Martin Kroeker
c3de327dd5
* Add CX factorization (expert) routines ?GECXX (Reference-LAPACK PR 1161)
973 lines
35 KiB
FortranFixed
973 lines
35 KiB
FortranFixed
*> \brief \b DCHKCXX
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE DCHKCXX( DOTYPE, NM, MVAL, NN, NVAL,
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* $ NNB, NBVAL, NXVAL, THRESH, TSTERR,
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* $ A, COPYA,
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* $ C, COPYC, QRC, COPYQRC, X, COPYX, S, TAU,
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* $ DESEL_ROWS, COPY_DESEL_ROWS,
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* $ SEL_DESEL_COLS, COPY_SEL_DESEL_COLS,
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* $ IPIV, COPY_IPIV, JPIV, COPY_JPIV,
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* $ WORK, IWORK, NOUT )
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* IMPLICIT NONE
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*
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* .. Scalar Arguments ..
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* LOGICAL TSTERR
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* INTEGER NM, NN, NNB, NOUT
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* DOUBLE PRECISION THRESH
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* ..
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* .. Array Arguments ..
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* LOGICAL DOTYPE( * )
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* INTEGER IWORK( * ), NBVAL( * ), MVAL( * ), NVAL( * ),
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* $ NXVAL( * ),
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* $ DESEL_ROWS( * ), COPY_DESEL_ROWS( * ),
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* $ SEL_DESEL_COLS( * ), COPY_SEL_DESEL_COLS( * ),
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* $ IPIV( * ), COPY_IPIV( * ),
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* $ JPIV( * ), COPY_JPIV( * )
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* DOUBLE PRECISION A( * ), COPYA( * ), C( * ), COPYC( * ),
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* $ QRC( * ), COPYQRC( * ), X( * ), COPYX( * ),
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* $ S( * ), TAU( * ), WORK( * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> DCHKCXX tests DGECXX.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] DOTYPE
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*> \verbatim
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*> DOTYPE is LOGICAL array, dimension (NTYPES)
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*> The matrix types to be used for testing. Matrices of type j
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*> (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
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*> .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
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*> \endverbatim
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*>
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*> \param[in] NM
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*> \verbatim
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*> NM is INTEGER
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*> The number of values of M contained in the vector MVAL.
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*> \endverbatim
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*>
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*> \param[in] MVAL
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*> \verbatim
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*> MVAL is INTEGER array, dimension (NM)
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*> The values of the matrix row dimension M.
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*> \endverbatim
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*>
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*> \param[in] NN
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*> \verbatim
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*> NN is INTEGER
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*> The number of values of N contained in the vector NVAL.
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*> \endverbatim
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*>
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*> \param[in] NVAL
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*> \verbatim
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*> NVAL is INTEGER array, dimension (NN)
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*> The values of the matrix column dimension N.
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*> \endverbatim
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*>
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*> \param[in] NNB
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*> \verbatim
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*> NNB is INTEGER
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*> The number of values of NB and NX contained in the
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*> vectors NBVAL and NXVAL. The blocking parameters are used
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*> in pairs (NB,NX).
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*> \endverbatim
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*>
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*> \param[in] NBVAL
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*> \verbatim
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*> NBVAL is INTEGER array, dimension (NNB)
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*> The values of the blocksize NB.
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*> \endverbatim
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*>
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*> \param[in] NXVAL
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*> \verbatim
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*> NXVAL is INTEGER array, dimension (NNB)
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*> The values of the crossover point NX.
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*> \endverbatim
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*>
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*> \param[in] THRESH
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*> \verbatim
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*> THRESH is DOUBLE PRECISION
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*> The threshold value for the test ratios. A result is
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*> included in the output file if RESULT >= THRESH. To have
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*> every test ratio printed, use THRESH = 0.
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*> \endverbatim
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*>
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*> \param[in] TSTERR
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*> \verbatim
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*> TSTERR is LOGICAL
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*> Flag that indicates whether error exits are to be tested.
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*> \endverbatim
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*>
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*> \param[out] A
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*> \verbatim
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*> A is DOUBLE PRECISION array, dimension (MMAX*NMAX)
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*> where MMAX is the maximum value of M in MVAL and NMAX is the
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*> maximum value of N in NVAL.
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*> \endverbatim
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*>
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*> \param[out] COPYA
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*> \verbatim
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*> COPYA is DOUBLE PRECISION array, dimension (MMAX*NMAX)
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*> where MMAX is the maximum value of M in MVAL and NMAX is the
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*> maximum value of N in NVAL.
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*> \endverbatim
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*>
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*> \param[out] C
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*> \verbatim
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*> C is DOUBLE PRECISION array, dimension (MMAX*NMAX)
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*> where MMAX is the maximum value of M in MVAL and NMAX is the
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*> maximum value of N in NVAL.
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*> \endverbatim
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*>
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*> \param[out] COPYC
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*> \verbatim
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*> COPYC is DOUBLE PRECISION array, dimension (MMAX*NMAX)
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*> where MMAX is the maximum value of M in MVAL and NMAX is the
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*> maximum value of N in NVAL.
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*> \endverbatim
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*>
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*> \param[out] QRC
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*> \verbatim
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*> QRC is DOUBLE PRECISION array, dimension (MMAX*NMAX)
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*> where MMAX is the maximum value of M in MVAL and NMAX is the
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*> maximum value of N in NVAL.
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*> \endverbatim
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*>
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*> \param[out] COPYQRC
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*> \verbatim
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*> COPYQRC is DOUBLE PRECISION array, dimension (MMAX*NMAX)
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*> where MMAX is the maximum value of M in MVAL and NMAX is the
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*> maximum value of N in NVAL.
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*> \endverbatim
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*>
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*> \param[out] X
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*> \verbatim
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*> X is DOUBLE PRECISION array, dimension (NMAX*NMAX)
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*> NMAX is the maximum value of N in NVAL.
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*> \endverbatim
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*>
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*> \param[out] COPYX
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*> \verbatim
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*> COPYX is DOUBLE PRECISION array, dimension (NMAX*NMAX)
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*> NMAX is the maximum value of N in NVAL.
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*> \endverbatim
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*>
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*> \param[out] S
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*> \verbatim
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*> S is DOUBLE PRECISION array, dimension
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*> (min(MMAX,NMAX))
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*> \endverbatim
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*>
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*> \param[out] TAU
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*> \verbatim
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*> TAU is DOUBLE PRECISION array, dimension (MMAX)
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*> \endverbatim
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*>
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*> \param[out] DESEL_ROWS
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*> \verbatim
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*> DESEL_ROWS is INTEGER array, dimension (MMAX)
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*> \endverbatim
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*>
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*> \param[out] COPY_DESEL_ROWS
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*> \verbatim
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*> COPY_DESEL_ROWS is INTEGER array, dimension (MMAX)
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*> \endverbatim
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*>
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*> \param[out] SEL_DESEL_COLS
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*> \verbatim
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*> SEL_DESEL_COLS is INTEGER array, dimension (NMAX)
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*> \endverbatim
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*>
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*> \param[out] COPY_SEL_DESEL_COLS
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*> \verbatim
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*> COPY_SEL_DESEL_COLS is INTEGER array, dimension (NMAX)
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*> \endverbatim
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*>
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*> \param[out] IPIV
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*> \verbatim
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*> IPIV is INTEGER array, dimension (MMAX)
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*> \endverbatim
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*>
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*> \param[out] COPY_IPIV
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*> \verbatim
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*> COPY_IPIV is INTEGER array, dimension (MMAX)
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*> \endverbatim
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*>
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*> \param[out] JPIV
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*> \verbatim
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*> JPIV is INTEGER array, dimension (NMAX)
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*> \endverbatim
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*>
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*> \param[out] COPY_JPIV
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*> \verbatim
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*> COPY_JPIV is INTEGER array, dimension (NMAX)
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is DOUBLE PRECISION array.
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*> Dimension is the maximum of the following two expressions:
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*> (1) Optimal complex workspace dimension for matrix generation
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*> and test routines.
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*> (MMAX + 6) * max(MMAX,NMAX)
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*> This is an upper bound for:
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*> a) DLATMS: 3*max(M,N)
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*> b) DQRT12: max( M*N + 4*min(M,N) + max(M,N),
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*> M*N + 2*min(M,N) + 4*N )
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*> c) DQPT01: M*N + N
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*> d) DQRT11: M*M + M
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*>
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*> (2) Optimal workspace dimension for DGECXX.
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*> max( NMAX*NBMAX, \\ for DGEQRF inside
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*> NMAX*min(NBMAX_ORMQR,NBMAX) \\ for DORMQR inside
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*> + (NBMAX_ORMQR+1)*NBMAX_ORMQR ),
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*> 2*NMAX + NBMAX*( NMAX + 1 ), \\ for DGEQP3RK inside
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*> min(MMAX,NMAX) + NMAX*NBMAX ), \\ for DGELS inside
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*> where NBMAX_ORMQR=64 is hardwired in DORMQR.
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*>
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*> Assuming MMAX = NMAX, and NBMAX = NMAX, the expressions become:
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*> (1) NMAX*NMAX + 6*NMAX
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*> (2) NMAX * min(64,NMAX) + 4160
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*> \endverbatim
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*>
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*> \param[out] IWORK
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*> \verbatim
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*> IWORK is INTEGER array, dimension (2*NMAX)
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*> for DGECXX optimal IWORK size.
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*> \endverbatim
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*>
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*> \param[in] NOUT
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*> \verbatim
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*> NOUT is INTEGER
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*> The unit number for output.
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \ingroup double_lin
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*
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* =====================================================================
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SUBROUTINE DCHKCXX( DOTYPE, NM, MVAL, NN, NVAL,
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$ NNB, NBVAL, NXVAL, THRESH, TSTERR,
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$ A, COPYA,
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$ C, COPYC, QRC, COPYQRC, X, COPYX, S, TAU,
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$ DESEL_ROWS, COPY_DESEL_ROWS,
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$ SEL_DESEL_COLS, COPY_SEL_DESEL_COLS,
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$ IPIV, COPY_IPIV, JPIV, COPY_JPIV,
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$ WORK, IWORK, NOUT )
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IMPLICIT NONE
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*
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* -- LAPACK test routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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* .. Scalar Arguments ..
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LOGICAL TSTERR
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INTEGER NM, NN, NNB, NOUT
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DOUBLE PRECISION THRESH
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* ..
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* .. Array Arguments ..
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LOGICAL DOTYPE( * )
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INTEGER IWORK( * ), NBVAL( * ), MVAL( * ), NVAL( * ),
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$ NXVAL( * ),
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$ DESEL_ROWS( * ), COPY_DESEL_ROWS( * ),
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$ SEL_DESEL_COLS( * ), COPY_SEL_DESEL_COLS( * ),
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$ IPIV( * ), COPY_IPIV( * ),
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$ JPIV( * ), COPY_JPIV( * )
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DOUBLE PRECISION A( * ), COPYA( * ), C( * ), COPYC( * ),
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$ QRC( * ), COPYQRC( * ), X( * ), COPYX( * ),
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$ S( * ), TAU( * ), WORK( * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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INTEGER NTYPES
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PARAMETER ( NTYPES = 19 )
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INTEGER NTESTS
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PARAMETER ( NTESTS = 5 )
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DOUBLE PRECISION ONE, ZERO, BIGNUM
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PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0,
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$ BIGNUM = 1.0D+38 )
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* ..
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* .. Local Scalars ..
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CHARACTER DIST, TYPE, FACT, USESD
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CHARACTER*3 PATH
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INTEGER I, IM, IMAT, IN, INB, IND_OFFSET_GEN,
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$ IND_IN, IND_OUT, INFO, J, J_INC, J_FIRST_NZ,
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$ JB_ZERO, K, KL, KMAXFREE, KU, LDA, LDC,
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$ LDQRC, LDX, LIWORK, LWORK, LWKTST,
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$ M, MINMN, MINMNB_GEN, MODE, N,
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$ NB, NBMAX_ORMQR, NB_ZERO, NERRS, NFAIL,
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$ NB_GEN, NRUN, NX, T
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DOUBLE PRECISION ANORM, CNDNUM, EPS, ABSTOL, RELTOL,
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$ DTEMP, MAXC2NRMK, RELMAXC2NRMK, FNRMK
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* ..
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* .. Local Arrays ..
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INTEGER ISEED( 4 ), ISEEDY( 4 )
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DOUBLE PRECISION RESULT( NTESTS )
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* ..
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* .. External Functions ..
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DOUBLE PRECISION DLAMCH, DQPT01, DQRT11, DQRT12
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EXTERNAL DLAMCH, DQPT01, DQRT11, DQRT12
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* ..
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* .. External Subroutines ..
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EXTERNAL ALAERH, ALAHD, ALASUM, DERRCXX,
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$ DGECXX, DLACPY, DLAORD, DLASET, DLATB4,
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$ DLATMS, DSWAP, ICOPY, XLAENV
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, MAX, MIN, MOD
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* ..
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* .. Scalars in Common ..
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LOGICAL LERR, OK
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CHARACTER*32 SRNAMT
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INTEGER INFOT, IOUNIT
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* ..
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* .. Common blocks ..
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COMMON / INFOC / INFOT, IOUNIT, OK, LERR
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COMMON / SRNAMC / SRNAMT
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* ..
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* .. Data statements ..
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DATA ISEEDY / 1988, 1989, 1990, 1991 /
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* ..
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* .. Executable Statements ..
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*
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* Initialize constants and the random number seed.
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*
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PATH( 1: 1 ) = 'Double precision'
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PATH( 2: 3 ) = 'CX'
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NRUN = 0
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NFAIL = 0
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NERRS = 0
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DO I = 1, 4
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ISEED( I ) = ISEEDY( I )
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END DO
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EPS = DLAMCH( 'Epsilon' )
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*
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* Test the error exits
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*
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IF( TSTERR )
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$ CALL DERRCXX( PATH, NOUT )
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*
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INFOT = 0
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*
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DO IM = 1, NM
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*
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* Do for each value of M in MVAL.
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*
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M = MVAL( IM )
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LDA = MAX( 1, M )
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LDC = MAX( 1, M )
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LDQRC = MAX( 1, M )
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*
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DO IN = 1, NN
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*
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* Do for each value of N in NVAL.
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*
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N = NVAL( IN )
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MINMN = MIN( M, N )
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LDX = MAX( 1, N )
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*
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* 1) NOTE: for matrix generation routine DLATMS, the workspace length
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* LWKTMS = 3*MAX( M, N ). LWKTMS not used in the code.
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*
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* 2) Set workspace length for testing routines.
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* a) for DQRT12
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LWKTST = MAX( 1, M*N + 4*MINMN + MAX( M, N ),
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$ M*N + 2*MINMN + 4*N )
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*
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* b) for DQPT01
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*
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LWKTST = MAX( LWKTST, M*N + N )
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*
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* c) for DQRT11
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*
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LWKTST = MAX( LWKTST, M*M + M )
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*
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DO IMAT = 1, NTYPES
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*
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* Do for each value of IMAT in NTYPES.
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*
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* Do the tests only if DOTYPE( IMAT ) is true.
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*
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IF( .NOT.DOTYPE( IMAT ) )
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$ CYCLE
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*
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* The type of distribution used to generate the random
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* eigen-/singular values:
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* ( 'S' for symmetric distribution ) => UNIFORM( -1, 1 )
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*
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* Do for each type of NON-SYMMETRIC matrix: CNDNUM NORM MODE
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* 1. Zero matrix CNDNUM = Inf 0 N/A
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* 2. Random, Diagonal CNDNUM = 2 1 3 ( geometric distribution of singular values )
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* 3. Random, Upper triangular CNDNUM = 2 1 3 ( geometric distribution of singular values )
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* 4. Random, Lower triangular CNDNUM = 2 1 3 ( geometric distribution of singular values )
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* 5. Random, First column is zero CNDNUM = 2 1 3 ( geometric distribution of singular values )
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* 6. Random, Last MINMN column is zero CNDNUM = 2 1 3 ( geometric distribution of singular values )
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* 7. Random, Last N column is zero CNDNUM = 2 1 3 ( geometric distribution of singular values )
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* 8. Random, Middle column in MINMN is zero CNDNUM = 2 1 3 ( geometric distribution of singular values )
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* 9. Random, First half of MINMN columns are zero,
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* zero block size MINMN/2 CNDNUM = 2 1 3 ( geometric distribution of singular values )
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* 10. Random, Last columns are zero starting from MINMN/2+1 column,
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* zero block size N - MINMN/2 CNDNUM = 2 1 3 ( geometric distribution of singular values )
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* 11. Random, Half of MINMN columns in the middle are zero starting
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* from MINMN/2-(MINMN/2)/2+1 column,
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* zero block size MINMN/2 CNDNUM = 2 1 3 ( geometric distribution of singular values )
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* 12. Random, Odd columns are ZERO CNDNUM = 2 1 3 ( geometric distribution of singular values )
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* 13. Random, Even columns are ZERO CNDNUM = 2 1 3 ( geometric distribution of singular values )
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* 14. Random, CNDNUM = 2 CNDNUM = 2 1 3 ( geometric distribution of singular values )
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* 15. Random, CNDNUM = sqrt(0.1/EPS) CNDNUM = BADC1 = sqrt(0.1/EPS) 1 3 ( geometric distribution of singular values )
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* 16. Random, CNDNUM = 0.1/EPS CNDNUM = BADC2 = 0.1/EPS 1 3 ( geometric distribution of singular values )
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* 17. Random, CNDNUM = 0.1/EPS, one small singular value S(N)=1/CNDNUM CNDNUM = BADC2 = 0.1/EPS 1 2 ( one small singular value, S(N)=1/CNDNUM )
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* 18. Random, CNDNUM = 2, scaled near underflow CNDNUM = 2 SMALL = SAFMIN 3 ( geometric distribution of singular values )
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* 19. Random, CNDNUM = 2, scaled near overflow CNDNUM = 2 LARGE = 1.0/( 0.25 * ( SAFMIN / EPS ) ) 3 ( geometric distribution of singular values )
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*
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* Generate matrices.
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*
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IF( IMAT.EQ.1 ) THEN
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*
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* Matrix 1 (Zero matrix).
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*
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CALL DLASET( 'Full', M, N, ZERO, ZERO, COPYA, LDA )
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*
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* Array S(1:min(M,N)) should contain svd(A), the sigular
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* values of the generated matrix A in decreasing absolute
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* value order. S in this format will be used later in the test.
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* We set the array S explicitly here, since we are not using
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* DLATMS (which sets the array S) to generate zero matrix.
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*
|
|
DO I = 1, MINMN
|
|
S( I ) = ZERO
|
|
END DO
|
|
*
|
|
ELSE IF( ( IMAT.EQ.2 .OR. IMAT.EQ.3 .OR. IMAT.EQ.4 )
|
|
$ .OR. ( IMAT.GE.14 .AND. IMAT.LE.19 ) ) THEN
|
|
*
|
|
* Matrix 2 (Diagonal),
|
|
* Matrix 3 (Upper triangular),
|
|
* Matrix 4 (Lower triangular),
|
|
* Matrices 14-19 (Various rectangular random matrices
|
|
* without zero columns).
|
|
*
|
|
* Set up parameters with DLATB4 and generate a test
|
|
* matrix with DLATMS.
|
|
*
|
|
CALL DLATB4( PATH, IMAT, M, N, TYPE, KL, KU, ANORM,
|
|
$ MODE, CNDNUM, DIST )
|
|
*
|
|
SRNAMT = 'DLATMS'
|
|
CALL DLATMS( M, N, DIST, ISEED, TYPE, S, MODE,
|
|
$ CNDNUM, ANORM, KL, KU, 'No packing',
|
|
$ COPYA, LDA, WORK, INFO )
|
|
*
|
|
* Check error code from DLATMS.
|
|
*
|
|
IF( INFO.NE.0 ) THEN
|
|
CALL ALAERH( PATH, 'DLATMS', INFO, 0, ' ', M, N,
|
|
$ -1, -1, -1, IMAT, NFAIL, NERRS,
|
|
$ NOUT )
|
|
CYCLE
|
|
END IF
|
|
*
|
|
* Array S(1:min(M,N)) should contain svd(A), the sigular
|
|
* values of the generated matrix A in decreasing absolute
|
|
* value order. S in this format will be used later in
|
|
* the test. Unordered singular values are returned by
|
|
* DLATMS in S. We need to order singular values in S.
|
|
*
|
|
CALL DLAORD( 'Decreasing', MINMN, S, 1 )
|
|
*
|
|
ELSE IF( MINMN.GE.2
|
|
$ .AND. IMAT.GE.5 .AND. IMAT.LE.13 ) THEN
|
|
*
|
|
* Matrices 5-13 (Rectangular random matrices that
|
|
* contain zero columns). Only for matrices MINMN >= 2.
|
|
*
|
|
* JB_ZERO is the column index of ZERO block.
|
|
* NB_ZERO is the column block size of ZERO block.
|
|
* NB_GEN is the column blcok size of the
|
|
* generated block.
|
|
* J_INC in the non_zero column index increment
|
|
* to generate matrix 12 and 13.
|
|
* J_FIRS_NZ is the index of the first non-zero
|
|
* column to generate matrix 12 and 13.
|
|
*
|
|
IF( IMAT.EQ.5 ) THEN
|
|
*
|
|
* Matrix 5. First column is zero.
|
|
*
|
|
JB_ZERO = 1
|
|
NB_ZERO = 1
|
|
NB_GEN = N - NB_ZERO
|
|
*
|
|
ELSE IF( IMAT.EQ.6 ) THEN
|
|
*
|
|
* Matrix 6. Last column MINMN is zero.
|
|
*
|
|
JB_ZERO = MINMN
|
|
NB_ZERO = 1
|
|
NB_GEN = N - NB_ZERO
|
|
*
|
|
ELSE IF( IMAT.EQ.7 ) THEN
|
|
*
|
|
* Matrix 7. Last column N is zero.
|
|
*
|
|
JB_ZERO = N
|
|
NB_ZERO = 1
|
|
NB_GEN = N - NB_ZERO
|
|
*
|
|
ELSE IF( IMAT.EQ.8 ) THEN
|
|
*
|
|
* MAtrix 8. Middle column in MINMN is zero.
|
|
*
|
|
JB_ZERO = MINMN / 2 + 1
|
|
NB_ZERO = 1
|
|
NB_GEN = N - NB_ZERO
|
|
*
|
|
ELSE IF( IMAT.EQ.9 ) THEN
|
|
*
|
|
* Matrix 9. First half of MINMN columns is zero, zero block size MINMN/2.
|
|
*
|
|
JB_ZERO = 1
|
|
NB_ZERO = MINMN / 2
|
|
NB_GEN = N - NB_ZERO
|
|
*
|
|
ELSE IF( IMAT.EQ.10 ) THEN
|
|
*
|
|
* Matrix 10. Last columns are zero columns,
|
|
* starting from (MINMN / 2 + 1) column,zero block size N - MINMN/2
|
|
*
|
|
JB_ZERO = MINMN / 2 + 1
|
|
NB_ZERO = N - MINMN / 2
|
|
NB_GEN = N - NB_ZERO
|
|
*
|
|
ELSE IF( IMAT.EQ.11 ) THEN
|
|
*
|
|
* Matrix 11. Half of the columns in the middle of first MINMN
|
|
* columns is zero, starting from MINMN/2 - (MINMN/2)/2 + 1 column,
|
|
* zero block size MINMN/2.
|
|
*
|
|
JB_ZERO = MINMN / 2 - (MINMN / 2) / 2 + 1
|
|
NB_ZERO = MINMN / 2
|
|
NB_GEN = N - NB_ZERO
|
|
*
|
|
ELSE IF( IMAT.EQ.12 ) THEN
|
|
*
|
|
* Matrix 12. Odd-numbered columns are zero,
|
|
*
|
|
NB_GEN = N / 2
|
|
NB_ZERO = N - NB_GEN
|
|
J_INC = 2
|
|
J_FIRST_NZ = 2
|
|
*
|
|
ELSE IF( IMAT.EQ.13 ) THEN
|
|
*
|
|
* Matrix 13. Even-numbered columns are zero.
|
|
*
|
|
NB_ZERO = N / 2
|
|
NB_GEN = N - NB_ZERO
|
|
J_INC = 2
|
|
J_FIRST_NZ = 1
|
|
*
|
|
END IF
|
|
*
|
|
*
|
|
* 1) Set the first NB_ZERO columns in COPYA(1:M,1:N)
|
|
* to zero.
|
|
*
|
|
CALL DLASET( 'Full', M, NB_ZERO, ZERO, ZERO,
|
|
$ COPYA, LDA )
|
|
*
|
|
* 2) Generate an M-by-(N-NB_ZERO) matrix with the
|
|
* chosen singular value distribution
|
|
* in COPYA(1:M,NB_ZERO+1:N).
|
|
*
|
|
CALL DLATB4( PATH, IMAT, M, NB_GEN, TYPE, KL, KU,
|
|
$ ANORM, MODE, CNDNUM, DIST )
|
|
*
|
|
SRNAMT = 'DLATMS'
|
|
*
|
|
IND_OFFSET_GEN = NB_ZERO * LDA
|
|
*
|
|
CALL DLATMS( M, NB_GEN, DIST, ISEED, TYPE, S, MODE,
|
|
$ CNDNUM, ANORM, KL, KU, 'No packing',
|
|
$ COPYA( IND_OFFSET_GEN + 1 ), LDA,
|
|
$ WORK, INFO )
|
|
*
|
|
* Check error code from DLATMS.
|
|
*
|
|
IF( INFO.NE.0 ) THEN
|
|
CALL ALAERH( PATH, 'DLATMS', INFO, 0, ' ', M,
|
|
$ NB_GEN, -1, -1, -1, IMAT, NFAIL,
|
|
$ NERRS, NOUT )
|
|
CYCLE
|
|
END IF
|
|
*
|
|
* 3) Swap the gererated colums from the right side
|
|
* NB_GEN-size block in COPYA into correct column
|
|
* positions.
|
|
*
|
|
IF( IMAT.EQ.6
|
|
$ .OR. IMAT.EQ.7
|
|
$ .OR. IMAT.EQ.8
|
|
$ .OR. IMAT.EQ.10
|
|
$ .OR. IMAT.EQ.11 ) THEN
|
|
*
|
|
* Move by swapping the generated columns
|
|
* from the right NB_GEN-size block from
|
|
* (NB_ZERO+1:NB_ZERO+JB_ZERO)
|
|
* into columns (1:JB_ZERO-1).
|
|
*
|
|
DO J = 1, JB_ZERO-1, 1
|
|
CALL DSWAP( M,
|
|
$ COPYA( ( NB_ZERO+J-1)*LDA+1), 1,
|
|
$ COPYA( (J-1)*LDA + 1 ), 1 )
|
|
END DO
|
|
*
|
|
ELSE IF( IMAT.EQ.12 .OR. IMAT.EQ.13 ) THEN
|
|
*
|
|
* ( IMAT = 12, Odd-numbered ZERO columns. )
|
|
* Swap the generated columns from the right
|
|
* NB_GEN-size block into the even zero colums in the
|
|
* left NB_ZERO-size block.
|
|
*
|
|
* ( IMAT = 13, Even-numbered ZERO columns. )
|
|
* Swap the generated columns from the right
|
|
* NB_GEN-size block into the odd zero colums in the
|
|
* left NB_ZERO-size block.
|
|
*
|
|
DO J = 1, NB_GEN, 1
|
|
IND_OUT = ( NB_ZERO+J-1 )*LDA + 1
|
|
IND_IN = ( J_INC*(J-1)+(J_FIRST_NZ-1) )*LDA
|
|
$ + 1
|
|
CALL DSWAP( M,
|
|
$ COPYA( IND_OUT ), 1,
|
|
$ COPYA( IND_IN ), 1 )
|
|
END DO
|
|
*
|
|
END IF
|
|
*
|
|
* 5) Order the singular values generated by
|
|
* DLAMTS in decreasing absolute value order and
|
|
* add trailing zeros that correspond to zero columns.
|
|
* The total number of singular values is MINMN.
|
|
*
|
|
MINMNB_GEN = MIN( M, NB_GEN )
|
|
CALL DLAORD( 'Decreasing', MINMNB_GEN, S, 1 )
|
|
*
|
|
DO I = MINMNB_GEN+1, MINMN
|
|
S( I ) = ZERO
|
|
END DO
|
|
*
|
|
ELSE
|
|
*
|
|
* IF( MINMN.LT.2 .AND. ( IMAT.GE.5 .AND. IMAT.LE.13 ) )
|
|
* skip this size for this matrix type.
|
|
*
|
|
CYCLE
|
|
END IF
|
|
*
|
|
* End generate COPYA matrix.
|
|
*
|
|
* Initialize COPYC matrix with zeros.
|
|
*
|
|
CALL DLASET( 'Full', M, N, ZERO, ZERO, COPYC, LDC )
|
|
*
|
|
* Initialize COPYQRC matrix with zeros.
|
|
*
|
|
CALL DLASET( 'Full', M, N, ZERO, ZERO, COPYQRC, LDQRC )
|
|
*
|
|
* Initialize COPYX matrix with zeros.
|
|
*
|
|
CALL DLASET( 'Full', MINMN, N, ZERO, ZERO, COPYX, LDX )
|
|
*
|
|
* Initialize a copy array for pivot IPIV for DGECXX.
|
|
*
|
|
DO I = 1, M
|
|
COPY_IPIV( I ) = 0
|
|
END DO
|
|
*
|
|
* Initialize a copy array for pivot JPIV for DGECXX.
|
|
*
|
|
DO J = 1, N
|
|
COPY_JPIV( J ) = 0
|
|
END DO
|
|
*
|
|
* Initialize a copy array COPY_DESEL_ROWS for DGECXX.
|
|
*
|
|
DO I = 1, M
|
|
COPY_DESEL_ROWS( I ) = 0
|
|
END DO
|
|
*
|
|
* Initialize a copy array COPY_SEL_DESEL_COLS for DGECXX.
|
|
*
|
|
DO J = 1, N
|
|
COPY_SEL_DESEL_COLS( J ) = 0
|
|
END DO
|
|
*
|
|
DO INB = 1, NNB
|
|
*
|
|
* Do for each pair of values (NB,NX) in NBVAL and NXVAL.
|
|
*
|
|
NB = NBVAL( INB )
|
|
CALL XLAENV( 1, NB )
|
|
NX = NXVAL( INB )
|
|
CALL XLAENV( 3, NX )
|
|
*
|
|
* We do MIN(M,N)+1 because we need a test for KMAX > N,
|
|
* when KMAX is larger than MIN(M,N), KMAX should be
|
|
* KMAX = MIN(M,N)
|
|
*
|
|
DO KMAXFREE = 0, MIN(M,N)+1
|
|
*
|
|
* Get a working copy of COPYA into A( 1:M,1:N ).
|
|
* Get a working copy of COPYC into C( 1:M,1:N ).
|
|
* Get a working copy of COPYQRC into QRC( 1:M,1:N ).
|
|
* Get a working copy of COPYX into X( 1:N,1:N ).
|
|
* Get a working copy of COPY_IPIV(1:M) into IPIV(1:M).
|
|
* Get a working copy of COPY_JPIV(1:N) into JPIV(1:N).
|
|
* Get a working copy of COPY_DESEL_ROWS(1:M) into DESEL_ROWS(1:M).
|
|
* Get a working copy of COPY_SEL_DESEL_COLS(1:N) into SEL_DESEL_COLS(1:N).
|
|
*
|
|
CALL DLACPY( 'All', M, N, COPYA, LDA, A, LDA )
|
|
CALL DLACPY( 'All', M, N, COPYC, LDC, C, LDC )
|
|
CALL DLACPY( 'All', M, N, COPYQRC, LDQRC, QRC, LDQRC )
|
|
CALL DLACPY( 'All', MINMN, N, COPYX, LDX, X, LDX )
|
|
CALL ICOPY( M, COPY_IPIV, 1, IPIV, 1 )
|
|
CALL ICOPY( N, COPY_JPIV, 1, JPIV, 1 )
|
|
CALL ICOPY( M, COPY_DESEL_ROWS, 1, DESEL_ROWS, 1 )
|
|
CALL ICOPY( N, COPY_SEL_DESEL_COLS, 1,
|
|
$ SEL_DESEL_COLS, 1 )
|
|
*
|
|
* Set test ratios for all tests to zero.
|
|
*
|
|
DO I = 1, NTESTS
|
|
RESULT( I ) = ZERO
|
|
END DO
|
|
*
|
|
* We are not testing with ABSTOL and RELTOL stopping criteria.
|
|
* Disable them.
|
|
*
|
|
FACT = 'C'
|
|
USESD = 'N'
|
|
ABSTOL = -ONE
|
|
RELTOL = -ONE
|
|
*
|
|
* Compute the QR factorization with pivoting of A
|
|
*
|
|
* Determine LWORK
|
|
*
|
|
* NBMAX_ORMQR is hardwired in DORMQR as NBMAX = 64.
|
|
*
|
|
NBMAX_ORMQR = 64
|
|
*
|
|
* a) For DGEQRF inside DGECXX
|
|
*
|
|
LWORK = MAX( 1, N*NB )
|
|
*
|
|
* b) For DORMQR inside DGECXX
|
|
*
|
|
LWORK = MAX( LWORK,
|
|
$ N*MIN(NBMAX_ORMQR,NB)+(NBMAX_ORMQR+1)*NBMAX_ORMQR )
|
|
*
|
|
* c) For DGEQP3RK inside DGECXX
|
|
*
|
|
LWORK = MAX( LWORK, 2*N + NB*( N + 1 ) )
|
|
*
|
|
* d) For DGELS inside DGECXX
|
|
*
|
|
LWORK = MAX( LWORK, MIN(M,N) + N*NB )
|
|
*
|
|
* Determine LIWORK
|
|
*
|
|
LIWORK = MAX( 1, 2*N )
|
|
*
|
|
* Compute DGECXX factorization of A.
|
|
*
|
|
SRNAMT = 'DGECXX'
|
|
CALL DGECXX( FACT, USESD, M, N,
|
|
$ DESEL_ROWS, SEL_DESEL_COLS,
|
|
$ KMAXFREE, ABSTOL, RELTOL, A, LDA,
|
|
$ K, MAXC2NRMK, RELMAXC2NRMK, FNRMK,
|
|
$ IPIV, JPIV, TAU, C, LDC, QRC, LDQRC,
|
|
$ X, LDX, WORK, LWORK, IWORK, LIWORK,
|
|
$ INFO )
|
|
*
|
|
* Check an error code from DGECXX.
|
|
*
|
|
IF( INFO.LT.0 )
|
|
$ CALL ALAERH( PATH, 'DGECXX', INFO, 0, ' ',
|
|
$ M, N, NX, -1, NB, IMAT,
|
|
$ NFAIL, NERRS, NOUT )
|
|
*
|
|
* Compute test 1:
|
|
*
|
|
* This test in only for the full rank factorization of
|
|
* the matrix A.
|
|
*
|
|
* Array S(1:min(M,N)) contains svd(A) the sigular values
|
|
* of the original matrix A in decreasing absolute value
|
|
* order. The test computes svd(R), the vector sigular
|
|
* values of the upper trapezoid of A(1:M,1:N) that
|
|
* contains the factor R, in decreasing order. The test
|
|
* returns the ratio:
|
|
*
|
|
* 2-norm(svd(R) - svd(A)) / ( max(M,N) * 2-norm(svd(A)) * EPS )
|
|
*
|
|
IF( K.EQ.MINMN ) THEN
|
|
*
|
|
RESULT( 1 ) = DQRT12( M, N, A, LDA, S, WORK,
|
|
$ LWKTST )
|
|
*
|
|
NRUN = NRUN + 1
|
|
*
|
|
* End test 1
|
|
*
|
|
END IF
|
|
*
|
|
* Compute test 2:
|
|
*
|
|
* The test returns the ratio:
|
|
*
|
|
* 1-norm( A*P - Q*R ) / ( max(M,N) * 1-norm(A) * EPS )
|
|
*
|
|
RESULT( 2 ) = DQPT01( M, N, K, COPYA, A, LDA, TAU,
|
|
$ JPIV, WORK, LWKTST )
|
|
*
|
|
* Compute test 3:
|
|
*
|
|
* The test returns the ratio:
|
|
*
|
|
* 1-norm( Q**T * Q - I ) / ( M * EPS )
|
|
*
|
|
RESULT( 3 ) = DQRT11( M, K, A, LDA, TAU, WORK,
|
|
$ LWKTST )
|
|
*
|
|
NRUN = NRUN + 2
|
|
*
|
|
* Compute test 4:
|
|
*
|
|
* This test is only for the factorizations with the
|
|
* rank greater then 1.
|
|
* The elements on the diagonal of R should be non-
|
|
* increasing.
|
|
*
|
|
* The test returns the ratio:
|
|
*
|
|
* Returns 1.0D+38 if abs(R(j+1,j+1)) > abs(R(j,j)),
|
|
* j=1:K-1
|
|
*
|
|
IF( MIN(K, MINMN).GT.1 ) THEN
|
|
*
|
|
DO J = 1, K-1, 1
|
|
|
|
DTEMP = (( ABS( A( (J-1)*LDA+J ) ) -
|
|
$ ABS( A( (J)*LDA+J+1 ) ) ) /
|
|
$ ABS( A(1) ) )
|
|
*
|
|
IF( DTEMP.LT.ZERO ) THEN
|
|
RESULT( 4 ) = BIGNUM
|
|
END IF
|
|
*
|
|
END DO
|
|
*
|
|
NRUN = NRUN + 1
|
|
*
|
|
* End test 4.
|
|
*
|
|
END IF
|
|
*
|
|
* ===============
|
|
* Compute test 5:
|
|
* ===============
|
|
* This test is only for the factorizations with the
|
|
* rank greater than 0.
|
|
* For J=1:K, the J-th column of C should be elementwise
|
|
* equal (including NaN and Inf)
|
|
* to the JPIV(J)-th column of A.
|
|
*
|
|
RESULT( 5 ) = ZERO
|
|
* Disable for now, incomplete test.
|
|
IF(.FALSE.) THEN
|
|
DO J = 1, K, 1
|
|
DO I = 1, M, 1
|
|
IF( .NOT. (C( (J-1)*LDC+I )
|
|
$ .EQ. A( (JPIV( J )-1)*LDA+I ) ) ) THEN
|
|
RESULT( 5 ) = BIGNUM
|
|
END IF
|
|
END DO
|
|
END DO
|
|
END IF
|
|
*
|
|
*
|
|
* Print information about the tests that did not
|
|
* pass the threshold.
|
|
*
|
|
DO T = 1, NTESTS
|
|
IF( RESULT( T ).GE.THRESH ) THEN
|
|
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
|
|
$ CALL ALAHD( NOUT, PATH )
|
|
WRITE( NOUT, FMT = 9999 ) 'DGECXX', M, N,
|
|
$ FACT, USESD, KMAXFREE, ABSTOL, RELTOL,
|
|
$ NB, NX, IMAT, T, RESULT( T )
|
|
NFAIL = NFAIL + 1
|
|
END IF
|
|
END DO
|
|
*
|
|
* END DO KMAX = 1, MIN(M,N)+1
|
|
*
|
|
END DO
|
|
*
|
|
* END DO for INB = 1, NNB
|
|
*
|
|
END DO
|
|
*
|
|
* END DO for IMAT = 1, NTYPES
|
|
*
|
|
END DO
|
|
*
|
|
* END DO for IN = 1, NN
|
|
*
|
|
END DO
|
|
*
|
|
* END DO for IM = 1, NM
|
|
*
|
|
END DO
|
|
*
|
|
* Print a summary of the results.
|
|
*
|
|
CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS )
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|
*
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|
9999 FORMAT( 1X, A, ' M =', I5, ', N =', I5,
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|
$ ', FACT = ''', A1, ''', USESD = ''', A1,
|
|
$ ''', KMAXFREE =', I5, ', ABSTOL =', G12.5,
|
|
$ ', RELTOL =', G12.5, ', NB =', I4, ', NX =', I4,
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|
$ ', type ', I2, ', test ', I2, ', ratio =', G12.5 )
|
|
*
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|
* End of DCHKCXX
|
|
*
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END
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