numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
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| lapack/TESTING/LIN/dqrt15.f | 8354B | -rw-r--r-- |
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*> \brief \b DQRT15 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE DQRT15( 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 * DOUBLE PRECISION NORMA, NORMB * .. * .. Array Arguments .. * INTEGER ISEED( 4 ) * DOUBLE PRECISION A( LDA, * ), B( LDB, * ), S( * ), WORK( LWORK ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DQRT15 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION *> one-norm of A. *> \endverbatim *> *> \param[out] NORMB *> \verbatim *> NORMB is DOUBLE PRECISION *> one-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 DOUBLE PRECISION 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 double_lin * * ===================================================================== SUBROUTINE DQRT15( 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 DOUBLE PRECISION NORMA, NORMB * .. * .. Array Arguments .. INTEGER ISEED( 4 ) DOUBLE PRECISION A( LDA, * ), B( LDB, * ), S( * ), WORK( LWORK ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE, TWO, SVMIN PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0, $ SVMIN = 0.1D0 ) * .. * .. Local Scalars .. INTEGER INFO, J, MN DOUBLE PRECISION BIGNUM, EPS, SMLNUM, TEMP * .. * .. Local Arrays .. DOUBLE PRECISION DUMMY( 1 ) * .. * .. External Functions .. DOUBLE PRECISION DASUM, DLAMCH, DLANGE, DLARND, DNRM2 EXTERNAL DASUM, DLAMCH, DLANGE, DLARND, DNRM2 * .. * .. External Subroutines .. EXTERNAL DGEMM, DLAORD, DLARF, DLARNV, DLAROR, DLASCL, $ DLASET, DSCAL, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, MIN * .. * .. Executable Statements .. * MN = MIN( M, N ) IF( LWORK.LT.MAX( M+MN, MN*NRHS, 2*N+M ) ) THEN CALL XERBLA( 'DQRT15', 16 ) RETURN END IF * SMLNUM = DLAMCH( 'Safe minimum' ) BIGNUM = ONE / SMLNUM EPS = DLAMCH( '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( 'DQRT15', 2 ) END IF * IF( RANK.GT.0 ) THEN * * Nontrivial case * S( 1 ) = ONE DO 30 J = 2, RANK 20 CONTINUE TEMP = DLARND( 1, ISEED ) IF( TEMP.GT.SVMIN ) THEN S( J ) = ABS( TEMP ) ELSE GO TO 20 END IF 30 CONTINUE CALL DLAORD( 'Decreasing', RANK, S, 1 ) * * Generate 'rank' columns of a random orthogonal matrix in A * CALL DLARNV( 2, ISEED, M, WORK ) CALL DSCAL( M, ONE / DNRM2( M, WORK, 1 ), WORK, 1 ) CALL DLASET( 'Full', M, RANK, ZERO, ONE, A, LDA ) CALL DLARF( 'Left', M, RANK, WORK, 1, TWO, A, LDA, $ WORK( M+1 ) ) * * workspace used: m+mn * * Generate consistent rhs in the range space of A * CALL DLARNV( 2, ISEED, RANK*NRHS, WORK ) CALL DGEMM( 'No transpose', 'No transpose', M, NRHS, RANK, ONE, $ A, LDA, WORK, RANK, ZERO, B, LDB ) * * work space used: <= mn *nrhs * * generate (unscaled) matrix A * DO 40 J = 1, RANK CALL DSCAL( M, S( J ), A( 1, J ), 1 ) 40 CONTINUE IF( RANK.LT.N ) $ CALL DLASET( 'Full', M, N-RANK, ZERO, ZERO, A( 1, RANK+1 ), $ LDA ) CALL DLAROR( '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 DLASET( 'Full', M, N, ZERO, ZERO, A, LDA ) CALL DLASET( 'Full', M, NRHS, ZERO, ZERO, B, LDB ) * END IF * * Scale the matrix * IF( SCALE.NE.1 ) THEN NORMA = DLANGE( 'Max', M, N, A, LDA, DUMMY ) IF( NORMA.NE.ZERO ) THEN IF( SCALE.EQ.2 ) THEN * * matrix scaled up * CALL DLASCL( 'General', 0, 0, NORMA, BIGNUM, M, N, A, $ LDA, INFO ) CALL DLASCL( 'General', 0, 0, NORMA, BIGNUM, MN, 1, S, $ MN, INFO ) CALL DLASCL( 'General', 0, 0, NORMA, BIGNUM, M, NRHS, B, $ LDB, INFO ) ELSE IF( SCALE.EQ.3 ) THEN * * matrix scaled down * CALL DLASCL( 'General', 0, 0, NORMA, SMLNUM, M, N, A, $ LDA, INFO ) CALL DLASCL( 'General', 0, 0, NORMA, SMLNUM, MN, 1, S, $ MN, INFO ) CALL DLASCL( 'General', 0, 0, NORMA, SMLNUM, M, NRHS, B, $ LDB, INFO ) ELSE CALL XERBLA( 'DQRT15', 1 ) RETURN END IF END IF END IF * NORMA = DASUM( MN, S, 1 ) NORMB = DLANGE( 'One-norm', M, NRHS, B, LDB, DUMMY ) * RETURN * * End of DQRT15 * END