cqrt15.f

Go to the documentation of this file.

*> \brief \b CQRT15
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE CQRT15( SCALE, RKSEL, M, N, NRHS, A, LDA, B, LDB, S,
*                          RANK, NORMA, NORMB, ISEED, WORK, LWORK )
*
*       .. Scalar Arguments ..
*       INTEGER            LDA, LDB, LWORK, M, N, NRHS, RANK, RKSEL, SCALE
*       REAL               NORMA, NORMB
*       ..
*       .. Array Arguments ..
*       INTEGER            ISEED( 4 )
*       REAL               S( * )
*       COMPLEX            A( LDA, * ), B( LDB, * ), WORK( LWORK )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> CQRT15 generates a matrix with full or deficient rank and of various
*> norms.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] SCALE
*> \verbatim
*>          SCALE is INTEGER
*>          SCALE = 1: normally scaled matrix
*>          SCALE = 2: matrix scaled up
*>          SCALE = 3: matrix scaled down
*> \endverbatim
*>
*> \param[in] RKSEL
*> \verbatim
*>          RKSEL is INTEGER
*>          RKSEL = 1: full rank matrix
*>          RKSEL = 2: rank-deficient matrix
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*>          M is INTEGER
*>          The number of rows of the matrix A.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The number of columns of A.
*> \endverbatim
*>
*> \param[in] NRHS
*> \verbatim
*>          NRHS is INTEGER
*>          The number of columns of B.
*> \endverbatim
*>
*> \param[out] A
*> \verbatim
*>          A is COMPLEX 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.
*> \endverbatim
*>
*> \param[out] B
*> \verbatim
*>          B is COMPLEX array, dimension (LDB, NRHS)
*>          A matrix that is in the range space of matrix A.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*>          LDB is INTEGER
*>          The leading dimension of the array B.
*> \endverbatim
*>
*> \param[out] S
*> \verbatim
*>          S is REAL array, dimension MIN(M,N)
*>          Singular values of A.
*> \endverbatim
*>
*> \param[out] RANK
*> \verbatim
*>          RANK is INTEGER
*>          number of nonzero singular values of A.
*> \endverbatim
*>
*> \param[out] NORMA
*> \verbatim
*>          NORMA is REAL
*>          one-norm norm of A.
*> \endverbatim
*>
*> \param[out] NORMB
*> \verbatim
*>          NORMB is REAL
*>          one-norm norm of B.
*> \endverbatim
*>
*> \param[in,out] ISEED
*> \verbatim
*>          ISEED is integer array, dimension (4)
*>          seed for random number generator.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is COMPLEX array, dimension (LWORK)
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*>          LWORK is INTEGER
*>          length of work space required.
*>          LWORK >= MAX(M+MIN(M,N),NRHS*MIN(M,N),2*N+M)
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup complex_lin
*
*  =====================================================================
      SUBROUTINE cqrt15( SCALE, RKSEL, M, N, NRHS, A, LDA, B, LDB, S,
     $                   RANK, NORMA, NORMB, ISEED, 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 ..
      INTEGER            LDA, LDB, LWORK, M, N, NRHS, RANK, RKSEL, SCALE
      REAL               NORMA, NORMB
*     ..
*     .. Array Arguments ..
      INTEGER            ISEED( 4 )
      REAL               S( * )
      COMPLEX            A( LDA, * ), B( LDB, * ), WORK( LWORK )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ZERO, ONE, TWO, SVMIN
      parameter( zero = 0.0e+0, one = 1.0e+0, two = 2.0e+0,
     $                   svmin = 0.1e+0 )
      COMPLEX            CZERO, CONE
      parameter( czero = ( 0.0e+0, 0.0e+0 ),
     $                   cone = ( 1.0e+0, 0.0e+0 ) )
*     ..
*     .. Local Scalars ..
      INTEGER            INFO, J, MN
      REAL               BIGNUM, EPS, SMLNUM, TEMP
*     ..
*     .. Local Arrays ..
      REAL               DUMMY( 1 )
*     ..
*     .. External Functions ..
      REAL               CLANGE, SASUM, SCNRM2, SLAMCH, SLARND
      EXTERNAL           clange, sasum, scnrm2, slamch, slarnd
*     ..
*     .. External Subroutines ..
      EXTERNAL           cgemm, clarf, clarnv, claror, clascl, claset,
     $                   csscal, slabad, slaord, slascl, xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs, cmplx, max, min
*     ..
*     .. Executable Statements ..
*
      mn = min( m, n )
      IF( lwork.LT.max( m+mn, mn*nrhs, 2*n+m ) ) THEN
         CALL xerbla( 'CQRT15', 16 )
         RETURN
      END IF
*
      smlnum = slamch( 'Safe minimum' )
      bignum = one / smlnum
      CALL slabad( smlnum, bignum )
      eps = slamch( 'Epsilon' )
      smlnum = ( smlnum / eps ) / eps
      bignum = one / smlnum
*
*     Determine rank and (unscaled) singular values
*
      IF( rksel.EQ.1 ) THEN
         rank = mn
      ELSE IF( rksel.EQ.2 ) THEN
         rank = ( 3*mn ) / 4
         DO 10 j = rank + 1, mn
            s( j ) = zero
   10    CONTINUE
      ELSE
         CALL xerbla( 'CQRT15', 2 )
      END IF
*
      IF( rank.GT.0 ) THEN
*
*        Nontrivial case
*
         s( 1 ) = one
         DO 30 j = 2, rank
   20       CONTINUE
            temp = slarnd( 1, iseed )
            IF( temp.GT.svmin ) THEN
               s( j ) = abs( temp )
            ELSE
               GO TO 20
            END IF
   30    CONTINUE
         CALL slaord( 'Decreasing', rank, s, 1 )
*
*        Generate 'rank' columns of a random orthogonal matrix in A
*
         CALL clarnv( 2, iseed, m, work )
         CALL csscal( m, one / scnrm2( m, work, 1 ), work, 1 )
         CALL claset( 'Full', m, rank, czero, cone, a, lda )
         CALL clarf( 'Left', m, rank, work, 1, cmplx( two ), a, lda,
     $               work( m+1 ) )
*
*        workspace used: m+mn
*
*        Generate consistent rhs in the range space of A
*
         CALL clarnv( 2, iseed, rank*nrhs, work )
         CALL cgemm( 'no transpose', 'no transpose', M, NRHS, RANK,
     $               CONE, A, LDA, WORK, RANK, CZERO, B, LDB )
*
*        work space used: <= mn *nrhs
*
*        generate (unscaled) matrix A
*
         DO 40 J = 1, RANK
            CALL CSSCAL( M, S( J ), A( 1, J ), 1 )
   40    CONTINUE
.LT.         IF( RANKN )
     $      CALL CLASET( 'full', M, N-RANK, CZERO, CZERO,
     $                   A( 1, RANK+1 ), LDA )
         CALL CLAROR( 'right', 'no initialization', M, N, A, LDA, ISEED,
     $                WORK, INFO )
*
      ELSE
*
*        work space used 2*n+m
*
*        Generate null matrix and rhs
*
         DO 50 J = 1, MN
            S( J ) = ZERO
   50    CONTINUE
         CALL CLASET( 'full', M, N, CZERO, CZERO, A, LDA )
         CALL CLASET( 'full', M, NRHS, CZERO, CZERO, B, LDB )
*
      END IF
*
*     Scale the matrix
*
.NE.      IF( SCALE1 ) THEN
         NORMA = CLANGE( 'max', M, N, A, LDA, DUMMY )
.NE.         IF( NORMAZERO ) THEN
.EQ.            IF( SCALE2 ) THEN
*
*              matrix scaled up
*
               CALL CLASCL( 'general', 0, 0, NORMA, BIGNUM, M, N, A,
     $                      LDA, INFO )
               CALL SLASCL( 'general', 0, 0, NORMA, BIGNUM, MN, 1, S,
     $                      MN, INFO )
               CALL CLASCL( 'general', 0, 0, NORMA, BIGNUM, M, NRHS, B,
     $                      LDB, INFO )
.EQ.            ELSE IF( SCALE3 ) THEN
*
*              matrix scaled down
*
               CALL CLASCL( 'general', 0, 0, NORMA, SMLNUM, M, N, A,
     $                      LDA, INFO )
               CALL SLASCL( 'general', 0, 0, NORMA, SMLNUM, MN, 1, S,
     $                      MN, INFO )
               CALL CLASCL( 'general', 0, 0, NORMA, SMLNUM, M, NRHS, B,
     $                      LDB, INFO )
            ELSE
               CALL XERBLA( 'cqrt15', 1 )
               RETURN
            END IF
         END IF
      END IF
*
      NORMA = SASUM( MN, S, 1 )
      NORMB = CLANGE( 'one-norm', M, NRHS, B, LDB, DUMMY )
*
      RETURN
*
*     End of CQRT15
*
      END