* ************************************************************************ * SUBROUTINE ESTRSV( UPLO, TRANS, DIAG, N, A, LDA, X, INCX ) * .. Scalar Arguments .. INTEGER INCX, LDA, N CHARACTER*1 DIAG, TRANS, UPLO * .. Array Arguments .. DOUBLE PRECISION X( * ) REAL A( LDA, * ) * .. * * Purpose * ======= * * ESTRSV 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. 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' 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 - 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. At least REAL * 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 .. REAL ZERO PARAMETER ( ZERO = 0.0E+0 ) * .. Local Scalars .. INTEGER I, INFO, IX, J, JX, KX LOGICAL NOUNIT * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC 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 ( .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( 'ESTRSV', 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.DBLE( ZERO ) )THEN IF( NOUNIT ) \$ X( J ) = X( J )/A( J, J ) DO 10, I = J - 1, 1, -1 X( I ) = X( I ) - X( J )*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.DBLE( ZERO ) )THEN IF( NOUNIT ) \$ X( JX ) = X( JX )/A( J, J ) IX = JX DO 30, I = J - 1, 1, -1 IX = IX - INCX X( IX ) = X( IX ) - X( JX )*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.DBLE( ZERO ) )THEN IF( NOUNIT ) \$ X( J ) = X( J )/A( J, J ) DO 50, I = J + 1, N X( I ) = X( I ) - X( J )*A( I, J ) 50 CONTINUE END IF 60 CONTINUE ELSE JX = KX DO 80, J = 1, N IF( X( JX ).NE.DBLE( ZERO ) )THEN IF( NOUNIT ) \$ X( JX ) = X( JX )/A( J, J ) IX = JX DO 70, I = J + 1, N IX = IX + INCX X( IX ) = X( IX ) - X( JX )*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 DO 90, I = 1, J - 1 X( J ) = X( J ) - A( I, J )*X( I ) 90 CONTINUE IF( NOUNIT ) \$ X( J ) = X( J )/A( J, J ) 100 CONTINUE ELSE JX = KX DO 120, J = 1, N IX = KX DO 110, I = 1, J - 1 X( JX ) = X( JX ) - A( I, J )*X( IX ) IX = IX + INCX 110 CONTINUE IF( NOUNIT ) \$ X( JX ) = X( JX )/A( J, J ) JX = JX + INCX 120 CONTINUE END IF ELSE IF( INCX.EQ.1 )THEN DO 140, J = N, 1, -1 DO 130, I = N, J + 1, -1 X( J ) = X( J ) - A( I, J )*X( I ) 130 CONTINUE IF( NOUNIT ) \$ X( J ) = X( J )/A( J, J ) 140 CONTINUE ELSE KX = KX + ( N - 1 )*INCX JX = KX DO 160, J = N, 1, -1 IX = KX DO 150, I = N, J + 1, -1 X( JX ) = X( JX ) - A( I, J )*X( IX ) IX = IX - INCX 150 CONTINUE IF( NOUNIT ) \$ X( JX ) = X( JX )/A( J, J ) JX = JX - INCX 160 CONTINUE END IF END IF END IF * RETURN * * End of ESTRSV. * END