numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
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| lapack/TESTING/LIN/schktz.f | 9076B | -rw-r--r-- |
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*> \brief \b SCHKTZ * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE SCHKTZ( DOTYPE, NM, MVAL, NN, NVAL, THRESH, TSTERR, A, * COPYA, S, TAU, WORK, NOUT ) * * .. Scalar Arguments .. * LOGICAL TSTERR * INTEGER NM, NN, NOUT * REAL THRESH * .. * .. Array Arguments .. * LOGICAL DOTYPE( * ) * INTEGER MVAL( * ), NVAL( * ) * REAL A( * ), COPYA( * ), S( * ), * $ TAU( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> SCHKTZ tests STZRZF. *> \endverbatim * * Arguments: * ========== * *> \param[in] DOTYPE *> \verbatim *> DOTYPE is LOGICAL array, dimension (NTYPES) *> The matrix types to be used for testing. Matrices of type j *> (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = *> .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used. *> \endverbatim *> *> \param[in] NM *> \verbatim *> NM is INTEGER *> The number of values of M contained in the vector MVAL. *> \endverbatim *> *> \param[in] MVAL *> \verbatim *> MVAL is INTEGER array, dimension (NM) *> The values of the matrix row dimension M. *> \endverbatim *> *> \param[in] NN *> \verbatim *> NN is INTEGER *> The number of values of N contained in the vector NVAL. *> \endverbatim *> *> \param[in] NVAL *> \verbatim *> NVAL is INTEGER array, dimension (NN) *> The values of the matrix column dimension N. *> \endverbatim *> *> \param[in] THRESH *> \verbatim *> THRESH is REAL *> The threshold value for the test ratios. A result is *> included in the output file if RESULT >= THRESH. To have *> every test ratio printed, use THRESH = 0. *> \endverbatim *> *> \param[in] TSTERR *> \verbatim *> TSTERR is LOGICAL *> Flag that indicates whether error exits are to be tested. *> \endverbatim *> *> \param[out] A *> \verbatim *> A is REAL array, dimension (MMAX*NMAX) *> where MMAX is the maximum value of M in MVAL and NMAX is the *> maximum value of N in NVAL. *> \endverbatim *> *> \param[out] COPYA *> \verbatim *> COPYA is REAL array, dimension (MMAX*NMAX) *> \endverbatim *> *> \param[out] S *> \verbatim *> S is REAL array, dimension *> (min(MMAX,NMAX)) *> \endverbatim *> *> \param[out] TAU *> \verbatim *> TAU is REAL array, dimension (MMAX) *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is REAL array, dimension *> (MMAX*NMAX + 4*NMAX + MMAX) *> \endverbatim *> *> \param[in] NOUT *> \verbatim *> NOUT is INTEGER *> The unit number for output. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup single_lin * * ===================================================================== SUBROUTINE SCHKTZ( DOTYPE, NM, MVAL, NN, NVAL, THRESH, TSTERR, A, $ COPYA, S, TAU, WORK, NOUT ) * * -- 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 .. LOGICAL TSTERR INTEGER NM, NN, NOUT REAL THRESH * .. * .. Array Arguments .. LOGICAL DOTYPE( * ) INTEGER MVAL( * ), NVAL( * ) REAL A( * ), COPYA( * ), S( * ), $ TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. INTEGER NTYPES PARAMETER ( NTYPES = 3 ) INTEGER NTESTS PARAMETER ( NTESTS = 3 ) REAL ONE, ZERO PARAMETER ( ONE = 1.0E0, ZERO = 0.0E0 ) * .. * .. Local Scalars .. CHARACTER*3 PATH INTEGER I, IM, IMODE, IN, INFO, K, LDA, LWORK, M, $ MNMIN, MODE, N, NERRS, NFAIL, NRUN REAL EPS * .. * .. Local Arrays .. INTEGER ISEED( 4 ), ISEEDY( 4 ) REAL RESULT( NTESTS ) * .. * .. External Functions .. REAL SLAMCH, SQRT12, SRZT01, SRZT02 EXTERNAL SLAMCH, SQRT12, SRZT01, SRZT02 * .. * .. External Subroutines .. EXTERNAL ALAHD, ALASUM, SERRTZ, SGEQR2, SLACPY, SLAORD, $ SLASET, SLATMS, STZRZF * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Scalars in Common .. LOGICAL LERR, OK CHARACTER*32 SRNAMT INTEGER INFOT, IOUNIT * .. * .. Common blocks .. COMMON / INFOC / INFOT, IOUNIT, OK, LERR COMMON / SRNAMC / SRNAMT * .. * .. Data statements .. DATA ISEEDY / 1988, 1989, 1990, 1991 / * .. * .. Executable Statements .. * * Initialize constants and the random number seed. * PATH( 1: 1 ) = 'Single precision' PATH( 2: 3 ) = 'TZ' NRUN = 0 NFAIL = 0 NERRS = 0 DO 10 I = 1, 4 ISEED( I ) = ISEEDY( I ) 10 CONTINUE EPS = SLAMCH( 'Epsilon' ) * * Test the error exits * IF( TSTERR ) $ CALL SERRTZ( PATH, NOUT ) INFOT = 0 * DO 70 IM = 1, NM * * Do for each value of M in MVAL. * M = MVAL( IM ) LDA = MAX( 1, M ) * DO 60 IN = 1, NN * * Do for each value of N in NVAL for which M .LE. N. * N = NVAL( IN ) MNMIN = MIN( M, N ) LWORK = MAX( 1, N*N+4*M+N, M*N+2*MNMIN+4*N ) * IF( M.LE.N ) THEN DO 50 IMODE = 1, NTYPES IF( .NOT.DOTYPE( IMODE ) ) $ GO TO 50 * * Do for each type of singular value distribution. * 0: zero matrix * 1: one small singular value * 2: exponential distribution * MODE = IMODE - 1 * * Test STZRQF * * Generate test matrix of size m by n using * singular value distribution indicated by `mode'. * IF( MODE.EQ.0 ) THEN CALL SLASET( 'Full', M, N, ZERO, ZERO, A, LDA ) DO 30 I = 1, MNMIN S( I ) = ZERO 30 CONTINUE ELSE CALL SLATMS( M, N, 'Uniform', ISEED, $ 'Nonsymmetric', S, IMODE, $ ONE / EPS, ONE, M, N, 'No packing', A, $ LDA, WORK, INFO ) CALL SGEQR2( M, N, A, LDA, WORK, WORK( MNMIN+1 ), $ INFO ) CALL SLASET( 'Lower', M-1, N, ZERO, ZERO, A( 2 ), $ LDA ) CALL SLAORD( 'Decreasing', MNMIN, S, 1 ) END IF * * Save A and its singular values * CALL SLACPY( 'All', M, N, A, LDA, COPYA, LDA ) * * Call STZRZF to reduce the upper trapezoidal matrix to * upper triangular form. * SRNAMT = 'STZRZF' CALL STZRZF( M, N, A, LDA, TAU, WORK, LWORK, INFO ) * * Compute norm(svd(a) - svd(r)) * RESULT( 1 ) = SQRT12( M, M, A, LDA, S, WORK, $ LWORK ) * * Compute norm( A - R*Q ) * RESULT( 2 ) = SRZT01( M, N, COPYA, A, LDA, TAU, WORK, $ LWORK ) * * Compute norm(Q'*Q - I). * RESULT( 3 ) = SRZT02( M, N, A, LDA, TAU, WORK, LWORK ) * * Print information about the tests that did not pass * the threshold. * DO 40 K = 1, NTESTS IF( RESULT( K ).GE.THRESH ) THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) $ CALL ALAHD( NOUT, PATH ) WRITE( NOUT, FMT = 9999 )M, N, IMODE, K, $ RESULT( K ) NFAIL = NFAIL + 1 END IF 40 CONTINUE NRUN = NRUN + 3 50 CONTINUE END IF 60 CONTINUE 70 CONTINUE * * Print a summary of the results. * CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS ) * 9999 FORMAT( ' M =', I5, ', N =', I5, ', type ', I2, ', test ', I2, $ ', ratio =', G12.5 ) * * End if SCHKTZ * END