sqrt17.f

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*> \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
*
.LT.      IF( LWORKNCOLS*NRHS ) THEN
         CALL XERBLA( 'sqrt17', 13 )
         RETURN
      END IF
*
.LE..OR..LE..OR..LE.      IF( M0  N0  NRHS0 ) 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 )
.GT.      IF( NORMRSSMLNUM ) 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 )
.NE.      IF( NORMAZERO )
     $   ERR = ERR / NORMA
*
.EQ.      IF( ISCL1 )
     $   ERR = ERR*NORMRS
*
.EQ.      IF( IRESID1 ) THEN
         NORMB = SLANGE( 'one-norm', NROWS, NRHS, B, LDB, RWORK )
.NE.         IF( NORMBZERO )
     $      ERR = ERR / NORMB
      ELSE
.NE.         IF( NORMRSZERO )
     $      ERR = ERR / NORMRS
      END IF
*
      SQRT17 = ERR / ( SLAMCH( 'epsilon' )*REAL( MAX( M, N, NRHS ) ) )
      RETURN
*
*     End of SQRT17
*
      END