OpenBLAS/lapack-netlib/TESTING/LIN/sqrt17.f

*> \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