*> \brief \b DTRT02 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE DTRT02( UPLO, TRANS, DIAG, N, NRHS, A, LDA, X, LDX, B, * LDB, WORK, RESID ) * * .. Scalar Arguments .. * CHARACTER DIAG, TRANS, UPLO * INTEGER LDA, LDB, LDX, N, NRHS * DOUBLE PRECISION RESID * .. * .. Array Arguments .. * DOUBLE PRECISION A( LDA, * ), B( LDB, * ), WORK( * ), * $ X( LDX, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DTRT02 computes the residual for the computed solution to a *> triangular system of linear equations A*x = b or A'*x = b. *> Here A is a triangular matrix, A' is the transpose of A, and x and b *> are N by NRHS matrices. The test ratio is the maximum over the *> number of right hand sides of *> norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ), *> where op(A) denotes A or A' and EPS is the machine epsilon. *> The norm used is the 1-norm. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> Specifies whether the matrix A is upper or lower triangular. *> = 'U': Upper triangular *> = 'L': Lower triangular *> \endverbatim *> *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 *> Specifies the operation applied to A. *> = 'N': A *x = b (No transpose) *> = 'T': A'*x = b (Transpose) *> = 'C': A'*x = b (Conjugate transpose = Transpose) *> \endverbatim *> *> \param[in] DIAG *> \verbatim *> DIAG is CHARACTER*1 *> Specifies whether or not the matrix A is unit triangular. *> = 'N': Non-unit triangular *> = 'U': Unit triangular *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in] NRHS *> \verbatim *> NRHS is INTEGER *> The number of right hand sides, i.e., the number of columns *> of the matrices X and B. NRHS >= 0. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA,N) *> The triangular matrix A. If UPLO = 'U', the leading n by n *> upper triangular part of the array A contains the upper *> triangular matrix, and the strictly lower triangular part of *> A is not referenced. If UPLO = 'L', the leading n by n lower *> triangular part of the array A contains the lower triangular *> matrix, and the strictly upper triangular part of A is not *> referenced. If DIAG = 'U', the diagonal elements of A are *> also not referenced and are assumed to be 1. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[in] X *> \verbatim *> X is DOUBLE PRECISION array, dimension (LDX,NRHS) *> The computed solution vectors for the system of linear *> equations. *> \endverbatim *> *> \param[in] LDX *> \verbatim *> LDX is INTEGER *> The leading dimension of the array X. LDX >= max(1,N). *> \endverbatim *> *> \param[in] B *> \verbatim *> B is DOUBLE PRECISION array, dimension (LDB,NRHS) *> The right hand side vectors for the system of linear *> equations. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> The leading dimension of the array B. LDB >= max(1,N). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension (N) *> \endverbatim *> *> \param[out] RESID *> \verbatim *> RESID is DOUBLE PRECISION *> The maximum over the number of right hand sides of *> norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup double_lin * * ===================================================================== SUBROUTINE DTRT02( UPLO, TRANS, DIAG, N, NRHS, A, LDA, X, LDX, B, $ LDB, WORK, RESID ) * * -- LAPACK test routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. CHARACTER DIAG, TRANS, UPLO INTEGER LDA, LDB, LDX, N, NRHS DOUBLE PRECISION RESID * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), B( LDB, * ), WORK( * ), $ X( LDX, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) * .. * .. Local Scalars .. INTEGER J DOUBLE PRECISION ANORM, BNORM, EPS, XNORM * .. * .. External Functions .. LOGICAL LSAME DOUBLE PRECISION DASUM, DLAMCH, DLANTR EXTERNAL LSAME, DASUM, DLAMCH, DLANTR * .. * .. External Subroutines .. EXTERNAL DAXPY, DCOPY, DTRMV * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Quick exit if N = 0 or NRHS = 0 * IF( N.LE.0 .OR. NRHS.LE.0 ) THEN RESID = ZERO RETURN END IF * * Compute the 1-norm of A or A'. * IF( LSAME( TRANS, 'N' ) ) THEN ANORM = DLANTR( '1', UPLO, DIAG, N, N, A, LDA, WORK ) ELSE ANORM = DLANTR( 'I', UPLO, DIAG, N, N, A, LDA, WORK ) END IF * * Exit with RESID = 1/EPS if ANORM = 0. * EPS = DLAMCH( 'Epsilon' ) IF( ANORM.LE.ZERO ) THEN RESID = ONE / EPS RETURN END IF * * Compute the maximum over the number of right hand sides of * norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ) * RESID = ZERO DO 10 J = 1, NRHS CALL DCOPY( N, X( 1, J ), 1, WORK, 1 ) CALL DTRMV( UPLO, TRANS, DIAG, N, A, LDA, WORK, 1 ) CALL DAXPY( N, -ONE, B( 1, J ), 1, WORK, 1 ) BNORM = DASUM( N, WORK, 1 ) XNORM = DASUM( N, X( 1, J ), 1 ) IF( XNORM.LE.ZERO ) THEN RESID = ONE / EPS ELSE RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS ) END IF 10 CONTINUE * RETURN * * End of DTRT02 * END