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*> \brief \b ZQRT17
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* DOUBLE PRECISION FUNCTION ZQRT17( 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 ..
* COMPLEX*16 A( LDA, * ), B( LDB, * ), C( LDB, * ),
* $ WORK( LWORK ), X( LDX, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZQRT17 computes the ratio
*>
*> || R'*op(A) ||/(||A||*alpha*max(M,N,NRHS)*eps)
*>
*> where R = op(A)*X - B, op(A) is A or A', and
*>
*> alpha = ||B|| if IRESID = 1 (zero-residual problem)
*> alpha = ||R|| if IRESID = 2 (otherwise).
*> \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.
*> = 'C': Conjugate transpose, op(A) = A'.
*> \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 = 'C', 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 = 'C', 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 COMPLEX*16 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 COMPLEX*16 array, dimension (LDX,NRHS)
*> If TRANS = 'N', the n-by-nrhs matrix X.
*> If TRANS = 'C', 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 = 'C', LDX >= M.
*> \endverbatim
*>
*> \param[in] B
*> \verbatim
*> B is COMPLEX*16 array, dimension (LDB,NRHS)
*> If TRANS = 'N', the m-by-nrhs matrix B.
*> If TRANS = 'C', 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 = 'C', LDB >= N.
*> \endverbatim
*>
*> \param[out] C
*> \verbatim
*> C is COMPLEX*16 array, dimension (LDB,NRHS)
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is COMPLEX*16 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.
*
*> \date November 2015
*
*> \ingroup complex16_lin
*
* =====================================================================
DOUBLE PRECISION FUNCTION ZQRT17( TRANS, IRESID, M, N, NRHS, A,
$ LDA, X, LDX, B, LDB, C, WORK, LWORK )
*
* -- LAPACK test routine (version 3.6.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2015
*
* .. Scalar Arguments ..
CHARACTER TRANS
INTEGER IRESID, LDA, LDB, LDX, LWORK, M, N, NRHS
* ..
* .. Array Arguments ..
COMPLEX*16 A( LDA, * ), B( LDB, * ), C( LDB, * ),
$ WORK( LWORK ), X( LDX, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
* ..
* .. Local Scalars ..
INTEGER INFO, ISCL, NCOLS, NROWS
DOUBLE PRECISION BIGNUM, ERR, NORMA, NORMB, NORMRS, SMLNUM
* ..
* .. Local Arrays ..
DOUBLE PRECISION RWORK( 1 )
* ..
* .. External Functions ..
LOGICAL LSAME
DOUBLE PRECISION DLAMCH, ZLANGE
EXTERNAL LSAME, DLAMCH, ZLANGE
* ..
* .. External Subroutines ..
EXTERNAL XERBLA, ZGEMM, ZLACPY, ZLASCL
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE, DCMPLX, MAX
* ..
* .. Executable Statements ..
*
ZQRT17 = ZERO
*
IF( LSAME( TRANS, 'N' ) ) THEN
NROWS = M
NCOLS = N
ELSE IF( LSAME( TRANS, 'C' ) ) THEN
NROWS = N
NCOLS = M
ELSE
CALL XERBLA( 'ZQRT17', 1 )
RETURN
END IF
*
IF( LWORK.LT.NCOLS*NRHS ) THEN
CALL XERBLA( 'ZQRT17', 13 )
RETURN
END IF
*
IF( M.LE.0 .OR. N.LE.0 .OR. NRHS.LE.0 )
$ RETURN
*
NORMA = ZLANGE( 'One-norm', M, N, A, LDA, RWORK )
SMLNUM = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
BIGNUM = ONE / SMLNUM
ISCL = 0
*
* compute residual and scale it
*
CALL ZLACPY( 'All', NROWS, NRHS, B, LDB, C, LDB )
CALL ZGEMM( TRANS, 'No transpose', NROWS, NRHS, NCOLS,
$ DCMPLX( -ONE ), A, LDA, X, LDX, DCMPLX( ONE ), C,
$ LDB )
NORMRS = ZLANGE( 'Max', NROWS, NRHS, C, LDB, RWORK )
IF( NORMRS.GT.SMLNUM ) THEN
ISCL = 1
CALL ZLASCL( 'General', 0, 0, NORMRS, ONE, NROWS, NRHS, C, LDB,
$ INFO )
END IF
*
* compute R'*A
*
CALL ZGEMM( 'Conjugate transpose', TRANS, NRHS, NCOLS, NROWS,
$ DCMPLX( ONE ), C, LDB, A, LDA, DCMPLX( ZERO ), WORK,
$ NRHS )
*
* compute and properly scale error
*
ERR = ZLANGE( '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 = ZLANGE( 'One-norm', NROWS, NRHS, B, LDB, RWORK )
IF( NORMB.NE.ZERO )
$ ERR = ERR / NORMB
ELSE
IF( NORMRS.NE.ZERO )
$ ERR = ERR / NORMRS
END IF
*
ZQRT17 = ERR / ( DLAMCH( 'Epsilon' )*DBLE( MAX( M, N, NRHS ) ) )
RETURN
*
* End of ZQRT17
*
END
|
