* ************************************************************************ * SUBROUTINE ECTBSV( 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 X( * ) COMPLEX A( LDA, * ) * .. * * Purpose * ======= * * ECTBSV 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. Additional precision arithmetic is used in the * computation. * * 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*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. At least double precision * arithmetic is used in the computation of 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 20-July-1986. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. COMPLEX*16 ZERO PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) ) * .. Local Scalars .. 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 MAX, MIN, 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 ( 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( 'ECTBSV', INFO ) RETURN END IF * * Quick return if possible. * IF( N.EQ.0 ) \$ RETURN * NOCONJ = LSAME( TRANS, 'T' ) NOUNIT = ( DIAG .EQ.'N' ).OR.( DIAG .EQ.'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 ) DO 10, I = J - 1, MAX( 1, J - K ), -1 X( I ) = X( I ) - X( J )*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 ) DO 30, I = J - 1, MAX( 1, J - K ), -1 X( IX ) = X( IX ) - X( JX )*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 ) DO 50, I = J + 1, MIN( N, J + K ) X( I ) = X( I ) - X( J )*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 ) DO 70, I = J + 1, MIN( N, J + K ) X( IX ) = X( IX ) - X( JX )*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 L = KPLUS1 - J IF( NOCONJ )THEN DO 90, I = MAX( 1, J - K ), J - 1 X( J ) = X( J ) - A( L + I, J )*X( I ) 90 CONTINUE IF( NOUNIT ) \$ X( J ) = X( J )/A( KPLUS1, J ) ELSE DO 100, I = MAX( 1, J - K ), J - 1 X( J ) = X( J ) - CONJG( A( L + I, J ) )*X( I ) 100 CONTINUE IF( NOUNIT ) \$ X( J ) = X( J )/CONJG( A( KPLUS1, J ) ) END IF 110 CONTINUE ELSE JX = KX DO 140, J = 1, N IX = KX L = KPLUS1 - J IF( NOCONJ )THEN DO 120, I = MAX( 1, J - K ), J - 1 X( JX ) = X( JX ) - A( L + I, J )*X( IX ) IX = IX + INCX 120 CONTINUE IF( NOUNIT ) \$ X( JX ) = X( JX )/A( KPLUS1, J ) ELSE DO 130, I = MAX( 1, J - K ), J - 1 X( JX ) = X( JX ) - \$ CONJG( A( L + I, J ) )*X( IX ) IX = IX + INCX 130 CONTINUE IF( NOUNIT ) \$ X( JX ) = X( JX )/CONJG( A( KPLUS1, J ) ) END IF 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 L = 1 - J IF( NOCONJ )THEN DO 150, I = MIN( N, J + K ), J + 1, -1 X( J ) = X( J ) - A( L + I, J )*X( I ) 150 CONTINUE IF( NOUNIT ) \$ X( J ) = X( J )/A( 1, J ) ELSE DO 160, I = MIN( N, J + K ), J + 1, -1 X( J ) = X( J ) - CONJG( A( L + I, J ) )*X( I ) 160 CONTINUE IF( NOUNIT ) \$ X( J ) = X( J )/CONJG( A( 1, J ) ) END IF 170 CONTINUE ELSE KX = KX + ( N - 1 )*INCX JX = KX DO 200, J = N, 1, -1 IX = KX L = 1 - J IF( NOCONJ )THEN DO 180, I = MIN( N, J + K ), J + 1, -1 X( JX ) = X( JX ) - A( L + I, J )*X( IX ) IX = IX - INCX 180 CONTINUE IF( NOUNIT ) \$ X( JX ) = X( JX )/A( 1, J ) ELSE DO 190, I = MIN( N, J + K ), J + 1, -1 X( JX ) = X( JX ) - \$ CONJG( A( L + I, J ) )*X( IX ) IX = IX - INCX 190 CONTINUE IF( NOUNIT ) \$ X( JX ) = X( JX )/CONJG( A( 1, J ) ) END IF JX = JX - INCX IF( ( N - J ).GE.K ) \$ KX = KX - INCX 200 CONTINUE END IF END IF END IF * RETURN * * End of ECTBSV. * END