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