT ) $ X( J ) = X( J )*A( 1, J ) END IF 60 CONTINUE ELSE KX = KX + ( N - 1 )*INCX JX = KX DO 80, J = N, 1, -1 IF( X( JX ).NE.ZERO )THEN TEMP = X( JX ) IX = KX L = 1 - J DO 70, I = MIN( N, J + K ), J + 1, -1 X( IX ) = X( IX ) + TEMP*A( L + I, J ) IX = IX - INCX 70 CONTINUE IF( NOUNIT ) $ X( JX ) = X( JX )*A( 1, J ) END IF JX = JX - INCX IF( ( N - J ).GE.K ) $ KX = KX - INCX 80 CONTINUE END IF END IF ELSE * * Form x := A'*x or x := conjg( A' )*x. * IF( LSAME( UPLO, 'U' ) )THEN KPLUS1 = K + 1 IF( INCX.EQ.1 )THEN DO 110, J = N, 1, -1 TEMP = X( J ) L = KPLUS1 - J IF( NOCONJ )THEN IF( NOUNIT ) $ TEMP = TEMP*A( KPLUS1, J ) DO 90, I = J - 1, MAX( 1, J - K ), -1 TEMP = TEMP + A( L + I, J )*X( I ) 90 CONTINUE ELSE IF( NOUNIT ) $ TEMP = TEMP*CONJG( A( KPLUS1, J ) ) DO 100, I = J - 1, MAX( 1, J - K ), -1 TEMP = TEMP + CONJG( A( L + I, J ) )*X( I ) 100 CONTINUE END IF X( J ) = TEMP 110 CONTINUE ELSE KX = KX + ( N - 1 )*INCX JX = KX DO 140, J = N, 1, -1 TEMP = X( JX ) KX = KX - INCX IX = KX L = KPLUS1 - J IF( NOCONJ )THEN IF( NOUNIT ) $ TEMP = TEMP*A( KPLUS1, J ) DO 120, I = J - 1, MAX( 1, J - K ), -1 TEMP = TEMP + A( L + I, J )*X( IX ) IX = IX - INCX 120 CONTINUE ELSE IF( NOUNIT ) $ TEMP = TEMP*CONJG( A( KPLUS1, J ) ) DO 130, I = J - 1, MAX( 1, J - K ), -1 TEMP = TEMP + CONJG( A( L + I, J ) )*X( IX ) IX = IX - INCX 130 CONTINUE END IF X( JX ) = TEMP JX = JX - INCX 140 CONTINUE END IF ELSE IF( INCX.EQ.1 )THEN DO 170, J = 1, N TEMP = X( J ) L = 1 - J IF( NOCONJ )THEN IF( NOUNIT ) $ TEMP = TEMP*A( 1, J ) DO 150, I = J + 1, MIN( N, J + K ) TEMP = TEMP + A( L + I, J )*X( I ) 150 CONTINUE ELSE IF( NOUNIT ) $ TEMP = TEMP*CONJG( A( 1, J ) ) DO 160, I = J + 1, MIN( N, J + K ) TEMP = TEMP + CONJG( A( L + I, J ) )*X( I ) 160 CONTINUE END IF X( J ) = TEMP 170 CONTINUE ELSE JX = KX DO 200, J = 1, N TEMP = X( JX ) KX = KX + INCX IX = KX L = 1 - J IF( NOCONJ )THEN IF( NOUNIT ) $ TEMP = TEMP*A( 1, J ) DO 180, I = J + 1, MIN( N, J + K ) TEMP = TEMP + A( L + I, J )*X( IX ) IX = IX + INCX 180 CONTINUE ELSE IF( NOUNIT ) $ TEMP = TEMP*CONJG( A( 1, J ) ) DO 190, I = J + 1, MIN( N, J + K ) TEMP = TEMP + CONJG( A( L + I, J ) )*X( IX ) IX = IX + INCX 190 CONTINUE END IF X( JX ) = TEMP JX = JX + INCX 200 CONTINUE END IF END IF END IF * RETURN * * End of CTBMV . * END * ************************************************************************ * SUBROUTINE CTPMV ( UPLO, TRANS, DIAG, N, AP, X, INCX ) * .. Scalar Arguments .. INTEGER INCX, N CHARACTER*1 DIAG, TRANS, UPLO * .. Array Arguments .. COMPLEX AP( * ), X( * ) * .. * * Purpose * ======= * * CTPMV performs one of the matrix-vector operations * * x := A*x, or x := A'*x, or x := conjg( A' )*x, * * where x is an n element vector and A is an n by n unit, or non-unit, * upper or lower triangular matrix, supplied in packed form. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the matrix is an upper or * lower triangular matrix as follows: * * UPLO = 'U' or 'u' A is an upper triangular matrix. * * UPLO = 'L' or 'l' A is a lower triangular matrix. * * Unchanged on exit. * * TRANS - CHARACTER*1. * On entry, TRANS specifies the operation to be performed as * follows: * * TRANS = 'N' or 'n' x := A*x. * * TRANS = 'T' or 't' x := A'*x. * * TRANS = 'C' or 'c' x := conjg( A' )*x. * * Unchanged on exit. * * DIAG - CHARACTER*1. * On entry, DIAG specifies whether or not A is unit * triangular as follows: * * DIAG = 'U' or 'u' A is assumed to be unit triangular. * * DIAG = 'N' or 'n' A is not assumed to be unit * triangular. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * AP - COMPLEX array of DIMENSION at least * ( ( n*( n + 1 ) )/2 ). * Before entry with UPLO = 'U' or 'u', the array AP must * contain the upper triangular matrix packed sequentially, * column by column, so that AP( 1 ) contains a( 1, 1 ), * AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) * respectively, and so on. * Before entry with UPLO = 'L' or 'l', the array AP must * contain the lower triangular matrix packed sequentially, * column by column, so that AP( 1 ) contains a( 1, 1 ), * AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) * respectively, and so on. * Note that when DIAG = 'U' or 'u', the diagonal elements of * A are not referenced, but are assumed to be unity. * Unchanged on exit. * * X - COMPLEX array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element vector x. On exit, X is overwritten with the * tranformed vector x. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. COMPLEX ZERO PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) ) * .. Local Scalars .. COMPLEX TEMP INTEGER I, INFO, IX, J, JX, K, KK, KX LOGICAL NOCONJ, NOUNIT * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC CONJG * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO , 'U' ).AND. $ .NOT.LSAME( UPLO , 'L' ) )THEN INFO = 1 ELSE IF( .NOT.LSAME( TRANS, 'N' ).AND. $ .NOT.LSAME( TRANS, 'T' ).AND. $ .NOT.LSAME( TRANS, 'C' ) )THEN INFO = 2 ELSE IF( .NOT.LSAME( DIAG , 'U' ).AND. $ .NOT.LSAME( DIAG , 'N' ) )THEN INFO = 3 ELSE IF( N.LT.0 )THEN INFO = 4 ELSE IF( INCX.EQ.0 )THEN INFO = 7 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'CTPMV ', INFO ) RETURN END IF * * Quick return if possible. * IF( N.EQ.0 ) $ RETURN * NOCONJ = LSAME( TRANS, 'T' ) NOUNIT = LSAME( DIAG , 'N' ) * * Set up the start point in X if the increment is not unity. This * will be ( N - 1 )*INCX too small for descending loops. * IF( INCX.LE.0 )THEN KX = 1 - ( N - 1 )*INCX ELSE IF( INCX.NE.1 )THEN KX = 1 END IF * * Start the operations. In this version the elements of AP are * accessed sequentially with one pass through AP. * IF( LSAME( TRANS, 'N' ) )THEN * * Form x:= A*x. * IF( LSAME( UPLO, 'U' ) )THEN KK = 1 IF( INCX.EQ.1 )THEN DO 20, J = 1, N IF( X( J ).NE.ZERO )THEN TEMP = X( J ) K = KK DO 10, I = 1, J - 1 X( I ) = X( I ) + TEMP*AP( K ) K = K + 1 10 CONTINUE IF( NOUNIT ) $ X( J ) = X( J )*AP( KK + J - 1 ) END IF KK = KK + J 20 CONTINUE ELSE JX = KX DO 40, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = X( JX ) IX = KX DO 30, K = KK, KK + J - 2 X( IX ) = X( IX ) + TEMP*AP( K ) IX = IX + INCX 30 CONTINUE IF( NOUNIT ) $ X( JX ) = X( JX )*AP( KK + J - 1 ) END IF JX = JX + INCX KK = KK + J 40 CONTINUE END IF ELSE KK = ( N*( N + 1 ) )/2 IF( INCX.EQ.1 )THEN DO 60, J = N, 1, -1 IF( X( J ).NE.ZERO )THEN TEMP = X( J ) K = KK DO 50, I = N, J + 1, -1 X( I ) = X( I ) + TEMP*AP( K ) K = K - 1 50 CONTINUE IF( NOUNIT ) $ X( J ) = X( J )*AP( KK - N + J ) END IF KK = KK - ( N - J + 1 ) 60 CONTINUE ELSE KX = KX + ( N - 1 )*INCX JX = KX DO 80, J = N, 1, -1 IF( X( JX ).NE.ZERO )THEN TEMP = X( JX ) IX = KX DO 70, K = KK, KK - ( N - ( J + 1 ) ), -1 X( IX ) = X( IX ) + TEMP*AP( K ) IX = IX - INCX 70 CONTINUE IF( NOUNIT ) $ X( JX ) = X( JX )*AP( KK - N + J ) END IF JX = JX - INCX KK = KK - ( N - J + 1 ) 80 CONTINUE END IF END IF ELSE * * Form x := A'*x or x := conjg( A' )*x. * IF( LSAME( UPLO, 'U' ) )THEN KK = ( N*( N + 1 ) )/2 IF( INCX.EQ.1 )THEN DO 110, J = N, 1, -1 TEMP = X( J ) K = KK - 1 IF( NOCONJ )THEN IF( NOUNIT ) $ TEMP = TEMP*AP( KK ) DO 90, I = J - 1, 1, -1 TEMP = TEMP + AP( K )*X( I ) K = K - 1 90 CONTINUE ELSE IF( NOUNIT ) $ TEMP = TEMP*CONJG( AP( KK ) ) DO 100, I = J - 1, 1, -1 TEMP = TEMP + CONJG( AP( K ) )*X( I ) K = K - 1 100 CONTINUE END IF X( J ) = TEMP KK = KK - J 110 CONTINUE ELSE JX = KX + ( N - 1 )*INCX DO 140, J = N, 1, -1 TEMP = X( JX ) IX = JX IF( NOCONJ )THEN IF( NOUNIT ) $ TEMP = TEMP*AP( KK ) DO 120, K = KK - 1, KK - J + 1, -1 IX = IX - INCX TEMP = TEMP + AP( K )*X( IX ) 120 CONTINUE ELSE IF( NOUNIT ) $ TEMP = TEMP*CONJG( AP( KK ) ) DO 130, K = KK - 1, KK - J + 1, -1 IX = IX - INCX TEMP = TEMP + CONJG( AP( K ) )*X( IX ) 130 CONTINUE END IF X( JX ) = TEMP JX = JX - INCX KK = KK - J 140 CONTINUE END IF ELSE KK = 1 IF( INCX.EQ.1 )THEN DO 170, J = 1, N TEMP = X( J ) K = KK + 1 IF( NOCONJ )THEN IF( NOUNIT ) $ TEMP = TEMP*AP( KK ) DO 150, I = J + 1, N TEMP = TEMP + AP( K )*X( I ) K = K + 1 150 CONTINUE ELSE IF( NOUNIT ) $ TEMP = TEMP*CONJG( AP( KK ) ) DO 160, I = J + 1, N TEMP = TEMP + CONJG( AP( K ) )*X( I ) K = K + 1 160 CONTINUE END IF X( J ) = TEMP KK = KK + ( N - J + 1 ) 170 CONTINUE ELSE JX = KX DO 200, J = 1, N TEMP = X( JX ) IX = JX IF( NOCONJ )THEN IF( NOUNIT ) $ TEMP = TEMP*AP( KK ) DO 180, K = KK + 1, KK + N - J IX = IX + INCX TEMP = TEMP + AP( K )*X( IX ) 180 CONTINUE ELSE IF( NOUNIT ) $ TEMP = TEMP*CONJG( AP( KK ) ) DO 190, K = KK + 1, KK + N - J IX = IX + INCX TEMP = TEMP + CONJG( AP( K ) )*X( IX ) 190 CONTINUE END IF X( JX ) = TEMP JX = JX + INCX KK = KK + ( N - J + 1 ) 200 CONTINUE END IF END IF END IF * RETURN * * End of CTPMV . * END * ************************************************************************ * SUBROUTINE CTRSV ( UPLO, TRANS, DIAG, N, A, LDA, X, INCX ) * .. Scalar Arguments .. INTEGER INCX, LDA, N CHARACTER*1 DIAG, TRANS, UPLO * .. Array Arguments .. COMPLEX A( LDA, * ), X( * ) * .. * * Purpose * ======= * * CTRSV solves one of the systems of equations * * A*x = b, or A'*x = b, or conjg( A' )*x = b, * * where b and x are n element vectors and A is an n by n unit, or * non-unit, upper or lower triangular matrix. * * No test for singularity or near-singularity is included in this * routine. Such tests must be performed before calling this routine. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the matrix is an upper or * lower triangular matrix as follows: * * UPLO = 'U' or 'u' A is an upper triangular matrix. * * UPLO = 'L' or 'l' A is a lower triangular matrix. * * Unchanged on exit. * * TRANS - CHARACTER*1. * On entry, TRANS specifies the equations to be solved as * follows: * * TRANS = 'N' or 'n' A*x = b. * * TRANS = 'T' or 't' A'*x = b. * * TRANS = 'C' or 'c' conjg( A' )*x = b. * * Unchanged on exit. * * DIAG - CHARACTER*1. * On entry, DIAG specifies whether or not A is unit * triangular as follows: * * DIAG = 'U' or 'u' A is assumed to be unit triangular. * * DIAG = 'N' or 'n' A is not assumed to be unit * triangular. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * A - COMPLEX array of DIMENSION ( LDA, n ). * Before entry with UPLO = 'U' or 'u', the leading n by n * upper triangular part of the array A must contain the upper * triangular matrix and the strictly lower triangular part of * A is not referenced. * Before entry with UPLO = 'L' or 'l', the leading n by n * lower triangular part of the array A must contain the lower * triangular matrix and the strictly upper triangular part of * A is not referenced. * Note that when DIAG = 'U' or 'u', the diagonal elements of * A are not referenced either, but are assumed to be unity. * Unchanged on exit. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * max( 1, n ). * Unchanged on exit. * * X - COMPLEX array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element right-hand side vector b. On exit, X is overwritten * with the solution vector x. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. COMPLEX ZERO PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) ) * .. Local Scalars .. COMPLEX TEMP INTEGER I, INFO, IX, J, JX, KX LOGICAL NOCONJ, NOUNIT * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC CONJG, MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO , 'U' ).AND. $ .NOT.LSAME( UPLO , 'L' ) )THEN INFO = 1 ELSE IF( .NOT.LSAME( TRANS, 'N' ).AND. $ .NOT.LSAME( TRANS, 'T' ).AND. $ .NOT.LSAME( TRANS, 'C' ) )THEN INFO = 2 ELSE IF( .NOT.LSAME( DIAG , 'U' ).AND. $ .NOT.LSAME( DIAG , 'N' ) )THEN INFO = 3 ELSE IF( N.LT.0 )THEN INFO = 4 ELSE IF( LDA.LT.MAX( 1, N ) )THEN INFO = 6 ELSE IF( INCX.EQ.0 )THEN INFO = 8 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'CTRSV ', INFO ) RETURN END IF * * Quick return if possible. * IF( N.EQ.0 ) $ RETURN * NOCONJ = LSAME( TRANS, 'T' ) NOUNIT = LSAME( DIAG , 'N' ) * * Set up the start point in X if the increment is not unity. This * will be ( N - 1 )*INCX too small for descending loops. * IF( INCX.LE.0 )THEN KX = 1 - ( N - 1 )*INCX ELSE IF( INCX.NE.1 )THEN KX = 1 END IF * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through A. * IF( LSAME( TRANS, 'N' ) )THEN * * Form x := inv( A )*x. * IF( LSAME( UPLO, 'U' ) )THEN IF( INCX.EQ.1 )THEN DO 20, J = N, 1, -1 IF( X( J ).NE.ZERO )THEN IF( NOUNIT ) $ X( J ) = X( J )/A( J, J ) TEMP = X( J ) DO 10, I = J - 1, 1, -1 X( I ) = X( I ) - TEMP*A( I, J ) 10 CONTINUE END IF 20 CONTINUE ELSE JX = KX + ( N - 1 )*INCX DO 40, J = N, 1, -1 IF( X( JX ).NE.ZERO )THEN IF( NOUNIT ) $ X( JX ) = X( JX )/A( J, J ) TEMP = X( JX ) IX = JX DO 30, I = J - 1, 1, -1 IX = IX - INCX X( IX ) = X( IX ) - TEMP*A( I, J ) 30 CONTINUE END IF JX = JX - INCX 40 CONTINUE END IF ELSE IF( INCX.EQ.1 )THEN DO 60, J = 1, N IF( X( J ).NE.ZERO )THEN IF( NOUNIT ) $ X( J ) = X( J )/A( J, J ) TEMP = X( J ) DO 50, I = J + 1, N X( I ) = X( I ) - TEMP*A( I, J ) 50 CONTINUE END IF 60 CONTINUE ELSE JX = KX DO 80, J = 1, N IF( X( JX ).NE.ZERO )THEN IF( NOUNIT ) $ X( JX ) = X( JX )/A( J, J ) TEMP = X( JX ) IX = JX DO 70, I = J + 1, N IX = IX + INCX X( IX ) = X( IX ) - TEMP*A( I, J ) 70 CONTINUE END IF JX = JX + INCX 80 CONTINUE END IF END IF ELSE * * Form x := inv( A' )*x or x := inv( conjg( A' ) )*x. * IF( LSAME( UPLO, 'U' ) )THEN IF( INCX.EQ.1 )THEN DO 110, J = 1, N TEMP = X( J ) IF( NOCONJ )THEN DO 90, I = 1, J - 1 TEMP = TEMP - A( I, J )*X( I ) 90 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/A( J, J ) ELSE DO 100, I = 1, J - 1 TEMP = TEMP - CONJG( A( I, J ) )*X( I ) 100 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/CONJG( A( J, J ) ) END IF X( J ) = TEMP 110 CONTINUE ELSE JX = KX DO 140, J = 1, N IX = KX TEMP = X( JX ) IF( NOCONJ )THEN DO 120, I = 1, J - 1 TEMP = TEMP - A( I, J )*X( IX ) IX = IX + INCX 120 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/A( J, J ) ELSE DO 130, I = 1, J - 1 TEMP = TEMP - CONJG( A( I, J ) )*X( IX ) IX = IX + INCX 130 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/CONJG( A( J, J ) ) END IF X( JX ) = TEMP JX = JX + INCX 140 CONTINUE END IF ELSE IF( INCX.EQ.1 )THEN DO 170, J = N, 1, -1 TEMP = X( J ) IF( NOCONJ )THEN DO 150, I = N, J + 1, -1 TEMP = TEMP - A( I, J )*X( I ) 150 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/A( J, J ) ELSE DO 160, I = N, J + 1, -1 TEMP = TEMP - CONJG( A( I, J ) )*X( I ) 160 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/CONJG( A( J, J ) ) END IF X( J ) = TEMP 170 CONTINUE ELSE KX = KX + ( N - 1 )*INCX JX = KX DO 200, J = N, 1, -1 IX = KX TEMP = X( JX ) IF( NOCONJ )THEN DO 180, I = N, J + 1, -1 TEMP = TEMP - A( I, J )*X( IX ) IX = IX - INCX 180 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/A( J, J ) ELSE DO 190, I = N, J + 1, -1 TEMP = TEMP - CONJG( A( I, J ) )*X( IX ) IX = IX - INCX 190 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/CONJG( A( J, J ) ) END IF X( JX ) = TEMP JX = JX - INCX 200 CONTINUE END IF END IF END IF * RETURN * * End of CTRSV . * END * ************************************************************************ * SUBROUTINE CTBSV ( UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX ) * .. Scalar Arguments .. INTEGER INCX, K, LDA, N CHARACTER*1 DIAG, TRANS, UPLO * .. Array Arguments .. COMPLEX A( LDA, * ), X( * ) * .. * * Purpose * ======= * * CTBSV solves one of the systems of equations * * A*x = b, or A'*x = b, or conjg( A' )*x = b, * * where b and x are n element vectors and A is an n by n unit, or * non-unit, upper or lower triangular band matrix, with ( k + 1 ) * diagonals. * * No test for singularity or near-singularity is included in this * routine. Such tests must be performed before calling this routine. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the matrix is an upper or * lower triangular matrix as follows: * * UPLO = 'U' or 'u' A is an upper triangular matrix. * * UPLO = 'L' or 'l' A is a lower triangular matrix. * * Unchanged on exit. * * TRANS - CHARACTER*1. * On entry, TRANS specifies the equations to be solved as * follows: * * TRANS = 'N' or 'n' A*x = b. * * TRANS = 'T' or 't' A'*x = b. * * TRANS = 'C' or 'c' conjg( A' )*x = b. * * Unchanged on exit. * * DIAG - CHARACTER*1. * On entry, DIAG specifies whether or not A is unit * triangular as follows: * * DIAG = 'U' or 'u' A is assumed to be unit triangular. * * DIAG = 'N' or 'n' A is not assumed to be unit * triangular. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * K - INTEGER. * On entry with UPLO = 'U' or 'u', K specifies the number of * super-diagonals of the matrix A. * On entry with UPLO = 'L' or 'l', K specifies the number of * sub-diagonals of the matrix A. * K must satisfy 0 .le. K. * Unchanged on exit. * * A - COMPLEX array of DIMENSION ( LDA, n ). * Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) * by n part of the array A must contain the upper triangular * band part of the matrix of coefficients, supplied column by * column, with the leading diagonal of the matrix in row * ( k + 1 ) of the array, the first super-diagonal starting at * position 2 in row k, and so on. The top left k by k triangle * of the array A is not referenced. * The following program segment will transfer an upper * triangular band matrix from conventional full matrix storage * to band storage: * * DO 20, J = 1, N * M = K + 1 - J * DO 10, I = MAX( 1, J - K ), J * A( M + I, J ) = matrix( I, J ) * 10 CONTINUE * 20 CONTINUE * * Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) * by n part of the array A must contain the lower triangular * band part of the matrix of coefficients, supplied column by * column, with the leading diagonal of the matrix in row 1 of * the array, the first sub-diagonal starting at position 1 in * row 2, and so on. The bottom right k by k triangle of the * array A is not referenced. * The following program segment will transfer a lower * triangular band matrix from conventional full matrix storage * to band storage: * * DO 20, J = 1, N * M = 1 - J * DO 10, I = J, MIN( N, J + K ) * A( M + I, J ) = matrix( I, J ) * 10 CONTINUE * 20 CONTINUE * * Note that when DIAG = 'U' or 'u' the elements of the array A * corresponding to the diagonal elements of the matrix are not * referenced, but are assumed to be unity. * Unchanged on exit. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * ( k + 1 ). * Unchanged on exit. * * X - COMPLEX array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element right-hand side vector b. On exit, X is overwritten * with the solution vector x. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. COMPLEX ZERO PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) ) * .. Local Scalars .. COMPLEX TEMP INTEGER I, INFO, IX, J, JX, KPLUS1, KX, L LOGICAL NOCONJ, NOUNIT * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC CONJG, MAX, MIN * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO , 'U' ).AND. $ .NOT.LSAME( UPLO , 'L' ) )THEN INFO = 1 ELSE IF( .NOT.LSAME( TRANS, 'N' ).AND. $ .NOT.LSAME( TRANS, 'T' ).AND. $ .NOT.LSAME( TRANS, 'C' ) )THEN INFO = 2 ELSE IF( .NOT.LSAME( DIAG , 'U' ).AND. $ .NOT.LSAME( DIAG , 'N' ) )THEN INFO = 3 ELSE IF( N.LT.0 )THEN INFO = 4 ELSE IF( K.LT.0 )THEN INFO = 5 ELSE IF( LDA.LT.( K + 1 ) )THEN INFO = 7 ELSE IF( INCX.EQ.0 )THEN INFO = 9 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'CTBSV ', INFO ) RETURN END IF * * Quick return if possible. * IF( N.EQ.0 ) $ RETURN * NOCONJ = LSAME( TRANS, 'T' ) NOUNIT = LSAME( DIAG , 'N' ) * * Set up the start point in X if the increment is not unity. This * will be ( N - 1 )*INCX too small for descending loops. * IF( INCX.LE.0 )THEN KX = 1 - ( N - 1 )*INCX ELSE IF( INCX.NE.1 )THEN KX = 1 END IF * * Start the operations. In this version the elements of A are * accessed by sequentially with one pass through A. * IF( LSAME( TRANS, 'N' ) )THEN * * Form x := inv( A )*x. * IF( LSAME( UPLO, 'U' ) )THEN KPLUS1 = K + 1 IF( INCX.EQ.1 )THEN DO 20, J = N, 1, -1 IF( X( J ).NE.ZERO )THEN L = KPLUS1 - J IF( NOUNIT ) $ X( J ) = X( J )/A( KPLUS1, J ) TEMP = X( J ) DO 10, I = J - 1, MAX( 1, J - K ), -1 X( I ) = X( I ) - TEMP*A( L + I, J ) 10 CONTINUE END IF 20 CONTINUE ELSE KX = KX + ( N - 1 )*INCX JX = KX DO 40, J = N, 1, -1 KX = KX - INCX IF( X( JX ).NE.ZERO )THEN IX = KX L = KPLUS1 - J IF( NOUNIT ) $ X( JX ) = X( JX )/A( KPLUS1, J ) TEMP = X( JX ) DO 30, I = J - 1, MAX( 1, J - K ), -1 X( IX ) = X( IX ) - TEMP*A( L + I, J ) IX = IX - INCX 30 CONTINUE END IF JX = JX - INCX 40 CONTINUE END IF ELSE IF( INCX.EQ.1 )THEN DO 60, J = 1, N IF( X( J ).NE.ZERO )THEN L = 1 - J IF( NOUNIT ) $ X( J ) = X( J )/A( 1, J ) TEMP = X( J ) DO 50, I = J + 1, MIN( N, J + K ) X( I ) = X( I ) - TEMP*A( L + I, J ) 50 CONTINUE END IF 60 CONTINUE ELSE JX = KX DO 80, J = 1, N KX = KX + INCX IF( X( JX ).NE.ZERO )THEN IX = KX L = 1 - J IF( NOUNIT ) $ X( JX ) = X( JX )/A( 1, J ) TEMP = X( JX ) DO 70, I = J + 1, MIN( N, J + K ) X( IX ) = X( IX ) - TEMP*A( L + I, J ) IX = IX + INCX 70 CONTINUE END IF JX = JX + INCX 80 CONTINUE END IF END IF ELSE * * Form x := inv( A' )*x or x := inv( conjg( A') )*x. * IF( LSAME( UPLO, 'U' ) )THEN KPLUS1 = K + 1 IF( INCX.EQ.1 )THEN DO 110, J = 1, N TEMP = X( J ) L = KPLUS1 - J IF( NOCONJ )THEN DO 90, I = MAX( 1, J - K ), J - 1 TEMP = TEMP - A( L + I, J )*X( I ) 90 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/A( KPLUS1, J ) ELSE DO 100, I = MAX( 1, J - K ), J - 1 TEMP = TEMP - CONJG( A( L + I, J ) )*X( I ) 100 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/CONJG( A( KPLUS1, J ) ) END IF X( J ) = TEMP 110 CONTINUE ELSE JX = KX DO 140, J = 1, N TEMP = X( JX ) IX = KX L = KPLUS1 - J IF( NOCONJ )THEN DO 120, I = MAX( 1, J - K ), J - 1 TEMP = TEMP - A( L + I, J )*X( IX ) IX = IX + INCX 120 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/A( KPLUS1, J ) ELSE DO 130, I = MAX( 1, J - K ), J - 1 TEMP = TEMP - CONJG( A( L + I, J ) )*X( IX ) IX = IX + INCX 130 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/CONJG( A( KPLUS1, J ) ) END IF X( JX ) = TEMP JX = JX + INCX IF( J.GT.K ) $ KX = KX + INCX 140 CONTINUE END IF ELSE IF( INCX.EQ.1 )THEN DO 170, J = N, 1, -1 TEMP = X( J ) L = 1 - J IF( NOCONJ )THEN DO 150, I = MIN( N, J + K ), J + 1, -1 TEMP = TEMP - A( L + I, J )*X( I ) 150 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/A( 1, J ) ELSE DO 160, I = MIN( N, J + K ), J + 1, -1 TEMP = TEMP - CONJG( A( L + I, J ) )*X( I ) 160 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/CONJG( A( 1, J ) ) END IF X( J ) = TEMP 170 CONTINUE ELSE KX = KX + ( N - 1 )*INCX JX = KX DO 200, J = N, 1, -1 TEMP = X( JX ) IX = KX L = 1 - J IF( NOCONJ )THEN DO 180, I = MIN( N, J + K ), J + 1, -1 TEMP = TEMP - A( L + I, J )*X( IX ) IX = IX - INCX 180 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/A( 1, J ) ELSE DO 190, I = MIN( N, J + K ), J + 1, -1 TEMP = TEMP - CONJG( A( L + I, J ) )*X( IX ) IX = IX - INCX 190 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/CONJG( A( 1, J ) ) END IF X( JX ) = TEMP JX = JX - INCX IF( ( N - J ).GE.K ) $ KX = KX - INCX 200 CONTINUE END IF END IF END IF * RETURN * * End of CTBSV . * END * ************************************************************************ * SUBROUTINE CTPSV ( UPLO, TRANS, DIAG, N, AP, X, INCX ) * .. Scalar Arguments .. INTEGER INCX, N CHARACTER*1 DIAG, TRANS, UPLO * .. Array Arguments .. COMPLEX AP( * ), X( * ) * .. * * Purpose * ======= * * CTPSV solves one of the systems of equations * * A*x = b, or A'*x = b, or conjg( A' )*x = b, * * where b and x are n element vectors and A is an n by n unit, or * non-unit, upper or lower triangular matrix, supplied in packed form. * * No test for singularity or near-singularity is included in this * routine. Such tests must be performed before calling this routine. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the matrix is an upper or * lower triangular matrix as follows: * * UPLO = 'U' or 'u' A is an upper triangular matrix. * * UPLO = 'L' or 'l' A is a lower triangular matrix. * * Unchanged on exit. * * TRANS - CHARACTER*1. * On entry, TRANS specifies the equations to be solved as * follows: * * TRANS = 'N' or 'n' A*x = b. * * TRANS = 'T' or 't' A'*x = b. * * TRANS = 'C' or 'c' conjg( A' )*x = b. * * Unchanged on exit. * * DIAG - CHARACTER*1. * On entry, DIAG specifies whether or not A is unit * triangular as follows: * * DIAG = 'U' or 'u' A is assumed to be unit triangular. * * DIAG = 'N' or 'n' A is not assumed to be unit * triangular. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * AP - COMPLEX array of DIMENSION at least * ( ( n*( n + 1 ) )/2 ). * Before entry with UPLO = 'U' or 'u', the array AP must * contain the upper triangular matrix packed sequentially, * column by column, so that AP( 1 ) contains a( 1, 1 ), * AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) * respectively, and so on. * Before entry with UPLO = 'L' or 'l', the array AP must * contain the lower triangular matrix packed sequentially, * column by column, so that AP( 1 ) contains a( 1, 1 ), * AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) * respectively, and so on. * Note that when DIAG = 'U' or 'u', the diagonal elements of * A are not referenced, but are assumed to be unity. * Unchanged on exit. * * X - COMPLEX array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element right-hand side vector b. On exit, X is overwritten * with the solution vector x. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. COMPLEX ZERO PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) ) * .. Local Scalars .. COMPLEX TEMP INTEGER I, INFO, IX, J, JX, K, KK, KX LOGICAL NOCONJ, NOUNIT * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC CONJG * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO , 'U' ).AND. $ .NOT.LSAME( UPLO , 'L' ) )THEN INFO = 1 ELSE IF( .NOT.LSAME( TRANS, 'N' ).AND. $ .NOT.LSAME( TRANS, 'T' ).AND. $ .NOT.LSAME( TRANS, 'C' ) )THEN INFO = 2 ELSE IF( .NOT.LSAME( DIAG , 'U' ).AND. $ .NOT.LSAME( DIAG , 'N' ) )THEN INFO = 3 ELSE IF( N.LT.0 )THEN INFO = 4 ELSE IF( INCX.EQ.0 )THEN INFO = 7 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'CTPSV ', INFO ) RETURN END IF * * Quick return if possible. * IF( N.EQ.0 ) $ RETURN * NOCONJ = LSAME( TRANS, 'T' ) NOUNIT = LSAME( DIAG , 'N' ) * * Set up the start point in X if the increment is not unity. This * will be ( N - 1 )*INCX too small for descending loops. * IF( INCX.LE.0 )THEN KX = 1 - ( N - 1 )*INCX ELSE IF( INCX.NE.1 )THEN KX = 1 END IF * * Start the operations. In this version the elements of AP are * accessed sequentially with one pass through AP. * IF( LSAME( TRANS, 'N' ) )THEN * * Form x := inv( A )*x. * IF( LSAME( UPLO, 'U' ) )THEN KK = ( N*( N + 1 ) )/2 IF( INCX.EQ.1 )THEN DO 20, J = N, 1, -1 IF( X( J ).NE.ZERO )THEN IF( NOUNIT ) $ X( J ) = X( J )/AP( KK ) TEMP = X( J ) K = KK - 1 DO 10, I = J - 1, 1, -1 X( I ) = X( I ) - TEMP*AP( K ) K = K - 1 10 CONTINUE END IF KK = KK - J 20 CONTINUE ELSE JX = KX + ( N - 1 )*INCX DO 40, J = N, 1, -1 IF( X( JX ).NE.ZERO )THEN IF( NOUNIT ) $ X( JX ) = X( JX )/AP( KK ) TEMP = X( JX ) IX = JX DO 30, K = KK - 1, KK - J + 1, -1 IX = IX - INCX X( IX ) = X( IX ) - TEMP*AP( K ) 30 CONTINUE END IF JX = JX - INCX KK = KK - J 40 CONTINUE END IF ELSE KK = 1 IF( INCX.EQ.1 )THEN DO 60, J = 1, N IF( X( J ).NE.ZERO )THEN IF( NOUNIT ) $ X( J ) = X( J )/AP( KK ) TEMP = X( J ) K = KK + 1 DO 50, I = J + 1, N X( I ) = X( I ) - TEMP*AP( K ) K = K + 1 50 CONTINUE END IF KK = KK + ( N - J + 1 ) 60 CONTINUE ELSE JX = KX DO 80, J = 1, N IF( X( JX ).NE.ZERO )THEN IF( NOUNIT ) $ X( JX ) = X( JX )/AP( KK ) TEMP = X( JX ) IX = JX DO 70, K = KK + 1, KK + N - J IX = IX + INCX X( IX ) = X( IX ) - TEMP*AP( K ) 70 CONTINUE END IF JX = JX + INCX KK = KK + ( N - J + 1 ) 80 CONTINUE END IF END IF ELSE * * Form x := inv( A' )*x or x := inv( conjg( A' ) )*x. * IF( LSAME( UPLO, 'U' ) )THEN KK = 1 IF( INCX.EQ.1 )THEN DO 110, J = 1, N TEMP = X( J ) K = KK IF( NOCONJ )THEN DO 90, I = 1, J - 1 TEMP = TEMP - AP( K )*X( I ) K = K + 1 90 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/AP( KK + J - 1 ) ELSE DO 100, I = 1, J - 1 TEMP = TEMP - CONJG( AP( K ) )*X( I ) K = K + 1 100 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/CONJG( AP( KK + J - 1 ) ) END IF X( J ) = TEMP KK = KK + J 110 CONTINUE ELSE JX = KX DO 140, J = 1, N TEMP = X( JX ) IX = KX IF( NOCONJ )THEN DO 120, K = KK, KK + J - 2 TEMP = TEMP - AP( K )*X( IX ) IX = IX + INCX 120 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/AP( KK + J - 1 ) ELSE DO 130, K = KK, KK + J - 2 TEMP = TEMP - CONJG( AP( K ) )*X( IX ) IX = IX + INCX 130 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/CONJG( AP( KK + J - 1 ) ) END IF X( JX ) = TEMP JX = JX + INCX KK = KK + J 140 CONTINUE END IF ELSE KK = ( N*( N + 1 ) )/2 IF( INCX.EQ.1 )THEN DO 170, J = N, 1, -1 TEMP = X( J ) K = KK IF( NOCONJ )THEN DO 150, I = N, J + 1, -1 TEMP = TEMP - AP( K )*X( I ) K = K - 1 150 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/AP( KK - N + J ) ELSE DO 160, I = N, J + 1, -1 TEMP = TEMP - CONJG( AP( K ) )*X( I ) K = K - 1 160 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/CONJG( AP( KK - N + J ) ) END IF X( J ) = TEMP KK = KK - ( N - J + 1 ) 170 CONTINUE ELSE KX = KX + ( N - 1 )*INCX JX = KX DO 200, J = N, 1, -1 TEMP = X( JX ) IX = KX IF( NOCONJ )THEN DO 180, K = KK, KK - ( N - ( J + 1 ) ), -1 TEMP = TEMP - AP( K )*X( IX ) IX = IX - INCX 180 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/AP( KK - N + J ) ELSE DO 190, K = KK, KK - ( N - ( J + 1 ) ), -1 TEMP = TEMP - CONJG( AP( K ) )*X( IX ) IX = IX - INCX 190 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/CONJG( AP( KK - N + J ) ) END IF X( JX ) = TEMP JX = JX - INCX KK = KK - ( N - J + 1 ) 200 CONTINUE END IF END IF END IF * RETURN * * End of CTPSV . * END * ************************************************************************ * SUBROUTINE CGERU ( M, N, ALPHA, X, INCX, Y, INCY, A, LDA ) * .. Scalar Arguments .. COMPLEX ALPHA INTEGER INCX, INCY, LDA, M, N * .. Array Arguments .. COMPLEX A( LDA, * ), X( * ), Y( * ) * .. * * Purpose * ======= * * CGERU performs the rank 1 operation * * A := alpha*x*y' + A, * * where alpha is a scalar, x is an m element vector, y is an n element * vector and A is an m by n matrix. * * Parameters * ========== * * M - INTEGER. * On entry, M specifies the number of rows of the matrix A. * M must be at least zero. * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the number of columns of the matrix A. * N must be at least zero. * Unchanged on exit. * * ALPHA - COMPLEX . * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * X - COMPLEX array of dimension at least * ( 1 + ( m - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the m * element vector x. * Unchanged on exit. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * Y - COMPLEX array of dimension at least * ( 1 + ( n - 1 )*abs( INCY ) ). * Before entry, the incremented array Y must contain the n * element vector y. * Unchanged on exit. * * INCY - INTEGER. * On entry, INCY specifies the increment for the elements of * Y. INCY must not be zero. * Unchanged on exit. * * A - COMPLEX array of DIMENSION ( LDA, n ). * Before entry, the leading m by n part of the array A must * contain the matrix of coefficients. On exit, A is * overwritten by the updated matrix. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * max( 1, m ). * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. COMPLEX ZERO PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) ) * .. Local Scalars .. COMPLEX TEMP INTEGER I, INFO, IX, J, JY, KX * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( M.LT.0 )THEN INFO = 1 ELSE IF( N.LT.0 )THEN INFO = 2 ELSE IF( INCX.EQ.0 )THEN INFO = 5 ELSE IF( INCY.EQ.0 )THEN INFO = 7 ELSE IF( LDA.LT.MAX( 1, M ) )THEN INFO = 9 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'CGERU ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( M.EQ.0 ).OR.( N.EQ.0 ).OR.( ALPHA.EQ.ZERO ) ) $ RETURN * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through A. * IF( INCY.GT.0 )THEN JY = 1 ELSE JY = 1 - ( N - 1 )*INCY END IF IF( INCX.EQ.1 )THEN DO 20, J = 1, N IF( Y( JY ).NE.ZERO )THEN TEMP = ALPHA*Y( JY ) DO 10, I = 1, M A( I, J ) = A( I, J ) + X( I )*TEMP 10 CONTINUE END IF JY = JY + INCY 20 CONTINUE ELSE IF( INCX.GT.0 )THEN KX = 1 ELSE KX = 1 - ( M - 1 )*INCX END IF DO 40, J = 1, N IF( Y( JY ).NE.ZERO )THEN TEMP = ALPHA*Y( JY ) IX = KX DO 30, I = 1, M A( I, J ) = A( I, J ) + X( IX )*TEMP IX = IX + INCX 30 CONTINUE END IF JY = JY + INCY 40 CONTINUE END IF * RETURN * * End of CGERU . * END * ************************************************************************ * SUBROUTINE CGERC ( M, N, ALPHA, X, INCX, Y, INCY, A, LDA ) * .. Scalar Arguments .. COMPLEX ALPHA INTEGER INCX, INCY, LDA, M, N * .. Array Arguments .. COMPLEX A( LDA, * ), X( * ), Y( * ) * .. * * Purpose * ======= * * CGERC performs the rank 1 operation * * A := alpha*x*conjg( y' ) + A, * * where alpha is a scalar, x is an m element vector, y is an n element * vector and A is an m by n matrix. * * Parameters * ========== * * M - INTEGER. * On entry, M specifies the number of rows of the matrix A. * M must be at least zero. * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the number of columns of the matrix A. * N must be at least zero. * Unchanged on exit. * * ALPHA - COMPLEX . * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * X - COMPLEX array of dimension at least * ( 1 + ( m - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the m * element vector x. * Unchanged on exit. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * Y - COMPLEX array of dimension at least * ( 1 + ( n - 1 )*abs( INCY ) ). * Before entry, the incremented array Y must contain the n * element vector y. * Unchanged on exit. * * INCY - INTEGER. * On entry, INCY specifies the increment for the elements of * Y. INCY must not be zero. * Unchanged on exit. * * A - COMPLEX array of DIMENSION ( LDA, n ). * Before entry, the leading m by n part of the array A must * contain the matrix of coefficients. On exit, A is * overwritten by the updated matrix. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * max( 1, m ). * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. COMPLEX ZERO PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) ) * .. Local Scalars .. COMPLEX TEMP INTEGER I, INFO, IX, J, JY, KX * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC CONJG, MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( M.LT.0 )THEN INFO = 1 ELSE IF( N.LT.0 )THEN INFO = 2 ELSE IF( INCX.EQ.0 )THEN INFO = 5 ELSE IF( INCY.EQ.0 )THEN INFO = 7 ELSE IF( LDA.LT.MAX( 1, M ) )THEN INFO = 9 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'CGERC ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( M.EQ.0 ).OR.( N.EQ.0 ).OR.( ALPHA.EQ.ZERO ) ) $ RETURN * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through A. * IF( INCY.GT.0 )THEN JY = 1 ELSE JY = 1 - ( N - 1 )*INCY END IF IF( INCX.EQ.1 )THEN DO 20, J = 1, N IF( Y( JY ).NE.ZERO )THEN TEMP = ALPHA*CONJG( Y( JY ) ) DO 10, I = 1, M A( I, J ) = A( I, J ) + X( I )*TEMP 10 CONTINUE END IF JY = JY + INCY 20 CONTINUE ELSE IF( INCX.GT.0 )THEN KX = 1 ELSE KX = 1 - ( M - 1 )*INCX END IF DO 40, J = 1, N IF( Y( JY ).NE.ZERO )THEN TEMP = ALPHA*CONJG( Y( JY ) ) IX = KX DO 30, I = 1, M A( I, J ) = A( I, J ) + X( IX )*TEMP IX = IX + INCX 30 CONTINUE END IF JY = JY + INCY 40 CONTINUE END IF * RETURN * * End of CGERC . * END * ************************************************************************ * SUBROUTINE CHER ( UPLO, N, ALPHA, X, INCX, A, LDA ) * .. Scalar Arguments .. REAL ALPHA INTEGER INCX, LDA, N CHARACTER*1 UPLO * .. Array Arguments .. COMPLEX A( LDA, * ), X( * ) * .. * * Purpose * ======= * * CHER performs the hermitian rank 1 operation * * A := alpha*x*conjg( x' ) + A, * * where alpha is a real scalar, x is an n element vector and A is an * n by n hermitian matrix. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the upper or lower * triangular part of the array A is to be referenced as * follows: * * UPLO = 'U' or 'u' Only the upper triangular part of A * is to be referenced. * * UPLO = 'L' or 'l' Only the lower triangular part of A * is to be referenced. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * ALPHA - REAL . * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * X - COMPLEX array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element vector x. * Unchanged on exit. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * A - COMPLEX array of DIMENSION ( LDA, n ). * Before entry with UPLO = 'U' or 'u', the leading n by n * upper triangular part of the array A must contain the upper * triangular part of the hermitian matrix and the strictly * lower triangular part of A is not referenced. On exit, the * upper triangular part of the array A is overwritten by the * upper triangular part of the updated matrix. * Before entry with UPLO = 'L' or 'l', the leading n by n * lower triangular part of the array A must contain the lower * triangular part of the hermitian matrix and the strictly * upper triangular part of A is not referenced. On exit, the * lower triangular part of the array A is overwritten by the * lower triangular part of the updated matrix. * Note that the imaginary parts of the diagonal elements need * not be set, they are assumed to be zero, and on exit they * are set to zero. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * max( 1, n ). * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. COMPLEX ZERO PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) ) * .. Local Scalars .. COMPLEX TEMP INTEGER I, INFO, IX, J, JX, KX * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC CONJG, MAX, REAL * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO, 'U' ).AND. $ .NOT.LSAME( UPLO, 'L' ) )THEN INFO = 1 ELSE IF( N.LT.0 )THEN INFO = 2 ELSE IF( INCX.EQ.0 )THEN INFO = 5 ELSE IF( LDA.LT.MAX( 1, N ) )THEN INFO = 7 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'CHER ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( N.EQ.0 ).OR.( ALPHA.EQ.REAL( ZERO ) ) ) $ RETURN * * Set the start point in X if the increment is not unity. * IF( INCX.LE.0 )THEN KX = 1 - ( N - 1 )*INCX ELSE IF( INCX.NE.1 )THEN KX = 1 END IF * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through the triangular part * of A. * IF( LSAME( UPLO, 'U' ) )THEN * * Form A when A is stored in upper triangle. * IF( INCX.EQ.1 )THEN DO 20, J = 1, N IF( X( J ).NE.ZERO )THEN TEMP = ALPHA*CONJG( X( J ) ) DO 10, I = 1, J - 1 A( I, J ) = A( I, J ) + X( I )*TEMP 10 CONTINUE A( J, J ) = REAL( A( J, J ) ) + REAL( X( J )*TEMP ) ELSE A( J, J ) = REAL( A( J, J ) ) END IF 20 CONTINUE ELSE JX = KX DO 40, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = ALPHA*CONJG( X( JX ) ) IX = KX DO 30, I = 1, J - 1 A( I, J ) = A( I, J ) + X( IX )*TEMP IX = IX + INCX 30 CONTINUE A( J, J ) = REAL( A( J, J ) ) + REAL( X( JX )*TEMP ) ELSE A( J, J ) = REAL( A( J, J ) ) END IF JX = JX + INCX 40 CONTINUE END IF ELSE * * Form A when A is stored in lower triangle. * IF( INCX.EQ.1 )THEN DO 60, J = 1, N IF( X( J ).NE.ZERO )THEN TEMP = ALPHA*CONJG( X( J ) ) A( J, J ) = REAL( A( J, J ) ) + REAL( TEMP*X( J ) ) DO 50, I = J + 1, N A( I, J ) = A( I, J ) + X( I )*TEMP 50 CONTINUE ELSE A( J, J ) = REAL( A( J, J ) ) END IF 60 CONTINUE ELSE JX = KX DO 80, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = ALPHA*CONJG( X( JX ) ) A( J, J ) = REAL( A( J, J ) ) + REAL( TEMP*X( JX ) ) IX = JX DO 70, I = J + 1, N IX = IX + INCX A( I, J ) = A( I, J ) + X( IX )*TEMP 70 CONTINUE ELSE A( J, J ) = REAL( A( J, J ) ) END IF JX = JX + INCX 80 CONTINUE END IF END IF * RETURN * * End of CHER . * END * ************************************************************************ * SUBROUTINE CHPR ( UPLO, N, ALPHA, X, INCX, AP ) * .. Scalar Arguments .. REAL ALPHA INTEGER INCX, N CHARACTER*1 UPLO * .. Array Arguments .. COMPLEX AP( * ), X( * ) * .. * * Purpose * ======= * * CHPR performs the hermitian rank 1 operation * * A := alpha*x*conjg( x' ) + A, * * where alpha is a real scalar, x is an n element vector and A is an * n by n hermitian matrix, supplied in packed form. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the upper or lower * triangular part of the matrix A is supplied in the packed * array AP as follows: * * UPLO = 'U' or 'u' The upper triangular part of A is * supplied in AP. * * UPLO = 'L' or 'l' The lower triangular part of A is * supplied in AP. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * ALPHA - REAL . * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * X - COMPLEX array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element vector x. * Unchanged on exit. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * AP - COMPLEX array of DIMENSION at least * ( ( n*( n + 1 ) )/2 ). * Before entry with UPLO = 'U' or 'u', the array AP must * contain the upper triangular part of the hermitian matrix * packed sequentially, column by column, so that AP( 1 ) * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) * and a( 2, 2 ) respectively, and so on. On exit, the array * AP is overwritten by the upper triangular part of the * updated matrix. * Before entry with UPLO = 'L' or 'l', the array AP must * contain the lower triangular part of the hermitian matrix * packed sequentially, column by column, so that AP( 1 ) * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) * and a( 3, 1 ) respectively, and so on. On exit, the array * AP is overwritten by the lower triangular part of the * updated matrix. * Note that the imaginary parts of the diagonal elements need * not be set, they are assumed to be zero, and on exit they * are set to zero. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. COMPLEX ZERO PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) ) * .. Local Scalars .. COMPLEX TEMP INTEGER I, INFO, IX, J, JX, K, KK, KX * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC CONJG, REAL * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO, 'U' ).AND. $ .NOT.LSAME( UPLO, 'L' ) )THEN INFO = 1 ELSE IF( N.LT.0 )THEN INFO = 2 ELSE IF( INCX.EQ.0 )THEN INFO = 5 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'CHPR ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( N.EQ.0 ).OR.( ALPHA.EQ.REAL( ZERO ) ) ) $ RETURN * * Set the start point in X if the increment is not unity. * IF( INCX.LE.0 )THEN KX = 1 - ( N - 1 )*INCX ELSE IF( INCX.NE.1 )THEN KX = 1 END IF * * Start the operations. In this version the elements of the array AP * are accessed sequentially with one pass through AP. * KK = 1 IF( LSAME( UPLO, 'U' ) )THEN * * Form A when upper triangle is stored in AP. * IF( INCX.EQ.1 )THEN DO 20, J = 1, N IF( X( J ).NE.ZERO )THEN TEMP = ALPHA*CONJG( X( J ) ) K = KK DO 10, I = 1, J - 1 AP( K ) = AP( K ) + X( I )*TEMP K = K + 1 10 CONTINUE AP( KK + J - 1 ) = REAL( AP( KK + J - 1 ) ) $ + REAL( X( J )*TEMP ) ELSE AP( KK + J - 1 ) = REAL( AP( KK + J - 1 ) ) END IF KK = KK + J 20 CONTINUE ELSE JX = KX DO 40, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = ALPHA*CONJG( X( JX ) ) IX = KX DO 30, K = KK, KK + J - 2 AP( K ) = AP( K ) + X( IX )*TEMP IX = IX + INCX 30 CONTINUE AP( KK + J - 1 ) = REAL( AP( KK + J - 1 ) ) $ + REAL( X( JX )*TEMP ) ELSE AP( KK + J - 1 ) = REAL( AP( KK + J - 1 ) ) END IF JX = JX + INCX KK = KK + J 40 CONTINUE END IF ELSE * * Form A when lower triangle is stored in AP. * IF( INCX.EQ.1 )THEN DO 60, J = 1, N IF( X( J ).NE.ZERO )THEN TEMP = ALPHA*CONJG( X( J ) ) AP( KK ) = REAL( AP( KK ) ) + REAL( TEMP*X( J ) ) K = KK + 1 DO 50, I = J + 1, N AP( K ) = AP( K ) + X( I )*TEMP K = K + 1 50 CONTINUE ELSE AP( KK ) = REAL( AP( KK ) ) END IF KK = KK + N - J + 1 60 CONTINUE ELSE JX = KX DO 80, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = ALPHA*CONJG( X( JX ) ) AP( KK ) = REAL( AP( KK ) ) + REAL( TEMP*X( JX ) ) IX = JX DO 70, K = KK + 1, KK + N - J IX = IX + INCX AP( K ) = AP( K ) + X( IX )*TEMP 70 CONTINUE ELSE AP( KK ) = REAL( AP( KK ) ) END IF JX = JX + INCX KK = KK + N - J + 1 80 CONTINUE END IF END IF * RETURN * * End of CHPR . * END * ************************************************************************ * SUBROUTINE CHER2 ( UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA ) * .. Scalar Arguments .. COMPLEX ALPHA INTEGER INCX, INCY, LDA, N CHARACTER*1 UPLO * .. Array Arguments .. COMPLEX A( LDA, * ), X( * ), Y( * ) * .. * * Purpose * ======= * * CHER2 performs the hermitian rank 2 operation * * A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A, * * where alpha is a scalar, x and y are n element vectors and A is an n * by n hermitian matrix. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the upper or lower * triangular part of the array A is to be referenced as * follows: * * UPLO = 'U' or 'u' Only the upper triangular part of A * is to be referenced. * * UPLO = 'L' or 'l' Only the lower triangular part of A * is to be referenced. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * ALPHA - COMPLEX . * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * X - COMPLEX array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element vector x. * Unchanged on exit. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * Y - COMPLEX array of dimension at least * ( 1 + ( n - 1 )*abs( INCY ) ). * Before entry, the incremented array Y must contain the n * element vector y. * Unchanged on exit. * * INCY - INTEGER. * On entry, INCY specifies the increment for the elements of * Y. INCY must not be zero. * Unchanged on exit. * * A - COMPLEX array of DIMENSION ( LDA, n ). * Before entry with UPLO = 'U' or 'u', the leading n by n * upper triangular part of the array A must contain the upper * triangular part of the hermitian matrix and the strictly * lower triangular part of A is not referenced. On exit, the * upper triangular part of the array A is overwritten by the * upper triangular part of the updated matrix. * Before entry with UPLO = 'L' or 'l', the leading n by n * lower triangular part of the array A must contain the lower * triangular part of the hermitian matrix and the strictly * upper triangular part of A is not referenced. On exit, the * lower triangular part of the array A is overwritten by the * lower triangular part of the updated matrix. * Note that the imaginary parts of the diagonal elements need * not be set, they are assumed to be zero, and on exit they * are set to zero. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * max( 1, n ). * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. COMPLEX ZERO PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) ) * .. Local Scalars .. COMPLEX TEMP1, TEMP2 INTEGER I, INFO, IX, IY, J, JX, JY, KX, KY * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC CONJG, MAX, REAL * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO, 'U' ).AND. $ .NOT.LSAME( UPLO, 'L' ) )THEN INFO = 1 ELSE IF( N.LT.0 )THEN INFO = 2 ELSE IF( INCX.EQ.0 )THEN INFO = 5 ELSE IF( INCY.EQ.0 )THEN INFO = 7 ELSE IF( LDA.LT.MAX( 1, N ) )THEN INFO = 9 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'CHER2 ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( N.EQ.0 ).OR.( ALPHA.EQ.ZERO ) ) $ RETURN * * Set up the start points in X and Y if the increments are not both * unity. * IF( ( INCX.NE.1 ).OR.( INCY.NE.1 ) )THEN IF( INCX.GT.0 )THEN KX = 1 ELSE KX = 1 - ( N - 1 )*INCX END IF IF( INCY.GT.0 )THEN KY = 1 ELSE KY = 1 - ( N - 1 )*INCY END IF JX = KX JY = KY END IF * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through the triangular part * of A. * IF( LSAME( UPLO, 'U' ) )THEN * * Form A when A is stored in the upper triangle. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 20, J = 1, N IF( ( X( J ).NE.ZERO ).OR.( Y( J ).NE.ZERO ) )THEN TEMP1 = ALPHA*CONJG( Y( J ) ) TEMP2 = CONJG( ALPHA*X( J ) ) DO 10, I = 1, J - 1 A( I, J ) = A( I, J ) + X( I )*TEMP1 + Y( I )*TEMP2 10 CONTINUE A( J, J ) = REAL( A( J, J ) ) + $ REAL( X( J )*TEMP1 + Y( J )*TEMP2 ) ELSE A( J, J ) = REAL( A( J, J ) ) END IF 20 CONTINUE ELSE DO 40, J = 1, N IF( ( X( JX ).NE.ZERO ).OR.( Y( JY ).NE.ZERO ) )THEN TEMP1 = ALPHA*CONJG( Y( JY ) ) TEMP2 = CONJG( ALPHA*X( JX ) ) IX = KX IY = KY DO 30, I = 1, J - 1 A( I, J ) = A( I, J ) + X( IX )*TEMP1 $ + Y( IY )*TEMP2 IX = IX + INCX IY = IY + INCY 30 CONTINUE A( J, J ) = REAL( A( J, J ) ) + $ REAL( X( JX )*TEMP1 + Y( JY )*TEMP2 ) ELSE A( J, J ) = REAL( A( J, J ) ) END IF JX = JX + INCX JY = JY + INCY 40 CONTINUE END IF ELSE * * Form A when A is stored in the lower triangle. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 60, J = 1, N IF( ( X( J ).NE.ZERO ).OR.( Y( J ).NE.ZERO ) )THEN TEMP1 = ALPHA*CONJG( Y( J ) ) TEMP2 = CONJG( ALPHA*X( J ) ) A( J, J ) = REAL( A( J, J ) ) + $ REAL( X( J )*TEMP1 + Y( J )*TEMP2 ) DO 50, I = J + 1, N A( I, J ) = A( I, J ) + X( I )*TEMP1 + Y( I )*TEMP2 50 CONTINUE ELSE A( J, J ) = REAL( A( J, J ) ) END IF 60 CONTINUE ELSE DO 80, J = 1, N IF( ( X( JX ).NE.ZERO ).OR.( Y( JY ).NE.ZERO ) )THEN TEMP1 = ALPHA*CONJG( Y( JY ) ) TEMP2 = CONJG( ALPHA*X( JX ) ) A( J, J ) = REAL( A( J, J ) ) + $ REAL( X( JX )*TEMP1 + Y( JY )*TEMP2 ) IX = JX IY = JY DO 70, I = J + 1, N IX = IX + INCX IY = IY + INCY A( I, J ) = A( I, J ) + X( IX )*TEMP1 $ + Y( IY )*TEMP2 70 CONTINUE ELSE A( J, J ) = REAL( A( J, J ) ) END IF JX = JX + INCX JY = JY + INCY 80 CONTINUE END IF END IF * RETURN * * End of CHER2 . * END * ************************************************************************ * SUBROUTINE CHPR2 ( UPLO, N, ALPHA, X, INCX, Y, INCY, AP ) * .. Scalar Arguments .. COMPLEX ALPHA INTEGER INCX, INCY, N CHARACTER*1 UPLO * .. Array Arguments .. COMPLEX AP( * ), X( * ), Y( * ) * .. * * Purpose * ======= * * CHPR2 performs the hermitian rank 2 operation * * A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A, * * where alpha is a scalar, x and y are n element vectors and A is an * n by n hermitian matrix, supplied in packed form. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the upper or lower * triangular part of the matrix A is supplied in the packed * array AP as follows: * * UPLO = 'U' or 'u' The upper triangular part of A is * supplied in AP. * * UPLO = 'L' or 'l' The lower triangular part of A is * supplied in AP. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * ALPHA - COMPLEX . * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * X - COMPLEX array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element vector x. * Unchanged on exit. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * Y - COMPLEX array of dimension at least * ( 1 + ( n - 1 )*abs( INCY ) ). * Before entry, the incremented array Y must contain the n * element vector y. * Unchanged on exit. * * INCY - INTEGER. * On entry, INCY specifies the increment for the elements of * Y. INCY must not be zero. * Unchanged on exit. * * AP - COMPLEX array of DIMENSION at least * ( ( n*( n + 1 ) )/2 ). * Before entry with UPLO = 'U' or 'u', the array AP must * contain the upper triangular part of the hermitian matrix * packed sequentially, column by column, so that AP( 1 ) * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) * and a( 2, 2 ) respectively, and so on. On exit, the array * AP is overwritten by the upper triangular part of the * updated matrix. * Before entry with UPLO = 'L' or 'l', the array AP must * contain the lower triangular part of the hermitian matrix * packed sequentially, column by column, so that AP( 1 ) * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) * and a( 3, 1 ) respectively, and so on. On exit, the array * AP is overwritten by the lower triangular part of the * updated matrix. * Note that the imaginary parts of the diagonal elements need * not be set, they are assumed to be zero, and on exit they * are set to zero. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. COMPLEX ZERO PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) ) * .. Local Scalars .. COMPLEX TEMP1, TEMP2 INTEGER I, INFO, IX, IY, J, JX, JY, K, KK, KX, KY * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC CONJG, REAL * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO, 'U' ).AND. $ .NOT.LSAME( UPLO, 'L' ) )THEN INFO = 1 ELSE IF( N.LT.0 )THEN INFO = 2 ELSE IF( INCX.EQ.0 )THEN INFO = 5 ELSE IF( INCY.EQ.0 )THEN INFO = 7 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'CHPR2 ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( N.EQ.0 ).OR.( ALPHA.EQ.ZERO ) ) $ RETURN * * Set up the start points in X and Y if the increments are not both * unity. * IF( ( INCX.NE.1 ).OR.( INCY.NE.1 ) )THEN IF( INCX.GT.0 )THEN KX = 1 ELSE KX = 1 - ( N - 1 )*INCX END IF IF( INCY.GT.0 )THEN KY = 1 ELSE KY = 1 - ( N - 1 )*INCY END IF JX = KX JY = KY END IF * * Start the operations. In this version the elements of the array AP * are accessed sequentially with one pass through AP. * KK = 1 IF( LSAME( UPLO, 'U' ) )THEN * * Form A when upper triangle is stored in AP. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 20, J = 1, N IF( ( X( J ).NE.ZERO ).OR.( Y( J ).NE.ZERO ) )THEN TEMP1 = ALPHA*CONJG( Y( J ) ) TEMP2 = CONJG( ALPHA*X( J ) ) K = KK DO 10, I = 1, J - 1 AP( K ) = AP( K ) + X( I )*TEMP1 + Y( I )*TEMP2 K = K + 1 10 CONTINUE AP( KK + J - 1 ) = REAL( AP( KK + J - 1 ) ) + $ REAL( X( J )*TEMP1 + Y( J )*TEMP2 ) ELSE AP( KK + J - 1 ) = REAL( AP( KK + J - 1 ) ) END IF KK = KK + J 20 CONTINUE ELSE DO 40, J = 1, N IF( ( X( JX ).NE.ZERO ).OR.( Y( JY ).NE.ZERO ) )THEN TEMP1 = ALPHA*CONJG( Y( JY ) ) TEMP2 = CONJG( ALPHA*X( JX ) ) IX = KX IY = KY DO 30, K = KK, KK + J - 2 AP( K ) = AP( K ) + X( IX )*TEMP1 + Y( IY )*TEMP2 IX = IX + INCX IY = IY + INCY 30 CONTINUE AP( KK + J - 1 ) = REAL( AP( KK + J - 1 ) ) + $ REAL( X( JX )*TEMP1 + $ Y( JY )*TEMP2 ) ELSE AP( KK + J - 1 ) = REAL( AP( KK + J - 1 ) ) END IF JX = JX + INCX JY = JY + INCY KK = KK + J 40 CONTINUE END IF ELSE * * Form A when lower triangle is stored in AP. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 60, J = 1, N IF( ( X( J ).NE.ZERO ).OR.( Y( J ).NE.ZERO ) )THEN TEMP1 = ALPHA*CONJG( Y( J ) ) TEMP2 = CONJG( ALPHA*X( J ) ) AP( KK ) = REAL( AP( KK ) ) + $ REAL( X( J )*TEMP1 + Y( J )*TEMP2 ) K = KK + 1 DO 50, I = J + 1, N AP( K ) = AP( K ) + X( I )*TEMP1 + Y( I )*TEMP2 K = K + 1 50 CONTINUE ELSE AP( KK ) = REAL( AP( KK ) ) END IF KK = KK + N - J + 1 60 CONTINUE ELSE DO 80, J = 1, N IF( ( X( JX ).NE.ZERO ).OR.( Y( JY ).NE.ZERO ) )THEN TEMP1 = ALPHA*CONJG( Y( JY ) ) TEMP2 = CONJG( ALPHA*X( JX ) ) AP( KK ) = REAL( AP( KK ) ) + $ REAL( X( JX )*TEMP1 + Y( JY )*TEMP2 ) IX = JX IY = JY DO 70, K = KK + 1, KK + N - J IX = IX + INCX IY = IY + INCY AP( K ) = AP( K ) + X( IX )*TEMP1 + Y( IY )*TEMP2 70 CONTINUE ELSE AP( KK ) = REAL( AP( KK ) ) END IF JX = JX + INCX JY = JY + INCY KK = KK + N - J + 1 80 CONTINUE END IF END IF * RETURN * * End of CHPR2 . * END LOGICAL FUNCTION LSAME ( CA, CB ) * .. Scalar Arguments .. CHARACTER*1 CA, CB * .. * * Purpose * ======= * * LSAME tests if CA is the same letter as CB regardless of case. * CB is assumed to be an upper case letter. LSAME returns .TRUE. if * CA is either the same as CB or the equivalent lower case letter. * * N.B. This version of the routine is only correct for ASCII code. * Installers must modify the routine for other character-codes. * * For EBCDIC systems the constant IOFF must be changed to -64. * For CDC systems using 6-12 bit representations, the system- * specific code in comments must be activated. * * Parameters * ========== * * CA - CHARACTER*1 * CB - CHARACTER*1 * On entry, CA and CB specify characters to be compared. * Unchanged on exit. * * * Auxiliary routine for Level 2 Blas. * * -- Written on 20-July-1986 * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, Nag Central Office. * * .. Parameters .. INTEGER IOFF PARAMETER ( IOFF=32 ) * .. Intrinsic Functions .. INTRINSIC ICHAR * .. Executable Statements .. * * Test if the characters are equal * LSAME = CA .EQ. CB * * Now test for equivalence * IF ( .NOT.LSAME ) THEN LSAME = ICHAR(CA) - IOFF .EQ. ICHAR(CB) END IF * RETURN * * The following comments contain code for CDC systems using 6-12 bit * representations. * * .. Parameters .. * INTEGER ICIRFX * PARAMETER ( ICIRFX=62 ) * .. Scalar Arguments .. * CHARACTER*1 CB * .. Array Arguments .. * CHARACTER*1 CA(*) * .. Local Scalars .. * INTEGER IVAL * .. Intrinsic Functions .. * INTRINSIC ICHAR, CHAR * .. Executable Statements .. * * See if the first character in string CA equals string CB. * * LSAME = CA(1) .EQ. CB .AND. CA(1) .NE. CHAR(ICIRFX) * * IF (LSAME) RETURN * * The characters are not identical. Now check them for equivalence. * Look for the 'escape' character, circumflex, followed by the * letter. * * IVAL = ICHAR(CA(2)) * IF (IVAL.GE.ICHAR('A') .AND. IVAL.LE.ICHAR('Z')) THEN * LSAME = CA(1) .EQ. CHAR(ICIRFX) .AND. CA(2) .EQ. CB * END IF * * RETURN * * End of LSAME. * END SUBROUTINE XERBLA ( SRNAME, INFO ) * .. Scalar Arguments .. INTEGER INFO CHARACTER*6 SRNAME * .. * * Purpose * ======= * * XERBLA is an error handler for the Level 2 BLAS routines. * * It is called by the Level 2 BLAS routines if an input parameter is * invalid. * * Installers should consider modifying the STOP statement in order to * call system-specific exception-handling facilities. * * Parameters * ========== * * SRNAME - CHARACTER*6. * On entry, SRNAME specifies the name of the routine which * called XERBLA. * * INFO - INTEGER. * On entry, INFO specifies the position of the invalid * parameter in the parameter-list of the calling routine. * * * Auxiliary routine for Level 2 Blas. * * Written on 20-July-1986. * * .. Executable Statements .. * WRITE (*,99999) SRNAME, INFO * STOP * 99999 FORMAT ( ' ** On entry to ', A6, ' parameter number ', I2, $ ' had an illegal value' ) * * End of XERBLA. * END * ************************************************************************ * * File of the DOUBLE PRECISION Level-2 BLAS. * =========================================== * * SUBROUTINE DGEMV ( TRANS, M, N, ALPHA, A, LDA, X, INCX, * $ BETA, Y, INCY ) * * SUBROUTINE DGBMV ( TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX, * $ BETA, Y, INCY ) * * SUBROUTINE DSYMV ( UPLO, N, ALPHA, A, LDA, X, INCX, * $ BETA, Y, INCY ) * * SUBROUTINE DSBMV ( UPLO, N, K, ALPHA, A, LDA, X, INCX, * $ BETA, Y, INCY ) * * SUBROUTINE DSPMV ( UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY ) * * SUBROUTINE DTRMV ( UPLO, TRANS, DIAG, N, A, LDA, X, INCX ) * * SUBROUTINE DTBMV ( UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX ) * * SUBROUTINE DTPMV ( UPLO, TRANS, DIAG, N, AP, X, INCX ) * * SUBROUTINE DTRSV ( UPLO, TRANS, DIAG, N, A, LDA, X, INCX ) * * SUBROUTINE DTBSV ( UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX ) * * SUBROUTINE DTPSV ( UPLO, TRANS, DIAG, N, AP, X, INCX ) * * SUBROUTINE DGER ( M, N, ALPHA, X, INCX, Y, INCY, A, LDA ) * * SUBROUTINE DSYR ( UPLO, N, ALPHA, X, INCX, A, LDA ) * * SUBROUTINE DSPR ( UPLO, N, ALPHA, X, INCX, AP ) * * SUBROUTINE DSYR2 ( UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA ) * * SUBROUTINE DSPR2 ( UPLO, N, ALPHA, X, INCX, Y, INCY, AP ) * * See: * * Dongarra J. J., Du Croz J. J., Hammarling S. and Hanson R. J.. * An extended set of Fortran Basic Linear Algebra Subprograms. * * Technical Memoranda Nos. 41 (revision 3) and 81, Mathematics * and Computer Science Division, Argonne National Laboratory, * 9700 South Cass Avenue, Argonne, Illinois 60439, US. * * Or * * NAG Technical Reports TR3/87 and TR4/87, Numerical Algorithms * Group Ltd., NAG Central Office, 256 Banbury Road, Oxford * OX2 7DE, UK, and Numerical Algorithms Group Inc., 1101 31st * Street, Suite 100, Downers Grove, Illinois 60515-1263, USA. * ************************************************************************ * SUBROUTINE DGEMV ( TRANS, M, N, ALPHA, A, LDA, X, INCX, $ BETA, Y, INCY ) * .. Scalar Arguments .. DOUBLE PRECISION ALPHA, BETA INTEGER INCX, INCY, LDA, M, N CHARACTER*1 TRANS * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), X( * ), Y( * ) * .. * * Purpose * ======= * * DGEMV performs one of the matrix-vector operations * * y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, * * where alpha and beta are scalars, x and y are vectors and A is an * m by n matrix. * * Parameters * ========== * * TRANS - CHARACTER*1. * On entry, TRANS specifies the operation to be performed as * follows: * * TRANS = 'N' or 'n' y := alpha*A*x + beta*y. * * TRANS = 'T' or 't' y := alpha*A'*x + beta*y. * * TRANS = 'C' or 'c' y := alpha*A'*x + beta*y. * * Unchanged on exit. * * M - INTEGER. * On entry, M specifies the number of rows of the matrix A. * M must be at least zero. * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the number of columns of the matrix A. * N must be at least zero. * Unchanged on exit. * * ALPHA - DOUBLE PRECISION. * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). * Before entry, the leading m by n part of the array A must * contain the matrix of coefficients. * Unchanged on exit. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * max( 1, m ). * Unchanged on exit. * * X - DOUBLE PRECISION array of DIMENSION at least * ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' * and at least * ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. * Before entry, the incremented array X must contain the * vector x. * Unchanged on exit. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * BETA - DOUBLE PRECISION. * On entry, BETA specifies the scalar beta. When BETA is * supplied as zero then Y need not be set on input. * Unchanged on exit. * * Y - DOUBLE PRECISION array of DIMENSION at least * ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' * and at least * ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. * Before entry with BETA non-zero, the incremented array Y * must contain the vector y. On exit, Y is overwritten by the * updated vector y. * * INCY - INTEGER. * On entry, INCY specifies the increment for the elements of * Y. INCY must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. DOUBLE PRECISION ONE , ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. Local Scalars .. DOUBLE PRECISION TEMP INTEGER I, INFO, IX, IY, J, JX, JY, KX, KY, LENX, LENY * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( TRANS, 'N' ).AND. $ .NOT.LSAME( TRANS, 'T' ).AND. $ .NOT.LSAME( TRANS, 'C' ) )THEN INFO = 1 ELSE IF( M.LT.0 )THEN INFO = 2 ELSE IF( N.LT.0 )THEN INFO = 3 ELSE IF( LDA.LT.MAX( 1, M ) )THEN INFO = 6 ELSE IF( INCX.EQ.0 )THEN INFO = 8 ELSE IF( INCY.EQ.0 )THEN INFO = 11 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'DGEMV ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( M.EQ.0 ).OR.( N.EQ.0 ).OR. $ ( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) ) $ RETURN * * Set LENX and LENY, the lengths of the vectors x and y, and set * up the start points in X and Y. * IF( LSAME( TRANS, 'N' ) )THEN LENX = N LENY = M ELSE LENX = M LENY = N END IF IF( INCX.GT.0 )THEN KX = 1 ELSE KX = 1 - ( LENX - 1 )*INCX END IF IF( INCY.GT.0 )THEN KY = 1 ELSE KY = 1 - ( LENY - 1 )*INCY END IF * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through A. * * First form y := beta*y. * IF( BETA.NE.ONE )THEN IF( INCY.EQ.1 )THEN IF( BETA.EQ.ZERO )THEN DO 10, I = 1, LENY Y( I ) = ZERO 10 CONTINUE ELSE DO 20, I = 1, LENY Y( I ) = BETA*Y( I ) 20 CONTINUE END IF ELSE IY = KY IF( BETA.EQ.ZERO )THEN DO 30, I = 1, LENY Y( IY ) = ZERO IY = IY + INCY 30 CONTINUE ELSE DO 40, I = 1, LENY Y( IY ) = BETA*Y( IY ) IY = IY + INCY 40 CONTINUE END IF END IF END IF IF( ALPHA.EQ.ZERO ) $ RETURN IF( LSAME( TRANS, 'N' ) )THEN * * Form y := alpha*A*x + y. * JX = KX IF( INCY.EQ.1 )THEN DO 60, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = ALPHA*X( JX ) DO 50, I = 1, M Y( I ) = Y( I ) + TEMP*A( I, J ) 50 CONTINUE END IF JX = JX + INCX 60 CONTINUE ELSE DO 80, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = ALPHA*X( JX ) IY = KY DO 70, I = 1, M Y( IY ) = Y( IY ) + TEMP*A( I, J ) IY = IY + INCY 70 CONTINUE END IF JX = JX + INCX 80 CONTINUE END IF ELSE * * Form y := alpha*A'*x + y. * JY = KY IF( INCX.EQ.1 )THEN DO 100, J = 1, N TEMP = ZERO DO 90, I = 1, M TEMP = TEMP + A( I, J )*X( I ) 90 CONTINUE Y( JY ) = Y( JY ) + ALPHA*TEMP JY = JY + INCY 100 CONTINUE ELSE DO 120, J = 1, N TEMP = ZERO IX = KX DO 110, I = 1, M TEMP = TEMP + A( I, J )*X( IX ) IX = IX + INCX 110 CONTINUE Y( JY ) = Y( JY ) + ALPHA*TEMP JY = JY + INCY 120 CONTINUE END IF END IF * RETURN * * End of DGEMV . * END * ************************************************************************ * SUBROUTINE DGBMV ( TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX, $ BETA, Y, INCY ) * .. Scalar Arguments .. DOUBLE PRECISION ALPHA, BETA INTEGER INCX, INCY, KL, KU, LDA, M, N CHARACTER*1 TRANS * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), X( * ), Y( * ) * .. * * Purpose * ======= * * DGBMV performs one of the matrix-vector operations * * y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, * * where alpha and beta are scalars, x and y are vectors and A is an * m by n band matrix, with kl sub-diagonals and ku super-diagonals. * * Parameters * ========== * * TRANS - CHARACTER*1. * On entry, TRANS specifies the operation to be performed as * follows: * * TRANS = 'N' or 'n' y := alpha*A*x + beta*y. * * TRANS = 'T' or 't' y := alpha*A'*x + beta*y. * * TRANS = 'C' or 'c' y := alpha*A'*x + beta*y. * * Unchanged on exit. * * M - INTEGER. * On entry, M specifies the number of rows of the matrix A. * M must be at least zero. * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the number of columns of the matrix A. * N must be at least zero. * Unchanged on exit. * * KL - INTEGER. * On entry, KL specifies the number of sub-diagonals of the * matrix A. KL must satisfy 0 .le. KL. * Unchanged on exit. * * KU - INTEGER. * On entry, KU specifies the number of super-diagonals of the * matrix A. KU must satisfy 0 .le. KU. * Unchanged on exit. * * ALPHA - DOUBLE PRECISION. * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). * Before entry, the leading ( kl + ku + 1 ) by n part of the * array A must contain the matrix of coefficients, supplied * column by column, with the leading diagonal of the matrix in * row ( ku + 1 ) of the array, the first super-diagonal * starting at position 2 in row ku, the first sub-diagonal * starting at position 1 in row ( ku + 2 ), and so on. * Elements in the array A that do not correspond to elements * in the band matrix (such as the top left ku by ku triangle) * are not referenced. * The following program segment will transfer a band matrix * from conventional full matrix storage to band storage: * * DO 20, J = 1, N * K = KU + 1 - J * DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL ) * A( K + I, J ) = matrix( I, J ) * 10 CONTINUE * 20 CONTINUE * * Unchanged on exit. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * ( kl + ku + 1 ). * Unchanged on exit. * * X - DOUBLE PRECISION array of DIMENSION at least * ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' * and at least * ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. * Before entry, the incremented array X must contain the * vector x. * Unchanged on exit. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * BETA - DOUBLE PRECISION. * On entry, BETA specifies the scalar beta. When BETA is * supplied as zero then Y need not be set on input. * Unchanged on exit. * * Y - DOUBLE PRECISION array of DIMENSION at least * ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' * and at least * ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. * Before entry, the incremented array Y must contain the * vector y. On exit, Y is overwritten by the updated vector y. * * INCY - INTEGER. * On entry, INCY specifies the increment for the elements of * Y. INCY must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * .. Parameters .. DOUBLE PRECISION ONE , ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. Local Scalars .. DOUBLE PRECISION TEMP INTEGER I, INFO, IX, IY, J, JX, JY, K, KUP1, KX, KY, $ LENX, LENY * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( TRANS, 'N' ).AND. $ .NOT.LSAME( TRANS, 'T' ).AND. $ .NOT.LSAME( TRANS, 'C' ) )THEN INFO = 1 ELSE IF( M.LT.0 )THEN INFO = 2 ELSE IF( N.LT.0 )THEN INFO = 3 ELSE IF( KL.LT.0 )THEN INFO = 4 ELSE IF( KU.LT.0 )THEN INFO = 5 ELSE IF( LDA.LT.( KL + KU + 1 ) )THEN INFO = 8 ELSE IF( INCX.EQ.0 )THEN INFO = 10 ELSE IF( INCY.EQ.0 )THEN INFO = 13 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'DGBMV ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( M.EQ.0 ).OR.( N.EQ.0 ).OR. $ ( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) ) $ RETURN * * Set LENX and LENY, the lengths of the vectors x and y, and set * up the start points in X and Y. * IF( LSAME( TRANS, 'N' ) )THEN LENX = N LENY = M ELSE LENX = M LENY = N END IF IF( INCX.GT.0 )THEN KX = 1 ELSE KX = 1 - ( LENX - 1 )*INCX END IF IF( INCY.GT.0 )THEN KY = 1 ELSE KY = 1 - ( LENY - 1 )*INCY END IF * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through the band part of A. * * First form y := beta*y. * IF( BETA.NE.ONE )THEN IF( INCY.EQ.1 )THEN IF( BETA.EQ.ZERO )THEN DO 10, I = 1, LENY Y( I ) = ZERO 10 CONTINUE ELSE DO 20, I = 1, LENY Y( I ) = BETA*Y( I ) 20 CONTINUE END IF ELSE IY = KY IF( BETA.EQ.ZERO )THEN DO 30, I = 1, LENY Y( IY ) = ZERO IY = IY + INCY 30 CONTINUE ELSE DO 40, I = 1, LENY Y( IY ) = BETA*Y( IY ) IY = IY + INCY 40 CONTINUE END IF END IF END IF IF( ALPHA.EQ.ZERO ) $ RETURN KUP1 = KU + 1 IF( LSAME( TRANS, 'N' ) )THEN * * Form y := alpha*A*x + y. * JX = KX IF( INCY.EQ.1 )THEN DO 60, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = ALPHA*X( JX ) K = KUP1 - J DO 50, I = MAX( 1, J - KU ), MIN( M, J + KL ) Y( I ) = Y( I ) + TEMP*A( K + I, J ) 50 CONTINUE END IF JX = JX + INCX 60 CONTINUE ELSE DO 80, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = ALPHA*X( JX ) IY = KY K = KUP1 - J DO 70, I = MAX( 1, J - KU ), MIN( M, J + KL ) Y( IY ) = Y( IY ) + TEMP*A( K + I, J ) IY = IY + INCY 70 CONTINUE END IF JX = JX + INCX IF( J.GT.KU ) $ KY = KY + INCY 80 CONTINUE END IF ELSE * * Form y := alpha*A'*x + y. * JY = KY IF( INCX.EQ.1 )THEN DO 100, J = 1, N TEMP = ZERO K = KUP1 - J DO 90, I = MAX( 1, J - KU ), MIN( M, J + KL ) TEMP = TEMP + A( K + I, J )*X( I ) 90 CONTINUE Y( JY ) = Y( JY ) + ALPHA*TEMP JY = JY + INCY 100 CONTINUE ELSE DO 120, J = 1, N TEMP = ZERO IX = KX K = KUP1 - J DO 110, I = MAX( 1, J - KU ), MIN( M, J + KL ) TEMP = TEMP + A( K + I, J )*X( IX ) IX = IX + INCX 110 CONTINUE Y( JY ) = Y( JY ) + ALPHA*TEMP JY = JY + INCY IF( J.GT.KU ) $ KX = KX + INCX 120 CONTINUE END IF END IF * RETURN * * End of DGBMV . * END * ************************************************************************ * SUBROUTINE DSYMV ( UPLO, N, ALPHA, A, LDA, X, INCX, $ BETA, Y, INCY ) * .. Scalar Arguments .. DOUBLE PRECISION ALPHA, BETA INTEGER INCX, INCY, LDA, N CHARACTER*1 UPLO * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), X( * ), Y( * ) * .. * * Purpose * ======= * * DSYMV performs the matrix-vector operation * * y := alpha*A*x + beta*y, * * where alpha and beta are scalars, x and y are n element vectors and * A is an n by n symmetric matrix. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the upper or lower * triangular part of the array A is to be referenced as * follows: * * UPLO = 'U' or 'u' Only the upper triangular part of A * is to be referenced. * * UPLO = 'L' or 'l' Only the lower triangular part of A * is to be referenced. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * ALPHA - DOUBLE PRECISION. * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). * Before entry with UPLO = 'U' or 'u', the leading n by n * upper triangular part of the array A must contain the upper * triangular part of the symmetric matrix and the strictly * lower triangular part of A is not referenced. * Before entry with UPLO = 'L' or 'l', the leading n by n * lower triangular part of the array A must contain the lower * triangular part of the symmetric matrix and the strictly * upper triangular part of A is not referenced. * Unchanged on exit. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * max( 1, n ). * Unchanged on exit. * * X - DOUBLE PRECISION array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element vector x. * Unchanged on exit. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * BETA - DOUBLE PRECISION. * On entry, BETA specifies the scalar beta. When BETA is * supplied as zero then Y need not be set on input. * Unchanged on exit. * * Y - DOUBLE PRECISION array of dimension at least * ( 1 + ( n - 1 )*abs( INCY ) ). * Before entry, the incremented array Y must contain the n * element vector y. On exit, Y is overwritten by the updated * vector y. * * INCY - INTEGER. * On entry, INCY specifies the increment for the elements of * Y. INCY must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. DOUBLE PRECISION ONE , ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. Local Scalars .. DOUBLE PRECISION TEMP1, TEMP2 INTEGER I, INFO, IX, IY, J, JX, JY, KX, KY * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO, 'U' ).AND. $ .NOT.LSAME( UPLO, 'L' ) )THEN INFO = 1 ELSE IF( N.LT.0 )THEN INFO = 2 ELSE IF( LDA.LT.MAX( 1, N ) )THEN INFO = 5 ELSE IF( INCX.EQ.0 )THEN INFO = 7 ELSE IF( INCY.EQ.0 )THEN INFO = 10 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'DSYMV ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( N.EQ.0 ).OR.( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) ) $ RETURN * * Set up the start points in X and Y. * IF( INCX.GT.0 )THEN KX = 1 ELSE KX = 1 - ( N - 1 )*INCX END IF IF( INCY.GT.0 )THEN KY = 1 ELSE KY = 1 - ( N - 1 )*INCY END IF * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through the triangular part * of A. * * First form y := beta*y. * IF( BETA.NE.ONE )THEN IF( INCY.EQ.1 )THEN IF( BETA.EQ.ZERO )THEN DO 10, I = 1, N Y( I ) = ZERO 10 CONTINUE ELSE DO 20, I = 1, N Y( I ) = BETA*Y( I ) 20 CONTINUE END IF ELSE IY = KY IF( BETA.EQ.ZERO )THEN DO 30, I = 1, N Y( IY ) = ZERO IY = IY + INCY 30 CONTINUE ELSE DO 40, I = 1, N Y( IY ) = BETA*Y( IY ) IY = IY + INCY 40 CONTINUE END IF END IF END IF IF( ALPHA.EQ.ZERO ) $ RETURN IF( LSAME( UPLO, 'U' ) )THEN * * Form y when A is stored in upper triangle. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 60, J = 1, N TEMP1 = ALPHA*X( J ) TEMP2 = ZERO DO 50, I = 1, J - 1 Y( I ) = Y( I ) + TEMP1*A( I, J ) TEMP2 = TEMP2 + A( I, J )*X( I ) 50 CONTINUE Y( J ) = Y( J ) + TEMP1*A( J, J ) + ALPHA*TEMP2 60 CONTINUE ELSE JX = KX JY = KY DO 80, J = 1, N TEMP1 = ALPHA*X( JX ) TEMP2 = ZERO IX = KX IY = KY DO 70, I = 1, J - 1 Y( IY ) = Y( IY ) + TEMP1*A( I, J ) TEMP2 = TEMP2 + A( I, J )*X( IX ) IX = IX + INCX IY = IY + INCY 70 CONTINUE Y( JY ) = Y( JY ) + TEMP1*A( J, J ) + ALPHA*TEMP2 JX = JX + INCX JY = JY + INCY 80 CONTINUE END IF ELSE * * Form y when A is stored in lower triangle. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 100, J = 1, N TEMP1 = ALPHA*X( J ) TEMP2 = ZERO Y( J ) = Y( J ) + TEMP1*A( J, J ) DO 90, I = J + 1, N Y( I ) = Y( I ) + TEMP1*A( I, J ) TEMP2 = TEMP2 + A( I, J )*X( I ) 90 CONTINUE Y( J ) = Y( J ) + ALPHA*TEMP2 100 CONTINUE ELSE JX = KX JY = KY DO 120, J = 1, N TEMP1 = ALPHA*X( JX ) TEMP2 = ZERO Y( JY ) = Y( JY ) + TEMP1*A( J, J ) IX = JX IY = JY DO 110, I = J + 1, N IX = IX + INCX IY = IY + INCY Y( IY ) = Y( IY ) + TEMP1*A( I, J ) TEMP2 = TEMP2 + A( I, J )*X( IX ) 110 CONTINUE Y( JY ) = Y( JY ) + ALPHA*TEMP2 JX = JX + INCX JY = JY + INCY 120 CONTINUE END IF END IF * RETURN * * End of DSYMV . * END * ************************************************************************ * SUBROUTINE DSBMV ( UPLO, N, K, ALPHA, A, LDA, X, INCX, $ BETA, Y, INCY ) * .. Scalar Arguments .. DOUBLE PRECISION ALPHA, BETA INTEGER INCX, INCY, K, LDA, N CHARACTER*1 UPLO * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), X( * ), Y( * ) * .. * * Purpose * ======= * * DSBMV performs the matrix-vector operation * * y := alpha*A*x + beta*y, * * where alpha and beta are scalars, x and y are n element vectors and * A is an n by n symmetric band matrix, with k super-diagonals. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the upper or lower * triangular part of the band matrix A is being supplied as * follows: * * UPLO = 'U' or 'u' The upper triangular part of A is * being supplied. * * UPLO = 'L' or 'l' The lower triangular part of A is * being supplied. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * K - INTEGER. * On entry, K specifies the number of super-diagonals of the * matrix A. K must satisfy 0 .le. K. * Unchanged on exit. * * ALPHA - DOUBLE PRECISION. * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). * Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) * by n part of the array A must contain the upper triangular * band part of the symmetric matrix, supplied column by * column, with the leading diagonal of the matrix in row * ( k + 1 ) of the array, the first super-diagonal starting at * position 2 in row k, and so on. The top left k by k triangle * of the array A is not referenced. * The following program segment will transfer the upper * triangular part of a symmetric band matrix from conventional * full matrix storage to band storage: * * DO 20, J = 1, N * M = K + 1 - J * DO 10, I = MAX( 1, J - K ), J * A( M + I, J ) = matrix( I, J ) * 10 CONTINUE * 20 CONTINUE * * Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) * by n part of the array A must contain the lower triangular * band part of the symmetric matrix, supplied column by * column, with the leading diagonal of the matrix in row 1 of * the array, the first sub-diagonal starting at position 1 in * row 2, and so on. The bottom right k by k triangle of the * array A is not referenced. * The following program segment will transfer the lower * triangular part of a symmetric band matrix from conventional * full matrix storage to band storage: * * DO 20, J = 1, N * M = 1 - J * DO 10, I = J, MIN( N, J + K ) * A( M + I, J ) = matrix( I, J ) * 10 CONTINUE * 20 CONTINUE * * Unchanged on exit. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * ( k + 1 ). * Unchanged on exit. * * X - DOUBLE PRECISION array of DIMENSION at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the * vector x. * Unchanged on exit. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * BETA - DOUBLE PRECISION. * On entry, BETA specifies the scalar beta. * Unchanged on exit. * * Y - DOUBLE PRECISION array of DIMENSION at least * ( 1 + ( n - 1 )*abs( INCY ) ). * Before entry, the incremented array Y must contain the * vector y. On exit, Y is overwritten by the updated vector y. * * INCY - INTEGER. * On entry, INCY specifies the increment for the elements of * Y. INCY must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. DOUBLE PRECISION ONE , ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. Local Scalars .. DOUBLE PRECISION TEMP1, TEMP2 INTEGER I, INFO, IX, IY, J, JX, JY, KPLUS1, KX, KY, L * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO, 'U' ).AND. $ .NOT.LSAME( UPLO, 'L' ) )THEN INFO = 1 ELSE IF( N.LT.0 )THEN INFO = 2 ELSE IF( K.LT.0 )THEN INFO = 3 ELSE IF( LDA.LT.( K + 1 ) )THEN INFO = 6 ELSE IF( INCX.EQ.0 )THEN INFO = 8 ELSE IF( INCY.EQ.0 )THEN INFO = 11 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'DSBMV ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( N.EQ.0 ).OR.( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) ) $ RETURN * * Set up the start points in X and Y. * IF( INCX.GT.0 )THEN KX = 1 ELSE KX = 1 - ( N - 1 )*INCX END IF IF( INCY.GT.0 )THEN KY = 1 ELSE KY = 1 - ( N - 1 )*INCY END IF * * Start the operations. In this version the elements of the array A * are accessed sequentially with one pass through A. * * First form y := beta*y. * IF( BETA.NE.ONE )THEN IF( INCY.EQ.1 )THEN IF( BETA.EQ.ZERO )THEN DO 10, I = 1, N Y( I ) = ZERO 10 CONTINUE ELSE DO 20, I = 1, N Y( I ) = BETA*Y( I ) 20 CONTINUE END IF ELSE IY = KY IF( BETA.EQ.ZERO )THEN DO 30, I = 1, N Y( IY ) = ZERO IY = IY + INCY 30 CONTINUE ELSE DO 40, I = 1, N Y( IY ) = BETA*Y( IY ) IY = IY + INCY 40 CONTINUE END IF END IF END IF IF( ALPHA.EQ.ZERO ) $ RETURN IF( LSAME( UPLO, 'U' ) )THEN * * Form y when upper triangle of A is stored. * KPLUS1 = K + 1 IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 60, J = 1, N TEMP1 = ALPHA*X( J ) TEMP2 = ZERO L = KPLUS1 - J DO 50, I = MAX( 1, J - K ), J - 1 Y( I ) = Y( I ) + TEMP1*A( L + I, J ) TEMP2 = TEMP2 + A( L + I, J )*X( I ) 50 CONTINUE Y( J ) = Y( J ) + TEMP1*A( KPLUS1, J ) + ALPHA*TEMP2 60 CONTINUE ELSE JX = KX JY = KY DO 80, J = 1, N TEMP1 = ALPHA*X( JX ) TEMP2 = ZERO IX = KX IY = KY L = KPLUS1 - J DO 70, I = MAX( 1, J - K ), J - 1 Y( IY ) = Y( IY ) + TEMP1*A( L + I, J ) TEMP2 = TEMP2 + A( L + I, J )*X( IX ) IX = IX + INCX IY = IY + INCY 70 CONTINUE Y( JY ) = Y( JY ) + TEMP1*A( KPLUS1, J ) + ALPHA*TEMP2 JX = JX + INCX JY = JY + INCY IF( J.GT.K )THEN KX = KX + INCX KY = KY + INCY END IF 80 CONTINUE END IF ELSE * * Form y when lower triangle of A is stored. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 100, J = 1, N TEMP1 = ALPHA*X( J ) TEMP2 = ZERO Y( J ) = Y( J ) + TEMP1*A( 1, J ) L = 1 - J DO 90, I = J + 1, MIN( N, J + K ) Y( I ) = Y( I ) + TEMP1*A( L + I, J ) TEMP2 = TEMP2 + A( L + I, J )*X( I ) 90 CONTINUE Y( J ) = Y( J ) + ALPHA*TEMP2 100 CONTINUE ELSE JX = KX JY = KY DO 120, J = 1, N TEMP1 = ALPHA*X( JX ) TEMP2 = ZERO Y( JY ) = Y( JY ) + TEMP1*A( 1, J ) L = 1 - J IX = JX IY = JY DO 110, I = J + 1, MIN( N, J + K ) IX = IX + INCX IY = IY + INCY Y( IY ) = Y( IY ) + TEMP1*A( L + I, J ) TEMP2 = TEMP2 + A( L + I, J )*X( IX ) 110 CONTINUE Y( JY ) = Y( JY ) + ALPHA*TEMP2 JX = JX + INCX JY = JY + INCY 120 CONTINUE END IF END IF * RETURN * * End of DSBMV . * END * ************************************************************************ * SUBROUTINE DSPMV ( UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY ) * .. Scalar Arguments .. DOUBLE PRECISION ALPHA, BETA INTEGER INCX, INCY, N CHARACTER*1 UPLO * .. Array Arguments .. DOUBLE PRECISION AP( * ), X( * ), Y( * ) * .. * * Purpose * ======= * * DSPMV performs the matrix-vector operation * * y := alpha*A*x + beta*y, * * where alpha and beta are scalars, x and y are n element vectors and * A is an n by n symmetric matrix, supplied in packed form. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the upper or lower * triangular part of the matrix A is supplied in the packed * array AP as follows: * * UPLO = 'U' or 'u' The upper triangular part of A is * supplied in AP. * * UPLO = 'L' or 'l' The lower triangular part of A is * supplied in AP. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * ALPHA - DOUBLE PRECISION. * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * AP - DOUBLE PRECISION array of DIMENSION at least * ( ( n*( n + 1 ) )/2 ). * Before entry with UPLO = 'U' or 'u', the array AP must * contain the upper triangular part of the symmetric matrix * packed sequentially, column by column, so that AP( 1 ) * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) * and a( 2, 2 ) respectively, and so on. * Before entry with UPLO = 'L' or 'l', the array AP must * contain the lower triangular part of the symmetric matrix * packed sequentially, column by column, so that AP( 1 ) * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) * and a( 3, 1 ) respectively, and so on. * Unchanged on exit. * * X - DOUBLE PRECISION array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element vector x. * Unchanged on exit. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * BETA - DOUBLE PRECISION. * On entry, BETA specifies the scalar beta. When BETA is * supplied as zero then Y need not be set on input. * Unchanged on exit. * * Y - DOUBLE PRECISION array of dimension at least * ( 1 + ( n - 1 )*abs( INCY ) ). * Before entry, the incremented array Y must contain the n * element vector y. On exit, Y is overwritten by the updated * vector y. * * INCY - INTEGER. * On entry, INCY specifies the increment for the elements of * Y. INCY must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. DOUBLE PRECISION ONE , ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. Local Scalars .. DOUBLE PRECISION TEMP1, TEMP2 INTEGER I, INFO, IX, IY, J, JX, JY, K, KK, KX, KY * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO, 'U' ).AND. $ .NOT.LSAME( UPLO, 'L' ) )THEN INFO = 1 ELSE IF( N.LT.0 )THEN INFO = 2 ELSE IF( INCX.EQ.0 )THEN INFO = 6 ELSE IF( INCY.EQ.0 )THEN INFO = 9 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'DSPMV ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( N.EQ.0 ).OR.( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) ) $ RETURN * * Set up the start points in X and Y. * IF( INCX.GT.0 )THEN KX = 1 ELSE KX = 1 - ( N - 1 )*INCX END IF IF( INCY.GT.0 )THEN KY = 1 ELSE KY = 1 - ( N - 1 )*INCY END IF * * Start the operations. In this version the elements of the array AP * are accessed sequentially with one pass through AP. * * First form y := beta*y. * IF( BETA.NE.ONE )THEN IF( INCY.EQ.1 )THEN IF( BETA.EQ.ZERO )THEN DO 10, I = 1, N Y( I ) = ZERO 10 CONTINUE ELSE DO 20, I = 1, N Y( I ) = BETA*Y( I ) 20 CONTINUE END IF ELSE IY = KY IF( BETA.EQ.ZERO )THEN DO 30, I = 1, N Y( IY ) = ZERO IY = IY + INCY 30 CONTINUE ELSE DO 40, I = 1, N Y( IY ) = BETA*Y( IY ) IY = IY + INCY 40 CONTINUE END IF END IF END IF IF( ALPHA.EQ.ZERO ) $ RETURN KK = 1 IF( LSAME( UPLO, 'U' ) )THEN * * Form y when AP contains the upper triangle. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 60, J = 1, N TEMP1 = ALPHA*X( J ) TEMP2 = ZERO K = KK DO 50, I = 1, J - 1 Y( I ) = Y( I ) + TEMP1*AP( K ) TEMP2 = TEMP2 + AP( K )*X( I ) K = K + 1 50 CONTINUE Y( J ) = Y( J ) + TEMP1*AP( KK + J - 1 ) + ALPHA*TEMP2 KK = KK + J 60 CONTINUE ELSE JX = KX JY = KY DO 80, J = 1, N TEMP1 = ALPHA*X( JX ) TEMP2 = ZERO IX = KX IY = KY DO 70, K = KK, KK + J - 2 Y( IY ) = Y( IY ) + TEMP1*AP( K ) TEMP2 = TEMP2 + AP( K )*X( IX ) IX = IX + INCX IY = IY + INCY 70 CONTINUE Y( JY ) = Y( JY ) + TEMP1*AP( KK + J - 1 ) + ALPHA*TEMP2 JX = JX + INCX JY = JY + INCY KK = KK + J 80 CONTINUE END IF ELSE * * Form y when AP contains the lower triangle. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 100, J = 1, N TEMP1 = ALPHA*X( J ) TEMP2 = ZERO Y( J ) = Y( J ) + TEMP1*AP( KK ) K = KK + 1 DO 90, I = J + 1, N Y( I ) = Y( I ) + TEMP1*AP( K ) TEMP2 = TEMP2 + AP( K )*X( I ) K = K + 1 90 CONTINUE Y( J ) = Y( J ) + ALPHA*TEMP2 KK = KK + ( N - J + 1 ) 100 CONTINUE ELSE JX = KX JY = KY DO 120, J = 1, N TEMP1 = ALPHA*X( JX ) TEMP2 = ZERO Y( JY ) = Y( JY ) + TEMP1*AP( KK ) IX = JX IY = JY DO 110, K = KK + 1, KK + N - J IX = IX + INCX IY = IY + INCY Y( IY ) = Y( IY ) + TEMP1*AP( K ) TEMP2 = TEMP2 + AP( K )*X( IX ) 110 CONTINUE Y( JY ) = Y( JY ) + ALPHA*TEMP2 JX = JX + INCX JY = JY + INCY KK = KK + ( N - J + 1 ) 120 CONTINUE END IF END IF * RETURN * * End of DSPMV . * END * ************************************************************************ * SUBROUTINE DTRMV ( UPLO, TRANS, DIAG, N, A, LDA, X, INCX ) * .. Scalar Arguments .. INTEGER INCX, LDA, N CHARACTER*1 DIAG, TRANS, UPLO * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), X( * ) * .. * * Purpose * ======= * * DTRMV performs one of the matrix-vector operations * * x := A*x, or x := A'*x, * * where x is an n element vector and A is an n by n unit, or non-unit, * upper or lower triangular matrix. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the matrix is an upper or * lower triangular matrix as follows: * * UPLO = 'U' or 'u' A is an upper triangular matrix. * * UPLO = 'L' or 'l' A is a lower triangular matrix. * * Unchanged on exit. * * TRANS - CHARACTER*1. * On entry, TRANS specifies the operation to be performed as * follows: * * TRANS = 'N' or 'n' x := A*x. * * TRANS = 'T' or 't' x := A'*x. * * TRANS = 'C' or 'c' x := A'*x. * * Unchanged on exit. * * DIAG - CHARACTER*1. * On entry, DIAG specifies whether or not A is unit * triangular as follows: * * DIAG = 'U' or 'u' A is assumed to be unit triangular. * * DIAG = 'N' or 'n' A is not assumed to be unit * triangular. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). * Before entry with UPLO = 'U' or 'u', the leading n by n * upper triangular part of the array A must contain the upper * triangular matrix and the strictly lower triangular part of * A is not referenced. * Before entry with UPLO = 'L' or 'l', the leading n by n * lower triangular part of the array A must contain the lower * triangular matrix and the strictly upper triangular part of * A is not referenced. * Note that when DIAG = 'U' or 'u', the diagonal elements of * A are not referenced either, but are assumed to be unity. * Unchanged on exit. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * max( 1, n ). * Unchanged on exit. * * X - DOUBLE PRECISION array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element vector x. On exit, X is overwritten with the * tranformed vector x. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D+0 ) * .. Local Scalars .. DOUBLE PRECISION TEMP INTEGER I, INFO, IX, J, JX, KX LOGICAL NOUNIT * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO , 'U' ).AND. $ .NOT.LSAME( UPLO , 'L' ) )THEN INFO = 1 ELSE IF( .NOT.LSAME( TRANS, 'N' ).AND. $ .NOT.LSAME( TRANS, 'T' ).AND. $ .NOT.LSAME( TRANS, 'C' ) )THEN INFO = 2 ELSE IF( .NOT.LSAME( DIAG , 'U' ).AND. $ .NOT.LSAME( DIAG , 'N' ) )THEN INFO = 3 ELSE IF( N.LT.0 )THEN INFO = 4 ELSE IF( LDA.LT.MAX( 1, N ) )THEN INFO = 6 ELSE IF( INCX.EQ.0 )THEN INFO = 8 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'DTRMV ', INFO ) RETURN END IF * * Quick return if possible. * IF( N.EQ.0 ) $ RETURN * NOUNIT = LSAME( DIAG, 'N' ) * * Set up the start point in X if the increment is not unity. This * will be ( N - 1 )*INCX too small for descending loops. * IF( INCX.LE.0 )THEN KX = 1 - ( N - 1 )*INCX ELSE IF( INCX.NE.1 )THEN KX = 1 END IF * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through A. * IF( LSAME( TRANS, 'N' ) )THEN * * Form x := A*x. * IF( LSAME( UPLO, 'U' ) )THEN IF( INCX.EQ.1 )THEN DO 20, J = 1, N IF( X( J ).NE.ZERO )THEN TEMP = X( J ) DO 10, I = 1, J - 1 X( I ) = X( I ) + TEMP*A( I, J ) 10 CONTINUE IF( NOUNIT ) $ X( J ) = X( J )*A( J, J ) END IF 20 CONTINUE ELSE JX = KX DO 40, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = X( JX ) IX = KX DO 30, I = 1, J - 1 X( IX ) = X( IX ) + TEMP*A( I, J ) IX = IX + INCX 30 CONTINUE IF( NOUNIT ) $ X( JX ) = X( JX )*A( J, J ) END IF JX = JX + INCX 40 CONTINUE END IF ELSE IF( INCX.EQ.1 )THEN DO 60, J = N, 1, -1 IF( X( J ).NE.ZERO )THEN TEMP = X( J ) DO 50, I = N, J + 1, -1 X( I ) = X( I ) + TEMP*A( I, J ) 50 CONTINUE IF( NOUNIT ) $ X( J ) = X( J )*A( J, J ) END IF 60 CONTINUE ELSE KX = KX + ( N - 1 )*INCX JX = KX DO 80, J = N, 1, -1 IF( X( JX ).NE.ZERO )THEN TEMP = X( JX ) IX = KX DO 70, I = N, J + 1, -1 X( IX ) = X( IX ) + TEMP*A( I, J ) IX = IX - INCX 70 CONTINUE IF( NOUNIT ) $ X( JX ) = X( JX )*A( J, J ) END IF JX = JX - INCX 80 CONTINUE END IF END IF ELSE * * Form x := A'*x. * IF( LSAME( UPLO, 'U' ) )THEN IF( INCX.EQ.1 )THEN DO 100, J = N, 1, -1 TEMP = X( J ) IF( NOUNIT ) $ TEMP = TEMP*A( J, J ) DO 90, I = J - 1, 1, -1 TEMP = TEMP + A( I, J )*X( I ) 90 CONTINUE X( J ) = TEMP 100 CONTINUE ELSE JX = KX + ( N - 1 )*INCX DO 120, J = N, 1, -1 TEMP = X( JX ) IX = JX IF( NOUNIT ) $ TEMP = TEMP*A( J, J ) DO 110, I = J - 1, 1, -1 IX = IX - INCX TEMP = TEMP + A( I, J )*X( IX ) 110 CONTINUE X( JX ) = TEMP JX = JX - INCX 120 CONTINUE END IF ELSE IF( INCX.EQ.1 )THEN DO 140, J = 1, N TEMP = X( J ) IF( NOUNIT ) $ TEMP = TEMP*A( J, J ) DO 130, I = J + 1, N TEMP = TEMP + A( I, J )*X( I ) 130 CONTINUE X( J ) = TEMP 140 CONTINUE ELSE JX = KX DO 160, J = 1, N TEMP = X( JX ) IX = JX IF( NOUNIT ) $ TEMP = TEMP*A( J, J ) DO 150, I = J + 1, N IX = IX + INCX TEMP = TEMP + A( I, J )*X( IX ) 150 CONTINUE X( JX ) = TEMP JX = JX + INCX 160 CONTINUE END IF END IF END IF * RETURN * * End of DTRMV . * END * ************************************************************************ * SUBROUTINE DTBMV ( UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX ) * .. Scalar Arguments .. INTEGER INCX, K, LDA, N CHARACTER*1 DIAG, TRANS, UPLO * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), X( * ) * .. * * Purpose * ======= * * DTBMV performs one of the matrix-vector operations * * x := A*x, or x := A'*x, * * where x is an n element vector and A is an n by n unit, or non-unit, * upper or lower triangular band matrix, with ( k + 1 ) diagonals. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the matrix is an upper or * lower triangular matrix as follows: * * UPLO = 'U' or 'u' A is an upper triangular matrix. * * UPLO = 'L' or 'l' A is a lower triangular matrix. * * Unchanged on exit. * * TRANS - CHARACTER*1. * On entry, TRANS specifies the operation to be performed as * follows: * * TRANS = 'N' or 'n' x := A*x. * * TRANS = 'T' or 't' x := A'*x. * * TRANS = 'C' or 'c' x := A'*x. * * Unchanged on exit. * * DIAG - CHARACTER*1. * On entry, DIAG specifies whether or not A is unit * triangular as follows: * * DIAG = 'U' or 'u' A is assumed to be unit triangular. * * DIAG = 'N' or 'n' A is not assumed to be unit * triangular. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * K - INTEGER. * On entry with UPLO = 'U' or 'u', K specifies the number of * super-diagonals of the matrix A. * On entry with UPLO = 'L' or 'l', K specifies the number of * sub-diagonals of the matrix A. * K must satisfy 0 .le. K. * Unchanged on exit. * * A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). * Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) * by n part of the array A must contain the upper triangular * band part of the matrix of coefficients, supplied column by * column, with the leading diagonal of the matrix in row * ( k + 1 ) of the array, the first super-diagonal starting at * position 2 in row k, and so on. The top left k by k triangle * of the array A is not referenced. * The following program segment will transfer an upper * triangular band matrix from conventional full matrix storage * to band storage: * * DO 20, J = 1, N * M = K + 1 - J * DO 10, I = MAX( 1, J - K ), J * A( M + I, J ) = matrix( I, J ) * 10 CONTINUE * 20 CONTINUE * * Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) * by n part of the array A must contain the lower triangular * band part of the matrix of coefficients, supplied column by * column, with the leading diagonal of the matrix in row 1 of * the array, the first sub-diagonal starting at position 1 in * row 2, and so on. The bottom right k by k triangle of the * array A is not referenced. * The following program segment will transfer a lower * triangular band matrix from conventional full matrix storage * to band storage: * * DO 20, J = 1, N * M = 1 - J * DO 10, I = J, MIN( N, J + K ) * A( M + I, J ) = matrix( I, J ) * 10 CONTINUE * 20 CONTINUE * * Note that when DIAG = 'U' or 'u' the elements of the array A * corresponding to the diagonal elements of the matrix are not * referenced, but are assumed to be unity. * Unchanged on exit. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * ( k + 1 ). * Unchanged on exit. * * X - DOUBLE PRECISION array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element vector x. On exit, X is overwritten with the * tranformed vector x. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D+0 ) * .. Local Scalars .. DOUBLE PRECISION TEMP INTEGER I, INFO, IX, J, JX, KPLUS1, KX, L LOGICAL NOUNIT * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO , 'U' ).AND. $ .NOT.LSAME( UPLO , 'L' ) )THEN INFO = 1 ELSE IF( .NOT.LSAME( TRANS, 'N' ).AND. $ .NOT.LSAME( TRANS, 'T' ).AND. $ .NOT.LSAME( TRANS, 'C' ) )THEN INFO = 2 ELSE IF( .NOT.LSAME( DIAG , 'U' ).AND. $ .NOT.LSAME( DIAG , 'N' ) )THEN INFO = 3 ELSE IF( N.LT.0 )THEN INFO = 4 ELSE IF( K.LT.0 )THEN INFO = 5 ELSE IF( LDA.LT.( K + 1 ) )THEN INFO = 7 ELSE IF( INCX.EQ.0 )THEN INFO = 9 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'DTBMV ', INFO ) RETURN END IF * * Quick return if possible. * IF( N.EQ.0 ) $ RETURN * NOUNIT = LSAME( DIAG, 'N' ) * * Set up the start point in X if the increment is not unity. This * will be ( N - 1 )*INCX too small for descending loops. * IF( INCX.LE.0 )THEN KX = 1 - ( N - 1 )*INCX ELSE IF( INCX.NE.1 )THEN KX = 1 END IF * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through A. * IF( LSAME( TRANS, 'N' ) )THEN * * Form x := A*x. * IF( LSAME( UPLO, 'U' ) )THEN KPLUS1 = K + 1 IF( INCX.EQ.1 )THEN DO 20, J = 1, N IF( X( J ).NE.ZERO )THEN TEMP = X( J ) L = KPLUS1 - J DO 10, I = MAX( 1, J - K ), J - 1 X( I ) = X( I ) + TEMP*A( L + I, J ) 10 CONTINUE IF( NOUNIT ) $ X( J ) = X( J )*A( KPLUS1, J ) END IF 20 CONTINUE ELSE JX = KX DO 40, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = X( JX ) IX = KX L = KPLUS1 - J DO 30, I = MAX( 1, J - K ), J - 1 X( IX ) = X( IX ) + TEMP*A( L + I, J ) IX = IX + INCX 30 CONTINUE IF( NOUNIT ) $ X( JX ) = X( JX )*A( KPLUS1, J ) END IF JX = JX + INCX IF( J.GT.K ) $ KX = KX + INCX 40 CONTINUE END IF ELSE IF( INCX.EQ.1 )THEN DO 60, J = N, 1, -1 IF( X( J ).NE.ZERO )THEN TEMP = X( J ) L = 1 - J DO 50, I = MIN( N, J + K ), J + 1, -1 X( I ) = X( I ) + TEMP*A( L + I, J ) 50 CONTINUE IF( NOUNIT ) $ X( J ) = X( J )*A( 1, J ) END IF 60 CONTINUE ELSE KX = KX + ( N - 1 )*INCX JX = KX DO 80, J = N, 1, -1 IF( X( JX ).NE.ZERO )THEN TEMP = X( JX ) IX = KX L = 1 - J DO 70, I = MIN( N, J + K ), J + 1, -1 X( IX ) = X( IX ) + TEMP*A( L + I, J ) IX = IX - INCX 70 CONTINUE IF( NOUNIT ) $ X( JX ) = X( JX )*A( 1, J ) END IF JX = JX - INCX IF( ( N - J ).GE.K ) $ KX = KX - INCX 80 CONTINUE END IF END IF ELSE * * Form x := A'*x. * IF( LSAME( UPLO, 'U' ) )THEN KPLUS1 = K + 1 IF( INCX.EQ.1 )THEN DO 100, J = N, 1, -1 TEMP = X( J ) L = KPLUS1 - J IF( NOUNIT ) $ TEMP = TEMP*A( KPLUS1, J ) DO 90, I = J - 1, MAX( 1, J - K ), -1 TEMP = TEMP + A( L + I, J )*X( I ) 90 CONTINUE X( J ) = TEMP 100 CONTINUE ELSE KX = KX + ( N - 1 )*INCX JX = KX DO 120, J = N, 1, -1 TEMP = X( JX ) KX = KX - INCX IX = KX L = KPLUS1 - J IF( NOUNIT ) $ TEMP = TEMP*A( KPLUS1, J ) DO 110, I = J - 1, MAX( 1, J - K ), -1 TEMP = TEMP + A( L + I, J )*X( IX ) IX = IX - INCX 110 CONTINUE X( JX ) = TEMP JX = JX - INCX 120 CONTINUE END IF ELSE IF( INCX.EQ.1 )THEN DO 140, J = 1, N TEMP = X( J ) L = 1 - J IF( NOUNIT ) $ TEMP = TEMP*A( 1, J ) DO 130, I = J + 1, MIN( N, J + K ) TEMP = TEMP + A( L + I, J )*X( I ) 130 CONTINUE X( J ) = TEMP 140 CONTINUE ELSE JX = KX DO 160, J = 1, N TEMP = X( JX ) KX = KX + INCX IX = KX L = 1 - J IF( NOUNIT ) $ TEMP = TEMP*A( 1, J ) DO 150, I = J + 1, MIN( N, J + K ) TEMP = TEMP + A( L + I, J )*X( IX ) IX = IX + INCX 150 CONTINUE X( JX ) = TEMP JX = JX + INCX 160 CONTINUE END IF END IF END IF * RETURN * * End of DTBMV . * END * ************************************************************************ * SUBROUTINE DTPMV ( UPLO, TRANS, DIAG, N, AP, X, INCX ) * .. Scalar Arguments .. INTEGER INCX, N CHARACTER*1 DIAG, TRANS, UPLO * .. Array Arguments .. DOUBLE PRECISION AP( * ), X( * ) * .. * * Purpose * ======= * * DTPMV performs one of the matrix-vector operations * * x := A*x, or x := A'*x, * * where x is an n element vector and A is an n by n unit, or non-unit, * upper or lower triangular matrix, supplied in packed form. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the matrix is an upper or * lower triangular matrix as follows: * * UPLO = 'U' or 'u' A is an upper triangular matrix. * * UPLO = 'L' or 'l' A is a lower triangular matrix. * * Unchanged on exit. * * TRANS - CHARACTER*1. * On entry, TRANS specifies the operation to be performed as * follows: * * TRANS = 'N' or 'n' x := A*x. * * TRANS = 'T' or 't' x := A'*x. * * TRANS = 'C' or 'c' x := A'*x. * * Unchanged on exit. * * DIAG - CHARACTER*1. * On entry, DIAG specifies whether or not A is unit * triangular as follows: * * DIAG = 'U' or 'u' A is assumed to be unit triangular. * * DIAG = 'N' or 'n' A is not assumed to be unit * triangular. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * AP - DOUBLE PRECISION array of DIMENSION at least * ( ( n*( n + 1 ) )/2 ). * Before entry with UPLO = 'U' or 'u', the array AP must * contain the upper triangular matrix packed sequentially, * column by column, so that AP( 1 ) contains a( 1, 1 ), * AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) * respectively, and so on. * Before entry with UPLO = 'L' or 'l', the array AP must * contain the lower triangular matrix packed sequentially, * column by column, so that AP( 1 ) contains a( 1, 1 ), * AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) * respectively, and so on. * Note that when DIAG = 'U' or 'u', the diagonal elements of * A are not referenced, but are assumed to be unity. * Unchanged on exit. * * X - DOUBLE PRECISION array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element vector x. On exit, X is overwritten with the * tranformed vector x. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D+0 ) * .. Local Scalars .. DOUBLE PRECISION TEMP INTEGER I, INFO, IX, J, JX, K, KK, KX LOGICAL NOUNIT * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO , 'U' ).AND. $ .NOT.LSAME( UPLO , 'L' ) )THEN INFO = 1 ELSE IF( .NOT.LSAME( TRANS, 'N' ).AND. $ .NOT.LSAME( TRANS, 'T' ).AND. $ .NOT.LSAME( TRANS, 'C' ) )THEN INFO = 2 ELSE IF( .NOT.LSAME( DIAG , 'U' ).AND. $ .NOT.LSAME( DIAG , 'N' ) )THEN INFO = 3 ELSE IF( N.LT.0 )THEN INFO = 4 ELSE IF( INCX.EQ.0 )THEN INFO = 7 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'DTPMV ', INFO ) RETURN END IF * * Quick return if possible. * IF( N.EQ.0 ) $ RETURN * NOUNIT = LSAME( DIAG, 'N' ) * * Set up the start point in X if the increment is not unity. This * will be ( N - 1 )*INCX too small for descending loops. * IF( INCX.LE.0 )THEN KX = 1 - ( N - 1 )*INCX ELSE IF( INCX.NE.1 )THEN KX = 1 END IF * * Start the operations. In this version the elements of AP are * accessed sequentially with one pass through AP. * IF( LSAME( TRANS, 'N' ) )THEN * * Form x:= A*x. * IF( LSAME( UPLO, 'U' ) )THEN KK =1 IF( INCX.EQ.1 )THEN DO 20, J = 1, N IF( X( J ).NE.ZERO )THEN TEMP = X( J ) K = KK DO 10, I = 1, J - 1 X( I ) = X( I ) + TEMP*AP( K ) K = K + 1 10 CONTINUE IF( NOUNIT ) $ X( J ) = X( J )*AP( KK + J - 1 ) END IF KK = KK + J 20 CONTINUE ELSE JX = KX DO 40, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = X( JX ) IX = KX DO 30, K = KK, KK + J - 2 X( IX ) = X( IX ) + TEMP*AP( K ) IX = IX + INCX 30 CONTINUE IF( NOUNIT ) $ X( JX ) = X( JX )*AP( KK + J - 1 ) END IF JX = JX + INCX KK = KK + J 40 CONTINUE END IF ELSE KK = ( N*( N + 1 ) )/2 IF( INCX.EQ.1 )THEN DO 60, J = N, 1, -1 IF( X( J ).NE.ZERO )THEN TEMP = X( J ) K = KK DO 50, I = N, J + 1, -1 X( I ) = X( I ) + TEMP*AP( K ) K = K - 1 50 CONTINUE IF( NOUNIT ) $ X( J ) = X( J )*AP( KK - N + J ) END IF KK = KK - ( N - J + 1 ) 60 CONTINUE ELSE KX = KX + ( N - 1 )*INCX JX = KX DO 80, J = N, 1, -1 IF( X( JX ).NE.ZERO )THEN TEMP = X( JX ) IX = KX DO 70, K = KK, KK - ( N - ( J + 1 ) ), -1 X( IX ) = X( IX ) + TEMP*AP( K ) IX = IX - INCX 70 CONTINUE IF( NOUNIT ) $ X( JX ) = X( JX )*AP( KK - N + J ) END IF JX = JX - INCX KK = KK - ( N - J + 1 ) 80 CONTINUE END IF END IF ELSE * * Form x := A'*x. * IF( LSAME( UPLO, 'U' ) )THEN KK = ( N*( N + 1 ) )/2 IF( INCX.EQ.1 )THEN DO 100, J = N, 1, -1 TEMP = X( J ) IF( NOUNIT ) $ TEMP = TEMP*AP( KK ) K = KK - 1 DO 90, I = J - 1, 1, -1 TEMP = TEMP + AP( K )*X( I ) K = K - 1 90 CONTINUE X( J ) = TEMP KK = KK - J 100 CONTINUE ELSE JX = KX + ( N - 1 )*INCX DO 120, J = N, 1, -1 TEMP = X( JX ) IX = JX IF( NOUNIT ) $ TEMP = TEMP*AP( KK ) DO 110, K = KK - 1, KK - J + 1, -1 IX = IX - INCX TEMP = TEMP + AP( K )*X( IX ) 110 CONTINUE X( JX ) = TEMP JX = JX - INCX KK = KK - J 120 CONTINUE END IF ELSE KK = 1 IF( INCX.EQ.1 )THEN DO 140, J = 1, N TEMP = X( J ) IF( NOUNIT ) $ TEMP = TEMP*AP( KK ) K = KK + 1 DO 130, I = J + 1, N TEMP = TEMP + AP( K )*X( I ) K = K + 1 130 CONTINUE X( J ) = TEMP KK = KK + ( N - J + 1 ) 140 CONTINUE ELSE JX = KX DO 160, J = 1, N TEMP = X( JX ) IX = JX IF( NOUNIT ) $ TEMP = TEMP*AP( KK ) DO 150, K = KK + 1, KK + N - J IX = IX + INCX TEMP = TEMP + AP( K )*X( IX ) 150 CONTINUE X( JX ) = TEMP JX = JX + INCX KK = KK + ( N - J + 1 ) 160 CONTINUE END IF END IF END IF * RETURN * * End of DTPMV . * END * ************************************************************************ * SUBROUTINE DTRSV ( UPLO, TRANS, DIAG, N, A, LDA, X, INCX ) * .. Scalar Arguments .. INTEGER INCX, LDA, N CHARACTER*1 DIAG, TRANS, UPLO * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), X( * ) * .. * * Purpose * ======= * * DTRSV solves one of the systems of equations * * A*x = b, or A'*x = b, * * where b and x are n element vectors and A is an n by n unit, or * non-unit, upper or lower triangular matrix. * * No test for singularity or near-singularity is included in this * routine. Such tests must be performed before calling this routine. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the matrix is an upper or * lower triangular matrix as follows: * * UPLO = 'U' or 'u' A is an upper triangular matrix. * * UPLO = 'L' or 'l' A is a lower triangular matrix. * * Unchanged on exit. * * TRANS - CHARACTER*1. * On entry, TRANS specifies the equations to be solved as * follows: * * TRANS = 'N' or 'n' A*x = b. * * TRANS = 'T' or 't' A'*x = b. * * TRANS = 'C' or 'c' A'*x = b. * * Unchanged on exit. * * DIAG - CHARACTER*1. * On entry, DIAG specifies whether or not A is unit * triangular as follows: * * DIAG = 'U' or 'u' A is assumed to be unit triangular. * * DIAG = 'N' or 'n' A is not assumed to be unit * triangular. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). * Before entry with UPLO = 'U' or 'u', the leading n by n * upper triangular part of the array A must contain the upper * triangular matrix and the strictly lower triangular part of * A is not referenced. * Before entry with UPLO = 'L' or 'l', the leading n by n * lower triangular part of the array A must contain the lower * triangular matrix and the strictly upper triangular part of * A is not referenced. * Note that when DIAG = 'U' or 'u', the diagonal elements of * A are not referenced either, but are assumed to be unity. * Unchanged on exit. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * max( 1, n ). * Unchanged on exit. * * X - DOUBLE PRECISION array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element right-hand side vector b. On exit, X is overwritten * with the solution vector x. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D+0 ) * .. Local Scalars .. DOUBLE PRECISION TEMP INTEGER I, INFO, IX, J, JX, KX LOGICAL NOUNIT * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO , 'U' ).AND. $ .NOT.LSAME( UPLO , 'L' ) )THEN INFO = 1 ELSE IF( .NOT.LSAME( TRANS, 'N' ).AND. $ .NOT.LSAME( TRANS, 'T' ).AND. $ .NOT.LSAME( TRANS, 'C' ) )THEN INFO = 2 ELSE IF( .NOT.LSAME( DIAG , 'U' ).AND. $ .NOT.LSAME( DIAG , 'N' ) )THEN INFO = 3 ELSE IF( N.LT.0 )THEN INFO = 4 ELSE IF( LDA.LT.MAX( 1, N ) )THEN INFO = 6 ELSE IF( INCX.EQ.0 )THEN INFO = 8 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'DTRSV ', INFO ) RETURN END IF * * Quick return if possible. * IF( N.EQ.0 ) $ RETURN * NOUNIT = LSAME( DIAG, 'N' ) * * Set up the start point in X if the increment is not unity. This * will be ( N - 1 )*INCX too small for descending loops. * IF( INCX.LE.0 )THEN KX = 1 - ( N - 1 )*INCX ELSE IF( INCX.NE.1 )THEN KX = 1 END IF * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through A. * IF( LSAME( TRANS, 'N' ) )THEN * * Form x := inv( A )*x. * IF( LSAME( UPLO, 'U' ) )THEN IF( INCX.EQ.1 )THEN DO 20, J = N, 1, -1 IF( X( J ).NE.ZERO )THEN IF( NOUNIT ) $ X( J ) = X( J )/A( J, J ) TEMP = X( J ) DO 10, I = J - 1, 1, -1 X( I ) = X( I ) - TEMP*A( I, J ) 10 CONTINUE END IF 20 CONTINUE ELSE JX = KX + ( N - 1 )*INCX DO 40, J = N, 1, -1 IF( X( JX ).NE.ZERO )THEN IF( NOUNIT ) $ X( JX ) = X( JX )/A( J, J ) TEMP = X( JX ) IX = JX DO 30, I = J - 1, 1, -1 IX = IX - INCX X( IX ) = X( IX ) - TEMP*A( I, J ) 30 CONTINUE END IF JX = JX - INCX 40 CONTINUE END IF ELSE IF( INCX.EQ.1 )THEN DO 60, J = 1, N IF( X( J ).NE.ZERO )THEN IF( NOUNIT ) $ X( J ) = X( J )/A( J, J ) TEMP = X( J ) DO 50, I = J + 1, N X( I ) = X( I ) - TEMP*A( I, J ) 50 CONTINUE END IF 60 CONTINUE ELSE JX = KX DO 80, J = 1, N IF( X( JX ).NE.ZERO )THEN IF( NOUNIT ) $ X( JX ) = X( JX )/A( J, J ) TEMP = X( JX ) IX = JX DO 70, I = J + 1, N IX = IX + INCX X( IX ) = X( IX ) - TEMP*A( I, J ) 70 CONTINUE END IF JX = JX + INCX 80 CONTINUE END IF END IF ELSE * * Form x := inv( A' )*x. * IF( LSAME( UPLO, 'U' ) )THEN IF( INCX.EQ.1 )THEN DO 100, J = 1, N TEMP = X( J ) DO 90, I = 1, J - 1 TEMP = TEMP - A( I, J )*X( I ) 90 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/A( J, J ) X( J ) = TEMP 100 CONTINUE ELSE JX = KX DO 120, J = 1, N TEMP = X( JX ) IX = KX DO 110, I = 1, J - 1 TEMP = TEMP - A( I, J )*X( IX ) IX = IX + INCX 110 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/A( J, J ) X( JX ) = TEMP JX = JX + INCX 120 CONTINUE END IF ELSE IF( INCX.EQ.1 )THEN DO 140, J = N, 1, -1 TEMP = X( J ) DO 130, I = N, J + 1, -1 TEMP = TEMP - A( I, J )*X( I ) 130 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/A( J, J ) X( J ) = TEMP 140 CONTINUE ELSE KX = KX + ( N - 1 )*INCX JX = KX DO 160, J = N, 1, -1 TEMP = X( JX ) IX = KX DO 150, I = N, J + 1, -1 TEMP = TEMP - A( I, J )*X( IX ) IX = IX - INCX 150 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/A( J, J ) X( JX ) = TEMP JX = JX - INCX 160 CONTINUE END IF END IF END IF * RETURN * * End of DTRSV . * END * ************************************************************************ * SUBROUTINE DTBSV ( UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX ) * .. Scalar Arguments .. INTEGER INCX, K, LDA, N CHARACTER*1 DIAG, TRANS, UPLO * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), X( * ) * .. * * Purpose * ======= * * DTBSV solves one of the systems of equations * * A*x = b, or A'*x = b, * * where b and x are n element vectors and A is an n by n unit, or * non-unit, upper or lower triangular band matrix, with ( k + 1 ) * diagonals. * * No test for singularity or near-singularity is included in this * routine. Such tests must be performed before calling this routine. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the matrix is an upper or * lower triangular matrix as follows: * * UPLO = 'U' or 'u' A is an upper triangular matrix. * * UPLO = 'L' or 'l' A is a lower triangular matrix. * * Unchanged on exit. * * TRANS - CHARACTER*1. * On entry, TRANS specifies the equations to be solved as * follows: * * TRANS = 'N' or 'n' A*x = b. * * TRANS = 'T' or 't' A'*x = b. * * TRANS = 'C' or 'c' A'*x = b. * * Unchanged on exit. * * DIAG - CHARACTER*1. * On entry, DIAG specifies whether or not A is unit * triangular as follows: * * DIAG = 'U' or 'u' A is assumed to be unit triangular. * * DIAG = 'N' or 'n' A is not assumed to be unit * triangular. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * K - INTEGER. * On entry with UPLO = 'U' or 'u', K specifies the number of * super-diagonals of the matrix A. * On entry with UPLO = 'L' or 'l', K specifies the number of * sub-diagonals of the matrix A. * K must satisfy 0 .le. K. * Unchanged on exit. * * A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). * Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) * by n part of the array A must contain the upper triangular * band part of the matrix of coefficients, supplied column by * column, with the leading diagonal of the matrix in row * ( k + 1 ) of the array, the first super-diagonal starting at * position 2 in row k, and so on. The top left k by k triangle * of the array A is not referenced. * The following program segment will transfer an upper * triangular band matrix from conventional full matrix storage * to band storage: * * DO 20, J = 1, N * M = K + 1 - J * DO 10, I = MAX( 1, J - K ), J * A( M + I, J ) = matrix( I, J ) * 10 CONTINUE * 20 CONTINUE * * Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) * by n part of the array A must contain the lower triangular * band part of the matrix of coefficients, supplied column by * column, with the leading diagonal of the matrix in row 1 of * the array, the first sub-diagonal starting at position 1 in * row 2, and so on. The bottom right k by k triangle of the * array A is not referenced. * The following program segment will transfer a lower * triangular band matrix from conventional full matrix storage * to band storage: * * DO 20, J = 1, N * M = 1 - J * DO 10, I = J, MIN( N, J + K ) * A( M + I, J ) = matrix( I, J ) * 10 CONTINUE * 20 CONTINUE * * Note that when DIAG = 'U' or 'u' the elements of the array A * corresponding to the diagonal elements of the matrix are not * referenced, but are assumed to be unity. * Unchanged on exit. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * ( k + 1 ). * Unchanged on exit. * * X - DOUBLE PRECISION array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element right-hand side vector b. On exit, X is overwritten * with the solution vector x. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D+0 ) * .. Local Scalars .. DOUBLE PRECISION TEMP INTEGER I, INFO, IX, J, JX, KPLUS1, KX, L LOGICAL NOUNIT * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO , 'U' ).AND. $ .NOT.LSAME( UPLO , 'L' ) )THEN INFO = 1 ELSE IF( .NOT.LSAME( TRANS, 'N' ).AND. $ .NOT.LSAME( TRANS, 'T' ).AND. $ .NOT.LSAME( TRANS, 'C' ) )THEN INFO = 2 ELSE IF( .NOT.LSAME( DIAG , 'U' ).AND. $ .NOT.LSAME( DIAG , 'N' ) )THEN INFO = 3 ELSE IF( N.LT.0 )THEN INFO = 4 ELSE IF( K.LT.0 )THEN INFO = 5 ELSE IF( LDA.LT.( K + 1 ) )THEN INFO = 7 ELSE IF( INCX.EQ.0 )THEN INFO = 9 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'DTBSV ', INFO ) RETURN END IF * * Quick return if possible. * IF( N.EQ.0 ) $ RETURN * NOUNIT = LSAME( DIAG, 'N' ) * * Set up the start point in X if the increment is not unity. This * will be ( N - 1 )*INCX too small for descending loops. * IF( INCX.LE.0 )THEN KX = 1 - ( N - 1 )*INCX ELSE IF( INCX.NE.1 )THEN KX = 1 END IF * * Start the operations. In this version the elements of A are * accessed by sequentially with one pass through A. * IF( LSAME( TRANS, 'N' ) )THEN * * Form x := inv( A )*x. * IF( LSAME( UPLO, 'U' ) )THEN KPLUS1 = K + 1 IF( INCX.EQ.1 )THEN DO 20, J = N, 1, -1 IF( X( J ).NE.ZERO )THEN L = KPLUS1 - J IF( NOUNIT ) $ X( J ) = X( J )/A( KPLUS1, J ) TEMP = X( J ) DO 10, I = J - 1, MAX( 1, J - K ), -1 X( I ) = X( I ) - TEMP*A( L + I, J ) 10 CONTINUE END IF 20 CONTINUE ELSE KX = KX + ( N - 1 )*INCX JX = KX DO 40, J = N, 1, -1 KX = KX - INCX IF( X( JX ).NE.ZERO )THEN IX = KX L = KPLUS1 - J IF( NOUNIT ) $ X( JX ) = X( JX )/A( KPLUS1, J ) TEMP = X( JX ) DO 30, I = J - 1, MAX( 1, J - K ), -1 X( IX ) = X( IX ) - TEMP*A( L + I, J ) IX = IX - INCX 30 CONTINUE END IF JX = JX - INCX 40 CONTINUE END IF ELSE IF( INCX.EQ.1 )THEN DO 60, J = 1, N IF( X( J ).NE.ZERO )THEN L = 1 - J IF( NOUNIT ) $ X( J ) = X( J )/A( 1, J ) TEMP = X( J ) DO 50, I = J + 1, MIN( N, J + K ) X( I ) = X( I ) - TEMP*A( L + I, J ) 50 CONTINUE END IF 60 CONTINUE ELSE JX = KX DO 80, J = 1, N KX = KX + INCX IF( X( JX ).NE.ZERO )THEN IX = KX L = 1 - J IF( NOUNIT ) $ X( JX ) = X( JX )/A( 1, J ) TEMP = X( JX ) DO 70, I = J + 1, MIN( N, J + K ) X( IX ) = X( IX ) - TEMP*A( L + I, J ) IX = IX + INCX 70 CONTINUE END IF JX = JX + INCX 80 CONTINUE END IF END IF ELSE * * Form x := inv( A')*x. * IF( LSAME( UPLO, 'U' ) )THEN KPLUS1 = K + 1 IF( INCX.EQ.1 )THEN DO 100, J = 1, N TEMP = X( J ) L = KPLUS1 - J DO 90, I = MAX( 1, J - K ), J - 1 TEMP = TEMP - A( L + I, J )*X( I ) 90 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/A( KPLUS1, J ) X( J ) = TEMP 100 CONTINUE ELSE JX = KX DO 120, J = 1, N TEMP = X( JX ) IX = KX L = KPLUS1 - J DO 110, I = MAX( 1, J - K ), J - 1 TEMP = TEMP - A( L + I, J )*X( IX ) IX = IX + INCX 110 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/A( KPLUS1, J ) X( JX ) = TEMP JX = JX + INCX IF( J.GT.K ) $ KX = KX + INCX 120 CONTINUE END IF ELSE IF( INCX.EQ.1 )THEN DO 140, J = N, 1, -1 TEMP = X( J ) L = 1 - J DO 130, I = MIN( N, J + K ), J + 1, -1 TEMP = TEMP - A( L + I, J )*X( I ) 130 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/A( 1, J ) X( J ) = TEMP 140 CONTINUE ELSE KX = KX + ( N - 1 )*INCX JX = KX DO 160, J = N, 1, -1 TEMP = X( JX ) IX = KX L = 1 - J DO 150, I = MIN( N, J + K ), J + 1, -1 TEMP = TEMP - A( L + I, J )*X( IX ) IX = IX - INCX 150 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/A( 1, J ) X( JX ) = TEMP JX = JX - INCX IF( ( N - J ).GE.K ) $ KX = KX - INCX 160 CONTINUE END IF END IF END IF * RETURN * * End of DTBSV . * END * ************************************************************************ * SUBROUTINE DTPSV ( UPLO, TRANS, DIAG, N, AP, X, INCX ) * .. Scalar Arguments .. INTEGER INCX, N CHARACTER*1 DIAG, TRANS, UPLO * .. Array Arguments .. DOUBLE PRECISION AP( * ), X( * ) * .. * * Purpose * ======= * * DTPSV solves one of the systems of equations * * A*x = b, or A'*x = b, * * where b and x are n element vectors and A is an n by n unit, or * non-unit, upper or lower triangular matrix, supplied in packed form. * * No test for singularity or near-singularity is included in this * routine. Such tests must be performed before calling this routine. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the matrix is an upper or * lower triangular matrix as follows: * * UPLO = 'U' or 'u' A is an upper triangular matrix. * * UPLO = 'L' or 'l' A is a lower triangular matrix. * * Unchanged on exit. * * TRANS - CHARACTER*1. * On entry, TRANS specifies the equations to be solved as * follows: * * TRANS = 'N' or 'n' A*x = b. * * TRANS = 'T' or 't' A'*x = b. * * TRANS = 'C' or 'c' A'*x = b. * * Unchanged on exit. * * DIAG - CHARACTER*1. * On entry, DIAG specifies whether or not A is unit * triangular as follows: * * DIAG = 'U' or 'u' A is assumed to be unit triangular. * * DIAG = 'N' or 'n' A is not assumed to be unit * triangular. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * AP - DOUBLE PRECISION array of DIMENSION at least * ( ( n*( n + 1 ) )/2 ). * Before entry with UPLO = 'U' or 'u', the array AP must * contain the upper triangular matrix packed sequentially, * column by column, so that AP( 1 ) contains a( 1, 1 ), * AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) * respectively, and so on. * Before entry with UPLO = 'L' or 'l', the array AP must * contain the lower triangular matrix packed sequentially, * column by column, so that AP( 1 ) contains a( 1, 1 ), * AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) * respectively, and so on. * Note that when DIAG = 'U' or 'u', the diagonal elements of * A are not referenced, but are assumed to be unity. * Unchanged on exit. * * X - DOUBLE PRECISION array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element right-hand side vector b. On exit, X is overwritten * with the solution vector x. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D+0 ) * .. Local Scalars .. DOUBLE PRECISION TEMP INTEGER I, INFO, IX, J, JX, K, KK, KX LOGICAL NOUNIT * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO , 'U' ).AND. $ .NOT.LSAME( UPLO , 'L' ) )THEN INFO = 1 ELSE IF( .NOT.LSAME( TRANS, 'N' ).AND. $ .NOT.LSAME( TRANS, 'T' ).AND. $ .NOT.LSAME( TRANS, 'C' ) )THEN INFO = 2 ELSE IF( .NOT.LSAME( DIAG , 'U' ).AND. $ .NOT.LSAME( DIAG , 'N' ) )THEN INFO = 3 ELSE IF( N.LT.0 )THEN INFO = 4 ELSE IF( INCX.EQ.0 )THEN INFO = 7 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'DTPSV ', INFO ) RETURN END IF * * Quick return if possible. * IF( N.EQ.0 ) $ RETURN * NOUNIT = LSAME( DIAG, 'N' ) * * Set up the start point in X if the increment is not unity. This * will be ( N - 1 )*INCX too small for descending loops. * IF( INCX.LE.0 )THEN KX = 1 - ( N - 1 )*INCX ELSE IF( INCX.NE.1 )THEN KX = 1 END IF * * Start the operations. In this version the elements of AP are * accessed sequentially with one pass through AP. * IF( LSAME( TRANS, 'N' ) )THEN * * Form x := inv( A )*x. * IF( LSAME( UPLO, 'U' ) )THEN KK = ( N*( N + 1 ) )/2 IF( INCX.EQ.1 )THEN DO 20, J = N, 1, -1 IF( X( J ).NE.ZERO )THEN IF( NOUNIT ) $ X( J ) = X( J )/AP( KK ) TEMP = X( J ) K = KK - 1 DO 10, I = J - 1, 1, -1 X( I ) = X( I ) - TEMP*AP( K ) K = K - 1 10 CONTINUE END IF KK = KK - J 20 CONTINUE ELSE JX = KX + ( N - 1 )*INCX DO 40, J = N, 1, -1 IF( X( JX ).NE.ZERO )THEN IF( NOUNIT ) $ X( JX ) = X( JX )/AP( KK ) TEMP = X( JX ) IX = JX DO 30, K = KK - 1, KK - J + 1, -1 IX = IX - INCX X( IX ) = X( IX ) - TEMP*AP( K ) 30 CONTINUE END IF JX = JX - INCX KK = KK - J 40 CONTINUE END IF ELSE KK = 1 IF( INCX.EQ.1 )THEN DO 60, J = 1, N IF( X( J ).NE.ZERO )THEN IF( NOUNIT ) $ X( J ) = X( J )/AP( KK ) TEMP = X( J ) K = KK + 1 DO 50, I = J + 1, N X( I ) = X( I ) - TEMP*AP( K ) K = K + 1 50 CONTINUE END IF KK = KK + ( N - J + 1 ) 60 CONTINUE ELSE JX = KX DO 80, J = 1, N IF( X( JX ).NE.ZERO )THEN IF( NOUNIT ) $ X( JX ) = X( JX )/AP( KK ) TEMP = X( JX ) IX = JX DO 70, K = KK + 1, KK + N - J IX = IX + INCX X( IX ) = X( IX ) - TEMP*AP( K ) 70 CONTINUE END IF JX = JX + INCX KK = KK + ( N - J + 1 ) 80 CONTINUE END IF END IF ELSE * * Form x := inv( A' )*x. * IF( LSAME( UPLO, 'U' ) )THEN KK = 1 IF( INCX.EQ.1 )THEN DO 100, J = 1, N TEMP = X( J ) K = KK DO 90, I = 1, J - 1 TEMP = TEMP - AP( K )*X( I ) K = K + 1 90 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/AP( KK + J - 1 ) X( J ) = TEMP KK = KK + J 100 CONTINUE ELSE JX = KX DO 120, J = 1, N TEMP = X( JX ) IX = KX DO 110, K = KK, KK + J - 2 TEMP = TEMP - AP( K )*X( IX ) IX = IX + INCX 110 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/AP( KK + J - 1 ) X( JX ) = TEMP JX = JX + INCX KK = KK + J 120 CONTINUE END IF ELSE KK = ( N*( N + 1 ) )/2 IF( INCX.EQ.1 )THEN DO 140, J = N, 1, -1 TEMP = X( J ) K = KK DO 130, I = N, J + 1, -1 TEMP = TEMP - AP( K )*X( I ) K = K - 1 130 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/AP( KK - N + J ) X( J ) = TEMP KK = KK - ( N - J + 1 ) 140 CONTINUE ELSE KX = KX + ( N - 1 )*INCX JX = KX DO 160, J = N, 1, -1 TEMP = X( JX ) IX = KX DO 150, K = KK, KK - ( N - ( J + 1 ) ), -1 TEMP = TEMP - AP( K )*X( IX ) IX = IX - INCX 150 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/AP( KK - N + J ) X( JX ) = TEMP JX = JX - INCX KK = KK - (N - J + 1 ) 160 CONTINUE END IF END IF END IF * RETURN * * End of DTPSV . * END * ************************************************************************ * SUBROUTINE DGER ( M, N, ALPHA, X, INCX, Y, INCY, A, LDA ) * .. Scalar Arguments .. DOUBLE PRECISION ALPHA INTEGER INCX, INCY, LDA, M, N * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), X( * ), Y( * ) * .. * * Purpose * ======= * * DGER performs the rank 1 operation * * A := alpha*x*y' + A, * * where alpha is a scalar, x is an m element vector, y is an n element * vector and A is an m by n matrix. * * Parameters * ========== * * M - INTEGER. * On entry, M specifies the number of rows of the matrix A. * M must be at least zero. * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the number of columns of the matrix A. * N must be at least zero. * Unchanged on exit. * * ALPHA - DOUBLE PRECISION. * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * X - DOUBLE PRECISION array of dimension at least * ( 1 + ( m - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the m * element vector x. * Unchanged on exit. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * Y - DOUBLE PRECISION array of dimension at least * ( 1 + ( n - 1 )*abs( INCY ) ). * Before entry, the incremented array Y must contain the n * element vector y. * Unchanged on exit. * * INCY - INTEGER. * On entry, INCY specifies the increment for the elements of * Y. INCY must not be zero. * Unchanged on exit. * * A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). * Before entry, the leading m by n part of the array A must * contain the matrix of coefficients. On exit, A is * overwritten by the updated matrix. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * max( 1, m ). * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D+0 ) * .. Local Scalars .. DOUBLE PRECISION TEMP INTEGER I, INFO, IX, J, JY, KX * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( M.LT.0 )THEN INFO = 1 ELSE IF( N.LT.0 )THEN INFO = 2 ELSE IF( INCX.EQ.0 )THEN INFO = 5 ELSE IF( INCY.EQ.0 )THEN INFO = 7 ELSE IF( LDA.LT.MAX( 1, M ) )THEN INFO = 9 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'DGER ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( M.EQ.0 ).OR.( N.EQ.0 ).OR.( ALPHA.EQ.ZERO ) ) $ RETURN * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through A. * IF( INCY.GT.0 )THEN JY = 1 ELSE JY = 1 - ( N - 1 )*INCY END IF IF( INCX.EQ.1 )THEN DO 20, J = 1, N IF( Y( JY ).NE.ZERO )THEN TEMP = ALPHA*Y( JY ) DO 10, I = 1, M A( I, J ) = A( I, J ) + X( I )*TEMP 10 CONTINUE END IF JY = JY + INCY 20 CONTINUE ELSE IF( INCX.GT.0 )THEN KX = 1 ELSE KX = 1 - ( M - 1 )*INCX END IF DO 40, J = 1, N IF( Y( JY ).NE.ZERO )THEN TEMP = ALPHA*Y( JY ) IX = KX DO 30, I = 1, M A( I, J ) = A( I, J ) + X( IX )*TEMP IX = IX + INCX 30 CONTINUE END IF JY = JY + INCY 40 CONTINUE END IF * RETURN * * End of DGER . * END * ************************************************************************ * SUBROUTINE DSYR ( UPLO, N, ALPHA, X, INCX, A, LDA ) * .. Scalar Arguments .. DOUBLE PRECISION ALPHA INTEGER INCX, LDA, N CHARACTER*1 UPLO * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), X( * ) * .. * * Purpose * ======= * * DSYR performs the symmetric rank 1 operation * * A := alpha*x*x' + A, * * where alpha is a real scalar, x is an n element vector and A is an * n by n symmetric matrix. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the upper or lower * triangular part of the array A is to be referenced as * follows: * * UPLO = 'U' or 'u' Only the upper triangular part of A * is to be referenced. * * UPLO = 'L' or 'l' Only the lower triangular part of A * is to be referenced. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * ALPHA - DOUBLE PRECISION. * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * X - DOUBLE PRECISION array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element vector x. * Unchanged on exit. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). * Before entry with UPLO = 'U' or 'u', the leading n by n * upper triangular part of the array A must contain the upper * triangular part of the symmetric matrix and the strictly * lower triangular part of A is not referenced. On exit, the * upper triangular part of the array A is overwritten by the * upper triangular part of the updated matrix. * Before entry with UPLO = 'L' or 'l', the leading n by n * lower triangular part of the array A must contain the lower * triangular part of the symmetric matrix and the strictly * upper triangular part of A is not referenced. On exit, the * lower triangular part of the array A is overwritten by the * lower triangular part of the updated matrix. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * max( 1, n ). * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D+0 ) * .. Local Scalars .. DOUBLE PRECISION TEMP INTEGER I, INFO, IX, J, JX, KX * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO, 'U' ).AND. $ .NOT.LSAME( UPLO, 'L' ) )THEN INFO = 1 ELSE IF( N.LT.0 )THEN INFO = 2 ELSE IF( INCX.EQ.0 )THEN INFO = 5 ELSE IF( LDA.LT.MAX( 1, N ) )THEN INFO = 7 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'DSYR ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( N.EQ.0 ).OR.( ALPHA.EQ.ZERO ) ) $ RETURN * * Set the start point in X if the increment is not unity. * IF( INCX.LE.0 )THEN KX = 1 - ( N - 1 )*INCX ELSE IF( INCX.NE.1 )THEN KX = 1 END IF * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through the triangular part * of A. * IF( LSAME( UPLO, 'U' ) )THEN * * Form A when A is stored in upper triangle. * IF( INCX.EQ.1 )THEN DO 20, J = 1, N IF( X( J ).NE.ZERO )THEN TEMP = ALPHA*X( J ) DO 10, I = 1, J A( I, J ) = A( I, J ) + X( I )*TEMP 10 CONTINUE END IF 20 CONTINUE ELSE JX = KX DO 40, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = ALPHA*X( JX ) IX = KX DO 30, I = 1, J A( I, J ) = A( I, J ) + X( IX )*TEMP IX = IX + INCX 30 CONTINUE END IF JX = JX + INCX 40 CONTINUE END IF ELSE * * Form A when A is stored in lower triangle. * IF( INCX.EQ.1 )THEN DO 60, J = 1, N IF( X( J ).NE.ZERO )THEN TEMP = ALPHA*X( J ) DO 50, I = J, N A( I, J ) = A( I, J ) + X( I )*TEMP 50 CONTINUE END IF 60 CONTINUE ELSE JX = KX DO 80, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = ALPHA*X( JX ) IX = JX DO 70, I = J, N A( I, J ) = A( I, J ) + X( IX )*TEMP IX = IX + INCX 70 CONTINUE END IF JX = JX + INCX 80 CONTINUE END IF END IF * RETURN * * End of DSYR . * END * ************************************************************************ * SUBROUTINE DSPR ( UPLO, N, ALPHA, X, INCX, AP ) * .. Scalar Arguments .. DOUBLE PRECISION ALPHA INTEGER INCX, N CHARACTER*1 UPLO * .. Array Arguments .. DOUBLE PRECISION AP( * ), X( * ) * .. * * Purpose * ======= * * DSPR performs the symmetric rank 1 operation * * A := alpha*x*x' + A, * * where alpha is a real scalar, x is an n element vector and A is an * n by n symmetric matrix, supplied in packed form. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the upper or lower * triangular part of the matrix A is supplied in the packed * array AP as follows: * * UPLO = 'U' or 'u' The upper triangular part of A is * supplied in AP. * * UPLO = 'L' or 'l' The lower triangular part of A is * supplied in AP. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * ALPHA - DOUBLE PRECISION. * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * X - DOUBLE PRECISION array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element vector x. * Unchanged on exit. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * AP - DOUBLE PRECISION array of DIMENSION at least * ( ( n*( n + 1 ) )/2 ). * Before entry with UPLO = 'U' or 'u', the array AP must * contain the upper triangular part of the symmetric matrix * packed sequentially, column by column, so that AP( 1 ) * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) * and a( 2, 2 ) respectively, and so on. On exit, the array * AP is overwritten by the upper triangular part of the * updated matrix. * Before entry with UPLO = 'L' or 'l', the array AP must * contain the lower triangular part of the symmetric matrix * packed sequentially, column by column, so that AP( 1 ) * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) * and a( 3, 1 ) respectively, and so on. On exit, the array * AP is overwritten by the lower triangular part of the * updated matrix. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D+0 ) * .. Local Scalars .. DOUBLE PRECISION TEMP INTEGER I, INFO, IX, J, JX, K, KK, KX * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO, 'U' ).AND. $ .NOT.LSAME( UPLO, 'L' ) )THEN INFO = 1 ELSE IF( N.LT.0 )THEN INFO = 2 ELSE IF( INCX.EQ.0 )THEN INFO = 5 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'DSPR ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( N.EQ.0 ).OR.( ALPHA.EQ.ZERO ) ) $ RETURN * * Set the start point in X if the increment is not unity. * IF( INCX.LE.0 )THEN KX = 1 - ( N - 1 )*INCX ELSE IF( INCX.NE.1 )THEN KX = 1 END IF * * Start the operations. In this version the elements of the array AP * are accessed sequentially with one pass through AP. * KK = 1 IF( LSAME( UPLO, 'U' ) )THEN * * Form A when upper triangle is stored in AP. * IF( INCX.EQ.1 )THEN DO 20, J = 1, N IF( X( J ).NE.ZERO )THEN TEMP = ALPHA*X( J ) K = KK DO 10, I = 1, J AP( K ) = AP( K ) + X( I )*TEMP K = K + 1 10 CONTINUE END IF KK = KK + J 20 CONTINUE ELSE JX = KX DO 40, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = ALPHA*X( JX ) IX = KX DO 30, K = KK, KK + J - 1 AP( K ) = AP( K ) + X( IX )*TEMP IX = IX + INCX 30 CONTINUE END IF JX = JX + INCX KK = KK + J 40 CONTINUE END IF ELSE * * Form A when lower triangle is stored in AP. * IF( INCX.EQ.1 )THEN DO 60, J = 1, N IF( X( J ).NE.ZERO )THEN TEMP = ALPHA*X( J ) K = KK DO 50, I = J, N AP( K ) = AP( K ) + X( I )*TEMP K = K + 1 50 CONTINUE END IF KK = KK + N - J + 1 60 CONTINUE ELSE JX = KX DO 80, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = ALPHA*X( JX ) IX = JX DO 70, K = KK, KK + N - J AP( K ) = AP( K ) + X( IX )*TEMP IX = IX + INCX 70 CONTINUE END IF JX = JX + INCX KK = KK + N - J + 1 80 CONTINUE END IF END IF * RETURN * * End of DSPR . * END * ************************************************************************ * SUBROUTINE DSYR2 ( UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA ) * .. Scalar Arguments .. DOUBLE PRECISION ALPHA INTEGER INCX, INCY, LDA, N CHARACTER*1 UPLO * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), X( * ), Y( * ) * .. * * Purpose * ======= * * DSYR2 performs the symmetric rank 2 operation * * A := alpha*x*y' + alpha*y*x' + A, * * where alpha is a scalar, x and y are n element vectors and A is an n * by n symmetric matrix. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the upper or lower * triangular part of the array A is to be referenced as * follows: * * UPLO = 'U' or 'u' Only the upper triangular part of A * is to be referenced. * * UPLO = 'L' or 'l' Only the lower triangular part of A * is to be referenced. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * ALPHA - DOUBLE PRECISION. * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * X - DOUBLE PRECISION array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element vector x. * Unchanged on exit. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * Y - DOUBLE PRECISION array of dimension at least * ( 1 + ( n - 1 )*abs( INCY ) ). * Before entry, the incremented array Y must contain the n * element vector y. * Unchanged on exit. * * INCY - INTEGER. * On entry, INCY specifies the increment for the elements of * Y. INCY must not be zero. * Unchanged on exit. * * A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). * Before entry with UPLO = 'U' or 'u', the leading n by n * upper triangular part of the array A must contain the upper * triangular part of the symmetric matrix and the strictly * lower triangular part of A is not referenced. On exit, the * upper triangular part of the array A is overwritten by the * upper triangular part of the updated matrix. * Before entry with UPLO = 'L' or 'l', the leading n by n * lower triangular part of the array A must contain the lower * triangular part of the symmetric matrix and the strictly * upper triangular part of A is not referenced. On exit, the * lower triangular part of the array A is overwritten by the * lower triangular part of the updated matrix. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * max( 1, n ). * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D+0 ) * .. Local Scalars .. DOUBLE PRECISION TEMP1, TEMP2 INTEGER I, INFO, IX, IY, J, JX, JY, KX, KY * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO, 'U' ).AND. $ .NOT.LSAME( UPLO, 'L' ) )THEN INFO = 1 ELSE IF( N.LT.0 )THEN INFO = 2 ELSE IF( INCX.EQ.0 )THEN INFO = 5 ELSE IF( INCY.EQ.0 )THEN INFO = 7 ELSE IF( LDA.LT.MAX( 1, N ) )THEN INFO = 9 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'DSYR2 ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( N.EQ.0 ).OR.( ALPHA.EQ.ZERO ) ) $ RETURN * * Set up the start points in X and Y if the increments are not both * unity. * IF( ( INCX.NE.1 ).OR.( INCY.NE.1 ) )THEN IF( INCX.GT.0 )THEN KX = 1 ELSE KX = 1 - ( N - 1 )*INCX END IF IF( INCY.GT.0 )THEN KY = 1 ELSE KY = 1 - ( N - 1 )*INCY END IF JX = KX JY = KY END IF * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through the triangular part * of A. * IF( LSAME( UPLO, 'U' ) )THEN * * Form A when A is stored in the upper triangle. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 20, J = 1, N IF( ( X( J ).NE.ZERO ).OR.( Y( J ).NE.ZERO ) )THEN TEMP1 = ALPHA*Y( J ) TEMP2 = ALPHA*X( J ) DO 10, I = 1, J A( I, J ) = A( I, J ) + X( I )*TEMP1 + Y( I )*TEMP2 10 CONTINUE END IF 20 CONTINUE ELSE DO 40, J = 1, N IF( ( X( JX ).NE.ZERO ).OR.( Y( JY ).NE.ZERO ) )THEN TEMP1 = ALPHA*Y( JY ) TEMP2 = ALPHA*X( JX ) IX = KX IY = KY DO 30, I = 1, J A( I, J ) = A( I, J ) + X( IX )*TEMP1 $ + Y( IY )*TEMP2 IX = IX + INCX IY = IY + INCY 30 CONTINUE END IF JX = JX + INCX JY = JY + INCY 40 CONTINUE END IF ELSE * * Form A when A is stored in the lower triangle. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 60, J = 1, N IF( ( X( J ).NE.ZERO ).OR.( Y( J ).NE.ZERO ) )THEN TEMP1 = ALPHA*Y( J ) TEMP2 = ALPHA*X( J ) DO 50, I = J, N A( I, J ) = A( I, J ) + X( I )*TEMP1 + Y( I )*TEMP2 50 CONTINUE END IF 60 CONTINUE ELSE DO 80, J = 1, N IF( ( X( JX ).NE.ZERO ).OR.( Y( JY ).NE.ZERO ) )THEN TEMP1 = ALPHA*Y( JY ) TEMP2 = ALPHA*X( JX ) IX = JX IY = JY DO 70, I = J, N A( I, J ) = A( I, J ) + X( IX )*TEMP1 $ + Y( IY )*TEMP2 IX = IX + INCX IY = IY + INCY 70 CONTINUE END IF JX = JX + INCX JY = JY + INCY 80 CONTINUE END IF END IF * RETURN * * End of DSYR2 . * END * ************************************************************************ * SUBROUTINE DSPR2 ( UPLO, N, ALPHA, X, INCX, Y, INCY, AP ) * .. Scalar Arguments .. DOUBLE PRECISION ALPHA INTEGER INCX, INCY, N CHARACTER*1 UPLO * .. Array Arguments .. DOUBLE PRECISION AP( * ), X( * ), Y( * ) * .. * * Purpose * ======= * * DSPR2 performs the symmetric rank 2 operation * * A := alpha*x*y' + alpha*y*x' + A, * * where alpha is a scalar, x and y are n element vectors and A is an * n by n symmetric matrix, supplied in packed form. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the upper or lower * triangular part of the matrix A is supplied in the packed * array AP as follows: * * UPLO = 'U' or 'u' The upper triangular part of A is * supplied in AP. * * UPLO = 'L' or 'l' The lower triangular part of A is * supplied in AP. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * ALPHA - DOUBLE PRECISION. * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * X - DOUBLE PRECISION array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element vector x. * Unchanged on exit. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * Y - DOUBLE PRECISION array of dimension at least * ( 1 + ( n - 1 )*abs( INCY ) ). * Before entry, the incremented array Y must contain the n * element vector y. * Unchanged on exit. * * INCY - INTEGER. * On entry, INCY specifies the increment for the elements of * Y. INCY must not be zero. * Unchanged on exit. * * AP - DOUBLE PRECISION array of DIMENSION at least * ( ( n*( n + 1 ) )/2 ). * Before entry with UPLO = 'U' or 'u', the array AP must * contain the upper triangular part of the symmetric matrix * packed sequentially, column by column, so that AP( 1 ) * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) * and a( 2, 2 ) respectively, and so on. On exit, the array * AP is overwritten by the upper triangular part of the * updated matrix. * Before entry with UPLO = 'L' or 'l', the array AP must * contain the lower triangular part of the symmetric matrix * packed sequentially, column by column, so that AP( 1 ) * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) * and a( 3, 1 ) respectively, and so on. On exit, the array * AP is overwritten by the lower triangular part of the * updated matrix. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D+0 ) * .. Local Scalars .. DOUBLE PRECISION TEMP1, TEMP2 INTEGER I, INFO, IX, IY, J, JX, JY, K, KK, KX, KY * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO, 'U' ).AND. $ .NOT.LSAME( UPLO, 'L' ) )THEN INFO = 1 ELSE IF( N.LT.0 )THEN INFO = 2 ELSE IF( INCX.EQ.0 )THEN INFO = 5 ELSE IF( INCY.EQ.0 )THEN INFO = 7 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'DSPR2 ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( N.EQ.0 ).OR.( ALPHA.EQ.ZERO ) ) $ RETURN * * Set up the start points in X and Y if the increments are not both * unity. * IF( ( INCX.NE.1 ).OR.( INCY.NE.1 ) )THEN IF( INCX.GT.0 )THEN KX = 1 ELSE KX = 1 - ( N - 1 )*INCX END IF IF( INCY.GT.0 )THEN KY = 1 ELSE KY = 1 - ( N - 1 )*INCY END IF JX = KX JY = KY END IF * * Start the operations. In this version the elements of the array AP * are accessed sequentially with one pass through AP. * KK = 1 IF( LSAME( UPLO, 'U' ) )THEN * * Form A when upper triangle is stored in AP. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 20, J = 1, N IF( ( X( J ).NE.ZERO ).OR.( Y( J ).NE.ZERO ) )THEN TEMP1 = ALPHA*Y( J ) TEMP2 = ALPHA*X( J ) K = KK DO 10, I = 1, J AP( K ) = AP( K ) + X( I )*TEMP1 + Y( I )*TEMP2 K = K + 1 10 CONTINUE END IF KK = KK + J 20 CONTINUE ELSE DO 40, J = 1, N IF( ( X( JX ).NE.ZERO ).OR.( Y( JY ).NE.ZERO ) )THEN TEMP1 = ALPHA*Y( JY ) TEMP2 = ALPHA*X( JX ) IX = KX IY = KY DO 30, K = KK, KK + J - 1 AP( K ) = AP( K ) + X( IX )*TEMP1 + Y( IY )*TEMP2 IX = IX + INCX IY = IY + INCY 30 CONTINUE END IF JX = JX + INCX JY = JY + INCY KK = KK + J 40 CONTINUE END IF ELSE * * Form A when lower triangle is stored in AP. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 60, J = 1, N IF( ( X( J ).NE.ZERO ).OR.( Y( J ).NE.ZERO ) )THEN TEMP1 = ALPHA*Y( J ) TEMP2 = ALPHA*X( J ) K = KK DO 50, I = J, N AP( K ) = AP( K ) + X( I )*TEMP1 + Y( I )*TEMP2 K = K + 1 50 CONTINUE END IF KK = KK + N - J + 1 60 CONTINUE ELSE DO 80, J = 1, N IF( ( X( JX ).NE.ZERO ).OR.( Y( JY ).NE.ZERO ) )THEN TEMP1 = ALPHA*Y( JY ) TEMP2 = ALPHA*X( JX ) IX = JX IY = JY DO 70, K = KK, KK + N - J AP( K ) = AP( K ) + X( IX )*TEMP1 + Y( IY )*TEMP2 IX = IX + INCX IY = IY + INCY 70 CONTINUE END IF JX = JX + INCX JY = JY + INCY KK = KK + N - J + 1 80 CONTINUE END IF END IF * RETURN * * End of DSPR2 . * END LOGICAL FUNCTION LSAME ( CA, CB ) * .. Scalar Arguments .. CHARACTER*1 CA, CB * .. * * Purpose * ======= * * LSAME tests if CA is the same letter as CB regardless of case. * CB is assumed to be an upper case letter. LSAME returns .TRUE. if * CA is either the same as CB or the equivalent lower case letter. * * N.B. This version of the routine is only correct for ASCII code. * Installers must modify the routine for other character-codes. * * For EBCDIC systems the constant IOFF must be changed to -64. * For CDC systems using 6-12 bit representations, the system- * specific code in comments must be activated. * * Parameters * ========== * * CA - CHARACTER*1 * CB - CHARACTER*1 * On entry, CA and CB specify characters to be compared. * Unchanged on exit. * * * Auxiliary routine for Level 2 Blas. * * -- Written on 20-July-1986 * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, Nag Central Office. * * .. Parameters .. INTEGER IOFF PARAMETER ( IOFF=32 ) * .. Intrinsic Functions .. INTRINSIC ICHAR * .. Executable Statements .. * * Test if the characters are equal * LSAME = CA .EQ. CB * * Now test for equivalence * IF ( .NOT.LSAME ) THEN LSAME = ICHAR(CA) - IOFF .EQ. ICHAR(CB) END IF * RETURN * * The following comments contain code for CDC systems using 6-12 bit * representations. * * .. Parameters .. * INTEGER ICIRFX * PARAMETER ( ICIRFX=62 ) * .. Scalar Arguments .. * CHARACTER*1 CB * .. Array Arguments .. * CHARACTER*1 CA(*) * .. Local Scalars .. * INTEGER IVAL * .. Intrinsic Functions .. * INTRINSIC ICHAR, CHAR * .. Executable Statements .. * * See if the first character in string CA equals string CB. * * LSAME = CA(1) .EQ. CB .AND. CA(1) .NE. CHAR(ICIRFX) * * IF (LSAME) RETURN * * The characters are not identical. Now check them for equivalence. * Look for the 'escape' character, circumflex, followed by the * letter. * * IVAL = ICHAR(CA(2)) * IF (IVAL.GE.ICHAR('A') .AND. IVAL.LE.ICHAR('Z')) THEN * LSAME = CA(1) .EQ. CHAR(ICIRFX) .AND. CA(2) .EQ. CB * END IF * * RETURN * * End of LSAME. * END SUBROUTINE XERBLA ( SRNAME, INFO ) * .. Scalar Arguments .. INTEGER INFO CHARACTER*6 SRNAME * .. * * Purpose * ======= * * XERBLA is an error handler for the Level 2 BLAS routines. * * It is called by the Level 2 BLAS routines if an input parameter is * invalid. * * Installers should consider modifying the STOP statement in order to * call system-specific exception-handling facilities. * * Parameters * ========== * * SRNAME - CHARACTER*6. * On entry, SRNAME specifies the name of the routine which * called XERBLA. * * INFO - INTEGER. * On entry, INFO specifies the position of the invalid * parameter in the parameter-list of the calling routine. * * * Auxiliary routine for Level 2 Blas. * * Written on 20-July-1986. * * .. Executable Statements .. * WRITE (*,99999) SRNAME, INFO * STOP * 99999 FORMAT ( ' ** On entry to ', A6, ' parameter number ', I2, $ ' had an illegal value' ) * * End of XERBLA. * END * ************************************************************************ * * File of the COMPLEX*16 Level-2 BLAS. * ========================================== * * SUBROUTINE ZGEMV ( TRANS, M, N, ALPHA, A, LDA, X, INCX, * $ BETA, Y, INCY ) * * SUBROUTINE ZGBMV ( TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX, * $ BETA, Y, INCY ) * * SUBROUTINE ZHEMV ( UPLO, N, ALPHA, A, LDA, X, INCX, * $ BETA, Y, INCY ) * * SUBROUTINE ZHBMV ( UPLO, N, K, ALPHA, A, LDA, X, INCX, * $ BETA, Y, INCY ) * * SUBROUTINE ZHPMV ( UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY ) * * SUBROUTINE ZTRMV ( UPLO, TRANS, DIAG, N, A, LDA, X, INCX ) * * SUBROUTINE ZTBMV ( UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX ) * * SUBROUTINE ZTPMV ( UPLO, TRANS, DIAG, N, AP, X, INCX ) * * SUBROUTINE ZTRSV ( UPLO, TRANS, DIAG, N, A, LDA, X, INCX ) * * SUBROUTINE ZTBSV ( UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX ) * * SUBROUTINE ZTPSV ( UPLO, TRANS, DIAG, N, AP, X, INCX ) * * SUBROUTINE ZGERU ( M, N, ALPHA, X, INCX, Y, INCY, A, LDA ) * * SUBROUTINE ZGERC ( M, N, ALPHA, X, INCX, Y, INCY, A, LDA ) * * SUBROUTINE ZHER ( UPLO, N, ALPHA, X, INCX, A, LDA ) * * SUBROUTINE ZHPR ( UPLO, N, ALPHA, X, INCX, AP ) * * SUBROUTINE ZHER2 ( UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA ) * * SUBROUTINE ZHPR2 ( UPLO, N, ALPHA, X, INCX, Y, INCY, AP ) * * See: * * Dongarra J. J., Du Croz J. J., Hammarling S. and Hanson R. J.. * An extended set of Fortran Basic Linear Algebra Subprograms. * * Technical Memoranda Nos. 41 (revision 3) and 81, Mathematics * and Computer Science Division, Argonne National Laboratory, * 9700 South Cass Avenue, Argonne, Illinois 60439, US. * * Or * * NAG Technical Reports TR3/87 and TR4/87, Numerical Algorithms * Group Ltd., NAG Central Office, 256 Banbury Road, Oxford * OX2 7DE, UK, and Numerical Algorithms Group Inc., 1101 31st * Street, Suite 100, Downers Grove, Illinois 60515-1263, USA. * ************************************************************************ * SUBROUTINE ZGEMV ( TRANS, M, N, ALPHA, A, LDA, X, INCX, $ BETA, Y, INCY ) * .. Scalar Arguments .. COMPLEX*16 ALPHA, BETA INTEGER INCX, INCY, LDA, M, N CHARACTER*1 TRANS * .. Array Arguments .. COMPLEX*16 A( LDA, * ), X( * ), Y( * ) * .. * * Purpose * ======= * * ZGEMV performs one of the matrix-vector operations * * y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, or * * y := alpha*conjg( A' )*x + beta*y, * * where alpha and beta are scalars, x and y are vectors and A is an * m by n matrix. * * Parameters * ========== * * TRANS - CHARACTER*1. * On entry, TRANS specifies the operation to be performed as * follows: * * TRANS = 'N' or 'n' y := alpha*A*x + beta*y. * * TRANS = 'T' or 't' y := alpha*A'*x + beta*y. * * TRANS = 'C' or 'c' y := alpha*conjg( A' )*x + beta*y. * * Unchanged on exit. * * M - INTEGER. * On entry, M specifies the number of rows of the matrix A. * M must be at least zero. * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the number of columns of the matrix A. * N must be at least zero. * Unchanged on exit. * * ALPHA - COMPLEX*16 . * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * A - COMPLEX*16 array of DIMENSION ( LDA, n ). * Before entry, the leading m by n part of the array A must * contain the matrix of coefficients. * Unchanged on exit. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * max( 1, m ). * Unchanged on exit. * * X - COMPLEX*16 array of DIMENSION at least * ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' * and at least * ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. * Before entry, the incremented array X must contain the * vector x. * Unchanged on exit. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * BETA - COMPLEX*16 . * On entry, BETA specifies the scalar beta. When BETA is * supplied as zero then Y need not be set on input. * Unchanged on exit. * * Y - COMPLEX*16 array of DIMENSION at least * ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' * and at least * ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. * Before entry with BETA non-zero, the incremented array Y * must contain the vector y. On exit, Y is overwritten by the * updated vector y. * * INCY - INTEGER. * On entry, INCY specifies the increment for the elements of * Y. INCY must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. COMPLEX*16 ONE PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) COMPLEX*16 ZERO PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) ) * .. Local Scalars .. COMPLEX*16 TEMP INTEGER I, INFO, IX, IY, J, JX, JY, KX, KY, LENX, LENY LOGICAL NOCONJ * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC DCONJG, MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( TRANS, 'N' ).AND. $ .NOT.LSAME( TRANS, 'T' ).AND. $ .NOT.LSAME( TRANS, 'C' ) )THEN INFO = 1 ELSE IF( M.LT.0 )THEN INFO = 2 ELSE IF( N.LT.0 )THEN INFO = 3 ELSE IF( LDA.LT.MAX( 1, M ) )THEN INFO = 6 ELSE IF( INCX.EQ.0 )THEN INFO = 8 ELSE IF( INCY.EQ.0 )THEN INFO = 11 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'ZGEMV ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( M.EQ.0 ).OR.( N.EQ.0 ).OR. $ ( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) ) $ RETURN * NOCONJ = LSAME( TRANS, 'T' ) * * Set LENX and LENY, the lengths of the vectors x and y, and set * up the start points in X and Y. * IF( LSAME( TRANS, 'N' ) )THEN LENX = N LENY = M ELSE LENX = M LENY = N END IF IF( INCX.GT.0 )THEN KX = 1 ELSE KX = 1 - ( LENX - 1 )*INCX END IF IF( INCY.GT.0 )THEN KY = 1 ELSE KY = 1 - ( LENY - 1 )*INCY END IF * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through A. * * First form y := beta*y. * IF( BETA.NE.ONE )THEN IF( INCY.EQ.1 )THEN IF( BETA.EQ.ZERO )THEN DO 10, I = 1, LENY Y( I ) = ZERO 10 CONTINUE ELSE DO 20, I = 1, LENY Y( I ) = BETA*Y( I ) 20 CONTINUE END IF ELSE IY = KY IF( BETA.EQ.ZERO )THEN DO 30, I = 1, LENY Y( IY ) = ZERO IY = IY + INCY 30 CONTINUE ELSE DO 40, I = 1, LENY Y( IY ) = BETA*Y( IY ) IY = IY + INCY 40 CONTINUE END IF END IF END IF IF( ALPHA.EQ.ZERO ) $ RETURN IF( LSAME( TRANS, 'N' ) )THEN * * Form y := alpha*A*x + y. * JX = KX IF( INCY.EQ.1 )THEN DO 60, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = ALPHA*X( JX ) DO 50, I = 1, M Y( I ) = Y( I ) + TEMP*A( I, J ) 50 CONTINUE END IF JX = JX + INCX 60 CONTINUE ELSE DO 80, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = ALPHA*X( JX ) IY = KY DO 70, I = 1, M Y( IY ) = Y( IY ) + TEMP*A( I, J ) IY = IY + INCY 70 CONTINUE END IF JX = JX + INCX 80 CONTINUE END IF ELSE * * Form y := alpha*A'*x + y or y := alpha*conjg( A' )*x + y. * JY = KY IF( INCX.EQ.1 )THEN DO 110, J = 1, N TEMP = ZERO IF( NOCONJ )THEN DO 90, I = 1, M TEMP = TEMP + A( I, J )*X( I ) 90 CONTINUE ELSE DO 100, I = 1, M TEMP = TEMP + DCONJG( A( I, J ) )*X( I ) 100 CONTINUE END IF Y( JY ) = Y( JY ) + ALPHA*TEMP JY = JY + INCY 110 CONTINUE ELSE DO 140, J = 1, N TEMP = ZERO IX = KX IF( NOCONJ )THEN DO 120, I = 1, M TEMP = TEMP + A( I, J )*X( IX ) IX = IX + INCX 120 CONTINUE ELSE DO 130, I = 1, M TEMP = TEMP + DCONJG( A( I, J ) )*X( IX ) IX = IX + INCX 130 CONTINUE END IF Y( JY ) = Y( JY ) + ALPHA*TEMP JY = JY + INCY 140 CONTINUE END IF END IF * RETURN * * End of ZGEMV . * END * ************************************************************************ * SUBROUTINE ZGBMV ( TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX, $ BETA, Y, INCY ) * .. Scalar Arguments .. COMPLEX*16 ALPHA, BETA INTEGER INCX, INCY, KL, KU, LDA, M, N CHARACTER*1 TRANS * .. Array Arguments .. COMPLEX*16 A( LDA, * ), X( * ), Y( * ) * .. * * Purpose * ======= * * ZGBMV performs one of the matrix-vector operations * * y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, or * * y := alpha*conjg( A' )*x + beta*y, * * where alpha and beta are scalars, x and y are vectors and A is an * m by n band matrix, with kl sub-diagonals and ku super-diagonals. * * Parameters * ========== * * TRANS - CHARACTER*1. * On entry, TRANS specifies the operation to be performed as * follows: * * TRANS = 'N' or 'n' y := alpha*A*x + beta*y. * * TRANS = 'T' or 't' y := alpha*A'*x + beta*y. * * TRANS = 'C' or 'c' y := alpha*conjg( A' )*x + beta*y. * * Unchanged on exit. * * M - INTEGER. * On entry, M specifies the number of rows of the matrix A. * M must be at least zero. * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the number of columns of the matrix A. * N must be at least zero. * Unchanged on exit. * * KL - INTEGER. * On entry, KL specifies the number of sub-diagonals of the * matrix A. KL must satisfy 0 .le. KL. * Unchanged on exit. * * KU - INTEGER. * On entry, KU specifies the number of super-diagonals of the * matrix A. KU must satisfy 0 .le. KU. * Unchanged on exit. * * ALPHA - COMPLEX*16 . * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * A - COMPLEX*16 array of DIMENSION ( LDA, n ). * Before entry, the leading ( kl + ku + 1 ) by n part of the * array A must contain the matrix of coefficients, supplied * column by column, with the leading diagonal of the matrix in * row ( ku + 1 ) of the array, the first super-diagonal * starting at position 2 in row ku, the first sub-diagonal * starting at position 1 in row ( ku + 2 ), and so on. * Elements in the array A that do not correspond to elements * in the band matrix (such as the top left ku by ku triangle) * are not referenced. * The following program segment will transfer a band matrix * from conventional full matrix storage to band storage: * * DO 20, J = 1, N * K = KU + 1 - J * DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL ) * A( K + I, J ) = matrix( I, J ) * 10 CONTINUE * 20 CONTINUE * * Unchanged on exit. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * ( kl + ku + 1 ). * Unchanged on exit. * * X - COMPLEX*16 array of DIMENSION at least * ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' * and at least * ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. * Before entry, the incremented array X must contain the * vector x. * Unchanged on exit. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * BETA - COMPLEX*16 . * On entry, BETA specifies the scalar beta. When BETA is * supplied as zero then Y need not be set on input. * Unchanged on exit. * * Y - COMPLEX*16 array of DIMENSION at least * ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' * and at least * ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. * Before entry, the incremented array Y must contain the * vector y. On exit, Y is overwritten by the updated vector y. * * * INCY - INTEGER. * On entry, INCY specifies the increment for the elements of * Y. INCY must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. COMPLEX*16 ONE PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) COMPLEX*16 ZERO PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) ) * .. Local Scalars .. COMPLEX*16 TEMP INTEGER I, INFO, IX, IY, J, JX, JY, K, KUP1, KX, KY, $ LENX, LENY LOGICAL NOCONJ * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC DCONJG, MAX, MIN * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( TRANS, 'N' ).AND. $ .NOT.LSAME( TRANS, 'T' ).AND. $ .NOT.LSAME( TRANS, 'C' ) )THEN INFO = 1 ELSE IF( M.LT.0 )THEN INFO = 2 ELSE IF( N.LT.0 )THEN INFO = 3 ELSE IF( KL.LT.0 )THEN INFO = 4 ELSE IF( KU.LT.0 )THEN INFO = 5 ELSE IF( LDA.LT.( KL + KU + 1 ) )THEN INFO = 8 ELSE IF( INCX.EQ.0 )THEN INFO = 10 ELSE IF( INCY.EQ.0 )THEN INFO = 13 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'ZGBMV ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( M.EQ.0 ).OR.( N.EQ.0 ).OR. $ ( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) ) $ RETURN * NOCONJ = LSAME( TRANS, 'T' ) * * Set LENX and LENY, the lengths of the vectors x and y, and set * up the start points in X and Y. * IF( LSAME( TRANS, 'N' ) )THEN LENX = N LENY = M ELSE LENX = M LENY = N END IF IF( INCX.GT.0 )THEN KX = 1 ELSE KX = 1 - ( LENX - 1 )*INCX END IF IF( INCY.GT.0 )THEN KY = 1 ELSE KY = 1 - ( LENY - 1 )*INCY END IF * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through the band part of A. * * First form y := beta*y. * IF( BETA.NE.ONE )THEN IF( INCY.EQ.1 )THEN IF( BETA.EQ.ZERO )THEN DO 10, I = 1, LENY Y( I ) = ZERO 10 CONTINUE ELSE DO 20, I = 1, LENY Y( I ) = BETA*Y( I ) 20 CONTINUE END IF ELSE IY = KY IF( BETA.EQ.ZERO )THEN DO 30, I = 1, LENY Y( IY ) = ZERO IY = IY + INCY 30 CONTINUE ELSE DO 40, I = 1, LENY Y( IY ) = BETA*Y( IY ) IY = IY + INCY 40 CONTINUE END IF END IF END IF IF( ALPHA.EQ.ZERO ) $ RETURN KUP1 = KU + 1 IF( LSAME( TRANS, 'N' ) )THEN * * Form y := alpha*A*x + y. * JX = KX IF( INCY.EQ.1 )THEN DO 60, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = ALPHA*X( JX ) K = KUP1 - J DO 50, I = MAX( 1, J - KU ), MIN( M, J + KL ) Y( I ) = Y( I ) + TEMP*A( K + I, J ) 50 CONTINUE END IF JX = JX + INCX 60 CONTINUE ELSE DO 80, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = ALPHA*X( JX ) IY = KY K = KUP1 - J DO 70, I = MAX( 1, J - KU ), MIN( M, J + KL ) Y( IY ) = Y( IY ) + TEMP*A( K + I, J ) IY = IY + INCY 70 CONTINUE END IF JX = JX + INCX IF( J.GT.KU ) $ KY = KY + INCY 80 CONTINUE END IF ELSE * * Form y := alpha*A'*x + y or y := alpha*conjg( A' )*x + y. * JY = KY IF( INCX.EQ.1 )THEN DO 110, J = 1, N TEMP = ZERO K = KUP1 - J IF( NOCONJ )THEN DO 90, I = MAX( 1, J - KU ), MIN( M, J + KL ) TEMP = TEMP + A( K + I, J )*X( I ) 90 CONTINUE ELSE DO 100, I = MAX( 1, J - KU ), MIN( M, J + KL ) TEMP = TEMP + DCONJG( A( K + I, J ) )*X( I ) 100 CONTINUE END IF Y( JY ) = Y( JY ) + ALPHA*TEMP JY = JY + INCY 110 CONTINUE ELSE DO 140, J = 1, N TEMP = ZERO IX = KX K = KUP1 - J IF( NOCONJ )THEN DO 120, I = MAX( 1, J - KU ), MIN( M, J + KL ) TEMP = TEMP + A( K + I, J )*X( IX ) IX = IX + INCX 120 CONTINUE ELSE DO 130, I = MAX( 1, J - KU ), MIN( M, J + KL ) TEMP = TEMP + DCONJG( A( K + I, J ) )*X( IX ) IX = IX + INCX 130 CONTINUE END IF Y( JY ) = Y( JY ) + ALPHA*TEMP JY = JY + INCY IF( J.GT.KU ) $ KX = KX + INCX 140 CONTINUE END IF END IF * RETURN * * End of ZGBMV . * END * ************************************************************************ * SUBROUTINE ZHEMV ( UPLO, N, ALPHA, A, LDA, X, INCX, $ BETA, Y, INCY ) * .. Scalar Arguments .. COMPLEX*16 ALPHA, BETA INTEGER INCX, INCY, LDA, N CHARACTER*1 UPLO * .. Array Arguments .. COMPLEX*16 A( LDA, * ), X( * ), Y( * ) * .. * * Purpose * ======= * * ZHEMV performs the matrix-vector operation * * y := alpha*A*x + beta*y, * * where alpha and beta are scalars, x and y are n element vectors and * A is an n by n hermitian matrix. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the upper or lower * triangular part of the array A is to be referenced as * follows: * * UPLO = 'U' or 'u' Only the upper triangular part of A * is to be referenced. * * UPLO = 'L' or 'l' Only the lower triangular part of A * is to be referenced. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * ALPHA - COMPLEX*16 . * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * A - COMPLEX*16 array of DIMENSION ( LDA, n ). * Before entry with UPLO = 'U' or 'u', the leading n by n * upper triangular part of the array A must contain the upper * triangular part of the hermitian matrix and the strictly * lower triangular part of A is not referenced. * Before entry with UPLO = 'L' or 'l', the leading n by n * lower triangular part of the array A must contain the lower * triangular part of the hermitian matrix and the strictly * upper triangular part of A is not referenced. * Note that the imaginary parts of the diagonal elements need * not be set and are assumed to be zero. * Unchanged on exit. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * max( 1, n ). * Unchanged on exit. * * X - COMPLEX*16 array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element vector x. * Unchanged on exit. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * BETA - COMPLEX*16 . * On entry, BETA specifies the scalar beta. When BETA is * supplied as zero then Y need not be set on input. * Unchanged on exit. * * Y - COMPLEX*16 array of dimension at least * ( 1 + ( n - 1 )*abs( INCY ) ). * Before entry, the incremented array Y must contain the n * element vector y. On exit, Y is overwritten by the updated * vector y. * * INCY - INTEGER. * On entry, INCY specifies the increment for the elements of * Y. INCY must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. COMPLEX*16 ONE PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) COMPLEX*16 ZERO PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) ) * .. Local Scalars .. COMPLEX*16 TEMP1, TEMP2 INTEGER I, INFO, IX, IY, J, JX, JY, KX, KY * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC DCONJG, MAX, DBLE * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO, 'U' ).AND. $ .NOT.LSAME( UPLO, 'L' ) )THEN INFO = 1 ELSE IF( N.LT.0 )THEN INFO = 2 ELSE IF( LDA.LT.MAX( 1, N ) )THEN INFO = 5 ELSE IF( INCX.EQ.0 )THEN INFO = 7 ELSE IF( INCY.EQ.0 )THEN INFO = 10 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'ZHEMV ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( N.EQ.0 ).OR.( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) ) $ RETURN * * Set up the start points in X and Y. * IF( INCX.GT.0 )THEN KX = 1 ELSE KX = 1 - ( N - 1 )*INCX END IF IF( INCY.GT.0 )THEN KY = 1 ELSE KY = 1 - ( N - 1 )*INCY END IF * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through the triangular part * of A. * * First form y := beta*y. * IF( BETA.NE.ONE )THEN IF( INCY.EQ.1 )THEN IF( BETA.EQ.ZERO )THEN DO 10, I = 1, N Y( I ) = ZERO 10 CONTINUE ELSE DO 20, I = 1, N Y( I ) = BETA*Y( I ) 20 CONTINUE END IF ELSE IY = KY IF( BETA.EQ.ZERO )THEN DO 30, I = 1, N Y( IY ) = ZERO IY = IY + INCY 30 CONTINUE ELSE DO 40, I = 1, N Y( IY ) = BETA*Y( IY ) IY = IY + INCY 40 CONTINUE END IF END IF END IF IF( ALPHA.EQ.ZERO ) $ RETURN IF( LSAME( UPLO, 'U' ) )THEN * * Form y when A is stored in upper triangle. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 60, J = 1, N TEMP1 = ALPHA*X( J ) TEMP2 = ZERO DO 50, I = 1, J - 1 Y( I ) = Y( I ) + TEMP1*A( I, J ) TEMP2 = TEMP2 + DCONJG( A( I, J ) )*X( I ) 50 CONTINUE Y( J ) = Y( J ) + TEMP1*DBLE( A( J, J ) ) + ALPHA*TEMP2 60 CONTINUE ELSE JX = KX JY = KY DO 80, J = 1, N TEMP1 = ALPHA*X( JX ) TEMP2 = ZERO IX = KX IY = KY DO 70, I = 1, J - 1 Y( IY ) = Y( IY ) + TEMP1*A( I, J ) TEMP2 = TEMP2 + DCONJG( A( I, J ) )*X( IX ) IX = IX + INCX IY = IY + INCY 70 CONTINUE Y( JY ) = Y( JY ) + TEMP1*DBLE( A( J, J ) ) + ALPHA*TEMP2 JX = JX + INCX JY = JY + INCY 80 CONTINUE END IF ELSE * * Form y when A is stored in lower triangle. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 100, J = 1, N TEMP1 = ALPHA*X( J ) TEMP2 = ZERO Y( J ) = Y( J ) + TEMP1*DBLE( A( J, J ) ) DO 90, I = J + 1, N Y( I ) = Y( I ) + TEMP1*A( I, J ) TEMP2 = TEMP2 + DCONJG( A( I, J ) )*X( I ) 90 CONTINUE Y( J ) = Y( J ) + ALPHA*TEMP2 100 CONTINUE ELSE JX = KX JY = KY DO 120, J = 1, N TEMP1 = ALPHA*X( JX ) TEMP2 = ZERO Y( JY ) = Y( JY ) + TEMP1*DBLE( A( J, J ) ) IX = JX IY = JY DO 110, I = J + 1, N IX = IX + INCX IY = IY + INCY Y( IY ) = Y( IY ) + TEMP1*A( I, J ) TEMP2 = TEMP2 + DCONJG( A( I, J ) )*X( IX ) 110 CONTINUE Y( JY ) = Y( JY ) + ALPHA*TEMP2 JX = JX + INCX JY = JY + INCY 120 CONTINUE END IF END IF * RETURN * * End of ZHEMV . * END * ************************************************************************ * SUBROUTINE ZHBMV ( UPLO, N, K, ALPHA, A, LDA, X, INCX, $ BETA, Y, INCY ) * .. Scalar Arguments .. COMPLEX*16 ALPHA, BETA INTEGER INCX, INCY, K, LDA, N CHARACTER*1 UPLO * .. Array Arguments .. COMPLEX*16 A( LDA, * ), X( * ), Y( * ) * .. * * Purpose * ======= * * ZHBMV performs the matrix-vector operation * * y := alpha*A*x + beta*y, * * where alpha and beta are scalars, x and y are n element vectors and * A is an n by n hermitian band matrix, with k super-diagonals. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the upper or lower * triangular part of the band matrix A is being supplied as * follows: * * UPLO = 'U' or 'u' The upper triangular part of A is * being supplied. * * UPLO = 'L' or 'l' The lower triangular part of A is * being supplied. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * K - INTEGER. * On entry, K specifies the number of super-diagonals of the * matrix A. K must satisfy 0 .le. K. * Unchanged on exit. * * ALPHA - COMPLEX*16 . * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * A - COMPLEX*16 array of DIMENSION ( LDA, n ). * Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) * by n part of the array A must contain the upper triangular * band part of the hermitian matrix, supplied column by * column, with the leading diagonal of the matrix in row * ( k + 1 ) of the array, the first super-diagonal starting at * position 2 in row k, and so on. The top left k by k triangle * of the array A is not referenced. * The following program segment will transfer the upper * triangular part of a hermitian band matrix from conventional * full matrix storage to band storage: * * DO 20, J = 1, N * M = K + 1 - J * DO 10, I = MAX( 1, J - K ), J * A( M + I, J ) = matrix( I, J ) * 10 CONTINUE * 20 CONTINUE * * Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) * by n part of the array A must contain the lower triangular * band part of the hermitian matrix, supplied column by * column, with the leading diagonal of the matrix in row 1 of * the array, the first sub-diagonal starting at position 1 in * row 2, and so on. The bottom right k by k triangle of the * array A is not referenced. * The following program segment will transfer the lower * triangular part of a hermitian band matrix from conventional * full matrix storage to band storage: * * DO 20, J = 1, N * M = 1 - J * DO 10, I = J, MIN( N, J + K ) * A( M + I, J ) = matrix( I, J ) * 10 CONTINUE * 20 CONTINUE * * Note that the imaginary parts of the diagonal elements need * not be set and are assumed to be zero. * Unchanged on exit. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * ( k + 1 ). * Unchanged on exit. * * X - COMPLEX*16 array of DIMENSION at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the * vector x. * Unchanged on exit. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * BETA - COMPLEX*16 . * On entry, BETA specifies the scalar beta. * Unchanged on exit. * * Y - COMPLEX*16 array of DIMENSION at least * ( 1 + ( n - 1 )*abs( INCY ) ). * Before entry, the incremented array Y must contain the * vector y. On exit, Y is overwritten by the updated vector y. * * INCY - INTEGER. * On entry, INCY specifies the increment for the elements of * Y. INCY must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. COMPLEX*16 ONE PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) COMPLEX*16 ZERO PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) ) * .. Local Scalars .. COMPLEX*16 TEMP1, TEMP2 INTEGER I, INFO, IX, IY, J, JX, JY, KPLUS1, KX, KY, L * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC DCONJG, MAX, MIN, DBLE * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO, 'U' ).AND. $ .NOT.LSAME( UPLO, 'L' ) )THEN INFO = 1 ELSE IF( N.LT.0 )THEN INFO = 2 ELSE IF( K.LT.0 )THEN INFO = 3 ELSE IF( LDA.LT.( K + 1 ) )THEN INFO = 6 ELSE IF( INCX.EQ.0 )THEN INFO = 8 ELSE IF( INCY.EQ.0 )THEN INFO = 11 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'ZHBMV ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( N.EQ.0 ).OR.( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) ) $ RETURN * * Set up the start points in X and Y. * IF( INCX.GT.0 )THEN KX = 1 ELSE KX = 1 - ( N - 1 )*INCX END IF IF( INCY.GT.0 )THEN KY = 1 ELSE KY = 1 - ( N - 1 )*INCY END IF * * Start the operations. In this version the elements of the array A * are accessed sequentially with one pass through A. * * First form y := beta*y. * IF( BETA.NE.ONE )THEN IF( INCY.EQ.1 )THEN IF( BETA.EQ.ZERO )THEN DO 10, I = 1, N Y( I ) = ZERO 10 CONTINUE ELSE DO 20, I = 1, N Y( I ) = BETA*Y( I ) 20 CONTINUE END IF ELSE IY = KY IF( BETA.EQ.ZERO )THEN DO 30, I = 1, N Y( IY ) = ZERO IY = IY + INCY 30 CONTINUE ELSE DO 40, I = 1, N Y( IY ) = BETA*Y( IY ) IY = IY + INCY 40 CONTINUE END IF END IF END IF IF( ALPHA.EQ.ZERO ) $ RETURN IF( LSAME( UPLO, 'U' ) )THEN * * Form y when upper triangle of A is stored. * KPLUS1 = K + 1 IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 60, J = 1, N TEMP1 = ALPHA*X( J ) TEMP2 = ZERO L = KPLUS1 - J DO 50, I = MAX( 1, J - K ), J - 1 Y( I ) = Y( I ) + TEMP1*A( L + I, J ) TEMP2 = TEMP2 + DCONJG( A( L + I, J ) )*X( I ) 50 CONTINUE Y( J ) = Y( J ) + TEMP1*DBLE( A( KPLUS1, J ) ) $ + ALPHA*TEMP2 60 CONTINUE ELSE JX = KX JY = KY DO 80, J = 1, N TEMP1 = ALPHA*X( JX ) TEMP2 = ZERO IX = KX IY = KY L = KPLUS1 - J DO 70, I = MAX( 1, J - K ), J - 1 Y( IY ) = Y( IY ) + TEMP1*A( L + I, J ) TEMP2 = TEMP2 + DCONJG( A( L + I, J ) )*X( IX ) IX = IX + INCX IY = IY + INCY 70 CONTINUE Y( JY ) = Y( JY ) + TEMP1*DBLE( A( KPLUS1, J ) ) $ + ALPHA*TEMP2 JX = JX + INCX JY = JY + INCY IF( J.GT.K )THEN KX = KX + INCX KY = KY + INCY END IF 80 CONTINUE END IF ELSE * * Form y when lower triangle of A is stored. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 100, J = 1, N TEMP1 = ALPHA*X( J ) TEMP2 = ZERO Y( J ) = Y( J ) + TEMP1*DBLE( A( 1, J ) ) L = 1 - J DO 90, I = J + 1, MIN( N, J + K ) Y( I ) = Y( I ) + TEMP1*A( L + I, J ) TEMP2 = TEMP2 + DCONJG( A( L + I, J ) )*X( I ) 90 CONTINUE Y( J ) = Y( J ) + ALPHA*TEMP2 100 CONTINUE ELSE JX = KX JY = KY DO 120, J = 1, N TEMP1 = ALPHA*X( JX ) TEMP2 = ZERO Y( JY ) = Y( JY ) + TEMP1*DBLE( A( 1, J ) ) L = 1 - J IX = JX IY = JY DO 110, I = J + 1, MIN( N, J + K ) IX = IX + INCX IY = IY + INCY Y( IY ) = Y( IY ) + TEMP1*A( L + I, J ) TEMP2 = TEMP2 + DCONJG( A( L + I, J ) )*X( IX ) 110 CONTINUE Y( JY ) = Y( JY ) + ALPHA*TEMP2 JX = JX + INCX JY = JY + INCY 120 CONTINUE END IF END IF * RETURN * * End of ZHBMV . * END * ************************************************************************ * SUBROUTINE ZHPMV ( UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY ) * .. Scalar Arguments .. COMPLEX*16 ALPHA, BETA INTEGER INCX, INCY, N CHARACTER*1 UPLO * .. Array Arguments .. COMPLEX*16 AP( * ), X( * ), Y( * ) * .. * * Purpose * ======= * * ZHPMV performs the matrix-vector operation * * y := alpha*A*x + beta*y, * * where alpha and beta are scalars, x and y are n element vectors and * A is an n by n hermitian matrix, supplied in packed form. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the upper or lower * triangular part of the matrix A is supplied in the packed * array AP as follows: * * UPLO = 'U' or 'u' The upper triangular part of A is * supplied in AP. * * UPLO = 'L' or 'l' The lower triangular part of A is * supplied in AP. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * ALPHA - COMPLEX*16 . * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * AP - COMPLEX*16 array of DIMENSION at least * ( ( n*( n + 1 ) )/2 ). * Before entry with UPLO = 'U' or 'u', the array AP must * contain the upper triangular part of the hermitian matrix * packed sequentially, column by column, so that AP( 1 ) * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) * and a( 2, 2 ) respectively, and so on. * Before entry with UPLO = 'L' or 'l', the array AP must * contain the lower triangular part of the hermitian matrix * packed sequentially, column by column, so that AP( 1 ) * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) * and a( 3, 1 ) respectively, and so on. * Note that the imaginary parts of the diagonal elements need * not be set and are assumed to be zero. * Unchanged on exit. * * X - COMPLEX*16 array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element vector x. * Unchanged on exit. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * BETA - COMPLEX*16 . * On entry, BETA specifies the scalar beta. When BETA is * supplied as zero then Y need not be set on input. * Unchanged on exit. * * Y - COMPLEX*16 array of dimension at least * ( 1 + ( n - 1 )*abs( INCY ) ). * Before entry, the incremented array Y must contain the n * element vector y. On exit, Y is overwritten by the updated * vector y. * * INCY - INTEGER. * On entry, INCY specifies the increment for the elements of * Y. INCY must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. COMPLEX*16 ONE PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) COMPLEX*16 ZERO PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) ) * .. Local Scalars .. COMPLEX*16 TEMP1, TEMP2 INTEGER I, INFO, IX, IY, J, JX, JY, K, KK, KX, KY * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC DCONJG, DBLE * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO, 'U' ).AND. $ .NOT.LSAME( UPLO, 'L' ) )THEN INFO = 1 ELSE IF( N.LT.0 )THEN INFO = 2 ELSE IF( INCX.EQ.0 )THEN INFO = 6 ELSE IF( INCY.EQ.0 )THEN INFO = 9 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'ZHPMV ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( N.EQ.0 ).OR.( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) ) $ RETURN * * Set up the start points in X and Y. * IF( INCX.GT.0 )THEN KX = 1 ELSE KX = 1 - ( N - 1 )*INCX END IF IF( INCY.GT.0 )THEN KY = 1 ELSE KY = 1 - ( N - 1 )*INCY END IF * * Start the operations. In this version the elements of the array AP * are accessed sequentially with one pass through AP. * * First form y := beta*y. * IF( BETA.NE.ONE )THEN IF( INCY.EQ.1 )THEN IF( BETA.EQ.ZERO )THEN DO 10, I = 1, N Y( I ) = ZERO 10 CONTINUE ELSE DO 20, I = 1, N Y( I ) = BETA*Y( I ) 20 CONTINUE END IF ELSE IY = KY IF( BETA.EQ.ZERO )THEN DO 30, I = 1, N Y( IY ) = ZERO IY = IY + INCY 30 CONTINUE ELSE DO 40, I = 1, N Y( IY ) = BETA*Y( IY ) IY = IY + INCY 40 CONTINUE END IF END IF END IF IF( ALPHA.EQ.ZERO ) $ RETURN KK = 1 IF( LSAME( UPLO, 'U' ) )THEN * * Form y when AP contains the upper triangle. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 60, J = 1, N TEMP1 = ALPHA*X( J ) TEMP2 = ZERO K = KK DO 50, I = 1, J - 1 Y( I ) = Y( I ) + TEMP1*AP( K ) TEMP2 = TEMP2 + DCONJG( AP( K ) )*X( I ) K = K + 1 50 CONTINUE Y( J ) = Y( J ) + TEMP1*DBLE( AP( KK + J - 1 ) ) $ + ALPHA*TEMP2 KK = KK + J 60 CONTINUE ELSE JX = KX JY = KY DO 80, J = 1, N TEMP1 = ALPHA*X( JX ) TEMP2 = ZERO IX = KX IY = KY DO 70, K = KK, KK + J - 2 Y( IY ) = Y( IY ) + TEMP1*AP( K ) TEMP2 = TEMP2 + DCONJG( AP( K ) )*X( IX ) IX = IX + INCX IY = IY + INCY 70 CONTINUE Y( JY ) = Y( JY ) + TEMP1*DBLE( AP( KK + J - 1 ) ) $ + ALPHA*TEMP2 JX = JX + INCX JY = JY + INCY KK = KK + J 80 CONTINUE END IF ELSE * * Form y when AP contains the lower triangle. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 100, J = 1, N TEMP1 = ALPHA*X( J ) TEMP2 = ZERO Y( J ) = Y( J ) + TEMP1*DBLE( AP( KK ) ) K = KK + 1 DO 90, I = J + 1, N Y( I ) = Y( I ) + TEMP1*AP( K ) TEMP2 = TEMP2 + DCONJG( AP( K ) )*X( I ) K = K + 1 90 CONTINUE Y( J ) = Y( J ) + ALPHA*TEMP2 KK = KK + ( N - J + 1 ) 100 CONTINUE ELSE JX = KX JY = KY DO 120, J = 1, N TEMP1 = ALPHA*X( JX ) TEMP2 = ZERO Y( JY ) = Y( JY ) + TEMP1*DBLE( AP( KK ) ) IX = JX IY = JY DO 110, K = KK + 1, KK + N - J IX = IX + INCX IY = IY + INCY Y( IY ) = Y( IY ) + TEMP1*AP( K ) TEMP2 = TEMP2 + DCONJG( AP( K ) )*X( IX ) 110 CONTINUE Y( JY ) = Y( JY ) + ALPHA*TEMP2 JX = JX + INCX JY = JY + INCY KK = KK + ( N - J + 1 ) 120 CONTINUE END IF END IF * RETURN * * End of ZHPMV . * END * ************************************************************************ * SUBROUTINE ZTRMV ( UPLO, TRANS, DIAG, N, A, LDA, X, INCX ) * .. Scalar Arguments .. INTEGER INCX, LDA, N CHARACTER*1 DIAG, TRANS, UPLO * .. Array Arguments .. COMPLEX*16 A( LDA, * ), X( * ) * .. * * Purpose * ======= * * ZTRMV performs one of the matrix-vector operations * * x := A*x, or x := A'*x, or x := conjg( A' )*x, * * where x is an n element vector and A is an n by n unit, or non-unit, * upper or lower triangular matrix. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the matrix is an upper or * lower triangular matrix as follows: * * UPLO = 'U' or 'u' A is an upper triangular matrix. * * UPLO = 'L' or 'l' A is a lower triangular matrix. * * Unchanged on exit. * * TRANS - CHARACTER*1. * On entry, TRANS specifies the operation to be performed as * follows: * * TRANS = 'N' or 'n' x := A*x. * * TRANS = 'T' or 't' x := A'*x. * * TRANS = 'C' or 'c' x := conjg( A' )*x. * * Unchanged on exit. * * DIAG - CHARACTER*1. * On entry, DIAG specifies whether or not A is unit * triangular as follows: * * DIAG = 'U' or 'u' A is assumed to be unit triangular. * * DIAG = 'N' or 'n' A is not assumed to be unit * triangular. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * A - COMPLEX*16 array of DIMENSION ( LDA, n ). * Before entry with UPLO = 'U' or 'u', the leading n by n * upper triangular part of the array A must contain the upper * triangular matrix and the strictly lower triangular part of * A is not referenced. * Before entry with UPLO = 'L' or 'l', the leading n by n * lower triangular part of the array A must contain the lower * triangular matrix and the strictly upper triangular part of * A is not referenced. * Note that when DIAG = 'U' or 'u', the diagonal elements of * A are not referenced either, but are assumed to be unity. * Unchanged on exit. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * max( 1, n ). * Unchanged on exit. * * X - COMPLEX*16 array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element vector x. On exit, X is overwritten with the * tranformed vector x. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. COMPLEX*16 ZERO PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) ) * .. Local Scalars .. COMPLEX*16 TEMP INTEGER I, INFO, IX, J, JX, KX LOGICAL NOCONJ, NOUNIT * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC DCONJG, MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO , 'U' ).AND. $ .NOT.LSAME( UPLO , 'L' ) )THEN INFO = 1 ELSE IF( .NOT.LSAME( TRANS, 'N' ).AND. $ .NOT.LSAME( TRANS, 'T' ).AND. $ .NOT.LSAME( TRANS, 'C' ) )THEN INFO = 2 ELSE IF( .NOT.LSAME( DIAG , 'U' ).AND. $ .NOT.LSAME( DIAG , 'N' ) )THEN INFO = 3 ELSE IF( N.LT.0 )THEN INFO = 4 ELSE IF( LDA.LT.MAX( 1, N ) )THEN INFO = 6 ELSE IF( INCX.EQ.0 )THEN INFO = 8 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'ZTRMV ', INFO ) RETURN END IF * * Quick return if possible. * IF( N.EQ.0 ) $ RETURN * NOCONJ = LSAME( TRANS, 'T' ) NOUNIT = LSAME( DIAG , 'N' ) * * Set up the start point in X if the increment is not unity. This * will be ( N - 1 )*INCX too small for descending loops. * IF( INCX.LE.0 )THEN KX = 1 - ( N - 1 )*INCX ELSE IF( INCX.NE.1 )THEN KX = 1 END IF * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through A. * IF( LSAME( TRANS, 'N' ) )THEN * * Form x := A*x. * IF( LSAME( UPLO, 'U' ) )THEN IF( INCX.EQ.1 )THEN DO 20, J = 1, N IF( X( J ).NE.ZERO )THEN TEMP = X( J ) DO 10, I = 1, J - 1 X( I ) = X( I ) + TEMP*A( I, J ) 10 CONTINUE IF( NOUNIT ) $ X( J ) = X( J )*A( J, J ) END IF 20 CONTINUE ELSE JX = KX DO 40, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = X( JX ) IX = KX DO 30, I = 1, J - 1 X( IX ) = X( IX ) + TEMP*A( I, J ) IX = IX + INCX 30 CONTINUE IF( NOUNIT ) $ X( JX ) = X( JX )*A( J, J ) END IF JX = JX + INCX 40 CONTINUE END IF ELSE IF( INCX.EQ.1 )THEN DO 60, J = N, 1, -1 IF( X( J ).NE.ZERO )THEN TEMP = X( J ) DO 50, I = N, J + 1, -1 X( I ) = X( I ) + TEMP*A( I, J ) 50 CONTINUE IF( NOUNIT ) $ X( J ) = X( J )*A( J, J ) END IF 60 CONTINUE ELSE KX = KX + ( N - 1 )*INCX JX = KX DO 80, J = N, 1, -1 IF( X( JX ).NE.ZERO )THEN TEMP = X( JX ) IX = KX DO 70, I = N, J + 1, -1 X( IX ) = X( IX ) + TEMP*A( I, J ) IX = IX - INCX 70 CONTINUE IF( NOUNIT ) $ X( JX ) = X( JX )*A( J, J ) END IF JX = JX - INCX 80 CONTINUE END IF END IF ELSE * * Form x := A'*x or x := conjg( A' )*x. * IF( LSAME( UPLO, 'U' ) )THEN IF( INCX.EQ.1 )THEN DO 110, J = N, 1, -1 TEMP = X( J ) IF( NOCONJ )THEN IF( NOUNIT ) $ TEMP = TEMP*A( J, J ) DO 90, I = J - 1, 1, -1 TEMP = TEMP + A( I, J )*X( I ) 90 CONTINUE ELSE IF( NOUNIT ) $ TEMP = TEMP*DCONJG( A( J, J ) ) DO 100, I = J - 1, 1, -1 TEMP = TEMP + DCONJG( A( I, J ) )*X( I ) 100 CONTINUE END IF X( J ) = TEMP 110 CONTINUE ELSE JX = KX + ( N - 1 )*INCX DO 140, J = N, 1, -1 TEMP = X( JX ) IX = JX IF( NOCONJ )THEN IF( NOUNIT ) $ TEMP = TEMP*A( J, J ) DO 120, I = J - 1, 1, -1 IX = IX - INCX TEMP = TEMP + A( I, J )*X( IX ) 120 CONTINUE ELSE IF( NOUNIT ) $ TEMP = TEMP*DCONJG( A( J, J ) ) DO 130, I = J - 1, 1, -1 IX = IX - INCX TEMP = TEMP + DCONJG( A( I, J ) )*X( IX ) 130 CONTINUE END IF X( JX ) = TEMP JX = JX - INCX 140 CONTINUE END IF ELSE IF( INCX.EQ.1 )THEN DO 170, J = 1, N TEMP = X( J ) IF( NOCONJ )THEN IF( NOUNIT ) $ TEMP = TEMP*A( J, J ) DO 150, I = J + 1, N TEMP = TEMP + A( I, J )*X( I ) 150 CONTINUE ELSE IF( NOUNIT ) $ TEMP = TEMP*DCONJG( A( J, J ) ) DO 160, I = J + 1, N TEMP = TEMP + DCONJG( A( I, J ) )*X( I ) 160 CONTINUE END IF X( J ) = TEMP 170 CONTINUE ELSE JX = KX DO 200, J = 1, N TEMP = X( JX ) IX = JX IF( NOCONJ )THEN IF( NOUNIT ) $ TEMP = TEMP*A( J, J ) DO 180, I = J + 1, N IX = IX + INCX TEMP = TEMP + A( I, J )*X( IX ) 180 CONTINUE ELSE IF( NOUNIT ) $ TEMP = TEMP*DCONJG( A( J, J ) ) DO 190, I = J + 1, N IX = IX + INCX TEMP = TEMP + DCONJG( A( I, J ) )*X( IX ) 190 CONTINUE END IF X( JX ) = TEMP JX = JX + INCX 200 CONTINUE END IF END IF END IF * RETURN * * End of ZTRMV . * END * ************************************************************************ * SUBROUTINE ZTBMV ( UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX ) * .. Scalar Arguments .. INTEGER INCX, K, LDA, N CHARACTER*1 DIAG, TRANS, UPLO * .. Array Arguments .. COMPLEX*16 A( LDA, * ), X( * ) * .. * * Purpose * ======= * * ZTBMV performs one of the matrix-vector operations * * x := A*x, or x := A'*x, or x := conjg( A' )*x, * * where x is an n element vector and A is an n by n unit, or non-unit, * upper or lower triangular band matrix, with ( k + 1 ) diagonals. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the matrix is an upper or * lower triangular matrix as follows: * * UPLO = 'U' or 'u' A is an upper triangular matrix. * * UPLO = 'L' or 'l' A is a lower triangular matrix. * * Unchanged on exit. * * TRANS - CHARACTER*1. * On entry, TRANS specifies the operation to be performed as * follows: * * TRANS = 'N' or 'n' x := A*x. * * TRANS = 'T' or 't' x := A'*x. * * TRANS = 'C' or 'c' x := conjg( A' )*x. * * Unchanged on exit. * * DIAG - CHARACTER*1. * On entry, DIAG specifies whether or not A is unit * triangular as follows: * * DIAG = 'U' or 'u' A is assumed to be unit triangular. * * DIAG = 'N' or 'n' A is not assumed to be unit * triangular. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * K - INTEGER. * On entry with UPLO = 'U' or 'u', K specifies the number of * super-diagonals of the matrix A. * On entry with UPLO = 'L' or 'l', K specifies the number of * sub-diagonals of the matrix A. * K must satisfy 0 .le. K. * Unchanged on exit. * * A - COMPLEX*16 array of DIMENSION ( LDA, n ). * Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) * by n part of the array A must contain the upper triangular * band part of the matrix of coefficients, supplied column by * column, with the leading diagonal of the matrix in row * ( k + 1 ) of the array, the first super-diagonal starting at * position 2 in row k, and so on. The top left k by k triangle * of the array A is not referenced. * The following program segment will transfer an upper * triangular band matrix from conventional full matrix storage * to band storage: * * DO 20, J = 1, N * M = K + 1 - J * DO 10, I = MAX( 1, J - K ), J * A( M + I, J ) = matrix( I, J ) * 10 CONTINUE * 20 CONTINUE * * Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) * by n part of the array A must contain the lower triangular * band part of the matrix of coefficients, supplied column by * column, with the leading diagonal of the matrix in row 1 of * the array, the first sub-diagonal starting at position 1 in * row 2, and so on. The bottom right k by k triangle of the * array A is not referenced. * The following program segment will transfer a lower * triangular band matrix from conventional full matrix storage * to band storage: * * DO 20, J = 1, N * M = 1 - J * DO 10, I = J, MIN( N, J + K ) * A( M + I, J ) = matrix( I, J ) * 10 CONTINUE * 20 CONTINUE * * Note that when DIAG = 'U' or 'u' the elements of the array A * corresponding to the diagonal elements of the matrix are not * referenced, but are assumed to be unity. * Unchanged on exit. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * ( k + 1 ). * Unchanged on exit. * * X - COMPLEX*16 array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element vector x. On exit, X is overwritten with the * tranformed vector x. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. COMPLEX*16 ZERO PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) ) * .. Local Scalars .. COMPLEX*16 TEMP INTEGER I, INFO, IX, J, JX, KPLUS1, KX, L LOGICAL NOCONJ, NOUNIT * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC DCONJG, MAX, MIN * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO , 'U' ).AND. $ .NOT.LSAME( UPLO , 'L' ) )THEN INFO = 1 ELSE IF( .NOT.LSAME( TRANS, 'N' ).AND. $ .NOT.LSAME( TRANS, 'T' ).AND. $ .NOT.LSAME( TRANS, 'C' ) )THEN INFO = 2 ELSE IF( .NOT.LSAME( DIAG , 'U' ).AND. $ .NOT.LSAME( DIAG , 'N' ) )THEN INFO = 3 ELSE IF( N.LT.0 )THEN INFO = 4 ELSE IF( K.LT.0 )THEN INFO = 5 ELSE IF( LDA.LT.( K + 1 ) )THEN INFO = 7 ELSE IF( INCX.EQ.0 )THEN INFO = 9 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'ZTBMV ', INFO ) RETURN END IF * * Quick return if possible. * IF( N.EQ.0 ) $ RETURN * NOCONJ = LSAME( TRANS, 'T' ) NOUNIT = LSAME( DIAG , 'N' ) * * Set up the start point in X if the increment is not unity. This * will be ( N - 1 )*INCX too small for descending loops. * IF( INCX.LE.0 )THEN KX = 1 - ( N - 1 )*INCX ELSE IF( INCX.NE.1 )THEN KX = 1 END IF * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through A. * IF( LSAME( TRANS, 'N' ) )THEN * * Form x := A*x. * IF( LSAME( UPLO, 'U' ) )THEN KPLUS1 = K + 1 IF( INCX.EQ.1 )THEN DO 20, J = 1, N IF( X( J ).NE.ZERO )THEN TEMP = X( J ) L = KPLUS1 - J DO 10, I = MAX( 1, J - K ), J - 1 X( I ) = X( I ) + TEMP*A( L + I, J ) 10 CONTINUE IF( NOUNIT ) $ X( J ) = X( J )*A( KPLUS1, J ) END IF 20 CONTINUE ELSE JX = KX DO 40, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = X( JX ) IX = KX L = KPLUS1 - J DO 30, I = MAX( 1, J - K ), J - 1 X( IX ) = X( IX ) + TEMP*A( L + I, J ) IX = IX + INCX 30 CONTINUE IF( NOUNIT ) $ X( JX ) = X( JX )*A( KPLUS1, J ) END IF JX = JX + INCX IF( J.GT.K ) $ KX = KX + INCX 40 CONTINUE END IF ELSE IF( INCX.EQ.1 )THEN DO 60, J = N, 1, -1 IF( X( J ).NE.ZERO )THEN TEMP = X( J ) L = 1 - J DO 50, I = MIN( N, J + K ), J + 1, -1 X( I ) = X( I ) + TEMP*A( L + I, J ) 50 CONTINUE IF( NOUNIT ) $ X( J ) = X( J )*A( 1, J ) END IF 60 CONTINUE ELSE KX = KX + ( N - 1 )*INCX JX = KX DO 80, J = N, 1, -1 IF( X( JX ).NE.ZERO )THEN TEMP = X( JX ) IX = KX L = 1 - J DO 70, I = MIN( N, J + K ), J + 1, -1 X( IX ) = X( IX ) + TEMP*A( L + I, J ) IX = IX - INCX 70 CONTINUE IF( NOUNIT ) $ X( JX ) = X( JX )*A( 1, J ) END IF JX = JX - INCX IF( ( N - J ).GE.K ) $ KX = KX - INCX 80 CONTINUE END IF END IF ELSE * * Form x := A'*x or x := conjg( A' )*x. * IF( LSAME( UPLO, 'U' ) )THEN KPLUS1 = K + 1 IF( INCX.EQ.1 )THEN DO 110, J = N, 1, -1 TEMP = X( J ) L = KPLUS1 - J IF( NOCONJ )THEN IF( NOUNIT ) $ TEMP = TEMP*A( KPLUS1, J ) DO 90, I = J - 1, MAX( 1, J - K ), -1 TEMP = TEMP + A( L + I, J )*X( I ) 90 CONTINUE ELSE IF( NOUNIT ) $ TEMP = TEMP*DCONJG( A( KPLUS1, J ) ) DO 100, I = J - 1, MAX( 1, J - K ), -1 TEMP = TEMP + DCONJG( A( L + I, J ) )*X( I ) 100 CONTINUE END IF X( J ) = TEMP 110 CONTINUE ELSE KX = KX + ( N - 1 )*INCX JX = KX DO 140, J = N, 1, -1 TEMP = X( JX ) KX = KX - INCX IX = KX L = KPLUS1 - J IF( NOCONJ )THEN IF( NOUNIT ) $ TEMP = TEMP*A( KPLUS1, J ) DO 120, I = J - 1, MAX( 1, J - K ), -1 TEMP = TEMP + A( L + I, J )*X( IX ) IX = IX - INCX 120 CONTINUE ELSE IF( NOUNIT ) $ TEMP = TEMP*DCONJG( A( KPLUS1, J ) ) DO 130, I = J - 1, MAX( 1, J - K ), -1 TEMP = TEMP + DCONJG( A( L + I, J ) )*X( IX ) IX = IX - INCX 130 CONTINUE END IF X( JX ) = TEMP JX = JX - INCX 140 CONTINUE END IF ELSE IF( INCX.EQ.1 )THEN DO 170, J = 1, N TEMP = X( J ) L = 1 - J IF( NOCONJ )THEN IF( NOUNIT ) $ TEMP = TEMP*A( 1, J ) DO 150, I = J + 1, MIN( N, J + K ) TEMP = TEMP + A( L + I, J )*X( I ) 150 CONTINUE ELSE IF( NOUNIT ) $ TEMP = TEMP*DCONJG( A( 1, J ) ) DO 160, I = J + 1, MIN( N, J + K ) TEMP = TEMP + DCONJG( A( L + I, J ) )*X( I ) 160 CONTINUE END IF X( J ) = TEMP 170 CONTINUE ELSE JX = KX DO 200, J = 1, N TEMP = X( JX ) KX = KX + INCX IX = KX L = 1 - J IF( NOCONJ )THEN IF( NOUNIT ) $ TEMP = TEMP*A( 1, J ) DO 180, I = J + 1, MIN( N, J + K ) TEMP = TEMP + A( L + I, J )*X( IX ) IX = IX + INCX 180 CONTINUE ELSE IF( NOUNIT ) $ TEMP = TEMP*DCONJG( A( 1, J ) ) DO 190, I = J + 1, MIN( N, J + K ) TEMP = TEMP + DCONJG( A( L + I, J ) )*X( IX ) IX = IX + INCX 190 CONTINUE END IF X( JX ) = TEMP JX = JX + INCX 200 CONTINUE END IF END IF END IF * RETURN * * End of ZTBMV . * END * ************************************************************************ * SUBROUTINE ZTPMV ( UPLO, TRANS, DIAG, N, AP, X, INCX ) * .. Scalar Arguments .. INTEGER INCX, N CHARACTER*1 DIAG, TRANS, UPLO * .. Array Arguments .. COMPLEX*16 AP( * ), X( * ) * .. * * Purpose * ======= * * ZTPMV performs one of the matrix-vector operations * * x := A*x, or x := A'*x, or x := conjg( A' )*x, * * where x is an n element vector and A is an n by n unit, or non-unit, * upper or lower triangular matrix, supplied in packed form. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the matrix is an upper or * lower triangular matrix as follows: * * UPLO = 'U' or 'u' A is an upper triangular matrix. * * UPLO = 'L' or 'l' A is a lower triangular matrix. * * Unchanged on exit. * * TRANS - CHARACTER*1. * On entry, TRANS specifies the operation to be performed as * follows: * * TRANS = 'N' or 'n' x := A*x. * * TRANS = 'T' or 't' x := A'*x. * * TRANS = 'C' or 'c' x := conjg( A' )*x. * * Unchanged on exit. * * DIAG - CHARACTER*1. * On entry, DIAG specifies whether or not A is unit * triangular as follows: * * DIAG = 'U' or 'u' A is assumed to be unit triangular. * * DIAG = 'N' or 'n' A is not assumed to be unit * triangular. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * AP - COMPLEX*16 array of DIMENSION at least * ( ( n*( n + 1 ) )/2 ). * Before entry with UPLO = 'U' or 'u', the array AP must * contain the upper triangular matrix packed sequentially, * column by column, so that AP( 1 ) contains a( 1, 1 ), * AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) * respectively, and so on. * Before entry with UPLO = 'L' or 'l', the array AP must * contain the lower triangular matrix packed sequentially, * column by column, so that AP( 1 ) contains a( 1, 1 ), * AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) * respectively, and so on. * Note that when DIAG = 'U' or 'u', the diagonal elements of * A are not referenced, but are assumed to be unity. * Unchanged on exit. * * X - COMPLEX*16 array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element vector x. On exit, X is overwritten with the * tranformed vector x. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. COMPLEX*16 ZERO PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) ) * .. Local Scalars .. COMPLEX*16 TEMP INTEGER I, INFO, IX, J, JX, K, KK, KX LOGICAL NOCONJ, NOUNIT * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC DCONJG * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO , 'U' ).AND. $ .NOT.LSAME( UPLO , 'L' ) )THEN INFO = 1 ELSE IF( .NOT.LSAME( TRANS, 'N' ).AND. $ .NOT.LSAME( TRANS, 'T' ).AND. $ .NOT.LSAME( TRANS, 'C' ) )THEN INFO = 2 ELSE IF( .NOT.LSAME( DIAG , 'U' ).AND. $ .NOT.LSAME( DIAG , 'N' ) )THEN INFO = 3 ELSE IF( N.LT.0 )THEN INFO = 4 ELSE IF( INCX.EQ.0 )THEN INFO = 7 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'ZTPMV ', INFO ) RETURN END IF * * Quick return if possible. * IF( N.EQ.0 ) $ RETURN * NOCONJ = LSAME( TRANS, 'T' ) NOUNIT = LSAME( DIAG , 'N' ) * * Set up the start point in X if the increment is not unity. This * will be ( N - 1 )*INCX too small for descending loops. * IF( INCX.LE.0 )THEN KX = 1 - ( N - 1 )*INCX ELSE IF( INCX.NE.1 )THEN KX = 1 END IF * * Start the operations. In this version the elements of AP are * accessed sequentially with one pass through AP. * IF( LSAME( TRANS, 'N' ) )THEN * * Form x:= A*x. * IF( LSAME( UPLO, 'U' ) )THEN KK = 1 IF( INCX.EQ.1 )THEN DO 20, J = 1, N IF( X( J ).NE.ZERO )THEN TEMP = X( J ) K = KK DO 10, I = 1, J - 1 X( I ) = X( I ) + TEMP*AP( K ) K = K + 1 10 CONTINUE IF( NOUNIT ) $ X( J ) = X( J )*AP( KK + J - 1 ) END IF KK = KK + J 20 CONTINUE ELSE JX = KX DO 40, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = X( JX ) IX = KX DO 30, K = KK, KK + J - 2 X( IX ) = X( IX ) + TEMP*AP( K ) IX = IX + INCX 30 CONTINUE IF( NOUNIT ) $ X( JX ) = X( JX )*AP( KK + J - 1 ) END IF JX = JX + INCX KK = KK + J 40 CONTINUE END IF ELSE KK = ( N*( N + 1 ) )/2 IF( INCX.EQ.1 )THEN DO 60, J = N, 1, -1 IF( X( J ).NE.ZERO )THEN TEMP = X( J ) K = KK DO 50, I = N, J + 1, -1 X( I ) = X( I ) + TEMP*AP( K ) K = K - 1 50 CONTINUE IF( NOUNIT ) $ X( J ) = X( J )*AP( KK - N + J ) END IF KK = KK - ( N - J + 1 ) 60 CONTINUE ELSE KX = KX + ( N - 1 )*INCX JX = KX DO 80, J = N, 1, -1 IF( X( JX ).NE.ZERO )THEN TEMP = X( JX ) IX = KX DO 70, K = KK, KK - ( N - ( J + 1 ) ), -1 X( IX ) = X( IX ) + TEMP*AP( K ) IX = IX - INCX 70 CONTINUE IF( NOUNIT ) $ X( JX ) = X( JX )*AP( KK - N + J ) END IF JX = JX - INCX KK = KK - ( N - J + 1 ) 80 CONTINUE END IF END IF ELSE * * Form x := A'*x or x := conjg( A' )*x. * IF( LSAME( UPLO, 'U' ) )THEN KK = ( N*( N + 1 ) )/2 IF( INCX.EQ.1 )THEN DO 110, J = N, 1, -1 TEMP = X( J ) K = KK - 1 IF( NOCONJ )THEN IF( NOUNIT ) $ TEMP = TEMP*AP( KK ) DO 90, I = J - 1, 1, -1 TEMP = TEMP + AP( K )*X( I ) K = K - 1 90 CONTINUE ELSE IF( NOUNIT ) $ TEMP = TEMP*DCONJG( AP( KK ) ) DO 100, I = J - 1, 1, -1 TEMP = TEMP + DCONJG( AP( K ) )*X( I ) K = K - 1 100 CONTINUE END IF X( J ) = TEMP KK = KK - J 110 CONTINUE ELSE JX = KX + ( N - 1 )*INCX DO 140, J = N, 1, -1 TEMP = X( JX ) IX = JX IF( NOCONJ )THEN IF( NOUNIT ) $ TEMP = TEMP*AP( KK ) DO 120, K = KK - 1, KK - J + 1, -1 IX = IX - INCX TEMP = TEMP + AP( K )*X( IX ) 120 CONTINUE ELSE IF( NOUNIT ) $ TEMP = TEMP*DCONJG( AP( KK ) ) DO 130, K = KK - 1, KK - J + 1, -1 IX = IX - INCX TEMP = TEMP + DCONJG( AP( K ) )*X( IX ) 130 CONTINUE END IF X( JX ) = TEMP JX = JX - INCX KK = KK - J 140 CONTINUE END IF ELSE KK = 1 IF( INCX.EQ.1 )THEN DO 170, J = 1, N TEMP = X( J ) K = KK + 1 IF( NOCONJ )THEN IF( NOUNIT ) $ TEMP = TEMP*AP( KK ) DO 150, I = J + 1, N TEMP = TEMP + AP( K )*X( I ) K = K + 1 150 CONTINUE ELSE IF( NOUNIT ) $ TEMP = TEMP*DCONJG( AP( KK ) ) DO 160, I = J + 1, N TEMP = TEMP + DCONJG( AP( K ) )*X( I ) K = K + 1 160 CONTINUE END IF X( J ) = TEMP KK = KK + ( N - J + 1 ) 170 CONTINUE ELSE JX = KX DO 200, J = 1, N TEMP = X( JX ) IX = JX IF( NOCONJ )THEN IF( NOUNIT ) $ TEMP = TEMP*AP( KK ) DO 180, K = KK + 1, KK + N - J IX = IX + INCX TEMP = TEMP + AP( K )*X( IX ) 180 CONTINUE ELSE IF( NOUNIT ) $ TEMP = TEMP*DCONJG( AP( KK ) ) DO 190, K = KK + 1, KK + N - J IX = IX + INCX TEMP = TEMP + DCONJG( AP( K ) )*X( IX ) 190 CONTINUE END IF X( JX ) = TEMP JX = JX + INCX KK = KK + ( N - J + 1 ) 200 CONTINUE END IF END IF END IF * RETURN * * End of ZTPMV . * END * ************************************************************************ * SUBROUTINE ZTRSV ( UPLO, TRANS, DIAG, N, A, LDA, X, INCX ) * .. Scalar Arguments .. INTEGER INCX, LDA, N CHARACTER*1 DIAG, TRANS, UPLO * .. Array Arguments .. COMPLEX*16 A( LDA, * ), X( * ) * .. * * Purpose * ======= * * ZTRSV solves one of the systems of equations * * A*x = b, or A'*x = b, or conjg( A' )*x = b, * * where b and x are n element vectors and A is an n by n unit, or * non-unit, upper or lower triangular matrix. * * No test for singularity or near-singularity is included in this * routine. Such tests must be performed before calling this routine. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the matrix is an upper or * lower triangular matrix as follows: * * UPLO = 'U' or 'u' A is an upper triangular matrix. * * UPLO = 'L' or 'l' A is a lower triangular matrix. * * Unchanged on exit. * * TRANS - CHARACTER*1. * On entry, TRANS specifies the equations to be solved as * follows: * * TRANS = 'N' or 'n' A*x = b. * * TRANS = 'T' or 't' A'*x = b. * * TRANS = 'C' or 'c' conjg( A' )*x = b. * * Unchanged on exit. * * DIAG - CHARACTER*1. * On entry, DIAG specifies whether or not A is unit * triangular as follows: * * DIAG = 'U' or 'u' A is assumed to be unit triangular. * * DIAG = 'N' or 'n' A is not assumed to be unit * triangular. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * A - COMPLEX*16 array of DIMENSION ( LDA, n ). * Before entry with UPLO = 'U' or 'u', the leading n by n * upper triangular part of the array A must contain the upper * triangular matrix and the strictly lower triangular part of * A is not referenced. * Before entry with UPLO = 'L' or 'l', the leading n by n * lower triangular part of the array A must contain the lower * triangular matrix and the strictly upper triangular part of * A is not referenced. * Note that when DIAG = 'U' or 'u', the diagonal elements of * A are not referenced either, but are assumed to be unity. * Unchanged on exit. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * max( 1, n ). * Unchanged on exit. * * X - COMPLEX*16 array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element right-hand side vector b. On exit, X is overwritten * with the solution vector x. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. COMPLEX*16 ZERO PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) ) * .. Local Scalars .. COMPLEX*16 TEMP INTEGER I, INFO, IX, J, JX, KX LOGICAL NOCONJ, NOUNIT * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC DCONJG, MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO , 'U' ).AND. $ .NOT.LSAME( UPLO , 'L' ) )THEN INFO = 1 ELSE IF( .NOT.LSAME( TRANS, 'N' ).AND. $ .NOT.LSAME( TRANS, 'T' ).AND. $ .NOT.LSAME( TRANS, 'C' ) )THEN INFO = 2 ELSE IF( .NOT.LSAME( DIAG , 'U' ).AND. $ .NOT.LSAME( DIAG , 'N' ) )THEN INFO = 3 ELSE IF( N.LT.0 )THEN INFO = 4 ELSE IF( LDA.LT.MAX( 1, N ) )THEN INFO = 6 ELSE IF( INCX.EQ.0 )THEN INFO = 8 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'ZTRSV ', INFO ) RETURN END IF * * Quick return if possible. * IF( N.EQ.0 ) $ RETURN * NOCONJ = LSAME( TRANS, 'T' ) NOUNIT = LSAME( DIAG , 'N' ) * * Set up the start point in X if the increment is not unity. This * will be ( N - 1 )*INCX too small for descending loops. * IF( INCX.LE.0 )THEN KX = 1 - ( N - 1 )*INCX ELSE IF( INCX.NE.1 )THEN KX = 1 END IF * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through A. * IF( LSAME( TRANS, 'N' ) )THEN * * Form x := inv( A )*x. * IF( LSAME( UPLO, 'U' ) )THEN IF( INCX.EQ.1 )THEN DO 20, J = N, 1, -1 IF( X( J ).NE.ZERO )THEN IF( NOUNIT ) $ X( J ) = X( J )/A( J, J ) TEMP = X( J ) DO 10, I = J - 1, 1, -1 X( I ) = X( I ) - TEMP*A( I, J ) 10 CONTINUE END IF 20 CONTINUE ELSE JX = KX + ( N - 1 )*INCX DO 40, J = N, 1, -1 IF( X( JX ).NE.ZERO )THEN IF( NOUNIT ) $ X( JX ) = X( JX )/A( J, J ) TEMP = X( JX ) IX = JX DO 30, I = J - 1, 1, -1 IX = IX - INCX X( IX ) = X( IX ) - TEMP*A( I, J ) 30 CONTINUE END IF JX = JX - INCX 40 CONTINUE END IF ELSE IF( INCX.EQ.1 )THEN DO 60, J = 1, N IF( X( J ).NE.ZERO )THEN IF( NOUNIT ) $ X( J ) = X( J )/A( J, J ) TEMP = X( J ) DO 50, I = J + 1, N X( I ) = X( I ) - TEMP*A( I, J ) 50 CONTINUE END IF 60 CONTINUE ELSE JX = KX DO 80, J = 1, N IF( X( JX ).NE.ZERO )THEN IF( NOUNIT ) $ X( JX ) = X( JX )/A( J, J ) TEMP = X( JX ) IX = JX DO 70, I = J + 1, N IX = IX + INCX X( IX ) = X( IX ) - TEMP*A( I, J ) 70 CONTINUE END IF JX = JX + INCX 80 CONTINUE END IF END IF ELSE * * Form x := inv( A' )*x or x := inv( conjg( A' ) )*x. * IF( LSAME( UPLO, 'U' ) )THEN IF( INCX.EQ.1 )THEN DO 110, J = 1, N TEMP = X( J ) IF( NOCONJ )THEN DO 90, I = 1, J - 1 TEMP = TEMP - A( I, J )*X( I ) 90 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/A( J, J ) ELSE DO 100, I = 1, J - 1 TEMP = TEMP - DCONJG( A( I, J ) )*X( I ) 100 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/DCONJG( A( J, J ) ) END IF X( J ) = TEMP 110 CONTINUE ELSE JX = KX DO 140, J = 1, N IX = KX TEMP = X( JX ) IF( NOCONJ )THEN DO 120, I = 1, J - 1 TEMP = TEMP - A( I, J )*X( IX ) IX = IX + INCX 120 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/A( J, J ) ELSE DO 130, I = 1, J - 1 TEMP = TEMP - DCONJG( A( I, J ) )*X( IX ) IX = IX + INCX 130 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/DCONJG( A( J, J ) ) END IF X( JX ) = TEMP JX = JX + INCX 140 CONTINUE END IF ELSE IF( INCX.EQ.1 )THEN DO 170, J = N, 1, -1 TEMP = X( J ) IF( NOCONJ )THEN DO 150, I = N, J + 1, -1 TEMP = TEMP - A( I, J )*X( I ) 150 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/A( J, J ) ELSE DO 160, I = N, J + 1, -1 TEMP = TEMP - DCONJG( A( I, J ) )*X( I ) 160 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/DCONJG( A( J, J ) ) END IF X( J ) = TEMP 170 CONTINUE ELSE KX = KX + ( N - 1 )*INCX JX = KX DO 200, J = N, 1, -1 IX = KX TEMP = X( JX ) IF( NOCONJ )THEN DO 180, I = N, J + 1, -1 TEMP = TEMP - A( I, J )*X( IX ) IX = IX - INCX 180 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/A( J, J ) ELSE DO 190, I = N, J + 1, -1 TEMP = TEMP - DCONJG( A( I, J ) )*X( IX ) IX = IX - INCX 190 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/DCONJG( A( J, J ) ) END IF X( JX ) = TEMP JX = JX - INCX 200 CONTINUE END IF END IF END IF * RETURN * * End of ZTRSV . * END * ************************************************************************ * SUBROUTINE ZTBSV ( UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX ) * .. Scalar Arguments .. INTEGER INCX, K, LDA, N CHARACTER*1 DIAG, TRANS, UPLO * .. Array Arguments .. COMPLEX*16 A( LDA, * ), X( * ) * .. * * Purpose * ======= * * ZTBSV solves one of the systems of equations * * A*x = b, or A'*x = b, or conjg( A' )*x = b, * * where b and x are n element vectors and A is an n by n unit, or * non-unit, upper or lower triangular band matrix, with ( k + 1 ) * diagonals. * * No test for singularity or near-singularity is included in this * routine. Such tests must be performed before calling this routine. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the matrix is an upper or * lower triangular matrix as follows: * * UPLO = 'U' or 'u' A is an upper triangular matrix. * * UPLO = 'L' or 'l' A is a lower triangular matrix. * * Unchanged on exit. * * TRANS - CHARACTER*1. * On entry, TRANS specifies the equations to be solved as * follows: * * TRANS = 'N' or 'n' A*x = b. * * TRANS = 'T' or 't' A'*x = b. * * TRANS = 'C' or 'c' conjg( A' )*x = b. * * Unchanged on exit. * * DIAG - CHARACTER*1. * On entry, DIAG specifies whether or not A is unit * triangular as follows: * * DIAG = 'U' or 'u' A is assumed to be unit triangular. * * DIAG = 'N' or 'n' A is not assumed to be unit * triangular. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * K - INTEGER. * On entry with UPLO = 'U' or 'u', K specifies the number of * super-diagonals of the matrix A. * On entry with UPLO = 'L' or 'l', K specifies the number of * sub-diagonals of the matrix A. * K must satisfy 0 .le. K. * Unchanged on exit. * * A - COMPLEX*16 array of DIMENSION ( LDA, n ). * Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) * by n part of the array A must contain the upper triangular * band part of the matrix of coefficients, supplied column by * column, with the leading diagonal of the matrix in row * ( k + 1 ) of the array, the first super-diagonal starting at * position 2 in row k, and so on. The top left k by k triangle * of the array A is not referenced. * The following program segment will transfer an upper * triangular band matrix from conventional full matrix storage * to band storage: * * DO 20, J = 1, N * M = K + 1 - J * DO 10, I = MAX( 1, J - K ), J * A( M + I, J ) = matrix( I, J ) * 10 CONTINUE * 20 CONTINUE * * Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) * by n part of the array A must contain the lower triangular * band part of the matrix of coefficients, supplied column by * column, with the leading diagonal of the matrix in row 1 of * the array, the first sub-diagonal starting at position 1 in * row 2, and so on. The bottom right k by k triangle of the * array A is not referenced. * The following program segment will transfer a lower * triangular band matrix from conventional full matrix storage * to band storage: * * DO 20, J = 1, N * M = 1 - J * DO 10, I = J, MIN( N, J + K ) * A( M + I, J ) = matrix( I, J ) * 10 CONTINUE * 20 CONTINUE * * Note that when DIAG = 'U' or 'u' the elements of the array A * corresponding to the diagonal elements of the matrix are not * referenced, but are assumed to be unity. * Unchanged on exit. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * ( k + 1 ). * Unchanged on exit. * * X - COMPLEX*16 array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element right-hand side vector b. On exit, X is overwritten * with the solution vector x. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. COMPLEX*16 ZERO PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) ) * .. Local Scalars .. COMPLEX*16 TEMP INTEGER I, INFO, IX, J, JX, KPLUS1, KX, L LOGICAL NOCONJ, NOUNIT * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC DCONJG, MAX, MIN * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO , 'U' ).AND. $ .NOT.LSAME( UPLO , 'L' ) )THEN INFO = 1 ELSE IF( .NOT.LSAME( TRANS, 'N' ).AND. $ .NOT.LSAME( TRANS, 'T' ).AND. $ .NOT.LSAME( TRANS, 'C' ) )THEN INFO = 2 ELSE IF( .NOT.LSAME( DIAG , 'U' ).AND. $ .NOT.LSAME( DIAG , 'N' ) )THEN INFO = 3 ELSE IF( N.LT.0 )THEN INFO = 4 ELSE IF( K.LT.0 )THEN INFO = 5 ELSE IF( LDA.LT.( K + 1 ) )THEN INFO = 7 ELSE IF( INCX.EQ.0 )THEN INFO = 9 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'ZTBSV ', INFO ) RETURN END IF * * Quick return if possible. * IF( N.EQ.0 ) $ RETURN * NOCONJ = LSAME( TRANS, 'T' ) NOUNIT = LSAME( DIAG , 'N' ) * * Set up the start point in X if the increment is not unity. This * will be ( N - 1 )*INCX too small for descending loops. * IF( INCX.LE.0 )THEN KX = 1 - ( N - 1 )*INCX ELSE IF( INCX.NE.1 )THEN KX = 1 END IF * * Start the operations. In this version the elements of A are * accessed by sequentially with one pass through A. * IF( LSAME( TRANS, 'N' ) )THEN * * Form x := inv( A )*x. * IF( LSAME( UPLO, 'U' ) )THEN KPLUS1 = K + 1 IF( INCX.EQ.1 )THEN DO 20, J = N, 1, -1 IF( X( J ).NE.ZERO )THEN L = KPLUS1 - J IF( NOUNIT ) $ X( J ) = X( J )/A( KPLUS1, J ) TEMP = X( J ) DO 10, I = J - 1, MAX( 1, J - K ), -1 X( I ) = X( I ) - TEMP*A( L + I, J ) 10 CONTINUE END IF 20 CONTINUE ELSE KX = KX + ( N - 1 )*INCX JX = KX DO 40, J = N, 1, -1 KX = KX - INCX IF( X( JX ).NE.ZERO )THEN IX = KX L = KPLUS1 - J IF( NOUNIT ) $ X( JX ) = X( JX )/A( KPLUS1, J ) TEMP = X( JX ) DO 30, I = J - 1, MAX( 1, J - K ), -1 X( IX ) = X( IX ) - TEMP*A( L + I, J ) IX = IX - INCX 30 CONTINUE END IF JX = JX - INCX 40 CONTINUE END IF ELSE IF( INCX.EQ.1 )THEN DO 60, J = 1, N IF( X( J ).NE.ZERO )THEN L = 1 - J IF( NOUNIT ) $ X( J ) = X( J )/A( 1, J ) TEMP = X( J ) DO 50, I = J + 1, MIN( N, J + K ) X( I ) = X( I ) - TEMP*A( L + I, J ) 50 CONTINUE END IF 60 CONTINUE ELSE JX = KX DO 80, J = 1, N KX = KX + INCX IF( X( JX ).NE.ZERO )THEN IX = KX L = 1 - J IF( NOUNIT ) $ X( JX ) = X( JX )/A( 1, J ) TEMP = X( JX ) DO 70, I = J + 1, MIN( N, J + K ) X( IX ) = X( IX ) - TEMP*A( L + I, J ) IX = IX + INCX 70 CONTINUE END IF JX = JX + INCX 80 CONTINUE END IF END IF ELSE * * Form x := inv( A' )*x or x := inv( conjg( A') )*x. * IF( LSAME( UPLO, 'U' ) )THEN KPLUS1 = K + 1 IF( INCX.EQ.1 )THEN DO 110, J = 1, N TEMP = X( J ) L = KPLUS1 - J IF( NOCONJ )THEN DO 90, I = MAX( 1, J - K ), J - 1 TEMP = TEMP - A( L + I, J )*X( I ) 90 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/A( KPLUS1, J ) ELSE DO 100, I = MAX( 1, J - K ), J - 1 TEMP = TEMP - DCONJG( A( L + I, J ) )*X( I ) 100 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/DCONJG( A( KPLUS1, J ) ) END IF X( J ) = TEMP 110 CONTINUE ELSE JX = KX DO 140, J = 1, N TEMP = X( JX ) IX = KX L = KPLUS1 - J IF( NOCONJ )THEN DO 120, I = MAX( 1, J - K ), J - 1 TEMP = TEMP - A( L + I, J )*X( IX ) IX = IX + INCX 120 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/A( KPLUS1, J ) ELSE DO 130, I = MAX( 1, J - K ), J - 1 TEMP = TEMP - DCONJG( A( L + I, J ) )*X( IX ) IX = IX + INCX 130 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/DCONJG( A( KPLUS1, J ) ) END IF X( JX ) = TEMP JX = JX + INCX IF( J.GT.K ) $ KX = KX + INCX 140 CONTINUE END IF ELSE IF( INCX.EQ.1 )THEN DO 170, J = N, 1, -1 TEMP = X( J ) L = 1 - J IF( NOCONJ )THEN DO 150, I = MIN( N, J + K ), J + 1, -1 TEMP = TEMP - A( L + I, J )*X( I ) 150 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/A( 1, J ) ELSE DO 160, I = MIN( N, J + K ), J + 1, -1 TEMP = TEMP - DCONJG( A( L + I, J ) )*X( I ) 160 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/DCONJG( A( 1, J ) ) END IF X( J ) = TEMP 170 CONTINUE ELSE KX = KX + ( N - 1 )*INCX JX = KX DO 200, J = N, 1, -1 TEMP = X( JX ) IX = KX L = 1 - J IF( NOCONJ )THEN DO 180, I = MIN( N, J + K ), J + 1, -1 TEMP = TEMP - A( L + I, J )*X( IX ) IX = IX - INCX 180 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/A( 1, J ) ELSE DO 190, I = MIN( N, J + K ), J + 1, -1 TEMP = TEMP - DCONJG( A( L + I, J ) )*X( IX ) IX = IX - INCX 190 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/DCONJG( A( 1, J ) ) END IF X( JX ) = TEMP JX = JX - INCX IF( ( N - J ).GE.K ) $ KX = KX - INCX 200 CONTINUE END IF END IF END IF * RETURN * * End of ZTBSV . * END * ************************************************************************ * SUBROUTINE ZTPSV ( UPLO, TRANS, DIAG, N, AP, X, INCX ) * .. Scalar Arguments .. INTEGER INCX, N CHARACTER*1 DIAG, TRANS, UPLO * .. Array Arguments .. COMPLEX*16 AP( * ), X( * ) * .. * * Purpose * ======= * * ZTPSV solves one of the systems of equations * * A*x = b, or A'*x = b, or conjg( A' )*x = b, * * where b and x are n element vectors and A is an n by n unit, or * non-unit, upper or lower triangular matrix, supplied in packed form. * * No test for singularity or near-singularity is included in this * routine. Such tests must be performed before calling this routine. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the matrix is an upper or * lower triangular matrix as follows: * * UPLO = 'U' or 'u' A is an upper triangular matrix. * * UPLO = 'L' or 'l' A is a lower triangular matrix. * * Unchanged on exit. * * TRANS - CHARACTER*1. * On entry, TRANS specifies the equations to be solved as * follows: * * TRANS = 'N' or 'n' A*x = b. * * TRANS = 'T' or 't' A'*x = b. * * TRANS = 'C' or 'c' conjg( A' )*x = b. * * Unchanged on exit. * * DIAG - CHARACTER*1. * On entry, DIAG specifies whether or not A is unit * triangular as follows: * * DIAG = 'U' or 'u' A is assumed to be unit triangular. * * DIAG = 'N' or 'n' A is not assumed to be unit * triangular. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * AP - COMPLEX*16 array of DIMENSION at least * ( ( n*( n + 1 ) )/2 ). * Before entry with UPLO = 'U' or 'u', the array AP must * contain the upper triangular matrix packed sequentially, * column by column, so that AP( 1 ) contains a( 1, 1 ), * AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) * respectively, and so on. * Before entry with UPLO = 'L' or 'l', the array AP must * contain the lower triangular matrix packed sequentially, * column by column, so that AP( 1 ) contains a( 1, 1 ), * AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) * respectively, and so on. * Note that when DIAG = 'U' or 'u', the diagonal elements of * A are not referenced, but are assumed to be unity. * Unchanged on exit. * * X - COMPLEX*16 array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element right-hand side vector b. On exit, X is overwritten * with the solution vector x. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. COMPLEX*16 ZERO PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) ) * .. Local Scalars .. COMPLEX*16 TEMP INTEGER I, INFO, IX, J, JX, K, KK, KX LOGICAL NOCONJ, NOUNIT * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC DCONJG * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO , 'U' ).AND. $ .NOT.LSAME( UPLO , 'L' ) )THEN INFO = 1 ELSE IF( .NOT.LSAME( TRANS, 'N' ).AND. $ .NOT.LSAME( TRANS, 'T' ).AND. $ .NOT.LSAME( TRANS, 'C' ) )THEN INFO = 2 ELSE IF( .NOT.LSAME( DIAG , 'U' ).AND. $ .NOT.LSAME( DIAG , 'N' ) )THEN INFO = 3 ELSE IF( N.LT.0 )THEN INFO = 4 ELSE IF( INCX.EQ.0 )THEN INFO = 7 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'ZTPSV ', INFO ) RETURN END IF * * Quick return if possible. * IF( N.EQ.0 ) $ RETURN * NOCONJ = LSAME( TRANS, 'T' ) NOUNIT = LSAME( DIAG , 'N' ) * * Set up the start point in X if the increment is not unity. This * will be ( N - 1 )*INCX too small for descending loops. * IF( INCX.LE.0 )THEN KX = 1 - ( N - 1 )*INCX ELSE IF( INCX.NE.1 )THEN KX = 1 END IF * * Start the operations. In this version the elements of AP are * accessed sequentially with one pass through AP. * IF( LSAME( TRANS, 'N' ) )THEN * * Form x := inv( A )*x. * IF( LSAME( UPLO, 'U' ) )THEN KK = ( N*( N + 1 ) )/2 IF( INCX.EQ.1 )THEN DO 20, J = N, 1, -1 IF( X( J ).NE.ZERO )THEN IF( NOUNIT ) $ X( J ) = X( J )/AP( KK ) TEMP = X( J ) K = KK - 1 DO 10, I = J - 1, 1, -1 X( I ) = X( I ) - TEMP*AP( K ) K = K - 1 10 CONTINUE END IF KK = KK - J 20 CONTINUE ELSE JX = KX + ( N - 1 )*INCX DO 40, J = N, 1, -1 IF( X( JX ).NE.ZERO )THEN IF( NOUNIT ) $ X( JX ) = X( JX )/AP( KK ) TEMP = X( JX ) IX = JX DO 30, K = KK - 1, KK - J + 1, -1 IX = IX - INCX X( IX ) = X( IX ) - TEMP*AP( K ) 30 CONTINUE END IF JX = JX - INCX KK = KK - J 40 CONTINUE END IF ELSE KK = 1 IF( INCX.EQ.1 )THEN DO 60, J = 1, N IF( X( J ).NE.ZERO )THEN IF( NOUNIT ) $ X( J ) = X( J )/AP( KK ) TEMP = X( J ) K = KK + 1 DO 50, I = J + 1, N X( I ) = X( I ) - TEMP*AP( K ) K = K + 1 50 CONTINUE END IF KK = KK + ( N - J + 1 ) 60 CONTINUE ELSE JX = KX DO 80, J = 1, N IF( X( JX ).NE.ZERO )THEN IF( NOUNIT ) $ X( JX ) = X( JX )/AP( KK ) TEMP = X( JX ) IX = JX DO 70, K = KK + 1, KK + N - J IX = IX + INCX X( IX ) = X( IX ) - TEMP*AP( K ) 70 CONTINUE END IF JX = JX + INCX KK = KK + ( N - J + 1 ) 80 CONTINUE END IF END IF ELSE * * Form x := inv( A' )*x or x := inv( conjg( A' ) )*x. * IF( LSAME( UPLO, 'U' ) )THEN KK = 1 IF( INCX.EQ.1 )THEN DO 110, J = 1, N TEMP = X( J ) K = KK IF( NOCONJ )THEN DO 90, I = 1, J - 1 TEMP = TEMP - AP( K )*X( I ) K = K + 1 90 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/AP( KK + J - 1 ) ELSE DO 100, I = 1, J - 1 TEMP = TEMP - DCONJG( AP( K ) )*X( I ) K = K + 1 100 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/DCONJG( AP( KK + J - 1 ) ) END IF X( J ) = TEMP KK = KK + J 110 CONTINUE ELSE JX = KX DO 140, J = 1, N TEMP = X( JX ) IX = KX IF( NOCONJ )THEN DO 120, K = KK, KK + J - 2 TEMP = TEMP - AP( K )*X( IX ) IX = IX + INCX 120 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/AP( KK + J - 1 ) ELSE DO 130, K = KK, KK + J - 2 TEMP = TEMP - DCONJG( AP( K ) )*X( IX ) IX = IX + INCX 130 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/DCONJG( AP( KK + J - 1 ) ) END IF X( JX ) = TEMP JX = JX + INCX KK = KK + J 140 CONTINUE END IF ELSE KK = ( N*( N + 1 ) )/2 IF( INCX.EQ.1 )THEN DO 170, J = N, 1, -1 TEMP = X( J ) K = KK IF( NOCONJ )THEN DO 150, I = N, J + 1, -1 TEMP = TEMP - AP( K )*X( I ) K = K - 1 150 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/AP( KK - N + J ) ELSE DO 160, I = N, J + 1, -1 TEMP = TEMP - DCONJG( AP( K ) )*X( I ) K = K - 1 160 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/DCONJG( AP( KK - N + J ) ) END IF X( J ) = TEMP KK = KK - ( N - J + 1 ) 170 CONTINUE ELSE KX = KX + ( N - 1 )*INCX JX = KX DO 200, J = N, 1, -1 TEMP = X( JX ) IX = KX IF( NOCONJ )THEN DO 180, K = KK, KK - ( N - ( J + 1 ) ), -1 TEMP = TEMP - AP( K )*X( IX ) IX = IX - INCX 180 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/AP( KK - N + J ) ELSE DO 190, K = KK, KK - ( N - ( J + 1 ) ), -1 TEMP = TEMP - DCONJG( AP( K ) )*X( IX ) IX = IX - INCX 190 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/DCONJG( AP( KK - N + J ) ) END IF X( JX ) = TEMP JX = JX - INCX KK = KK - ( N - J + 1 ) 200 CONTINUE END IF END IF END IF * RETURN * * End of ZTPSV . * END * ************************************************************************ * SUBROUTINE ZGERU ( M, N, ALPHA, X, INCX, Y, INCY, A, LDA ) * .. Scalar Arguments .. COMPLEX*16 ALPHA INTEGER INCX, INCY, LDA, M, N * .. Array Arguments .. COMPLEX*16 A( LDA, * ), X( * ), Y( * ) * .. * * Purpose * ======= * * ZGERU performs the rank 1 operation * * A := alpha*x*y' + A, * * where alpha is a scalar, x is an m element vector, y is an n element * vector and A is an m by n matrix. * * Parameters * ========== * * M - INTEGER. * On entry, M specifies the number of rows of the matrix A. * M must be at least zero. * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the number of columns of the matrix A. * N must be at least zero. * Unchanged on exit. * * ALPHA - COMPLEX*16 . * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * X - COMPLEX*16 array of dimension at least * ( 1 + ( m - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the m * element vector x. * Unchanged on exit. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * Y - COMPLEX*16 array of dimension at least * ( 1 + ( n - 1 )*abs( INCY ) ). * Before entry, the incremented array Y must contain the n * element vector y. * Unchanged on exit. * * INCY - INTEGER. * On entry, INCY specifies the increment for the elements of * Y. INCY must not be zero. * Unchanged on exit. * * A - COMPLEX*16 array of DIMENSION ( LDA, n ). * Before entry, the leading m by n part of the array A must * contain the matrix of coefficients. On exit, A is * overwritten by the updated matrix. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * max( 1, m ). * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. COMPLEX*16 ZERO PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) ) * .. Local Scalars .. COMPLEX*16 TEMP INTEGER I, INFO, IX, J, JY, KX * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( M.LT.0 )THEN INFO = 1 ELSE IF( N.LT.0 )THEN INFO = 2 ELSE IF( INCX.EQ.0 )THEN INFO = 5 ELSE IF( INCY.EQ.0 )THEN INFO = 7 ELSE IF( LDA.LT.MAX( 1, M ) )THEN INFO = 9 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'ZGERU ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( M.EQ.0 ).OR.( N.EQ.0 ).OR.( ALPHA.EQ.ZERO ) ) $ RETURN * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through A. * IF( INCY.GT.0 )THEN JY = 1 ELSE JY = 1 - ( N - 1 )*INCY END IF IF( INCX.EQ.1 )THEN DO 20, J = 1, N IF( Y( JY ).NE.ZERO )THEN TEMP = ALPHA*Y( JY ) DO 10, I = 1, M A( I, J ) = A( I, J ) + X( I )*TEMP 10 CONTINUE END IF JY = JY + INCY 20 CONTINUE ELSE IF( INCX.GT.0 )THEN KX = 1 ELSE KX = 1 - ( M - 1 )*INCX END IF DO 40, J = 1, N IF( Y( JY ).NE.ZERO )THEN TEMP = ALPHA*Y( JY ) IX = KX DO 30, I = 1, M A( I, J ) = A( I, J ) + X( IX )*TEMP IX = IX + INCX 30 CONTINUE END IF JY = JY + INCY 40 CONTINUE END IF * RETURN * * End of ZGERU . * END * ************************************************************************ * SUBROUTINE ZGERC ( M, N, ALPHA, X, INCX, Y, INCY, A, LDA ) * .. Scalar Arguments .. COMPLEX*16 ALPHA INTEGER INCX, INCY, LDA, M, N * .. Array Arguments .. COMPLEX*16 A( LDA, * ), X( * ), Y( * ) * .. * * Purpose * ======= * * ZGERC performs the rank 1 operation * * A := alpha*x*conjg( y' ) + A, * * where alpha is a scalar, x is an m element vector, y is an n element * vector and A is an m by n matrix. * * Parameters * ========== * * M - INTEGER. * On entry, M specifies the number of rows of the matrix A. * M must be at least zero. * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the number of columns of the matrix A. * N must be at least zero. * Unchanged on exit. * * ALPHA - COMPLEX*16 . * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * X - COMPLEX*16 array of dimension at least * ( 1 + ( m - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the m * element vector x. * Unchanged on exit. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * Y - COMPLEX*16 array of dimension at least * ( 1 + ( n - 1 )*abs( INCY ) ). * Before entry, the incremented array Y must contain the n * element vector y. * Unchanged on exit. * * INCY - INTEGER. * On entry, INCY specifies the increment for the elements of * Y. INCY must not be zero. * Unchanged on exit. * * A - COMPLEX*16 array of DIMENSION ( LDA, n ). * Before entry, the leading m by n part of the array A must * contain the matrix of coefficients. On exit, A is * overwritten by the updated matrix. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * max( 1, m ). * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. COMPLEX*16 ZERO PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) ) * .. Local Scalars .. COMPLEX*16 TEMP INTEGER I, INFO, IX, J, JY, KX * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC DCONJG, MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( M.LT.0 )THEN INFO = 1 ELSE IF( N.LT.0 )THEN INFO = 2 ELSE IF( INCX.EQ.0 )THEN INFO = 5 ELSE IF( INCY.EQ.0 )THEN INFO = 7 ELSE IF( LDA.LT.MAX( 1, M ) )THEN INFO = 9 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'ZGERC ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( M.EQ.0 ).OR.( N.EQ.0 ).OR.( ALPHA.EQ.ZERO ) ) $ RETURN * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through A. * IF( INCY.GT.0 )THEN JY = 1 ELSE JY = 1 - ( N - 1 )*INCY END IF IF( INCX.EQ.1 )THEN DO 20, J = 1, N IF( Y( JY ).NE.ZERO )THEN TEMP = ALPHA*DCONJG( Y( JY ) ) DO 10, I = 1, M A( I, J ) = A( I, J ) + X( I )*TEMP 10 CONTINUE END IF JY = JY + INCY 20 CONTINUE ELSE IF( INCX.GT.0 )THEN KX = 1 ELSE KX = 1 - ( M - 1 )*INCX END IF DO 40, J = 1, N IF( Y( JY ).NE.ZERO )THEN TEMP = ALPHA*DCONJG( Y( JY ) ) IX = KX DO 30, I = 1, M A( I, J ) = A( I, J ) + X( IX )*TEMP IX = IX + INCX 30 CONTINUE END IF JY = JY + INCY 40 CONTINUE END IF * RETURN * * End of ZGERC . * END * ************************************************************************ * SUBROUTINE ZHER ( UPLO, N, ALPHA, X, INCX, A, LDA ) * .. Scalar Arguments .. DOUBLE PRECISION ALPHA INTEGER INCX, LDA, N CHARACTER*1 UPLO * .. Array Arguments .. COMPLEX*16 A( LDA, * ), X( * ) * .. * * Purpose * ======= * * ZHER performs the hermitian rank 1 operation * * A := alpha*x*conjg( x' ) + A, * * where alpha is a real scalar, x is an n element vector and A is an * n by n hermitian matrix. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the upper or lower * triangular part of the array A is to be referenced as * follows: * * UPLO = 'U' or 'u' Only the upper triangular part of A * is to be referenced. * * UPLO = 'L' or 'l' Only the lower triangular part of A * is to be referenced. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * ALPHA - DOUBLE PRECISION. * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * X - COMPLEX*16 array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element vector x. * Unchanged on exit. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * A - COMPLEX*16 array of DIMENSION ( LDA, n ). * Before entry with UPLO = 'U' or 'u', the leading n by n * upper triangular part of the array A must contain the upper * triangular part of the hermitian matrix and the strictly * lower triangular part of A is not referenced. On exit, the * upper triangular part of the array A is overwritten by the * upper triangular part of the updated matrix. * Before entry with UPLO = 'L' or 'l', the leading n by n * lower triangular part of the array A must contain the lower * triangular part of the hermitian matrix and the strictly * upper triangular part of A is not referenced. On exit, the * lower triangular part of the array A is overwritten by the * lower triangular part of the updated matrix. * Note that the imaginary parts of the diagonal elements need * not be set, they are assumed to be zero, and on exit they * are set to zero. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * max( 1, n ). * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. COMPLEX*16 ZERO PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) ) * .. Local Scalars .. COMPLEX*16 TEMP INTEGER I, INFO, IX, J, JX, KX * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC DCONJG, MAX, DBLE * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO, 'U' ).AND. $ .NOT.LSAME( UPLO, 'L' ) )THEN INFO = 1 ELSE IF( N.LT.0 )THEN INFO = 2 ELSE IF( INCX.EQ.0 )THEN INFO = 5 ELSE IF( LDA.LT.MAX( 1, N ) )THEN INFO = 7 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'ZHER ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( N.EQ.0 ).OR.( ALPHA.EQ.DBLE( ZERO ) ) ) $ RETURN * * Set the start point in X if the increment is not unity. * IF( INCX.LE.0 )THEN KX = 1 - ( N - 1 )*INCX ELSE IF( INCX.NE.1 )THEN KX = 1 END IF * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through the triangular part * of A. * IF( LSAME( UPLO, 'U' ) )THEN * * Form A when A is stored in upper triangle. * IF( INCX.EQ.1 )THEN DO 20, J = 1, N IF( X( J ).NE.ZERO )THEN TEMP = ALPHA*DCONJG( X( J ) ) DO 10, I = 1, J - 1 A( I, J ) = A( I, J ) + X( I )*TEMP 10 CONTINUE A( J, J ) = DBLE( A( J, J ) ) + DBLE( X( J )*TEMP ) ELSE A( J, J ) = DBLE( A( J, J ) ) END IF 20 CONTINUE ELSE JX = KX DO 40, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = ALPHA*DCONJG( X( JX ) ) IX = KX DO 30, I = 1, J - 1 A( I, J ) = A( I, J ) + X( IX )*TEMP IX = IX + INCX 30 CONTINUE A( J, J ) = DBLE( A( J, J ) ) + DBLE( X( JX )*TEMP ) ELSE A( J, J ) = DBLE( A( J, J ) ) END IF JX = JX + INCX 40 CONTINUE END IF ELSE * * Form A when A is stored in lower triangle. * IF( INCX.EQ.1 )THEN DO 60, J = 1, N IF( X( J ).NE.ZERO )THEN TEMP = ALPHA*DCONJG( X( J ) ) A( J, J ) = DBLE( A( J, J ) ) + DBLE( TEMP*X( J ) ) DO 50, I = J + 1, N A( I, J ) = A( I, J ) + X( I )*TEMP 50 CONTINUE ELSE A( J, J ) = DBLE( A( J, J ) ) END IF 60 CONTINUE ELSE JX = KX DO 80, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = ALPHA*DCONJG( X( JX ) ) A( J, J ) = DBLE( A( J, J ) ) + DBLE( TEMP*X( JX ) ) IX = JX DO 70, I = J + 1, N IX = IX + INCX A( I, J ) = A( I, J ) + X( IX )*TEMP 70 CONTINUE ELSE A( J, J ) = DBLE( A( J, J ) ) END IF JX = JX + INCX 80 CONTINUE END IF END IF * RETURN * * End of ZHER . * END * ************************************************************************ * SUBROUTINE ZHPR ( UPLO, N, ALPHA, X, INCX, AP ) * .. Scalar Arguments .. DOUBLE PRECISION ALPHA INTEGER INCX, N CHARACTER*1 UPLO * .. Array Arguments .. COMPLEX*16 AP( * ), X( * ) * .. * * Purpose * ======= * * ZHPR performs the hermitian rank 1 operation * * A := alpha*x*conjg( x' ) + A, * * where alpha is a real scalar, x is an n element vector and A is an * n by n hermitian matrix, supplied in packed form. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the upper or lower * triangular part of the matrix A is supplied in the packed * array AP as follows: * * UPLO = 'U' or 'u' The upper triangular part of A is * supplied in AP. * * UPLO = 'L' or 'l' The lower triangular part of A is * supplied in AP. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * ALPHA - DOUBLE PRECISION. * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * X - COMPLEX*16 array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element vector x. * Unchanged on exit. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * AP - COMPLEX*16 array of DIMENSION at least * ( ( n*( n + 1 ) )/2 ). * Before entry with UPLO = 'U' or 'u', the array AP must * contain the upper triangular part of the hermitian matrix * packed sequentially, column by column, so that AP( 1 ) * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) * and a( 2, 2 ) respectively, and so on. On exit, the array * AP is overwritten by the upper triangular part of the * updated matrix. * Before entry with UPLO = 'L' or 'l', the array AP must * contain the lower triangular part of the hermitian matrix * packed sequentially, column by column, so that AP( 1 ) * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) * and a( 3, 1 ) respectively, and so on. On exit, the array * AP is overwritten by the lower triangular part of the * updated matrix. * Note that the imaginary parts of the diagonal elements need * not be set, they are assumed to be zero, and on exit they * are set to zero. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. COMPLEX*16 ZERO PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) ) * .. Local Scalars .. COMPLEX*16 TEMP INTEGER I, INFO, IX, J, JX, K, KK, KX * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC DCONJG, DBLE * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO, 'U' ).AND. $ .NOT.LSAME( UPLO, 'L' ) )THEN INFO = 1 ELSE IF( N.LT.0 )THEN INFO = 2 ELSE IF( INCX.EQ.0 )THEN INFO = 5 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'ZHPR ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( N.EQ.0 ).OR.( ALPHA.EQ.DBLE( ZERO ) ) ) $ RETURN * * Set the start point in X if the increment is not unity. * IF( INCX.LE.0 )THEN KX = 1 - ( N - 1 )*INCX ELSE IF( INCX.NE.1 )THEN KX = 1 END IF * * Start the operations. In this version the elements of the array AP * are accessed sequentially with one pass through AP. * KK = 1 IF( LSAME( UPLO, 'U' ) )THEN * * Form A when upper triangle is stored in AP. * IF( INCX.EQ.1 )THEN DO 20, J = 1, N IF( X( J ).NE.ZERO )THEN TEMP = ALPHA*DCONJG( X( J ) ) K = KK DO 10, I = 1, J - 1 AP( K ) = AP( K ) + X( I )*TEMP K = K + 1 10 CONTINUE AP( KK + J - 1 ) = DBLE( AP( KK + J - 1 ) ) $ + DBLE( X( J )*TEMP ) ELSE AP( KK + J - 1 ) = DBLE( AP( KK + J - 1 ) ) END IF KK = KK + J 20 CONTINUE ELSE JX = KX DO 40, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = ALPHA*DCONJG( X( JX ) ) IX = KX DO 30, K = KK, KK + J - 2 AP( K ) = AP( K ) + X( IX )*TEMP IX = IX + INCX 30 CONTINUE AP( KK + J - 1 ) = DBLE( AP( KK + J - 1 ) ) $ + DBLE( X( JX )*TEMP ) ELSE AP( KK + J - 1 ) = DBLE( AP( KK + J - 1 ) ) END IF JX = JX + INCX KK = KK + J 40 CONTINUE END IF ELSE * * Form A when lower triangle is stored in AP. * IF( INCX.EQ.1 )THEN DO 60, J = 1, N IF( X( J ).NE.ZERO )THEN TEMP = ALPHA*DCONJG( X( J ) ) AP( KK ) = DBLE( AP( KK ) ) + DBLE( TEMP*X( J ) ) K = KK + 1 DO 50, I = J + 1, N AP( K ) = AP( K ) + X( I )*TEMP K = K + 1 50 CONTINUE ELSE AP( KK ) = DBLE( AP( KK ) ) END IF KK = KK + N - J + 1 60 CONTINUE ELSE JX = KX DO 80, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = ALPHA*DCONJG( X( JX ) ) AP( KK ) = DBLE( AP( KK ) ) + DBLE( TEMP*X( JX ) ) IX = JX DO 70, K = KK + 1, KK + N - J IX = IX + INCX AP( K ) = AP( K ) + X( IX )*TEMP 70 CONTINUE ELSE AP( KK ) = DBLE( AP( KK ) ) END IF JX = JX + INCX KK = KK + N - J + 1 80 CONTINUE END IF END IF * RETURN * * End of ZHPR . * END * ************************************************************************ * SUBROUTINE ZHER2 ( UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA ) * .. Scalar Arguments .. COMPLEX*16 ALPHA INTEGER INCX, INCY, LDA, N CHARACTER*1 UPLO * .. Array Arguments .. COMPLEX*16 A( LDA, * ), X( * ), Y( * ) * .. * * Purpose * ======= * * ZHER2 performs the hermitian rank 2 operation * * A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A, * * where alpha is a scalar, x and y are n element vectors and A is an n * by n hermitian matrix. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the upper or lower * triangular part of the array A is to be referenced as * follows: * * UPLO = 'U' or 'u' Only the upper triangular part of A * is to be referenced. * * UPLO = 'L' or 'l' Only the lower triangular part of A * is to be referenced. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * ALPHA - COMPLEX*16 . * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * X - COMPLEX*16 array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element vector x. * Unchanged on exit. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * Y - COMPLEX*16 array of dimension at least * ( 1 + ( n - 1 )*abs( INCY ) ). * Before entry, the incremented array Y must contain the n * element vector y. * Unchanged on exit. * * INCY - INTEGER. * On entry, INCY specifies the increment for the elements of * Y. INCY must not be zero. * Unchanged on exit. * * A - COMPLEX*16 array of DIMENSION ( LDA, n ). * Before entry with UPLO = 'U' or 'u', the leading n by n * upper triangular part of the array A must contain the upper * triangular part of the hermitian matrix and the strictly * lower triangular part of A is not referenced. On exit, the * upper triangular part of the array A is overwritten by the * upper triangular part of the updated matrix. * Before entry with UPLO = 'L' or 'l', the leading n by n * lower triangular part of the array A must contain the lower * triangular part of the hermitian matrix and the strictly * upper triangular part of A is not referenced. On exit, the * lower triangular part of the array A is overwritten by the * lower triangular part of the updated matrix. * Note that the imaginary parts of the diagonal elements need * not be set, they are assumed to be zero, and on exit they * are set to zero. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * max( 1, n ). * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. COMPLEX*16 ZERO PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) ) * .. Local Scalars .. COMPLEX*16 TEMP1, TEMP2 INTEGER I, INFO, IX, IY, J, JX, JY, KX, KY * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC DCONJG, MAX, DBLE * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO, 'U' ).AND. $ .NOT.LSAME( UPLO, 'L' ) )THEN INFO = 1 ELSE IF( N.LT.0 )THEN INFO = 2 ELSE IF( INCX.EQ.0 )THEN INFO = 5 ELSE IF( INCY.EQ.0 )THEN INFO = 7 ELSE IF( LDA.LT.MAX( 1, N ) )THEN INFO = 9 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'ZHER2 ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( N.EQ.0 ).OR.( ALPHA.EQ.ZERO ) ) $ RETURN * * Set up the start points in X and Y if the increments are not both * unity. * IF( ( INCX.NE.1 ).OR.( INCY.NE.1 ) )THEN IF( INCX.GT.0 )THEN KX = 1 ELSE KX = 1 - ( N - 1 )*INCX END IF IF( INCY.GT.0 )THEN KY = 1 ELSE KY = 1 - ( N - 1 )*INCY END IF JX = KX JY = KY END IF * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through the triangular part * of A. * IF( LSAME( UPLO, 'U' ) )THEN * * Form A when A is stored in the upper triangle. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 20, J = 1, N IF( ( X( J ).NE.ZERO ).OR.( Y( J ).NE.ZERO ) )THEN TEMP1 = ALPHA*DCONJG( Y( J ) ) TEMP2 = DCONJG( ALPHA*X( J ) ) DO 10, I = 1, J - 1 A( I, J ) = A( I, J ) + X( I )*TEMP1 + Y( I )*TEMP2 10 CONTINUE A( J, J ) = DBLE( A( J, J ) ) + $ DBLE( X( J )*TEMP1 + Y( J )*TEMP2 ) ELSE A( J, J ) = DBLE( A( J, J ) ) END IF 20 CONTINUE ELSE DO 40, J = 1, N IF( ( X( JX ).NE.ZERO ).OR.( Y( JY ).NE.ZERO ) )THEN TEMP1 = ALPHA*DCONJG( Y( JY ) ) TEMP2 = DCONJG( ALPHA*X( JX ) ) IX = KX IY = KY DO 30, I = 1, J - 1 A( I, J ) = A( I, J ) + X( IX )*TEMP1 $ + Y( IY )*TEMP2 IX = IX + INCX IY = IY + INCY 30 CONTINUE A( J, J ) = DBLE( A( J, J ) ) + $ DBLE( X( JX )*TEMP1 + Y( JY )*TEMP2 ) ELSE A( J, J ) = DBLE( A( J, J ) ) END IF JX = JX + INCX JY = JY + INCY 40 CONTINUE END IF ELSE * * Form A when A is stored in the lower triangle. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 60, J = 1, N IF( ( X( J ).NE.ZERO ).OR.( Y( J ).NE.ZERO ) )THEN TEMP1 = ALPHA*DCONJG( Y( J ) ) TEMP2 = DCONJG( ALPHA*X( J ) ) A( J, J ) = DBLE( A( J, J ) ) + $ DBLE( X( J )*TEMP1 + Y( J )*TEMP2 ) DO 50, I = J + 1, N A( I, J ) = A( I, J ) + X( I )*TEMP1 + Y( I )*TEMP2 50 CONTINUE ELSE A( J, J ) = DBLE( A( J, J ) ) END IF 60 CONTINUE ELSE DO 80, J = 1, N IF( ( X( JX ).NE.ZERO ).OR.( Y( JY ).NE.ZERO ) )THEN TEMP1 = ALPHA*DCONJG( Y( JY ) ) TEMP2 = DCONJG( ALPHA*X( JX ) ) A( J, J ) = DBLE( A( J, J ) ) + $ DBLE( X( JX )*TEMP1 + Y( JY )*TEMP2 ) IX = JX IY = JY DO 70, I = J + 1, N IX = IX + INCX IY = IY + INCY A( I, J ) = A( I, J ) + X( IX )*TEMP1 $ + Y( IY )*TEMP2 70 CONTINUE ELSE A( J, J ) = DBLE( A( J, J ) ) END IF JX = JX + INCX JY = JY + INCY 80 CONTINUE END IF END IF * RETURN * * End of ZHER2 . * END * ************************************************************************ * SUBROUTINE ZHPR2 ( UPLO, N, ALPHA, X, INCX, Y, INCY, AP ) * .. Scalar Arguments .. COMPLEX*16 ALPHA INTEGER INCX, INCY, N CHARACTER*1 UPLO * .. Array Arguments .. COMPLEX*16 AP( * ), X( * ), Y( * ) * .. * * Purpose * ======= * * ZHPR2 performs the hermitian rank 2 operation * * A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A, * * where alpha is a scalar, x and y are n element vectors and A is an * n by n hermitian matrix, supplied in packed form. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the upper or lower * triangular part of the matrix A is supplied in the packed * array AP as follows: * * UPLO = 'U' or 'u' The upper triangular part of A is * supplied in AP. * * UPLO = 'L' or 'l' The lower triangular part of A is * supplied in AP. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * ALPHA - COMPLEX*16 . * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * X - COMPLEX*16 array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element vector x. * Unchanged on exit. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * Y - COMPLEX*16 array of dimension at least * ( 1 + ( n - 1 )*abs( INCY ) ). * Before entry, the incremented array Y must contain the n * element vector y. * Unchanged on exit. * * INCY - INTEGER. * On entry, INCY specifies the increment for the elements of * Y. INCY must not be zero. * Unchanged on exit. * * AP - COMPLEX*16 array of DIMENSION at least * ( ( n*( n + 1 ) )/2 ). * Before entry with UPLO = 'U' or 'u', the array AP must * contain the upper triangular part of the hermitian matrix * packed sequentially, column by column, so that AP( 1 ) * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) * and a( 2, 2 ) respectively, and so on. On exit, the array * AP is overwritten by the upper triangular part of the * updated matrix. * Before entry with UPLO = 'L' or 'l', the array AP must * contain the lower triangular part of the hermitian matrix * packed sequentially, column by column, so that AP( 1 ) * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) * and a( 3, 1 ) respectively, and so on. On exit, the array * AP is overwritten by the lower triangular part of the * updated matrix. * Note that the imaginary parts of the diagonal elements need * not be set, they are assumed to be zero, and on exit they * are set to zero. * * * Level 2 Blas routine. * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. COMPLEX*16 ZERO PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) ) * .. Local Scalars .. COMPLEX*16 TEMP1, TEMP2 INTEGER I, INFO, IX, IY, J, JX, JY, K, KK, KX, KY * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC DCONJG, DBLE * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO, 'U' ).AND. $ .NOT.LSAME( UPLO, 'L' ) )THEN INFO = 1 ELSE IF( N.LT.0 )THEN INFO = 2 ELSE IF( INCX.EQ.0 )THEN INFO = 5 ELSE IF( INCY.EQ.0 )THEN INFO = 7 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'ZHPR2 ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( N.EQ.0 ).OR.( ALPHA.EQ.ZERO ) ) $ RETURN * * Set up the start points in X and Y if the increments are not both * unity. * IF( ( INCX.NE.1 ).OR.( INCY.NE.1 ) )THEN IF( INCX.GT.0 )THEN KX = 1 ELSE KX = 1 - ( N - 1 )*INCX END IF IF( INCY.GT.0 )THEN KY = 1 ELSE KY = 1 - ( N - 1 )*INCY END IF JX = KX JY = KY END IF * * Start the operations. In this version the elements of the array AP * are accessed sequentially with one pass through AP. * KK = 1 IF( LSAME( UPLO, 'U' ) )THEN * * Form A when upper triangle is stored in AP. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 20, J = 1, N IF( ( X( J ).NE.ZERO ).OR.( Y( J ).NE.ZERO ) )THEN TEMP1 = ALPHA*DCONJG( Y( J ) ) TEMP2 = DCONJG( ALPHA*X( J ) ) K = KK DO 10, I = 1, J - 1 AP( K ) = AP( K ) + X( I )*TEMP1 + Y( I )*TEMP2 K = K + 1 10 CONTINUE AP( KK + J - 1 ) = DBLE( AP( KK + J - 1 ) ) + $ DBLE( X( J )*TEMP1 + Y( J )*TEMP2 ) ELSE AP( KK + J - 1 ) = DBLE( AP( KK + J - 1 ) ) END IF KK = KK + J 20 CONTINUE ELSE DO 40, J = 1, N IF( ( X( JX ).NE.ZERO ).OR.( Y( JY ).NE.ZERO ) )THEN TEMP1 = ALPHA*DCONJG( Y( JY ) ) TEMP2 = DCONJG( ALPHA*X( JX ) ) IX = KX IY = KY DO 30, K = KK, KK + J - 2 AP( K ) = AP( K ) + X( IX )*TEMP1 + Y( IY )*TEMP2 IX = IX + INCX IY = IY + INCY 30 CONTINUE AP( KK + J - 1 ) = DBLE( AP( KK + J - 1 ) ) + $ DBLE( X( JX )*TEMP1 + $ Y( JY )*TEMP2 ) ELSE AP( KK + J - 1 ) = DBLE( AP( KK + J - 1 ) ) END IF JX = JX + INCX JY = JY + INCY KK = KK + J 40 CONTINUE END IF ELSE * * Form A when lower triangle is stored in AP. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 60, J = 1, N IF( ( X( J ).NE.ZERO ).OR.( Y( J ).NE.ZERO ) )THEN TEMP1 = ALPHA*DCONJG( Y( J ) ) TEMP2 = DCONJG( ALPHA*X( J ) ) AP( KK ) = DBLE( AP( KK ) ) + $ DBLE( X( J )*TEMP1 + Y( J )*TEMP2 ) K = KK + 1 DO 50, I = J + 1, N AP( K ) = AP( K ) + X( I )*TEMP1 + Y( I )*TEMP2 K = K + 1 50 CONTINUE ELSE AP( KK ) = DBLE( AP( KK ) ) END IF KK = KK + N - J + 1 60 CONTINUE ELSE DO 80, J = 1, N IF( ( X( JX ).NE.ZERO ).OR.( Y( JY ).NE.ZERO ) )THEN TEMP1 = ALPHA*DCONJG( Y( JY ) ) TEMP2 = DCONJG( ALPHA*X( JX ) ) AP( KK ) = DBLE( AP( KK ) ) + $ DBLE( X( JX )*TEMP1 + Y( JY )*TEMP2 ) IX = JX IY = JY DO 70, K = KK + 1, KK + N - J IX = IX + INCX IY = IY + INCY AP( K ) = AP( K ) + X( IX )*TEMP1 + Y( IY )*TEMP2 70 CONTINUE ELSE AP( KK ) = DBLE( AP( KK ) ) END IF JX = JX + INCX JY = JY + INCY KK = KK + N - J + 1 80 CONTINUE END IF END IF * RETURN * * End of ZHPR2 . * END LOGICAL FUNCTION LSAME ( CA, CB ) * .. Scalar Arguments .. CHARACTER*1 CA, CB * .. * * Purpose * ======= * * LSAME tests if CA is the same letter as CB regardless of case. * CB is assumed to be an upper case letter. LSAME returns .TRUE. if * CA is either the same as CB or the equivalent lower case letter. * * N.B. This version of the routine is only correct for ASCII code. * Installers must modify the routine for other character-codes. * * For EBCDIC systems the constant IOFF must be changed to -64. * For CDC systems using 6-12 bit representations, the system- * specific code in comments must be activated. * * Parameters * ========== * * CA - CHARACTER*1 * CB - CHARACTER*1 * On entry, CA and CB specify characters to be compared. * Unchanged on exit. * * * Auxiliary routine for Level 2 Blas. * * -- Written on 20-July-1986 * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, Nag Central Office. * * .. Parameters .. INTEGER IOFF PARAMETER ( IOFF=32 ) * .. Intrinsic Functions .. INTRINSIC ICHAR * .. Executable Statements .. * * Test if the characters are equal * LSAME = CA .EQ. CB * * Now test for equivalence * IF ( .NOT.LSAME ) THEN LSAME = ICHAR(CA) - IOFF .EQ. ICHAR(CB) END IF * RETURN * * The following comments contain code for CDC systems using 6-12 bit * representations. * * .. Parameters .. * INTEGER ICIRFX * PARAMETER ( ICIRFX=62 ) * .. Scalar Arguments .. * CHARACTER*1 CB * .. Array Arguments .. * CHARACTER*1 CA(*) * .. Local Scalars .. * INTEGER IVAL * .. Intrinsic Functions .. * INTRINSIC ICHAR, CHAR * .. Executable Statements .. * * See if the first character in string CA equals string CB. * * LSAME = CA(1) .EQ. CB .AND. CA(1) .NE. CHAR(ICIRFX) * * IF (LSAME) RETURN * * The characters are not identical. Now check them for equivalence. * Look for the 'escape' character, circumflex, followed by the * letter. * * IVAL = ICHAR(CA(2)) * IF (IVAL.GE.ICHAR('A') .AND. IVAL.LE.ICHAR('Z')) THEN * LSAME = CA(1) .EQ. CHAR(ICIRFX) .AND. CA(2) .EQ. CB * END IF * * RETURN * * End of LSAME. * END SUBROUTINE XERBLA ( SRNAME, INFO ) * .. Scalar Arguments .. INTEGER INFO CHARACTER*6 SRNAME * .. * * Purpose * ======= * * XERBLA is an error handler for the Level 2 BLAS routines. * * It is called by the Level 2 BLAS routines if an input parameter is * invalid. * * Installers should consider modifying the STOP statement in order to * call system-specific exception-handling facilities. * * Parameters * ========== * * SRNAME - CHARACTER*6. * On entry, SRNAME specifies the name of the routine which * called XERBLA. * * INFO - INTEGER. * On entry, INFO specifies the position of the invalid * parameter in the parameter-list of the calling routine. * * * Auxiliary routine for Level 2 Blas. * * Written on 20-July-1986. * * .. Executable Statements .. * WRITE (*,99999) SRNAME, INFO * STOP * 99999 FORMAT ( ' ** On entry to ', A6, ' parameter number ', I2, $ ' had an illegal value' ) * * End of XERBLA. * END PROGRAM SBLAT2 * * Test program for the REAL Level 2 Blas. * * The program must be driven by a short data file. The first 18 records * of the file are read using list-directed input, the last 16 records * are read using the format ( A6, L2 ). An annotated example of a data * file can be obtained by deleting the first 3 characters from the * following 34 lines: * 'SBLAT2.SUMM' NAME OF SUMMARY OUTPUT FILE * 6 UNIT NUMBER OF SUMMARY FILE * 'SBLAT2.SNAP' NAME OF SNAPSHOT OUTPUT FILE * -1 UNIT NUMBER OF SNAPSHOT FILE (NOT USED IF .LT. 0) * F LOGICAL FLAG, T TO REWIND SNAPSHOT FILE AFTER EACH RECORD. * F LOGICAL FLAG, T TO STOP ON FAILURES. * T LOGICAL FLAG, T TO TEST ERROR EXITS. * 16.0 THRESHOLD VALUE OF TEST RATIO * 6 NUMBER OF VALUES OF N * 0 1 2 3 5 9 VALUES OF N * 4 NUMBER OF VALUES OF K * 0 1 2 4 VALUES OF K * 4 NUMBER OF VALUES OF INCX AND INCY * 1 2 -1 -2 VALUES OF INCX AND INCY * 3 NUMBER OF VALUES OF ALPHA * 0.0 1.0 0.7 VALUES OF ALPHA * 3 NUMBER OF VALUES OF BETA * 0.0 1.0 0.9 VALUES OF BETA * SGEMV T PUT F FOR NO TEST. SAME COLUMNS. * SGBMV T PUT F FOR NO TEST. SAME COLUMNS. * SSYMV T PUT F FOR NO TEST. SAME COLUMNS. * SSBMV T PUT F FOR NO TEST. SAME COLUMNS. * SSPMV T PUT F FOR NO TEST. SAME COLUMNS. * STRMV T PUT F FOR NO TEST. SAME COLUMNS. * STBMV T PUT F FOR NO TEST. SAME COLUMNS. * STPMV T PUT F FOR NO TEST. SAME COLUMNS. * STRSV T PUT F FOR NO TEST. SAME COLUMNS. * STBSV T PUT F FOR NO TEST. SAME COLUMNS. * STPSV T PUT F FOR NO TEST. SAME COLUMNS. * SGER T PUT F FOR NO TEST. SAME COLUMNS. * SSYR T PUT F FOR NO TEST. SAME COLUMNS. * SSPR T PUT F FOR NO TEST. SAME COLUMNS. * SSYR2 T PUT F FOR NO TEST. SAME COLUMNS. * SSPR2 T PUT F FOR NO TEST. SAME COLUMNS. * * See: * * Dongarra J. J., Du Croz J. J., Hammarling S. and Hanson R. J.. * An extended set of Fortran Basic Linear Algebra Subprograms. * * Technical Memoranda Nos. 41 (revision 3) and 81, Mathematics * and Computer Science Division, Argonne National Laboratory, * 9700 South Cass Avenue, Argonne, Illinois 60439, US. * * Or * * NAG Technical Reports TR3/87 and TR4/87, Numerical Algorithms * Group Ltd., NAG Central Office, 256 Banbury Road, Oxford * OX2 7DE, UK, and Numerical Algorithms Group Inc., 1101 31st * Street, Suite 100, Downers Grove, Illinois 60515-1263, USA. * * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Parameters .. INTEGER NIN PARAMETER ( NIN = 5 ) INTEGER NSUBS PARAMETER ( NSUBS = 16 ) REAL ZERO, HALF, ONE PARAMETER ( ZERO = 0.0, HALF = 0.5, ONE = 1.0 ) INTEGER NMAX, INCMAX PARAMETER ( NMAX = 65, INCMAX = 2 ) INTEGER NINMAX, NIDMAX, NKBMAX, NALMAX, NBEMAX PARAMETER ( NINMAX = 7, NIDMAX = 9, NKBMAX = 7, $ NALMAX = 7, NBEMAX = 7 ) * .. Local Scalars .. REAL EPS, ERR, THRESH INTEGER I, ISNUM, J, N, NALF, NBET, NIDIM, NINC, NKB, $ NOUT, NTRA LOGICAL FATAL, LTESTT, REWI, SAME, SFATAL, TRACE, $ TSTERR CHARACTER*1 TRANS CHARACTER*6 SNAMET CHARACTER*32 SNAPS, SUMMRY * .. Local Arrays .. REAL A( NMAX, NMAX ), AA( NMAX*NMAX ), $ ALF( NALMAX ), AS( NMAX*NMAX ), BET( NBEMAX ), $ G( NMAX ), X( NMAX ), XS( NMAX*INCMAX ), $ XX( NMAX*INCMAX ), Y( NMAX ), $ YS( NMAX*INCMAX ), YT( NMAX ), $ YY( NMAX*INCMAX ), Z( 2*NMAX ) INTEGER IDIM( NIDMAX ), INC( NINMAX ), KB( NKBMAX ) LOGICAL LTEST( NSUBS ) CHARACTER*6 SNAMES( NSUBS ) * .. External Functions .. REAL SDIFF LOGICAL LSE EXTERNAL SDIFF, LSE * .. External Subroutines .. EXTERNAL SCHK1, SCHK2, SCHK3, SCHK4, SCHK5, SCHK6, $ SCHKE, SMVCH * .. Intrinsic Functions .. INTRINSIC ABS, MAX, MIN * .. Scalars in Common .. INTEGER INFOT, NOUTC LOGICAL LERR, OK CHARACTER*6 SRNAMT * .. Common blocks .. COMMON /INFOC/INFOT, NOUTC, OK, LERR COMMON /SRNAMC/SRNAMT * .. Data statements .. DATA SNAMES/'SGEMV ', 'SGBMV ', 'SSYMV ', 'SSBMV ', $ 'SSPMV ', 'STRMV ', 'STBMV ', 'STPMV ', $ 'STRSV ', 'STBSV ', 'STPSV ', 'SGER ', $ 'SSYR ', 'SSPR ', 'SSYR2 ', 'SSPR2 '/ * .. Executable Statements .. * * Read name and unit number for summary output file and open file. * READ( NIN, FMT = * )SUMMRY READ( NIN, FMT = * )NOUT OPEN( NOUT, FILE = SUMMRY, STATUS = 'NEW' ) NOUTC = NOUT * * Read name and unit number for snapshot output file and open file. * READ( NIN, FMT = * )SNAPS READ( NIN, FMT = * )NTRA TRACE = NTRA.GE.0 IF( TRACE )THEN OPEN( NTRA, FILE = SNAPS, STATUS = 'NEW' ) END IF * Read the flag that directs rewinding of the snapshot file. READ( NIN, FMT = * )REWI REWI = REWI.AND.TRACE * Read the flag that directs stopping on any failure. READ( NIN, FMT = * )SFATAL * Read the flag that indicates whether error exits are to be tested. READ( NIN, FMT = * )TSTERR * Read the threshold value of the test ratio READ( NIN, FMT = * )THRESH * * Read and check the parameter values for the tests. * * Values of N READ( NIN, FMT = * )NIDIM IF( NIDIM.LT.1.OR.NIDIM.GT.NIDMAX )THEN WRITE( NOUT, FMT = 9997 )'N', NIDMAX GO TO 230 END IF READ( NIN, FMT = * )( IDIM( I ), I = 1, NIDIM ) DO 10 I = 1, NIDIM IF( IDIM( I ).LT.0.OR.IDIM( I ).GT.NMAX )THEN WRITE( NOUT, FMT = 9996 )NMAX GO TO 230 END IF 10 CONTINUE * Values of K READ( NIN, FMT = * )NKB IF( NKB.LT.1.OR.NKB.GT.NKBMAX )THEN WRITE( NOUT, FMT = 9997 )'K', NKBMAX GO TO 230 END IF READ( NIN, FMT = * )( KB( I ), I = 1, NKB ) DO 20 I = 1, NKB IF( KB( I ).LT.0 )THEN WRITE( NOUT, FMT = 9995 ) GO TO 230 END IF 20 CONTINUE * Values of INCX and INCY READ( NIN, FMT = * )NINC IF( NINC.LT.1.OR.NINC.GT.NINMAX )THEN WRITE( NOUT, FMT = 9997 )'INCX AND INCY', NINMAX GO TO 230 END IF READ( NIN, FMT = * )( INC( I ), I = 1, NINC ) DO 30 I = 1, NINC IF( INC( I ).EQ.0.OR.ABS( INC( I ) ).GT.INCMAX )THEN WRITE( NOUT, FMT = 9994 )INCMAX GO TO 230 END IF 30 CONTINUE * Values of ALPHA READ( NIN, FMT = * )NALF IF( NALF.LT.1.OR.NALF.GT.NALMAX )THEN WRITE( NOUT, FMT = 9997 )'ALPHA', NALMAX GO TO 230 END IF READ( NIN, FMT = * )( ALF( I ), I = 1, NALF ) * Values of BETA READ( NIN, FMT = * )NBET IF( NBET.LT.1.OR.NBET.GT.NBEMAX )THEN WRITE( NOUT, FMT = 9997 )'BETA', NBEMAX GO TO 230 END IF READ( NIN, FMT = * )( BET( I ), I = 1, NBET ) * * Report values of parameters. * WRITE( NOUT, FMT = 9993 ) WRITE( NOUT, FMT = 9992 )( IDIM( I ), I = 1, NIDIM ) WRITE( NOUT, FMT = 9991 )( KB( I ), I = 1, NKB ) WRITE( NOUT, FMT = 9990 )( INC( I ), I = 1, NINC ) WRITE( NOUT, FMT = 9989 )( ALF( I ), I = 1, NALF ) WRITE( NOUT, FMT = 9988 )( BET( I ), I = 1, NBET ) IF( .NOT.TSTERR )THEN WRITE( NOUT, FMT = * ) WRITE( NOUT, FMT = 9980 ) END IF WRITE( NOUT, FMT = * ) WRITE( NOUT, FMT = 9999 )THRESH WRITE( NOUT, FMT = * ) * * Read names of subroutines and flags which indicate * whether they are to be tested. * DO 40 I = 1, NSUBS LTEST( I ) = .FALSE. 40 CONTINUE 50 READ( NIN, FMT = 9984, END = 80 )SNAMET, LTESTT DO 60 I = 1, NSUBS IF( SNAMET.EQ.SNAMES( I ) ) $ GO TO 70 60 CONTINUE WRITE( NOUT, FMT = 9986 )SNAMET STOP 70 LTEST( I ) = LTESTT GO TO 50 * 80 CONTINUE CLOSE ( NIN ) * * Compute EPS (the machine precision). * EPS = ONE 90 CONTINUE IF( SDIFF( ONE + EPS, ONE ).EQ.ZERO ) $ GO TO 100 EPS = HALF*EPS GO TO 90 100 CONTINUE EPS = EPS + EPS WRITE( NOUT, FMT = 9998 )EPS * * Check the reliability of SMVCH using exact data. * N = MIN( 32, NMAX ) DO 120 J = 1, N DO 110 I = 1, N A( I, J ) = MAX( I - J + 1, 0 ) 110 CONTINUE X( J ) = J Y( J ) = ZERO 120 CONTINUE DO 130 J = 1, N YY( J ) = J*( ( J + 1 )*J )/2 - ( ( J + 1 )*J*( J - 1 ) )/3 130 CONTINUE * YY holds the exact result. On exit from SMVCH YT holds * the result computed by SMVCH. TRANS = 'N' CALL SMVCH( TRANS, N, N, ONE, A, NMAX, X, 1, ZERO, Y, 1, YT, G, $ YY, EPS, ERR, FATAL, NOUT, .TRUE. ) SAME = LSE( YY, YT, N ) IF( .NOT.SAME.OR.ERR.NE.ZERO )THEN WRITE( NOUT, FMT = 9985 )TRANS, SAME, ERR STOP END IF TRANS = 'T' CALL SMVCH( TRANS, N, N, ONE, A, NMAX, X, -1, ZERO, Y, -1, YT, G, $ YY, EPS, ERR, FATAL, NOUT, .TRUE. ) SAME = LSE( YY, YT, N ) IF( .NOT.SAME.OR.ERR.NE.ZERO )THEN WRITE( NOUT, FMT = 9985 )TRANS, SAME, ERR STOP END IF * * Test each subroutine in turn. * DO 210 ISNUM = 1, NSUBS WRITE( NOUT, FMT = * ) IF( .NOT.LTEST( ISNUM ) )THEN * Subprogram is not to be tested. WRITE( NOUT, FMT = 9983 )SNAMES( ISNUM ) ELSE SRNAMT = SNAMES( ISNUM ) * Test error exits. IF( TSTERR )THEN CALL SCHKE( ISNUM, SNAMES( ISNUM ), NOUT ) WRITE( NOUT, FMT = * ) END IF * Test computations. INFOT = 0 OK = .TRUE. FATAL = .FALSE. GO TO ( 140, 140, 150, 150, 150, 160, 160, $ 160, 160, 160, 160, 170, 180, 180, $ 190, 190 )ISNUM * Test SGEMV, 01, and SGBMV, 02. 140 CALL SCHK1( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE, $ REWI, FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF, $ NBET, BET, NINC, INC, NMAX, INCMAX, A, AA, AS, $ X, XX, XS, Y, YY, YS, YT, G ) GO TO 200 * Test SSYMV, 03, SSBMV, 04, and SSPMV, 05. 150 CALL SCHK2( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE, $ REWI, FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF, $ NBET, BET, NINC, INC, NMAX, INCMAX, A, AA, AS, $ X, XX, XS, Y, YY, YS, YT, G ) GO TO 200 * Test STRMV, 06, STBMV, 07, STPMV, 08, * STRSV, 09, STBSV, 10, and STPSV, 11. 160 CALL SCHK3( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE, $ REWI, FATAL, NIDIM, IDIM, NKB, KB, NINC, INC, $ NMAX, INCMAX, A, AA, AS, Y, YY, YS, YT, G, Z ) GO TO 200 * Test SGER, 12. 170 CALL SCHK4( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE, $ REWI, FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, $ NMAX, INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, $ YT, G, Z ) GO TO 200 * Test SSYR, 13, and SSPR, 14. 180 CALL SCHK5( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE, $ REWI, FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, $ NMAX, INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, $ YT, G, Z ) GO TO 200 * Test SSYR2, 15, and SSPR2, 16. 190 CALL SCHK6( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE, $ REWI, FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, $ NMAX, INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, $ YT, G, Z ) * 200 IF( FATAL.AND.SFATAL ) $ GO TO 220 END IF 210 CONTINUE WRITE( NOUT, FMT = 9982 ) GO TO 240 * 220 CONTINUE WRITE( NOUT, FMT = 9981 ) GO TO 240 * 230 CONTINUE WRITE( NOUT, FMT = 9987 ) * 240 CONTINUE IF( TRACE ) $ CLOSE ( NTRA ) CLOSE ( NOUT ) STOP * 9999 FORMAT( ' ROUTINES PASS COMPUTATIONAL TESTS IF TEST RATIO IS LES', $ 'S THAN', F8.2 ) 9998 FORMAT( ' RELATIVE MACHINE PRECISION IS TAKEN TO BE', 1P, E9.1 ) 9997 FORMAT( ' NUMBER OF VALUES OF ', A, ' IS LESS THAN 1 OR GREATER ', $ 'THAN ', I2 ) 9996 FORMAT( ' VALUE OF N IS LESS THAN 0 OR GREATER THAN ', I2 ) 9995 FORMAT( ' VALUE OF K IS LESS THAN 0' ) 9994 FORMAT( ' ABSOLUTE VALUE OF INCX OR INCY IS 0 OR GREATER THAN ', $ I2 ) 9993 FORMAT( ' TESTS OF THE REAL LEVEL 2 BLAS', //' THE F', $ 'OLLOWING PARAMETER VALUES WILL BE USED:' ) 9992 FORMAT( ' FOR N ', 9I6 ) 9991 FORMAT( ' FOR K ', 7I6 ) 9990 FORMAT( ' FOR INCX AND INCY ', 7I6 ) 9989 FORMAT( ' FOR ALPHA ', 7F6.1 ) 9988 FORMAT( ' FOR BETA ', 7F6.1 ) 9987 FORMAT( ' AMEND DATA FILE OR INCREASE ARRAY SIZES IN PROGRAM', $ /' ******* TESTS ABANDONED *******' ) 9986 FORMAT( ' SUBPROGRAM NAME ', A6, ' NOT RECOGNIZED', /' ******* T', $ 'ESTS ABANDONED *******' ) 9985 FORMAT( ' ERROR IN SMVCH - IN-LINE DOT PRODUCTS ARE BEING EVALU', $ 'ATED WRONGLY.', /' SMVCH WAS CALLED WITH TRANS = ', A1, $ ' AND RETURNED SAME = ', L1, ' AND ERR = ', F12.3, '.', / $ ' THIS MAY BE DUE TO FAULTS IN THE ARITHMETIC OR THE COMPILER.' $ , /' ******* TESTS ABANDONED *******' ) 9984 FORMAT( A6, L2 ) 9983 FORMAT( 1X, A6, ' WAS NOT TESTED' ) 9982 FORMAT( /' END OF TESTS' ) 9981 FORMAT( /' ******* FATAL ERROR - TESTS ABANDONED *******' ) 9980 FORMAT( ' ERROR-EXITS WILL NOT BE TESTED' ) * * End of SBLAT2. * END SUBROUTINE SCHK1( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI, $ FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF, NBET, $ BET, NINC, INC, NMAX, INCMAX, A, AA, AS, X, XX, $ XS, Y, YY, YS, YT, G ) * * Tests SGEMV and SGBMV. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Parameters .. REAL ZERO, HALF PARAMETER ( ZERO = 0.0, HALF = 0.5 ) * .. Scalar Arguments .. REAL EPS, THRESH INTEGER INCMAX, NALF, NBET, NIDIM, NINC, NKB, NMAX, $ NOUT, NTRA LOGICAL FATAL, REWI, TRACE CHARACTER*6 SNAME * .. Array Arguments .. REAL A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ), $ AS( NMAX*NMAX ), BET( NBET ), G( NMAX ), $ X( NMAX ), XS( NMAX*INCMAX ), $ XX( NMAX*INCMAX ), Y( NMAX ), $ YS( NMAX*INCMAX ), YT( NMAX ), $ YY( NMAX*INCMAX ) INTEGER IDIM( NIDIM ), INC( NINC ), KB( NKB ) * .. Local Scalars .. REAL ALPHA, ALS, BETA, BLS, ERR, ERRMAX, TRANSL INTEGER I, IA, IB, IC, IKU, IM, IN, INCX, INCXS, INCY, $ INCYS, IX, IY, KL, KLS, KU, KUS, LAA, LDA, $ LDAS, LX, LY, M, ML, MS, N, NARGS, NC, ND, NK, $ NL, NS LOGICAL BANDED, FULL, NULL, RESET, SAME, TRAN CHARACTER*1 TRANS, TRANSS CHARACTER*3 ICH * .. Local Arrays .. LOGICAL ISAME( 13 ) * .. External Functions .. LOGICAL LSE, LSERES EXTERNAL LSE, LSERES * .. External Subroutines .. EXTERNAL SGBMV, SGEMV, SMAKE, SMVCH * .. Intrinsic Functions .. INTRINSIC ABS, MAX, MIN * .. Scalars in Common .. INTEGER INFOT, NOUTC LOGICAL LERR, OK * .. Common blocks .. COMMON /INFOC/INFOT, NOUTC, OK, LERR * .. Data statements .. DATA ICH/'NTC'/ * .. Executable Statements .. FULL = SNAME( 3: 3 ).EQ.'E' BANDED = SNAME( 3: 3 ).EQ.'B' * Define the number of arguments. IF( FULL )THEN NARGS = 11 ELSE IF( BANDED )THEN NARGS = 13 END IF * NC = 0 RESET = .TRUE. ERRMAX = ZERO * DO 120 IN = 1, NIDIM N = IDIM( IN ) ND = N/2 + 1 * DO 110 IM = 1, 2 IF( IM.EQ.1 ) $ M = MAX( N - ND, 0 ) IF( IM.EQ.2 ) $ M = MIN( N + ND, NMAX ) * IF( BANDED )THEN NK = NKB ELSE NK = 1 END IF DO 100 IKU = 1, NK IF( BANDED )THEN KU = KB( IKU ) KL = MAX( KU - 1, 0 ) ELSE KU = N - 1 KL = M - 1 END IF * Set LDA to 1 more than minimum value if room. IF( BANDED )THEN LDA = KL + KU + 1 ELSE LDA = M END IF IF( LDA.LT.NMAX ) $ LDA = LDA + 1 * Skip tests if not enough room. IF( LDA.GT.NMAX ) $ GO TO 100 LAA = LDA*N NULL = N.LE.0.OR.M.LE.0 * * Generate the matrix A. * TRANSL = ZERO CALL SMAKE( SNAME( 2: 3 ), ' ', ' ', M, N, A, NMAX, AA, $ LDA, KL, KU, RESET, TRANSL ) * DO 90 IC = 1, 3 TRANS = ICH( IC: IC ) TRAN = TRANS.EQ.'T'.OR.TRANS.EQ.'C' * IF( TRAN )THEN ML = N NL = M ELSE ML = M NL = N END IF * DO 80 IX = 1, NINC INCX = INC( IX ) LX = ABS( INCX )*NL * * Generate the vector X. * TRANSL = HALF CALL SMAKE( 'GE', ' ', ' ', 1, NL, X, 1, XX, $ ABS( INCX ), 0, NL - 1, RESET, TRANSL ) IF( NL.GT.1 )THEN X( NL/2 ) = ZERO XX( 1 + ABS( INCX )*( NL/2 - 1 ) ) = ZERO END IF * DO 70 IY = 1, NINC INCY = INC( IY ) LY = ABS( INCY )*ML * DO 60 IA = 1, NALF ALPHA = ALF( IA ) * DO 50 IB = 1, NBET BETA = BET( IB ) * * Generate the vector Y. * TRANSL = ZERO CALL SMAKE( 'GE', ' ', ' ', 1, ML, Y, 1, $ YY, ABS( INCY ), 0, ML - 1, $ RESET, TRANSL ) * NC = NC + 1 * * Save every datum before calling the * subroutine. * TRANSS = TRANS MS = M NS = N KLS = KL KUS = KU ALS = ALPHA DO 10 I = 1, LAA AS( I ) = AA( I ) 10 CONTINUE LDAS = LDA DO 20 I = 1, LX XS( I ) = XX( I ) 20 CONTINUE INCXS = INCX BLS = BETA DO 30 I = 1, LY YS( I ) = YY( I ) 30 CONTINUE INCYS = INCY * * Call the subroutine. * IF( FULL )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9994 )NC, SNAME, $ TRANS, M, N, ALPHA, LDA, INCX, BETA, $ INCY IF( REWI ) $ REWIND NTRA CALL SGEMV( TRANS, M, N, ALPHA, AA, $ LDA, XX, INCX, BETA, YY, $ INCY ) ELSE IF( BANDED )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9995 )NC, SNAME, $ TRANS, M, N, KL, KU, ALPHA, LDA, $ INCX, BETA, INCY IF( REWI ) $ REWIND NTRA CALL SGBMV( TRANS, M, N, KL, KU, ALPHA, $ AA, LDA, XX, INCX, BETA, $ YY, INCY ) END IF * * Check if error-exit was taken incorrectly. * IF( .NOT.OK )THEN WRITE( NOUT, FMT = 9993 ) FATAL = .TRUE. GO TO 130 END IF * * See what data changed inside subroutines. * ISAME( 1 ) = TRANS.EQ.TRANSS ISAME( 2 ) = MS.EQ.M ISAME( 3 ) = NS.EQ.N IF( FULL )THEN ISAME( 4 ) = ALS.EQ.ALPHA ISAME( 5 ) = LSE( AS, AA, LAA ) ISAME( 6 ) = LDAS.EQ.LDA ISAME( 7 ) = LSE( XS, XX, LX ) ISAME( 8 ) = INCXS.EQ.INCX ISAME( 9 ) = BLS.EQ.BETA IF( NULL )THEN ISAME( 10 ) = LSE( YS, YY, LY ) ELSE ISAME( 10 ) = LSERES( 'GE', ' ', 1, $ ML, YS, YY, $ ABS( INCY ) ) END IF ISAME( 11 ) = INCYS.EQ.INCY ELSE IF( BANDED )THEN ISAME( 4 ) = KLS.EQ.KL ISAME( 5 ) = KUS.EQ.KU ISAME( 6 ) = ALS.EQ.ALPHA ISAME( 7 ) = LSE( AS, AA, LAA ) ISAME( 8 ) = LDAS.EQ.LDA ISAME( 9 ) = LSE( XS, XX, LX ) ISAME( 10 ) = INCXS.EQ.INCX ISAME( 11 ) = BLS.EQ.BETA IF( NULL )THEN ISAME( 12 ) = LSE( YS, YY, LY ) ELSE ISAME( 12 ) = LSERES( 'GE', ' ', 1, $ ML, YS, YY, $ ABS( INCY ) ) END IF ISAME( 13 ) = INCYS.EQ.INCY END IF * * If data was incorrectly changed, report * and return. * SAME = .TRUE. DO 40 I = 1, NARGS SAME = SAME.AND.ISAME( I ) IF( .NOT.ISAME( I ) ) $ WRITE( NOUT, FMT = 9998 )I 40 CONTINUE IF( .NOT.SAME )THEN FATAL = .TRUE. GO TO 130 END IF * IF( .NOT.NULL )THEN * * Check the result. * CALL SMVCH( TRANS, M, N, ALPHA, A, $ NMAX, X, INCX, BETA, Y, $ INCY, YT, G, YY, EPS, ERR, $ FATAL, NOUT, .TRUE. ) ERRMAX = MAX( ERRMAX, ERR ) * If got really bad answer, report and * return. IF( FATAL ) $ GO TO 130 ELSE * Avoid repeating tests with M.le.0 or * N.le.0. GO TO 110 END IF * 50 CONTINUE * 60 CONTINUE * 70 CONTINUE * 80 CONTINUE * 90 CONTINUE * 100 CONTINUE * 110 CONTINUE * 120 CONTINUE * * Report result. * IF( ERRMAX.LT.THRESH )THEN WRITE( NOUT, FMT = 9999 )SNAME, NC ELSE WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX END IF GO TO 140 * 130 CONTINUE WRITE( NOUT, FMT = 9996 )SNAME IF( FULL )THEN WRITE( NOUT, FMT = 9994 )NC, SNAME, TRANS, M, N, ALPHA, LDA, $ INCX, BETA, INCY ELSE IF( BANDED )THEN WRITE( NOUT, FMT = 9995 )NC, SNAME, TRANS, M, N, KL, KU, $ ALPHA, LDA, INCX, BETA, INCY END IF * 140 CONTINUE RETURN * 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL', $ 'S)' ) 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH', $ 'ANGED INCORRECTLY *******' ) 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C', $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2, $ ' - SUSPECT *******' ) 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' ) 9995 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', 4( I3, ',' ), F4.1, $ ', A,', I3, ', X,', I2, ',', F4.1, ', Y,', I2, ') .' ) 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', 2( I3, ',' ), F4.1, $ ', A,', I3, ', X,', I2, ',', F4.1, ', Y,', I2, $ ') .' ) 9993 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *', $ '******' ) * * End of SCHK1. * END SUBROUTINE SCHK2( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI, $ FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF, NBET, $ BET, NINC, INC, NMAX, INCMAX, A, AA, AS, X, XX, $ XS, Y, YY, YS, YT, G ) * * Tests SSYMV, SSBMV and SSPMV. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Parameters .. REAL ZERO, HALF PARAMETER ( ZERO = 0.0, HALF = 0.5 ) * .. Scalar Arguments .. REAL EPS, THRESH INTEGER INCMAX, NALF, NBET, NIDIM, NINC, NKB, NMAX, $ NOUT, NTRA LOGICAL FATAL, REWI, TRACE CHARACTER*6 SNAME * .. Array Arguments .. REAL A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ), $ AS( NMAX*NMAX ), BET( NBET ), G( NMAX ), $ X( NMAX ), XS( NMAX*INCMAX ), $ XX( NMAX*INCMAX ), Y( NMAX ), $ YS( NMAX*INCMAX ), YT( NMAX ), $ YY( NMAX*INCMAX ) INTEGER IDIM( NIDIM ), INC( NINC ), KB( NKB ) * .. Local Scalars .. REAL ALPHA, ALS, BETA, BLS, ERR, ERRMAX, TRANSL INTEGER I, IA, IB, IC, IK, IN, INCX, INCXS, INCY, $ INCYS, IX, IY, K, KS, LAA, LDA, LDAS, LX, LY, $ N, NARGS, NC, NK, NS LOGICAL BANDED, FULL, NULL, PACKED, RESET, SAME CHARACTER*1 UPLO, UPLOS CHARACTER*2 ICH * .. Local Arrays .. LOGICAL ISAME( 13 ) * .. External Functions .. LOGICAL LSE, LSERES EXTERNAL LSE, LSERES * .. External Subroutines .. EXTERNAL SMAKE, SMVCH, SSBMV, SSPMV, SSYMV * .. Intrinsic Functions .. INTRINSIC ABS, MAX * .. Scalars in Common .. INTEGER INFOT, NOUTC LOGICAL LERR, OK * .. Common blocks .. COMMON /INFOC/INFOT, NOUTC, OK, LERR * .. Data statements .. DATA ICH/'UL'/ * .. Executable Statements .. FULL = SNAME( 3: 3 ).EQ.'Y' BANDED = SNAME( 3: 3 ).EQ.'B' PACKED = SNAME( 3: 3 ).EQ.'P' * Define the number of arguments. IF( FULL )THEN NARGS = 10 ELSE IF( BANDED )THEN NARGS = 11 ELSE IF( PACKED )THEN NARGS = 9 END IF * NC = 0 RESET = .TRUE. ERRMAX = ZERO * DO 110 IN = 1, NIDIM N = IDIM( IN ) * IF( BANDED )THEN NK = NKB ELSE NK = 1 END IF DO 100 IK = 1, NK IF( BANDED )THEN K = KB( IK ) ELSE K = N - 1 END IF * Set LDA to 1 more than minimum value if room. IF( BANDED )THEN LDA = K + 1 ELSE LDA = N END IF IF( LDA.LT.NMAX ) $ LDA = LDA + 1 * Skip tests if not enough room. IF( LDA.GT.NMAX ) $ GO TO 100 IF( PACKED )THEN LAA = ( N*( N + 1 ) )/2 ELSE LAA = LDA*N END IF NULL = N.LE.0 * DO 90 IC = 1, 2 UPLO = ICH( IC: IC ) * * Generate the matrix A. * TRANSL = ZERO CALL SMAKE( SNAME( 2: 3 ), UPLO, ' ', N, N, A, NMAX, AA, $ LDA, K, K, RESET, TRANSL ) * DO 80 IX = 1, NINC INCX = INC( IX ) LX = ABS( INCX )*N * * Generate the vector X. * TRANSL = HALF CALL SMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX, $ ABS( INCX ), 0, N - 1, RESET, TRANSL ) IF( N.GT.1 )THEN X( N/2 ) = ZERO XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO END IF * DO 70 IY = 1, NINC INCY = INC( IY ) LY = ABS( INCY )*N * DO 60 IA = 1, NALF ALPHA = ALF( IA ) * DO 50 IB = 1, NBET BETA = BET( IB ) * * Generate the vector Y. * TRANSL = ZERO CALL SMAKE( 'GE', ' ', ' ', 1, N, Y, 1, YY, $ ABS( INCY ), 0, N - 1, RESET, $ TRANSL ) * NC = NC + 1 * * Save every datum before calling the * subroutine. * UPLOS = UPLO NS = N KS = K ALS = ALPHA DO 10 I = 1, LAA AS( I ) = AA( I ) 10 CONTINUE LDAS = LDA DO 20 I = 1, LX XS( I ) = XX( I ) 20 CONTINUE INCXS = INCX BLS = BETA DO 30 I = 1, LY YS( I ) = YY( I ) 30 CONTINUE INCYS = INCY * * Call the subroutine. * IF( FULL )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9993 )NC, SNAME, $ UPLO, N, ALPHA, LDA, INCX, BETA, INCY IF( REWI ) $ REWIND NTRA CALL SSYMV( UPLO, N, ALPHA, AA, LDA, XX, $ INCX, BETA, YY, INCY ) ELSE IF( BANDED )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9994 )NC, SNAME, $ UPLO, N, K, ALPHA, LDA, INCX, BETA, $ INCY IF( REWI ) $ REWIND NTRA CALL SSBMV( UPLO, N, K, ALPHA, AA, LDA, $ XX, INCX, BETA, YY, INCY ) ELSE IF( PACKED )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9995 )NC, SNAME, $ UPLO, N, ALPHA, INCX, BETA, INCY IF( REWI ) $ REWIND NTRA CALL SSPMV( UPLO, N, ALPHA, AA, XX, INCX, $ BETA, YY, INCY ) END IF * * Check if error-exit was taken incorrectly. * IF( .NOT.OK )THEN WRITE( NOUT, FMT = 9992 ) FATAL = .TRUE. GO TO 120 END IF * * See what data changed inside subroutines. * ISAME( 1 ) = UPLO.EQ.UPLOS ISAME( 2 ) = NS.EQ.N IF( FULL )THEN ISAME( 3 ) = ALS.EQ.ALPHA ISAME( 4 ) = LSE( AS, AA, LAA ) ISAME( 5 ) = LDAS.EQ.LDA ISAME( 6 ) = LSE( XS, XX, LX ) ISAME( 7 ) = INCXS.EQ.INCX ISAME( 8 ) = BLS.EQ.BETA IF( NULL )THEN ISAME( 9 ) = LSE( YS, YY, LY ) ELSE ISAME( 9 ) = LSERES( 'GE', ' ', 1, N, $ YS, YY, ABS( INCY ) ) END IF ISAME( 10 ) = INCYS.EQ.INCY ELSE IF( BANDED )THEN ISAME( 3 ) = KS.EQ.K ISAME( 4 ) = ALS.EQ.ALPHA ISAME( 5 ) = LSE( AS, AA, LAA ) ISAME( 6 ) = LDAS.EQ.LDA ISAME( 7 ) = LSE( XS, XX, LX ) ISAME( 8 ) = INCXS.EQ.INCX ISAME( 9 ) = BLS.EQ.BETA IF( NULL )THEN ISAME( 10 ) = LSE( YS, YY, LY ) ELSE ISAME( 10 ) = LSERES( 'GE', ' ', 1, N, $ YS, YY, ABS( INCY ) ) END IF ISAME( 11 ) = INCYS.EQ.INCY ELSE IF( PACKED )THEN ISAME( 3 ) = ALS.EQ.ALPHA ISAME( 4 ) = LSE( AS, AA, LAA ) ISAME( 5 ) = LSE( XS, XX, LX ) ISAME( 6 ) = INCXS.EQ.INCX ISAME( 7 ) = BLS.EQ.BETA IF( NULL )THEN ISAME( 8 ) = LSE( YS, YY, LY ) ELSE ISAME( 8 ) = LSERES( 'GE', ' ', 1, N, $ YS, YY, ABS( INCY ) ) END IF ISAME( 9 ) = INCYS.EQ.INCY END IF * * If data was incorrectly changed, report and * return. * SAME = .TRUE. DO 40 I = 1, NARGS SAME = SAME.AND.ISAME( I ) IF( .NOT.ISAME( I ) ) $ WRITE( NOUT, FMT = 9998 )I 40 CONTINUE IF( .NOT.SAME )THEN FATAL = .TRUE. GO TO 120 END IF * IF( .NOT.NULL )THEN * * Check the result. * CALL SMVCH( 'N', N, N, ALPHA, A, NMAX, X, $ INCX, BETA, Y, INCY, YT, G, $ YY, EPS, ERR, FATAL, NOUT, $ .TRUE. ) ERRMAX = MAX( ERRMAX, ERR ) * If got really bad answer, report and * return. IF( FATAL ) $ GO TO 120 ELSE * Avoid repeating tests with N.le.0 GO TO 110 END IF * 50 CONTINUE * 60 CONTINUE * 70 CONTINUE * 80 CONTINUE * 90 CONTINUE * 100 CONTINUE * 110 CONTINUE * * Report result. * IF( ERRMAX.LT.THRESH )THEN WRITE( NOUT, FMT = 9999 )SNAME, NC ELSE WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX END IF GO TO 130 * 120 CONTINUE WRITE( NOUT, FMT = 9996 )SNAME IF( FULL )THEN WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, N, ALPHA, LDA, INCX, $ BETA, INCY ELSE IF( BANDED )THEN WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, N, K, ALPHA, LDA, $ INCX, BETA, INCY ELSE IF( PACKED )THEN WRITE( NOUT, FMT = 9995 )NC, SNAME, UPLO, N, ALPHA, INCX, $ BETA, INCY END IF * 130 CONTINUE RETURN * 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL', $ 'S)' ) 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH', $ 'ANGED INCORRECTLY *******' ) 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C', $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2, $ ' - SUSPECT *******' ) 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' ) 9995 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', AP', $ ', X,', I2, ',', F4.1, ', Y,', I2, ') .' ) 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', 2( I3, ',' ), F4.1, $ ', A,', I3, ', X,', I2, ',', F4.1, ', Y,', I2, $ ') .' ) 9993 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', A,', $ I3, ', X,', I2, ',', F4.1, ', Y,', I2, ') .' ) 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *', $ '******' ) * * End of SCHK2. * END SUBROUTINE SCHK3( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI, $ FATAL, NIDIM, IDIM, NKB, KB, NINC, INC, NMAX, $ INCMAX, A, AA, AS, X, XX, XS, XT, G, Z ) * * Tests STRMV, STBMV, STPMV, STRSV, STBSV and STPSV. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Parameters .. REAL ZERO, HALF, ONE PARAMETER ( ZERO = 0.0, HALF = 0.5, ONE = 1.0 ) * .. Scalar Arguments .. REAL EPS, THRESH INTEGER INCMAX, NIDIM, NINC, NKB, NMAX, NOUT, NTRA LOGICAL FATAL, REWI, TRACE CHARACTER*6 SNAME * .. Array Arguments .. REAL A( NMAX, NMAX ), AA( NMAX*NMAX ), $ AS( NMAX*NMAX ), G( NMAX ), X( NMAX ), $ XS( NMAX*INCMAX ), XT( NMAX ), $ XX( NMAX*INCMAX ), Z( NMAX ) INTEGER IDIM( NIDIM ), INC( NINC ), KB( NKB ) * .. Local Scalars .. REAL ERR, ERRMAX, TRANSL INTEGER I, ICD, ICT, ICU, IK, IN, INCX, INCXS, IX, K, $ KS, LAA, LDA, LDAS, LX, N, NARGS, NC, NK, NS LOGICAL BANDED, FULL, NULL, PACKED, RESET, SAME CHARACTER*1 DIAG, DIAGS, TRANS, TRANSS, UPLO, UPLOS CHARACTER*2 ICHD, ICHU CHARACTER*3 ICHT * .. Local Arrays .. LOGICAL ISAME( 13 ) * .. External Functions .. LOGICAL LSE, LSERES EXTERNAL LSE, LSERES * .. External Subroutines .. EXTERNAL SMAKE, SMVCH, STBMV, STBSV, STPMV, STPSV, $ STRMV, STRSV * .. Intrinsic Functions .. INTRINSIC ABS, MAX * .. Scalars in Common .. INTEGER INFOT, NOUTC LOGICAL LERR, OK * .. Common blocks .. COMMON /INFOC/INFOT, NOUTC, OK, LERR * .. Data statements .. DATA ICHU/'UL'/, ICHT/'NTC'/, ICHD/'UN'/ * .. Executable Statements .. FULL = SNAME( 3: 3 ).EQ.'R' BANDED = SNAME( 3: 3 ).EQ.'B' PACKED = SNAME( 3: 3 ).EQ.'P' * Define the number of arguments. IF( FULL )THEN NARGS = 8 ELSE IF( BANDED )THEN NARGS = 9 ELSE IF( PACKED )THEN NARGS = 7 END IF * NC = 0 RESET = .TRUE. ERRMAX = ZERO * Set up zero vector for SMVCH. DO 10 I = 1, NMAX Z( I ) = ZERO 10 CONTINUE * DO 110 IN = 1, NIDIM N = IDIM( IN ) * IF( BANDED )THEN NK = NKB ELSE NK = 1 END IF DO 100 IK = 1, NK IF( BANDED )THEN K = KB( IK ) ELSE K = N - 1 END IF * Set LDA to 1 more than minimum value if room. IF( BANDED )THEN LDA = K + 1 ELSE LDA = N END IF IF( LDA.LT.NMAX ) $ LDA = LDA + 1 * Skip tests if not enough room. IF( LDA.GT.NMAX ) $ GO TO 100 IF( PACKED )THEN LAA = ( N*( N + 1 ) )/2 ELSE LAA = LDA*N END IF NULL = N.LE.0 * DO 90 ICU = 1, 2 UPLO = ICHU( ICU: ICU ) * DO 80 ICT = 1, 3 TRANS = ICHT( ICT: ICT ) * DO 70 ICD = 1, 2 DIAG = ICHD( ICD: ICD ) * * Generate the matrix A. * TRANSL = ZERO CALL SMAKE( SNAME( 2: 3 ), UPLO, DIAG, N, N, A, $ NMAX, AA, LDA, K, K, RESET, TRANSL ) * DO 60 IX = 1, NINC INCX = INC( IX ) LX = ABS( INCX )*N * * Generate the vector X. * TRANSL = HALF CALL SMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX, $ ABS( INCX ), 0, N - 1, RESET, $ TRANSL ) IF( N.GT.1 )THEN X( N/2 ) = ZERO XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO END IF * NC = NC + 1 * * Save every datum before calling the subroutine. * UPLOS = UPLO TRANSS = TRANS DIAGS = DIAG NS = N KS = K DO 20 I = 1, LAA AS( I ) = AA( I ) 20 CONTINUE LDAS = LDA DO 30 I = 1, LX XS( I ) = XX( I ) 30 CONTINUE INCXS = INCX * * Call the subroutine. * IF( SNAME( 4: 5 ).EQ.'MV' )THEN IF( FULL )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9993 )NC, SNAME, $ UPLO, TRANS, DIAG, N, LDA, INCX IF( REWI ) $ REWIND NTRA CALL STRMV( UPLO, TRANS, DIAG, N, AA, LDA, $ XX, INCX ) ELSE IF( BANDED )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9994 )NC, SNAME, $ UPLO, TRANS, DIAG, N, K, LDA, INCX IF( REWI ) $ REWIND NTRA CALL STBMV( UPLO, TRANS, DIAG, N, K, AA, $ LDA, XX, INCX ) ELSE IF( PACKED )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9995 )NC, SNAME, $ UPLO, TRANS, DIAG, N, INCX IF( REWI ) $ REWIND NTRA CALL STPMV( UPLO, TRANS, DIAG, N, AA, XX, $ INCX ) END IF ELSE IF( SNAME( 4: 5 ).EQ.'SV' )THEN IF( FULL )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9993 )NC, SNAME, $ UPLO, TRANS, DIAG, N, LDA, INCX IF( REWI ) $ REWIND NTRA CALL STRSV( UPLO, TRANS, DIAG, N, AA, LDA, $ XX, INCX ) ELSE IF( BANDED )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9994 )NC, SNAME, $ UPLO, TRANS, DIAG, N, K, LDA, INCX IF( REWI ) $ REWIND NTRA CALL STBSV( UPLO, TRANS, DIAG, N, K, AA, $ LDA, XX, INCX ) ELSE IF( PACKED )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9995 )NC, SNAME, $ UPLO, TRANS, DIAG, N, INCX IF( REWI ) $ REWIND NTRA CALL STPSV( UPLO, TRANS, DIAG, N, AA, XX, $ INCX ) END IF END IF * * Check if error-exit was taken incorrectly. * IF( .NOT.OK )THEN WRITE( NOUT, FMT = 9992 ) FATAL = .TRUE. GO TO 120 END IF * * See what data changed inside subroutines. * ISAME( 1 ) = UPLO.EQ.UPLOS ISAME( 2 ) = TRANS.EQ.TRANSS ISAME( 3 ) = DIAG.EQ.DIAGS ISAME( 4 ) = NS.EQ.N IF( FULL )THEN ISAME( 5 ) = LSE( AS, AA, LAA ) ISAME( 6 ) = LDAS.EQ.LDA IF( NULL )THEN ISAME( 7 ) = LSE( XS, XX, LX ) ELSE ISAME( 7 ) = LSERES( 'GE', ' ', 1, N, XS, $ XX, ABS( INCX ) ) END IF ISAME( 8 ) = INCXS.EQ.INCX ELSE IF( BANDED )THEN ISAME( 5 ) = KS.EQ.K ISAME( 6 ) = LSE( AS, AA, LAA ) ISAME( 7 ) = LDAS.EQ.LDA IF( NULL )THEN ISAME( 8 ) = LSE( XS, XX, LX ) ELSE ISAME( 8 ) = LSERES( 'GE', ' ', 1, N, XS, $ XX, ABS( INCX ) ) END IF ISAME( 9 ) = INCXS.EQ.INCX ELSE IF( PACKED )THEN ISAME( 5 ) = LSE( AS, AA, LAA ) IF( NULL )THEN ISAME( 6 ) = LSE( XS, XX, LX ) ELSE ISAME( 6 ) = LSERES( 'GE', ' ', 1, N, XS, $ XX, ABS( INCX ) ) END IF ISAME( 7 ) = INCXS.EQ.INCX END IF * * If data was incorrectly changed, report and * return. * SAME = .TRUE. DO 40 I = 1, NARGS SAME = SAME.AND.ISAME( I ) IF( .NOT.ISAME( I ) ) $ WRITE( NOUT, FMT = 9998 )I 40 CONTINUE IF( .NOT.SAME )THEN FATAL = .TRUE. GO TO 120 END IF * IF( .NOT.NULL )THEN IF( SNAME( 4: 5 ).EQ.'MV' )THEN * * Check the result. * CALL SMVCH( TRANS, N, N, ONE, A, NMAX, X, $ INCX, ZERO, Z, INCX, XT, G, $ XX, EPS, ERR, FATAL, NOUT, $ .TRUE. ) ELSE IF( SNAME( 4: 5 ).EQ.'SV' )THEN * * Compute approximation to original vector. * DO 50 I = 1, N Z( I ) = XX( 1 + ( I - 1 )* $ ABS( INCX ) ) XX( 1 + ( I - 1 )*ABS( INCX ) ) $ = X( I ) 50 CONTINUE CALL SMVCH( TRANS, N, N, ONE, A, NMAX, Z, $ INCX, ZERO, X, INCX, XT, G, $ XX, EPS, ERR, FATAL, NOUT, $ .FALSE. ) END IF ERRMAX = MAX( ERRMAX, ERR ) * If got really bad answer, report and return. IF( FATAL ) $ GO TO 120 ELSE * Avoid repeating tests with N.le.0. GO TO 110 END IF * 60 CONTINUE * 70 CONTINUE * 80 CONTINUE * 90 CONTINUE * 100 CONTINUE * 110 CONTINUE * * Report result. * IF( ERRMAX.LT.THRESH )THEN WRITE( NOUT, FMT = 9999 )SNAME, NC ELSE WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX END IF GO TO 130 * 120 CONTINUE WRITE( NOUT, FMT = 9996 )SNAME IF( FULL )THEN WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, TRANS, DIAG, N, LDA, $ INCX ELSE IF( BANDED )THEN WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, TRANS, DIAG, N, K, $ LDA, INCX ELSE IF( PACKED )THEN WRITE( NOUT, FMT = 9995 )NC, SNAME, UPLO, TRANS, DIAG, N, INCX END IF * 130 CONTINUE RETURN * 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL', $ 'S)' ) 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH', $ 'ANGED INCORRECTLY *******' ) 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C', $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2, $ ' - SUSPECT *******' ) 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' ) 9995 FORMAT( 1X, I6, ': ', A6, '(', 3( '''', A1, ''',' ), I3, ', AP, ', $ 'X,', I2, ') .' ) 9994 FORMAT( 1X, I6, ': ', A6, '(', 3( '''', A1, ''',' ), 2( I3, ',' ), $ ' A,', I3, ', X,', I2, ') .' ) 9993 FORMAT( 1X, I6, ': ', A6, '(', 3( '''', A1, ''',' ), I3, ', A,', $ I3, ', X,', I2, ') .' ) 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *', $ '******' ) * * End of SCHK3. * END SUBROUTINE SCHK4( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI, $ FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, NMAX, $ INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, YT, G, $ Z ) * * Tests SGER. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Parameters .. REAL ZERO, HALF, ONE PARAMETER ( ZERO = 0.0, HALF = 0.5, ONE = 1.0 ) * .. Scalar Arguments .. REAL EPS, THRESH INTEGER INCMAX, NALF, NIDIM, NINC, NMAX, NOUT, NTRA LOGICAL FATAL, REWI, TRACE CHARACTER*6 SNAME * .. Array Arguments .. REAL A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ), $ AS( NMAX*NMAX ), G( NMAX ), X( NMAX ), $ XS( NMAX*INCMAX ), XX( NMAX*INCMAX ), $ Y( NMAX ), YS( NMAX*INCMAX ), YT( NMAX ), $ YY( NMAX*INCMAX ), Z( NMAX ) INTEGER IDIM( NIDIM ), INC( NINC ) * .. Local Scalars .. REAL ALPHA, ALS, ERR, ERRMAX, TRANSL INTEGER I, IA, IM, IN, INCX, INCXS, INCY, INCYS, IX, $ IY, J, LAA, LDA, LDAS, LX, LY, M, MS, N, NARGS, $ NC, ND, NS LOGICAL NULL, RESET, SAME * .. Local Arrays .. REAL W( 1 ) LOGICAL ISAME( 13 ) * .. External Functions .. LOGICAL LSE, LSERES EXTERNAL LSE, LSERES * .. External Subroutines .. EXTERNAL SGER, SMAKE, SMVCH * .. Intrinsic Functions .. INTRINSIC ABS, MAX, MIN * .. Scalars in Common .. INTEGER INFOT, NOUTC LOGICAL LERR, OK * .. Common blocks .. COMMON /INFOC/INFOT, NOUTC, OK, LERR * .. Executable Statements .. * Define the number of arguments. NARGS = 9 * NC = 0 RESET = .TRUE. ERRMAX = ZERO * DO 120 IN = 1, NIDIM N = IDIM( IN ) ND = N/2 + 1 * DO 110 IM = 1, 2 IF( IM.EQ.1 ) $ M = MAX( N - ND, 0 ) IF( IM.EQ.2 ) $ M = MIN( N + ND, NMAX ) * * Set LDA to 1 more than minimum value if room. LDA = M IF( LDA.LT.NMAX ) $ LDA = LDA + 1 * Skip tests if not enough room. IF( LDA.GT.NMAX ) $ GO TO 110 LAA = LDA*N NULL = N.LE.0.OR.M.LE.0 * DO 100 IX = 1, NINC INCX = INC( IX ) LX = ABS( INCX )*M * * Generate the vector X. * TRANSL = HALF CALL SMAKE( 'GE', ' ', ' ', 1, M, X, 1, XX, ABS( INCX ), $ 0, M - 1, RESET, TRANSL ) IF( M.GT.1 )THEN X( M/2 ) = ZERO XX( 1 + ABS( INCX )*( M/2 - 1 ) ) = ZERO END IF * DO 90 IY = 1, NINC INCY = INC( IY ) LY = ABS( INCY )*N * * Generate the vector Y. * TRANSL = ZERO CALL SMAKE( 'GE', ' ', ' ', 1, N, Y, 1, YY, $ ABS( INCY ), 0, N - 1, RESET, TRANSL ) IF( N.GT.1 )THEN Y( N/2 ) = ZERO YY( 1 + ABS( INCY )*( N/2 - 1 ) ) = ZERO END IF * DO 80 IA = 1, NALF ALPHA = ALF( IA ) * * Generate the matrix A. * TRANSL = ZERO CALL SMAKE( SNAME( 2: 3 ), ' ', ' ', M, N, A, NMAX, $ AA, LDA, M - 1, N - 1, RESET, TRANSL ) * NC = NC + 1 * * Save every datum before calling the subroutine. * MS = M NS = N ALS = ALPHA DO 10 I = 1, LAA AS( I ) = AA( I ) 10 CONTINUE LDAS = LDA DO 20 I = 1, LX XS( I ) = XX( I ) 20 CONTINUE INCXS = INCX DO 30 I = 1, LY YS( I ) = YY( I ) 30 CONTINUE INCYS = INCY * * Call the subroutine. * IF( TRACE ) $ WRITE( NTRA, FMT = 9994 )NC, SNAME, M, N, $ ALPHA, INCX, INCY, LDA IF( REWI ) $ REWIND NTRA CALL SGER( M, N, ALPHA, XX, INCX, YY, INCY, AA, $ LDA ) * * Check if error-exit was taken incorrectly. * IF( .NOT.OK )THEN WRITE( NOUT, FMT = 9993 ) FATAL = .TRUE. GO TO 140 END IF * * See what data changed inside subroutine. * ISAME( 1 ) = MS.EQ.M ISAME( 2 ) = NS.EQ.N ISAME( 3 ) = ALS.EQ.ALPHA ISAME( 4 ) = LSE( XS, XX, LX ) ISAME( 5 ) = INCXS.EQ.INCX ISAME( 6 ) = LSE( YS, YY, LY ) ISAME( 7 ) = INCYS.EQ.INCY IF( NULL )THEN ISAME( 8 ) = LSE( AS, AA, LAA ) ELSE ISAME( 8 ) = LSERES( 'GE', ' ', M, N, AS, AA, $ LDA ) END IF ISAME( 9 ) = LDAS.EQ.LDA * * If data was incorrectly changed, report and return. * SAME = .TRUE. DO 40 I = 1, NARGS SAME = SAME.AND.ISAME( I ) IF( .NOT.ISAME( I ) ) $ WRITE( NOUT, FMT = 9998 )I 40 CONTINUE IF( .NOT.SAME )THEN FATAL = .TRUE. GO TO 140 END IF * IF( .NOT.NULL )THEN * * Check the result column by column. * IF( INCX.GT.0 )THEN DO 50 I = 1, M Z( I ) = X( I ) 50 CONTINUE ELSE DO 60 I = 1, M Z( I ) = X( M - I + 1 ) 60 CONTINUE END IF DO 70 J = 1, N IF( INCY.GT.0 )THEN W( 1 ) = Y( J ) ELSE W( 1 ) = Y( N - J + 1 ) END IF CALL SMVCH( 'N', M, 1, ALPHA, Z, NMAX, W, 1, $ ONE, A( 1, J ), 1, YT, G, $ AA( 1 + ( J - 1 )*LDA ), EPS, $ ERR, FATAL, NOUT, .TRUE. ) ERRMAX = MAX( ERRMAX, ERR ) * If got really bad answer, report and return. IF( FATAL ) $ GO TO 130 70 CONTINUE ELSE * Avoid repeating tests with M.le.0 or N.le.0. GO TO 110 END IF * 80 CONTINUE * 90 CONTINUE * 100 CONTINUE * 110 CONTINUE * 120 CONTINUE * * Report result. * IF( ERRMAX.LT.THRESH )THEN WRITE( NOUT, FMT = 9999 )SNAME, NC ELSE WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX END IF GO TO 150 * 130 CONTINUE WRITE( NOUT, FMT = 9995 )J * 140 CONTINUE WRITE( NOUT, FMT = 9996 )SNAME WRITE( NOUT, FMT = 9994 )NC, SNAME, M, N, ALPHA, INCX, INCY, LDA * 150 CONTINUE RETURN * 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL', $ 'S)' ) 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH', $ 'ANGED INCORRECTLY *******' ) 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C', $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2, $ ' - SUSPECT *******' ) 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' ) 9995 FORMAT( ' THESE ARE THE RESULTS FOR COLUMN ', I3 ) 9994 FORMAT( 1X, I6, ': ', A6, '(', 2( I3, ',' ), F4.1, ', X,', I2, $ ', Y,', I2, ', A,', I3, ') .' ) 9993 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *', $ '******' ) * * End of SCHK4. * END SUBROUTINE SCHK5( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI, $ FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, NMAX, $ INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, YT, G, $ Z ) * * Tests SSYR and SSPR. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Parameters .. REAL ZERO, HALF, ONE PARAMETER ( ZERO = 0.0, HALF = 0.5, ONE = 1.0 ) * .. Scalar Arguments .. REAL EPS, THRESH INTEGER INCMAX, NALF, NIDIM, NINC, NMAX, NOUT, NTRA LOGICAL FATAL, REWI, TRACE CHARACTER*6 SNAME * .. Array Arguments .. REAL A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ), $ AS( NMAX*NMAX ), G( NMAX ), X( NMAX ), $ XS( NMAX*INCMAX ), XX( NMAX*INCMAX ), $ Y( NMAX ), YS( NMAX*INCMAX ), YT( NMAX ), $ YY( NMAX*INCMAX ), Z( NMAX ) INTEGER IDIM( NIDIM ), INC( NINC ) * .. Local Scalars .. REAL ALPHA, ALS, ERR, ERRMAX, TRANSL INTEGER I, IA, IC, IN, INCX, INCXS, IX, J, JA, JJ, LAA, $ LDA, LDAS, LJ, LX, N, NARGS, NC, NS LOGICAL FULL, NULL, PACKED, RESET, SAME, UPPER CHARACTER*1 UPLO, UPLOS CHARACTER*2 ICH * .. Local Arrays .. REAL W( 1 ) LOGICAL ISAME( 13 ) * .. External Functions .. LOGICAL LSE, LSERES EXTERNAL LSE, LSERES * .. External Subroutines .. EXTERNAL SMAKE, SMVCH, SSPR, SSYR * .. Intrinsic Functions .. INTRINSIC ABS, MAX * .. Scalars in Common .. INTEGER INFOT, NOUTC LOGICAL LERR, OK * .. Common blocks .. COMMON /INFOC/INFOT, NOUTC, OK, LERR * .. Data statements .. DATA ICH/'UL'/ * .. Executable Statements .. FULL = SNAME( 3: 3 ).EQ.'Y' PACKED = SNAME( 3: 3 ).EQ.'P' * Define the number of arguments. IF( FULL )THEN NARGS = 7 ELSE IF( PACKED )THEN NARGS = 6 END IF * NC = 0 RESET = .TRUE. ERRMAX = ZERO * DO 100 IN = 1, NIDIM N = IDIM( IN ) * Set LDA to 1 more than minimum value if room. LDA = N IF( LDA.LT.NMAX ) $ LDA = LDA + 1 * Skip tests if not enough room. IF( LDA.GT.NMAX ) $ GO TO 100 IF( PACKED )THEN LAA = ( N*( N + 1 ) )/2 ELSE LAA = LDA*N END IF * DO 90 IC = 1, 2 UPLO = ICH( IC: IC ) UPPER = UPLO.EQ.'U' * DO 80 IX = 1, NINC INCX = INC( IX ) LX = ABS( INCX )*N * * Generate the vector X. * TRANSL = HALF CALL SMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX, ABS( INCX ), $ 0, N - 1, RESET, TRANSL ) IF( N.GT.1 )THEN X( N/2 ) = ZERO XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO END IF * DO 70 IA = 1, NALF ALPHA = ALF( IA ) NULL = N.LE.0.OR.ALPHA.EQ.ZERO * * Generate the matrix A. * TRANSL = ZERO CALL SMAKE( SNAME( 2: 3 ), UPLO, ' ', N, N, A, NMAX, $ AA, LDA, N - 1, N - 1, RESET, TRANSL ) * NC = NC + 1 * * Save every datum before calling the subroutine. * UPLOS = UPLO NS = N ALS = ALPHA DO 10 I = 1, LAA AS( I ) = AA( I ) 10 CONTINUE LDAS = LDA DO 20 I = 1, LX XS( I ) = XX( I ) 20 CONTINUE INCXS = INCX * * Call the subroutine. * IF( FULL )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9993 )NC, SNAME, UPLO, N, $ ALPHA, INCX, LDA IF( REWI ) $ REWIND NTRA CALL SSYR( UPLO, N, ALPHA, XX, INCX, AA, LDA ) ELSE IF( PACKED )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9994 )NC, SNAME, UPLO, N, $ ALPHA, INCX IF( REWI ) $ REWIND NTRA CALL SSPR( UPLO, N, ALPHA, XX, INCX, AA ) END IF * * Check if error-exit was taken incorrectly. * IF( .NOT.OK )THEN WRITE( NOUT, FMT = 9992 ) FATAL = .TRUE. GO TO 120 END IF * * See what data changed inside subroutines. * ISAME( 1 ) = UPLO.EQ.UPLOS ISAME( 2 ) = NS.EQ.N ISAME( 3 ) = ALS.EQ.ALPHA ISAME( 4 ) = LSE( XS, XX, LX ) ISAME( 5 ) = INCXS.EQ.INCX IF( NULL )THEN ISAME( 6 ) = LSE( AS, AA, LAA ) ELSE ISAME( 6 ) = LSERES( SNAME( 2: 3 ), UPLO, N, N, AS, $ AA, LDA ) END IF IF( .NOT.PACKED )THEN ISAME( 7 ) = LDAS.EQ.LDA END IF * * If data was incorrectly changed, report and return. * SAME = .TRUE. DO 30 I = 1, NARGS SAME = SAME.AND.ISAME( I ) IF( .NOT.ISAME( I ) ) $ WRITE( NOUT, FMT = 9998 )I 30 CONTINUE IF( .NOT.SAME )THEN FATAL = .TRUE. GO TO 120 END IF * IF( .NOT.NULL )THEN * * Check the result column by column. * IF( INCX.GT.0 )THEN DO 40 I = 1, N Z( I ) = X( I ) 40 CONTINUE ELSE DO 50 I = 1, N Z( I ) = X( N - I + 1 ) 50 CONTINUE END IF JA = 1 DO 60 J = 1, N W( 1 ) = Z( J ) IF( UPPER )THEN JJ = 1 LJ = J ELSE JJ = J LJ = N - J + 1 END IF CALL SMVCH( 'N', LJ, 1, ALPHA, Z( JJ ), LJ, W, $ 1, ONE, A( JJ, J ), 1, YT, G, $ AA( JA ), EPS, ERR, FATAL, NOUT, $ .TRUE. ) IF( FULL )THEN IF( UPPER )THEN JA = JA + LDA ELSE JA = JA + LDA + 1 END IF ELSE JA = JA + LJ END IF ERRMAX = MAX( ERRMAX, ERR ) * If got really bad answer, report and return. IF( FATAL ) $ GO TO 110 60 CONTINUE ELSE * Avoid repeating tests if N.le.0. IF( N.LE.0 ) $ GO TO 100 END IF * 70 CONTINUE * 80 CONTINUE * 90 CONTINUE * 100 CONTINUE * * Report result. * IF( ERRMAX.LT.THRESH )THEN WRITE( NOUT, FMT = 9999 )SNAME, NC ELSE WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX END IF GO TO 130 * 110 CONTINUE WRITE( NOUT, FMT = 9995 )J * 120 CONTINUE WRITE( NOUT, FMT = 9996 )SNAME IF( FULL )THEN WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, N, ALPHA, INCX, LDA ELSE IF( PACKED )THEN WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, N, ALPHA, INCX END IF * 130 CONTINUE RETURN * 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL', $ 'S)' ) 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH', $ 'ANGED INCORRECTLY *******' ) 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C', $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2, $ ' - SUSPECT *******' ) 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' ) 9995 FORMAT( ' THESE ARE THE RESULTS FOR COLUMN ', I3 ) 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', X,', $ I2, ', AP) .' ) 9993 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', X,', $ I2, ', A,', I3, ') .' ) 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *', $ '******' ) * * End of SCHK5. * END SUBROUTINE SCHK6( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI, $ FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, NMAX, $ INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, YT, G, $ Z ) * * Tests SSYR2 and SSPR2. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Parameters .. REAL ZERO, HALF, ONE PARAMETER ( ZERO = 0.0, HALF = 0.5, ONE = 1.0 ) * .. Scalar Arguments .. REAL EPS, THRESH INTEGER INCMAX, NALF, NIDIM, NINC, NMAX, NOUT, NTRA LOGICAL FATAL, REWI, TRACE CHARACTER*6 SNAME * .. Array Arguments .. REAL A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ), $ AS( NMAX*NMAX ), G( NMAX ), X( NMAX ), $ XS( NMAX*INCMAX ), XX( NMAX*INCMAX ), $ Y( NMAX ), YS( NMAX*INCMAX ), YT( NMAX ), $ YY( NMAX*INCMAX ), Z( NMAX, 2 ) INTEGER IDIM( NIDIM ), INC( NINC ) * .. Local Scalars .. REAL ALPHA, ALS, ERR, ERRMAX, TRANSL INTEGER I, IA, IC, IN, INCX, INCXS, INCY, INCYS, IX, $ IY, J, JA, JJ, LAA, LDA, LDAS, LJ, LX, LY, N, $ NARGS, NC, NS LOGICAL FULL, NULL, PACKED, RESET, SAME, UPPER CHARACTER*1 UPLO, UPLOS CHARACTER*2 ICH * .. Local Arrays .. REAL W( 2 ) LOGICAL ISAME( 13 ) * .. External Functions .. LOGICAL LSE, LSERES EXTERNAL LSE, LSERES * .. External Subroutines .. EXTERNAL SMAKE, SMVCH, SSPR2, SSYR2 * .. Intrinsic Functions .. INTRINSIC ABS, MAX * .. Scalars in Common .. INTEGER INFOT, NOUTC LOGICAL LERR, OK * .. Common blocks .. COMMON /INFOC/INFOT, NOUTC, OK, LERR * .. Data statements .. DATA ICH/'UL'/ * .. Executable Statements .. FULL = SNAME( 3: 3 ).EQ.'Y' PACKED = SNAME( 3: 3 ).EQ.'P' * Define the number of arguments. IF( FULL )THEN NARGS = 9 ELSE IF( PACKED )THEN NARGS = 8 END IF * NC = 0 RESET = .TRUE. ERRMAX = ZERO * DO 140 IN = 1, NIDIM N = IDIM( IN ) * Set LDA to 1 more than minimum value if room. LDA = N IF( LDA.LT.NMAX ) $ LDA = LDA + 1 * Skip tests if not enough room. IF( LDA.GT.NMAX ) $ GO TO 140 IF( PACKED )THEN LAA = ( N*( N + 1 ) )/2 ELSE LAA = LDA*N END IF * DO 130 IC = 1, 2 UPLO = ICH( IC: IC ) UPPER = UPLO.EQ.'U' * DO 120 IX = 1, NINC INCX = INC( IX ) LX = ABS( INCX )*N * * Generate the vector X. * TRANSL = HALF CALL SMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX, ABS( INCX ), $ 0, N - 1, RESET, TRANSL ) IF( N.GT.1 )THEN X( N/2 ) = ZERO XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO END IF * DO 110 IY = 1, NINC INCY = INC( IY ) LY = ABS( INCY )*N * * Generate the vector Y. * TRANSL = ZERO CALL SMAKE( 'GE', ' ', ' ', 1, N, Y, 1, YY, $ ABS( INCY ), 0, N - 1, RESET, TRANSL ) IF( N.GT.1 )THEN Y( N/2 ) = ZERO YY( 1 + ABS( INCY )*( N/2 - 1 ) ) = ZERO END IF * DO 100 IA = 1, NALF ALPHA = ALF( IA ) NULL = N.LE.0.OR.ALPHA.EQ.ZERO * * Generate the matrix A. * TRANSL = ZERO CALL SMAKE( SNAME( 2: 3 ), UPLO, ' ', N, N, A, $ NMAX, AA, LDA, N - 1, N - 1, RESET, $ TRANSL ) * NC = NC + 1 * * Save every datum before calling the subroutine. * UPLOS = UPLO NS = N ALS = ALPHA DO 10 I = 1, LAA AS( I ) = AA( I ) 10 CONTINUE LDAS = LDA DO 20 I = 1, LX XS( I ) = XX( I ) 20 CONTINUE INCXS = INCX DO 30 I = 1, LY YS( I ) = YY( I ) 30 CONTINUE INCYS = INCY * * Call the subroutine. * IF( FULL )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9993 )NC, SNAME, UPLO, N, $ ALPHA, INCX, INCY, LDA IF( REWI ) $ REWIND NTRA CALL SSYR2( UPLO, N, ALPHA, XX, INCX, YY, INCY, $ AA, LDA ) ELSE IF( PACKED )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9994 )NC, SNAME, UPLO, N, $ ALPHA, INCX, INCY IF( REWI ) $ REWIND NTRA CALL SSPR2( UPLO, N, ALPHA, XX, INCX, YY, INCY, $ AA ) END IF * * Check if error-exit was taken incorrectly. * IF( .NOT.OK )THEN WRITE( NOUT, FMT = 9992 ) FATAL = .TRUE. GO TO 160 END IF * * See what data changed inside subroutines. * ISAME( 1 ) = UPLO.EQ.UPLOS ISAME( 2 ) = NS.EQ.N ISAME( 3 ) = ALS.EQ.ALPHA ISAME( 4 ) = LSE( XS, XX, LX ) ISAME( 5 ) = INCXS.EQ.INCX ISAME( 6 ) = LSE( YS, YY, LY ) ISAME( 7 ) = INCYS.EQ.INCY IF( NULL )THEN ISAME( 8 ) = LSE( AS, AA, LAA ) ELSE ISAME( 8 ) = LSERES( SNAME( 2: 3 ), UPLO, N, N, $ AS, AA, LDA ) END IF IF( .NOT.PACKED )THEN ISAME( 9 ) = LDAS.EQ.LDA END IF * * If data was incorrectly changed, report and return. * SAME = .TRUE. DO 40 I = 1, NARGS SAME = SAME.AND.ISAME( I ) IF( .NOT.ISAME( I ) ) $ WRITE( NOUT, FMT = 9998 )I 40 CONTINUE IF( .NOT.SAME )THEN FATAL = .TRUE. GO TO 160 END IF * IF( .NOT.NULL )THEN * * Check the result column by column. * IF( INCX.GT.0 )THEN DO 50 I = 1, N Z( I, 1 ) = X( I ) 50 CONTINUE ELSE DO 60 I = 1, N Z( I, 1 ) = X( N - I + 1 ) 60 CONTINUE END IF IF( INCY.GT.0 )THEN DO 70 I = 1, N Z( I, 2 ) = Y( I ) 70 CONTINUE ELSE DO 80 I = 1, N Z( I, 2 ) = Y( N - I + 1 ) 80 CONTINUE END IF JA = 1 DO 90 J = 1, N W( 1 ) = Z( J, 2 ) W( 2 ) = Z( J, 1 ) IF( UPPER )THEN JJ = 1 LJ = J ELSE JJ = J LJ = N - J + 1 END IF CALL SMVCH( 'N', LJ, 2, ALPHA, Z( JJ, 1 ), $ NMAX, W, 1, ONE, A( JJ, J ), 1, $ YT, G, AA( JA ), EPS, ERR, FATAL, $ NOUT, .TRUE. ) IF( FULL )THEN IF( UPPER )THEN JA = JA + LDA ELSE JA = JA + LDA + 1 END IF ELSE JA = JA + LJ END IF ERRMAX = MAX( ERRMAX, ERR ) * If got really bad answer, report and return. IF( FATAL ) $ GO TO 150 90 CONTINUE ELSE * Avoid repeating tests with N.le.0. IF( N.LE.0 ) $ GO TO 140 END IF * 100 CONTINUE * 110 CONTINUE * 120 CONTINUE * 130 CONTINUE * 140 CONTINUE * * Report result. * IF( ERRMAX.LT.THRESH )THEN WRITE( NOUT, FMT = 9999 )SNAME, NC ELSE WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX END IF GO TO 170 * 150 CONTINUE WRITE( NOUT, FMT = 9995 )J * 160 CONTINUE WRITE( NOUT, FMT = 9996 )SNAME IF( FULL )THEN WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, N, ALPHA, INCX, $ INCY, LDA ELSE IF( PACKED )THEN WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, N, ALPHA, INCX, INCY END IF * 170 CONTINUE RETURN * 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL', $ 'S)' ) 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH', $ 'ANGED INCORRECTLY *******' ) 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C', $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2, $ ' - SUSPECT *******' ) 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' ) 9995 FORMAT( ' THESE ARE THE RESULTS FOR COLUMN ', I3 ) 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', X,', $ I2, ', Y,', I2, ', AP) .' ) 9993 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', X,', $ I2, ', Y,', I2, ', A,', I3, ') .' ) 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *', $ '******' ) * * End of SCHK6. * END SUBROUTINE SCHKE( ISNUM, SRNAMT, NOUT ) * * Tests the error exits from the Level 2 Blas. * Requires a special version of the error-handling routine XERBLA. * ALPHA, BETA, A, X and Y should not need to be defined. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Scalar Arguments .. INTEGER ISNUM, NOUT CHARACTER*6 SRNAMT * .. Scalars in Common .. INTEGER INFOT, NOUTC LOGICAL LERR, OK * .. Local Scalars .. REAL ALPHA, BETA * .. Local Arrays .. REAL A( 1, 1 ), X( 1 ), Y( 1 ) * .. External Subroutines .. EXTERNAL CHKXER, SGBMV, SGEMV, SGER, SSBMV, SSPMV, SSPR, $ SSPR2, SSYMV, SSYR, SSYR2, STBMV, STBSV, STPMV, $ STPSV, STRMV, STRSV * .. Common blocks .. COMMON /INFOC/INFOT, NOUTC, OK, LERR * .. Executable Statements .. * OK is set to .FALSE. by the special version of XERBLA or by CHKXER * if anything is wrong. OK = .TRUE. * LERR is set to .TRUE. by the special version of XERBLA each time * it is called, and is then tested and re-set by CHKXER. LERR = .FALSE. GO TO ( 10, 20, 30, 40, 50, 60, 70, 80, $ 90, 100, 110, 120, 130, 140, 150, $ 160 )ISNUM 10 INFOT = 1 CALL SGEMV( '/', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL SGEMV( 'N', -1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 3 CALL SGEMV( 'N', 0, -1, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 6 CALL SGEMV( 'N', 2, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 8 CALL SGEMV( 'N', 0, 0, ALPHA, A, 1, X, 0, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 11 CALL SGEMV( 'N', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 0 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 170 20 INFOT = 1 CALL SGBMV( '/', 0, 0, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL SGBMV( 'N', -1, 0, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 3 CALL SGBMV( 'N', 0, -1, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 4 CALL SGBMV( 'N', 0, 0, -1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 5 CALL SGBMV( 'N', 2, 0, 0, -1, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 8 CALL SGBMV( 'N', 0, 0, 1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 10 CALL SGBMV( 'N', 0, 0, 0, 0, ALPHA, A, 1, X, 0, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 13 CALL SGBMV( 'N', 0, 0, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 0 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 170 30 INFOT = 1 CALL SSYMV( '/', 0, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL SSYMV( 'U', -1, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 5 CALL SSYMV( 'U', 2, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 7 CALL SSYMV( 'U', 0, ALPHA, A, 1, X, 0, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 10 CALL SSYMV( 'U', 0, ALPHA, A, 1, X, 1, BETA, Y, 0 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 170 40 INFOT = 1 CALL SSBMV( '/', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL SSBMV( 'U', -1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 3 CALL SSBMV( 'U', 0, -1, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 6 CALL SSBMV( 'U', 0, 1, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 8 CALL SSBMV( 'U', 0, 0, ALPHA, A, 1, X, 0, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 11 CALL SSBMV( 'U', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 0 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 170 50 INFOT = 1 CALL SSPMV( '/', 0, ALPHA, A, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL SSPMV( 'U', -1, ALPHA, A, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 6 CALL SSPMV( 'U', 0, ALPHA, A, X, 0, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 9 CALL SSPMV( 'U', 0, ALPHA, A, X, 1, BETA, Y, 0 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 170 60 INFOT = 1 CALL STRMV( '/', 'N', 'N', 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL STRMV( 'U', '/', 'N', 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 3 CALL STRMV( 'U', 'N', '/', 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 4 CALL STRMV( 'U', 'N', 'N', -1, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 6 CALL STRMV( 'U', 'N', 'N', 2, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 8 CALL STRMV( 'U', 'N', 'N', 0, A, 1, X, 0 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 170 70 INFOT = 1 CALL STBMV( '/', 'N', 'N', 0, 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL STBMV( 'U', '/', 'N', 0, 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 3 CALL STBMV( 'U', 'N', '/', 0, 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 4 CALL STBMV( 'U', 'N', 'N', -1, 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 5 CALL STBMV( 'U', 'N', 'N', 0, -1, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 7 CALL STBMV( 'U', 'N', 'N', 0, 1, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 9 CALL STBMV( 'U', 'N', 'N', 0, 0, A, 1, X, 0 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 170 80 INFOT = 1 CALL STPMV( '/', 'N', 'N', 0, A, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL STPMV( 'U', '/', 'N', 0, A, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 3 CALL STPMV( 'U', 'N', '/', 0, A, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 4 CALL STPMV( 'U', 'N', 'N', -1, A, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 7 CALL STPMV( 'U', 'N', 'N', 0, A, X, 0 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 170 90 INFOT = 1 CALL STRSV( '/', 'N', 'N', 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL STRSV( 'U', '/', 'N', 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 3 CALL STRSV( 'U', 'N', '/', 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 4 CALL STRSV( 'U', 'N', 'N', -1, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 6 CALL STRSV( 'U', 'N', 'N', 2, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 8 CALL STRSV( 'U', 'N', 'N', 0, A, 1, X, 0 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 170 100 INFOT = 1 CALL STBSV( '/', 'N', 'N', 0, 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL STBSV( 'U', '/', 'N', 0, 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 3 CALL STBSV( 'U', 'N', '/', 0, 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 4 CALL STBSV( 'U', 'N', 'N', -1, 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 5 CALL STBSV( 'U', 'N', 'N', 0, -1, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 7 CALL STBSV( 'U', 'N', 'N', 0, 1, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 9 CALL STBSV( 'U', 'N', 'N', 0, 0, A, 1, X, 0 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 170 110 INFOT = 1 CALL STPSV( '/', 'N', 'N', 0, A, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL STPSV( 'U', '/', 'N', 0, A, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 3 CALL STPSV( 'U', 'N', '/', 0, A, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 4 CALL STPSV( 'U', 'N', 'N', -1, A, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 7 CALL STPSV( 'U', 'N', 'N', 0, A, X, 0 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 170 120 INFOT = 1 CALL SGER( -1, 0, ALPHA, X, 1, Y, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL SGER( 0, -1, ALPHA, X, 1, Y, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 5 CALL SGER( 0, 0, ALPHA, X, 0, Y, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 7 CALL SGER( 0, 0, ALPHA, X, 1, Y, 0, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 9 CALL SGER( 2, 0, ALPHA, X, 1, Y, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 170 130 INFOT = 1 CALL SSYR( '/', 0, ALPHA, X, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL SSYR( 'U', -1, ALPHA, X, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 5 CALL SSYR( 'U', 0, ALPHA, X, 0, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 7 CALL SSYR( 'U', 2, ALPHA, X, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 170 140 INFOT = 1 CALL SSPR( '/', 0, ALPHA, X, 1, A ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL SSPR( 'U', -1, ALPHA, X, 1, A ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 5 CALL SSPR( 'U', 0, ALPHA, X, 0, A ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 170 150 INFOT = 1 CALL SSYR2( '/', 0, ALPHA, X, 1, Y, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL SSYR2( 'U', -1, ALPHA, X, 1, Y, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 5 CALL SSYR2( 'U', 0, ALPHA, X, 0, Y, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 7 CALL SSYR2( 'U', 0, ALPHA, X, 1, Y, 0, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 9 CALL SSYR2( 'U', 2, ALPHA, X, 1, Y, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 170 160 INFOT = 1 CALL SSPR2( '/', 0, ALPHA, X, 1, Y, 1, A ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL SSPR2( 'U', -1, ALPHA, X, 1, Y, 1, A ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 5 CALL SSPR2( 'U', 0, ALPHA, X, 0, Y, 1, A ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 7 CALL SSPR2( 'U', 0, ALPHA, X, 1, Y, 0, A ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) * 170 IF( OK )THEN WRITE( NOUT, FMT = 9999 )SRNAMT ELSE WRITE( NOUT, FMT = 9998 )SRNAMT END IF RETURN * 9999 FORMAT( ' ', A6, ' PASSED THE TESTS OF ERROR-EXITS' ) 9998 FORMAT( ' ******* ', A6, ' FAILED THE TESTS OF ERROR-EXITS *****', $ '**' ) * * End of SCHKE. * END SUBROUTINE SMAKE( TYPE, UPLO, DIAG, M, N, A, NMAX, AA, LDA, KL, $ KU, RESET, TRANSL ) * * Generates values for an M by N matrix A within the bandwidth * defined by KL and KU. * Stores the values in the array AA in the data structure required * by the routine, with unwanted elements set to rogue value. * * TYPE is 'GE', 'GB', 'SY', 'SB', 'SP', 'TR', 'TB' OR 'TP'. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Parameters .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0, ONE = 1.0 ) REAL ROGUE PARAMETER ( ROGUE = -1.0E10 ) * .. Scalar Arguments .. REAL TRANSL INTEGER KL, KU, LDA, M, N, NMAX LOGICAL RESET CHARACTER*1 DIAG, UPLO CHARACTER*2 TYPE * .. Array Arguments .. REAL A( NMAX, * ), AA( * ) * .. Local Scalars .. INTEGER I, I1, I2, I3, IBEG, IEND, IOFF, J, KK LOGICAL GEN, LOWER, SYM, TRI, UNIT, UPPER * .. External Functions .. REAL SBEG EXTERNAL SBEG * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. Executable Statements .. GEN = TYPE( 1: 1 ).EQ.'G' SYM = TYPE( 1: 1 ).EQ.'S' TRI = TYPE( 1: 1 ).EQ.'T' UPPER = ( SYM.OR.TRI ).AND.UPLO.EQ.'U' LOWER = ( SYM.OR.TRI ).AND.UPLO.EQ.'L' UNIT = TRI.AND.DIAG.EQ.'U' * * Generate data in array A. * DO 20 J = 1, N DO 10 I = 1, M IF( GEN.OR.( UPPER.AND.I.LE.J ).OR.( LOWER.AND.I.GE.J ) ) $ THEN IF( ( I.LE.J.AND.J - I.LE.KU ).OR. $ ( I.GE.J.AND.I - J.LE.KL ) )THEN A( I, J ) = SBEG( RESET ) + TRANSL ELSE A( I, J ) = ZERO END IF IF( I.NE.J )THEN IF( SYM )THEN A( J, I ) = A( I, J ) ELSE IF( TRI )THEN A( J, I ) = ZERO END IF END IF END IF 10 CONTINUE IF( TRI ) $ A( J, J ) = A( J, J ) + ONE IF( UNIT ) $ A( J, J ) = ONE 20 CONTINUE * * Store elements in array AS in data structure required by routine. * IF( TYPE.EQ.'GE' )THEN DO 50 J = 1, N DO 30 I = 1, M AA( I + ( J - 1 )*LDA ) = A( I, J ) 30 CONTINUE DO 40 I = M + 1, LDA AA( I + ( J - 1 )*LDA ) = ROGUE 40 CONTINUE 50 CONTINUE ELSE IF( TYPE.EQ.'GB' )THEN DO 90 J = 1, N DO 60 I1 = 1, KU + 1 - J AA( I1 + ( J - 1 )*LDA ) = ROGUE 60 CONTINUE DO 70 I2 = I1, MIN( KL + KU + 1, KU + 1 + M - J ) AA( I2 + ( J - 1 )*LDA ) = A( I2 + J - KU - 1, J ) 70 CONTINUE DO 80 I3 = I2, LDA AA( I3 + ( J - 1 )*LDA ) = ROGUE 80 CONTINUE 90 CONTINUE ELSE IF( TYPE.EQ.'SY'.OR.TYPE.EQ.'TR' )THEN DO 130 J = 1, N IF( UPPER )THEN IBEG = 1 IF( UNIT )THEN IEND = J - 1 ELSE IEND = J END IF ELSE IF( UNIT )THEN IBEG = J + 1 ELSE IBEG = J END IF IEND = N END IF DO 100 I = 1, IBEG - 1 AA( I + ( J - 1 )*LDA ) = ROGUE 100 CONTINUE DO 110 I = IBEG, IEND AA( I + ( J - 1 )*LDA ) = A( I, J ) 110 CONTINUE DO 120 I = IEND + 1, LDA AA( I + ( J - 1 )*LDA ) = ROGUE 120 CONTINUE 130 CONTINUE ELSE IF( TYPE.EQ.'SB'.OR.TYPE.EQ.'TB' )THEN DO 170 J = 1, N IF( UPPER )THEN KK = KL + 1 IBEG = MAX( 1, KL + 2 - J ) IF( UNIT )THEN IEND = KL ELSE IEND = KL + 1 END IF ELSE KK = 1 IF( UNIT )THEN IBEG = 2 ELSE IBEG = 1 END IF IEND = MIN( KL + 1, 1 + M - J ) END IF DO 140 I = 1, IBEG - 1 AA( I + ( J - 1 )*LDA ) = ROGUE 140 CONTINUE DO 150 I = IBEG, IEND AA( I + ( J - 1 )*LDA ) = A( I + J - KK, J ) 150 CONTINUE DO 160 I = IEND + 1, LDA AA( I + ( J - 1 )*LDA ) = ROGUE 160 CONTINUE 170 CONTINUE ELSE IF( TYPE.EQ.'SP'.OR.TYPE.EQ.'TP' )THEN IOFF = 0 DO 190 J = 1, N IF( UPPER )THEN IBEG = 1 IEND = J ELSE IBEG = J IEND = N END IF DO 180 I = IBEG, IEND IOFF = IOFF + 1 AA( IOFF ) = A( I, J ) IF( I.EQ.J )THEN IF( UNIT ) $ AA( IOFF ) = ROGUE END IF 180 CONTINUE 190 CONTINUE END IF RETURN * * End of SMAKE. * END SUBROUTINE SMVCH( TRANS, M, N, ALPHA, A, NMAX, X, INCX, BETA, Y, $ INCY, YT, G, YY, EPS, ERR, FATAL, NOUT, MV ) * * Checks the results of the computational tests. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Parameters .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0, ONE = 1.0 ) * .. Scalar Arguments .. REAL ALPHA, BETA, EPS, ERR INTEGER INCX, INCY, M, N, NMAX, NOUT LOGICAL FATAL, MV CHARACTER*1 TRANS * .. Array Arguments .. REAL A( NMAX, * ), G( * ), X( * ), Y( * ), YT( * ), $ YY( * ) * .. Local Scalars .. REAL ERRI INTEGER I, INCXL, INCYL, IY, J, JX, KX, KY, ML, NL LOGICAL TRAN * .. Intrinsic Functions .. INTRINSIC ABS, MAX, SQRT * .. Executable Statements .. TRAN = TRANS.EQ.'T'.OR.TRANS.EQ.'C' IF( TRAN )THEN ML = N NL = M ELSE ML = M NL = N END IF IF( INCX.LT.0 )THEN KX = NL INCXL = -1 ELSE KX = 1 INCXL = 1 END IF IF( INCY.LT.0 )THEN KY = ML INCYL = -1 ELSE KY = 1 INCYL = 1 END IF * * Compute expected result in YT using data in A, X and Y. * Compute gauges in G. * IY = KY DO 30 I = 1, ML YT( IY ) = ZERO G( IY ) = ZERO JX = KX IF( TRAN )THEN DO 10 J = 1, NL YT( IY ) = YT( IY ) + A( J, I )*X( JX ) G( IY ) = G( IY ) + ABS( A( J, I )*X( JX ) ) JX = JX + INCXL 10 CONTINUE ELSE DO 20 J = 1, NL YT( IY ) = YT( IY ) + A( I, J )*X( JX ) G( IY ) = G( IY ) + ABS( A( I, J )*X( JX ) ) JX = JX + INCXL 20 CONTINUE END IF YT( IY ) = ALPHA*YT( IY ) + BETA*Y( IY ) G( IY ) = ABS( ALPHA )*G( IY ) + ABS( BETA*Y( IY ) ) IY = IY + INCYL 30 CONTINUE * * Compute the error ratio for this result. * ERR = ZERO DO 40 I = 1, ML ERRI = ABS( YT( I ) - YY( 1 + ( I - 1 )*ABS( INCY ) ) )/EPS IF( G( I ).NE.ZERO ) $ ERRI = ERRI/G( I ) ERR = MAX( ERR, ERRI ) IF( ERR*SQRT( EPS ).GE.ONE ) $ GO TO 50 40 CONTINUE * If the loop completes, all results are at least half accurate. GO TO 70 * * Report fatal error. * 50 FATAL = .TRUE. WRITE( NOUT, FMT = 9999 ) DO 60 I = 1, ML IF( MV )THEN WRITE( NOUT, FMT = 9998 )I, YT( I ), $ YY( 1 + ( I - 1 )*ABS( INCY ) ) ELSE WRITE( NOUT, FMT = 9998 )I, $ YY( 1 + ( I - 1 )*ABS( INCY ) ), YT(I) END IF 60 CONTINUE * 70 CONTINUE RETURN * 9999 FORMAT( ' ******* FATAL ERROR - COMPUTED RESULT IS LESS THAN HAL', $ 'F ACCURATE *******', /' EXPECTED RESULT COMPU', $ 'TED RESULT' ) 9998 FORMAT( 1X, I7, 2G18.6 ) * * End of SMVCH. * END LOGICAL FUNCTION LSE( RI, RJ, LR ) * * Tests if two arrays are identical. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Scalar Arguments .. INTEGER LR * .. Array Arguments .. REAL RI( * ), RJ( * ) * .. Local Scalars .. INTEGER I * .. Executable Statements .. DO 10 I = 1, LR IF( RI( I ).NE.RJ( I ) ) $ GO TO 20 10 CONTINUE LSE = .TRUE. GO TO 30 20 CONTINUE LSE = .FALSE. 30 RETURN * * End of LSE. * END LOGICAL FUNCTION LSERES( TYPE, UPLO, M, N, AA, AS, LDA ) * * Tests if selected elements in two arrays are equal. * * TYPE is 'GE', 'SY' or 'SP'. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Scalar Arguments .. INTEGER LDA, M, N CHARACTER*1 UPLO CHARACTER*2 TYPE * .. Array Arguments .. REAL AA( LDA, * ), AS( LDA, * ) * .. Local Scalars .. INTEGER I, IBEG, IEND, J LOGICAL UPPER * .. Executable Statements .. UPPER = UPLO.EQ.'U' IF( TYPE.EQ.'GE' )THEN DO 20 J = 1, N DO 10 I = M + 1, LDA IF( AA( I, J ).NE.AS( I, J ) ) $ GO TO 70 10 CONTINUE 20 CONTINUE ELSE IF( TYPE.EQ.'SY' )THEN DO 50 J = 1, N IF( UPPER )THEN IBEG = 1 IEND = J ELSE IBEG = J IEND = N END IF DO 30 I = 1, IBEG - 1 IF( AA( I, J ).NE.AS( I, J ) ) $ GO TO 70 30 CONTINUE DO 40 I = IEND + 1, LDA IF( AA( I, J ).NE.AS( I, J ) ) $ GO TO 70 40 CONTINUE 50 CONTINUE END IF * 60 CONTINUE LSERES = .TRUE. GO TO 80 70 CONTINUE LSERES = .FALSE. 80 RETURN * * End of LSERES. * END REAL FUNCTION SBEG( RESET ) * * Generates random numbers uniformly distributed between -0.5 and 0.5. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Scalar Arguments .. LOGICAL RESET * .. Local Scalars .. INTEGER I, IC, MI * .. Save statement .. SAVE I, IC, MI * .. Intrinsic Functions .. INTRINSIC REAL * .. Executable Statements .. IF( RESET )THEN * Initialize local variables. MI = 891 I = 7 IC = 0 RESET = .FALSE. END IF * * The sequence of values of I is bounded between 1 and 999. * If initial I = 1,2,3,6,7 or 9, the period will be 50. * If initial I = 4 or 8, the period will be 25. * If initial I = 5, the period will be 10. * IC is used to break up the period by skipping 1 value of I in 6. * IC = IC + 1 10 I = I*MI I = I - 1000*( I/1000 ) IF( IC.GE.5 )THEN IC = 0 GO TO 10 END IF SBEG = REAL( I - 500 )/1001.0 RETURN * * End of SBEG. * END REAL FUNCTION SDIFF( X, Y ) * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * * .. Scalar Arguments .. REAL X, Y * .. Executable Statements .. SDIFF = X - Y RETURN * * End of SDIFF. * END SUBROUTINE CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) * * Tests whether XERBLA has detected an error when it should. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Scalar Arguments .. INTEGER INFOT, NOUT LOGICAL LERR, OK CHARACTER*6 SRNAMT * .. Executable Statements .. IF( .NOT.LERR )THEN WRITE( NOUT, FMT = 9999 )INFOT, SRNAMT OK = .FALSE. END IF LERR = .FALSE. RETURN * 9999 FORMAT( ' ***** ILLEGAL VALUE OF PARAMETER NUMBER ', I2, ' NOT D', $ 'ETECTED BY ', A6, ' *****' ) * * End of CHKXER. * END SUBROUTINE XERBLA( SRNAME, INFO ) * * This is a special version of XERBLA to be used only as part of * the test program for testing error exits from the Level 2 BLAS * routines. * * XERBLA is an error handler for the Level 2 BLAS routines. * * It is called by the Level 2 BLAS routines if an input parameter is * invalid. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Scalar Arguments .. INTEGER INFO CHARACTER*6 SRNAME * .. Scalars in Common .. INTEGER INFOT, NOUT LOGICAL LERR, OK CHARACTER*6 SRNAMT * .. Common blocks .. COMMON /INFOC/INFOT, NOUT, OK, LERR COMMON /SRNAMC/SRNAMT * .. Executable Statements .. LERR = .TRUE. IF( INFO.NE.INFOT )THEN IF( INFOT.NE.0 )THEN WRITE( NOUT, FMT = 9999 )INFO, INFOT ELSE WRITE( NOUT, FMT = 9997 )INFO END IF OK = .FALSE. END IF IF( SRNAME.NE.SRNAMT )THEN WRITE( NOUT, FMT = 9998 )SRNAME, SRNAMT OK = .FALSE. END IF RETURN * 9999 FORMAT( ' ******* XERBLA WAS CALLED WITH INFO = ', I6, ' INSTEAD', $ ' OF ', I2, ' *******' ) 9998 FORMAT( ' ******* XERBLA WAS CALLED WITH SRNAME = ', A6, ' INSTE', $ 'AD OF ', A6, ' *******' ) 9997 FORMAT( ' ******* XERBLA WAS CALLED WITH INFO = ', I6, $ ' *******' ) * * End of XERBLA * END PROGRAM CBLAT2 * * Test program for the COMPLEX Level 2 Blas. * * The program must be driven by a short data file. The first 18 records * of the file are read using list-directed input, the last 17 records * are read using the format ( A6, L2 ). An annotated example of a data * file can be obtained by deleting the first 3 characters from the * following 35 lines: * 'CBLAT2.SUMM' NAME OF SUMMARY OUTPUT FILE * 6 UNIT NUMBER OF SUMMARY FILE * 'CBLA2T.SNAP' NAME OF SNAPSHOT OUTPUT FILE * -1 UNIT NUMBER OF SNAPSHOT FILE (NOT USED IF .LT. 0) * F LOGICAL FLAG, T TO REWIND SNAPSHOT FILE AFTER EACH RECORD. * F LOGICAL FLAG, T TO STOP ON FAILURES. * T LOGICAL FLAG, T TO TEST ERROR EXITS. * 16.0 THRESHOLD VALUE OF TEST RATIO * 6 NUMBER OF VALUES OF N * 0 1 2 3 5 9 VALUES OF N * 4 NUMBER OF VALUES OF K * 0 1 2 4 VALUES OF K * 4 NUMBER OF VALUES OF INCX AND INCY * 1 2 -1 -2 VALUES OF INCX AND INCY * 3 NUMBER OF VALUES OF ALPHA * (0.0,0.0) (1.0,0.0) (0.7,-0.9) VALUES OF ALPHA * 3 NUMBER OF VALUES OF BETA * (0.0,0.0) (1.0,0.0) (1.3,-1.1) VALUES OF BETA * CGEMV T PUT F FOR NO TEST. SAME COLUMNS. * CGBMV T PUT F FOR NO TEST. SAME COLUMNS. * CHEMV T PUT F FOR NO TEST. SAME COLUMNS. * CHBMV T PUT F FOR NO TEST. SAME COLUMNS. * CHPMV T PUT F FOR NO TEST. SAME COLUMNS. * CTRMV T PUT F FOR NO TEST. SAME COLUMNS. * CTBMV T PUT F FOR NO TEST. SAME COLUMNS. * CTPMV T PUT F FOR NO TEST. SAME COLUMNS. * CTRSV T PUT F FOR NO TEST. SAME COLUMNS. * CTBSV T PUT F FOR NO TEST. SAME COLUMNS. * CTPSV T PUT F FOR NO TEST. SAME COLUMNS. * CGERC T PUT F FOR NO TEST. SAME COLUMNS. * CGERU T PUT F FOR NO TEST. SAME COLUMNS. * CHER T PUT F FOR NO TEST. SAME COLUMNS. * CHPR T PUT F FOR NO TEST. SAME COLUMNS. * CHER2 T PUT F FOR NO TEST. SAME COLUMNS. * CHPR2 T PUT F FOR NO TEST. SAME COLUMNS. * * See: * * Dongarra J. J., Du Croz J. J., Hammarling S. and Hanson R. J.. * An extended set of Fortran Basic Linear Algebra Subprograms. * * Technical Memoranda Nos. 41 (revision 3) and 81, Mathematics * and Computer Science Division, Argonne National Laboratory, * 9700 South Cass Avenue, Argonne, Illinois 60439, US. * * Or * * NAG Technical Reports TR3/87 and TR4/87, Numerical Algorithms * Group Ltd., NAG Central Office, 256 Banbury Road, Oxford * OX2 7DE, UK, and Numerical Algorithms Group Inc., 1101 31st * Street, Suite 100, Downers Grove, Illinois 60515-1263, USA. * * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Parameters .. INTEGER NIN PARAMETER ( NIN = 5 ) INTEGER NSUBS PARAMETER ( NSUBS = 17 ) COMPLEX ZERO, ONE PARAMETER ( ZERO = ( 0.0, 0.0 ), ONE = ( 1.0, 0.0 ) ) REAL RZERO, RHALF, RONE PARAMETER ( RZERO = 0.0, RHALF = 0.5, RONE = 1.0 ) INTEGER NMAX, INCMAX PARAMETER ( NMAX = 65, INCMAX = 2 ) INTEGER NINMAX, NIDMAX, NKBMAX, NALMAX, NBEMAX PARAMETER ( NINMAX = 7, NIDMAX = 9, NKBMAX = 7, $ NALMAX = 7, NBEMAX = 7 ) * .. Local Scalars .. REAL EPS, ERR, THRESH INTEGER I, ISNUM, J, N, NALF, NBET, NIDIM, NINC, NKB, $ NOUT, NTRA LOGICAL FATAL, LTESTT, REWI, SAME, SFATAL, TRACE, $ TSTERR CHARACTER*1 TRANS CHARACTER*6 SNAMET CHARACTER*32 SNAPS, SUMMRY * .. Local Arrays .. COMPLEX A( NMAX, NMAX ), AA( NMAX*NMAX ), $ ALF( NALMAX ), AS( NMAX*NMAX ), BET( NBEMAX ), $ X( NMAX ), XS( NMAX*INCMAX ), $ XX( NMAX*INCMAX ), Y( NMAX ), $ YS( NMAX*INCMAX ), YT( NMAX ), $ YY( NMAX*INCMAX ), Z( 2*NMAX ) REAL G( NMAX ) INTEGER IDIM( NIDMAX ), INC( NINMAX ), KB( NKBMAX ) LOGICAL LTEST( NSUBS ) CHARACTER*6 SNAMES( NSUBS ) * .. External Functions .. REAL SDIFF LOGICAL LCE EXTERNAL SDIFF, LCE * .. External Subroutines .. EXTERNAL CCHK1, CCHK2, CCHK3, CCHK4, CCHK5, CCHK6, $ CCHKE, CMVCH * .. Intrinsic Functions .. INTRINSIC ABS, MAX, MIN * .. Scalars in Common .. INTEGER INFOT, NOUTC LOGICAL LERR, OK CHARACTER*6 SRNAMT * .. Common blocks .. COMMON /INFOC/INFOT, NOUTC, OK, LERR COMMON /SRNAMC/SRNAMT * .. Data statements .. DATA SNAMES/'CGEMV ', 'CGBMV ', 'CHEMV ', 'CHBMV ', $ 'CHPMV ', 'CTRMV ', 'CTBMV ', 'CTPMV ', $ 'CTRSV ', 'CTBSV ', 'CTPSV ', 'CGERC ', $ 'CGERU ', 'CHER ', 'CHPR ', 'CHER2 ', $ 'CHPR2 '/ * .. Executable Statements .. * * Read name and unit number for summary output file and open file. * READ( NIN, FMT = * )SUMMRY READ( NIN, FMT = * )NOUT OPEN( NOUT, FILE = SUMMRY, STATUS = 'NEW' ) NOUTC = NOUT * * Read name and unit number for snapshot output file and open file. * READ( NIN, FMT = * )SNAPS READ( NIN, FMT = * )NTRA TRACE = NTRA.GE.0 IF( TRACE )THEN OPEN( NTRA, FILE = SNAPS, STATUS = 'NEW' ) END IF * Read the flag that directs rewinding of the snapshot file. READ( NIN, FMT = * )REWI REWI = REWI.AND.TRACE * Read the flag that directs stopping on any failure. READ( NIN, FMT = * )SFATAL * Read the flag that indicates whether error exits are to be tested. READ( NIN, FMT = * )TSTERR * Read the threshold value of the test ratio READ( NIN, FMT = * )THRESH * * Read and check the parameter values for the tests. * * Values of N READ( NIN, FMT = * )NIDIM IF( NIDIM.LT.1.OR.NIDIM.GT.NIDMAX )THEN WRITE( NOUT, FMT = 9997 )'N', NIDMAX GO TO 230 END IF READ( NIN, FMT = * )( IDIM( I ), I = 1, NIDIM ) DO 10 I = 1, NIDIM IF( IDIM( I ).LT.0.OR.IDIM( I ).GT.NMAX )THEN WRITE( NOUT, FMT = 9996 )NMAX GO TO 230 END IF 10 CONTINUE * Values of K READ( NIN, FMT = * )NKB IF( NKB.LT.1.OR.NKB.GT.NKBMAX )THEN WRITE( NOUT, FMT = 9997 )'K', NKBMAX GO TO 230 END IF READ( NIN, FMT = * )( KB( I ), I = 1, NKB ) DO 20 I = 1, NKB IF( KB( I ).LT.0 )THEN WRITE( NOUT, FMT = 9995 ) GO TO 230 END IF 20 CONTINUE * Values of INCX and INCY READ( NIN, FMT = * )NINC IF( NINC.LT.1.OR.NINC.GT.NINMAX )THEN WRITE( NOUT, FMT = 9997 )'INCX AND INCY', NINMAX GO TO 230 END IF READ( NIN, FMT = * )( INC( I ), I = 1, NINC ) DO 30 I = 1, NINC IF( INC( I ).EQ.0.OR.ABS( INC( I ) ).GT.INCMAX )THEN WRITE( NOUT, FMT = 9994 )INCMAX GO TO 230 END IF 30 CONTINUE * Values of ALPHA READ( NIN, FMT = * )NALF IF( NALF.LT.1.OR.NALF.GT.NALMAX )THEN WRITE( NOUT, FMT = 9997 )'ALPHA', NALMAX GO TO 230 END IF READ( NIN, FMT = * )( ALF( I ), I = 1, NALF ) * Values of BETA READ( NIN, FMT = * )NBET IF( NBET.LT.1.OR.NBET.GT.NBEMAX )THEN WRITE( NOUT, FMT = 9997 )'BETA', NBEMAX GO TO 230 END IF READ( NIN, FMT = * )( BET( I ), I = 1, NBET ) * * Report values of parameters. * WRITE( NOUT, FMT = 9993 ) WRITE( NOUT, FMT = 9992 )( IDIM( I ), I = 1, NIDIM ) WRITE( NOUT, FMT = 9991 )( KB( I ), I = 1, NKB ) WRITE( NOUT, FMT = 9990 )( INC( I ), I = 1, NINC ) WRITE( NOUT, FMT = 9989 )( ALF( I ), I = 1, NALF ) WRITE( NOUT, FMT = 9988 )( BET( I ), I = 1, NBET ) IF( .NOT.TSTERR )THEN WRITE( NOUT, FMT = * ) WRITE( NOUT, FMT = 9980 ) END IF WRITE( NOUT, FMT = * ) WRITE( NOUT, FMT = 9999 )THRESH WRITE( NOUT, FMT = * ) * * Read names of subroutines and flags which indicate * whether they are to be tested. * DO 40 I = 1, NSUBS LTEST( I ) = .FALSE. 40 CONTINUE 50 READ( NIN, FMT = 9984, END = 80 )SNAMET, LTESTT DO 60 I = 1, NSUBS IF( SNAMET.EQ.SNAMES( I ) ) $ GO TO 70 60 CONTINUE WRITE( NOUT, FMT = 9986 )SNAMET STOP 70 LTEST( I ) = LTESTT GO TO 50 * 80 CONTINUE CLOSE ( NIN ) * * Compute EPS (the machine precision). * EPS = RONE 90 CONTINUE IF( SDIFF( RONE + EPS, RONE ).EQ.RZERO ) $ GO TO 100 EPS = RHALF*EPS GO TO 90 100 CONTINUE EPS = EPS + EPS WRITE( NOUT, FMT = 9998 )EPS * * Check the reliability of CMVCH using exact data. * N = MIN( 32, NMAX ) DO 120 J = 1, N DO 110 I = 1, N A( I, J ) = MAX( I - J + 1, 0 ) 110 CONTINUE X( J ) = J Y( J ) = ZERO 120 CONTINUE DO 130 J = 1, N YY( J ) = J*( ( J + 1 )*J )/2 - ( ( J + 1 )*J*( J - 1 ) )/3 130 CONTINUE * YY holds the exact result. On exit from CMVCH YT holds * the result computed by CMVCH. TRANS = 'N' CALL CMVCH( TRANS, N, N, ONE, A, NMAX, X, 1, ZERO, Y, 1, YT, G, $ YY, EPS, ERR, FATAL, NOUT, .TRUE. ) SAME = LCE( YY, YT, N ) IF( .NOT.SAME.OR.ERR.NE.RZERO )THEN WRITE( NOUT, FMT = 9985 )TRANS, SAME, ERR STOP END IF TRANS = 'T' CALL CMVCH( TRANS, N, N, ONE, A, NMAX, X, -1, ZERO, Y, -1, YT, G, $ YY, EPS, ERR, FATAL, NOUT, .TRUE. ) SAME = LCE( YY, YT, N ) IF( .NOT.SAME.OR.ERR.NE.RZERO )THEN WRITE( NOUT, FMT = 9985 )TRANS, SAME, ERR STOP END IF * * Test each subroutine in turn. * DO 210 ISNUM = 1, NSUBS WRITE( NOUT, FMT = * ) IF( .NOT.LTEST( ISNUM ) )THEN * Subprogram is not to be tested. WRITE( NOUT, FMT = 9983 )SNAMES( ISNUM ) ELSE SRNAMT = SNAMES( ISNUM ) * Test error exits. IF( TSTERR )THEN CALL CCHKE( ISNUM, SNAMES( ISNUM ), NOUT ) WRITE( NOUT, FMT = * ) END IF * Test computations. INFOT = 0 OK = .TRUE. FATAL = .FALSE. GO TO ( 140, 140, 150, 150, 150, 160, 160, $ 160, 160, 160, 160, 170, 170, 180, $ 180, 190, 190 )ISNUM * Test CGEMV, 01, and CGBMV, 02. 140 CALL CCHK1( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE, $ REWI, FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF, $ NBET, BET, NINC, INC, NMAX, INCMAX, A, AA, AS, $ X, XX, XS, Y, YY, YS, YT, G ) GO TO 200 * Test CHEMV, 03, CHBMV, 04, and CHPMV, 05. 150 CALL CCHK2( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE, $ REWI, FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF, $ NBET, BET, NINC, INC, NMAX, INCMAX, A, AA, AS, $ X, XX, XS, Y, YY, YS, YT, G ) GO TO 200 * Test CTRMV, 06, CTBMV, 07, CTPMV, 08, * CTRSV, 09, CTBSV, 10, and CTPSV, 11. 160 CALL CCHK3( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE, $ REWI, FATAL, NIDIM, IDIM, NKB, KB, NINC, INC, $ NMAX, INCMAX, A, AA, AS, Y, YY, YS, YT, G, Z ) GO TO 200 * Test CGERC, 12, CGERU, 13. 170 CALL CCHK4( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE, $ REWI, FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, $ NMAX, INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, $ YT, G, Z ) GO TO 200 * Test CHER, 14, and CHPR, 15. 180 CALL CCHK5( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE, $ REWI, FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, $ NMAX, INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, $ YT, G, Z ) GO TO 200 * Test CHER2, 16, and CHPR2, 17. 190 CALL CCHK6( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE, $ REWI, FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, $ NMAX, INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, $ YT, G, Z ) * 200 IF( FATAL.AND.SFATAL ) $ GO TO 220 END IF 210 CONTINUE WRITE( NOUT, FMT = 9982 ) GO TO 240 * 220 CONTINUE WRITE( NOUT, FMT = 9981 ) GO TO 240 * 230 CONTINUE WRITE( NOUT, FMT = 9987 ) * 240 CONTINUE IF( TRACE ) $ CLOSE ( NTRA ) CLOSE ( NOUT ) STOP * 9999 FORMAT( ' ROUTINES PASS COMPUTATIONAL TESTS IF TEST RATIO IS LES', $ 'S THAN', F8.2 ) 9998 FORMAT( ' RELATIVE MACHINE PRECISION IS TAKEN TO BE', 1P, E9.1 ) 9997 FORMAT( ' NUMBER OF VALUES OF ', A, ' IS LESS THAN 1 OR GREATER ', $ 'THAN ', I2 ) 9996 FORMAT( ' VALUE OF N IS LESS THAN 0 OR GREATER THAN ', I2 ) 9995 FORMAT( ' VALUE OF K IS LESS THAN 0' ) 9994 FORMAT( ' ABSOLUTE VALUE OF INCX OR INCY IS 0 OR GREATER THAN ', $ I2 ) 9993 FORMAT( ' TESTS OF THE COMPLEX LEVEL 2 BLAS', //' THE F', $ 'OLLOWING PARAMETER VALUES WILL BE USED:' ) 9992 FORMAT( ' FOR N ', 9I6 ) 9991 FORMAT( ' FOR K ', 7I6 ) 9990 FORMAT( ' FOR INCX AND INCY ', 7I6 ) 9989 FORMAT( ' FOR ALPHA ', $ 7( '(', F4.1, ',', F4.1, ') ', : ) ) 9988 FORMAT( ' FOR BETA ', $ 7( '(', F4.1, ',', F4.1, ') ', : ) ) 9987 FORMAT( ' AMEND DATA FILE OR INCREASE ARRAY SIZES IN PROGRAM', $ /' ******* TESTS ABANDONED *******' ) 9986 FORMAT( ' SUBPROGRAM NAME ', A6, ' NOT RECOGNIZED', /' ******* T', $ 'ESTS ABANDONED *******' ) 9985 FORMAT( ' ERROR IN CMVCH - IN-LINE DOT PRODUCTS ARE BEING EVALU', $ 'ATED WRONGLY.', /' CMVCH WAS CALLED WITH TRANS = ', A1, $ ' AND RETURNED SAME = ', L1, ' AND ERR = ', F12.3, '.', / $ ' THIS MAY BE DUE TO FAULTS IN THE ARITHMETIC OR THE COMPILER.' $ , /' ******* TESTS ABANDONED *******' ) 9984 FORMAT( A6, L2 ) 9983 FORMAT( 1X, A6, ' WAS NOT TESTED' ) 9982 FORMAT( /' END OF TESTS' ) 9981 FORMAT( /' ******* FATAL ERROR - TESTS ABANDONED *******' ) 9980 FORMAT( ' ERROR-EXITS WILL NOT BE TESTED' ) * * End of CBLAT2. * END SUBROUTINE CCHK1( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI, $ FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF, NBET, $ BET, NINC, INC, NMAX, INCMAX, A, AA, AS, X, XX, $ XS, Y, YY, YS, YT, G ) * * Tests CGEMV and CGBMV. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Parameters .. COMPLEX ZERO, HALF PARAMETER ( ZERO = ( 0.0, 0.0 ), HALF = ( 0.5, 0.0 ) ) REAL RZERO PARAMETER ( RZERO = 0.0 ) * .. Scalar Arguments .. REAL EPS, THRESH INTEGER INCMAX, NALF, NBET, NIDIM, NINC, NKB, NMAX, $ NOUT, NTRA LOGICAL FATAL, REWI, TRACE CHARACTER*6 SNAME * .. Array Arguments .. COMPLEX A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ), $ AS( NMAX*NMAX ), BET( NBET ), X( NMAX ), $ XS( NMAX*INCMAX ), XX( NMAX*INCMAX ), $ Y( NMAX ), YS( NMAX*INCMAX ), YT( NMAX ), $ YY( NMAX*INCMAX ) REAL G( NMAX ) INTEGER IDIM( NIDIM ), INC( NINC ), KB( NKB ) * .. Local Scalars .. COMPLEX ALPHA, ALS, BETA, BLS, TRANSL REAL ERR, ERRMAX INTEGER I, IA, IB, IC, IKU, IM, IN, INCX, INCXS, INCY, $ INCYS, IX, IY, KL, KLS, KU, KUS, LAA, LDA, $ LDAS, LX, LY, M, ML, MS, N, NARGS, NC, ND, NK, $ NL, NS LOGICAL BANDED, FULL, NULL, RESET, SAME, TRAN CHARACTER*1 TRANS, TRANSS CHARACTER*3 ICH * .. Local Arrays .. LOGICAL ISAME( 13 ) * .. External Functions .. LOGICAL LCE, LCERES EXTERNAL LCE, LCERES * .. External Subroutines .. EXTERNAL CGBMV, CGEMV, CMAKE, CMVCH * .. Intrinsic Functions .. INTRINSIC ABS, MAX, MIN * .. Scalars in Common .. INTEGER INFOT, NOUTC LOGICAL LERR, OK * .. Common blocks .. COMMON /INFOC/INFOT, NOUTC, OK, LERR * .. Data statements .. DATA ICH/'NTC'/ * .. Executable Statements .. FULL = SNAME( 3: 3 ).EQ.'E' BANDED = SNAME( 3: 3 ).EQ.'B' * Define the number of arguments. IF( FULL )THEN NARGS = 11 ELSE IF( BANDED )THEN NARGS = 13 END IF * NC = 0 RESET = .TRUE. ERRMAX = RZERO * DO 120 IN = 1, NIDIM N = IDIM( IN ) ND = N/2 + 1 * DO 110 IM = 1, 2 IF( IM.EQ.1 ) $ M = MAX( N - ND, 0 ) IF( IM.EQ.2 ) $ M = MIN( N + ND, NMAX ) * IF( BANDED )THEN NK = NKB ELSE NK = 1 END IF DO 100 IKU = 1, NK IF( BANDED )THEN KU = KB( IKU ) KL = MAX( KU - 1, 0 ) ELSE KU = N - 1 KL = M - 1 END IF * Set LDA to 1 more than minimum value if room. IF( BANDED )THEN LDA = KL + KU + 1 ELSE LDA = M END IF IF( LDA.LT.NMAX ) $ LDA = LDA + 1 * Skip tests if not enough room. IF( LDA.GT.NMAX ) $ GO TO 100 LAA = LDA*N NULL = N.LE.0.OR.M.LE.0 * * Generate the matrix A. * TRANSL = ZERO CALL CMAKE( SNAME( 2: 3 ), ' ', ' ', M, N, A, NMAX, AA, $ LDA, KL, KU, RESET, TRANSL ) * DO 90 IC = 1, 3 TRANS = ICH( IC: IC ) TRAN = TRANS.EQ.'T'.OR.TRANS.EQ.'C' * IF( TRAN )THEN ML = N NL = M ELSE ML = M NL = N END IF * DO 80 IX = 1, NINC INCX = INC( IX ) LX = ABS( INCX )*NL * * Generate the vector X. * TRANSL = HALF CALL CMAKE( 'GE', ' ', ' ', 1, NL, X, 1, XX, $ ABS( INCX ), 0, NL - 1, RESET, TRANSL ) IF( NL.GT.1 )THEN X( NL/2 ) = ZERO XX( 1 + ABS( INCX )*( NL/2 - 1 ) ) = ZERO END IF * DO 70 IY = 1, NINC INCY = INC( IY ) LY = ABS( INCY )*ML * DO 60 IA = 1, NALF ALPHA = ALF( IA ) * DO 50 IB = 1, NBET BETA = BET( IB ) * * Generate the vector Y. * TRANSL = ZERO CALL CMAKE( 'GE', ' ', ' ', 1, ML, Y, 1, $ YY, ABS( INCY ), 0, ML - 1, $ RESET, TRANSL ) * NC = NC + 1 * * Save every datum before calling the * subroutine. * TRANSS = TRANS MS = M NS = N KLS = KL KUS = KU ALS = ALPHA DO 10 I = 1, LAA AS( I ) = AA( I ) 10 CONTINUE LDAS = LDA DO 20 I = 1, LX XS( I ) = XX( I ) 20 CONTINUE INCXS = INCX BLS = BETA DO 30 I = 1, LY YS( I ) = YY( I ) 30 CONTINUE INCYS = INCY * * Call the subroutine. * IF( FULL )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9994 )NC, SNAME, $ TRANS, M, N, ALPHA, LDA, INCX, BETA, $ INCY IF( REWI ) $ REWIND NTRA CALL CGEMV( TRANS, M, N, ALPHA, AA, $ LDA, XX, INCX, BETA, YY, $ INCY ) ELSE IF( BANDED )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9995 )NC, SNAME, $ TRANS, M, N, KL, KU, ALPHA, LDA, $ INCX, BETA, INCY IF( REWI ) $ REWIND NTRA CALL CGBMV( TRANS, M, N, KL, KU, ALPHA, $ AA, LDA, XX, INCX, BETA, $ YY, INCY ) END IF * * Check if error-exit was taken incorrectly. * IF( .NOT.OK )THEN WRITE( NOUT, FMT = 9993 ) FATAL = .TRUE. GO TO 130 END IF * * See what data changed inside subroutines. * ISAME( 1 ) = TRANS.EQ.TRANSS ISAME( 2 ) = MS.EQ.M ISAME( 3 ) = NS.EQ.N IF( FULL )THEN ISAME( 4 ) = ALS.EQ.ALPHA ISAME( 5 ) = LCE( AS, AA, LAA ) ISAME( 6 ) = LDAS.EQ.LDA ISAME( 7 ) = LCE( XS, XX, LX ) ISAME( 8 ) = INCXS.EQ.INCX ISAME( 9 ) = BLS.EQ.BETA IF( NULL )THEN ISAME( 10 ) = LCE( YS, YY, LY ) ELSE ISAME( 10 ) = LCERES( 'GE', ' ', 1, $ ML, YS, YY, $ ABS( INCY ) ) END IF ISAME( 11 ) = INCYS.EQ.INCY ELSE IF( BANDED )THEN ISAME( 4 ) = KLS.EQ.KL ISAME( 5 ) = KUS.EQ.KU ISAME( 6 ) = ALS.EQ.ALPHA ISAME( 7 ) = LCE( AS, AA, LAA ) ISAME( 8 ) = LDAS.EQ.LDA ISAME( 9 ) = LCE( XS, XX, LX ) ISAME( 10 ) = INCXS.EQ.INCX ISAME( 11 ) = BLS.EQ.BETA IF( NULL )THEN ISAME( 12 ) = LCE( YS, YY, LY ) ELSE ISAME( 12 ) = LCERES( 'GE', ' ', 1, $ ML, YS, YY, $ ABS( INCY ) ) END IF ISAME( 13 ) = INCYS.EQ.INCY END IF * * If data was incorrectly changed, report * and return. * SAME = .TRUE. DO 40 I = 1, NARGS SAME = SAME.AND.ISAME( I ) IF( .NOT.ISAME( I ) ) $ WRITE( NOUT, FMT = 9998 )I 40 CONTINUE IF( .NOT.SAME )THEN FATAL = .TRUE. GO TO 130 END IF * IF( .NOT.NULL )THEN * * Check the result. * CALL CMVCH( TRANS, M, N, ALPHA, A, $ NMAX, X, INCX, BETA, Y, $ INCY, YT, G, YY, EPS, ERR, $ FATAL, NOUT, .TRUE. ) ERRMAX = MAX( ERRMAX, ERR ) * If got really bad answer, report and * return. IF( FATAL ) $ GO TO 130 ELSE * Avoid repeating tests with M.le.0 or * N.le.0. GO TO 110 END IF * 50 CONTINUE * 60 CONTINUE * 70 CONTINUE * 80 CONTINUE * 90 CONTINUE * 100 CONTINUE * 110 CONTINUE * 120 CONTINUE * * Report result. * IF( ERRMAX.LT.THRESH )THEN WRITE( NOUT, FMT = 9999 )SNAME, NC ELSE WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX END IF GO TO 140 * 130 CONTINUE WRITE( NOUT, FMT = 9996 )SNAME IF( FULL )THEN WRITE( NOUT, FMT = 9994 )NC, SNAME, TRANS, M, N, ALPHA, LDA, $ INCX, BETA, INCY ELSE IF( BANDED )THEN WRITE( NOUT, FMT = 9995 )NC, SNAME, TRANS, M, N, KL, KU, $ ALPHA, LDA, INCX, BETA, INCY END IF * 140 CONTINUE RETURN * 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL', $ 'S)' ) 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH', $ 'ANGED INCORRECTLY *******' ) 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C', $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2, $ ' - SUSPECT *******' ) 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' ) 9995 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', 4( I3, ',' ), '(', $ F4.1, ',', F4.1, '), A,', I3, ', X,', I2, ',(', F4.1, ',', $ F4.1, '), Y,', I2, ') .' ) 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', 2( I3, ',' ), '(', $ F4.1, ',', F4.1, '), A,', I3, ', X,', I2, ',(', F4.1, ',', $ F4.1, '), Y,', I2, ') .' ) 9993 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *', $ '******' ) * * End of CCHK1. * END SUBROUTINE CCHK2( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI, $ FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF, NBET, $ BET, NINC, INC, NMAX, INCMAX, A, AA, AS, X, XX, $ XS, Y, YY, YS, YT, G ) * * Tests CHEMV, CHBMV and CHPMV. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Parameters .. COMPLEX ZERO, HALF PARAMETER ( ZERO = ( 0.0, 0.0 ), HALF = ( 0.5, 0.0 ) ) REAL RZERO PARAMETER ( RZERO = 0.0 ) * .. Scalar Arguments .. REAL EPS, THRESH INTEGER INCMAX, NALF, NBET, NIDIM, NINC, NKB, NMAX, $ NOUT, NTRA LOGICAL FATAL, REWI, TRACE CHARACTER*6 SNAME * .. Array Arguments .. COMPLEX A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ), $ AS( NMAX*NMAX ), BET( NBET ), X( NMAX ), $ XS( NMAX*INCMAX ), XX( NMAX*INCMAX ), $ Y( NMAX ), YS( NMAX*INCMAX ), YT( NMAX ), $ YY( NMAX*INCMAX ) REAL G( NMAX ) INTEGER IDIM( NIDIM ), INC( NINC ), KB( NKB ) * .. Local Scalars .. COMPLEX ALPHA, ALS, BETA, BLS, TRANSL REAL ERR, ERRMAX INTEGER I, IA, IB, IC, IK, IN, INCX, INCXS, INCY, $ INCYS, IX, IY, K, KS, LAA, LDA, LDAS, LX, LY, $ N, NARGS, NC, NK, NS LOGICAL BANDED, FULL, NULL, PACKED, RESET, SAME CHARACTER*1 UPLO, UPLOS CHARACTER*2 ICH * .. Local Arrays .. LOGICAL ISAME( 13 ) * .. External Functions .. LOGICAL LCE, LCERES EXTERNAL LCE, LCERES * .. External Subroutines .. EXTERNAL CHBMV, CHEMV, CHPMV, CMAKE, CMVCH * .. Intrinsic Functions .. INTRINSIC ABS, MAX * .. Scalars in Common .. INTEGER INFOT, NOUTC LOGICAL LERR, OK * .. Common blocks .. COMMON /INFOC/INFOT, NOUTC, OK, LERR * .. Data statements .. DATA ICH/'UL'/ * .. Executable Statements .. FULL = SNAME( 3: 3 ).EQ.'E' BANDED = SNAME( 3: 3 ).EQ.'B' PACKED = SNAME( 3: 3 ).EQ.'P' * Define the number of arguments. IF( FULL )THEN NARGS = 10 ELSE IF( BANDED )THEN NARGS = 11 ELSE IF( PACKED )THEN NARGS = 9 END IF * NC = 0 RESET = .TRUE. ERRMAX = RZERO * DO 110 IN = 1, NIDIM N = IDIM( IN ) * IF( BANDED )THEN NK = NKB ELSE NK = 1 END IF DO 100 IK = 1, NK IF( BANDED )THEN K = KB( IK ) ELSE K = N - 1 END IF * Set LDA to 1 more than minimum value if room. IF( BANDED )THEN LDA = K + 1 ELSE LDA = N END IF IF( LDA.LT.NMAX ) $ LDA = LDA + 1 * Skip tests if not enough room. IF( LDA.GT.NMAX ) $ GO TO 100 IF( PACKED )THEN LAA = ( N*( N + 1 ) )/2 ELSE LAA = LDA*N END IF NULL = N.LE.0 * DO 90 IC = 1, 2 UPLO = ICH( IC: IC ) * * Generate the matrix A. * TRANSL = ZERO CALL CMAKE( SNAME( 2: 3 ), UPLO, ' ', N, N, A, NMAX, AA, $ LDA, K, K, RESET, TRANSL ) * DO 80 IX = 1, NINC INCX = INC( IX ) LX = ABS( INCX )*N * * Generate the vector X. * TRANSL = HALF CALL CMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX, $ ABS( INCX ), 0, N - 1, RESET, TRANSL ) IF( N.GT.1 )THEN X( N/2 ) = ZERO XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO END IF * DO 70 IY = 1, NINC INCY = INC( IY ) LY = ABS( INCY )*N * DO 60 IA = 1, NALF ALPHA = ALF( IA ) * DO 50 IB = 1, NBET BETA = BET( IB ) * * Generate the vector Y. * TRANSL = ZERO CALL CMAKE( 'GE', ' ', ' ', 1, N, Y, 1, YY, $ ABS( INCY ), 0, N - 1, RESET, $ TRANSL ) * NC = NC + 1 * * Save every datum before calling the * subroutine. * UPLOS = UPLO NS = N KS = K ALS = ALPHA DO 10 I = 1, LAA AS( I ) = AA( I ) 10 CONTINUE LDAS = LDA DO 20 I = 1, LX XS( I ) = XX( I ) 20 CONTINUE INCXS = INCX BLS = BETA DO 30 I = 1, LY YS( I ) = YY( I ) 30 CONTINUE INCYS = INCY * * Call the subroutine. * IF( FULL )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9993 )NC, SNAME, $ UPLO, N, ALPHA, LDA, INCX, BETA, INCY IF( REWI ) $ REWIND NTRA CALL CHEMV( UPLO, N, ALPHA, AA, LDA, XX, $ INCX, BETA, YY, INCY ) ELSE IF( BANDED )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9994 )NC, SNAME, $ UPLO, N, K, ALPHA, LDA, INCX, BETA, $ INCY IF( REWI ) $ REWIND NTRA CALL CHBMV( UPLO, N, K, ALPHA, AA, LDA, $ XX, INCX, BETA, YY, INCY ) ELSE IF( PACKED )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9995 )NC, SNAME, $ UPLO, N, ALPHA, INCX, BETA, INCY IF( REWI ) $ REWIND NTRA CALL CHPMV( UPLO, N, ALPHA, AA, XX, INCX, $ BETA, YY, INCY ) END IF * * Check if error-exit was taken incorrectly. * IF( .NOT.OK )THEN WRITE( NOUT, FMT = 9992 ) FATAL = .TRUE. GO TO 120 END IF * * See what data changed inside subroutines. * ISAME( 1 ) = UPLO.EQ.UPLOS ISAME( 2 ) = NS.EQ.N IF( FULL )THEN ISAME( 3 ) = ALS.EQ.ALPHA ISAME( 4 ) = LCE( AS, AA, LAA ) ISAME( 5 ) = LDAS.EQ.LDA ISAME( 6 ) = LCE( XS, XX, LX ) ISAME( 7 ) = INCXS.EQ.INCX ISAME( 8 ) = BLS.EQ.BETA IF( NULL )THEN ISAME( 9 ) = LCE( YS, YY, LY ) ELSE ISAME( 9 ) = LCERES( 'GE', ' ', 1, N, $ YS, YY, ABS( INCY ) ) END IF ISAME( 10 ) = INCYS.EQ.INCY ELSE IF( BANDED )THEN ISAME( 3 ) = KS.EQ.K ISAME( 4 ) = ALS.EQ.ALPHA ISAME( 5 ) = LCE( AS, AA, LAA ) ISAME( 6 ) = LDAS.EQ.LDA ISAME( 7 ) = LCE( XS, XX, LX ) ISAME( 8 ) = INCXS.EQ.INCX ISAME( 9 ) = BLS.EQ.BETA IF( NULL )THEN ISAME( 10 ) = LCE( YS, YY, LY ) ELSE ISAME( 10 ) = LCERES( 'GE', ' ', 1, N, $ YS, YY, ABS( INCY ) ) END IF ISAME( 11 ) = INCYS.EQ.INCY ELSE IF( PACKED )THEN ISAME( 3 ) = ALS.EQ.ALPHA ISAME( 4 ) = LCE( AS, AA, LAA ) ISAME( 5 ) = LCE( XS, XX, LX ) ISAME( 6 ) = INCXS.EQ.INCX ISAME( 7 ) = BLS.EQ.BETA IF( NULL )THEN ISAME( 8 ) = LCE( YS, YY, LY ) ELSE ISAME( 8 ) = LCERES( 'GE', ' ', 1, N, $ YS, YY, ABS( INCY ) ) END IF ISAME( 9 ) = INCYS.EQ.INCY END IF * * If data was incorrectly changed, report and * return. * SAME = .TRUE. DO 40 I = 1, NARGS SAME = SAME.AND.ISAME( I ) IF( .NOT.ISAME( I ) ) $ WRITE( NOUT, FMT = 9998 )I 40 CONTINUE IF( .NOT.SAME )THEN FATAL = .TRUE. GO TO 120 END IF * IF( .NOT.NULL )THEN * * Check the result. * CALL CMVCH( 'N', N, N, ALPHA, A, NMAX, X, $ INCX, BETA, Y, INCY, YT, G, $ YY, EPS, ERR, FATAL, NOUT, $ .TRUE. ) ERRMAX = MAX( ERRMAX, ERR ) * If got really bad answer, report and * return. IF( FATAL ) $ GO TO 120 ELSE * Avoid repeating tests with N.le.0 GO TO 110 END IF * 50 CONTINUE * 60 CONTINUE * 70 CONTINUE * 80 CONTINUE * 90 CONTINUE * 100 CONTINUE * 110 CONTINUE * * Report result. * IF( ERRMAX.LT.THRESH )THEN WRITE( NOUT, FMT = 9999 )SNAME, NC ELSE WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX END IF GO TO 130 * 120 CONTINUE WRITE( NOUT, FMT = 9996 )SNAME IF( FULL )THEN WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, N, ALPHA, LDA, INCX, $ BETA, INCY ELSE IF( BANDED )THEN WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, N, K, ALPHA, LDA, $ INCX, BETA, INCY ELSE IF( PACKED )THEN WRITE( NOUT, FMT = 9995 )NC, SNAME, UPLO, N, ALPHA, INCX, $ BETA, INCY END IF * 130 CONTINUE RETURN * 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL', $ 'S)' ) 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH', $ 'ANGED INCORRECTLY *******' ) 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C', $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2, $ ' - SUSPECT *******' ) 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' ) 9995 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',(', F4.1, ',', $ F4.1, '), AP, X,', I2, ',(', F4.1, ',', F4.1, '), Y,', I2, $ ') .' ) 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', 2( I3, ',' ), '(', $ F4.1, ',', F4.1, '), A,', I3, ', X,', I2, ',(', F4.1, ',', $ F4.1, '), Y,', I2, ') .' ) 9993 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',(', F4.1, ',', $ F4.1, '), A,', I3, ', X,', I2, ',(', F4.1, ',', F4.1, '), ', $ 'Y,', I2, ') .' ) 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *', $ '******' ) * * End of CCHK2. * END SUBROUTINE CCHK3( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI, $ FATAL, NIDIM, IDIM, NKB, KB, NINC, INC, NMAX, $ INCMAX, A, AA, AS, X, XX, XS, XT, G, Z ) * * Tests CTRMV, CTBMV, CTPMV, CTRSV, CTBSV and CTPSV. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Parameters .. COMPLEX ZERO, HALF, ONE PARAMETER ( ZERO = ( 0.0, 0.0 ), HALF = ( 0.5, 0.0 ), $ ONE = ( 1.0, 0.0 ) ) REAL RZERO PARAMETER ( RZERO = 0.0 ) * .. Scalar Arguments .. REAL EPS, THRESH INTEGER INCMAX, NIDIM, NINC, NKB, NMAX, NOUT, NTRA LOGICAL FATAL, REWI, TRACE CHARACTER*6 SNAME * .. Array Arguments .. COMPLEX A( NMAX, NMAX ), AA( NMAX*NMAX ), $ AS( NMAX*NMAX ), X( NMAX ), XS( NMAX*INCMAX ), $ XT( NMAX ), XX( NMAX*INCMAX ), Z( NMAX ) REAL G( NMAX ) INTEGER IDIM( NIDIM ), INC( NINC ), KB( NKB ) * .. Local Scalars .. COMPLEX TRANSL REAL ERR, ERRMAX INTEGER I, ICD, ICT, ICU, IK, IN, INCX, INCXS, IX, K, $ KS, LAA, LDA, LDAS, LX, N, NARGS, NC, NK, NS LOGICAL BANDED, FULL, NULL, PACKED, RESET, SAME CHARACTER*1 DIAG, DIAGS, TRANS, TRANSS, UPLO, UPLOS CHARACTER*2 ICHD, ICHU CHARACTER*3 ICHT * .. Local Arrays .. LOGICAL ISAME( 13 ) * .. External Functions .. LOGICAL LCE, LCERES EXTERNAL LCE, LCERES * .. External Subroutines .. EXTERNAL CMAKE, CMVCH, CTBMV, CTBSV, CTPMV, CTPSV, $ CTRMV, CTRSV * .. Intrinsic Functions .. INTRINSIC ABS, MAX * .. Scalars in Common .. INTEGER INFOT, NOUTC LOGICAL LERR, OK * .. Common blocks .. COMMON /INFOC/INFOT, NOUTC, OK, LERR * .. Data statements .. DATA ICHU/'UL'/, ICHT/'NTC'/, ICHD/'UN'/ * .. Executable Statements .. FULL = SNAME( 3: 3 ).EQ.'R' BANDED = SNAME( 3: 3 ).EQ.'B' PACKED = SNAME( 3: 3 ).EQ.'P' * Define the number of arguments. IF( FULL )THEN NARGS = 8 ELSE IF( BANDED )THEN NARGS = 9 ELSE IF( PACKED )THEN NARGS = 7 END IF * NC = 0 RESET = .TRUE. ERRMAX = RZERO * Set up zero vector for CMVCH. DO 10 I = 1, NMAX Z( I ) = ZERO 10 CONTINUE * DO 110 IN = 1, NIDIM N = IDIM( IN ) * IF( BANDED )THEN NK = NKB ELSE NK = 1 END IF DO 100 IK = 1, NK IF( BANDED )THEN K = KB( IK ) ELSE K = N - 1 END IF * Set LDA to 1 more than minimum value if room. IF( BANDED )THEN LDA = K + 1 ELSE LDA = N END IF IF( LDA.LT.NMAX ) $ LDA = LDA + 1 * Skip tests if not enough room. IF( LDA.GT.NMAX ) $ GO TO 100 IF( PACKED )THEN LAA = ( N*( N + 1 ) )/2 ELSE LAA = LDA*N END IF NULL = N.LE.0 * DO 90 ICU = 1, 2 UPLO = ICHU( ICU: ICU ) * DO 80 ICT = 1, 3 TRANS = ICHT( ICT: ICT ) * DO 70 ICD = 1, 2 DIAG = ICHD( ICD: ICD ) * * Generate the matrix A. * TRANSL = ZERO CALL CMAKE( SNAME( 2: 3 ), UPLO, DIAG, N, N, A, $ NMAX, AA, LDA, K, K, RESET, TRANSL ) * DO 60 IX = 1, NINC INCX = INC( IX ) LX = ABS( INCX )*N * * Generate the vector X. * TRANSL = HALF CALL CMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX, $ ABS( INCX ), 0, N - 1, RESET, $ TRANSL ) IF( N.GT.1 )THEN X( N/2 ) = ZERO XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO END IF * NC = NC + 1 * * Save every datum before calling the subroutine. * UPLOS = UPLO TRANSS = TRANS DIAGS = DIAG NS = N KS = K DO 20 I = 1, LAA AS( I ) = AA( I ) 20 CONTINUE LDAS = LDA DO 30 I = 1, LX XS( I ) = XX( I ) 30 CONTINUE INCXS = INCX * * Call the subroutine. * IF( SNAME( 4: 5 ).EQ.'MV' )THEN IF( FULL )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9993 )NC, SNAME, $ UPLO, TRANS, DIAG, N, LDA, INCX IF( REWI ) $ REWIND NTRA CALL CTRMV( UPLO, TRANS, DIAG, N, AA, LDA, $ XX, INCX ) ELSE IF( BANDED )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9994 )NC, SNAME, $ UPLO, TRANS, DIAG, N, K, LDA, INCX IF( REWI ) $ REWIND NTRA CALL CTBMV( UPLO, TRANS, DIAG, N, K, AA, $ LDA, XX, INCX ) ELSE IF( PACKED )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9995 )NC, SNAME, $ UPLO, TRANS, DIAG, N, INCX IF( REWI ) $ REWIND NTRA CALL CTPMV( UPLO, TRANS, DIAG, N, AA, XX, $ INCX ) END IF ELSE IF( SNAME( 4: 5 ).EQ.'SV' )THEN IF( FULL )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9993 )NC, SNAME, $ UPLO, TRANS, DIAG, N, LDA, INCX IF( REWI ) $ REWIND NTRA CALL CTRSV( UPLO, TRANS, DIAG, N, AA, LDA, $ XX, INCX ) ELSE IF( BANDED )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9994 )NC, SNAME, $ UPLO, TRANS, DIAG, N, K, LDA, INCX IF( REWI ) $ REWIND NTRA CALL CTBSV( UPLO, TRANS, DIAG, N, K, AA, $ LDA, XX, INCX ) ELSE IF( PACKED )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9995 )NC, SNAME, $ UPLO, TRANS, DIAG, N, INCX IF( REWI ) $ REWIND NTRA CALL CTPSV( UPLO, TRANS, DIAG, N, AA, XX, $ INCX ) END IF END IF * * Check if error-exit was taken incorrectly. * IF( .NOT.OK )THEN WRITE( NOUT, FMT = 9992 ) FATAL = .TRUE. GO TO 120 END IF * * See what data changed inside subroutines. * ISAME( 1 ) = UPLO.EQ.UPLOS ISAME( 2 ) = TRANS.EQ.TRANSS ISAME( 3 ) = DIAG.EQ.DIAGS ISAME( 4 ) = NS.EQ.N IF( FULL )THEN ISAME( 5 ) = LCE( AS, AA, LAA ) ISAME( 6 ) = LDAS.EQ.LDA IF( NULL )THEN ISAME( 7 ) = LCE( XS, XX, LX ) ELSE ISAME( 7 ) = LCERES( 'GE', ' ', 1, N, XS, $ XX, ABS( INCX ) ) END IF ISAME( 8 ) = INCXS.EQ.INCX ELSE IF( BANDED )THEN ISAME( 5 ) = KS.EQ.K ISAME( 6 ) = LCE( AS, AA, LAA ) ISAME( 7 ) = LDAS.EQ.LDA IF( NULL )THEN ISAME( 8 ) = LCE( XS, XX, LX ) ELSE ISAME( 8 ) = LCERES( 'GE', ' ', 1, N, XS, $ XX, ABS( INCX ) ) END IF ISAME( 9 ) = INCXS.EQ.INCX ELSE IF( PACKED )THEN ISAME( 5 ) = LCE( AS, AA, LAA ) IF( NULL )THEN ISAME( 6 ) = LCE( XS, XX, LX ) ELSE ISAME( 6 ) = LCERES( 'GE', ' ', 1, N, XS, $ XX, ABS( INCX ) ) END IF ISAME( 7 ) = INCXS.EQ.INCX END IF * * If data was incorrectly changed, report and * return. * SAME = .TRUE. DO 40 I = 1, NARGS SAME = SAME.AND.ISAME( I ) IF( .NOT.ISAME( I ) ) $ WRITE( NOUT, FMT = 9998 )I 40 CONTINUE IF( .NOT.SAME )THEN FATAL = .TRUE. GO TO 120 END IF * IF( .NOT.NULL )THEN IF( SNAME( 4: 5 ).EQ.'MV' )THEN * * Check the result. * CALL CMVCH( TRANS, N, N, ONE, A, NMAX, X, $ INCX, ZERO, Z, INCX, XT, G, $ XX, EPS, ERR, FATAL, NOUT, $ .TRUE. ) ELSE IF( SNAME( 4: 5 ).EQ.'SV' )THEN * * Compute approximation to original vector. * DO 50 I = 1, N Z( I ) = XX( 1 + ( I - 1 )* $ ABS( INCX ) ) XX( 1 + ( I - 1 )*ABS( INCX ) ) $ = X( I ) 50 CONTINUE CALL CMVCH( TRANS, N, N, ONE, A, NMAX, Z, $ INCX, ZERO, X, INCX, XT, G, $ XX, EPS, ERR, FATAL, NOUT, $ .FALSE. ) END IF ERRMAX = MAX( ERRMAX, ERR ) * If got really bad answer, report and return. IF( FATAL ) $ GO TO 120 ELSE * Avoid repeating tests with N.le.0. GO TO 110 END IF * 60 CONTINUE * 70 CONTINUE * 80 CONTINUE * 90 CONTINUE * 100 CONTINUE * 110 CONTINUE * * Report result. * IF( ERRMAX.LT.THRESH )THEN WRITE( NOUT, FMT = 9999 )SNAME, NC ELSE WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX END IF GO TO 130 * 120 CONTINUE WRITE( NOUT, FMT = 9996 )SNAME IF( FULL )THEN WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, TRANS, DIAG, N, LDA, $ INCX ELSE IF( BANDED )THEN WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, TRANS, DIAG, N, K, $ LDA, INCX ELSE IF( PACKED )THEN WRITE( NOUT, FMT = 9995 )NC, SNAME, UPLO, TRANS, DIAG, N, INCX END IF * 130 CONTINUE RETURN * 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL', $ 'S)' ) 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH', $ 'ANGED INCORRECTLY *******' ) 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C', $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2, $ ' - SUSPECT *******' ) 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' ) 9995 FORMAT( 1X, I6, ': ', A6, '(', 3( '''', A1, ''',' ), I3, ', AP, ', $ 'X,', I2, ') .' ) 9994 FORMAT( 1X, I6, ': ', A6, '(', 3( '''', A1, ''',' ), 2( I3, ',' ), $ ' A,', I3, ', X,', I2, ') .' ) 9993 FORMAT( 1X, I6, ': ', A6, '(', 3( '''', A1, ''',' ), I3, ', A,', $ I3, ', X,', I2, ') .' ) 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *', $ '******' ) * * End of CCHK3. * END SUBROUTINE CCHK4( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI, $ FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, NMAX, $ INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, YT, G, $ Z ) * * Tests CGERC and CGERU. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Parameters .. COMPLEX ZERO, HALF, ONE PARAMETER ( ZERO = ( 0.0, 0.0 ), HALF = ( 0.5, 0.0 ), $ ONE = ( 1.0, 0.0 ) ) REAL RZERO PARAMETER ( RZERO = 0.0 ) * .. Scalar Arguments .. REAL EPS, THRESH INTEGER INCMAX, NALF, NIDIM, NINC, NMAX, NOUT, NTRA LOGICAL FATAL, REWI, TRACE CHARACTER*6 SNAME * .. Array Arguments .. COMPLEX A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ), $ AS( NMAX*NMAX ), X( NMAX ), XS( NMAX*INCMAX ), $ XX( NMAX*INCMAX ), Y( NMAX ), $ YS( NMAX*INCMAX ), YT( NMAX ), $ YY( NMAX*INCMAX ), Z( NMAX ) REAL G( NMAX ) INTEGER IDIM( NIDIM ), INC( NINC ) * .. Local Scalars .. COMPLEX ALPHA, ALS, TRANSL REAL ERR, ERRMAX INTEGER I, IA, IM, IN, INCX, INCXS, INCY, INCYS, IX, $ IY, J, LAA, LDA, LDAS, LX, LY, M, MS, N, NARGS, $ NC, ND, NS LOGICAL CONJ, NULL, RESET, SAME * .. Local Arrays .. COMPLEX W( 1 ) LOGICAL ISAME( 13 ) * .. External Functions .. LOGICAL LCE, LCERES EXTERNAL LCE, LCERES * .. External Subroutines .. EXTERNAL CGERC, CGERU, CMAKE, CMVCH * .. Intrinsic Functions .. INTRINSIC ABS, CONJG, MAX, MIN * .. Scalars in Common .. INTEGER INFOT, NOUTC LOGICAL LERR, OK * .. Common blocks .. COMMON /INFOC/INFOT, NOUTC, OK, LERR * .. Executable Statements .. CONJ = SNAME( 5: 5 ).EQ.'C' * Define the number of arguments. NARGS = 9 * NC = 0 RESET = .TRUE. ERRMAX = RZERO * DO 120 IN = 1, NIDIM N = IDIM( IN ) ND = N/2 + 1 * DO 110 IM = 1, 2 IF( IM.EQ.1 ) $ M = MAX( N - ND, 0 ) IF( IM.EQ.2 ) $ M = MIN( N + ND, NMAX ) * * Set LDA to 1 more than minimum value if room. LDA = M IF( LDA.LT.NMAX ) $ LDA = LDA + 1 * Skip tests if not enough room. IF( LDA.GT.NMAX ) $ GO TO 110 LAA = LDA*N NULL = N.LE.0.OR.M.LE.0 * DO 100 IX = 1, NINC INCX = INC( IX ) LX = ABS( INCX )*M * * Generate the vector X. * TRANSL = HALF CALL CMAKE( 'GE', ' ', ' ', 1, M, X, 1, XX, ABS( INCX ), $ 0, M - 1, RESET, TRANSL ) IF( M.GT.1 )THEN X( M/2 ) = ZERO XX( 1 + ABS( INCX )*( M/2 - 1 ) ) = ZERO END IF * DO 90 IY = 1, NINC INCY = INC( IY ) LY = ABS( INCY )*N * * Generate the vector Y. * TRANSL = ZERO CALL CMAKE( 'GE', ' ', ' ', 1, N, Y, 1, YY, $ ABS( INCY ), 0, N - 1, RESET, TRANSL ) IF( N.GT.1 )THEN Y( N/2 ) = ZERO YY( 1 + ABS( INCY )*( N/2 - 1 ) ) = ZERO END IF * DO 80 IA = 1, NALF ALPHA = ALF( IA ) * * Generate the matrix A. * TRANSL = ZERO CALL CMAKE( SNAME( 2: 3 ), ' ', ' ', M, N, A, NMAX, $ AA, LDA, M - 1, N - 1, RESET, TRANSL ) * NC = NC + 1 * * Save every datum before calling the subroutine. * MS = M NS = N ALS = ALPHA DO 10 I = 1, LAA AS( I ) = AA( I ) 10 CONTINUE LDAS = LDA DO 20 I = 1, LX XS( I ) = XX( I ) 20 CONTINUE INCXS = INCX DO 30 I = 1, LY YS( I ) = YY( I ) 30 CONTINUE INCYS = INCY * * Call the subroutine. * IF( TRACE ) $ WRITE( NTRA, FMT = 9994 )NC, SNAME, M, N, $ ALPHA, INCX, INCY, LDA IF( CONJ )THEN IF( REWI ) $ REWIND NTRA CALL CGERC( M, N, ALPHA, XX, INCX, YY, INCY, AA, $ LDA ) ELSE IF( REWI ) $ REWIND NTRA CALL CGERU( M, N, ALPHA, XX, INCX, YY, INCY, AA, $ LDA ) END IF * * Check if error-exit was taken incorrectly. * IF( .NOT.OK )THEN WRITE( NOUT, FMT = 9993 ) FATAL = .TRUE. GO TO 140 END IF * * See what data changed inside subroutine. * ISAME( 1 ) = MS.EQ.M ISAME( 2 ) = NS.EQ.N ISAME( 3 ) = ALS.EQ.ALPHA ISAME( 4 ) = LCE( XS, XX, LX ) ISAME( 5 ) = INCXS.EQ.INCX ISAME( 6 ) = LCE( YS, YY, LY ) ISAME( 7 ) = INCYS.EQ.INCY IF( NULL )THEN ISAME( 8 ) = LCE( AS, AA, LAA ) ELSE ISAME( 8 ) = LCERES( 'GE', ' ', M, N, AS, AA, $ LDA ) END IF ISAME( 9 ) = LDAS.EQ.LDA * * If data was incorrectly changed, report and return. * SAME = .TRUE. DO 40 I = 1, NARGS SAME = SAME.AND.ISAME( I ) IF( .NOT.ISAME( I ) ) $ WRITE( NOUT, FMT = 9998 )I 40 CONTINUE IF( .NOT.SAME )THEN FATAL = .TRUE. GO TO 140 END IF * IF( .NOT.NULL )THEN * * Check the result column by column. * IF( INCX.GT.0 )THEN DO 50 I = 1, M Z( I ) = X( I ) 50 CONTINUE ELSE DO 60 I = 1, M Z( I ) = X( M - I + 1 ) 60 CONTINUE END IF DO 70 J = 1, N IF( INCY.GT.0 )THEN W( 1 ) = Y( J ) ELSE W( 1 ) = Y( N - J + 1 ) END IF IF( CONJ ) $ W( 1 ) = CONJG( W( 1 ) ) CALL CMVCH( 'N', M, 1, ALPHA, Z, NMAX, W, 1, $ ONE, A( 1, J ), 1, YT, G, $ AA( 1 + ( J - 1 )*LDA ), EPS, $ ERR, FATAL, NOUT, .TRUE. ) ERRMAX = MAX( ERRMAX, ERR ) * If got really bad answer, report and return. IF( FATAL ) $ GO TO 130 70 CONTINUE ELSE * Avoid repeating tests with M.le.0 or N.le.0. GO TO 110 END IF * 80 CONTINUE * 90 CONTINUE * 100 CONTINUE * 110 CONTINUE * 120 CONTINUE * * Report result. * IF( ERRMAX.LT.THRESH )THEN WRITE( NOUT, FMT = 9999 )SNAME, NC ELSE WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX END IF GO TO 150 * 130 CONTINUE WRITE( NOUT, FMT = 9995 )J * 140 CONTINUE WRITE( NOUT, FMT = 9996 )SNAME WRITE( NOUT, FMT = 9994 )NC, SNAME, M, N, ALPHA, INCX, INCY, LDA * 150 CONTINUE RETURN * 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL', $ 'S)' ) 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH', $ 'ANGED INCORRECTLY *******' ) 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C', $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2, $ ' - SUSPECT *******' ) 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' ) 9995 FORMAT( ' THESE ARE THE RESULTS FOR COLUMN ', I3 ) 9994 FORMAT( 1X, I6, ': ', A6, '(', 2( I3, ',' ), '(', F4.1, ',', F4.1, $ '), X,', I2, ', Y,', I2, ', A,', I3, ') ', $ ' .' ) 9993 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *', $ '******' ) * * End of CCHK4. * END SUBROUTINE CCHK5( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI, $ FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, NMAX, $ INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, YT, G, $ Z ) * * Tests CHER and CHPR. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Parameters .. COMPLEX ZERO, HALF, ONE PARAMETER ( ZERO = ( 0.0, 0.0 ), HALF = ( 0.5, 0.0 ), $ ONE = ( 1.0, 0.0 ) ) REAL RZERO PARAMETER ( RZERO = 0.0 ) * .. Scalar Arguments .. REAL EPS, THRESH INTEGER INCMAX, NALF, NIDIM, NINC, NMAX, NOUT, NTRA LOGICAL FATAL, REWI, TRACE CHARACTER*6 SNAME * .. Array Arguments .. COMPLEX A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ), $ AS( NMAX*NMAX ), X( NMAX ), XS( NMAX*INCMAX ), $ XX( NMAX*INCMAX ), Y( NMAX ), $ YS( NMAX*INCMAX ), YT( NMAX ), $ YY( NMAX*INCMAX ), Z( NMAX ) REAL G( NMAX ) INTEGER IDIM( NIDIM ), INC( NINC ) * .. Local Scalars .. COMPLEX ALPHA, TRANSL REAL ERR, ERRMAX, RALPHA, RALS INTEGER I, IA, IC, IN, INCX, INCXS, IX, J, JA, JJ, LAA, $ LDA, LDAS, LJ, LX, N, NARGS, NC, NS LOGICAL FULL, NULL, PACKED, RESET, SAME, UPPER CHARACTER*1 UPLO, UPLOS CHARACTER*2 ICH * .. Local Arrays .. COMPLEX W( 1 ) LOGICAL ISAME( 13 ) * .. External Functions .. LOGICAL LCE, LCERES EXTERNAL LCE, LCERES * .. External Subroutines .. EXTERNAL CHER, CHPR, CMAKE, CMVCH * .. Intrinsic Functions .. INTRINSIC ABS, CMPLX, CONJG, MAX, REAL * .. Scalars in Common .. INTEGER INFOT, NOUTC LOGICAL LERR, OK * .. Common blocks .. COMMON /INFOC/INFOT, NOUTC, OK, LERR * .. Data statements .. DATA ICH/'UL'/ * .. Executable Statements .. FULL = SNAME( 3: 3 ).EQ.'E' PACKED = SNAME( 3: 3 ).EQ.'P' * Define the number of arguments. IF( FULL )THEN NARGS = 7 ELSE IF( PACKED )THEN NARGS = 6 END IF * NC = 0 RESET = .TRUE. ERRMAX = RZERO * DO 100 IN = 1, NIDIM N = IDIM( IN ) * Set LDA to 1 more than minimum value if room. LDA = N IF( LDA.LT.NMAX ) $ LDA = LDA + 1 * Skip tests if not enough room. IF( LDA.GT.NMAX ) $ GO TO 100 IF( PACKED )THEN LAA = ( N*( N + 1 ) )/2 ELSE LAA = LDA*N END IF * DO 90 IC = 1, 2 UPLO = ICH( IC: IC ) UPPER = UPLO.EQ.'U' * DO 80 IX = 1, NINC INCX = INC( IX ) LX = ABS( INCX )*N * * Generate the vector X. * TRANSL = HALF CALL CMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX, ABS( INCX ), $ 0, N - 1, RESET, TRANSL ) IF( N.GT.1 )THEN X( N/2 ) = ZERO XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO END IF * DO 70 IA = 1, NALF RALPHA = REAL( ALF( IA ) ) ALPHA = CMPLX( RALPHA, RZERO ) NULL = N.LE.0.OR.RALPHA.EQ.RZERO * * Generate the matrix A. * TRANSL = ZERO CALL CMAKE( SNAME( 2: 3 ), UPLO, ' ', N, N, A, NMAX, $ AA, LDA, N - 1, N - 1, RESET, TRANSL ) * NC = NC + 1 * * Save every datum before calling the subroutine. * UPLOS = UPLO NS = N RALS = RALPHA DO 10 I = 1, LAA AS( I ) = AA( I ) 10 CONTINUE LDAS = LDA DO 20 I = 1, LX XS( I ) = XX( I ) 20 CONTINUE INCXS = INCX * * Call the subroutine. * IF( FULL )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9993 )NC, SNAME, UPLO, N, $ RALPHA, INCX, LDA IF( REWI ) $ REWIND NTRA CALL CHER( UPLO, N, RALPHA, XX, INCX, AA, LDA ) ELSE IF( PACKED )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9994 )NC, SNAME, UPLO, N, $ RALPHA, INCX IF( REWI ) $ REWIND NTRA CALL CHPR( UPLO, N, RALPHA, XX, INCX, AA ) END IF * * Check if error-exit was taken incorrectly. * IF( .NOT.OK )THEN WRITE( NOUT, FMT = 9992 ) FATAL = .TRUE. GO TO 120 END IF * * See what data changed inside subroutines. * ISAME( 1 ) = UPLO.EQ.UPLOS ISAME( 2 ) = NS.EQ.N ISAME( 3 ) = RALS.EQ.RALPHA ISAME( 4 ) = LCE( XS, XX, LX ) ISAME( 5 ) = INCXS.EQ.INCX IF( NULL )THEN ISAME( 6 ) = LCE( AS, AA, LAA ) ELSE ISAME( 6 ) = LCERES( SNAME( 2: 3 ), UPLO, N, N, AS, $ AA, LDA ) END IF IF( .NOT.PACKED )THEN ISAME( 7 ) = LDAS.EQ.LDA END IF * * If data was incorrectly changed, report and return. * SAME = .TRUE. DO 30 I = 1, NARGS SAME = SAME.AND.ISAME( I ) IF( .NOT.ISAME( I ) ) $ WRITE( NOUT, FMT = 9998 )I 30 CONTINUE IF( .NOT.SAME )THEN FATAL = .TRUE. GO TO 120 END IF * IF( .NOT.NULL )THEN * * Check the result column by column. * IF( INCX.GT.0 )THEN DO 40 I = 1, N Z( I ) = X( I ) 40 CONTINUE ELSE DO 50 I = 1, N Z( I ) = X( N - I + 1 ) 50 CONTINUE END IF JA = 1 DO 60 J = 1, N W( 1 ) = CONJG( Z( J ) ) IF( UPPER )THEN JJ = 1 LJ = J ELSE JJ = J LJ = N - J + 1 END IF CALL CMVCH( 'N', LJ, 1, ALPHA, Z( JJ ), LJ, W, $ 1, ONE, A( JJ, J ), 1, YT, G, $ AA( JA ), EPS, ERR, FATAL, NOUT, $ .TRUE. ) IF( FULL )THEN IF( UPPER )THEN JA = JA + LDA ELSE JA = JA + LDA + 1 END IF ELSE JA = JA + LJ END IF ERRMAX = MAX( ERRMAX, ERR ) * If got really bad answer, report and return. IF( FATAL ) $ GO TO 110 60 CONTINUE ELSE * Avoid repeating tests if N.le.0. IF( N.LE.0 ) $ GO TO 100 END IF * 70 CONTINUE * 80 CONTINUE * 90 CONTINUE * 100 CONTINUE * * Report result. * IF( ERRMAX.LT.THRESH )THEN WRITE( NOUT, FMT = 9999 )SNAME, NC ELSE WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX END IF GO TO 130 * 110 CONTINUE WRITE( NOUT, FMT = 9995 )J * 120 CONTINUE WRITE( NOUT, FMT = 9996 )SNAME IF( FULL )THEN WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, N, RALPHA, INCX, LDA ELSE IF( PACKED )THEN WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, N, RALPHA, INCX END IF * 130 CONTINUE RETURN * 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL', $ 'S)' ) 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH', $ 'ANGED INCORRECTLY *******' ) 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C', $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2, $ ' - SUSPECT *******' ) 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' ) 9995 FORMAT( ' THESE ARE THE RESULTS FOR COLUMN ', I3 ) 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', X,', $ I2, ', AP) .' ) 9993 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', X,', $ I2, ', A,', I3, ') .' ) 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *', $ '******' ) * * End of CCHK5. * END SUBROUTINE CCHK6( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI, $ FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, NMAX, $ INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, YT, G, $ Z ) * * Tests CHER2 and CHPR2. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Parameters .. COMPLEX ZERO, HALF, ONE PARAMETER ( ZERO = ( 0.0, 0.0 ), HALF = ( 0.5, 0.0 ), $ ONE = ( 1.0, 0.0 ) ) REAL RZERO PARAMETER ( RZERO = 0.0 ) * .. Scalar Arguments .. REAL EPS, THRESH INTEGER INCMAX, NALF, NIDIM, NINC, NMAX, NOUT, NTRA LOGICAL FATAL, REWI, TRACE CHARACTER*6 SNAME * .. Array Arguments .. COMPLEX A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ), $ AS( NMAX*NMAX ), X( NMAX ), XS( NMAX*INCMAX ), $ XX( NMAX*INCMAX ), Y( NMAX ), $ YS( NMAX*INCMAX ), YT( NMAX ), $ YY( NMAX*INCMAX ), Z( NMAX, 2 ) REAL G( NMAX ) INTEGER IDIM( NIDIM ), INC( NINC ) * .. Local Scalars .. COMPLEX ALPHA, ALS, TRANSL REAL ERR, ERRMAX INTEGER I, IA, IC, IN, INCX, INCXS, INCY, INCYS, IX, $ IY, J, JA, JJ, LAA, LDA, LDAS, LJ, LX, LY, N, $ NARGS, NC, NS LOGICAL FULL, NULL, PACKED, RESET, SAME, UPPER CHARACTER*1 UPLO, UPLOS CHARACTER*2 ICH * .. Local Arrays .. COMPLEX W( 2 ) LOGICAL ISAME( 13 ) * .. External Functions .. LOGICAL LCE, LCERES EXTERNAL LCE, LCERES * .. External Subroutines .. EXTERNAL CHER2, CHPR2, CMAKE, CMVCH * .. Intrinsic Functions .. INTRINSIC ABS, CONJG, MAX * .. Scalars in Common .. INTEGER INFOT, NOUTC LOGICAL LERR, OK * .. Common blocks .. COMMON /INFOC/INFOT, NOUTC, OK, LERR * .. Data statements .. DATA ICH/'UL'/ * .. Executable Statements .. FULL = SNAME( 3: 3 ).EQ.'E' PACKED = SNAME( 3: 3 ).EQ.'P' * Define the number of arguments. IF( FULL )THEN NARGS = 9 ELSE IF( PACKED )THEN NARGS = 8 END IF * NC = 0 RESET = .TRUE. ERRMAX = RZERO * DO 140 IN = 1, NIDIM N = IDIM( IN ) * Set LDA to 1 more than minimum value if room. LDA = N IF( LDA.LT.NMAX ) $ LDA = LDA + 1 * Skip tests if not enough room. IF( LDA.GT.NMAX ) $ GO TO 140 IF( PACKED )THEN LAA = ( N*( N + 1 ) )/2 ELSE LAA = LDA*N END IF * DO 130 IC = 1, 2 UPLO = ICH( IC: IC ) UPPER = UPLO.EQ.'U' * DO 120 IX = 1, NINC INCX = INC( IX ) LX = ABS( INCX )*N * * Generate the vector X. * TRANSL = HALF CALL CMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX, ABS( INCX ), $ 0, N - 1, RESET, TRANSL ) IF( N.GT.1 )THEN X( N/2 ) = ZERO XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO END IF * DO 110 IY = 1, NINC INCY = INC( IY ) LY = ABS( INCY )*N * * Generate the vector Y. * TRANSL = ZERO CALL CMAKE( 'GE', ' ', ' ', 1, N, Y, 1, YY, $ ABS( INCY ), 0, N - 1, RESET, TRANSL ) IF( N.GT.1 )THEN Y( N/2 ) = ZERO YY( 1 + ABS( INCY )*( N/2 - 1 ) ) = ZERO END IF * DO 100 IA = 1, NALF ALPHA = ALF( IA ) NULL = N.LE.0.OR.ALPHA.EQ.ZERO * * Generate the matrix A. * TRANSL = ZERO CALL CMAKE( SNAME( 2: 3 ), UPLO, ' ', N, N, A, $ NMAX, AA, LDA, N - 1, N - 1, RESET, $ TRANSL ) * NC = NC + 1 * * Save every datum before calling the subroutine. * UPLOS = UPLO NS = N ALS = ALPHA DO 10 I = 1, LAA AS( I ) = AA( I ) 10 CONTINUE LDAS = LDA DO 20 I = 1, LX XS( I ) = XX( I ) 20 CONTINUE INCXS = INCX DO 30 I = 1, LY YS( I ) = YY( I ) 30 CONTINUE INCYS = INCY * * Call the subroutine. * IF( FULL )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9993 )NC, SNAME, UPLO, N, $ ALPHA, INCX, INCY, LDA IF( REWI ) $ REWIND NTRA CALL CHER2( UPLO, N, ALPHA, XX, INCX, YY, INCY, $ AA, LDA ) ELSE IF( PACKED )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9994 )NC, SNAME, UPLO, N, $ ALPHA, INCX, INCY IF( REWI ) $ REWIND NTRA CALL CHPR2( UPLO, N, ALPHA, XX, INCX, YY, INCY, $ AA ) END IF * * Check if error-exit was taken incorrectly. * IF( .NOT.OK )THEN WRITE( NOUT, FMT = 9992 ) FATAL = .TRUE. GO TO 160 END IF * * See what data changed inside subroutines. * ISAME( 1 ) = UPLO.EQ.UPLOS ISAME( 2 ) = NS.EQ.N ISAME( 3 ) = ALS.EQ.ALPHA ISAME( 4 ) = LCE( XS, XX, LX ) ISAME( 5 ) = INCXS.EQ.INCX ISAME( 6 ) = LCE( YS, YY, LY ) ISAME( 7 ) = INCYS.EQ.INCY IF( NULL )THEN ISAME( 8 ) = LCE( AS, AA, LAA ) ELSE ISAME( 8 ) = LCERES( SNAME( 2: 3 ), UPLO, N, N, $ AS, AA, LDA ) END IF IF( .NOT.PACKED )THEN ISAME( 9 ) = LDAS.EQ.LDA END IF * * If data was incorrectly changed, report and return. * SAME = .TRUE. DO 40 I = 1, NARGS SAME = SAME.AND.ISAME( I ) IF( .NOT.ISAME( I ) ) $ WRITE( NOUT, FMT = 9998 )I 40 CONTINUE IF( .NOT.SAME )THEN FATAL = .TRUE. GO TO 160 END IF * IF( .NOT.NULL )THEN * * Check the result column by column. * IF( INCX.GT.0 )THEN DO 50 I = 1, N Z( I, 1 ) = X( I ) 50 CONTINUE ELSE DO 60 I = 1, N Z( I, 1 ) = X( N - I + 1 ) 60 CONTINUE END IF IF( INCY.GT.0 )THEN DO 70 I = 1, N Z( I, 2 ) = Y( I ) 70 CONTINUE ELSE DO 80 I = 1, N Z( I, 2 ) = Y( N - I + 1 ) 80 CONTINUE END IF JA = 1 DO 90 J = 1, N W( 1 ) = ALPHA*CONJG( Z( J, 2 ) ) W( 2 ) = CONJG( ALPHA )*CONJG( Z( J, 1 ) ) IF( UPPER )THEN JJ = 1 LJ = J ELSE JJ = J LJ = N - J + 1 END IF CALL CMVCH( 'N', LJ, 2, ONE, Z( JJ, 1 ), $ NMAX, W, 1, ONE, A( JJ, J ), 1, $ YT, G, AA( JA ), EPS, ERR, FATAL, $ NOUT, .TRUE. ) IF( FULL )THEN IF( UPPER )THEN JA = JA + LDA ELSE JA = JA + LDA + 1 END IF ELSE JA = JA + LJ END IF ERRMAX = MAX( ERRMAX, ERR ) * If got really bad answer, report and return. IF( FATAL ) $ GO TO 150 90 CONTINUE ELSE * Avoid repeating tests with N.le.0. IF( N.LE.0 ) $ GO TO 140 END IF * 100 CONTINUE * 110 CONTINUE * 120 CONTINUE * 130 CONTINUE * 140 CONTINUE * * Report result. * IF( ERRMAX.LT.THRESH )THEN WRITE( NOUT, FMT = 9999 )SNAME, NC ELSE WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX END IF GO TO 170 * 150 CONTINUE WRITE( NOUT, FMT = 9995 )J * 160 CONTINUE WRITE( NOUT, FMT = 9996 )SNAME IF( FULL )THEN WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, N, ALPHA, INCX, $ INCY, LDA ELSE IF( PACKED )THEN WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, N, ALPHA, INCX, INCY END IF * 170 CONTINUE RETURN * 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL', $ 'S)' ) 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH', $ 'ANGED INCORRECTLY *******' ) 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C', $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2, $ ' - SUSPECT *******' ) 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' ) 9995 FORMAT( ' THESE ARE THE RESULTS FOR COLUMN ', I3 ) 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',(', F4.1, ',', $ F4.1, '), X,', I2, ', Y,', I2, ', AP) ', $ ' .' ) 9993 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',(', F4.1, ',', $ F4.1, '), X,', I2, ', Y,', I2, ', A,', I3, ') ', $ ' .' ) 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *', $ '******' ) * * End of CCHK6. * END SUBROUTINE CCHKE( ISNUM, SRNAMT, NOUT ) * * Tests the error exits from the Level 2 Blas. * Requires a special version of the error-handling routine XERBLA. * ALPHA, RALPHA, BETA, A, X and Y should not need to be defined. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Scalar Arguments .. INTEGER ISNUM, NOUT CHARACTER*6 SRNAMT * .. Scalars in Common .. INTEGER INFOT, NOUTC LOGICAL LERR, OK * .. Local Scalars .. COMPLEX ALPHA, BETA REAL RALPHA * .. Local Arrays .. COMPLEX A( 1, 1 ), X( 1 ), Y( 1 ) * .. External Subroutines .. EXTERNAL CGBMV, CGEMV, CGERC, CGERU, CHBMV, CHEMV, CHER, $ CHER2, CHKXER, CHPMV, CHPR, CHPR2, CTBMV, $ CTBSV, CTPMV, CTPSV, CTRMV, CTRSV * .. Common blocks .. COMMON /INFOC/INFOT, NOUTC, OK, LERR * .. Executable Statements .. * OK is set to .FALSE. by the special version of XERBLA or by CHKXER * if anything is wrong. OK = .TRUE. * LERR is set to .TRUE. by the special version of XERBLA each time * it is called, and is then tested and re-set by CHKXER. LERR = .FALSE. GO TO ( 10, 20, 30, 40, 50, 60, 70, 80, $ 90, 100, 110, 120, 130, 140, 150, 160, $ 170 )ISNUM 10 INFOT = 1 CALL CGEMV( '/', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL CGEMV( 'N', -1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 3 CALL CGEMV( 'N', 0, -1, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 6 CALL CGEMV( 'N', 2, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 8 CALL CGEMV( 'N', 0, 0, ALPHA, A, 1, X, 0, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 11 CALL CGEMV( 'N', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 0 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 180 20 INFOT = 1 CALL CGBMV( '/', 0, 0, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL CGBMV( 'N', -1, 0, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 3 CALL CGBMV( 'N', 0, -1, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 4 CALL CGBMV( 'N', 0, 0, -1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 5 CALL CGBMV( 'N', 2, 0, 0, -1, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 8 CALL CGBMV( 'N', 0, 0, 1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 10 CALL CGBMV( 'N', 0, 0, 0, 0, ALPHA, A, 1, X, 0, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 13 CALL CGBMV( 'N', 0, 0, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 0 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 180 30 INFOT = 1 CALL CHEMV( '/', 0, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL CHEMV( 'U', -1, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 5 CALL CHEMV( 'U', 2, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 7 CALL CHEMV( 'U', 0, ALPHA, A, 1, X, 0, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 10 CALL CHEMV( 'U', 0, ALPHA, A, 1, X, 1, BETA, Y, 0 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 180 40 INFOT = 1 CALL CHBMV( '/', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL CHBMV( 'U', -1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 3 CALL CHBMV( 'U', 0, -1, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 6 CALL CHBMV( 'U', 0, 1, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 8 CALL CHBMV( 'U', 0, 0, ALPHA, A, 1, X, 0, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 11 CALL CHBMV( 'U', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 0 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 180 50 INFOT = 1 CALL CHPMV( '/', 0, ALPHA, A, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL CHPMV( 'U', -1, ALPHA, A, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 6 CALL CHPMV( 'U', 0, ALPHA, A, X, 0, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 9 CALL CHPMV( 'U', 0, ALPHA, A, X, 1, BETA, Y, 0 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 180 60 INFOT = 1 CALL CTRMV( '/', 'N', 'N', 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL CTRMV( 'U', '/', 'N', 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 3 CALL CTRMV( 'U', 'N', '/', 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 4 CALL CTRMV( 'U', 'N', 'N', -1, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 6 CALL CTRMV( 'U', 'N', 'N', 2, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 8 CALL CTRMV( 'U', 'N', 'N', 0, A, 1, X, 0 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 180 70 INFOT = 1 CALL CTBMV( '/', 'N', 'N', 0, 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL CTBMV( 'U', '/', 'N', 0, 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 3 CALL CTBMV( 'U', 'N', '/', 0, 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 4 CALL CTBMV( 'U', 'N', 'N', -1, 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 5 CALL CTBMV( 'U', 'N', 'N', 0, -1, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 7 CALL CTBMV( 'U', 'N', 'N', 0, 1, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 9 CALL CTBMV( 'U', 'N', 'N', 0, 0, A, 1, X, 0 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 180 80 INFOT = 1 CALL CTPMV( '/', 'N', 'N', 0, A, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL CTPMV( 'U', '/', 'N', 0, A, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 3 CALL CTPMV( 'U', 'N', '/', 0, A, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 4 CALL CTPMV( 'U', 'N', 'N', -1, A, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 7 CALL CTPMV( 'U', 'N', 'N', 0, A, X, 0 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 180 90 INFOT = 1 CALL CTRSV( '/', 'N', 'N', 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL CTRSV( 'U', '/', 'N', 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 3 CALL CTRSV( 'U', 'N', '/', 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 4 CALL CTRSV( 'U', 'N', 'N', -1, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 6 CALL CTRSV( 'U', 'N', 'N', 2, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 8 CALL CTRSV( 'U', 'N', 'N', 0, A, 1, X, 0 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 180 100 INFOT = 1 CALL CTBSV( '/', 'N', 'N', 0, 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL CTBSV( 'U', '/', 'N', 0, 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 3 CALL CTBSV( 'U', 'N', '/', 0, 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 4 CALL CTBSV( 'U', 'N', 'N', -1, 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 5 CALL CTBSV( 'U', 'N', 'N', 0, -1, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 7 CALL CTBSV( 'U', 'N', 'N', 0, 1, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 9 CALL CTBSV( 'U', 'N', 'N', 0, 0, A, 1, X, 0 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 180 110 INFOT = 1 CALL CTPSV( '/', 'N', 'N', 0, A, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL CTPSV( 'U', '/', 'N', 0, A, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 3 CALL CTPSV( 'U', 'N', '/', 0, A, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 4 CALL CTPSV( 'U', 'N', 'N', -1, A, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 7 CALL CTPSV( 'U', 'N', 'N', 0, A, X, 0 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 180 120 INFOT = 1 CALL CGERC( -1, 0, ALPHA, X, 1, Y, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL CGERC( 0, -1, ALPHA, X, 1, Y, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 5 CALL CGERC( 0, 0, ALPHA, X, 0, Y, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 7 CALL CGERC( 0, 0, ALPHA, X, 1, Y, 0, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 9 CALL CGERC( 2, 0, ALPHA, X, 1, Y, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 180 130 INFOT = 1 CALL CGERU( -1, 0, ALPHA, X, 1, Y, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL CGERU( 0, -1, ALPHA, X, 1, Y, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 5 CALL CGERU( 0, 0, ALPHA, X, 0, Y, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 7 CALL CGERU( 0, 0, ALPHA, X, 1, Y, 0, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 9 CALL CGERU( 2, 0, ALPHA, X, 1, Y, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 180 140 INFOT = 1 CALL CHER( '/', 0, RALPHA, X, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL CHER( 'U', -1, RALPHA, X, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 5 CALL CHER( 'U', 0, RALPHA, X, 0, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 7 CALL CHER( 'U', 2, RALPHA, X, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 180 150 INFOT = 1 CALL CHPR( '/', 0, RALPHA, X, 1, A ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL CHPR( 'U', -1, RALPHA, X, 1, A ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 5 CALL CHPR( 'U', 0, RALPHA, X, 0, A ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 180 160 INFOT = 1 CALL CHER2( '/', 0, ALPHA, X, 1, Y, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL CHER2( 'U', -1, ALPHA, X, 1, Y, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 5 CALL CHER2( 'U', 0, ALPHA, X, 0, Y, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 7 CALL CHER2( 'U', 0, ALPHA, X, 1, Y, 0, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 9 CALL CHER2( 'U', 2, ALPHA, X, 1, Y, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 180 170 INFOT = 1 CALL CHPR2( '/', 0, ALPHA, X, 1, Y, 1, A ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL CHPR2( 'U', -1, ALPHA, X, 1, Y, 1, A ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 5 CALL CHPR2( 'U', 0, ALPHA, X, 0, Y, 1, A ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 7 CALL CHPR2( 'U', 0, ALPHA, X, 1, Y, 0, A ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) * 180 IF( OK )THEN WRITE( NOUT, FMT = 9999 )SRNAMT ELSE WRITE( NOUT, FMT = 9998 )SRNAMT END IF RETURN * 9999 FORMAT( ' ', A6, ' PASSED THE TESTS OF ERROR-EXITS' ) 9998 FORMAT( ' ******* ', A6, ' FAILED THE TESTS OF ERROR-EXITS *****', $ '**' ) * * End of CCHKE. * END SUBROUTINE CMAKE( TYPE, UPLO, DIAG, M, N, A, NMAX, AA, LDA, KL, $ KU, RESET, TRANSL ) * * Generates values for an M by N matrix A within the bandwidth * defined by KL and KU. * Stores the values in the array AA in the data structure required * by the routine, with unwanted elements set to rogue value. * * TYPE is 'GE', 'GB', 'HE', 'HB', 'HP', 'TR', 'TB' OR 'TP'. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Parameters .. COMPLEX ZERO, ONE PARAMETER ( ZERO = ( 0.0, 0.0 ), ONE = ( 1.0, 0.0 ) ) COMPLEX ROGUE PARAMETER ( ROGUE = ( -1.0E10, 1.0E10 ) ) REAL RZERO PARAMETER ( RZERO = 0.0 ) REAL RROGUE PARAMETER ( RROGUE = -1.0E10 ) * .. Scalar Arguments .. COMPLEX TRANSL INTEGER KL, KU, LDA, M, N, NMAX LOGICAL RESET CHARACTER*1 DIAG, UPLO CHARACTER*2 TYPE * .. Array Arguments .. COMPLEX A( NMAX, * ), AA( * ) * .. Local Scalars .. INTEGER I, I1, I2, I3, IBEG, IEND, IOFF, J, JJ, KK LOGICAL GEN, LOWER, SYM, TRI, UNIT, UPPER * .. External Functions .. COMPLEX CBEG EXTERNAL CBEG * .. Intrinsic Functions .. INTRINSIC CMPLX, CONJG, MAX, MIN, REAL * .. Executable Statements .. GEN = TYPE( 1: 1 ).EQ.'G' SYM = TYPE( 1: 1 ).EQ.'H' TRI = TYPE( 1: 1 ).EQ.'T' UPPER = ( SYM.OR.TRI ).AND.UPLO.EQ.'U' LOWER = ( SYM.OR.TRI ).AND.UPLO.EQ.'L' UNIT = TRI.AND.DIAG.EQ.'U' * * Generate data in array A. * DO 20 J = 1, N DO 10 I = 1, M IF( GEN.OR.( UPPER.AND.I.LE.J ).OR.( LOWER.AND.I.GE.J ) ) $ THEN IF( ( I.LE.J.AND.J - I.LE.KU ).OR. $ ( I.GE.J.AND.I - J.LE.KL ) )THEN A( I, J ) = CBEG( RESET ) + TRANSL ELSE A( I, J ) = ZERO END IF IF( I.NE.J )THEN IF( SYM )THEN A( J, I ) = CONJG( A( I, J ) ) ELSE IF( TRI )THEN A( J, I ) = ZERO END IF END IF END IF 10 CONTINUE IF( SYM ) $ A( J, J ) = CMPLX( REAL( A( J, J ) ), RZERO ) IF( TRI ) $ A( J, J ) = A( J, J ) + ONE IF( UNIT ) $ A( J, J ) = ONE 20 CONTINUE * * Store elements in array AS in data structure required by routine. * IF( TYPE.EQ.'GE' )THEN DO 50 J = 1, N DO 30 I = 1, M AA( I + ( J - 1 )*LDA ) = A( I, J ) 30 CONTINUE DO 40 I = M + 1, LDA AA( I + ( J - 1 )*LDA ) = ROGUE 40 CONTINUE 50 CONTINUE ELSE IF( TYPE.EQ.'GB' )THEN DO 90 J = 1, N DO 60 I1 = 1, KU + 1 - J AA( I1 + ( J - 1 )*LDA ) = ROGUE 60 CONTINUE DO 70 I2 = I1, MIN( KL + KU + 1, KU + 1 + M - J ) AA( I2 + ( J - 1 )*LDA ) = A( I2 + J - KU - 1, J ) 70 CONTINUE DO 80 I3 = I2, LDA AA( I3 + ( J - 1 )*LDA ) = ROGUE 80 CONTINUE 90 CONTINUE ELSE IF( TYPE.EQ.'HE'.OR.TYPE.EQ.'TR' )THEN DO 130 J = 1, N IF( UPPER )THEN IBEG = 1 IF( UNIT )THEN IEND = J - 1 ELSE IEND = J END IF ELSE IF( UNIT )THEN IBEG = J + 1 ELSE IBEG = J END IF IEND = N END IF DO 100 I = 1, IBEG - 1 AA( I + ( J - 1 )*LDA ) = ROGUE 100 CONTINUE DO 110 I = IBEG, IEND AA( I + ( J - 1 )*LDA ) = A( I, J ) 110 CONTINUE DO 120 I = IEND + 1, LDA AA( I + ( J - 1 )*LDA ) = ROGUE 120 CONTINUE IF( SYM )THEN JJ = J + ( J - 1 )*LDA AA( JJ ) = CMPLX( REAL( AA( JJ ) ), RROGUE ) END IF 130 CONTINUE ELSE IF( TYPE.EQ.'HB'.OR.TYPE.EQ.'TB' )THEN DO 170 J = 1, N IF( UPPER )THEN KK = KL + 1 IBEG = MAX( 1, KL + 2 - J ) IF( UNIT )THEN IEND = KL ELSE IEND = KL + 1 END IF ELSE KK = 1 IF( UNIT )THEN IBEG = 2 ELSE IBEG = 1 END IF IEND = MIN( KL + 1, 1 + M - J ) END IF DO 140 I = 1, IBEG - 1 AA( I + ( J - 1 )*LDA ) = ROGUE 140 CONTINUE DO 150 I = IBEG, IEND AA( I + ( J - 1 )*LDA ) = A( I + J - KK, J ) 150 CONTINUE DO 160 I = IEND + 1, LDA AA( I + ( J - 1 )*LDA ) = ROGUE 160 CONTINUE IF( SYM )THEN JJ = KK + ( J - 1 )*LDA AA( JJ ) = CMPLX( REAL( AA( JJ ) ), RROGUE ) END IF 170 CONTINUE ELSE IF( TYPE.EQ.'HP'.OR.TYPE.EQ.'TP' )THEN IOFF = 0 DO 190 J = 1, N IF( UPPER )THEN IBEG = 1 IEND = J ELSE IBEG = J IEND = N END IF DO 180 I = IBEG, IEND IOFF = IOFF + 1 AA( IOFF ) = A( I, J ) IF( I.EQ.J )THEN IF( UNIT ) $ AA( IOFF ) = ROGUE IF( SYM ) $ AA( IOFF ) = CMPLX( REAL( AA( IOFF ) ), RROGUE ) END IF 180 CONTINUE 190 CONTINUE END IF RETURN * * End of CMAKE. * END SUBROUTINE CMVCH( TRANS, M, N, ALPHA, A, NMAX, X, INCX, BETA, Y, $ INCY, YT, G, YY, EPS, ERR, FATAL, NOUT, MV ) * * Checks the results of the computational tests. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Parameters .. COMPLEX ZERO PARAMETER ( ZERO = ( 0.0, 0.0 ) ) REAL RZERO, RONE PARAMETER ( RZERO = 0.0, RONE = 1.0 ) * .. Scalar Arguments .. COMPLEX ALPHA, BETA REAL EPS, ERR INTEGER INCX, INCY, M, N, NMAX, NOUT LOGICAL FATAL, MV CHARACTER*1 TRANS * .. Array Arguments .. COMPLEX A( NMAX, * ), X( * ), Y( * ), YT( * ), YY( * ) REAL G( * ) * .. Local Scalars .. COMPLEX C REAL ERRI INTEGER I, INCXL, INCYL, IY, J, JX, KX, KY, ML, NL LOGICAL CTRAN, TRAN * .. Intrinsic Functions .. INTRINSIC ABS, AIMAG, CONJG, MAX, REAL, SQRT * .. Statement Functions .. REAL ABS1 * .. Statement Function definitions .. ABS1( C ) = ABS( REAL( C ) ) + ABS( AIMAG( C ) ) * .. Executable Statements .. TRAN = TRANS.EQ.'T' CTRAN = TRANS.EQ.'C' IF( TRAN.OR.CTRAN )THEN ML = N NL = M ELSE ML = M NL = N END IF IF( INCX.LT.0 )THEN KX = NL INCXL = -1 ELSE KX = 1 INCXL = 1 END IF IF( INCY.LT.0 )THEN KY = ML INCYL = -1 ELSE KY = 1 INCYL = 1 END IF * * Compute expected result in YT using data in A, X and Y. * Compute gauges in G. * IY = KY DO 40 I = 1, ML YT( IY ) = ZERO G( IY ) = RZERO JX = KX IF( TRAN )THEN DO 10 J = 1, NL YT( IY ) = YT( IY ) + A( J, I )*X( JX ) G( IY ) = G( IY ) + ABS1( A( J, I ) )*ABS1( X( JX ) ) JX = JX + INCXL 10 CONTINUE ELSE IF( CTRAN )THEN DO 20 J = 1, NL YT( IY ) = YT( IY ) + CONJG( A( J, I ) )*X( JX ) G( IY ) = G( IY ) + ABS1( A( J, I ) )*ABS1( X( JX ) ) JX = JX + INCXL 20 CONTINUE ELSE DO 30 J = 1, NL YT( IY ) = YT( IY ) + A( I, J )*X( JX ) G( IY ) = G( IY ) + ABS1( A( I, J ) )*ABS1( X( JX ) ) JX = JX + INCXL 30 CONTINUE END IF YT( IY ) = ALPHA*YT( IY ) + BETA*Y( IY ) G( IY ) = ABS1( ALPHA )*G( IY ) + ABS1( BETA )*ABS1( Y( IY ) ) IY = IY + INCYL 40 CONTINUE * * Compute the error ratio for this result. * ERR = ZERO DO 50 I = 1, ML ERRI = ABS( YT( I ) - YY( 1 + ( I - 1 )*ABS( INCY ) ) )/EPS IF( G( I ).NE.RZERO ) $ ERRI = ERRI/G( I ) ERR = MAX( ERR, ERRI ) IF( ERR*SQRT( EPS ).GE.RONE ) $ GO TO 60 50 CONTINUE * If the loop completes, all results are at least half accurate. GO TO 80 * * Report fatal error. * 60 FATAL = .TRUE. WRITE( NOUT, FMT = 9999 ) DO 70 I = 1, ML IF( MV )THEN WRITE( NOUT, FMT = 9998 )I, YT( I ), $ YY( 1 + ( I - 1 )*ABS( INCY ) ) ELSE WRITE( NOUT, FMT = 9998 )I, $ YY( 1 + ( I - 1 )*ABS( INCY ) ), YT( I ) END IF 70 CONTINUE * 80 CONTINUE RETURN * 9999 FORMAT( ' ******* FATAL ERROR - COMPUTED RESULT IS LESS THAN HAL', $ 'F ACCURATE *******', /' EXPECTED RE', $ 'SULT COMPUTED RESULT' ) 9998 FORMAT( 1X, I7, 2( ' (', G15.6, ',', G15.6, ')' ) ) * * End of CMVCH. * END LOGICAL FUNCTION LCE( RI, RJ, LR ) * * Tests if two arrays are identical. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Scalar Arguments .. INTEGER LR * .. Array Arguments .. COMPLEX RI( * ), RJ( * ) * .. Local Scalars .. INTEGER I * .. Executable Statements .. DO 10 I = 1, LR IF( RI( I ).NE.RJ( I ) ) $ GO TO 20 10 CONTINUE LCE = .TRUE. GO TO 30 20 CONTINUE LCE = .FALSE. 30 RETURN * * End of LCE. * END LOGICAL FUNCTION LCERES( TYPE, UPLO, M, N, AA, AS, LDA ) * * Tests if selected elements in two arrays are equal. * * TYPE is 'GE', 'HE' or 'HP'. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Scalar Arguments .. INTEGER LDA, M, N CHARACTER*1 UPLO CHARACTER*2 TYPE * .. Array Arguments .. COMPLEX AA( LDA, * ), AS( LDA, * ) * .. Local Scalars .. INTEGER I, IBEG, IEND, J LOGICAL UPPER * .. Executable Statements .. UPPER = UPLO.EQ.'U' IF( TYPE.EQ.'GE' )THEN DO 20 J = 1, N DO 10 I = M + 1, LDA IF( AA( I, J ).NE.AS( I, J ) ) $ GO TO 70 10 CONTINUE 20 CONTINUE ELSE IF( TYPE.EQ.'HE' )THEN DO 50 J = 1, N IF( UPPER )THEN IBEG = 1 IEND = J ELSE IBEG = J IEND = N END IF DO 30 I = 1, IBEG - 1 IF( AA( I, J ).NE.AS( I, J ) ) $ GO TO 70 30 CONTINUE DO 40 I = IEND + 1, LDA IF( AA( I, J ).NE.AS( I, J ) ) $ GO TO 70 40 CONTINUE 50 CONTINUE END IF * 60 CONTINUE LCERES = .TRUE. GO TO 80 70 CONTINUE LCERES = .FALSE. 80 RETURN * * End of LCERES. * END COMPLEX FUNCTION CBEG( RESET ) * * Generates complex numbers as pairs of random numbers uniformly * distributed between -0.5 and 0.5. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Scalar Arguments .. LOGICAL RESET * .. Local Scalars .. INTEGER I, IC, J, MI, MJ * .. Save statement .. SAVE I, IC, J, MI, MJ * .. Intrinsic Functions .. INTRINSIC CMPLX * .. Executable Statements .. IF( RESET )THEN * Initialize local variables. MI = 891 MJ = 457 I = 7 J = 7 IC = 0 RESET = .FALSE. END IF * * The sequence of values of I or J is bounded between 1 and 999. * If initial I or J = 1,2,3,6,7 or 9, the period will be 50. * If initial I or J = 4 or 8, the period will be 25. * If initial I or J = 5, the period will be 10. * IC is used to break up the period by skipping 1 value of I or J * in 6. * IC = IC + 1 10 I = I*MI J = J*MJ I = I - 1000*( I/1000 ) J = J - 1000*( J/1000 ) IF( IC.GE.5 )THEN IC = 0 GO TO 10 END IF CBEG = CMPLX( ( I - 500 )/1001.0, ( J - 500 )/1001.0 ) RETURN * * End of CBEG. * END REAL FUNCTION SDIFF( X, Y ) * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * * .. Scalar Arguments .. REAL X, Y * .. Executable Statements .. SDIFF = X - Y RETURN * * End of SDIFF. * END SUBROUTINE CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) * * Tests whether XERBLA has detected an error when it should. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Scalar Arguments .. INTEGER INFOT, NOUT LOGICAL LERR, OK CHARACTER*6 SRNAMT * .. Executable Statements .. IF( .NOT.LERR )THEN WRITE( NOUT, FMT = 9999 )INFOT, SRNAMT OK = .FALSE. END IF LERR = .FALSE. RETURN * 9999 FORMAT( ' ***** ILLEGAL VALUE OF PARAMETER NUMBER ', I2, ' NOT D', $ 'ETECTED BY ', A6, ' *****' ) * * End of CHKXER. * END SUBROUTINE XERBLA( SRNAME, INFO ) * * This is a special version of XERBLA to be used only as part of * the test program for testing error exits from the Level 2 BLAS * routines. * * XERBLA is an error handler for the Level 2 BLAS routines. * * It is called by the Level 2 BLAS routines if an input parameter is * invalid. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Scalar Arguments .. INTEGER INFO CHARACTER*6 SRNAME * .. Scalars in Common .. INTEGER INFOT, NOUT LOGICAL LERR, OK CHARACTER*6 SRNAMT * .. Common blocks .. COMMON /INFOC/INFOT, NOUT, OK, LERR COMMON /SRNAMC/SRNAMT * .. Executable Statements .. LERR = .TRUE. IF( INFO.NE.INFOT )THEN IF( INFOT.NE.0 )THEN WRITE( NOUT, FMT = 9999 )INFO, INFOT ELSE WRITE( NOUT, FMT = 9997 )INFO END IF OK = .FALSE. END IF IF( SRNAME.NE.SRNAMT )THEN WRITE( NOUT, FMT = 9998 )SRNAME, SRNAMT OK = .FALSE. END IF RETURN * 9999 FORMAT( ' ******* XERBLA WAS CALLED WITH INFO = ', I6, ' INSTEAD', $ ' OF ', I2, ' *******' ) 9998 FORMAT( ' ******* XERBLA WAS CALLED WITH SRNAME = ', A6, ' INSTE', $ 'AD OF ', A6, ' *******' ) 9997 FORMAT( ' ******* XERBLA WAS CALLED WITH INFO = ', I6, $ ' *******' ) * * End of XERBLA * END PROGRAM DBLAT2 * * Test program for the DOUBLE PRECISION Level 2 Blas. * * The program must be driven by a short data file. The first 18 records * of the file are read using list-directed input, the last 16 records * are read using the format ( A6, L2 ). An annotated example of a data * file can be obtained by deleting the first 3 characters from the * following 34 lines: * 'DBLAT2.SUMM' NAME OF SUMMARY OUTPUT FILE * 6 UNIT NUMBER OF SUMMARY FILE * 'DBLAT2.SNAP' NAME OF SNAPSHOT OUTPUT FILE * -1 UNIT NUMBER OF SNAPSHOT FILE (NOT USED IF .LT. 0) * F LOGICAL FLAG, T TO REWIND SNAPSHOT FILE AFTER EACH RECORD. * F LOGICAL FLAG, T TO STOP ON FAILURES. * T LOGICAL FLAG, T TO TEST ERROR EXITS. * 16.0 THRESHOLD VALUE OF TEST RATIO * 6 NUMBER OF VALUES OF N * 0 1 2 3 5 9 VALUES OF N * 4 NUMBER OF VALUES OF K * 0 1 2 4 VALUES OF K * 4 NUMBER OF VALUES OF INCX AND INCY * 1 2 -1 -2 VALUES OF INCX AND INCY * 3 NUMBER OF VALUES OF ALPHA * 0.0 1.0 0.7 VALUES OF ALPHA * 3 NUMBER OF VALUES OF BETA * 0.0 1.0 0.9 VALUES OF BETA * DGEMV T PUT F FOR NO TEST. SAME COLUMNS. * DGBMV T PUT F FOR NO TEST. SAME COLUMNS. * DSYMV T PUT F FOR NO TEST. SAME COLUMNS. * DSBMV T PUT F FOR NO TEST. SAME COLUMNS. * DSPMV T PUT F FOR NO TEST. SAME COLUMNS. * DTRMV T PUT F FOR NO TEST. SAME COLUMNS. * DTBMV T PUT F FOR NO TEST. SAME COLUMNS. * DTPMV T PUT F FOR NO TEST. SAME COLUMNS. * DTRSV T PUT F FOR NO TEST. SAME COLUMNS. * DTBSV T PUT F FOR NO TEST. SAME COLUMNS. * DTPSV T PUT F FOR NO TEST. SAME COLUMNS. * DGER T PUT F FOR NO TEST. SAME COLUMNS. * DSYR T PUT F FOR NO TEST. SAME COLUMNS. * DSPR T PUT F FOR NO TEST. SAME COLUMNS. * DSYR2 T PUT F FOR NO TEST. SAME COLUMNS. * DSPR2 T PUT F FOR NO TEST. SAME COLUMNS. * * See: * * Dongarra J. J., Du Croz J. J., Hammarling S. and Hanson R. J.. * An extended set of Fortran Basic Linear Algebra Subprograms. * * Technical Memoranda Nos. 41 (revision 3) and 81, Mathematics * and Computer Science Division, Argonne National Laboratory, * 9700 South Cass Avenue, Argonne, Illinois 60439, US. * * Or * * NAG Technical Reports TR3/87 and TR4/87, Numerical Algorithms * Group Ltd., NAG Central Office, 256 Banbury Road, Oxford * OX2 7DE, UK, and Numerical Algorithms Group Inc., 1101 31st * Street, Suite 100, Downers Grove, Illinois 60515-1263, USA. * * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Parameters .. INTEGER NIN PARAMETER ( NIN = 5 ) INTEGER NSUBS PARAMETER ( NSUBS = 16 ) DOUBLE PRECISION ZERO, HALF, ONE PARAMETER ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0 ) INTEGER NMAX, INCMAX PARAMETER ( NMAX = 65, INCMAX = 2 ) INTEGER NINMAX, NIDMAX, NKBMAX, NALMAX, NBEMAX PARAMETER ( NINMAX = 7, NIDMAX = 9, NKBMAX = 7, $ NALMAX = 7, NBEMAX = 7 ) * .. Local Scalars .. DOUBLE PRECISION EPS, ERR, THRESH INTEGER I, ISNUM, J, N, NALF, NBET, NIDIM, NINC, NKB, $ NOUT, NTRA LOGICAL FATAL, LTESTT, REWI, SAME, SFATAL, TRACE, $ TSTERR CHARACTER*1 TRANS CHARACTER*6 SNAMET CHARACTER*32 SNAPS, SUMMRY * .. Local Arrays .. DOUBLE PRECISION A( NMAX, NMAX ), AA( NMAX*NMAX ), $ ALF( NALMAX ), AS( NMAX*NMAX ), BET( NBEMAX ), $ G( NMAX ), X( NMAX ), XS( NMAX*INCMAX ), $ XX( NMAX*INCMAX ), Y( NMAX ), $ YS( NMAX*INCMAX ), YT( NMAX ), $ YY( NMAX*INCMAX ), Z( 2*NMAX ) INTEGER IDIM( NIDMAX ), INC( NINMAX ), KB( NKBMAX ) LOGICAL LTEST( NSUBS ) CHARACTER*6 SNAMES( NSUBS ) * .. External Functions .. DOUBLE PRECISION DDIFF LOGICAL LDE EXTERNAL DDIFF, LDE * .. External Subroutines .. EXTERNAL DCHK1, DCHK2, DCHK3, DCHK4, DCHK5, DCHK6, $ DCHKE, DMVCH * .. Intrinsic Functions .. INTRINSIC ABS, MAX, MIN * .. Scalars in Common .. INTEGER INFOT, NOUTC LOGICAL LERR, OK CHARACTER*6 SRNAMT * .. Common blocks .. COMMON /INFOC/INFOT, NOUTC, OK, LERR COMMON /SRNAMC/SRNAMT * .. Data statements .. DATA SNAMES/'DGEMV ', 'DGBMV ', 'DSYMV ', 'DSBMV ', $ 'DSPMV ', 'DTRMV ', 'DTBMV ', 'DTPMV ', $ 'DTRSV ', 'DTBSV ', 'DTPSV ', 'DGER ', $ 'DSYR ', 'DSPR ', 'DSYR2 ', 'DSPR2 '/ * .. Executable Statements .. * * Read name and unit number for summary output file and open file. * READ( NIN, FMT = * )SUMMRY READ( NIN, FMT = * )NOUT OPEN( NOUT, FILE = SUMMRY, STATUS = 'NEW' ) NOUTC = NOUT * * Read name and unit number for snapshot output file and open file. * READ( NIN, FMT = * )SNAPS READ( NIN, FMT = * )NTRA TRACE = NTRA.GE.0 IF( TRACE )THEN OPEN( NTRA, FILE = SNAPS, STATUS = 'NEW' ) END IF * Read the flag that directs rewinding of the snapshot file. READ( NIN, FMT = * )REWI REWI = REWI.AND.TRACE * Read the flag that directs stopping on any failure. READ( NIN, FMT = * )SFATAL * Read the flag that indicates whether error exits are to be tested. READ( NIN, FMT = * )TSTERR * Read the threshold value of the test ratio READ( NIN, FMT = * )THRESH * * Read and check the parameter values for the tests. * * Values of N READ( NIN, FMT = * )NIDIM IF( NIDIM.LT.1.OR.NIDIM.GT.NIDMAX )THEN WRITE( NOUT, FMT = 9997 )'N', NIDMAX GO TO 230 END IF READ( NIN, FMT = * )( IDIM( I ), I = 1, NIDIM ) DO 10 I = 1, NIDIM IF( IDIM( I ).LT.0.OR.IDIM( I ).GT.NMAX )THEN WRITE( NOUT, FMT = 9996 )NMAX GO TO 230 END IF 10 CONTINUE * Values of K READ( NIN, FMT = * )NKB IF( NKB.LT.1.OR.NKB.GT.NKBMAX )THEN WRITE( NOUT, FMT = 9997 )'K', NKBMAX GO TO 230 END IF READ( NIN, FMT = * )( KB( I ), I = 1, NKB ) DO 20 I = 1, NKB IF( KB( I ).LT.0 )THEN WRITE( NOUT, FMT = 9995 ) GO TO 230 END IF 20 CONTINUE * Values of INCX and INCY READ( NIN, FMT = * )NINC IF( NINC.LT.1.OR.NINC.GT.NINMAX )THEN WRITE( NOUT, FMT = 9997 )'INCX AND INCY', NINMAX GO TO 230 END IF READ( NIN, FMT = * )( INC( I ), I = 1, NINC ) DO 30 I = 1, NINC IF( INC( I ).EQ.0.OR.ABS( INC( I ) ).GT.INCMAX )THEN WRITE( NOUT, FMT = 9994 )INCMAX GO TO 230 END IF 30 CONTINUE * Values of ALPHA READ( NIN, FMT = * )NALF IF( NALF.LT.1.OR.NALF.GT.NALMAX )THEN WRITE( NOUT, FMT = 9997 )'ALPHA', NALMAX GO TO 230 END IF READ( NIN, FMT = * )( ALF( I ), I = 1, NALF ) * Values of BETA READ( NIN, FMT = * )NBET IF( NBET.LT.1.OR.NBET.GT.NBEMAX )THEN WRITE( NOUT, FMT = 9997 )'BETA', NBEMAX GO TO 230 END IF READ( NIN, FMT = * )( BET( I ), I = 1, NBET ) * * Report values of parameters. * WRITE( NOUT, FMT = 9993 ) WRITE( NOUT, FMT = 9992 )( IDIM( I ), I = 1, NIDIM ) WRITE( NOUT, FMT = 9991 )( KB( I ), I = 1, NKB ) WRITE( NOUT, FMT = 9990 )( INC( I ), I = 1, NINC ) WRITE( NOUT, FMT = 9989 )( ALF( I ), I = 1, NALF ) WRITE( NOUT, FMT = 9988 )( BET( I ), I = 1, NBET ) IF( .NOT.TSTERR )THEN WRITE( NOUT, FMT = * ) WRITE( NOUT, FMT = 9980 ) END IF WRITE( NOUT, FMT = * ) WRITE( NOUT, FMT = 9999 )THRESH WRITE( NOUT, FMT = * ) * * Read names of subroutines and flags which indicate * whether they are to be tested. * DO 40 I = 1, NSUBS LTEST( I ) = .FALSE. 40 CONTINUE 50 READ( NIN, FMT = 9984, END = 80 )SNAMET, LTESTT DO 60 I = 1, NSUBS IF( SNAMET.EQ.SNAMES( I ) ) $ GO TO 70 60 CONTINUE WRITE( NOUT, FMT = 9986 )SNAMET STOP 70 LTEST( I ) = LTESTT GO TO 50 * 80 CONTINUE CLOSE ( NIN ) * * Compute EPS (the machine precision). * EPS = ONE 90 CONTINUE IF( DDIFF( ONE + EPS, ONE ).EQ.ZERO ) $ GO TO 100 EPS = HALF*EPS GO TO 90 100 CONTINUE EPS = EPS + EPS WRITE( NOUT, FMT = 9998 )EPS * * Check the reliability of DMVCH using exact data. * N = MIN( 32, NMAX ) DO 120 J = 1, N DO 110 I = 1, N A( I, J ) = MAX( I - J + 1, 0 ) 110 CONTINUE X( J ) = J Y( J ) = ZERO 120 CONTINUE DO 130 J = 1, N YY( J ) = J*( ( J + 1 )*J )/2 - ( ( J + 1 )*J*( J - 1 ) )/3 130 CONTINUE * YY holds the exact result. On exit from DMVCH YT holds * the result computed by DMVCH. TRANS = 'N' CALL DMVCH( TRANS, N, N, ONE, A, NMAX, X, 1, ZERO, Y, 1, YT, G, $ YY, EPS, ERR, FATAL, NOUT, .TRUE. ) SAME = LDE( YY, YT, N ) IF( .NOT.SAME.OR.ERR.NE.ZERO )THEN WRITE( NOUT, FMT = 9985 )TRANS, SAME, ERR STOP END IF TRANS = 'T' CALL DMVCH( TRANS, N, N, ONE, A, NMAX, X, -1, ZERO, Y, -1, YT, G, $ YY, EPS, ERR, FATAL, NOUT, .TRUE. ) SAME = LDE( YY, YT, N ) IF( .NOT.SAME.OR.ERR.NE.ZERO )THEN WRITE( NOUT, FMT = 9985 )TRANS, SAME, ERR STOP END IF * * Test each subroutine in turn. * DO 210 ISNUM = 1, NSUBS WRITE( NOUT, FMT = * ) IF( .NOT.LTEST( ISNUM ) )THEN * Subprogram is not to be tested. WRITE( NOUT, FMT = 9983 )SNAMES( ISNUM ) ELSE SRNAMT = SNAMES( ISNUM ) * Test error exits. IF( TSTERR )THEN CALL DCHKE( ISNUM, SNAMES( ISNUM ), NOUT ) WRITE( NOUT, FMT = * ) END IF * Test computations. INFOT = 0 OK = .TRUE. FATAL = .FALSE. GO TO ( 140, 140, 150, 150, 150, 160, 160, $ 160, 160, 160, 160, 170, 180, 180, $ 190, 190 )ISNUM * Test DGEMV, 01, and DGBMV, 02. 140 CALL DCHK1( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE, $ REWI, FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF, $ NBET, BET, NINC, INC, NMAX, INCMAX, A, AA, AS, $ X, XX, XS, Y, YY, YS, YT, G ) GO TO 200 * Test DSYMV, 03, DSBMV, 04, and DSPMV, 05. 150 CALL DCHK2( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE, $ REWI, FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF, $ NBET, BET, NINC, INC, NMAX, INCMAX, A, AA, AS, $ X, XX, XS, Y, YY, YS, YT, G ) GO TO 200 * Test DTRMV, 06, DTBMV, 07, DTPMV, 08, * DTRSV, 09, DTBSV, 10, and DTPSV, 11. 160 CALL DCHK3( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE, $ REWI, FATAL, NIDIM, IDIM, NKB, KB, NINC, INC, $ NMAX, INCMAX, A, AA, AS, Y, YY, YS, YT, G, Z ) GO TO 200 * Test DGER, 12. 170 CALL DCHK4( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE, $ REWI, FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, $ NMAX, INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, $ YT, G, Z ) GO TO 200 * Test DSYR, 13, and DSPR, 14. 180 CALL DCHK5( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE, $ REWI, FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, $ NMAX, INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, $ YT, G, Z ) GO TO 200 * Test DSYR2, 15, and DSPR2, 16. 190 CALL DCHK6( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE, $ REWI, FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, $ NMAX, INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, $ YT, G, Z ) * 200 IF( FATAL.AND.SFATAL ) $ GO TO 220 END IF 210 CONTINUE WRITE( NOUT, FMT = 9982 ) GO TO 240 * 220 CONTINUE WRITE( NOUT, FMT = 9981 ) GO TO 240 * 230 CONTINUE WRITE( NOUT, FMT = 9987 ) * 240 CONTINUE IF( TRACE ) $ CLOSE ( NTRA ) CLOSE ( NOUT ) STOP * 9999 FORMAT( ' ROUTINES PASS COMPUTATIONAL TESTS IF TEST RATIO IS LES', $ 'S THAN', F8.2 ) 9998 FORMAT( ' RELATIVE MACHINE PRECISION IS TAKEN TO BE', 1P, D9.1 ) 9997 FORMAT( ' NUMBER OF VALUES OF ', A, ' IS LESS THAN 1 OR GREATER ', $ 'THAN ', I2 ) 9996 FORMAT( ' VALUE OF N IS LESS THAN 0 OR GREATER THAN ', I2 ) 9995 FORMAT( ' VALUE OF K IS LESS THAN 0' ) 9994 FORMAT( ' ABSOLUTE VALUE OF INCX OR INCY IS 0 OR GREATER THAN ', $ I2 ) 9993 FORMAT( ' TESTS OF THE DOUBLE PRECISION LEVEL 2 BLAS', //' THE F', $ 'OLLOWING PARAMETER VALUES WILL BE USED:' ) 9992 FORMAT( ' FOR N ', 9I6 ) 9991 FORMAT( ' FOR K ', 7I6 ) 9990 FORMAT( ' FOR INCX AND INCY ', 7I6 ) 9989 FORMAT( ' FOR ALPHA ', 7F6.1 ) 9988 FORMAT( ' FOR BETA ', 7F6.1 ) 9987 FORMAT( ' AMEND DATA FILE OR INCREASE ARRAY SIZES IN PROGRAM', $ /' ******* TESTS ABANDONED *******' ) 9986 FORMAT( ' SUBPROGRAM NAME ', A6, ' NOT RECOGNIZED', /' ******* T', $ 'ESTS ABANDONED *******' ) 9985 FORMAT( ' ERROR IN DMVCH - IN-LINE DOT PRODUCTS ARE BEING EVALU', $ 'ATED WRONGLY.', /' DMVCH WAS CALLED WITH TRANS = ', A1, $ ' AND RETURNED SAME = ', L1, ' AND ERR = ', F12.3, '.', / $ ' THIS MAY BE DUE TO FAULTS IN THE ARITHMETIC OR THE COMPILER.' $ , /' ******* TESTS ABANDONED *******' ) 9984 FORMAT( A6, L2 ) 9983 FORMAT( 1X, A6, ' WAS NOT TESTED' ) 9982 FORMAT( /' END OF TESTS' ) 9981 FORMAT( /' ******* FATAL ERROR - TESTS ABANDONED *******' ) 9980 FORMAT( ' ERROR-EXITS WILL NOT BE TESTED' ) * * End of DBLAT2. * END SUBROUTINE DCHK1( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI, $ FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF, NBET, $ BET, NINC, INC, NMAX, INCMAX, A, AA, AS, X, XX, $ XS, Y, YY, YS, YT, G ) * * Tests DGEMV and DGBMV. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Parameters .. DOUBLE PRECISION ZERO, HALF PARAMETER ( ZERO = 0.0D0, HALF = 0.5D0 ) * .. Scalar Arguments .. DOUBLE PRECISION EPS, THRESH INTEGER INCMAX, NALF, NBET, NIDIM, NINC, NKB, NMAX, $ NOUT, NTRA LOGICAL FATAL, REWI, TRACE CHARACTER*6 SNAME * .. Array Arguments .. DOUBLE PRECISION A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ), $ AS( NMAX*NMAX ), BET( NBET ), G( NMAX ), $ X( NMAX ), XS( NMAX*INCMAX ), $ XX( NMAX*INCMAX ), Y( NMAX ), $ YS( NMAX*INCMAX ), YT( NMAX ), $ YY( NMAX*INCMAX ) INTEGER IDIM( NIDIM ), INC( NINC ), KB( NKB ) * .. Local Scalars .. DOUBLE PRECISION ALPHA, ALS, BETA, BLS, ERR, ERRMAX, TRANSL INTEGER I, IA, IB, IC, IKU, IM, IN, INCX, INCXS, INCY, $ INCYS, IX, IY, KL, KLS, KU, KUS, LAA, LDA, $ LDAS, LX, LY, M, ML, MS, N, NARGS, NC, ND, NK, $ NL, NS LOGICAL BANDED, FULL, NULL, RESET, SAME, TRAN CHARACTER*1 TRANS, TRANSS CHARACTER*3 ICH * .. Local Arrays .. LOGICAL ISAME( 13 ) * .. External Functions .. LOGICAL LDE, LDERES EXTERNAL LDE, LDERES * .. External Subroutines .. EXTERNAL DGBMV, DGEMV, DMAKE, DMVCH * .. Intrinsic Functions .. INTRINSIC ABS, MAX, MIN * .. Scalars in Common .. INTEGER INFOT, NOUTC LOGICAL LERR, OK * .. Common blocks .. COMMON /INFOC/INFOT, NOUTC, OK, LERR * .. Data statements .. DATA ICH/'NTC'/ * .. Executable Statements .. FULL = SNAME( 3: 3 ).EQ.'E' BANDED = SNAME( 3: 3 ).EQ.'B' * Define the number of arguments. IF( FULL )THEN NARGS = 11 ELSE IF( BANDED )THEN NARGS = 13 END IF * NC = 0 RESET = .TRUE. ERRMAX = ZERO * DO 120 IN = 1, NIDIM N = IDIM( IN ) ND = N/2 + 1 * DO 110 IM = 1, 2 IF( IM.EQ.1 ) $ M = MAX( N - ND, 0 ) IF( IM.EQ.2 ) $ M = MIN( N + ND, NMAX ) * IF( BANDED )THEN NK = NKB ELSE NK = 1 END IF DO 100 IKU = 1, NK IF( BANDED )THEN KU = KB( IKU ) KL = MAX( KU - 1, 0 ) ELSE KU = N - 1 KL = M - 1 END IF * Set LDA to 1 more than minimum value if room. IF( BANDED )THEN LDA = KL + KU + 1 ELSE LDA = M END IF IF( LDA.LT.NMAX ) $ LDA = LDA + 1 * Skip tests if not enough room. IF( LDA.GT.NMAX ) $ GO TO 100 LAA = LDA*N NULL = N.LE.0.OR.M.LE.0 * * Generate the matrix A. * TRANSL = ZERO CALL DMAKE( SNAME( 2: 3 ), ' ', ' ', M, N, A, NMAX, AA, $ LDA, KL, KU, RESET, TRANSL ) * DO 90 IC = 1, 3 TRANS = ICH( IC: IC ) TRAN = TRANS.EQ.'T'.OR.TRANS.EQ.'C' * IF( TRAN )THEN ML = N NL = M ELSE ML = M NL = N END IF * DO 80 IX = 1, NINC INCX = INC( IX ) LX = ABS( INCX )*NL * * Generate the vector X. * TRANSL = HALF CALL DMAKE( 'GE', ' ', ' ', 1, NL, X, 1, XX, $ ABS( INCX ), 0, NL - 1, RESET, TRANSL ) IF( NL.GT.1 )THEN X( NL/2 ) = ZERO XX( 1 + ABS( INCX )*( NL/2 - 1 ) ) = ZERO END IF * DO 70 IY = 1, NINC INCY = INC( IY ) LY = ABS( INCY )*ML * DO 60 IA = 1, NALF ALPHA = ALF( IA ) * DO 50 IB = 1, NBET BETA = BET( IB ) * * Generate the vector Y. * TRANSL = ZERO CALL DMAKE( 'GE', ' ', ' ', 1, ML, Y, 1, $ YY, ABS( INCY ), 0, ML - 1, $ RESET, TRANSL ) * NC = NC + 1 * * Save every datum before calling the * subroutine. * TRANSS = TRANS MS = M NS = N KLS = KL KUS = KU ALS = ALPHA DO 10 I = 1, LAA AS( I ) = AA( I ) 10 CONTINUE LDAS = LDA DO 20 I = 1, LX XS( I ) = XX( I ) 20 CONTINUE INCXS = INCX BLS = BETA DO 30 I = 1, LY YS( I ) = YY( I ) 30 CONTINUE INCYS = INCY * * Call the subroutine. * IF( FULL )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9994 )NC, SNAME, $ TRANS, M, N, ALPHA, LDA, INCX, BETA, $ INCY IF( REWI ) $ REWIND NTRA CALL DGEMV( TRANS, M, N, ALPHA, AA, $ LDA, XX, INCX, BETA, YY, $ INCY ) ELSE IF( BANDED )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9995 )NC, SNAME, $ TRANS, M, N, KL, KU, ALPHA, LDA, $ INCX, BETA, INCY IF( REWI ) $ REWIND NTRA CALL DGBMV( TRANS, M, N, KL, KU, ALPHA, $ AA, LDA, XX, INCX, BETA, $ YY, INCY ) END IF * * Check if error-exit was taken incorrectly. * IF( .NOT.OK )THEN WRITE( NOUT, FMT = 9993 ) FATAL = .TRUE. GO TO 130 END IF * * See what data changed inside subroutines. * ISAME( 1 ) = TRANS.EQ.TRANSS ISAME( 2 ) = MS.EQ.M ISAME( 3 ) = NS.EQ.N IF( FULL )THEN ISAME( 4 ) = ALS.EQ.ALPHA ISAME( 5 ) = LDE( AS, AA, LAA ) ISAME( 6 ) = LDAS.EQ.LDA ISAME( 7 ) = LDE( XS, XX, LX ) ISAME( 8 ) = INCXS.EQ.INCX ISAME( 9 ) = BLS.EQ.BETA IF( NULL )THEN ISAME( 10 ) = LDE( YS, YY, LY ) ELSE ISAME( 10 ) = LDERES( 'GE', ' ', 1, $ ML, YS, YY, $ ABS( INCY ) ) END IF ISAME( 11 ) = INCYS.EQ.INCY ELSE IF( BANDED )THEN ISAME( 4 ) = KLS.EQ.KL ISAME( 5 ) = KUS.EQ.KU ISAME( 6 ) = ALS.EQ.ALPHA ISAME( 7 ) = LDE( AS, AA, LAA ) ISAME( 8 ) = LDAS.EQ.LDA ISAME( 9 ) = LDE( XS, XX, LX ) ISAME( 10 ) = INCXS.EQ.INCX ISAME( 11 ) = BLS.EQ.BETA IF( NULL )THEN ISAME( 12 ) = LDE( YS, YY, LY ) ELSE ISAME( 12 ) = LDERES( 'GE', ' ', 1, $ ML, YS, YY, $ ABS( INCY ) ) END IF ISAME( 13 ) = INCYS.EQ.INCY END IF * * If data was incorrectly changed, report * and return. * SAME = .TRUE. DO 40 I = 1, NARGS SAME = SAME.AND.ISAME( I ) IF( .NOT.ISAME( I ) ) $ WRITE( NOUT, FMT = 9998 )I 40 CONTINUE IF( .NOT.SAME )THEN FATAL = .TRUE. GO TO 130 END IF * IF( .NOT.NULL )THEN * * Check the result. * CALL DMVCH( TRANS, M, N, ALPHA, A, $ NMAX, X, INCX, BETA, Y, $ INCY, YT, G, YY, EPS, ERR, $ FATAL, NOUT, .TRUE. ) ERRMAX = MAX( ERRMAX, ERR ) * If got really bad answer, report and * return. IF( FATAL ) $ GO TO 130 ELSE * Avoid repeating tests with M.le.0 or * N.le.0. GO TO 110 END IF * 50 CONTINUE * 60 CONTINUE * 70 CONTINUE * 80 CONTINUE * 90 CONTINUE * 100 CONTINUE * 110 CONTINUE * 120 CONTINUE * * Report result. * IF( ERRMAX.LT.THRESH )THEN WRITE( NOUT, FMT = 9999 )SNAME, NC ELSE WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX END IF GO TO 140 * 130 CONTINUE WRITE( NOUT, FMT = 9996 )SNAME IF( FULL )THEN WRITE( NOUT, FMT = 9994 )NC, SNAME, TRANS, M, N, ALPHA, LDA, $ INCX, BETA, INCY ELSE IF( BANDED )THEN WRITE( NOUT, FMT = 9995 )NC, SNAME, TRANS, M, N, KL, KU, $ ALPHA, LDA, INCX, BETA, INCY END IF * 140 CONTINUE RETURN * 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL', $ 'S)' ) 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH', $ 'ANGED INCORRECTLY *******' ) 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C', $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2, $ ' - SUSPECT *******' ) 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' ) 9995 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', 4( I3, ',' ), F4.1, $ ', A,', I3, ', X,', I2, ',', F4.1, ', Y,', I2, ') .' ) 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', 2( I3, ',' ), F4.1, $ ', A,', I3, ', X,', I2, ',', F4.1, ', Y,', I2, $ ') .' ) 9993 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *', $ '******' ) * * End of DCHK1. * END SUBROUTINE DCHK2( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI, $ FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF, NBET, $ BET, NINC, INC, NMAX, INCMAX, A, AA, AS, X, XX, $ XS, Y, YY, YS, YT, G ) * * Tests DSYMV, DSBMV and DSPMV. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Parameters .. DOUBLE PRECISION ZERO, HALF PARAMETER ( ZERO = 0.0D0, HALF = 0.5D0 ) * .. Scalar Arguments .. DOUBLE PRECISION EPS, THRESH INTEGER INCMAX, NALF, NBET, NIDIM, NINC, NKB, NMAX, $ NOUT, NTRA LOGICAL FATAL, REWI, TRACE CHARACTER*6 SNAME * .. Array Arguments .. DOUBLE PRECISION A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ), $ AS( NMAX*NMAX ), BET( NBET ), G( NMAX ), $ X( NMAX ), XS( NMAX*INCMAX ), $ XX( NMAX*INCMAX ), Y( NMAX ), $ YS( NMAX*INCMAX ), YT( NMAX ), $ YY( NMAX*INCMAX ) INTEGER IDIM( NIDIM ), INC( NINC ), KB( NKB ) * .. Local Scalars .. DOUBLE PRECISION ALPHA, ALS, BETA, BLS, ERR, ERRMAX, TRANSL INTEGER I, IA, IB, IC, IK, IN, INCX, INCXS, INCY, $ INCYS, IX, IY, K, KS, LAA, LDA, LDAS, LX, LY, $ N, NARGS, NC, NK, NS LOGICAL BANDED, FULL, NULL, PACKED, RESET, SAME CHARACTER*1 UPLO, UPLOS CHARACTER*2 ICH * .. Local Arrays .. LOGICAL ISAME( 13 ) * .. External Functions .. LOGICAL LDE, LDERES EXTERNAL LDE, LDERES * .. External Subroutines .. EXTERNAL DMAKE, DMVCH, DSBMV, DSPMV, DSYMV * .. Intrinsic Functions .. INTRINSIC ABS, MAX * .. Scalars in Common .. INTEGER INFOT, NOUTC LOGICAL LERR, OK * .. Common blocks .. COMMON /INFOC/INFOT, NOUTC, OK, LERR * .. Data statements .. DATA ICH/'UL'/ * .. Executable Statements .. FULL = SNAME( 3: 3 ).EQ.'Y' BANDED = SNAME( 3: 3 ).EQ.'B' PACKED = SNAME( 3: 3 ).EQ.'P' * Define the number of arguments. IF( FULL )THEN NARGS = 10 ELSE IF( BANDED )THEN NARGS = 11 ELSE IF( PACKED )THEN NARGS = 9 END IF * NC = 0 RESET = .TRUE. ERRMAX = ZERO * DO 110 IN = 1, NIDIM N = IDIM( IN ) * IF( BANDED )THEN NK = NKB ELSE NK = 1 END IF DO 100 IK = 1, NK IF( BANDED )THEN K = KB( IK ) ELSE K = N - 1 END IF * Set LDA to 1 more than minimum value if room. IF( BANDED )THEN LDA = K + 1 ELSE LDA = N END IF IF( LDA.LT.NMAX ) $ LDA = LDA + 1 * Skip tests if not enough room. IF( LDA.GT.NMAX ) $ GO TO 100 IF( PACKED )THEN LAA = ( N*( N + 1 ) )/2 ELSE LAA = LDA*N END IF NULL = N.LE.0 * DO 90 IC = 1, 2 UPLO = ICH( IC: IC ) * * Generate the matrix A. * TRANSL = ZERO CALL DMAKE( SNAME( 2: 3 ), UPLO, ' ', N, N, A, NMAX, AA, $ LDA, K, K, RESET, TRANSL ) * DO 80 IX = 1, NINC INCX = INC( IX ) LX = ABS( INCX )*N * * Generate the vector X. * TRANSL = HALF CALL DMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX, $ ABS( INCX ), 0, N - 1, RESET, TRANSL ) IF( N.GT.1 )THEN X( N/2 ) = ZERO XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO END IF * DO 70 IY = 1, NINC INCY = INC( IY ) LY = ABS( INCY )*N * DO 60 IA = 1, NALF ALPHA = ALF( IA ) * DO 50 IB = 1, NBET BETA = BET( IB ) * * Generate the vector Y. * TRANSL = ZERO CALL DMAKE( 'GE', ' ', ' ', 1, N, Y, 1, YY, $ ABS( INCY ), 0, N - 1, RESET, $ TRANSL ) * NC = NC + 1 * * Save every datum before calling the * subroutine. * UPLOS = UPLO NS = N KS = K ALS = ALPHA DO 10 I = 1, LAA AS( I ) = AA( I ) 10 CONTINUE LDAS = LDA DO 20 I = 1, LX XS( I ) = XX( I ) 20 CONTINUE INCXS = INCX BLS = BETA DO 30 I = 1, LY YS( I ) = YY( I ) 30 CONTINUE INCYS = INCY * * Call the subroutine. * IF( FULL )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9993 )NC, SNAME, $ UPLO, N, ALPHA, LDA, INCX, BETA, INCY IF( REWI ) $ REWIND NTRA CALL DSYMV( UPLO, N, ALPHA, AA, LDA, XX, $ INCX, BETA, YY, INCY ) ELSE IF( BANDED )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9994 )NC, SNAME, $ UPLO, N, K, ALPHA, LDA, INCX, BETA, $ INCY IF( REWI ) $ REWIND NTRA CALL DSBMV( UPLO, N, K, ALPHA, AA, LDA, $ XX, INCX, BETA, YY, INCY ) ELSE IF( PACKED )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9995 )NC, SNAME, $ UPLO, N, ALPHA, INCX, BETA, INCY IF( REWI ) $ REWIND NTRA CALL DSPMV( UPLO, N, ALPHA, AA, XX, INCX, $ BETA, YY, INCY ) END IF * * Check if error-exit was taken incorrectly. * IF( .NOT.OK )THEN WRITE( NOUT, FMT = 9992 ) FATAL = .TRUE. GO TO 120 END IF * * See what data changed inside subroutines. * ISAME( 1 ) = UPLO.EQ.UPLOS ISAME( 2 ) = NS.EQ.N IF( FULL )THEN ISAME( 3 ) = ALS.EQ.ALPHA ISAME( 4 ) = LDE( AS, AA, LAA ) ISAME( 5 ) = LDAS.EQ.LDA ISAME( 6 ) = LDE( XS, XX, LX ) ISAME( 7 ) = INCXS.EQ.INCX ISAME( 8 ) = BLS.EQ.BETA IF( NULL )THEN ISAME( 9 ) = LDE( YS, YY, LY ) ELSE ISAME( 9 ) = LDERES( 'GE', ' ', 1, N, $ YS, YY, ABS( INCY ) ) END IF ISAME( 10 ) = INCYS.EQ.INCY ELSE IF( BANDED )THEN ISAME( 3 ) = KS.EQ.K ISAME( 4 ) = ALS.EQ.ALPHA ISAME( 5 ) = LDE( AS, AA, LAA ) ISAME( 6 ) = LDAS.EQ.LDA ISAME( 7 ) = LDE( XS, XX, LX ) ISAME( 8 ) = INCXS.EQ.INCX ISAME( 9 ) = BLS.EQ.BETA IF( NULL )THEN ISAME( 10 ) = LDE( YS, YY, LY ) ELSE ISAME( 10 ) = LDERES( 'GE', ' ', 1, N, $ YS, YY, ABS( INCY ) ) END IF ISAME( 11 ) = INCYS.EQ.INCY ELSE IF( PACKED )THEN ISAME( 3 ) = ALS.EQ.ALPHA ISAME( 4 ) = LDE( AS, AA, LAA ) ISAME( 5 ) = LDE( XS, XX, LX ) ISAME( 6 ) = INCXS.EQ.INCX ISAME( 7 ) = BLS.EQ.BETA IF( NULL )THEN ISAME( 8 ) = LDE( YS, YY, LY ) ELSE ISAME( 8 ) = LDERES( 'GE', ' ', 1, N, $ YS, YY, ABS( INCY ) ) END IF ISAME( 9 ) = INCYS.EQ.INCY END IF * * If data was incorrectly changed, report and * return. * SAME = .TRUE. DO 40 I = 1, NARGS SAME = SAME.AND.ISAME( I ) IF( .NOT.ISAME( I ) ) $ WRITE( NOUT, FMT = 9998 )I 40 CONTINUE IF( .NOT.SAME )THEN FATAL = .TRUE. GO TO 120 END IF * IF( .NOT.NULL )THEN * * Check the result. * CALL DMVCH( 'N', N, N, ALPHA, A, NMAX, X, $ INCX, BETA, Y, INCY, YT, G, $ YY, EPS, ERR, FATAL, NOUT, $ .TRUE. ) ERRMAX = MAX( ERRMAX, ERR ) * If got really bad answer, report and * return. IF( FATAL ) $ GO TO 120 ELSE * Avoid repeating tests with N.le.0 GO TO 110 END IF * 50 CONTINUE * 60 CONTINUE * 70 CONTINUE * 80 CONTINUE * 90 CONTINUE * 100 CONTINUE * 110 CONTINUE * * Report result. * IF( ERRMAX.LT.THRESH )THEN WRITE( NOUT, FMT = 9999 )SNAME, NC ELSE WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX END IF GO TO 130 * 120 CONTINUE WRITE( NOUT, FMT = 9996 )SNAME IF( FULL )THEN WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, N, ALPHA, LDA, INCX, $ BETA, INCY ELSE IF( BANDED )THEN WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, N, K, ALPHA, LDA, $ INCX, BETA, INCY ELSE IF( PACKED )THEN WRITE( NOUT, FMT = 9995 )NC, SNAME, UPLO, N, ALPHA, INCX, $ BETA, INCY END IF * 130 CONTINUE RETURN * 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL', $ 'S)' ) 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH', $ 'ANGED INCORRECTLY *******' ) 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C', $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2, $ ' - SUSPECT *******' ) 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' ) 9995 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', AP', $ ', X,', I2, ',', F4.1, ', Y,', I2, ') .' ) 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', 2( I3, ',' ), F4.1, $ ', A,', I3, ', X,', I2, ',', F4.1, ', Y,', I2, $ ') .' ) 9993 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', A,', $ I3, ', X,', I2, ',', F4.1, ', Y,', I2, ') .' ) 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *', $ '******' ) * * End of DCHK2. * END SUBROUTINE DCHK3( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI, $ FATAL, NIDIM, IDIM, NKB, KB, NINC, INC, NMAX, $ INCMAX, A, AA, AS, X, XX, XS, XT, G, Z ) * * Tests DTRMV, DTBMV, DTPMV, DTRSV, DTBSV and DTPSV. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Parameters .. DOUBLE PRECISION ZERO, HALF, ONE PARAMETER ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0 ) * .. Scalar Arguments .. DOUBLE PRECISION EPS, THRESH INTEGER INCMAX, NIDIM, NINC, NKB, NMAX, NOUT, NTRA LOGICAL FATAL, REWI, TRACE CHARACTER*6 SNAME * .. Array Arguments .. DOUBLE PRECISION A( NMAX, NMAX ), AA( NMAX*NMAX ), $ AS( NMAX*NMAX ), G( NMAX ), X( NMAX ), $ XS( NMAX*INCMAX ), XT( NMAX ), $ XX( NMAX*INCMAX ), Z( NMAX ) INTEGER IDIM( NIDIM ), INC( NINC ), KB( NKB ) * .. Local Scalars .. DOUBLE PRECISION ERR, ERRMAX, TRANSL INTEGER I, ICD, ICT, ICU, IK, IN, INCX, INCXS, IX, K, $ KS, LAA, LDA, LDAS, LX, N, NARGS, NC, NK, NS LOGICAL BANDED, FULL, NULL, PACKED, RESET, SAME CHARACTER*1 DIAG, DIAGS, TRANS, TRANSS, UPLO, UPLOS CHARACTER*2 ICHD, ICHU CHARACTER*3 ICHT * .. Local Arrays .. LOGICAL ISAME( 13 ) * .. External Functions .. LOGICAL LDE, LDERES EXTERNAL LDE, LDERES * .. External Subroutines .. EXTERNAL DMAKE, DMVCH, DTBMV, DTBSV, DTPMV, DTPSV, $ DTRMV, DTRSV * .. Intrinsic Functions .. INTRINSIC ABS, MAX * .. Scalars in Common .. INTEGER INFOT, NOUTC LOGICAL LERR, OK * .. Common blocks .. COMMON /INFOC/INFOT, NOUTC, OK, LERR * .. Data statements .. DATA ICHU/'UL'/, ICHT/'NTC'/, ICHD/'UN'/ * .. Executable Statements .. FULL = SNAME( 3: 3 ).EQ.'R' BANDED = SNAME( 3: 3 ).EQ.'B' PACKED = SNAME( 3: 3 ).EQ.'P' * Define the number of arguments. IF( FULL )THEN NARGS = 8 ELSE IF( BANDED )THEN NARGS = 9 ELSE IF( PACKED )THEN NARGS = 7 END IF * NC = 0 RESET = .TRUE. ERRMAX = ZERO * Set up zero vector for DMVCH. DO 10 I = 1, NMAX Z( I ) = ZERO 10 CONTINUE * DO 110 IN = 1, NIDIM N = IDIM( IN ) * IF( BANDED )THEN NK = NKB ELSE NK = 1 END IF DO 100 IK = 1, NK IF( BANDED )THEN K = KB( IK ) ELSE K = N - 1 END IF * Set LDA to 1 more than minimum value if room. IF( BANDED )THEN LDA = K + 1 ELSE LDA = N END IF IF( LDA.LT.NMAX ) $ LDA = LDA + 1 * Skip tests if not enough room. IF( LDA.GT.NMAX ) $ GO TO 100 IF( PACKED )THEN LAA = ( N*( N + 1 ) )/2 ELSE LAA = LDA*N END IF NULL = N.LE.0 * DO 90 ICU = 1, 2 UPLO = ICHU( ICU: ICU ) * DO 80 ICT = 1, 3 TRANS = ICHT( ICT: ICT ) * DO 70 ICD = 1, 2 DIAG = ICHD( ICD: ICD ) * * Generate the matrix A. * TRANSL = ZERO CALL DMAKE( SNAME( 2: 3 ), UPLO, DIAG, N, N, A, $ NMAX, AA, LDA, K, K, RESET, TRANSL ) * DO 60 IX = 1, NINC INCX = INC( IX ) LX = ABS( INCX )*N * * Generate the vector X. * TRANSL = HALF CALL DMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX, $ ABS( INCX ), 0, N - 1, RESET, $ TRANSL ) IF( N.GT.1 )THEN X( N/2 ) = ZERO XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO END IF * NC = NC + 1 * * Save every datum before calling the subroutine. * UPLOS = UPLO TRANSS = TRANS DIAGS = DIAG NS = N KS = K DO 20 I = 1, LAA AS( I ) = AA( I ) 20 CONTINUE LDAS = LDA DO 30 I = 1, LX XS( I ) = XX( I ) 30 CONTINUE INCXS = INCX * * Call the subroutine. * IF( SNAME( 4: 5 ).EQ.'MV' )THEN IF( FULL )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9993 )NC, SNAME, $ UPLO, TRANS, DIAG, N, LDA, INCX IF( REWI ) $ REWIND NTRA CALL DTRMV( UPLO, TRANS, DIAG, N, AA, LDA, $ XX, INCX ) ELSE IF( BANDED )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9994 )NC, SNAME, $ UPLO, TRANS, DIAG, N, K, LDA, INCX IF( REWI ) $ REWIND NTRA CALL DTBMV( UPLO, TRANS, DIAG, N, K, AA, $ LDA, XX, INCX ) ELSE IF( PACKED )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9995 )NC, SNAME, $ UPLO, TRANS, DIAG, N, INCX IF( REWI ) $ REWIND NTRA CALL DTPMV( UPLO, TRANS, DIAG, N, AA, XX, $ INCX ) END IF ELSE IF( SNAME( 4: 5 ).EQ.'SV' )THEN IF( FULL )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9993 )NC, SNAME, $ UPLO, TRANS, DIAG, N, LDA, INCX IF( REWI ) $ REWIND NTRA CALL DTRSV( UPLO, TRANS, DIAG, N, AA, LDA, $ XX, INCX ) ELSE IF( BANDED )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9994 )NC, SNAME, $ UPLO, TRANS, DIAG, N, K, LDA, INCX IF( REWI ) $ REWIND NTRA CALL DTBSV( UPLO, TRANS, DIAG, N, K, AA, $ LDA, XX, INCX ) ELSE IF( PACKED )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9995 )NC, SNAME, $ UPLO, TRANS, DIAG, N, INCX IF( REWI ) $ REWIND NTRA CALL DTPSV( UPLO, TRANS, DIAG, N, AA, XX, $ INCX ) END IF END IF * * Check if error-exit was taken incorrectly. * IF( .NOT.OK )THEN WRITE( NOUT, FMT = 9992 ) FATAL = .TRUE. GO TO 120 END IF * * See what data changed inside subroutines. * ISAME( 1 ) = UPLO.EQ.UPLOS ISAME( 2 ) = TRANS.EQ.TRANSS ISAME( 3 ) = DIAG.EQ.DIAGS ISAME( 4 ) = NS.EQ.N IF( FULL )THEN ISAME( 5 ) = LDE( AS, AA, LAA ) ISAME( 6 ) = LDAS.EQ.LDA IF( NULL )THEN ISAME( 7 ) = LDE( XS, XX, LX ) ELSE ISAME( 7 ) = LDERES( 'GE', ' ', 1, N, XS, $ XX, ABS( INCX ) ) END IF ISAME( 8 ) = INCXS.EQ.INCX ELSE IF( BANDED )THEN ISAME( 5 ) = KS.EQ.K ISAME( 6 ) = LDE( AS, AA, LAA ) ISAME( 7 ) = LDAS.EQ.LDA IF( NULL )THEN ISAME( 8 ) = LDE( XS, XX, LX ) ELSE ISAME( 8 ) = LDERES( 'GE', ' ', 1, N, XS, $ XX, ABS( INCX ) ) END IF ISAME( 9 ) = INCXS.EQ.INCX ELSE IF( PACKED )THEN ISAME( 5 ) = LDE( AS, AA, LAA ) IF( NULL )THEN ISAME( 6 ) = LDE( XS, XX, LX ) ELSE ISAME( 6 ) = LDERES( 'GE', ' ', 1, N, XS, $ XX, ABS( INCX ) ) END IF ISAME( 7 ) = INCXS.EQ.INCX END IF * * If data was incorrectly changed, report and * return. * SAME = .TRUE. DO 40 I = 1, NARGS SAME = SAME.AND.ISAME( I ) IF( .NOT.ISAME( I ) ) $ WRITE( NOUT, FMT = 9998 )I 40 CONTINUE IF( .NOT.SAME )THEN FATAL = .TRUE. GO TO 120 END IF * IF( .NOT.NULL )THEN IF( SNAME( 4: 5 ).EQ.'MV' )THEN * * Check the result. * CALL DMVCH( TRANS, N, N, ONE, A, NMAX, X, $ INCX, ZERO, Z, INCX, XT, G, $ XX, EPS, ERR, FATAL, NOUT, $ .TRUE. ) ELSE IF( SNAME( 4: 5 ).EQ.'SV' )THEN * * Compute approximation to original vector. * DO 50 I = 1, N Z( I ) = XX( 1 + ( I - 1 )* $ ABS( INCX ) ) XX( 1 + ( I - 1 )*ABS( INCX ) ) $ = X( I ) 50 CONTINUE CALL DMVCH( TRANS, N, N, ONE, A, NMAX, Z, $ INCX, ZERO, X, INCX, XT, G, $ XX, EPS, ERR, FATAL, NOUT, $ .FALSE. ) END IF ERRMAX = MAX( ERRMAX, ERR ) * If got really bad answer, report and return. IF( FATAL ) $ GO TO 120 ELSE * Avoid repeating tests with N.le.0. GO TO 110 END IF * 60 CONTINUE * 70 CONTINUE * 80 CONTINUE * 90 CONTINUE * 100 CONTINUE * 110 CONTINUE * * Report result. * IF( ERRMAX.LT.THRESH )THEN WRITE( NOUT, FMT = 9999 )SNAME, NC ELSE WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX END IF GO TO 130 * 120 CONTINUE WRITE( NOUT, FMT = 9996 )SNAME IF( FULL )THEN WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, TRANS, DIAG, N, LDA, $ INCX ELSE IF( BANDED )THEN WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, TRANS, DIAG, N, K, $ LDA, INCX ELSE IF( PACKED )THEN WRITE( NOUT, FMT = 9995 )NC, SNAME, UPLO, TRANS, DIAG, N, INCX END IF * 130 CONTINUE RETURN * 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL', $ 'S)' ) 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH', $ 'ANGED INCORRECTLY *******' ) 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C', $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2, $ ' - SUSPECT *******' ) 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' ) 9995 FORMAT( 1X, I6, ': ', A6, '(', 3( '''', A1, ''',' ), I3, ', AP, ', $ 'X,', I2, ') .' ) 9994 FORMAT( 1X, I6, ': ', A6, '(', 3( '''', A1, ''',' ), 2( I3, ',' ), $ ' A,', I3, ', X,', I2, ') .' ) 9993 FORMAT( 1X, I6, ': ', A6, '(', 3( '''', A1, ''',' ), I3, ', A,', $ I3, ', X,', I2, ') .' ) 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *', $ '******' ) * * End of DCHK3. * END SUBROUTINE DCHK4( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI, $ FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, NMAX, $ INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, YT, G, $ Z ) * * Tests DGER. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Parameters .. DOUBLE PRECISION ZERO, HALF, ONE PARAMETER ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0 ) * .. Scalar Arguments .. DOUBLE PRECISION EPS, THRESH INTEGER INCMAX, NALF, NIDIM, NINC, NMAX, NOUT, NTRA LOGICAL FATAL, REWI, TRACE CHARACTER*6 SNAME * .. Array Arguments .. DOUBLE PRECISION A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ), $ AS( NMAX*NMAX ), G( NMAX ), X( NMAX ), $ XS( NMAX*INCMAX ), XX( NMAX*INCMAX ), $ Y( NMAX ), YS( NMAX*INCMAX ), YT( NMAX ), $ YY( NMAX*INCMAX ), Z( NMAX ) INTEGER IDIM( NIDIM ), INC( NINC ) * .. Local Scalars .. DOUBLE PRECISION ALPHA, ALS, ERR, ERRMAX, TRANSL INTEGER I, IA, IM, IN, INCX, INCXS, INCY, INCYS, IX, $ IY, J, LAA, LDA, LDAS, LX, LY, M, MS, N, NARGS, $ NC, ND, NS LOGICAL NULL, RESET, SAME * .. Local Arrays .. DOUBLE PRECISION W( 1 ) LOGICAL ISAME( 13 ) * .. External Functions .. LOGICAL LDE, LDERES EXTERNAL LDE, LDERES * .. External Subroutines .. EXTERNAL DGER, DMAKE, DMVCH * .. Intrinsic Functions .. INTRINSIC ABS, MAX, MIN * .. Scalars in Common .. INTEGER INFOT, NOUTC LOGICAL LERR, OK * .. Common blocks .. COMMON /INFOC/INFOT, NOUTC, OK, LERR * .. Executable Statements .. * Define the number of arguments. NARGS = 9 * NC = 0 RESET = .TRUE. ERRMAX = ZERO * DO 120 IN = 1, NIDIM N = IDIM( IN ) ND = N/2 + 1 * DO 110 IM = 1, 2 IF( IM.EQ.1 ) $ M = MAX( N - ND, 0 ) IF( IM.EQ.2 ) $ M = MIN( N + ND, NMAX ) * * Set LDA to 1 more than minimum value if room. LDA = M IF( LDA.LT.NMAX ) $ LDA = LDA + 1 * Skip tests if not enough room. IF( LDA.GT.NMAX ) $ GO TO 110 LAA = LDA*N NULL = N.LE.0.OR.M.LE.0 * DO 100 IX = 1, NINC INCX = INC( IX ) LX = ABS( INCX )*M * * Generate the vector X. * TRANSL = HALF CALL DMAKE( 'GE', ' ', ' ', 1, M, X, 1, XX, ABS( INCX ), $ 0, M - 1, RESET, TRANSL ) IF( M.GT.1 )THEN X( M/2 ) = ZERO XX( 1 + ABS( INCX )*( M/2 - 1 ) ) = ZERO END IF * DO 90 IY = 1, NINC INCY = INC( IY ) LY = ABS( INCY )*N * * Generate the vector Y. * TRANSL = ZERO CALL DMAKE( 'GE', ' ', ' ', 1, N, Y, 1, YY, $ ABS( INCY ), 0, N - 1, RESET, TRANSL ) IF( N.GT.1 )THEN Y( N/2 ) = ZERO YY( 1 + ABS( INCY )*( N/2 - 1 ) ) = ZERO END IF * DO 80 IA = 1, NALF ALPHA = ALF( IA ) * * Generate the matrix A. * TRANSL = ZERO CALL DMAKE( SNAME( 2: 3 ), ' ', ' ', M, N, A, NMAX, $ AA, LDA, M - 1, N - 1, RESET, TRANSL ) * NC = NC + 1 * * Save every datum before calling the subroutine. * MS = M NS = N ALS = ALPHA DO 10 I = 1, LAA AS( I ) = AA( I ) 10 CONTINUE LDAS = LDA DO 20 I = 1, LX XS( I ) = XX( I ) 20 CONTINUE INCXS = INCX DO 30 I = 1, LY YS( I ) = YY( I ) 30 CONTINUE INCYS = INCY * * Call the subroutine. * IF( TRACE ) $ WRITE( NTRA, FMT = 9994 )NC, SNAME, M, N, $ ALPHA, INCX, INCY, LDA IF( REWI ) $ REWIND NTRA CALL DGER( M, N, ALPHA, XX, INCX, YY, INCY, AA, $ LDA ) * * Check if error-exit was taken incorrectly. * IF( .NOT.OK )THEN WRITE( NOUT, FMT = 9993 ) FATAL = .TRUE. GO TO 140 END IF * * See what data changed inside subroutine. * ISAME( 1 ) = MS.EQ.M ISAME( 2 ) = NS.EQ.N ISAME( 3 ) = ALS.EQ.ALPHA ISAME( 4 ) = LDE( XS, XX, LX ) ISAME( 5 ) = INCXS.EQ.INCX ISAME( 6 ) = LDE( YS, YY, LY ) ISAME( 7 ) = INCYS.EQ.INCY IF( NULL )THEN ISAME( 8 ) = LDE( AS, AA, LAA ) ELSE ISAME( 8 ) = LDERES( 'GE', ' ', M, N, AS, AA, $ LDA ) END IF ISAME( 9 ) = LDAS.EQ.LDA * * If data was incorrectly changed, report and return. * SAME = .TRUE. DO 40 I = 1, NARGS SAME = SAME.AND.ISAME( I ) IF( .NOT.ISAME( I ) ) $ WRITE( NOUT, FMT = 9998 )I 40 CONTINUE IF( .NOT.SAME )THEN FATAL = .TRUE. GO TO 140 END IF * IF( .NOT.NULL )THEN * * Check the result column by column. * IF( INCX.GT.0 )THEN DO 50 I = 1, M Z( I ) = X( I ) 50 CONTINUE ELSE DO 60 I = 1, M Z( I ) = X( M - I + 1 ) 60 CONTINUE END IF DO 70 J = 1, N IF( INCY.GT.0 )THEN W( 1 ) = Y( J ) ELSE W( 1 ) = Y( N - J + 1 ) END IF CALL DMVCH( 'N', M, 1, ALPHA, Z, NMAX, W, 1, $ ONE, A( 1, J ), 1, YT, G, $ AA( 1 + ( J - 1 )*LDA ), EPS, $ ERR, FATAL, NOUT, .TRUE. ) ERRMAX = MAX( ERRMAX, ERR ) * If got really bad answer, report and return. IF( FATAL ) $ GO TO 130 70 CONTINUE ELSE * Avoid repeating tests with M.le.0 or N.le.0. GO TO 110 END IF * 80 CONTINUE * 90 CONTINUE * 100 CONTINUE * 110 CONTINUE * 120 CONTINUE * * Report result. * IF( ERRMAX.LT.THRESH )THEN WRITE( NOUT, FMT = 9999 )SNAME, NC ELSE WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX END IF GO TO 150 * 130 CONTINUE WRITE( NOUT, FMT = 9995 )J * 140 CONTINUE WRITE( NOUT, FMT = 9996 )SNAME WRITE( NOUT, FMT = 9994 )NC, SNAME, M, N, ALPHA, INCX, INCY, LDA * 150 CONTINUE RETURN * 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL', $ 'S)' ) 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH', $ 'ANGED INCORRECTLY *******' ) 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C', $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2, $ ' - SUSPECT *******' ) 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' ) 9995 FORMAT( ' THESE ARE THE RESULTS FOR COLUMN ', I3 ) 9994 FORMAT( 1X, I6, ': ', A6, '(', 2( I3, ',' ), F4.1, ', X,', I2, $ ', Y,', I2, ', A,', I3, ') .' ) 9993 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *', $ '******' ) * * End of DCHK4. * END SUBROUTINE DCHK5( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI, $ FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, NMAX, $ INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, YT, G, $ Z ) * * Tests DSYR and DSPR. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Parameters .. DOUBLE PRECISION ZERO, HALF, ONE PARAMETER ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0 ) * .. Scalar Arguments .. DOUBLE PRECISION EPS, THRESH INTEGER INCMAX, NALF, NIDIM, NINC, NMAX, NOUT, NTRA LOGICAL FATAL, REWI, TRACE CHARACTER*6 SNAME * .. Array Arguments .. DOUBLE PRECISION A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ), $ AS( NMAX*NMAX ), G( NMAX ), X( NMAX ), $ XS( NMAX*INCMAX ), XX( NMAX*INCMAX ), $ Y( NMAX ), YS( NMAX*INCMAX ), YT( NMAX ), $ YY( NMAX*INCMAX ), Z( NMAX ) INTEGER IDIM( NIDIM ), INC( NINC ) * .. Local Scalars .. DOUBLE PRECISION ALPHA, ALS, ERR, ERRMAX, TRANSL INTEGER I, IA, IC, IN, INCX, INCXS, IX, J, JA, JJ, LAA, $ LDA, LDAS, LJ, LX, N, NARGS, NC, NS LOGICAL FULL, NULL, PACKED, RESET, SAME, UPPER CHARACTER*1 UPLO, UPLOS CHARACTER*2 ICH * .. Local Arrays .. DOUBLE PRECISION W( 1 ) LOGICAL ISAME( 13 ) * .. External Functions .. LOGICAL LDE, LDERES EXTERNAL LDE, LDERES * .. External Subroutines .. EXTERNAL DMAKE, DMVCH, DSPR, DSYR * .. Intrinsic Functions .. INTRINSIC ABS, MAX * .. Scalars in Common .. INTEGER INFOT, NOUTC LOGICAL LERR, OK * .. Common blocks .. COMMON /INFOC/INFOT, NOUTC, OK, LERR * .. Data statements .. DATA ICH/'UL'/ * .. Executable Statements .. FULL = SNAME( 3: 3 ).EQ.'Y' PACKED = SNAME( 3: 3 ).EQ.'P' * Define the number of arguments. IF( FULL )THEN NARGS = 7 ELSE IF( PACKED )THEN NARGS = 6 END IF * NC = 0 RESET = .TRUE. ERRMAX = ZERO * DO 100 IN = 1, NIDIM N = IDIM( IN ) * Set LDA to 1 more than minimum value if room. LDA = N IF( LDA.LT.NMAX ) $ LDA = LDA + 1 * Skip tests if not enough room. IF( LDA.GT.NMAX ) $ GO TO 100 IF( PACKED )THEN LAA = ( N*( N + 1 ) )/2 ELSE LAA = LDA*N END IF * DO 90 IC = 1, 2 UPLO = ICH( IC: IC ) UPPER = UPLO.EQ.'U' * DO 80 IX = 1, NINC INCX = INC( IX ) LX = ABS( INCX )*N * * Generate the vector X. * TRANSL = HALF CALL DMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX, ABS( INCX ), $ 0, N - 1, RESET, TRANSL ) IF( N.GT.1 )THEN X( N/2 ) = ZERO XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO END IF * DO 70 IA = 1, NALF ALPHA = ALF( IA ) NULL = N.LE.0.OR.ALPHA.EQ.ZERO * * Generate the matrix A. * TRANSL = ZERO CALL DMAKE( SNAME( 2: 3 ), UPLO, ' ', N, N, A, NMAX, $ AA, LDA, N - 1, N - 1, RESET, TRANSL ) * NC = NC + 1 * * Save every datum before calling the subroutine. * UPLOS = UPLO NS = N ALS = ALPHA DO 10 I = 1, LAA AS( I ) = AA( I ) 10 CONTINUE LDAS = LDA DO 20 I = 1, LX XS( I ) = XX( I ) 20 CONTINUE INCXS = INCX * * Call the subroutine. * IF( FULL )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9993 )NC, SNAME, UPLO, N, $ ALPHA, INCX, LDA IF( REWI ) $ REWIND NTRA CALL DSYR( UPLO, N, ALPHA, XX, INCX, AA, LDA ) ELSE IF( PACKED )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9994 )NC, SNAME, UPLO, N, $ ALPHA, INCX IF( REWI ) $ REWIND NTRA CALL DSPR( UPLO, N, ALPHA, XX, INCX, AA ) END IF * * Check if error-exit was taken incorrectly. * IF( .NOT.OK )THEN WRITE( NOUT, FMT = 9992 ) FATAL = .TRUE. GO TO 120 END IF * * See what data changed inside subroutines. * ISAME( 1 ) = UPLO.EQ.UPLOS ISAME( 2 ) = NS.EQ.N ISAME( 3 ) = ALS.EQ.ALPHA ISAME( 4 ) = LDE( XS, XX, LX ) ISAME( 5 ) = INCXS.EQ.INCX IF( NULL )THEN ISAME( 6 ) = LDE( AS, AA, LAA ) ELSE ISAME( 6 ) = LDERES( SNAME( 2: 3 ), UPLO, N, N, AS, $ AA, LDA ) END IF IF( .NOT.PACKED )THEN ISAME( 7 ) = LDAS.EQ.LDA END IF * * If data was incorrectly changed, report and return. * SAME = .TRUE. DO 30 I = 1, NARGS SAME = SAME.AND.ISAME( I ) IF( .NOT.ISAME( I ) ) $ WRITE( NOUT, FMT = 9998 )I 30 CONTINUE IF( .NOT.SAME )THEN FATAL = .TRUE. GO TO 120 END IF * IF( .NOT.NULL )THEN * * Check the result column by column. * IF( INCX.GT.0 )THEN DO 40 I = 1, N Z( I ) = X( I ) 40 CONTINUE ELSE DO 50 I = 1, N Z( I ) = X( N - I + 1 ) 50 CONTINUE END IF JA = 1 DO 60 J = 1, N W( 1 ) = Z( J ) IF( UPPER )THEN JJ = 1 LJ = J ELSE JJ = J LJ = N - J + 1 END IF CALL DMVCH( 'N', LJ, 1, ALPHA, Z( JJ ), LJ, W, $ 1, ONE, A( JJ, J ), 1, YT, G, $ AA( JA ), EPS, ERR, FATAL, NOUT, $ .TRUE. ) IF( FULL )THEN IF( UPPER )THEN JA = JA + LDA ELSE JA = JA + LDA + 1 END IF ELSE JA = JA + LJ END IF ERRMAX = MAX( ERRMAX, ERR ) * If got really bad answer, report and return. IF( FATAL ) $ GO TO 110 60 CONTINUE ELSE * Avoid repeating tests if N.le.0. IF( N.LE.0 ) $ GO TO 100 END IF * 70 CONTINUE * 80 CONTINUE * 90 CONTINUE * 100 CONTINUE * * Report result. * IF( ERRMAX.LT.THRESH )THEN WRITE( NOUT, FMT = 9999 )SNAME, NC ELSE WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX END IF GO TO 130 * 110 CONTINUE WRITE( NOUT, FMT = 9995 )J * 120 CONTINUE WRITE( NOUT, FMT = 9996 )SNAME IF( FULL )THEN WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, N, ALPHA, INCX, LDA ELSE IF( PACKED )THEN WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, N, ALPHA, INCX END IF * 130 CONTINUE RETURN * 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL', $ 'S)' ) 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH', $ 'ANGED INCORRECTLY *******' ) 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C', $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2, $ ' - SUSPECT *******' ) 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' ) 9995 FORMAT( ' THESE ARE THE RESULTS FOR COLUMN ', I3 ) 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', X,', $ I2, ', AP) .' ) 9993 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', X,', $ I2, ', A,', I3, ') .' ) 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *', $ '******' ) * * End of DCHK5. * END SUBROUTINE DCHK6( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI, $ FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, NMAX, $ INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, YT, G, $ Z ) * * Tests DSYR2 and DSPR2. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Parameters .. DOUBLE PRECISION ZERO, HALF, ONE PARAMETER ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0 ) * .. Scalar Arguments .. DOUBLE PRECISION EPS, THRESH INTEGER INCMAX, NALF, NIDIM, NINC, NMAX, NOUT, NTRA LOGICAL FATAL, REWI, TRACE CHARACTER*6 SNAME * .. Array Arguments .. DOUBLE PRECISION A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ), $ AS( NMAX*NMAX ), G( NMAX ), X( NMAX ), $ XS( NMAX*INCMAX ), XX( NMAX*INCMAX ), $ Y( NMAX ), YS( NMAX*INCMAX ), YT( NMAX ), $ YY( NMAX*INCMAX ), Z( NMAX, 2 ) INTEGER IDIM( NIDIM ), INC( NINC ) * .. Local Scalars .. DOUBLE PRECISION ALPHA, ALS, ERR, ERRMAX, TRANSL INTEGER I, IA, IC, IN, INCX, INCXS, INCY, INCYS, IX, $ IY, J, JA, JJ, LAA, LDA, LDAS, LJ, LX, LY, N, $ NARGS, NC, NS LOGICAL FULL, NULL, PACKED, RESET, SAME, UPPER CHARACTER*1 UPLO, UPLOS CHARACTER*2 ICH * .. Local Arrays .. DOUBLE PRECISION W( 2 ) LOGICAL ISAME( 13 ) * .. External Functions .. LOGICAL LDE, LDERES EXTERNAL LDE, LDERES * .. External Subroutines .. EXTERNAL DMAKE, DMVCH, DSPR2, DSYR2 * .. Intrinsic Functions .. INTRINSIC ABS, MAX * .. Scalars in Common .. INTEGER INFOT, NOUTC LOGICAL LERR, OK * .. Common blocks .. COMMON /INFOC/INFOT, NOUTC, OK, LERR * .. Data statements .. DATA ICH/'UL'/ * .. Executable Statements .. FULL = SNAME( 3: 3 ).EQ.'Y' PACKED = SNAME( 3: 3 ).EQ.'P' * Define the number of arguments. IF( FULL )THEN NARGS = 9 ELSE IF( PACKED )THEN NARGS = 8 END IF * NC = 0 RESET = .TRUE. ERRMAX = ZERO * DO 140 IN = 1, NIDIM N = IDIM( IN ) * Set LDA to 1 more than minimum value if room. LDA = N IF( LDA.LT.NMAX ) $ LDA = LDA + 1 * Skip tests if not enough room. IF( LDA.GT.NMAX ) $ GO TO 140 IF( PACKED )THEN LAA = ( N*( N + 1 ) )/2 ELSE LAA = LDA*N END IF * DO 130 IC = 1, 2 UPLO = ICH( IC: IC ) UPPER = UPLO.EQ.'U' * DO 120 IX = 1, NINC INCX = INC( IX ) LX = ABS( INCX )*N * * Generate the vector X. * TRANSL = HALF CALL DMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX, ABS( INCX ), $ 0, N - 1, RESET, TRANSL ) IF( N.GT.1 )THEN X( N/2 ) = ZERO XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO END IF * DO 110 IY = 1, NINC INCY = INC( IY ) LY = ABS( INCY )*N * * Generate the vector Y. * TRANSL = ZERO CALL DMAKE( 'GE', ' ', ' ', 1, N, Y, 1, YY, $ ABS( INCY ), 0, N - 1, RESET, TRANSL ) IF( N.GT.1 )THEN Y( N/2 ) = ZERO YY( 1 + ABS( INCY )*( N/2 - 1 ) ) = ZERO END IF * DO 100 IA = 1, NALF ALPHA = ALF( IA ) NULL = N.LE.0.OR.ALPHA.EQ.ZERO * * Generate the matrix A. * TRANSL = ZERO CALL DMAKE( SNAME( 2: 3 ), UPLO, ' ', N, N, A, $ NMAX, AA, LDA, N - 1, N - 1, RESET, $ TRANSL ) * NC = NC + 1 * * Save every datum before calling the subroutine. * UPLOS = UPLO NS = N ALS = ALPHA DO 10 I = 1, LAA AS( I ) = AA( I ) 10 CONTINUE LDAS = LDA DO 20 I = 1, LX XS( I ) = XX( I ) 20 CONTINUE INCXS = INCX DO 30 I = 1, LY YS( I ) = YY( I ) 30 CONTINUE INCYS = INCY * * Call the subroutine. * IF( FULL )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9993 )NC, SNAME, UPLO, N, $ ALPHA, INCX, INCY, LDA IF( REWI ) $ REWIND NTRA CALL DSYR2( UPLO, N, ALPHA, XX, INCX, YY, INCY, $ AA, LDA ) ELSE IF( PACKED )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9994 )NC, SNAME, UPLO, N, $ ALPHA, INCX, INCY IF( REWI ) $ REWIND NTRA CALL DSPR2( UPLO, N, ALPHA, XX, INCX, YY, INCY, $ AA ) END IF * * Check if error-exit was taken incorrectly. * IF( .NOT.OK )THEN WRITE( NOUT, FMT = 9992 ) FATAL = .TRUE. GO TO 160 END IF * * See what data changed inside subroutines. * ISAME( 1 ) = UPLO.EQ.UPLOS ISAME( 2 ) = NS.EQ.N ISAME( 3 ) = ALS.EQ.ALPHA ISAME( 4 ) = LDE( XS, XX, LX ) ISAME( 5 ) = INCXS.EQ.INCX ISAME( 6 ) = LDE( YS, YY, LY ) ISAME( 7 ) = INCYS.EQ.INCY IF( NULL )THEN ISAME( 8 ) = LDE( AS, AA, LAA ) ELSE ISAME( 8 ) = LDERES( SNAME( 2: 3 ), UPLO, N, N, $ AS, AA, LDA ) END IF IF( .NOT.PACKED )THEN ISAME( 9 ) = LDAS.EQ.LDA END IF * * If data was incorrectly changed, report and return. * SAME = .TRUE. DO 40 I = 1, NARGS SAME = SAME.AND.ISAME( I ) IF( .NOT.ISAME( I ) ) $ WRITE( NOUT, FMT = 9998 )I 40 CONTINUE IF( .NOT.SAME )THEN FATAL = .TRUE. GO TO 160 END IF * IF( .NOT.NULL )THEN * * Check the result column by column. * IF( INCX.GT.0 )THEN DO 50 I = 1, N Z( I, 1 ) = X( I ) 50 CONTINUE ELSE DO 60 I = 1, N Z( I, 1 ) = X( N - I + 1 ) 60 CONTINUE END IF IF( INCY.GT.0 )THEN DO 70 I = 1, N Z( I, 2 ) = Y( I ) 70 CONTINUE ELSE DO 80 I = 1, N Z( I, 2 ) = Y( N - I + 1 ) 80 CONTINUE END IF JA = 1 DO 90 J = 1, N W( 1 ) = Z( J, 2 ) W( 2 ) = Z( J, 1 ) IF( UPPER )THEN JJ = 1 LJ = J ELSE JJ = J LJ = N - J + 1 END IF CALL DMVCH( 'N', LJ, 2, ALPHA, Z( JJ, 1 ), $ NMAX, W, 1, ONE, A( JJ, J ), 1, $ YT, G, AA( JA ), EPS, ERR, FATAL, $ NOUT, .TRUE. ) IF( FULL )THEN IF( UPPER )THEN JA = JA + LDA ELSE JA = JA + LDA + 1 END IF ELSE JA = JA + LJ END IF ERRMAX = MAX( ERRMAX, ERR ) * If got really bad answer, report and return. IF( FATAL ) $ GO TO 150 90 CONTINUE ELSE * Avoid repeating tests with N.le.0. IF( N.LE.0 ) $ GO TO 140 END IF * 100 CONTINUE * 110 CONTINUE * 120 CONTINUE * 130 CONTINUE * 140 CONTINUE * * Report result. * IF( ERRMAX.LT.THRESH )THEN WRITE( NOUT, FMT = 9999 )SNAME, NC ELSE WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX END IF GO TO 170 * 150 CONTINUE WRITE( NOUT, FMT = 9995 )J * 160 CONTINUE WRITE( NOUT, FMT = 9996 )SNAME IF( FULL )THEN WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, N, ALPHA, INCX, $ INCY, LDA ELSE IF( PACKED )THEN WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, N, ALPHA, INCX, INCY END IF * 170 CONTINUE RETURN * 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL', $ 'S)' ) 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH', $ 'ANGED INCORRECTLY *******' ) 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C', $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2, $ ' - SUSPECT *******' ) 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' ) 9995 FORMAT( ' THESE ARE THE RESULTS FOR COLUMN ', I3 ) 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', X,', $ I2, ', Y,', I2, ', AP) .' ) 9993 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', X,', $ I2, ', Y,', I2, ', A,', I3, ') .' ) 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *', $ '******' ) * * End of DCHK6. * END SUBROUTINE DCHKE( ISNUM, SRNAMT, NOUT ) * * Tests the error exits from the Level 2 Blas. * Requires a special version of the error-handling routine XERBLA. * ALPHA, BETA, A, X and Y should not need to be defined. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Scalar Arguments .. INTEGER ISNUM, NOUT CHARACTER*6 SRNAMT * .. Scalars in Common .. INTEGER INFOT, NOUTC LOGICAL LERR, OK * .. Local Scalars .. DOUBLE PRECISION ALPHA, BETA * .. Local Arrays .. DOUBLE PRECISION A( 1, 1 ), X( 1 ), Y( 1 ) * .. External Subroutines .. EXTERNAL CHKXER, DGBMV, DGEMV, DGER, DSBMV, DSPMV, DSPR, $ DSPR2, DSYMV, DSYR, DSYR2, DTBMV, DTBSV, DTPMV, $ DTPSV, DTRMV, DTRSV * .. Common blocks .. COMMON /INFOC/INFOT, NOUTC, OK, LERR * .. Executable Statements .. * OK is set to .FALSE. by the special version of XERBLA or by CHKXER * if anything is wrong. OK = .TRUE. * LERR is set to .TRUE. by the special version of XERBLA each time * it is called, and is then tested and re-set by CHKXER. LERR = .FALSE. GO TO ( 10, 20, 30, 40, 50, 60, 70, 80, $ 90, 100, 110, 120, 130, 140, 150, $ 160 )ISNUM 10 INFOT = 1 CALL DGEMV( '/', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL DGEMV( 'N', -1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 3 CALL DGEMV( 'N', 0, -1, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 6 CALL DGEMV( 'N', 2, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 8 CALL DGEMV( 'N', 0, 0, ALPHA, A, 1, X, 0, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 11 CALL DGEMV( 'N', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 0 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 170 20 INFOT = 1 CALL DGBMV( '/', 0, 0, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL DGBMV( 'N', -1, 0, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 3 CALL DGBMV( 'N', 0, -1, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 4 CALL DGBMV( 'N', 0, 0, -1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 5 CALL DGBMV( 'N', 2, 0, 0, -1, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 8 CALL DGBMV( 'N', 0, 0, 1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 10 CALL DGBMV( 'N', 0, 0, 0, 0, ALPHA, A, 1, X, 0, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 13 CALL DGBMV( 'N', 0, 0, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 0 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 170 30 INFOT = 1 CALL DSYMV( '/', 0, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL DSYMV( 'U', -1, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 5 CALL DSYMV( 'U', 2, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 7 CALL DSYMV( 'U', 0, ALPHA, A, 1, X, 0, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 10 CALL DSYMV( 'U', 0, ALPHA, A, 1, X, 1, BETA, Y, 0 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 170 40 INFOT = 1 CALL DSBMV( '/', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL DSBMV( 'U', -1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 3 CALL DSBMV( 'U', 0, -1, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 6 CALL DSBMV( 'U', 0, 1, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 8 CALL DSBMV( 'U', 0, 0, ALPHA, A, 1, X, 0, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 11 CALL DSBMV( 'U', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 0 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 170 50 INFOT = 1 CALL DSPMV( '/', 0, ALPHA, A, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL DSPMV( 'U', -1, ALPHA, A, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 6 CALL DSPMV( 'U', 0, ALPHA, A, X, 0, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 9 CALL DSPMV( 'U', 0, ALPHA, A, X, 1, BETA, Y, 0 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 170 60 INFOT = 1 CALL DTRMV( '/', 'N', 'N', 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL DTRMV( 'U', '/', 'N', 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 3 CALL DTRMV( 'U', 'N', '/', 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 4 CALL DTRMV( 'U', 'N', 'N', -1, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 6 CALL DTRMV( 'U', 'N', 'N', 2, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 8 CALL DTRMV( 'U', 'N', 'N', 0, A, 1, X, 0 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 170 70 INFOT = 1 CALL DTBMV( '/', 'N', 'N', 0, 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL DTBMV( 'U', '/', 'N', 0, 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 3 CALL DTBMV( 'U', 'N', '/', 0, 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 4 CALL DTBMV( 'U', 'N', 'N', -1, 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 5 CALL DTBMV( 'U', 'N', 'N', 0, -1, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 7 CALL DTBMV( 'U', 'N', 'N', 0, 1, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 9 CALL DTBMV( 'U', 'N', 'N', 0, 0, A, 1, X, 0 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 170 80 INFOT = 1 CALL DTPMV( '/', 'N', 'N', 0, A, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL DTPMV( 'U', '/', 'N', 0, A, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 3 CALL DTPMV( 'U', 'N', '/', 0, A, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 4 CALL DTPMV( 'U', 'N', 'N', -1, A, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 7 CALL DTPMV( 'U', 'N', 'N', 0, A, X, 0 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 170 90 INFOT = 1 CALL DTRSV( '/', 'N', 'N', 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL DTRSV( 'U', '/', 'N', 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 3 CALL DTRSV( 'U', 'N', '/', 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 4 CALL DTRSV( 'U', 'N', 'N', -1, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 6 CALL DTRSV( 'U', 'N', 'N', 2, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 8 CALL DTRSV( 'U', 'N', 'N', 0, A, 1, X, 0 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 170 100 INFOT = 1 CALL DTBSV( '/', 'N', 'N', 0, 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL DTBSV( 'U', '/', 'N', 0, 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 3 CALL DTBSV( 'U', 'N', '/', 0, 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 4 CALL DTBSV( 'U', 'N', 'N', -1, 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 5 CALL DTBSV( 'U', 'N', 'N', 0, -1, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 7 CALL DTBSV( 'U', 'N', 'N', 0, 1, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 9 CALL DTBSV( 'U', 'N', 'N', 0, 0, A, 1, X, 0 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 170 110 INFOT = 1 CALL DTPSV( '/', 'N', 'N', 0, A, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL DTPSV( 'U', '/', 'N', 0, A, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 3 CALL DTPSV( 'U', 'N', '/', 0, A, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 4 CALL DTPSV( 'U', 'N', 'N', -1, A, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 7 CALL DTPSV( 'U', 'N', 'N', 0, A, X, 0 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 170 120 INFOT = 1 CALL DGER( -1, 0, ALPHA, X, 1, Y, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL DGER( 0, -1, ALPHA, X, 1, Y, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 5 CALL DGER( 0, 0, ALPHA, X, 0, Y, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 7 CALL DGER( 0, 0, ALPHA, X, 1, Y, 0, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 9 CALL DGER( 2, 0, ALPHA, X, 1, Y, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 170 130 INFOT = 1 CALL DSYR( '/', 0, ALPHA, X, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL DSYR( 'U', -1, ALPHA, X, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 5 CALL DSYR( 'U', 0, ALPHA, X, 0, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 7 CALL DSYR( 'U', 2, ALPHA, X, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 170 140 INFOT = 1 CALL DSPR( '/', 0, ALPHA, X, 1, A ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL DSPR( 'U', -1, ALPHA, X, 1, A ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 5 CALL DSPR( 'U', 0, ALPHA, X, 0, A ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 170 150 INFOT = 1 CALL DSYR2( '/', 0, ALPHA, X, 1, Y, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL DSYR2( 'U', -1, ALPHA, X, 1, Y, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 5 CALL DSYR2( 'U', 0, ALPHA, X, 0, Y, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 7 CALL DSYR2( 'U', 0, ALPHA, X, 1, Y, 0, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 9 CALL DSYR2( 'U', 2, ALPHA, X, 1, Y, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 170 160 INFOT = 1 CALL DSPR2( '/', 0, ALPHA, X, 1, Y, 1, A ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL DSPR2( 'U', -1, ALPHA, X, 1, Y, 1, A ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 5 CALL DSPR2( 'U', 0, ALPHA, X, 0, Y, 1, A ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 7 CALL DSPR2( 'U', 0, ALPHA, X, 1, Y, 0, A ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) * 170 IF( OK )THEN WRITE( NOUT, FMT = 9999 )SRNAMT ELSE WRITE( NOUT, FMT = 9998 )SRNAMT END IF RETURN * 9999 FORMAT( ' ', A6, ' PASSED THE TESTS OF ERROR-EXITS' ) 9998 FORMAT( ' ******* ', A6, ' FAILED THE TESTS OF ERROR-EXITS *****', $ '**' ) * * End of DCHKE. * END SUBROUTINE DMAKE( TYPE, UPLO, DIAG, M, N, A, NMAX, AA, LDA, KL, $ KU, RESET, TRANSL ) * * Generates values for an M by N matrix A within the bandwidth * defined by KL and KU. * Stores the values in the array AA in the data structure required * by the routine, with unwanted elements set to rogue value. * * TYPE is 'GE', 'GB', 'SY', 'SB', 'SP', 'TR', 'TB' OR 'TP'. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) DOUBLE PRECISION ROGUE PARAMETER ( ROGUE = -1.0D10 ) * .. Scalar Arguments .. DOUBLE PRECISION TRANSL INTEGER KL, KU, LDA, M, N, NMAX LOGICAL RESET CHARACTER*1 DIAG, UPLO CHARACTER*2 TYPE * .. Array Arguments .. DOUBLE PRECISION A( NMAX, * ), AA( * ) * .. Local Scalars .. INTEGER I, I1, I2, I3, IBEG, IEND, IOFF, J, KK LOGICAL GEN, LOWER, SYM, TRI, UNIT, UPPER * .. External Functions .. DOUBLE PRECISION DBEG EXTERNAL DBEG * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. Executable Statements .. GEN = TYPE( 1: 1 ).EQ.'G' SYM = TYPE( 1: 1 ).EQ.'S' TRI = TYPE( 1: 1 ).EQ.'T' UPPER = ( SYM.OR.TRI ).AND.UPLO.EQ.'U' LOWER = ( SYM.OR.TRI ).AND.UPLO.EQ.'L' UNIT = TRI.AND.DIAG.EQ.'U' * * Generate data in array A. * DO 20 J = 1, N DO 10 I = 1, M IF( GEN.OR.( UPPER.AND.I.LE.J ).OR.( LOWER.AND.I.GE.J ) ) $ THEN IF( ( I.LE.J.AND.J - I.LE.KU ).OR. $ ( I.GE.J.AND.I - J.LE.KL ) )THEN A( I, J ) = DBEG( RESET ) + TRANSL ELSE A( I, J ) = ZERO END IF IF( I.NE.J )THEN IF( SYM )THEN A( J, I ) = A( I, J ) ELSE IF( TRI )THEN A( J, I ) = ZERO END IF END IF END IF 10 CONTINUE IF( TRI ) $ A( J, J ) = A( J, J ) + ONE IF( UNIT ) $ A( J, J ) = ONE 20 CONTINUE * * Store elements in array AS in data structure required by routine. * IF( TYPE.EQ.'GE' )THEN DO 50 J = 1, N DO 30 I = 1, M AA( I + ( J - 1 )*LDA ) = A( I, J ) 30 CONTINUE DO 40 I = M + 1, LDA AA( I + ( J - 1 )*LDA ) = ROGUE 40 CONTINUE 50 CONTINUE ELSE IF( TYPE.EQ.'GB' )THEN DO 90 J = 1, N DO 60 I1 = 1, KU + 1 - J AA( I1 + ( J - 1 )*LDA ) = ROGUE 60 CONTINUE DO 70 I2 = I1, MIN( KL + KU + 1, KU + 1 + M - J ) AA( I2 + ( J - 1 )*LDA ) = A( I2 + J - KU - 1, J ) 70 CONTINUE DO 80 I3 = I2, LDA AA( I3 + ( J - 1 )*LDA ) = ROGUE 80 CONTINUE 90 CONTINUE ELSE IF( TYPE.EQ.'SY'.OR.TYPE.EQ.'TR' )THEN DO 130 J = 1, N IF( UPPER )THEN IBEG = 1 IF( UNIT )THEN IEND = J - 1 ELSE IEND = J END IF ELSE IF( UNIT )THEN IBEG = J + 1 ELSE IBEG = J END IF IEND = N END IF DO 100 I = 1, IBEG - 1 AA( I + ( J - 1 )*LDA ) = ROGUE 100 CONTINUE DO 110 I = IBEG, IEND AA( I + ( J - 1 )*LDA ) = A( I, J ) 110 CONTINUE DO 120 I = IEND + 1, LDA AA( I + ( J - 1 )*LDA ) = ROGUE 120 CONTINUE 130 CONTINUE ELSE IF( TYPE.EQ.'SB'.OR.TYPE.EQ.'TB' )THEN DO 170 J = 1, N IF( UPPER )THEN KK = KL + 1 IBEG = MAX( 1, KL + 2 - J ) IF( UNIT )THEN IEND = KL ELSE IEND = KL + 1 END IF ELSE KK = 1 IF( UNIT )THEN IBEG = 2 ELSE IBEG = 1 END IF IEND = MIN( KL + 1, 1 + M - J ) END IF DO 140 I = 1, IBEG - 1 AA( I + ( J - 1 )*LDA ) = ROGUE 140 CONTINUE DO 150 I = IBEG, IEND AA( I + ( J - 1 )*LDA ) = A( I + J - KK, J ) 150 CONTINUE DO 160 I = IEND + 1, LDA AA( I + ( J - 1 )*LDA ) = ROGUE 160 CONTINUE 170 CONTINUE ELSE IF( TYPE.EQ.'SP'.OR.TYPE.EQ.'TP' )THEN IOFF = 0 DO 190 J = 1, N IF( UPPER )THEN IBEG = 1 IEND = J ELSE IBEG = J IEND = N END IF DO 180 I = IBEG, IEND IOFF = IOFF + 1 AA( IOFF ) = A( I, J ) IF( I.EQ.J )THEN IF( UNIT ) $ AA( IOFF ) = ROGUE END IF 180 CONTINUE 190 CONTINUE END IF RETURN * * End of DMAKE. * END SUBROUTINE DMVCH( TRANS, M, N, ALPHA, A, NMAX, X, INCX, BETA, Y, $ INCY, YT, G, YY, EPS, ERR, FATAL, NOUT, MV ) * * Checks the results of the computational tests. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) * .. Scalar Arguments .. DOUBLE PRECISION ALPHA, BETA, EPS, ERR INTEGER INCX, INCY, M, N, NMAX, NOUT LOGICAL FATAL, MV CHARACTER*1 TRANS * .. Array Arguments .. DOUBLE PRECISION A( NMAX, * ), G( * ), X( * ), Y( * ), YT( * ), $ YY( * ) * .. Local Scalars .. DOUBLE PRECISION ERRI INTEGER I, INCXL, INCYL, IY, J, JX, KX, KY, ML, NL LOGICAL TRAN * .. Intrinsic Functions .. INTRINSIC ABS, MAX, SQRT * .. Executable Statements .. TRAN = TRANS.EQ.'T'.OR.TRANS.EQ.'C' IF( TRAN )THEN ML = N NL = M ELSE ML = M NL = N END IF IF( INCX.LT.0 )THEN KX = NL INCXL = -1 ELSE KX = 1 INCXL = 1 END IF IF( INCY.LT.0 )THEN KY = ML INCYL = -1 ELSE KY = 1 INCYL = 1 END IF * * Compute expected result in YT using data in A, X and Y. * Compute gauges in G. * IY = KY DO 30 I = 1, ML YT( IY ) = ZERO G( IY ) = ZERO JX = KX IF( TRAN )THEN DO 10 J = 1, NL YT( IY ) = YT( IY ) + A( J, I )*X( JX ) G( IY ) = G( IY ) + ABS( A( J, I )*X( JX ) ) JX = JX + INCXL 10 CONTINUE ELSE DO 20 J = 1, NL YT( IY ) = YT( IY ) + A( I, J )*X( JX ) G( IY ) = G( IY ) + ABS( A( I, J )*X( JX ) ) JX = JX + INCXL 20 CONTINUE END IF YT( IY ) = ALPHA*YT( IY ) + BETA*Y( IY ) G( IY ) = ABS( ALPHA )*G( IY ) + ABS( BETA*Y( IY ) ) IY = IY + INCYL 30 CONTINUE * * Compute the error ratio for this result. * ERR = ZERO DO 40 I = 1, ML ERRI = ABS( YT( I ) - YY( 1 + ( I - 1 )*ABS( INCY ) ) )/EPS IF( G( I ).NE.ZERO ) $ ERRI = ERRI/G( I ) ERR = MAX( ERR, ERRI ) IF( ERR*SQRT( EPS ).GE.ONE ) $ GO TO 50 40 CONTINUE * If the loop completes, all results are at least half accurate. GO TO 70 * * Report fatal error. * 50 FATAL = .TRUE. WRITE( NOUT, FMT = 9999 ) DO 60 I = 1, ML IF( MV )THEN WRITE( NOUT, FMT = 9998 )I, YT( I ), $ YY( 1 + ( I - 1 )*ABS( INCY ) ) ELSE WRITE( NOUT, FMT = 9998 )I, $ YY( 1 + ( I - 1 )*ABS( INCY ) ), YT( I ) END IF 60 CONTINUE * 70 CONTINUE RETURN * 9999 FORMAT( ' ******* FATAL ERROR - COMPUTED RESULT IS LESS THAN HAL', $ 'F ACCURATE *******', /' EXPECTED RESULT COMPU', $ 'TED RESULT' ) 9998 FORMAT( 1X, I7, 2G18.6 ) * * End of DMVCH. * END LOGICAL FUNCTION LDE( RI, RJ, LR ) * * Tests if two arrays are identical. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Scalar Arguments .. INTEGER LR * .. Array Arguments .. DOUBLE PRECISION RI( * ), RJ( * ) * .. Local Scalars .. INTEGER I * .. Executable Statements .. DO 10 I = 1, LR IF( RI( I ).NE.RJ( I ) ) $ GO TO 20 10 CONTINUE LDE = .TRUE. GO TO 30 20 CONTINUE LDE = .FALSE. 30 RETURN * * End of LDE. * END LOGICAL FUNCTION LDERES( TYPE, UPLO, M, N, AA, AS, LDA ) * * Tests if selected elements in two arrays are equal. * * TYPE is 'GE', 'SY' or 'SP'. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Scalar Arguments .. INTEGER LDA, M, N CHARACTER*1 UPLO CHARACTER*2 TYPE * .. Array Arguments .. DOUBLE PRECISION AA( LDA, * ), AS( LDA, * ) * .. Local Scalars .. INTEGER I, IBEG, IEND, J LOGICAL UPPER * .. Executable Statements .. UPPER = UPLO.EQ.'U' IF( TYPE.EQ.'GE' )THEN DO 20 J = 1, N DO 10 I = M + 1, LDA IF( AA( I, J ).NE.AS( I, J ) ) $ GO TO 70 10 CONTINUE 20 CONTINUE ELSE IF( TYPE.EQ.'SY' )THEN DO 50 J = 1, N IF( UPPER )THEN IBEG = 1 IEND = J ELSE IBEG = J IEND = N END IF DO 30 I = 1, IBEG - 1 IF( AA( I, J ).NE.AS( I, J ) ) $ GO TO 70 30 CONTINUE DO 40 I = IEND + 1, LDA IF( AA( I, J ).NE.AS( I, J ) ) $ GO TO 70 40 CONTINUE 50 CONTINUE END IF * 60 CONTINUE LDERES = .TRUE. GO TO 80 70 CONTINUE LDERES = .FALSE. 80 RETURN * * End of LDERES. * END DOUBLE PRECISION FUNCTION DBEG( RESET ) * * Generates random numbers uniformly distributed between -0.5 and 0.5. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Scalar Arguments .. LOGICAL RESET * .. Local Scalars .. INTEGER I, IC, MI * .. Save statement .. SAVE I, IC, MI * .. Intrinsic Functions .. INTRINSIC DBLE * .. Executable Statements .. IF( RESET )THEN * Initialize local variables. MI = 891 I = 7 IC = 0 RESET = .FALSE. END IF * * The sequence of values of I is bounded between 1 and 999. * If initial I = 1,2,3,6,7 or 9, the period will be 50. * If initial I = 4 or 8, the period will be 25. * If initial I = 5, the period will be 10. * IC is used to break up the period by skipping 1 value of I in 6. * IC = IC + 1 10 I = I*MI I = I - 1000*( I/1000 ) IF( IC.GE.5 )THEN IC = 0 GO TO 10 END IF DBEG = DBLE( I - 500 )/1001.0D0 RETURN * * End of DBEG. * END DOUBLE PRECISION FUNCTION DDIFF( X, Y ) * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * * .. Scalar Arguments .. DOUBLE PRECISION X, Y * .. Executable Statements .. DDIFF = X - Y RETURN * * End of DDIFF. * END SUBROUTINE CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) * * Tests whether XERBLA has detected an error when it should. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Scalar Arguments .. INTEGER INFOT, NOUT LOGICAL LERR, OK CHARACTER*6 SRNAMT * .. Executable Statements .. IF( .NOT.LERR )THEN WRITE( NOUT, FMT = 9999 )INFOT, SRNAMT OK = .FALSE. END IF LERR = .FALSE. RETURN * 9999 FORMAT( ' ***** ILLEGAL VALUE OF PARAMETER NUMBER ', I2, ' NOT D', $ 'ETECTED BY ', A6, ' *****' ) * * End of CHKXER. * END SUBROUTINE XERBLA( SRNAME, INFO ) * * This is a special version of XERBLA to be used only as part of * the test program for testing error exits from the Level 2 BLAS * routines. * * XERBLA is an error handler for the Level 2 BLAS routines. * * It is called by the Level 2 BLAS routines if an input parameter is * invalid. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Scalar Arguments .. INTEGER INFO CHARACTER*6 SRNAME * .. Scalars in Common .. INTEGER INFOT, NOUT LOGICAL LERR, OK CHARACTER*6 SRNAMT * .. Common blocks .. COMMON /INFOC/INFOT, NOUT, OK, LERR COMMON /SRNAMC/SRNAMT * .. Executable Statements .. LERR = .TRUE. IF( INFO.NE.INFOT )THEN IF( INFOT.NE.0 )THEN WRITE( NOUT, FMT = 9999 )INFO, INFOT ELSE WRITE( NOUT, FMT = 9997 )INFO END IF OK = .FALSE. END IF IF( SRNAME.NE.SRNAMT )THEN WRITE( NOUT, FMT = 9998 )SRNAME, SRNAMT OK = .FALSE. END IF RETURN * 9999 FORMAT( ' ******* XERBLA WAS CALLED WITH INFO = ', I6, ' INSTEAD', $ ' OF ', I2, ' *******' ) 9998 FORMAT( ' ******* XERBLA WAS CALLED WITH SRNAME = ', A6, ' INSTE', $ 'AD OF ', A6, ' *******' ) 9997 FORMAT( ' ******* XERBLA WAS CALLED WITH INFO = ', I6, $ ' *******' ) * * End of XERBLA * END PROGRAM ZBLAT2 * * Test program for the COMPLEX*16 Level 2 Blas. * * The program must be driven by a short data file. The first 18 records * of the file are read using list-directed input, the last 17 records * are read using the format ( A6, L2 ). An annotated example of a data * file can be obtained by deleting the first 3 characters from the * following 35 lines: * 'ZBLAT2.SUMM' NAME OF SUMMARY OUTPUT FILE * 6 UNIT NUMBER OF SUMMARY FILE * 'CBLA2T.SNAP' NAME OF SNAPSHOT OUTPUT FILE * -1 UNIT NUMBER OF SNAPSHOT FILE (NOT USED IF .LT. 0) * F LOGICAL FLAG, T TO REWIND SNAPSHOT FILE AFTER EACH RECORD. * F LOGICAL FLAG, T TO STOP ON FAILURES. * T LOGICAL FLAG, T TO TEST ERROR EXITS. * 16.0 THRESHOLD VALUE OF TEST RATIO * 6 NUMBER OF VALUES OF N * 0 1 2 3 5 9 VALUES OF N * 4 NUMBER OF VALUES OF K * 0 1 2 4 VALUES OF K * 4 NUMBER OF VALUES OF INCX AND INCY * 1 2 -1 -2 VALUES OF INCX AND INCY * 3 NUMBER OF VALUES OF ALPHA * (0.0,0.0) (1.0,0.0) (0.7,-0.9) VALUES OF ALPHA * 3 NUMBER OF VALUES OF BETA * (0.0,0.0) (1.0,0.0) (1.3,-1.1) VALUES OF BETA * ZGEMV T PUT F FOR NO TEST. SAME COLUMNS. * ZGBMV T PUT F FOR NO TEST. SAME COLUMNS. * ZHEMV T PUT F FOR NO TEST. SAME COLUMNS. * ZHBMV T PUT F FOR NO TEST. SAME COLUMNS. * ZHPMV T PUT F FOR NO TEST. SAME COLUMNS. * ZTRMV T PUT F FOR NO TEST. SAME COLUMNS. * ZTBMV T PUT F FOR NO TEST. SAME COLUMNS. * ZTPMV T PUT F FOR NO TEST. SAME COLUMNS. * ZTRSV T PUT F FOR NO TEST. SAME COLUMNS. * ZTBSV T PUT F FOR NO TEST. SAME COLUMNS. * ZTPSV T PUT F FOR NO TEST. SAME COLUMNS. * ZGERC T PUT F FOR NO TEST. SAME COLUMNS. * ZGERU T PUT F FOR NO TEST. SAME COLUMNS. * ZHER T PUT F FOR NO TEST. SAME COLUMNS. * ZHPR T PUT F FOR NO TEST. SAME COLUMNS. * ZHER2 T PUT F FOR NO TEST. SAME COLUMNS. * ZHPR2 T PUT F FOR NO TEST. SAME COLUMNS. * * See: * * Dongarra J. J., Du Croz J. J., Hammarling S. and Hanson R. J.. * An extended set of Fortran Basic Linear Algebra Subprograms. * * Technical Memoranda Nos. 41 (revision 3) and 81, Mathematics * and Computer Science Division, Argonne National Laboratory, * 9700 South Cass Avenue, Argonne, Illinois 60439, US. * * Or * * NAG Technical Reports TR3/87 and TR4/87, Numerical Algorithms * Group Ltd., NAG Central Office, 256 Banbury Road, Oxford * OX2 7DE, UK, and Numerical Algorithms Group Inc., 1101 31st * Street, Suite 100, Downers Grove, Illinois 60515-1263, USA. * * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Parameters .. INTEGER NIN PARAMETER ( NIN = 5 ) INTEGER NSUBS PARAMETER ( NSUBS = 17 ) COMPLEX*16 ZERO, ONE PARAMETER ( ZERO = ( 0.0D0, 0.0D0 ), $ ONE = ( 1.0D0, 0.0D0 ) ) DOUBLE PRECISION RZERO, RHALF, RONE PARAMETER ( RZERO = 0.0D0, RHALF = 0.5D0, RONE = 1.0D0 ) INTEGER NMAX, INCMAX PARAMETER ( NMAX = 65, INCMAX = 2 ) INTEGER NINMAX, NIDMAX, NKBMAX, NALMAX, NBEMAX PARAMETER ( NINMAX = 7, NIDMAX = 9, NKBMAX = 7, $ NALMAX = 7, NBEMAX = 7 ) * .. Local Scalars .. DOUBLE PRECISION EPS, ERR, THRESH INTEGER I, ISNUM, J, N, NALF, NBET, NIDIM, NINC, NKB, $ NOUT, NTRA LOGICAL FATAL, LTESTT, REWI, SAME, SFATAL, TRACE, $ TSTERR CHARACTER*1 TRANS CHARACTER*6 SNAMET CHARACTER*32 SNAPS, SUMMRY * .. Local Arrays .. COMPLEX*16 A( NMAX, NMAX ), AA( NMAX*NMAX ), $ ALF( NALMAX ), AS( NMAX*NMAX ), BET( NBEMAX ), $ X( NMAX ), XS( NMAX*INCMAX ), $ XX( NMAX*INCMAX ), Y( NMAX ), $ YS( NMAX*INCMAX ), YT( NMAX ), $ YY( NMAX*INCMAX ), Z( 2*NMAX ) DOUBLE PRECISION G( NMAX ) INTEGER IDIM( NIDMAX ), INC( NINMAX ), KB( NKBMAX ) LOGICAL LTEST( NSUBS ) CHARACTER*6 SNAMES( NSUBS ) * .. External Functions .. DOUBLE PRECISION DDIFF LOGICAL LZE EXTERNAL DDIFF, LZE * .. External Subroutines .. EXTERNAL ZCHK1, ZCHK2, ZCHK3, ZCHK4, ZCHK5, ZCHK6, $ ZCHKE, ZMVCH * .. Intrinsic Functions .. INTRINSIC ABS, MAX, MIN * .. Scalars in Common .. INTEGER INFOT, NOUTC LOGICAL LERR, OK CHARACTER*6 SRNAMT * .. Common blocks .. COMMON /INFOC/INFOT, NOUTC, OK, LERR COMMON /SRNAMC/SRNAMT * .. Data statements .. DATA SNAMES/'ZGEMV ', 'ZGBMV ', 'ZHEMV ', 'ZHBMV ', $ 'ZHPMV ', 'ZTRMV ', 'ZTBMV ', 'ZTPMV ', $ 'ZTRSV ', 'ZTBSV ', 'ZTPSV ', 'ZGERC ', $ 'ZGERU ', 'ZHER ', 'ZHPR ', 'ZHER2 ', $ 'ZHPR2 '/ * .. Executable Statements .. * * Read name and unit number for summary output file and open file. * READ( NIN, FMT = * )SUMMRY READ( NIN, FMT = * )NOUT OPEN( NOUT, FILE = SUMMRY, STATUS = 'NEW' ) NOUTC = NOUT * * Read name and unit number for snapshot output file and open file. * READ( NIN, FMT = * )SNAPS READ( NIN, FMT = * )NTRA TRACE = NTRA.GE.0 IF( TRACE )THEN OPEN( NTRA, FILE = SNAPS, STATUS = 'NEW' ) END IF * Read the flag that directs rewinding of the snapshot file. READ( NIN, FMT = * )REWI REWI = REWI.AND.TRACE * Read the flag that directs stopping on any failure. READ( NIN, FMT = * )SFATAL * Read the flag that indicates whether error exits are to be tested. READ( NIN, FMT = * )TSTERR * Read the threshold value of the test ratio READ( NIN, FMT = * )THRESH * * Read and check the parameter values for the tests. * * Values of N READ( NIN, FMT = * )NIDIM IF( NIDIM.LT.1.OR.NIDIM.GT.NIDMAX )THEN WRITE( NOUT, FMT = 9997 )'N', NIDMAX GO TO 230 END IF READ( NIN, FMT = * )( IDIM( I ), I = 1, NIDIM ) DO 10 I = 1, NIDIM IF( IDIM( I ).LT.0.OR.IDIM( I ).GT.NMAX )THEN WRITE( NOUT, FMT = 9996 )NMAX GO TO 230 END IF 10 CONTINUE * Values of K READ( NIN, FMT = * )NKB IF( NKB.LT.1.OR.NKB.GT.NKBMAX )THEN WRITE( NOUT, FMT = 9997 )'K', NKBMAX GO TO 230 END IF READ( NIN, FMT = * )( KB( I ), I = 1, NKB ) DO 20 I = 1, NKB IF( KB( I ).LT.0 )THEN WRITE( NOUT, FMT = 9995 ) GO TO 230 END IF 20 CONTINUE * Values of INCX and INCY READ( NIN, FMT = * )NINC IF( NINC.LT.1.OR.NINC.GT.NINMAX )THEN WRITE( NOUT, FMT = 9997 )'INCX AND INCY', NINMAX GO TO 230 END IF READ( NIN, FMT = * )( INC( I ), I = 1, NINC ) DO 30 I = 1, NINC IF( INC( I ).EQ.0.OR.ABS( INC( I ) ).GT.INCMAX )THEN WRITE( NOUT, FMT = 9994 )INCMAX GO TO 230 END IF 30 CONTINUE * Values of ALPHA READ( NIN, FMT = * )NALF IF( NALF.LT.1.OR.NALF.GT.NALMAX )THEN WRITE( NOUT, FMT = 9997 )'ALPHA', NALMAX GO TO 230 END IF READ( NIN, FMT = * )( ALF( I ), I = 1, NALF ) * Values of BETA READ( NIN, FMT = * )NBET IF( NBET.LT.1.OR.NBET.GT.NBEMAX )THEN WRITE( NOUT, FMT = 9997 )'BETA', NBEMAX GO TO 230 END IF READ( NIN, FMT = * )( BET( I ), I = 1, NBET ) * * Report values of parameters. * WRITE( NOUT, FMT = 9993 ) WRITE( NOUT, FMT = 9992 )( IDIM( I ), I = 1, NIDIM ) WRITE( NOUT, FMT = 9991 )( KB( I ), I = 1, NKB ) WRITE( NOUT, FMT = 9990 )( INC( I ), I = 1, NINC ) WRITE( NOUT, FMT = 9989 )( ALF( I ), I = 1, NALF ) WRITE( NOUT, FMT = 9988 )( BET( I ), I = 1, NBET ) IF( .NOT.TSTERR )THEN WRITE( NOUT, FMT = * ) WRITE( NOUT, FMT = 9980 ) END IF WRITE( NOUT, FMT = * ) WRITE( NOUT, FMT = 9999 )THRESH WRITE( NOUT, FMT = * ) * * Read names of subroutines and flags which indicate * whether they are to be tested. * DO 40 I = 1, NSUBS LTEST( I ) = .FALSE. 40 CONTINUE 50 READ( NIN, FMT = 9984, END = 80 )SNAMET, LTESTT DO 60 I = 1, NSUBS IF( SNAMET.EQ.SNAMES( I ) ) $ GO TO 70 60 CONTINUE WRITE( NOUT, FMT = 9986 )SNAMET STOP 70 LTEST( I ) = LTESTT GO TO 50 * 80 CONTINUE CLOSE ( NIN ) * * Compute EPS (the machine precision). * EPS = RONE 90 CONTINUE IF( DDIFF( RONE + EPS, RONE ).EQ.RZERO ) $ GO TO 100 EPS = RHALF*EPS GO TO 90 100 CONTINUE EPS = EPS + EPS WRITE( NOUT, FMT = 9998 )EPS * * Check the reliability of ZMVCH using exact data. * N = MIN( 32, NMAX ) DO 120 J = 1, N DO 110 I = 1, N A( I, J ) = MAX( I - J + 1, 0 ) 110 CONTINUE X( J ) = J Y( J ) = ZERO 120 CONTINUE DO 130 J = 1, N YY( J ) = J*( ( J + 1 )*J )/2 - ( ( J + 1 )*J*( J - 1 ) )/3 130 CONTINUE * YY holds the exact result. On exit from ZMVCH YT holds * the result computed by ZMVCH. TRANS = 'N' CALL ZMVCH( TRANS, N, N, ONE, A, NMAX, X, 1, ZERO, Y, 1, YT, G, $ YY, EPS, ERR, FATAL, NOUT, .TRUE. ) SAME = LZE( YY, YT, N ) IF( .NOT.SAME.OR.ERR.NE.RZERO )THEN WRITE( NOUT, FMT = 9985 )TRANS, SAME, ERR STOP END IF TRANS = 'T' CALL ZMVCH( TRANS, N, N, ONE, A, NMAX, X, -1, ZERO, Y, -1, YT, G, $ YY, EPS, ERR, FATAL, NOUT, .TRUE. ) SAME = LZE( YY, YT, N ) IF( .NOT.SAME.OR.ERR.NE.RZERO )THEN WRITE( NOUT, FMT = 9985 )TRANS, SAME, ERR STOP END IF * * Test each subroutine in turn. * DO 210 ISNUM = 1, NSUBS WRITE( NOUT, FMT = * ) IF( .NOT.LTEST( ISNUM ) )THEN * Subprogram is not to be tested. WRITE( NOUT, FMT = 9983 )SNAMES( ISNUM ) ELSE SRNAMT = SNAMES( ISNUM ) * Test error exits. IF( TSTERR )THEN CALL ZCHKE( ISNUM, SNAMES( ISNUM ), NOUT ) WRITE( NOUT, FMT = * ) END IF * Test computations. INFOT = 0 OK = .TRUE. FATAL = .FALSE. GO TO ( 140, 140, 150, 150, 150, 160, 160, $ 160, 160, 160, 160, 170, 170, 180, $ 180, 190, 190 )ISNUM * Test ZGEMV, 01, and ZGBMV, 02. 140 CALL ZCHK1( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE, $ REWI, FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF, $ NBET, BET, NINC, INC, NMAX, INCMAX, A, AA, AS, $ X, XX, XS, Y, YY, YS, YT, G ) GO TO 200 * Test ZHEMV, 03, ZHBMV, 04, and ZHPMV, 05. 150 CALL ZCHK2( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE, $ REWI, FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF, $ NBET, BET, NINC, INC, NMAX, INCMAX, A, AA, AS, $ X, XX, XS, Y, YY, YS, YT, G ) GO TO 200 * Test ZTRMV, 06, ZTBMV, 07, ZTPMV, 08, * ZTRSV, 09, ZTBSV, 10, and ZTPSV, 11. 160 CALL ZCHK3( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE, $ REWI, FATAL, NIDIM, IDIM, NKB, KB, NINC, INC, $ NMAX, INCMAX, A, AA, AS, Y, YY, YS, YT, G, Z ) GO TO 200 * Test ZGERC, 12, ZGERU, 13. 170 CALL ZCHK4( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE, $ REWI, FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, $ NMAX, INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, $ YT, G, Z ) GO TO 200 * Test ZHER, 14, and ZHPR, 15. 180 CALL ZCHK5( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE, $ REWI, FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, $ NMAX, INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, $ YT, G, Z ) GO TO 200 * Test ZHER2, 16, and ZHPR2, 17. 190 CALL ZCHK6( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE, $ REWI, FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, $ NMAX, INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, $ YT, G, Z ) * 200 IF( FATAL.AND.SFATAL ) $ GO TO 220 END IF 210 CONTINUE WRITE( NOUT, FMT = 9982 ) GO TO 240 * 220 CONTINUE WRITE( NOUT, FMT = 9981 ) GO TO 240 * 230 CONTINUE WRITE( NOUT, FMT = 9987 ) * 240 CONTINUE IF( TRACE ) $ CLOSE ( NTRA ) CLOSE ( NOUT ) STOP * 9999 FORMAT( ' ROUTINES PASS COMPUTATIONAL TESTS IF TEST RATIO IS LES', $ 'S THAN', F8.2 ) 9998 FORMAT( ' RELATIVE MACHINE PRECISION IS TAKEN TO BE', 1P, D9.1 ) 9997 FORMAT( ' NUMBER OF VALUES OF ', A, ' IS LESS THAN 1 OR GREATER ', $ 'THAN ', I2 ) 9996 FORMAT( ' VALUE OF N IS LESS THAN 0 OR GREATER THAN ', I2 ) 9995 FORMAT( ' VALUE OF K IS LESS THAN 0' ) 9994 FORMAT( ' ABSOLUTE VALUE OF INCX OR INCY IS 0 OR GREATER THAN ', $ I2 ) 9993 FORMAT( ' TESTS OF THE COMPLEX*16 LEVEL 2 BLAS', //' THE F', $ 'OLLOWING PARAMETER VALUES WILL BE USED:' ) 9992 FORMAT( ' FOR N ', 9I6 ) 9991 FORMAT( ' FOR K ', 7I6 ) 9990 FORMAT( ' FOR INCX AND INCY ', 7I6 ) 9989 FORMAT( ' FOR ALPHA ', $ 7( '(', F4.1, ',', F4.1, ') ', : ) ) 9988 FORMAT( ' FOR BETA ', $ 7( '(', F4.1, ',', F4.1, ') ', : ) ) 9987 FORMAT( ' AMEND DATA FILE OR INCREASE ARRAY SIZES IN PROGRAM', $ /' ******* TESTS ABANDONED *******' ) 9986 FORMAT( ' SUBPROGRAM NAME ', A6, ' NOT RECOGNIZED', /' ******* T', $ 'ESTS ABANDONED *******' ) 9985 FORMAT( ' ERROR IN ZMVCH - IN-LINE DOT PRODUCTS ARE BEING EVALU', $ 'ATED WRONGLY.', /' ZMVCH WAS CALLED WITH TRANS = ', A1, $ ' AND RETURNED SAME = ', L1, ' AND ERR = ', F12.3, '.', / $ ' THIS MAY BE DUE TO FAULTS IN THE ARITHMETIC OR THE COMPILER.' $ , /' ******* TESTS ABANDONED *******' ) 9984 FORMAT( A6, L2 ) 9983 FORMAT( 1X, A6, ' WAS NOT TESTED' ) 9982 FORMAT( /' END OF TESTS' ) 9981 FORMAT( /' ******* FATAL ERROR - TESTS ABANDONED *******' ) 9980 FORMAT( ' ERROR-EXITS WILL NOT BE TESTED' ) * * End of ZBLAT2. * END SUBROUTINE ZCHK1( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI, $ FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF, NBET, $ BET, NINC, INC, NMAX, INCMAX, A, AA, AS, X, XX, $ XS, Y, YY, YS, YT, G ) * * Tests ZGEMV and ZGBMV. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Parameters .. COMPLEX*16 ZERO, HALF PARAMETER ( ZERO = ( 0.0D0, 0.0D0 ), $ HALF = ( 0.5D0, 0.0D0 ) ) DOUBLE PRECISION RZERO PARAMETER ( RZERO = 0.0D0 ) * .. Scalar Arguments .. DOUBLE PRECISION EPS, THRESH INTEGER INCMAX, NALF, NBET, NIDIM, NINC, NKB, NMAX, $ NOUT, NTRA LOGICAL FATAL, REWI, TRACE CHARACTER*6 SNAME * .. Array Arguments .. COMPLEX*16 A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ), $ AS( NMAX*NMAX ), BET( NBET ), X( NMAX ), $ XS( NMAX*INCMAX ), XX( NMAX*INCMAX ), $ Y( NMAX ), YS( NMAX*INCMAX ), YT( NMAX ), $ YY( NMAX*INCMAX ) DOUBLE PRECISION G( NMAX ) INTEGER IDIM( NIDIM ), INC( NINC ), KB( NKB ) * .. Local Scalars .. COMPLEX*16 ALPHA, ALS, BETA, BLS, TRANSL DOUBLE PRECISION ERR, ERRMAX INTEGER I, IA, IB, IC, IKU, IM, IN, INCX, INCXS, INCY, $ INCYS, IX, IY, KL, KLS, KU, KUS, LAA, LDA, $ LDAS, LX, LY, M, ML, MS, N, NARGS, NC, ND, NK, $ NL, NS LOGICAL BANDED, FULL, NULL, RESET, SAME, TRAN CHARACTER*1 TRANS, TRANSS CHARACTER*3 ICH * .. Local Arrays .. LOGICAL ISAME( 13 ) * .. External Functions .. LOGICAL LZE, LZERES EXTERNAL LZE, LZERES * .. External Subroutines .. EXTERNAL ZGBMV, ZGEMV, ZMAKE, ZMVCH * .. Intrinsic Functions .. INTRINSIC ABS, MAX, MIN * .. Scalars in Common .. INTEGER INFOT, NOUTC LOGICAL LERR, OK * .. Common blocks .. COMMON /INFOC/INFOT, NOUTC, OK, LERR * .. Data statements .. DATA ICH/'NTC'/ * .. Executable Statements .. FULL = SNAME( 3: 3 ).EQ.'E' BANDED = SNAME( 3: 3 ).EQ.'B' * Define the number of arguments. IF( FULL )THEN NARGS = 11 ELSE IF( BANDED )THEN NARGS = 13 END IF * NC = 0 RESET = .TRUE. ERRMAX = RZERO * DO 120 IN = 1, NIDIM N = IDIM( IN ) ND = N/2 + 1 * DO 110 IM = 1, 2 IF( IM.EQ.1 ) $ M = MAX( N - ND, 0 ) IF( IM.EQ.2 ) $ M = MIN( N + ND, NMAX ) * IF( BANDED )THEN NK = NKB ELSE NK = 1 END IF DO 100 IKU = 1, NK IF( BANDED )THEN KU = KB( IKU ) KL = MAX( KU - 1, 0 ) ELSE KU = N - 1 KL = M - 1 END IF * Set LDA to 1 more than minimum value if room. IF( BANDED )THEN LDA = KL + KU + 1 ELSE LDA = M END IF IF( LDA.LT.NMAX ) $ LDA = LDA + 1 * Skip tests if not enough room. IF( LDA.GT.NMAX ) $ GO TO 100 LAA = LDA*N NULL = N.LE.0.OR.M.LE.0 * * Generate the matrix A. * TRANSL = ZERO CALL ZMAKE( SNAME( 2: 3 ), ' ', ' ', M, N, A, NMAX, AA, $ LDA, KL, KU, RESET, TRANSL ) * DO 90 IC = 1, 3 TRANS = ICH( IC: IC ) TRAN = TRANS.EQ.'T'.OR.TRANS.EQ.'C' * IF( TRAN )THEN ML = N NL = M ELSE ML = M NL = N END IF * DO 80 IX = 1, NINC INCX = INC( IX ) LX = ABS( INCX )*NL * * Generate the vector X. * TRANSL = HALF CALL ZMAKE( 'GE', ' ', ' ', 1, NL, X, 1, XX, $ ABS( INCX ), 0, NL - 1, RESET, TRANSL ) IF( NL.GT.1 )THEN X( NL/2 ) = ZERO XX( 1 + ABS( INCX )*( NL/2 - 1 ) ) = ZERO END IF * DO 70 IY = 1, NINC INCY = INC( IY ) LY = ABS( INCY )*ML * DO 60 IA = 1, NALF ALPHA = ALF( IA ) * DO 50 IB = 1, NBET BETA = BET( IB ) * * Generate the vector Y. * TRANSL = ZERO CALL ZMAKE( 'GE', ' ', ' ', 1, ML, Y, 1, $ YY, ABS( INCY ), 0, ML - 1, $ RESET, TRANSL ) * NC = NC + 1 * * Save every datum before calling the * subroutine. * TRANSS = TRANS MS = M NS = N KLS = KL KUS = KU ALS = ALPHA DO 10 I = 1, LAA AS( I ) = AA( I ) 10 CONTINUE LDAS = LDA DO 20 I = 1, LX XS( I ) = XX( I ) 20 CONTINUE INCXS = INCX BLS = BETA DO 30 I = 1, LY YS( I ) = YY( I ) 30 CONTINUE INCYS = INCY * * Call the subroutine. * IF( FULL )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9994 )NC, SNAME, $ TRANS, M, N, ALPHA, LDA, INCX, BETA, $ INCY IF( REWI ) $ REWIND NTRA CALL ZGEMV( TRANS, M, N, ALPHA, AA, $ LDA, XX, INCX, BETA, YY, $ INCY ) ELSE IF( BANDED )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9995 )NC, SNAME, $ TRANS, M, N, KL, KU, ALPHA, LDA, $ INCX, BETA, INCY IF( REWI ) $ REWIND NTRA CALL ZGBMV( TRANS, M, N, KL, KU, ALPHA, $ AA, LDA, XX, INCX, BETA, $ YY, INCY ) END IF * * Check if error-exit was taken incorrectly. * IF( .NOT.OK )THEN WRITE( NOUT, FMT = 9993 ) FATAL = .TRUE. GO TO 130 END IF * * See what data changed inside subroutines. * ISAME( 1 ) = TRANS.EQ.TRANSS ISAME( 2 ) = MS.EQ.M ISAME( 3 ) = NS.EQ.N IF( FULL )THEN ISAME( 4 ) = ALS.EQ.ALPHA ISAME( 5 ) = LZE( AS, AA, LAA ) ISAME( 6 ) = LDAS.EQ.LDA ISAME( 7 ) = LZE( XS, XX, LX ) ISAME( 8 ) = INCXS.EQ.INCX ISAME( 9 ) = BLS.EQ.BETA IF( NULL )THEN ISAME( 10 ) = LZE( YS, YY, LY ) ELSE ISAME( 10 ) = LZERES( 'GE', ' ', 1, $ ML, YS, YY, $ ABS( INCY ) ) END IF ISAME( 11 ) = INCYS.EQ.INCY ELSE IF( BANDED )THEN ISAME( 4 ) = KLS.EQ.KL ISAME( 5 ) = KUS.EQ.KU ISAME( 6 ) = ALS.EQ.ALPHA ISAME( 7 ) = LZE( AS, AA, LAA ) ISAME( 8 ) = LDAS.EQ.LDA ISAME( 9 ) = LZE( XS, XX, LX ) ISAME( 10 ) = INCXS.EQ.INCX ISAME( 11 ) = BLS.EQ.BETA IF( NULL )THEN ISAME( 12 ) = LZE( YS, YY, LY ) ELSE ISAME( 12 ) = LZERES( 'GE', ' ', 1, $ ML, YS, YY, $ ABS( INCY ) ) END IF ISAME( 13 ) = INCYS.EQ.INCY END IF * * If data was incorrectly changed, report * and return. * SAME = .TRUE. DO 40 I = 1, NARGS SAME = SAME.AND.ISAME( I ) IF( .NOT.ISAME( I ) ) $ WRITE( NOUT, FMT = 9998 )I 40 CONTINUE IF( .NOT.SAME )THEN FATAL = .TRUE. GO TO 130 END IF * IF( .NOT.NULL )THEN * * Check the result. * CALL ZMVCH( TRANS, M, N, ALPHA, A, $ NMAX, X, INCX, BETA, Y, $ INCY, YT, G, YY, EPS, ERR, $ FATAL, NOUT, .TRUE. ) ERRMAX = MAX( ERRMAX, ERR ) * If got really bad answer, report and * return. IF( FATAL ) $ GO TO 130 ELSE * Avoid repeating tests with M.le.0 or * N.le.0. GO TO 110 END IF * 50 CONTINUE * 60 CONTINUE * 70 CONTINUE * 80 CONTINUE * 90 CONTINUE * 100 CONTINUE * 110 CONTINUE * 120 CONTINUE * * Report result. * IF( ERRMAX.LT.THRESH )THEN WRITE( NOUT, FMT = 9999 )SNAME, NC ELSE WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX END IF GO TO 140 * 130 CONTINUE WRITE( NOUT, FMT = 9996 )SNAME IF( FULL )THEN WRITE( NOUT, FMT = 9994 )NC, SNAME, TRANS, M, N, ALPHA, LDA, $ INCX, BETA, INCY ELSE IF( BANDED )THEN WRITE( NOUT, FMT = 9995 )NC, SNAME, TRANS, M, N, KL, KU, $ ALPHA, LDA, INCX, BETA, INCY END IF * 140 CONTINUE RETURN * 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL', $ 'S)' ) 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH', $ 'ANGED INCORRECTLY *******' ) 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C', $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2, $ ' - SUSPECT *******' ) 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' ) 9995 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', 4( I3, ',' ), '(', $ F4.1, ',', F4.1, '), A,', I3, ', X,', I2, ',(', F4.1, ',', $ F4.1, '), Y,', I2, ') .' ) 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', 2( I3, ',' ), '(', $ F4.1, ',', F4.1, '), A,', I3, ', X,', I2, ',(', F4.1, ',', $ F4.1, '), Y,', I2, ') .' ) 9993 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *', $ '******' ) * * End of ZCHK1. * END SUBROUTINE ZCHK2( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI, $ FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF, NBET, $ BET, NINC, INC, NMAX, INCMAX, A, AA, AS, X, XX, $ XS, Y, YY, YS, YT, G ) * * Tests ZHEMV, ZHBMV and ZHPMV. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Parameters .. COMPLEX*16 ZERO, HALF PARAMETER ( ZERO = ( 0.0D0, 0.0D0 ), $ HALF = ( 0.5D0, 0.0D0 ) ) DOUBLE PRECISION RZERO PARAMETER ( RZERO = 0.0D0 ) * .. Scalar Arguments .. DOUBLE PRECISION EPS, THRESH INTEGER INCMAX, NALF, NBET, NIDIM, NINC, NKB, NMAX, $ NOUT, NTRA LOGICAL FATAL, REWI, TRACE CHARACTER*6 SNAME * .. Array Arguments .. COMPLEX*16 A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ), $ AS( NMAX*NMAX ), BET( NBET ), X( NMAX ), $ XS( NMAX*INCMAX ), XX( NMAX*INCMAX ), $ Y( NMAX ), YS( NMAX*INCMAX ), YT( NMAX ), $ YY( NMAX*INCMAX ) DOUBLE PRECISION G( NMAX ) INTEGER IDIM( NIDIM ), INC( NINC ), KB( NKB ) * .. Local Scalars .. COMPLEX*16 ALPHA, ALS, BETA, BLS, TRANSL DOUBLE PRECISION ERR, ERRMAX INTEGER I, IA, IB, IC, IK, IN, INCX, INCXS, INCY, $ INCYS, IX, IY, K, KS, LAA, LDA, LDAS, LX, LY, $ N, NARGS, NC, NK, NS LOGICAL BANDED, FULL, NULL, PACKED, RESET, SAME CHARACTER*1 UPLO, UPLOS CHARACTER*2 ICH * .. Local Arrays .. LOGICAL ISAME( 13 ) * .. External Functions .. LOGICAL LZE, LZERES EXTERNAL LZE, LZERES * .. External Subroutines .. EXTERNAL ZHBMV, ZHEMV, ZHPMV, ZMAKE, ZMVCH * .. Intrinsic Functions .. INTRINSIC ABS, MAX * .. Scalars in Common .. INTEGER INFOT, NOUTC LOGICAL LERR, OK * .. Common blocks .. COMMON /INFOC/INFOT, NOUTC, OK, LERR * .. Data statements .. DATA ICH/'UL'/ * .. Executable Statements .. FULL = SNAME( 3: 3 ).EQ.'E' BANDED = SNAME( 3: 3 ).EQ.'B' PACKED = SNAME( 3: 3 ).EQ.'P' * Define the number of arguments. IF( FULL )THEN NARGS = 10 ELSE IF( BANDED )THEN NARGS = 11 ELSE IF( PACKED )THEN NARGS = 9 END IF * NC = 0 RESET = .TRUE. ERRMAX = RZERO * DO 110 IN = 1, NIDIM N = IDIM( IN ) * IF( BANDED )THEN NK = NKB ELSE NK = 1 END IF DO 100 IK = 1, NK IF( BANDED )THEN K = KB( IK ) ELSE K = N - 1 END IF * Set LDA to 1 more than minimum value if room. IF( BANDED )THEN LDA = K + 1 ELSE LDA = N END IF IF( LDA.LT.NMAX ) $ LDA = LDA + 1 * Skip tests if not enough room. IF( LDA.GT.NMAX ) $ GO TO 100 IF( PACKED )THEN LAA = ( N*( N + 1 ) )/2 ELSE LAA = LDA*N END IF NULL = N.LE.0 * DO 90 IC = 1, 2 UPLO = ICH( IC: IC ) * * Generate the matrix A. * TRANSL = ZERO CALL ZMAKE( SNAME( 2: 3 ), UPLO, ' ', N, N, A, NMAX, AA, $ LDA, K, K, RESET, TRANSL ) * DO 80 IX = 1, NINC INCX = INC( IX ) LX = ABS( INCX )*N * * Generate the vector X. * TRANSL = HALF CALL ZMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX, $ ABS( INCX ), 0, N - 1, RESET, TRANSL ) IF( N.GT.1 )THEN X( N/2 ) = ZERO XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO END IF * DO 70 IY = 1, NINC INCY = INC( IY ) LY = ABS( INCY )*N * DO 60 IA = 1, NALF ALPHA = ALF( IA ) * DO 50 IB = 1, NBET BETA = BET( IB ) * * Generate the vector Y. * TRANSL = ZERO CALL ZMAKE( 'GE', ' ', ' ', 1, N, Y, 1, YY, $ ABS( INCY ), 0, N - 1, RESET, $ TRANSL ) * NC = NC + 1 * * Save every datum before calling the * subroutine. * UPLOS = UPLO NS = N KS = K ALS = ALPHA DO 10 I = 1, LAA AS( I ) = AA( I ) 10 CONTINUE LDAS = LDA DO 20 I = 1, LX XS( I ) = XX( I ) 20 CONTINUE INCXS = INCX BLS = BETA DO 30 I = 1, LY YS( I ) = YY( I ) 30 CONTINUE INCYS = INCY * * Call the subroutine. * IF( FULL )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9993 )NC, SNAME, $ UPLO, N, ALPHA, LDA, INCX, BETA, INCY IF( REWI ) $ REWIND NTRA CALL ZHEMV( UPLO, N, ALPHA, AA, LDA, XX, $ INCX, BETA, YY, INCY ) ELSE IF( BANDED )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9994 )NC, SNAME, $ UPLO, N, K, ALPHA, LDA, INCX, BETA, $ INCY IF( REWI ) $ REWIND NTRA CALL ZHBMV( UPLO, N, K, ALPHA, AA, LDA, $ XX, INCX, BETA, YY, INCY ) ELSE IF( PACKED )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9995 )NC, SNAME, $ UPLO, N, ALPHA, INCX, BETA, INCY IF( REWI ) $ REWIND NTRA CALL ZHPMV( UPLO, N, ALPHA, AA, XX, INCX, $ BETA, YY, INCY ) END IF * * Check if error-exit was taken incorrectly. * IF( .NOT.OK )THEN WRITE( NOUT, FMT = 9992 ) FATAL = .TRUE. GO TO 120 END IF * * See what data changed inside subroutines. * ISAME( 1 ) = UPLO.EQ.UPLOS ISAME( 2 ) = NS.EQ.N IF( FULL )THEN ISAME( 3 ) = ALS.EQ.ALPHA ISAME( 4 ) = LZE( AS, AA, LAA ) ISAME( 5 ) = LDAS.EQ.LDA ISAME( 6 ) = LZE( XS, XX, LX ) ISAME( 7 ) = INCXS.EQ.INCX ISAME( 8 ) = BLS.EQ.BETA IF( NULL )THEN ISAME( 9 ) = LZE( YS, YY, LY ) ELSE ISAME( 9 ) = LZERES( 'GE', ' ', 1, N, $ YS, YY, ABS( INCY ) ) END IF ISAME( 10 ) = INCYS.EQ.INCY ELSE IF( BANDED )THEN ISAME( 3 ) = KS.EQ.K ISAME( 4 ) = ALS.EQ.ALPHA ISAME( 5 ) = LZE( AS, AA, LAA ) ISAME( 6 ) = LDAS.EQ.LDA ISAME( 7 ) = LZE( XS, XX, LX ) ISAME( 8 ) = INCXS.EQ.INCX ISAME( 9 ) = BLS.EQ.BETA IF( NULL )THEN ISAME( 10 ) = LZE( YS, YY, LY ) ELSE ISAME( 10 ) = LZERES( 'GE', ' ', 1, N, $ YS, YY, ABS( INCY ) ) END IF ISAME( 11 ) = INCYS.EQ.INCY ELSE IF( PACKED )THEN ISAME( 3 ) = ALS.EQ.ALPHA ISAME( 4 ) = LZE( AS, AA, LAA ) ISAME( 5 ) = LZE( XS, XX, LX ) ISAME( 6 ) = INCXS.EQ.INCX ISAME( 7 ) = BLS.EQ.BETA IF( NULL )THEN ISAME( 8 ) = LZE( YS, YY, LY ) ELSE ISAME( 8 ) = LZERES( 'GE', ' ', 1, N, $ YS, YY, ABS( INCY ) ) END IF ISAME( 9 ) = INCYS.EQ.INCY END IF * * If data was incorrectly changed, report and * return. * SAME = .TRUE. DO 40 I = 1, NARGS SAME = SAME.AND.ISAME( I ) IF( .NOT.ISAME( I ) ) $ WRITE( NOUT, FMT = 9998 )I 40 CONTINUE IF( .NOT.SAME )THEN FATAL = .TRUE. GO TO 120 END IF * IF( .NOT.NULL )THEN * * Check the result. * CALL ZMVCH( 'N', N, N, ALPHA, A, NMAX, X, $ INCX, BETA, Y, INCY, YT, G, $ YY, EPS, ERR, FATAL, NOUT, $ .TRUE. ) ERRMAX = MAX( ERRMAX, ERR ) * If got really bad answer, report and * return. IF( FATAL ) $ GO TO 120 ELSE * Avoid repeating tests with N.le.0 GO TO 110 END IF * 50 CONTINUE * 60 CONTINUE * 70 CONTINUE * 80 CONTINUE * 90 CONTINUE * 100 CONTINUE * 110 CONTINUE * * Report result. * IF( ERRMAX.LT.THRESH )THEN WRITE( NOUT, FMT = 9999 )SNAME, NC ELSE WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX END IF GO TO 130 * 120 CONTINUE WRITE( NOUT, FMT = 9996 )SNAME IF( FULL )THEN WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, N, ALPHA, LDA, INCX, $ BETA, INCY ELSE IF( BANDED )THEN WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, N, K, ALPHA, LDA, $ INCX, BETA, INCY ELSE IF( PACKED )THEN WRITE( NOUT, FMT = 9995 )NC, SNAME, UPLO, N, ALPHA, INCX, $ BETA, INCY END IF * 130 CONTINUE RETURN * 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL', $ 'S)' ) 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH', $ 'ANGED INCORRECTLY *******' ) 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C', $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2, $ ' - SUSPECT *******' ) 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' ) 9995 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',(', F4.1, ',', $ F4.1, '), AP, X,', I2, ',(', F4.1, ',', F4.1, '), Y,', I2, $ ') .' ) 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', 2( I3, ',' ), '(', $ F4.1, ',', F4.1, '), A,', I3, ', X,', I2, ',(', F4.1, ',', $ F4.1, '), Y,', I2, ') .' ) 9993 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',(', F4.1, ',', $ F4.1, '), A,', I3, ', X,', I2, ',(', F4.1, ',', F4.1, '), ', $ 'Y,', I2, ') .' ) 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *', $ '******' ) * * End of ZCHK2. * END SUBROUTINE ZCHK3( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI, $ FATAL, NIDIM, IDIM, NKB, KB, NINC, INC, NMAX, $ INCMAX, A, AA, AS, X, XX, XS, XT, G, Z ) * * Tests ZTRMV, ZTBMV, ZTPMV, ZTRSV, ZTBSV and ZTPSV. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Parameters .. COMPLEX*16 ZERO, HALF, ONE PARAMETER ( ZERO = ( 0.0D0, 0.0D0 ), $ HALF = ( 0.5D0, 0.0D0 ), $ ONE = ( 1.0D0, 0.0D0 ) ) DOUBLE PRECISION RZERO PARAMETER ( RZERO = 0.0D0 ) * .. Scalar Arguments .. DOUBLE PRECISION EPS, THRESH INTEGER INCMAX, NIDIM, NINC, NKB, NMAX, NOUT, NTRA LOGICAL FATAL, REWI, TRACE CHARACTER*6 SNAME * .. Array Arguments .. COMPLEX*16 A( NMAX, NMAX ), AA( NMAX*NMAX ), $ AS( NMAX*NMAX ), X( NMAX ), XS( NMAX*INCMAX ), $ XT( NMAX ), XX( NMAX*INCMAX ), Z( NMAX ) DOUBLE PRECISION G( NMAX ) INTEGER IDIM( NIDIM ), INC( NINC ), KB( NKB ) * .. Local Scalars .. COMPLEX*16 TRANSL DOUBLE PRECISION ERR, ERRMAX INTEGER I, ICD, ICT, ICU, IK, IN, INCX, INCXS, IX, K, $ KS, LAA, LDA, LDAS, LX, N, NARGS, NC, NK, NS LOGICAL BANDED, FULL, NULL, PACKED, RESET, SAME CHARACTER*1 DIAG, DIAGS, TRANS, TRANSS, UPLO, UPLOS CHARACTER*2 ICHD, ICHU CHARACTER*3 ICHT * .. Local Arrays .. LOGICAL ISAME( 13 ) * .. External Functions .. LOGICAL LZE, LZERES EXTERNAL LZE, LZERES * .. External Subroutines .. EXTERNAL ZMAKE, ZMVCH, ZTBMV, ZTBSV, ZTPMV, ZTPSV, $ ZTRMV, ZTRSV * .. Intrinsic Functions .. INTRINSIC ABS, MAX * .. Scalars in Common .. INTEGER INFOT, NOUTC LOGICAL LERR, OK * .. Common blocks .. COMMON /INFOC/INFOT, NOUTC, OK, LERR * .. Data statements .. DATA ICHU/'UL'/, ICHT/'NTC'/, ICHD/'UN'/ * .. Executable Statements .. FULL = SNAME( 3: 3 ).EQ.'R' BANDED = SNAME( 3: 3 ).EQ.'B' PACKED = SNAME( 3: 3 ).EQ.'P' * Define the number of arguments. IF( FULL )THEN NARGS = 8 ELSE IF( BANDED )THEN NARGS = 9 ELSE IF( PACKED )THEN NARGS = 7 END IF * NC = 0 RESET = .TRUE. ERRMAX = RZERO * Set up zero vector for ZMVCH. DO 10 I = 1, NMAX Z( I ) = ZERO 10 CONTINUE * DO 110 IN = 1, NIDIM N = IDIM( IN ) * IF( BANDED )THEN NK = NKB ELSE NK = 1 END IF DO 100 IK = 1, NK IF( BANDED )THEN K = KB( IK ) ELSE K = N - 1 END IF * Set LDA to 1 more than minimum value if room. IF( BANDED )THEN LDA = K + 1 ELSE LDA = N END IF IF( LDA.LT.NMAX ) $ LDA = LDA + 1 * Skip tests if not enough room. IF( LDA.GT.NMAX ) $ GO TO 100 IF( PACKED )THEN LAA = ( N*( N + 1 ) )/2 ELSE LAA = LDA*N END IF NULL = N.LE.0 * DO 90 ICU = 1, 2 UPLO = ICHU( ICU: ICU ) * DO 80 ICT = 1, 3 TRANS = ICHT( ICT: ICT ) * DO 70 ICD = 1, 2 DIAG = ICHD( ICD: ICD ) * * Generate the matrix A. * TRANSL = ZERO CALL ZMAKE( SNAME( 2: 3 ), UPLO, DIAG, N, N, A, $ NMAX, AA, LDA, K, K, RESET, TRANSL ) * DO 60 IX = 1, NINC INCX = INC( IX ) LX = ABS( INCX )*N * * Generate the vector X. * TRANSL = HALF CALL ZMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX, $ ABS( INCX ), 0, N - 1, RESET, $ TRANSL ) IF( N.GT.1 )THEN X( N/2 ) = ZERO XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO END IF * NC = NC + 1 * * Save every datum before calling the subroutine. * UPLOS = UPLO TRANSS = TRANS DIAGS = DIAG NS = N KS = K DO 20 I = 1, LAA AS( I ) = AA( I ) 20 CONTINUE LDAS = LDA DO 30 I = 1, LX XS( I ) = XX( I ) 30 CONTINUE INCXS = INCX * * Call the subroutine. * IF( SNAME( 4: 5 ).EQ.'MV' )THEN IF( FULL )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9993 )NC, SNAME, $ UPLO, TRANS, DIAG, N, LDA, INCX IF( REWI ) $ REWIND NTRA CALL ZTRMV( UPLO, TRANS, DIAG, N, AA, LDA, $ XX, INCX ) ELSE IF( BANDED )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9994 )NC, SNAME, $ UPLO, TRANS, DIAG, N, K, LDA, INCX IF( REWI ) $ REWIND NTRA CALL ZTBMV( UPLO, TRANS, DIAG, N, K, AA, $ LDA, XX, INCX ) ELSE IF( PACKED )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9995 )NC, SNAME, $ UPLO, TRANS, DIAG, N, INCX IF( REWI ) $ REWIND NTRA CALL ZTPMV( UPLO, TRANS, DIAG, N, AA, XX, $ INCX ) END IF ELSE IF( SNAME( 4: 5 ).EQ.'SV' )THEN IF( FULL )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9993 )NC, SNAME, $ UPLO, TRANS, DIAG, N, LDA, INCX IF( REWI ) $ REWIND NTRA CALL ZTRSV( UPLO, TRANS, DIAG, N, AA, LDA, $ XX, INCX ) ELSE IF( BANDED )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9994 )NC, SNAME, $ UPLO, TRANS, DIAG, N, K, LDA, INCX IF( REWI ) $ REWIND NTRA CALL ZTBSV( UPLO, TRANS, DIAG, N, K, AA, $ LDA, XX, INCX ) ELSE IF( PACKED )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9995 )NC, SNAME, $ UPLO, TRANS, DIAG, N, INCX IF( REWI ) $ REWIND NTRA CALL ZTPSV( UPLO, TRANS, DIAG, N, AA, XX, $ INCX ) END IF END IF * * Check if error-exit was taken incorrectly. * IF( .NOT.OK )THEN WRITE( NOUT, FMT = 9992 ) FATAL = .TRUE. GO TO 120 END IF * * See what data changed inside subroutines. * ISAME( 1 ) = UPLO.EQ.UPLOS ISAME( 2 ) = TRANS.EQ.TRANSS ISAME( 3 ) = DIAG.EQ.DIAGS ISAME( 4 ) = NS.EQ.N IF( FULL )THEN ISAME( 5 ) = LZE( AS, AA, LAA ) ISAME( 6 ) = LDAS.EQ.LDA IF( NULL )THEN ISAME( 7 ) = LZE( XS, XX, LX ) ELSE ISAME( 7 ) = LZERES( 'GE', ' ', 1, N, XS, $ XX, ABS( INCX ) ) END IF ISAME( 8 ) = INCXS.EQ.INCX ELSE IF( BANDED )THEN ISAME( 5 ) = KS.EQ.K ISAME( 6 ) = LZE( AS, AA, LAA ) ISAME( 7 ) = LDAS.EQ.LDA IF( NULL )THEN ISAME( 8 ) = LZE( XS, XX, LX ) ELSE ISAME( 8 ) = LZERES( 'GE', ' ', 1, N, XS, $ XX, ABS( INCX ) ) END IF ISAME( 9 ) = INCXS.EQ.INCX ELSE IF( PACKED )THEN ISAME( 5 ) = LZE( AS, AA, LAA ) IF( NULL )THEN ISAME( 6 ) = LZE( XS, XX, LX ) ELSE ISAME( 6 ) = LZERES( 'GE', ' ', 1, N, XS, $ XX, ABS( INCX ) ) END IF ISAME( 7 ) = INCXS.EQ.INCX END IF * * If data was incorrectly changed, report and * return. * SAME = .TRUE. DO 40 I = 1, NARGS SAME = SAME.AND.ISAME( I ) IF( .NOT.ISAME( I ) ) $ WRITE( NOUT, FMT = 9998 )I 40 CONTINUE IF( .NOT.SAME )THEN FATAL = .TRUE. GO TO 120 END IF * IF( .NOT.NULL )THEN IF( SNAME( 4: 5 ).EQ.'MV' )THEN * * Check the result. * CALL ZMVCH( TRANS, N, N, ONE, A, NMAX, X, $ INCX, ZERO, Z, INCX, XT, G, $ XX, EPS, ERR, FATAL, NOUT, $ .TRUE. ) ELSE IF( SNAME( 4: 5 ).EQ.'SV' )THEN * * Compute approximation to original vector. * DO 50 I = 1, N Z( I ) = XX( 1 + ( I - 1 )* $ ABS( INCX ) ) XX( 1 + ( I - 1 )*ABS( INCX ) ) $ = X( I ) 50 CONTINUE CALL ZMVCH( TRANS, N, N, ONE, A, NMAX, Z, $ INCX, ZERO, X, INCX, XT, G, $ XX, EPS, ERR, FATAL, NOUT, $ .FALSE. ) END IF ERRMAX = MAX( ERRMAX, ERR ) * If got really bad answer, report and return. IF( FATAL ) $ GO TO 120 ELSE * Avoid repeating tests with N.le.0. GO TO 110 END IF * 60 CONTINUE * 70 CONTINUE * 80 CONTINUE * 90 CONTINUE * 100 CONTINUE * 110 CONTINUE * * Report result. * IF( ERRMAX.LT.THRESH )THEN WRITE( NOUT, FMT = 9999 )SNAME, NC ELSE WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX END IF GO TO 130 * 120 CONTINUE WRITE( NOUT, FMT = 9996 )SNAME IF( FULL )THEN WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, TRANS, DIAG, N, LDA, $ INCX ELSE IF( BANDED )THEN WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, TRANS, DIAG, N, K, $ LDA, INCX ELSE IF( PACKED )THEN WRITE( NOUT, FMT = 9995 )NC, SNAME, UPLO, TRANS, DIAG, N, INCX END IF * 130 CONTINUE RETURN * 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL', $ 'S)' ) 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH', $ 'ANGED INCORRECTLY *******' ) 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C', $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2, $ ' - SUSPECT *******' ) 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' ) 9995 FORMAT( 1X, I6, ': ', A6, '(', 3( '''', A1, ''',' ), I3, ', AP, ', $ 'X,', I2, ') .' ) 9994 FORMAT( 1X, I6, ': ', A6, '(', 3( '''', A1, ''',' ), 2( I3, ',' ), $ ' A,', I3, ', X,', I2, ') .' ) 9993 FORMAT( 1X, I6, ': ', A6, '(', 3( '''', A1, ''',' ), I3, ', A,', $ I3, ', X,', I2, ') .' ) 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *', $ '******' ) * * End of ZCHK3. * END SUBROUTINE ZCHK4( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI, $ FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, NMAX, $ INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, YT, G, $ Z ) * * Tests ZGERC and ZGERU. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Parameters .. COMPLEX*16 ZERO, HALF, ONE PARAMETER ( ZERO = ( 0.0D0, 0.0D0 ), $ HALF = ( 0.5D0, 0.0D0 ), $ ONE = ( 1.0D0, 0.0D0 ) ) DOUBLE PRECISION RZERO PARAMETER ( RZERO = 0.0D0 ) * .. Scalar Arguments .. DOUBLE PRECISION EPS, THRESH INTEGER INCMAX, NALF, NIDIM, NINC, NMAX, NOUT, NTRA LOGICAL FATAL, REWI, TRACE CHARACTER*6 SNAME * .. Array Arguments .. COMPLEX*16 A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ), $ AS( NMAX*NMAX ), X( NMAX ), XS( NMAX*INCMAX ), $ XX( NMAX*INCMAX ), Y( NMAX ), $ YS( NMAX*INCMAX ), YT( NMAX ), $ YY( NMAX*INCMAX ), Z( NMAX ) DOUBLE PRECISION G( NMAX ) INTEGER IDIM( NIDIM ), INC( NINC ) * .. Local Scalars .. COMPLEX*16 ALPHA, ALS, TRANSL DOUBLE PRECISION ERR, ERRMAX INTEGER I, IA, IM, IN, INCX, INCXS, INCY, INCYS, IX, $ IY, J, LAA, LDA, LDAS, LX, LY, M, MS, N, NARGS, $ NC, ND, NS LOGICAL CONJ, NULL, RESET, SAME * .. Local Arrays .. COMPLEX*16 W( 1 ) LOGICAL ISAME( 13 ) * .. External Functions .. LOGICAL LZE, LZERES EXTERNAL LZE, LZERES * .. External Subroutines .. EXTERNAL ZGERC, ZGERU, ZMAKE, ZMVCH * .. Intrinsic Functions .. INTRINSIC ABS, DCONJG, MAX, MIN * .. Scalars in Common .. INTEGER INFOT, NOUTC LOGICAL LERR, OK * .. Common blocks .. COMMON /INFOC/INFOT, NOUTC, OK, LERR * .. Executable Statements .. CONJ = SNAME( 5: 5 ).EQ.'C' * Define the number of arguments. NARGS = 9 * NC = 0 RESET = .TRUE. ERRMAX = RZERO * DO 120 IN = 1, NIDIM N = IDIM( IN ) ND = N/2 + 1 * DO 110 IM = 1, 2 IF( IM.EQ.1 ) $ M = MAX( N - ND, 0 ) IF( IM.EQ.2 ) $ M = MIN( N + ND, NMAX ) * * Set LDA to 1 more than minimum value if room. LDA = M IF( LDA.LT.NMAX ) $ LDA = LDA + 1 * Skip tests if not enough room. IF( LDA.GT.NMAX ) $ GO TO 110 LAA = LDA*N NULL = N.LE.0.OR.M.LE.0 * DO 100 IX = 1, NINC INCX = INC( IX ) LX = ABS( INCX )*M * * Generate the vector X. * TRANSL = HALF CALL ZMAKE( 'GE', ' ', ' ', 1, M, X, 1, XX, ABS( INCX ), $ 0, M - 1, RESET, TRANSL ) IF( M.GT.1 )THEN X( M/2 ) = ZERO XX( 1 + ABS( INCX )*( M/2 - 1 ) ) = ZERO END IF * DO 90 IY = 1, NINC INCY = INC( IY ) LY = ABS( INCY )*N * * Generate the vector Y. * TRANSL = ZERO CALL ZMAKE( 'GE', ' ', ' ', 1, N, Y, 1, YY, $ ABS( INCY ), 0, N - 1, RESET, TRANSL ) IF( N.GT.1 )THEN Y( N/2 ) = ZERO YY( 1 + ABS( INCY )*( N/2 - 1 ) ) = ZERO END IF * DO 80 IA = 1, NALF ALPHA = ALF( IA ) * * Generate the matrix A. * TRANSL = ZERO CALL ZMAKE( SNAME( 2: 3 ), ' ', ' ', M, N, A, NMAX, $ AA, LDA, M - 1, N - 1, RESET, TRANSL ) * NC = NC + 1 * * Save every datum before calling the subroutine. * MS = M NS = N ALS = ALPHA DO 10 I = 1, LAA AS( I ) = AA( I ) 10 CONTINUE LDAS = LDA DO 20 I = 1, LX XS( I ) = XX( I ) 20 CONTINUE INCXS = INCX DO 30 I = 1, LY YS( I ) = YY( I ) 30 CONTINUE INCYS = INCY * * Call the subroutine. * IF( TRACE ) $ WRITE( NTRA, FMT = 9994 )NC, SNAME, M, N, $ ALPHA, INCX, INCY, LDA IF( CONJ )THEN IF( REWI ) $ REWIND NTRA CALL ZGERC( M, N, ALPHA, XX, INCX, YY, INCY, AA, $ LDA ) ELSE IF( REWI ) $ REWIND NTRA CALL ZGERU( M, N, ALPHA, XX, INCX, YY, INCY, AA, $ LDA ) END IF * * Check if error-exit was taken incorrectly. * IF( .NOT.OK )THEN WRITE( NOUT, FMT = 9993 ) FATAL = .TRUE. GO TO 140 END IF * * See what data changed inside subroutine. * ISAME( 1 ) = MS.EQ.M ISAME( 2 ) = NS.EQ.N ISAME( 3 ) = ALS.EQ.ALPHA ISAME( 4 ) = LZE( XS, XX, LX ) ISAME( 5 ) = INCXS.EQ.INCX ISAME( 6 ) = LZE( YS, YY, LY ) ISAME( 7 ) = INCYS.EQ.INCY IF( NULL )THEN ISAME( 8 ) = LZE( AS, AA, LAA ) ELSE ISAME( 8 ) = LZERES( 'GE', ' ', M, N, AS, AA, $ LDA ) END IF ISAME( 9 ) = LDAS.EQ.LDA * * If data was incorrectly changed, report and return. * SAME = .TRUE. DO 40 I = 1, NARGS SAME = SAME.AND.ISAME( I ) IF( .NOT.ISAME( I ) ) $ WRITE( NOUT, FMT = 9998 )I 40 CONTINUE IF( .NOT.SAME )THEN FATAL = .TRUE. GO TO 140 END IF * IF( .NOT.NULL )THEN * * Check the result column by column. * IF( INCX.GT.0 )THEN DO 50 I = 1, M Z( I ) = X( I ) 50 CONTINUE ELSE DO 60 I = 1, M Z( I ) = X( M - I + 1 ) 60 CONTINUE END IF DO 70 J = 1, N IF( INCY.GT.0 )THEN W( 1 ) = Y( J ) ELSE W( 1 ) = Y( N - J + 1 ) END IF IF( CONJ ) $ W( 1 ) = DCONJG( W( 1 ) ) CALL ZMVCH( 'N', M, 1, ALPHA, Z, NMAX, W, 1, $ ONE, A( 1, J ), 1, YT, G, $ AA( 1 + ( J - 1 )*LDA ), EPS, $ ERR, FATAL, NOUT, .TRUE. ) ERRMAX = MAX( ERRMAX, ERR ) * If got really bad answer, report and return. IF( FATAL ) $ GO TO 130 70 CONTINUE ELSE * Avoid repeating tests with M.le.0 or N.le.0. GO TO 110 END IF * 80 CONTINUE * 90 CONTINUE * 100 CONTINUE * 110 CONTINUE * 120 CONTINUE * * Report result. * IF( ERRMAX.LT.THRESH )THEN WRITE( NOUT, FMT = 9999 )SNAME, NC ELSE WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX END IF GO TO 150 * 130 CONTINUE WRITE( NOUT, FMT = 9995 )J * 140 CONTINUE WRITE( NOUT, FMT = 9996 )SNAME WRITE( NOUT, FMT = 9994 )NC, SNAME, M, N, ALPHA, INCX, INCY, LDA * 150 CONTINUE RETURN * 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL', $ 'S)' ) 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH', $ 'ANGED INCORRECTLY *******' ) 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C', $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2, $ ' - SUSPECT *******' ) 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' ) 9995 FORMAT( ' THESE ARE THE RESULTS FOR COLUMN ', I3 ) 9994 FORMAT( 1X, I6, ': ', A6, '(', 2( I3, ',' ), '(', F4.1, ',', F4.1, $ '), X,', I2, ', Y,', I2, ', A,', I3, ') ', $ ' .' ) 9993 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *', $ '******' ) * * End of ZCHK4. * END SUBROUTINE ZCHK5( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI, $ FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, NMAX, $ INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, YT, G, $ Z ) * * Tests ZHER and ZHPR. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Parameters .. COMPLEX*16 ZERO, HALF, ONE PARAMETER ( ZERO = ( 0.0D0, 0.0D0 ), $ HALF = ( 0.5D0, 0.0D0 ), $ ONE = ( 1.0D0, 0.0D0 ) ) DOUBLE PRECISION RZERO PARAMETER ( RZERO = 0.0D0 ) * .. Scalar Arguments .. DOUBLE PRECISION EPS, THRESH INTEGER INCMAX, NALF, NIDIM, NINC, NMAX, NOUT, NTRA LOGICAL FATAL, REWI, TRACE CHARACTER*6 SNAME * .. Array Arguments .. COMPLEX*16 A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ), $ AS( NMAX*NMAX ), X( NMAX ), XS( NMAX*INCMAX ), $ XX( NMAX*INCMAX ), Y( NMAX ), $ YS( NMAX*INCMAX ), YT( NMAX ), $ YY( NMAX*INCMAX ), Z( NMAX ) DOUBLE PRECISION G( NMAX ) INTEGER IDIM( NIDIM ), INC( NINC ) * .. Local Scalars .. COMPLEX*16 ALPHA, TRANSL DOUBLE PRECISION ERR, ERRMAX, RALPHA, RALS INTEGER I, IA, IC, IN, INCX, INCXS, IX, J, JA, JJ, LAA, $ LDA, LDAS, LJ, LX, N, NARGS, NC, NS LOGICAL FULL, NULL, PACKED, RESET, SAME, UPPER CHARACTER*1 UPLO, UPLOS CHARACTER*2 ICH * .. Local Arrays .. COMPLEX*16 W( 1 ) LOGICAL ISAME( 13 ) * .. External Functions .. LOGICAL LZE, LZERES EXTERNAL LZE, LZERES * .. External Subroutines .. EXTERNAL ZHER, ZHPR, ZMAKE, ZMVCH * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, DCMPLX, DCONJG, MAX * .. Scalars in Common .. INTEGER INFOT, NOUTC LOGICAL LERR, OK * .. Common blocks .. COMMON /INFOC/INFOT, NOUTC, OK, LERR * .. Data statements .. DATA ICH/'UL'/ * .. Executable Statements .. FULL = SNAME( 3: 3 ).EQ.'E' PACKED = SNAME( 3: 3 ).EQ.'P' * Define the number of arguments. IF( FULL )THEN NARGS = 7 ELSE IF( PACKED )THEN NARGS = 6 END IF * NC = 0 RESET = .TRUE. ERRMAX = RZERO * DO 100 IN = 1, NIDIM N = IDIM( IN ) * Set LDA to 1 more than minimum value if room. LDA = N IF( LDA.LT.NMAX ) $ LDA = LDA + 1 * Skip tests if not enough room. IF( LDA.GT.NMAX ) $ GO TO 100 IF( PACKED )THEN LAA = ( N*( N + 1 ) )/2 ELSE LAA = LDA*N END IF * DO 90 IC = 1, 2 UPLO = ICH( IC: IC ) UPPER = UPLO.EQ.'U' * DO 80 IX = 1, NINC INCX = INC( IX ) LX = ABS( INCX )*N * * Generate the vector X. * TRANSL = HALF CALL ZMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX, ABS( INCX ), $ 0, N - 1, RESET, TRANSL ) IF( N.GT.1 )THEN X( N/2 ) = ZERO XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO END IF * DO 70 IA = 1, NALF RALPHA = DBLE( ALF( IA ) ) ALPHA = DCMPLX( RALPHA, RZERO ) NULL = N.LE.0.OR.RALPHA.EQ.RZERO * * Generate the matrix A. * TRANSL = ZERO CALL ZMAKE( SNAME( 2: 3 ), UPLO, ' ', N, N, A, NMAX, $ AA, LDA, N - 1, N - 1, RESET, TRANSL ) * NC = NC + 1 * * Save every datum before calling the subroutine. * UPLOS = UPLO NS = N RALS = RALPHA DO 10 I = 1, LAA AS( I ) = AA( I ) 10 CONTINUE LDAS = LDA DO 20 I = 1, LX XS( I ) = XX( I ) 20 CONTINUE INCXS = INCX * * Call the subroutine. * IF( FULL )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9993 )NC, SNAME, UPLO, N, $ RALPHA, INCX, LDA IF( REWI ) $ REWIND NTRA CALL ZHER( UPLO, N, RALPHA, XX, INCX, AA, LDA ) ELSE IF( PACKED )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9994 )NC, SNAME, UPLO, N, $ RALPHA, INCX IF( REWI ) $ REWIND NTRA CALL ZHPR( UPLO, N, RALPHA, XX, INCX, AA ) END IF * * Check if error-exit was taken incorrectly. * IF( .NOT.OK )THEN WRITE( NOUT, FMT = 9992 ) FATAL = .TRUE. GO TO 120 END IF * * See what data changed inside subroutines. * ISAME( 1 ) = UPLO.EQ.UPLOS ISAME( 2 ) = NS.EQ.N ISAME( 3 ) = RALS.EQ.RALPHA ISAME( 4 ) = LZE( XS, XX, LX ) ISAME( 5 ) = INCXS.EQ.INCX IF( NULL )THEN ISAME( 6 ) = LZE( AS, AA, LAA ) ELSE ISAME( 6 ) = LZERES( SNAME( 2: 3 ), UPLO, N, N, AS, $ AA, LDA ) END IF IF( .NOT.PACKED )THEN ISAME( 7 ) = LDAS.EQ.LDA END IF * * If data was incorrectly changed, report and return. * SAME = .TRUE. DO 30 I = 1, NARGS SAME = SAME.AND.ISAME( I ) IF( .NOT.ISAME( I ) ) $ WRITE( NOUT, FMT = 9998 )I 30 CONTINUE IF( .NOT.SAME )THEN FATAL = .TRUE. GO TO 120 END IF * IF( .NOT.NULL )THEN * * Check the result column by column. * IF( INCX.GT.0 )THEN DO 40 I = 1, N Z( I ) = X( I ) 40 CONTINUE ELSE DO 50 I = 1, N Z( I ) = X( N - I + 1 ) 50 CONTINUE END IF JA = 1 DO 60 J = 1, N W( 1 ) = DCONJG( Z( J ) ) IF( UPPER )THEN JJ = 1 LJ = J ELSE JJ = J LJ = N - J + 1 END IF CALL ZMVCH( 'N', LJ, 1, ALPHA, Z( JJ ), LJ, W, $ 1, ONE, A( JJ, J ), 1, YT, G, $ AA( JA ), EPS, ERR, FATAL, NOUT, $ .TRUE. ) IF( FULL )THEN IF( UPPER )THEN JA = JA + LDA ELSE JA = JA + LDA + 1 END IF ELSE JA = JA + LJ END IF ERRMAX = MAX( ERRMAX, ERR ) * If got really bad answer, report and return. IF( FATAL ) $ GO TO 110 60 CONTINUE ELSE * Avoid repeating tests if N.le.0. IF( N.LE.0 ) $ GO TO 100 END IF * 70 CONTINUE * 80 CONTINUE * 90 CONTINUE * 100 CONTINUE * * Report result. * IF( ERRMAX.LT.THRESH )THEN WRITE( NOUT, FMT = 9999 )SNAME, NC ELSE WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX END IF GO TO 130 * 110 CONTINUE WRITE( NOUT, FMT = 9995 )J * 120 CONTINUE WRITE( NOUT, FMT = 9996 )SNAME IF( FULL )THEN WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, N, RALPHA, INCX, LDA ELSE IF( PACKED )THEN WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, N, RALPHA, INCX END IF * 130 CONTINUE RETURN * 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL', $ 'S)' ) 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH', $ 'ANGED INCORRECTLY *******' ) 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C', $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2, $ ' - SUSPECT *******' ) 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' ) 9995 FORMAT( ' THESE ARE THE RESULTS FOR COLUMN ', I3 ) 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', X,', $ I2, ', AP) .' ) 9993 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', X,', $ I2, ', A,', I3, ') .' ) 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *', $ '******' ) * * End of ZCHK5. * END SUBROUTINE ZCHK6( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI, $ FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, NMAX, $ INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, YT, G, $ Z ) * * Tests ZHER2 and ZHPR2. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Parameters .. COMPLEX*16 ZERO, HALF, ONE PARAMETER ( ZERO = ( 0.0D0, 0.0D0 ), $ HALF = ( 0.5D0, 0.0D0 ), $ ONE = ( 1.0D0, 0.0D0 ) ) DOUBLE PRECISION RZERO PARAMETER ( RZERO = 0.0D0 ) * .. Scalar Arguments .. DOUBLE PRECISION EPS, THRESH INTEGER INCMAX, NALF, NIDIM, NINC, NMAX, NOUT, NTRA LOGICAL FATAL, REWI, TRACE CHARACTER*6 SNAME * .. Array Arguments .. COMPLEX*16 A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ), $ AS( NMAX*NMAX ), X( NMAX ), XS( NMAX*INCMAX ), $ XX( NMAX*INCMAX ), Y( NMAX ), $ YS( NMAX*INCMAX ), YT( NMAX ), $ YY( NMAX*INCMAX ), Z( NMAX, 2 ) DOUBLE PRECISION G( NMAX ) INTEGER IDIM( NIDIM ), INC( NINC ) * .. Local Scalars .. COMPLEX*16 ALPHA, ALS, TRANSL DOUBLE PRECISION ERR, ERRMAX INTEGER I, IA, IC, IN, INCX, INCXS, INCY, INCYS, IX, $ IY, J, JA, JJ, LAA, LDA, LDAS, LJ, LX, LY, N, $ NARGS, NC, NS LOGICAL FULL, NULL, PACKED, RESET, SAME, UPPER CHARACTER*1 UPLO, UPLOS CHARACTER*2 ICH * .. Local Arrays .. COMPLEX*16 W( 2 ) LOGICAL ISAME( 13 ) * .. External Functions .. LOGICAL LZE, LZERES EXTERNAL LZE, LZERES * .. External Subroutines .. EXTERNAL ZHER2, ZHPR2, ZMAKE, ZMVCH * .. Intrinsic Functions .. INTRINSIC ABS, DCONJG, MAX * .. Scalars in Common .. INTEGER INFOT, NOUTC LOGICAL LERR, OK * .. Common blocks .. COMMON /INFOC/INFOT, NOUTC, OK, LERR * .. Data statements .. DATA ICH/'UL'/ * .. Executable Statements .. FULL = SNAME( 3: 3 ).EQ.'E' PACKED = SNAME( 3: 3 ).EQ.'P' * Define the number of arguments. IF( FULL )THEN NARGS = 9 ELSE IF( PACKED )THEN NARGS = 8 END IF * NC = 0 RESET = .TRUE. ERRMAX = RZERO * DO 140 IN = 1, NIDIM N = IDIM( IN ) * Set LDA to 1 more than minimum value if room. LDA = N IF( LDA.LT.NMAX ) $ LDA = LDA + 1 * Skip tests if not enough room. IF( LDA.GT.NMAX ) $ GO TO 140 IF( PACKED )THEN LAA = ( N*( N + 1 ) )/2 ELSE LAA = LDA*N END IF * DO 130 IC = 1, 2 UPLO = ICH( IC: IC ) UPPER = UPLO.EQ.'U' * DO 120 IX = 1, NINC INCX = INC( IX ) LX = ABS( INCX )*N * * Generate the vector X. * TRANSL = HALF CALL ZMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX, ABS( INCX ), $ 0, N - 1, RESET, TRANSL ) IF( N.GT.1 )THEN X( N/2 ) = ZERO XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO END IF * DO 110 IY = 1, NINC INCY = INC( IY ) LY = ABS( INCY )*N * * Generate the vector Y. * TRANSL = ZERO CALL ZMAKE( 'GE', ' ', ' ', 1, N, Y, 1, YY, $ ABS( INCY ), 0, N - 1, RESET, TRANSL ) IF( N.GT.1 )THEN Y( N/2 ) = ZERO YY( 1 + ABS( INCY )*( N/2 - 1 ) ) = ZERO END IF * DO 100 IA = 1, NALF ALPHA = ALF( IA ) NULL = N.LE.0.OR.ALPHA.EQ.ZERO * * Generate the matrix A. * TRANSL = ZERO CALL ZMAKE( SNAME( 2: 3 ), UPLO, ' ', N, N, A, $ NMAX, AA, LDA, N - 1, N - 1, RESET, $ TRANSL ) * NC = NC + 1 * * Save every datum before calling the subroutine. * UPLOS = UPLO NS = N ALS = ALPHA DO 10 I = 1, LAA AS( I ) = AA( I ) 10 CONTINUE LDAS = LDA DO 20 I = 1, LX XS( I ) = XX( I ) 20 CONTINUE INCXS = INCX DO 30 I = 1, LY YS( I ) = YY( I ) 30 CONTINUE INCYS = INCY * * Call the subroutine. * IF( FULL )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9993 )NC, SNAME, UPLO, N, $ ALPHA, INCX, INCY, LDA IF( REWI ) $ REWIND NTRA CALL ZHER2( UPLO, N, ALPHA, XX, INCX, YY, INCY, $ AA, LDA ) ELSE IF( PACKED )THEN IF( TRACE ) $ WRITE( NTRA, FMT = 9994 )NC, SNAME, UPLO, N, $ ALPHA, INCX, INCY IF( REWI ) $ REWIND NTRA CALL ZHPR2( UPLO, N, ALPHA, XX, INCX, YY, INCY, $ AA ) END IF * * Check if error-exit was taken incorrectly. * IF( .NOT.OK )THEN WRITE( NOUT, FMT = 9992 ) FATAL = .TRUE. GO TO 160 END IF * * See what data changed inside subroutines. * ISAME( 1 ) = UPLO.EQ.UPLOS ISAME( 2 ) = NS.EQ.N ISAME( 3 ) = ALS.EQ.ALPHA ISAME( 4 ) = LZE( XS, XX, LX ) ISAME( 5 ) = INCXS.EQ.INCX ISAME( 6 ) = LZE( YS, YY, LY ) ISAME( 7 ) = INCYS.EQ.INCY IF( NULL )THEN ISAME( 8 ) = LZE( AS, AA, LAA ) ELSE ISAME( 8 ) = LZERES( SNAME( 2: 3 ), UPLO, N, N, $ AS, AA, LDA ) END IF IF( .NOT.PACKED )THEN ISAME( 9 ) = LDAS.EQ.LDA END IF * * If data was incorrectly changed, report and return. * SAME = .TRUE. DO 40 I = 1, NARGS SAME = SAME.AND.ISAME( I ) IF( .NOT.ISAME( I ) ) $ WRITE( NOUT, FMT = 9998 )I 40 CONTINUE IF( .NOT.SAME )THEN FATAL = .TRUE. GO TO 160 END IF * IF( .NOT.NULL )THEN * * Check the result column by column. * IF( INCX.GT.0 )THEN DO 50 I = 1, N Z( I, 1 ) = X( I ) 50 CONTINUE ELSE DO 60 I = 1, N Z( I, 1 ) = X( N - I + 1 ) 60 CONTINUE END IF IF( INCY.GT.0 )THEN DO 70 I = 1, N Z( I, 2 ) = Y( I ) 70 CONTINUE ELSE DO 80 I = 1, N Z( I, 2 ) = Y( N - I + 1 ) 80 CONTINUE END IF JA = 1 DO 90 J = 1, N W( 1 ) = ALPHA*DCONJG( Z( J, 2 ) ) W( 2 ) = DCONJG( ALPHA )*DCONJG( Z( J, 1 ) ) IF( UPPER )THEN JJ = 1 LJ = J ELSE JJ = J LJ = N - J + 1 END IF CALL ZMVCH( 'N', LJ, 2, ONE, Z( JJ, 1 ), $ NMAX, W, 1, ONE, A( JJ, J ), 1, $ YT, G, AA( JA ), EPS, ERR, FATAL, $ NOUT, .TRUE. ) IF( FULL )THEN IF( UPPER )THEN JA = JA + LDA ELSE JA = JA + LDA + 1 END IF ELSE JA = JA + LJ END IF ERRMAX = MAX( ERRMAX, ERR ) * If got really bad answer, report and return. IF( FATAL ) $ GO TO 150 90 CONTINUE ELSE * Avoid repeating tests with N.le.0. IF( N.LE.0 ) $ GO TO 140 END IF * 100 CONTINUE * 110 CONTINUE * 120 CONTINUE * 130 CONTINUE * 140 CONTINUE * * Report result. * IF( ERRMAX.LT.THRESH )THEN WRITE( NOUT, FMT = 9999 )SNAME, NC ELSE WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX END IF GO TO 170 * 150 CONTINUE WRITE( NOUT, FMT = 9995 )J * 160 CONTINUE WRITE( NOUT, FMT = 9996 )SNAME IF( FULL )THEN WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, N, ALPHA, INCX, $ INCY, LDA ELSE IF( PACKED )THEN WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, N, ALPHA, INCX, INCY END IF * 170 CONTINUE RETURN * 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL', $ 'S)' ) 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH', $ 'ANGED INCORRECTLY *******' ) 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C', $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2, $ ' - SUSPECT *******' ) 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' ) 9995 FORMAT( ' THESE ARE THE RESULTS FOR COLUMN ', I3 ) 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',(', F4.1, ',', $ F4.1, '), X,', I2, ', Y,', I2, ', AP) ', $ ' .' ) 9993 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',(', F4.1, ',', $ F4.1, '), X,', I2, ', Y,', I2, ', A,', I3, ') ', $ ' .' ) 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *', $ '******' ) * * End of ZCHK6. * END SUBROUTINE ZCHKE( ISNUM, SRNAMT, NOUT ) * * Tests the error exits from the Level 2 Blas. * Requires a special version of the error-handling routine XERBLA. * ALPHA, RALPHA, BETA, A, X and Y should not need to be defined. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Scalar Arguments .. INTEGER ISNUM, NOUT CHARACTER*6 SRNAMT * .. Scalars in Common .. INTEGER INFOT, NOUTC LOGICAL LERR, OK * .. Local Scalars .. COMPLEX*16 ALPHA, BETA DOUBLE PRECISION RALPHA * .. Local Arrays .. COMPLEX*16 A( 1, 1 ), X( 1 ), Y( 1 ) * .. External Subroutines .. EXTERNAL CHKXER, ZGBMV, ZGEMV, ZGERC, ZGERU, ZHBMV, $ ZHEMV, ZHER, ZHER2, ZHPMV, ZHPR, ZHPR2, ZTBMV, $ ZTBSV, ZTPMV, ZTPSV, ZTRMV, ZTRSV * .. Common blocks .. COMMON /INFOC/INFOT, NOUTC, OK, LERR * .. Executable Statements .. * OK is set to .FALSE. by the special version of XERBLA or by CHKXER * if anything is wrong. OK = .TRUE. * LERR is set to .TRUE. by the special version of XERBLA each time * it is called, and is then tested and re-set by CHKXER. LERR = .FALSE. GO TO ( 10, 20, 30, 40, 50, 60, 70, 80, $ 90, 100, 110, 120, 130, 140, 150, 160, $ 170 )ISNUM 10 INFOT = 1 CALL ZGEMV( '/', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL ZGEMV( 'N', -1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 3 CALL ZGEMV( 'N', 0, -1, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 6 CALL ZGEMV( 'N', 2, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 8 CALL ZGEMV( 'N', 0, 0, ALPHA, A, 1, X, 0, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 11 CALL ZGEMV( 'N', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 0 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 180 20 INFOT = 1 CALL ZGBMV( '/', 0, 0, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL ZGBMV( 'N', -1, 0, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 3 CALL ZGBMV( 'N', 0, -1, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 4 CALL ZGBMV( 'N', 0, 0, -1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 5 CALL ZGBMV( 'N', 2, 0, 0, -1, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 8 CALL ZGBMV( 'N', 0, 0, 1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 10 CALL ZGBMV( 'N', 0, 0, 0, 0, ALPHA, A, 1, X, 0, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 13 CALL ZGBMV( 'N', 0, 0, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 0 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 180 30 INFOT = 1 CALL ZHEMV( '/', 0, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL ZHEMV( 'U', -1, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 5 CALL ZHEMV( 'U', 2, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 7 CALL ZHEMV( 'U', 0, ALPHA, A, 1, X, 0, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 10 CALL ZHEMV( 'U', 0, ALPHA, A, 1, X, 1, BETA, Y, 0 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 180 40 INFOT = 1 CALL ZHBMV( '/', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL ZHBMV( 'U', -1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 3 CALL ZHBMV( 'U', 0, -1, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 6 CALL ZHBMV( 'U', 0, 1, ALPHA, A, 1, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 8 CALL ZHBMV( 'U', 0, 0, ALPHA, A, 1, X, 0, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 11 CALL ZHBMV( 'U', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 0 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 180 50 INFOT = 1 CALL ZHPMV( '/', 0, ALPHA, A, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL ZHPMV( 'U', -1, ALPHA, A, X, 1, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 6 CALL ZHPMV( 'U', 0, ALPHA, A, X, 0, BETA, Y, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 9 CALL ZHPMV( 'U', 0, ALPHA, A, X, 1, BETA, Y, 0 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 180 60 INFOT = 1 CALL ZTRMV( '/', 'N', 'N', 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL ZTRMV( 'U', '/', 'N', 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 3 CALL ZTRMV( 'U', 'N', '/', 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 4 CALL ZTRMV( 'U', 'N', 'N', -1, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 6 CALL ZTRMV( 'U', 'N', 'N', 2, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 8 CALL ZTRMV( 'U', 'N', 'N', 0, A, 1, X, 0 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 180 70 INFOT = 1 CALL ZTBMV( '/', 'N', 'N', 0, 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL ZTBMV( 'U', '/', 'N', 0, 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 3 CALL ZTBMV( 'U', 'N', '/', 0, 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 4 CALL ZTBMV( 'U', 'N', 'N', -1, 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 5 CALL ZTBMV( 'U', 'N', 'N', 0, -1, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 7 CALL ZTBMV( 'U', 'N', 'N', 0, 1, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 9 CALL ZTBMV( 'U', 'N', 'N', 0, 0, A, 1, X, 0 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 180 80 INFOT = 1 CALL ZTPMV( '/', 'N', 'N', 0, A, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL ZTPMV( 'U', '/', 'N', 0, A, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 3 CALL ZTPMV( 'U', 'N', '/', 0, A, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 4 CALL ZTPMV( 'U', 'N', 'N', -1, A, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 7 CALL ZTPMV( 'U', 'N', 'N', 0, A, X, 0 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 180 90 INFOT = 1 CALL ZTRSV( '/', 'N', 'N', 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL ZTRSV( 'U', '/', 'N', 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 3 CALL ZTRSV( 'U', 'N', '/', 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 4 CALL ZTRSV( 'U', 'N', 'N', -1, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 6 CALL ZTRSV( 'U', 'N', 'N', 2, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 8 CALL ZTRSV( 'U', 'N', 'N', 0, A, 1, X, 0 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 180 100 INFOT = 1 CALL ZTBSV( '/', 'N', 'N', 0, 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL ZTBSV( 'U', '/', 'N', 0, 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 3 CALL ZTBSV( 'U', 'N', '/', 0, 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 4 CALL ZTBSV( 'U', 'N', 'N', -1, 0, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 5 CALL ZTBSV( 'U', 'N', 'N', 0, -1, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 7 CALL ZTBSV( 'U', 'N', 'N', 0, 1, A, 1, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 9 CALL ZTBSV( 'U', 'N', 'N', 0, 0, A, 1, X, 0 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 180 110 INFOT = 1 CALL ZTPSV( '/', 'N', 'N', 0, A, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL ZTPSV( 'U', '/', 'N', 0, A, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 3 CALL ZTPSV( 'U', 'N', '/', 0, A, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 4 CALL ZTPSV( 'U', 'N', 'N', -1, A, X, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 7 CALL ZTPSV( 'U', 'N', 'N', 0, A, X, 0 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 180 120 INFOT = 1 CALL ZGERC( -1, 0, ALPHA, X, 1, Y, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL ZGERC( 0, -1, ALPHA, X, 1, Y, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 5 CALL ZGERC( 0, 0, ALPHA, X, 0, Y, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 7 CALL ZGERC( 0, 0, ALPHA, X, 1, Y, 0, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 9 CALL ZGERC( 2, 0, ALPHA, X, 1, Y, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 180 130 INFOT = 1 CALL ZGERU( -1, 0, ALPHA, X, 1, Y, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL ZGERU( 0, -1, ALPHA, X, 1, Y, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 5 CALL ZGERU( 0, 0, ALPHA, X, 0, Y, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 7 CALL ZGERU( 0, 0, ALPHA, X, 1, Y, 0, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 9 CALL ZGERU( 2, 0, ALPHA, X, 1, Y, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 180 140 INFOT = 1 CALL ZHER( '/', 0, RALPHA, X, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL ZHER( 'U', -1, RALPHA, X, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 5 CALL ZHER( 'U', 0, RALPHA, X, 0, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 7 CALL ZHER( 'U', 2, RALPHA, X, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 180 150 INFOT = 1 CALL ZHPR( '/', 0, RALPHA, X, 1, A ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL ZHPR( 'U', -1, RALPHA, X, 1, A ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 5 CALL ZHPR( 'U', 0, RALPHA, X, 0, A ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 180 160 INFOT = 1 CALL ZHER2( '/', 0, ALPHA, X, 1, Y, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL ZHER2( 'U', -1, ALPHA, X, 1, Y, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 5 CALL ZHER2( 'U', 0, ALPHA, X, 0, Y, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 7 CALL ZHER2( 'U', 0, ALPHA, X, 1, Y, 0, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 9 CALL ZHER2( 'U', 2, ALPHA, X, 1, Y, 1, A, 1 ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) GO TO 180 170 INFOT = 1 CALL ZHPR2( '/', 0, ALPHA, X, 1, Y, 1, A ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 2 CALL ZHPR2( 'U', -1, ALPHA, X, 1, Y, 1, A ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 5 CALL ZHPR2( 'U', 0, ALPHA, X, 0, Y, 1, A ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) INFOT = 7 CALL ZHPR2( 'U', 0, ALPHA, X, 1, Y, 0, A ) CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) * 180 IF( OK )THEN WRITE( NOUT, FMT = 9999 )SRNAMT ELSE WRITE( NOUT, FMT = 9998 )SRNAMT END IF RETURN * 9999 FORMAT( ' ', A6, ' PASSED THE TESTS OF ERROR-EXITS' ) 9998 FORMAT( ' ******* ', A6, ' FAILED THE TESTS OF ERROR-EXITS *****', $ '**' ) * * End of ZCHKE. * END SUBROUTINE ZMAKE( TYPE, UPLO, DIAG, M, N, A, NMAX, AA, LDA, KL, $ KU, RESET, TRANSL ) * * Generates values for an M by N matrix A within the bandwidth * defined by KL and KU. * Stores the values in the array AA in the data structure required * by the routine, with unwanted elements set to rogue value. * * TYPE is 'GE', 'GB', 'HE', 'HB', 'HP', 'TR', 'TB' OR 'TP'. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Parameters .. COMPLEX*16 ZERO, ONE PARAMETER ( ZERO = ( 0.0D0, 0.0D0 ), $ ONE = ( 1.0D0, 0.0D0 ) ) COMPLEX*16 ROGUE PARAMETER ( ROGUE = ( -1.0D10, 1.0D10 ) ) DOUBLE PRECISION RZERO PARAMETER ( RZERO = 0.0D0 ) DOUBLE PRECISION RROGUE PARAMETER ( RROGUE = -1.0D10 ) * .. Scalar Arguments .. COMPLEX*16 TRANSL INTEGER KL, KU, LDA, M, N, NMAX LOGICAL RESET CHARACTER*1 DIAG, UPLO CHARACTER*2 TYPE * .. Array Arguments .. COMPLEX*16 A( NMAX, * ), AA( * ) * .. Local Scalars .. INTEGER I, I1, I2, I3, IBEG, IEND, IOFF, J, JJ, KK LOGICAL GEN, LOWER, SYM, TRI, UNIT, UPPER * .. External Functions .. COMPLEX*16 ZBEG EXTERNAL ZBEG * .. Intrinsic Functions .. INTRINSIC DBLE, DCMPLX, DCONJG, MAX, MIN * .. Executable Statements .. GEN = TYPE( 1: 1 ).EQ.'G' SYM = TYPE( 1: 1 ).EQ.'H' TRI = TYPE( 1: 1 ).EQ.'T' UPPER = ( SYM.OR.TRI ).AND.UPLO.EQ.'U' LOWER = ( SYM.OR.TRI ).AND.UPLO.EQ.'L' UNIT = TRI.AND.DIAG.EQ.'U' * * Generate data in array A. * DO 20 J = 1, N DO 10 I = 1, M IF( GEN.OR.( UPPER.AND.I.LE.J ).OR.( LOWER.AND.I.GE.J ) ) $ THEN IF( ( I.LE.J.AND.J - I.LE.KU ).OR. $ ( I.GE.J.AND.I - J.LE.KL ) )THEN A( I, J ) = ZBEG( RESET ) + TRANSL ELSE A( I, J ) = ZERO END IF IF( I.NE.J )THEN IF( SYM )THEN A( J, I ) = DCONJG( A( I, J ) ) ELSE IF( TRI )THEN A( J, I ) = ZERO END IF END IF END IF 10 CONTINUE IF( SYM ) $ A( J, J ) = DCMPLX( DBLE( A( J, J ) ), RZERO ) IF( TRI ) $ A( J, J ) = A( J, J ) + ONE IF( UNIT ) $ A( J, J ) = ONE 20 CONTINUE * * Store elements in array AS in data structure required by routine. * IF( TYPE.EQ.'GE' )THEN DO 50 J = 1, N DO 30 I = 1, M AA( I + ( J - 1 )*LDA ) = A( I, J ) 30 CONTINUE DO 40 I = M + 1, LDA AA( I + ( J - 1 )*LDA ) = ROGUE 40 CONTINUE 50 CONTINUE ELSE IF( TYPE.EQ.'GB' )THEN DO 90 J = 1, N DO 60 I1 = 1, KU + 1 - J AA( I1 + ( J - 1 )*LDA ) = ROGUE 60 CONTINUE DO 70 I2 = I1, MIN( KL + KU + 1, KU + 1 + M - J ) AA( I2 + ( J - 1 )*LDA ) = A( I2 + J - KU - 1, J ) 70 CONTINUE DO 80 I3 = I2, LDA AA( I3 + ( J - 1 )*LDA ) = ROGUE 80 CONTINUE 90 CONTINUE ELSE IF( TYPE.EQ.'HE'.OR.TYPE.EQ.'TR' )THEN DO 130 J = 1, N IF( UPPER )THEN IBEG = 1 IF( UNIT )THEN IEND = J - 1 ELSE IEND = J END IF ELSE IF( UNIT )THEN IBEG = J + 1 ELSE IBEG = J END IF IEND = N END IF DO 100 I = 1, IBEG - 1 AA( I + ( J - 1 )*LDA ) = ROGUE 100 CONTINUE DO 110 I = IBEG, IEND AA( I + ( J - 1 )*LDA ) = A( I, J ) 110 CONTINUE DO 120 I = IEND + 1, LDA AA( I + ( J - 1 )*LDA ) = ROGUE 120 CONTINUE IF( SYM )THEN JJ = J + ( J - 1 )*LDA AA( JJ ) = DCMPLX( DBLE( AA( JJ ) ), RROGUE ) END IF 130 CONTINUE ELSE IF( TYPE.EQ.'HB'.OR.TYPE.EQ.'TB' )THEN DO 170 J = 1, N IF( UPPER )THEN KK = KL + 1 IBEG = MAX( 1, KL + 2 - J ) IF( UNIT )THEN IEND = KL ELSE IEND = KL + 1 END IF ELSE KK = 1 IF( UNIT )THEN IBEG = 2 ELSE IBEG = 1 END IF IEND = MIN( KL + 1, 1 + M - J ) END IF DO 140 I = 1, IBEG - 1 AA( I + ( J - 1 )*LDA ) = ROGUE 140 CONTINUE DO 150 I = IBEG, IEND AA( I + ( J - 1 )*LDA ) = A( I + J - KK, J ) 150 CONTINUE DO 160 I = IEND + 1, LDA AA( I + ( J - 1 )*LDA ) = ROGUE 160 CONTINUE IF( SYM )THEN JJ = KK + ( J - 1 )*LDA AA( JJ ) = DCMPLX( DBLE( AA( JJ ) ), RROGUE ) END IF 170 CONTINUE ELSE IF( TYPE.EQ.'HP'.OR.TYPE.EQ.'TP' )THEN IOFF = 0 DO 190 J = 1, N IF( UPPER )THEN IBEG = 1 IEND = J ELSE IBEG = J IEND = N END IF DO 180 I = IBEG, IEND IOFF = IOFF + 1 AA( IOFF ) = A( I, J ) IF( I.EQ.J )THEN IF( UNIT ) $ AA( IOFF ) = ROGUE IF( SYM ) $ AA( IOFF ) = DCMPLX( DBLE( AA( IOFF ) ), RROGUE ) END IF 180 CONTINUE 190 CONTINUE END IF RETURN * * End of ZMAKE. * END SUBROUTINE ZMVCH( TRANS, M, N, ALPHA, A, NMAX, X, INCX, BETA, Y, $ INCY, YT, G, YY, EPS, ERR, FATAL, NOUT, MV ) * * Checks the results of the computational tests. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Parameters .. COMPLEX*16 ZERO PARAMETER ( ZERO = ( 0.0D0, 0.0D0 ) ) DOUBLE PRECISION RZERO, RONE PARAMETER ( RZERO = 0.0D0, RONE = 1.0D0 ) * .. Scalar Arguments .. COMPLEX*16 ALPHA, BETA DOUBLE PRECISION EPS, ERR INTEGER INCX, INCY, M, N, NMAX, NOUT LOGICAL FATAL, MV CHARACTER*1 TRANS * .. Array Arguments .. COMPLEX*16 A( NMAX, * ), X( * ), Y( * ), YT( * ), YY( * ) DOUBLE PRECISION G( * ) * .. Local Scalars .. COMPLEX*16 C DOUBLE PRECISION ERRI INTEGER I, INCXL, INCYL, IY, J, JX, KX, KY, ML, NL LOGICAL CTRAN, TRAN * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, DCONJG, DIMAG, MAX, SQRT * .. Statement Functions .. DOUBLE PRECISION ABS1 * .. Statement Function definitions .. ABS1( C ) = ABS( DBLE( C ) ) + ABS( DIMAG( C ) ) * .. Executable Statements .. TRAN = TRANS.EQ.'T' CTRAN = TRANS.EQ.'C' IF( TRAN.OR.CTRAN )THEN ML = N NL = M ELSE ML = M NL = N END IF IF( INCX.LT.0 )THEN KX = NL INCXL = -1 ELSE KX = 1 INCXL = 1 END IF IF( INCY.LT.0 )THEN KY = ML INCYL = -1 ELSE KY = 1 INCYL = 1 END IF * * Compute expected result in YT using data in A, X and Y. * Compute gauges in G. * IY = KY DO 40 I = 1, ML YT( IY ) = ZERO G( IY ) = RZERO JX = KX IF( TRAN )THEN DO 10 J = 1, NL YT( IY ) = YT( IY ) + A( J, I )*X( JX ) G( IY ) = G( IY ) + ABS1( A( J, I ) )*ABS1( X( JX ) ) JX = JX + INCXL 10 CONTINUE ELSE IF( CTRAN )THEN DO 20 J = 1, NL YT( IY ) = YT( IY ) + DCONJG( A( J, I ) )*X( JX ) G( IY ) = G( IY ) + ABS1( A( J, I ) )*ABS1( X( JX ) ) JX = JX + INCXL 20 CONTINUE ELSE DO 30 J = 1, NL YT( IY ) = YT( IY ) + A( I, J )*X( JX ) G( IY ) = G( IY ) + ABS1( A( I, J ) )*ABS1( X( JX ) ) JX = JX + INCXL 30 CONTINUE END IF YT( IY ) = ALPHA*YT( IY ) + BETA*Y( IY ) G( IY ) = ABS1( ALPHA )*G( IY ) + ABS1( BETA )*ABS1( Y( IY ) ) IY = IY + INCYL 40 CONTINUE * * Compute the error ratio for this result. * ERR = ZERO DO 50 I = 1, ML ERRI = ABS( YT( I ) - YY( 1 + ( I - 1 )*ABS( INCY ) ) )/EPS IF( G( I ).NE.RZERO ) $ ERRI = ERRI/G( I ) ERR = MAX( ERR, ERRI ) IF( ERR*SQRT( EPS ).GE.RONE ) $ GO TO 60 50 CONTINUE * If the loop completes, all results are at least half accurate. GO TO 80 * * Report fatal error. * 60 FATAL = .TRUE. WRITE( NOUT, FMT = 9999 ) DO 70 I = 1, ML IF( MV )THEN WRITE( NOUT, FMT = 9998 )I, YT( I ), $ YY( 1 + ( I - 1 )*ABS( INCY ) ) ELSE WRITE( NOUT, FMT = 9998 )I, $ YY( 1 + ( I - 1 )*ABS( INCY ) ), YT( I ) END IF 70 CONTINUE * 80 CONTINUE RETURN * 9999 FORMAT( ' ******* FATAL ERROR - COMPUTED RESULT IS LESS THAN HAL', $ 'F ACCURATE *******', /' EXPECTED RE', $ 'SULT COMPUTED RESULT' ) 9998 FORMAT( 1X, I7, 2( ' (', G15.6, ',', G15.6, ')' ) ) * * End of ZMVCH. * END LOGICAL FUNCTION LZE( RI, RJ, LR ) * * Tests if two arrays are identical. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Scalar Arguments .. INTEGER LR * .. Array Arguments .. COMPLEX*16 RI( * ), RJ( * ) * .. Local Scalars .. INTEGER I * .. Executable Statements .. DO 10 I = 1, LR IF( RI( I ).NE.RJ( I ) ) $ GO TO 20 10 CONTINUE LZE = .TRUE. GO TO 30 20 CONTINUE LZE = .FALSE. 30 RETURN * * End of LZE. * END LOGICAL FUNCTION LZERES( TYPE, UPLO, M, N, AA, AS, LDA ) * * Tests if selected elements in two arrays are equal. * * TYPE is 'GE', 'HE' or 'HP'. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Scalar Arguments .. INTEGER LDA, M, N CHARACTER*1 UPLO CHARACTER*2 TYPE * .. Array Arguments .. COMPLEX*16 AA( LDA, * ), AS( LDA, * ) * .. Local Scalars .. INTEGER I, IBEG, IEND, J LOGICAL UPPER * .. Executable Statements .. UPPER = UPLO.EQ.'U' IF( TYPE.EQ.'GE' )THEN DO 20 J = 1, N DO 10 I = M + 1, LDA IF( AA( I, J ).NE.AS( I, J ) ) $ GO TO 70 10 CONTINUE 20 CONTINUE ELSE IF( TYPE.EQ.'HE' )THEN DO 50 J = 1, N IF( UPPER )THEN IBEG = 1 IEND = J ELSE IBEG = J IEND = N END IF DO 30 I = 1, IBEG - 1 IF( AA( I, J ).NE.AS( I, J ) ) $ GO TO 70 30 CONTINUE DO 40 I = IEND + 1, LDA IF( AA( I, J ).NE.AS( I, J ) ) $ GO TO 70 40 CONTINUE 50 CONTINUE END IF * 60 CONTINUE LZERES = .TRUE. GO TO 80 70 CONTINUE LZERES = .FALSE. 80 RETURN * * End of LZERES. * END COMPLEX*16 FUNCTION ZBEG( RESET ) * * Generates complex numbers as pairs of random numbers uniformly * distributed between -0.5 and 0.5. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Scalar Arguments .. LOGICAL RESET * .. Local Scalars .. INTEGER I, IC, J, MI, MJ * .. Save statement .. SAVE I, IC, J, MI, MJ * .. Intrinsic Functions .. INTRINSIC DCMPLX * .. Executable Statements .. IF( RESET )THEN * Initialize local variables. MI = 891 MJ = 457 I = 7 J = 7 IC = 0 RESET = .FALSE. END IF * * The sequence of values of I or J is bounded between 1 and 999. * If initial I or J = 1,2,3,6,7 or 9, the period will be 50. * If initial I or J = 4 or 8, the period will be 25. * If initial I or J = 5, the period will be 10. * IC is used to break up the period by skipping 1 value of I or J * in 6. * IC = IC + 1 10 I = I*MI J = J*MJ I = I - 1000*( I/1000 ) J = J - 1000*( J/1000 ) IF( IC.GE.5 )THEN IC = 0 GO TO 10 END IF ZBEG = DCMPLX( ( I - 500 )/1001.0D0, ( J - 500 )/1001.0D0 ) RETURN * * End of ZBEG. * END DOUBLE PRECISION FUNCTION DDIFF( X, Y ) * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * * .. Scalar Arguments .. DOUBLE PRECISION X, Y * .. Executable Statements .. DDIFF = X - Y RETURN * * End of DDIFF. * END SUBROUTINE CHKXER( SRNAMT, INFOT, NOUT, LERR, OK ) * * Tests whether XERBLA has detected an error when it should. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Scalar Arguments .. INTEGER INFOT, NOUT LOGICAL LERR, OK CHARACTER*6 SRNAMT * .. Executable Statements .. IF( .NOT.LERR )THEN WRITE( NOUT, FMT = 9999 )INFOT, SRNAMT OK = .FALSE. END IF LERR = .FALSE. RETURN * 9999 FORMAT( ' ***** ILLEGAL VALUE OF PARAMETER NUMBER ', I2, ' NOT D', $ 'ETECTED BY ', A6, ' *****' ) * * End of CHKXER. * END SUBROUTINE XERBLA( SRNAME, INFO ) * * This is a special version of XERBLA to be used only as part of * the test program for testing error exits from the Level 2 BLAS * routines. * * XERBLA is an error handler for the Level 2 BLAS routines. * * It is called by the Level 2 BLAS routines if an input parameter is * invalid. * * Auxiliary routine for test program for Level 2 Blas. * * -- Written on 10-August-1987. * Richard Hanson, Sandia National Labs. * Jeremy Du Croz, NAG Central Office. * * .. Scalar Arguments .. INTEGER INFO CHARACTER*6 SRNAME * .. Scalars in Common .. INTEGER INFOT, NOUT LOGICAL LERR, OK CHARACTER*6 SRNAMT * .. Common blocks .. COMMON /INFOC/INFOT, NOUT, OK, LERR COMMON /SRNAMC/SRNAMT * .. Executable Statements .. LERR = .TRUE. IF( INFO.NE.INFOT )THEN IF( INFOT.NE.0 )THEN WRITE( NOUT, FMT = 9999 )INFO, INFOT ELSE WRITE( NOUT, FMT = 9997 )INFO END IF OK = .FALSE. END IF IF( SRNAME.NE.SRNAMT )THEN WRITE( NOUT, FMT = 9998 )SRNAME, SRNAMT OK = .FALSE. END IF RETURN * 9999 FORMAT( ' ******* XERBLA WAS CALLED WITH INFO = ', I6, ' INSTEAD', $ ' OF ', I2, ' *******' ) 9998 FORMAT( ' ******* XERBLA WAS CALLED WITH SRNAME = ', A6, ' INSTE', $ 'AD OF ', A6, ' *******' ) 9997 FORMAT( ' ******* XERBLA WAS CALLED WITH INFO = ', I6, $ ' *******' ) * * End of XERBLA * END