*> \brief \b SQRT17 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * REAL FUNCTION SQRT17( TRANS, IRESID, M, N, NRHS, A, * LDA, X, LDX, B, LDB, C, WORK, LWORK ) * * .. Scalar Arguments .. * CHARACTER TRANS * INTEGER IRESID, LDA, LDB, LDX, LWORK, M, N, NRHS * .. * .. Array Arguments .. * REAL A( LDA, * ), B( LDB, * ), C( LDB, * ), * $ WORK( LWORK ), X( LDX, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> SQRT17 computes the ratio *> *> norm(R**T * op(A)) / ( norm(A) * alpha * max(M,N,NRHS) * EPS ), *> *> where R = B - op(A)*X, op(A) is A or A**T, depending on TRANS, EPS *> is the machine epsilon, and *> *> alpha = norm(B) if IRESID = 1 (zero-residual problem) *> alpha = norm(R) if IRESID = 2 (otherwise). *> *> The norm used is the 1-norm. *> \endverbatim * * Arguments: * ========== * *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 *> Specifies whether or not the transpose of A is used. *> = 'N': No transpose, op(A) = A. *> = 'T': Transpose, op(A) = A**T. *> \endverbatim *> *> \param[in] IRESID *> \verbatim *> IRESID is INTEGER *> IRESID = 1 indicates zero-residual problem. *> IRESID = 2 indicates non-zero residual. *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix A. *> If TRANS = 'N', the number of rows of the matrix B. *> If TRANS = 'T', the number of rows of the matrix X. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix A. *> If TRANS = 'N', the number of rows of the matrix X. *> If TRANS = 'T', the number of rows of the matrix B. *> \endverbatim *> *> \param[in] NRHS *> \verbatim *> NRHS is INTEGER *> The number of columns of the matrices X and B. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is REAL array, dimension (LDA,N) *> The m-by-n matrix A. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= M. *> \endverbatim *> *> \param[in] X *> \verbatim *> X is REAL array, dimension (LDX,NRHS) *> If TRANS = 'N', the n-by-nrhs matrix X. *> If TRANS = 'T', the m-by-nrhs matrix X. *> \endverbatim *> *> \param[in] LDX *> \verbatim *> LDX is INTEGER *> The leading dimension of the array X. *> If TRANS = 'N', LDX >= N. *> If TRANS = 'T', LDX >= M. *> \endverbatim *> *> \param[in] B *> \verbatim *> B is REAL array, dimension (LDB,NRHS) *> If TRANS = 'N', the m-by-nrhs matrix B. *> If TRANS = 'T', the n-by-nrhs matrix B. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> The leading dimension of the array B. *> If TRANS = 'N', LDB >= M. *> If TRANS = 'T', LDB >= N. *> \endverbatim *> *> \param[out] C *> \verbatim *> C is REAL array, dimension (LDB,NRHS) *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is REAL array, dimension (LWORK) *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The length of the array WORK. LWORK >= NRHS*(M+N). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup single_lin * * ===================================================================== REAL FUNCTION SQRT17( TRANS, IRESID, M, N, NRHS, A, $ LDA, X, LDX, B, LDB, C, WORK, LWORK ) * * -- 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 TRANS INTEGER IRESID, LDA, LDB, LDX, LWORK, M, N, NRHS * .. * .. Array Arguments .. REAL A( LDA, * ), B( LDB, * ), C( LDB, * ), $ WORK( LWORK ), X( LDX, * ) * .. * * ===================================================================== * * .. Parameters .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 ) * .. * .. Local Scalars .. INTEGER INFO, ISCL, NCOLS, NROWS REAL ERR, NORMA, NORMB, NORMRS, SMLNUM * .. * .. Local Arrays .. REAL RWORK( 1 ) * .. * .. External Functions .. LOGICAL LSAME REAL SLAMCH, SLANGE EXTERNAL LSAME, SLAMCH, SLANGE * .. * .. External Subroutines .. EXTERNAL SGEMM, SLACPY, SLASCL, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, REAL * .. * .. Executable Statements .. * SQRT17 = ZERO * IF( LSAME( TRANS, 'N' ) ) THEN NROWS = M NCOLS = N ELSE IF( LSAME( TRANS, 'T' ) ) THEN NROWS = N NCOLS = M ELSE CALL XERBLA( 'SQRT17', 1 ) RETURN END IF * IF( LWORK.LT.NCOLS*NRHS ) THEN CALL XERBLA( 'SQRT17', 13 ) RETURN END IF * IF( M.LE.0 .OR. N.LE.0 .OR. NRHS.LE.0 ) THEN RETURN END IF * NORMA = SLANGE( 'One-norm', M, N, A, LDA, RWORK ) SMLNUM = SLAMCH( 'Safe minimum' ) / SLAMCH( 'Precision' ) ISCL = 0 * * compute residual and scale it * CALL SLACPY( 'All', NROWS, NRHS, B, LDB, C, LDB ) CALL SGEMM( TRANS, 'No transpose', NROWS, NRHS, NCOLS, -ONE, A, $ LDA, X, LDX, ONE, C, LDB ) NORMRS = SLANGE( 'Max', NROWS, NRHS, C, LDB, RWORK ) IF( NORMRS.GT.SMLNUM ) THEN ISCL = 1 CALL SLASCL( 'General', 0, 0, NORMRS, ONE, NROWS, NRHS, C, LDB, $ INFO ) END IF * * compute R**T * op(A) * CALL SGEMM( 'Transpose', TRANS, NRHS, NCOLS, NROWS, ONE, C, LDB, $ A, LDA, ZERO, WORK, NRHS ) * * compute and properly scale error * ERR = SLANGE( 'One-norm', NRHS, NCOLS, WORK, NRHS, RWORK ) IF( NORMA.NE.ZERO ) $ ERR = ERR / NORMA * IF( ISCL.EQ.1 ) $ ERR = ERR*NORMRS * IF( IRESID.EQ.1 ) THEN NORMB = SLANGE( 'One-norm', NROWS, NRHS, B, LDB, RWORK ) IF( NORMB.NE.ZERO ) $ ERR = ERR / NORMB ELSE IF( NORMRS.NE.ZERO ) $ ERR = ERR / NORMRS END IF * SQRT17 = ERR / ( SLAMCH( 'Epsilon' )*REAL( MAX( M, N, NRHS ) ) ) RETURN * * End of SQRT17 * END