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1021 lines
40 KiB
1021 lines
40 KiB
2 years ago
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*> \brief \b DDRVLS
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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 DDRVLS( DOTYPE, NM, MVAL, NN, NVAL, NNS, NSVAL, NNB,
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* NBVAL, NXVAL, THRESH, TSTERR, A, COPYA, B,
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* COPYB, C, S, COPYS, NOUT )
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*
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* .. Scalar Arguments ..
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* LOGICAL TSTERR
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* INTEGER NM, NN, NNB, NNS, 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 MVAL( * ), NBVAL( * ), NSVAL( * ),
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* $ NVAL( * ), NXVAL( * )
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* DOUBLE PRECISION A( * ), B( * ), C( * ), COPYA( * ), COPYB( * ),
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* $ COPYS( * ), S( * )
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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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*> DDRVLS tests the least squares driver routines DGELS, DGELST,
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*> DGETSLS, DGELSS, DGELSY, and DGELSD.
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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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*> The matrix of type j is generated as follows:
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*> j=1: A = U*D*V where U and V are random orthogonal matrices
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*> and D has random entries (> 0.1) taken from a uniform
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*> distribution (0,1). A is full rank.
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*> j=2: The same of 1, but A is scaled up.
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*> j=3: The same of 1, but A is scaled down.
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*> j=4: A = U*D*V where U and V are random orthogonal matrices
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*> and D has 3*min(M,N)/4 random entries (> 0.1) taken
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*> from a uniform distribution (0,1) and the remaining
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*> entries set to 0. A is rank-deficient.
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*> j=5: The same of 4, but A is scaled up.
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*> j=6: The same of 5, but A is scaled down.
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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] NNS
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*> \verbatim
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*> NNS is INTEGER
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*> The number of values of NRHS contained in the vector NSVAL.
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*> \endverbatim
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*>
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*> \param[in] NSVAL
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*> \verbatim
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*> NSVAL is INTEGER array, dimension (NNS)
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*> The values of the number of right hand sides NRHS.
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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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*> \endverbatim
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*>
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*> \param[out] B
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*> \verbatim
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*> B is DOUBLE PRECISION array, dimension (MMAX*NSMAX)
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*> where MMAX is the maximum value of M in MVAL and NSMAX is the
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*> maximum value of NRHS in NSVAL.
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*> \endverbatim
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*>
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*> \param[out] COPYB
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*> \verbatim
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*> COPYB is DOUBLE PRECISION array, dimension (MMAX*NSMAX)
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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*NSMAX)
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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] COPYS
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*> \verbatim
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*> COPYS 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[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 DDRVLS( DOTYPE, NM, MVAL, NN, NVAL, NNS, NSVAL, NNB,
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$ NBVAL, NXVAL, THRESH, TSTERR, A, COPYA, B,
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$ COPYB, C, S, COPYS, NOUT )
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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, NNS, 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 MVAL( * ), NBVAL( * ), NSVAL( * ),
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$ NVAL( * ), NXVAL( * )
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DOUBLE PRECISION A( * ), B( * ), C( * ), COPYA( * ), COPYB( * ),
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$ COPYS( * ), S( * )
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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 NTESTS
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PARAMETER ( NTESTS = 18 )
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INTEGER SMLSIZ
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PARAMETER ( SMLSIZ = 25 )
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DOUBLE PRECISION ONE, TWO, ZERO
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PARAMETER ( ONE = 1.0D0, TWO = 2.0D0, ZERO = 0.0D0 )
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* ..
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* .. Local Scalars ..
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CHARACTER TRANS
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CHARACTER*3 PATH
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INTEGER CRANK, I, IM, IMB, IN, INB, INFO, INS, IRANK,
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$ ISCALE, ITRAN, ITYPE, J, K, LDA, LDB, LDWORK,
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$ LWLSY, LWORK, M, MNMIN, N, NB, NCOLS, NERRS,
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$ NFAIL, NRHS, NROWS, NRUN, RANK, MB,
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$ MMAX, NMAX, NSMAX, LIWORK,
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$ LWORK_DGELS, LWORK_DGELST, LWORK_DGETSLS,
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$ LWORK_DGELSS, LWORK_DGELSY, LWORK_DGELSD
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DOUBLE PRECISION EPS, NORMA, NORMB, RCOND
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* ..
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* .. Local Arrays ..
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INTEGER ISEED( 4 ), ISEEDY( 4 ), IWQ( 1 )
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DOUBLE PRECISION RESULT( NTESTS ), WQ( 1 )
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* ..
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* .. Allocatable Arrays ..
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DOUBLE PRECISION, ALLOCATABLE :: WORK (:)
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INTEGER, ALLOCATABLE :: IWORK (:)
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* ..
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* .. External Functions ..
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DOUBLE PRECISION DASUM, DLAMCH, DQRT12, DQRT14, DQRT17
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EXTERNAL DASUM, DLAMCH, DQRT12, DQRT14, DQRT17
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* ..
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* .. External Subroutines ..
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EXTERNAL ALAERH, ALAHD, ALASVM, DAXPY, DERRLS, DGELS,
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$ DGELSD, DGELSS, DGELST, DGELSY, DGEMM,
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$ DGETSLS, DLACPY, DLARNV, DQRT13, DQRT15,
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$ DQRT16, DSCAL, XLAENV
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC DBLE, INT, MAX, MIN, SQRT
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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 ) = 'LS'
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NRUN = 0
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NFAIL = 0
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NERRS = 0
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DO 10 I = 1, 4
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ISEED( I ) = ISEEDY( I )
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10 CONTINUE
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EPS = DLAMCH( 'Epsilon' )
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*
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* Threshold for rank estimation
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*
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RCOND = SQRT( EPS ) - ( SQRT( EPS )-EPS ) / 2
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*
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* Test the error exits
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*
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CALL XLAENV( 2, 2 )
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CALL XLAENV( 9, SMLSIZ )
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IF( TSTERR )
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$ CALL DERRLS( PATH, NOUT )
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*
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* Print the header if NM = 0 or NN = 0 and THRESH = 0.
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*
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IF( ( NM.EQ.0 .OR. NN.EQ.0 ) .AND. THRESH.EQ.ZERO )
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$ CALL ALAHD( NOUT, PATH )
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INFOT = 0
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CALL XLAENV( 2, 2 )
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CALL XLAENV( 9, SMLSIZ )
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*
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* Compute maximal workspace needed for all routines
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*
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NMAX = 0
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MMAX = 0
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NSMAX = 0
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DO I = 1, NM
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IF ( MVAL( I ).GT.MMAX ) THEN
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MMAX = MVAL( I )
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END IF
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ENDDO
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DO I = 1, NN
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IF ( NVAL( I ).GT.NMAX ) THEN
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NMAX = NVAL( I )
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END IF
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ENDDO
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DO I = 1, NNS
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IF ( NSVAL( I ).GT.NSMAX ) THEN
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NSMAX = NSVAL( I )
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END IF
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ENDDO
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M = MMAX
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N = NMAX
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NRHS = NSMAX
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MNMIN = MAX( MIN( M, N ), 1 )
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*
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* Compute workspace needed for routines
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* DQRT14, DQRT17 (two side cases), DQRT15 and DQRT12
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*
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LWORK = MAX( 1, ( M+N )*NRHS,
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$ ( N+NRHS )*( M+2 ), ( M+NRHS )*( N+2 ),
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$ MAX( M+MNMIN, NRHS*MNMIN,2*N+M ),
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$ MAX( M*N+4*MNMIN+MAX(M,N), M*N+2*MNMIN+4*N ) )
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LIWORK = 1
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*
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* Iterate through all test cases and compute necessary workspace
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* sizes for ?GELS, ?GELST, ?GETSLS, ?GELSY, ?GELSS and ?GELSD
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* routines.
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*
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DO IM = 1, NM
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M = MVAL( IM )
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LDA = MAX( 1, M )
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DO IN = 1, NN
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N = NVAL( IN )
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MNMIN = MAX(MIN( M, N ),1)
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LDB = MAX( 1, M, N )
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DO INS = 1, NNS
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NRHS = NSVAL( INS )
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DO IRANK = 1, 2
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DO ISCALE = 1, 3
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ITYPE = ( IRANK-1 )*3 + ISCALE
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IF( DOTYPE( ITYPE ) ) THEN
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IF( IRANK.EQ.1 ) THEN
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DO ITRAN = 1, 2
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IF( ITRAN.EQ.1 ) THEN
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TRANS = 'N'
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ELSE
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TRANS = 'T'
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END IF
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*
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* Compute workspace needed for DGELS
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CALL DGELS( TRANS, M, N, NRHS, A, LDA,
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$ B, LDB, WQ, -1, INFO )
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LWORK_DGELS = INT ( WQ ( 1 ) )
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* Compute workspace needed for DGELST
|
||
|
|
CALL DGELST( TRANS, M, N, NRHS, A, LDA,
|
||
|
|
$ B, LDB, WQ, -1, INFO )
|
||
|
|
LWORK_DGELST = INT ( WQ ( 1 ) )
|
||
|
|
* Compute workspace needed for DGETSLS
|
||
|
|
CALL DGETSLS( TRANS, M, N, NRHS, A, LDA,
|
||
|
|
$ B, LDB, WQ, -1, INFO )
|
||
|
|
LWORK_DGETSLS = INT( WQ ( 1 ) )
|
||
|
|
ENDDO
|
||
|
|
END IF
|
||
|
|
* Compute workspace needed for DGELSY
|
||
|
|
CALL DGELSY( M, N, NRHS, A, LDA, B, LDB, IWQ,
|
||
|
|
$ RCOND, CRANK, WQ, -1, INFO )
|
||
|
|
LWORK_DGELSY = INT( WQ ( 1 ) )
|
||
|
|
* Compute workspace needed for DGELSS
|
||
|
|
CALL DGELSS( M, N, NRHS, A, LDA, B, LDB, S,
|
||
|
|
$ RCOND, CRANK, WQ, -1 , INFO )
|
||
|
|
LWORK_DGELSS = INT( WQ ( 1 ) )
|
||
|
|
* Compute workspace needed for DGELSD
|
||
|
|
CALL DGELSD( M, N, NRHS, A, LDA, B, LDB, S,
|
||
|
|
$ RCOND, CRANK, WQ, -1, IWQ, INFO )
|
||
|
|
LWORK_DGELSD = INT( WQ ( 1 ) )
|
||
|
|
* Compute LIWORK workspace needed for DGELSY and DGELSD
|
||
|
|
LIWORK = MAX( LIWORK, N, IWQ( 1 ) )
|
||
|
|
* Compute LWORK workspace needed for all functions
|
||
|
|
LWORK = MAX( LWORK, LWORK_DGELS, LWORK_DGELST,
|
||
|
|
$ LWORK_DGETSLS, LWORK_DGELSY,
|
||
|
|
$ LWORK_DGELSS, LWORK_DGELSD )
|
||
|
|
END IF
|
||
|
|
ENDDO
|
||
|
|
ENDDO
|
||
|
|
ENDDO
|
||
|
|
ENDDO
|
||
|
|
ENDDO
|
||
|
|
*
|
||
|
|
LWLSY = LWORK
|
||
|
|
*
|
||
|
|
ALLOCATE( WORK( LWORK ) )
|
||
|
|
ALLOCATE( IWORK( LIWORK ) )
|
||
|
|
*
|
||
|
|
DO 150 IM = 1, NM
|
||
|
|
M = MVAL( IM )
|
||
|
|
LDA = MAX( 1, M )
|
||
|
|
*
|
||
|
|
DO 140 IN = 1, NN
|
||
|
|
N = NVAL( IN )
|
||
|
|
MNMIN = MAX(MIN( M, N ),1)
|
||
|
|
LDB = MAX( 1, M, N )
|
||
|
|
MB = (MNMIN+1)
|
||
|
|
*
|
||
|
|
DO 130 INS = 1, NNS
|
||
|
|
NRHS = NSVAL( INS )
|
||
|
|
*
|
||
|
|
DO 120 IRANK = 1, 2
|
||
|
|
DO 110 ISCALE = 1, 3
|
||
|
|
ITYPE = ( IRANK-1 )*3 + ISCALE
|
||
|
|
IF( .NOT.DOTYPE( ITYPE ) )
|
||
|
|
$ GO TO 110
|
||
|
|
* =====================================================
|
||
|
|
* Begin test DGELS
|
||
|
|
* =====================================================
|
||
|
|
IF( IRANK.EQ.1 ) THEN
|
||
|
|
*
|
||
|
|
* Generate a matrix of scaling type ISCALE
|
||
|
|
*
|
||
|
|
CALL DQRT13( ISCALE, M, N, COPYA, LDA, NORMA,
|
||
|
|
$ ISEED )
|
||
|
|
*
|
||
|
|
* Loop for testing different block sizes.
|
||
|
|
*
|
||
|
|
DO INB = 1, NNB
|
||
|
|
NB = NBVAL( INB )
|
||
|
|
CALL XLAENV( 1, NB )
|
||
|
|
CALL XLAENV( 3, NXVAL( INB ) )
|
||
|
|
*
|
||
|
|
* Loop for testing non-transposed and transposed.
|
||
|
|
*
|
||
|
|
DO ITRAN = 1, 2
|
||
|
|
IF( ITRAN.EQ.1 ) THEN
|
||
|
|
TRANS = 'N'
|
||
|
|
NROWS = M
|
||
|
|
NCOLS = N
|
||
|
|
ELSE
|
||
|
|
TRANS = 'T'
|
||
|
|
NROWS = N
|
||
|
|
NCOLS = M
|
||
|
|
END IF
|
||
|
|
LDWORK = MAX( 1, NCOLS )
|
||
|
|
*
|
||
|
|
* Set up a consistent rhs
|
||
|
|
*
|
||
|
|
IF( NCOLS.GT.0 ) THEN
|
||
|
|
CALL DLARNV( 2, ISEED, NCOLS*NRHS,
|
||
|
|
$ WORK )
|
||
|
|
CALL DSCAL( NCOLS*NRHS,
|
||
|
|
$ ONE / DBLE( NCOLS ), WORK,
|
||
|
|
$ 1 )
|
||
|
|
END IF
|
||
|
|
CALL DGEMM( TRANS, 'No transpose', NROWS,
|
||
|
|
$ NRHS, NCOLS, ONE, COPYA, LDA,
|
||
|
|
$ WORK, LDWORK, ZERO, B, LDB )
|
||
|
|
CALL DLACPY( 'Full', NROWS, NRHS, B, LDB,
|
||
|
|
$ COPYB, LDB )
|
||
|
|
*
|
||
|
|
* Solve LS or overdetermined system
|
||
|
|
*
|
||
|
|
IF( M.GT.0 .AND. N.GT.0 ) THEN
|
||
|
|
CALL DLACPY( 'Full', M, N, COPYA, LDA,
|
||
|
|
$ A, LDA )
|
||
|
|
CALL DLACPY( 'Full', NROWS, NRHS,
|
||
|
|
$ COPYB, LDB, B, LDB )
|
||
|
|
END IF
|
||
|
|
SRNAMT = 'DGELS '
|
||
|
|
CALL DGELS( TRANS, M, N, NRHS, A, LDA, B,
|
||
|
|
$ LDB, WORK, LWORK, INFO )
|
||
|
|
IF( INFO.NE.0 )
|
||
|
|
$ CALL ALAERH( PATH, 'DGELS ', INFO, 0,
|
||
|
|
$ TRANS, M, N, NRHS, -1, NB,
|
||
|
|
$ ITYPE, NFAIL, NERRS,
|
||
|
|
$ NOUT )
|
||
|
|
*
|
||
|
|
* Test 1: Check correctness of results
|
||
|
|
* for DGELS, compute the residual:
|
||
|
|
* RESID = norm(B - A*X) /
|
||
|
|
* / ( max(m,n) * norm(A) * norm(X) * EPS )
|
||
|
|
*
|
||
|
|
IF( NROWS.GT.0 .AND. NRHS.GT.0 )
|
||
|
|
$ CALL DLACPY( 'Full', NROWS, NRHS,
|
||
|
|
$ COPYB, LDB, C, LDB )
|
||
|
|
CALL DQRT16( TRANS, M, N, NRHS, COPYA,
|
||
|
|
$ LDA, B, LDB, C, LDB, WORK,
|
||
|
|
$ RESULT( 1 ) )
|
||
|
|
*
|
||
|
|
* Test 2: Check correctness of results
|
||
|
|
* for DGELS.
|
||
|
|
*
|
||
|
|
IF( ( ITRAN.EQ.1 .AND. M.GE.N ) .OR.
|
||
|
|
$ ( ITRAN.EQ.2 .AND. M.LT.N ) ) THEN
|
||
|
|
*
|
||
|
|
* Solving LS system, compute:
|
||
|
|
* r = norm((B- A*X)**T * A) /
|
||
|
|
* / (norm(A)*norm(B)*max(M,N,NRHS)*EPS)
|
||
|
|
*
|
||
|
|
RESULT( 2 ) = DQRT17( TRANS, 1, M, N,
|
||
|
|
$ NRHS, COPYA, LDA, B, LDB,
|
||
|
|
$ COPYB, LDB, C, WORK,
|
||
|
|
$ LWORK )
|
||
|
|
ELSE
|
||
|
|
*
|
||
|
|
* Solving overdetermined system
|
||
|
|
*
|
||
|
|
RESULT( 2 ) = DQRT14( TRANS, M, N,
|
||
|
|
$ NRHS, COPYA, LDA, B, LDB,
|
||
|
|
$ WORK, LWORK )
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Print information about the tests that
|
||
|
|
* did not pass the threshold.
|
||
|
|
*
|
||
|
|
DO K = 1, 2
|
||
|
|
IF( RESULT( K ).GE.THRESH ) THEN
|
||
|
|
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
|
||
|
|
$ CALL ALAHD( NOUT, PATH )
|
||
|
|
WRITE( NOUT, FMT = 9999 ) TRANS, M,
|
||
|
|
$ N, NRHS, NB, ITYPE, K,
|
||
|
|
$ RESULT( K )
|
||
|
|
NFAIL = NFAIL + 1
|
||
|
|
END IF
|
||
|
|
END DO
|
||
|
|
NRUN = NRUN + 2
|
||
|
|
END DO
|
||
|
|
END DO
|
||
|
|
END IF
|
||
|
|
* =====================================================
|
||
|
|
* End test DGELS
|
||
|
|
* =====================================================
|
||
|
|
* =====================================================
|
||
|
|
* Begin test DGELST
|
||
|
|
* =====================================================
|
||
|
|
IF( IRANK.EQ.1 ) THEN
|
||
|
|
*
|
||
|
|
* Generate a matrix of scaling type ISCALE
|
||
|
|
*
|
||
|
|
CALL DQRT13( ISCALE, M, N, COPYA, LDA, NORMA,
|
||
|
|
$ ISEED )
|
||
|
|
*
|
||
|
|
* Loop for testing different block sizes.
|
||
|
|
*
|
||
|
|
DO INB = 1, NNB
|
||
|
|
NB = NBVAL( INB )
|
||
|
|
CALL XLAENV( 1, NB )
|
||
|
|
*
|
||
|
|
* Loop for testing non-transposed and transposed.
|
||
|
|
*
|
||
|
|
DO ITRAN = 1, 2
|
||
|
|
IF( ITRAN.EQ.1 ) THEN
|
||
|
|
TRANS = 'N'
|
||
|
|
NROWS = M
|
||
|
|
NCOLS = N
|
||
|
|
ELSE
|
||
|
|
TRANS = 'T'
|
||
|
|
NROWS = N
|
||
|
|
NCOLS = M
|
||
|
|
END IF
|
||
|
|
LDWORK = MAX( 1, NCOLS )
|
||
|
|
*
|
||
|
|
* Set up a consistent rhs
|
||
|
|
*
|
||
|
|
IF( NCOLS.GT.0 ) THEN
|
||
|
|
CALL DLARNV( 2, ISEED, NCOLS*NRHS,
|
||
|
|
$ WORK )
|
||
|
|
CALL DSCAL( NCOLS*NRHS,
|
||
|
|
$ ONE / DBLE( NCOLS ), WORK,
|
||
|
|
$ 1 )
|
||
|
|
END IF
|
||
|
|
CALL DGEMM( TRANS, 'No transpose', NROWS,
|
||
|
|
$ NRHS, NCOLS, ONE, COPYA, LDA,
|
||
|
|
$ WORK, LDWORK, ZERO, B, LDB )
|
||
|
|
CALL DLACPY( 'Full', NROWS, NRHS, B, LDB,
|
||
|
|
$ COPYB, LDB )
|
||
|
|
*
|
||
|
|
* Solve LS or overdetermined system
|
||
|
|
*
|
||
|
|
IF( M.GT.0 .AND. N.GT.0 ) THEN
|
||
|
|
CALL DLACPY( 'Full', M, N, COPYA, LDA,
|
||
|
|
$ A, LDA )
|
||
|
|
CALL DLACPY( 'Full', NROWS, NRHS,
|
||
|
|
$ COPYB, LDB, B, LDB )
|
||
|
|
END IF
|
||
|
|
SRNAMT = 'DGELST'
|
||
|
|
CALL DGELST( TRANS, M, N, NRHS, A, LDA, B,
|
||
|
|
$ LDB, WORK, LWORK, INFO )
|
||
|
|
IF( INFO.NE.0 )
|
||
|
|
$ CALL ALAERH( PATH, 'DGELST', INFO, 0,
|
||
|
|
$ TRANS, M, N, NRHS, -1, NB,
|
||
|
|
$ ITYPE, NFAIL, NERRS,
|
||
|
|
$ NOUT )
|
||
|
|
*
|
||
|
|
* Test 3: Check correctness of results
|
||
|
|
* for DGELST, compute the residual:
|
||
|
|
* RESID = norm(B - A*X) /
|
||
|
|
* / ( max(m,n) * norm(A) * norm(X) * EPS )
|
||
|
|
*
|
||
|
|
IF( NROWS.GT.0 .AND. NRHS.GT.0 )
|
||
|
|
$ CALL DLACPY( 'Full', NROWS, NRHS,
|
||
|
|
$ COPYB, LDB, C, LDB )
|
||
|
|
CALL DQRT16( TRANS, M, N, NRHS, COPYA,
|
||
|
|
$ LDA, B, LDB, C, LDB, WORK,
|
||
|
|
$ RESULT( 3 ) )
|
||
|
|
*
|
||
|
|
* Test 4: Check correctness of results
|
||
|
|
* for DGELST.
|
||
|
|
*
|
||
|
|
IF( ( ITRAN.EQ.1 .AND. M.GE.N ) .OR.
|
||
|
|
$ ( ITRAN.EQ.2 .AND. M.LT.N ) ) THEN
|
||
|
|
*
|
||
|
|
* Solving LS system, compute:
|
||
|
|
* r = norm((B- A*X)**T * A) /
|
||
|
|
* / (norm(A)*norm(B)*max(M,N,NRHS)*EPS)
|
||
|
|
*
|
||
|
|
RESULT( 4 ) = DQRT17( TRANS, 1, M, N,
|
||
|
|
$ NRHS, COPYA, LDA, B, LDB,
|
||
|
|
$ COPYB, LDB, C, WORK,
|
||
|
|
$ LWORK )
|
||
|
|
ELSE
|
||
|
|
*
|
||
|
|
* Solving overdetermined system
|
||
|
|
*
|
||
|
|
RESULT( 4 ) = DQRT14( TRANS, M, N,
|
||
|
|
$ NRHS, COPYA, LDA, B, LDB,
|
||
|
|
$ WORK, LWORK )
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Print information about the tests that
|
||
|
|
* did not pass the threshold.
|
||
|
|
*
|
||
|
|
DO K = 3, 4
|
||
|
|
IF( RESULT( K ).GE.THRESH ) THEN
|
||
|
|
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
|
||
|
|
$ CALL ALAHD( NOUT, PATH )
|
||
|
|
WRITE( NOUT, FMT = 9999 ) TRANS, M,
|
||
|
|
$ N, NRHS, NB, ITYPE, K,
|
||
|
|
$ RESULT( K )
|
||
|
|
NFAIL = NFAIL + 1
|
||
|
|
END IF
|
||
|
|
END DO
|
||
|
|
NRUN = NRUN + 2
|
||
|
|
END DO
|
||
|
|
END DO
|
||
|
|
END IF
|
||
|
|
* =====================================================
|
||
|
|
* End test DGELST
|
||
|
|
* =====================================================
|
||
|
|
* =====================================================
|
||
|
|
* Begin test DGETSLS
|
||
|
|
* =====================================================
|
||
|
|
IF( IRANK.EQ.1 ) THEN
|
||
|
|
*
|
||
|
|
* Generate a matrix of scaling type ISCALE
|
||
|
|
*
|
||
|
|
CALL DQRT13( ISCALE, M, N, COPYA, LDA, NORMA,
|
||
|
|
$ ISEED )
|
||
|
|
*
|
||
|
|
* Loop for testing different block sizes MB.
|
||
|
|
*
|
||
|
|
DO IMB = 1, NNB
|
||
|
|
MB = NBVAL( IMB )
|
||
|
|
CALL XLAENV( 1, MB )
|
||
|
|
*
|
||
|
|
* Loop for testing different block sizes NB.
|
||
|
|
*
|
||
|
|
DO INB = 1, NNB
|
||
|
|
NB = NBVAL( INB )
|
||
|
|
CALL XLAENV( 2, NB )
|
||
|
|
*
|
||
|
|
* Loop for testing non-transposed
|
||
|
|
* and transposed.
|
||
|
|
*
|
||
|
|
DO ITRAN = 1, 2
|
||
|
|
IF( ITRAN.EQ.1 ) THEN
|
||
|
|
TRANS = 'N'
|
||
|
|
NROWS = M
|
||
|
|
NCOLS = N
|
||
|
|
ELSE
|
||
|
|
TRANS = 'T'
|
||
|
|
NROWS = N
|
||
|
|
NCOLS = M
|
||
|
|
END IF
|
||
|
|
LDWORK = MAX( 1, NCOLS )
|
||
|
|
*
|
||
|
|
* Set up a consistent rhs
|
||
|
|
*
|
||
|
|
IF( NCOLS.GT.0 ) THEN
|
||
|
|
CALL DLARNV( 2, ISEED, NCOLS*NRHS,
|
||
|
|
$ WORK )
|
||
|
|
CALL DSCAL( NCOLS*NRHS,
|
||
|
|
$ ONE / DBLE( NCOLS ),
|
||
|
|
$ WORK, 1 )
|
||
|
|
END IF
|
||
|
|
CALL DGEMM( TRANS, 'No transpose',
|
||
|
|
$ NROWS, NRHS, NCOLS, ONE,
|
||
|
|
$ COPYA, LDA, WORK, LDWORK,
|
||
|
|
$ ZERO, B, LDB )
|
||
|
|
CALL DLACPY( 'Full', NROWS, NRHS,
|
||
|
|
$ B, LDB, COPYB, LDB )
|
||
|
|
*
|
||
|
|
* Solve LS or overdetermined system
|
||
|
|
*
|
||
|
|
IF( M.GT.0 .AND. N.GT.0 ) THEN
|
||
|
|
CALL DLACPY( 'Full', M, N,
|
||
|
|
$ COPYA, LDA, A, LDA )
|
||
|
|
CALL DLACPY( 'Full', NROWS, NRHS,
|
||
|
|
$ COPYB, LDB, B, LDB )
|
||
|
|
END IF
|
||
|
|
SRNAMT = 'DGETSLS'
|
||
|
|
CALL DGETSLS( TRANS, M, N, NRHS,
|
||
|
|
$ A, LDA, B, LDB, WORK, LWORK,
|
||
|
|
$ INFO )
|
||
|
|
IF( INFO.NE.0 )
|
||
|
|
$ CALL ALAERH( PATH, 'DGETSLS', INFO,
|
||
|
|
$ 0, TRANS, M, N, NRHS,
|
||
|
|
$ -1, NB, ITYPE, NFAIL,
|
||
|
|
$ NERRS, NOUT )
|
||
|
|
*
|
||
|
|
* Test 5: Check correctness of results
|
||
|
|
* for DGETSLS, compute the residual:
|
||
|
|
* RESID = norm(B - A*X) /
|
||
|
|
* / ( max(m,n) * norm(A) * norm(X) * EPS )
|
||
|
|
*
|
||
|
|
IF( NROWS.GT.0 .AND. NRHS.GT.0 )
|
||
|
|
$ CALL DLACPY( 'Full', NROWS, NRHS,
|
||
|
|
$ COPYB, LDB, C, LDB )
|
||
|
|
CALL DQRT16( TRANS, M, N, NRHS,
|
||
|
|
$ COPYA, LDA, B, LDB,
|
||
|
|
$ C, LDB, WORK,
|
||
|
|
$ RESULT( 5 ) )
|
||
|
|
*
|
||
|
|
* Test 6: Check correctness of results
|
||
|
|
* for DGETSLS.
|
||
|
|
*
|
||
|
|
IF( ( ITRAN.EQ.1 .AND. M.GE.N ) .OR.
|
||
|
|
$ ( ITRAN.EQ.2 .AND. M.LT.N ) ) THEN
|
||
|
|
*
|
||
|
|
* Solving LS system, compute:
|
||
|
|
* r = norm((B- A*X)**T * A) /
|
||
|
|
* / (norm(A)*norm(B)*max(M,N,NRHS)*EPS)
|
||
|
|
*
|
||
|
|
RESULT( 6 ) = DQRT17( TRANS, 1, M,
|
||
|
|
$ N, NRHS, COPYA, LDA,
|
||
|
|
$ B, LDB, COPYB, LDB,
|
||
|
|
$ C, WORK, LWORK )
|
||
|
|
ELSE
|
||
|
|
*
|
||
|
|
* Solving overdetermined system
|
||
|
|
*
|
||
|
|
RESULT( 6 ) = DQRT14( TRANS, M, N,
|
||
|
|
$ NRHS, COPYA, LDA,
|
||
|
|
$ B, LDB, WORK, LWORK )
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Print information about the tests that
|
||
|
|
* did not pass the threshold.
|
||
|
|
*
|
||
|
|
DO K = 5, 6
|
||
|
|
IF( RESULT( K ).GE.THRESH ) THEN
|
||
|
|
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
|
||
|
|
$ CALL ALAHD( NOUT, PATH )
|
||
|
|
WRITE( NOUT, FMT = 9997 ) TRANS,
|
||
|
|
$ M, N, NRHS, MB, NB, ITYPE,
|
||
|
|
$ K, RESULT( K )
|
||
|
|
NFAIL = NFAIL + 1
|
||
|
|
END IF
|
||
|
|
END DO
|
||
|
|
NRUN = NRUN + 2
|
||
|
|
END DO
|
||
|
|
END DO
|
||
|
|
END DO
|
||
|
|
END IF
|
||
|
|
* =====================================================
|
||
|
|
* End test DGETSLS
|
||
|
|
* =====================================================
|
||
|
|
*
|
||
|
|
* Generate a matrix of scaling type ISCALE and rank
|
||
|
|
* type IRANK.
|
||
|
|
*
|
||
|
|
CALL DQRT15( ISCALE, IRANK, M, N, NRHS, COPYA, LDA,
|
||
|
|
$ COPYB, LDB, COPYS, RANK, NORMA, NORMB,
|
||
|
|
$ ISEED, WORK, LWORK )
|
||
|
|
*
|
||
|
|
* workspace used: MAX(M+MIN(M,N),NRHS*MIN(M,N),2*N+M)
|
||
|
|
*
|
||
|
|
LDWORK = MAX( 1, M )
|
||
|
|
*
|
||
|
|
* Loop for testing different block sizes.
|
||
|
|
*
|
||
|
|
DO 100 INB = 1, NNB
|
||
|
|
NB = NBVAL( INB )
|
||
|
|
CALL XLAENV( 1, NB )
|
||
|
|
CALL XLAENV( 3, NXVAL( INB ) )
|
||
|
|
*
|
||
|
|
* Test DGELSY
|
||
|
|
*
|
||
|
|
* DGELSY: Compute the minimum-norm solution X
|
||
|
|
* to min( norm( A * X - B ) )
|
||
|
|
* using the rank-revealing orthogonal
|
||
|
|
* factorization.
|
||
|
|
*
|
||
|
|
* Initialize vector IWORK.
|
||
|
|
*
|
||
|
|
DO 70 J = 1, N
|
||
|
|
IWORK( J ) = 0
|
||
|
|
70 CONTINUE
|
||
|
|
*
|
||
|
|
CALL DLACPY( 'Full', M, N, COPYA, LDA, A, LDA )
|
||
|
|
CALL DLACPY( 'Full', M, NRHS, COPYB, LDB, B,
|
||
|
|
$ LDB )
|
||
|
|
*
|
||
|
|
SRNAMT = 'DGELSY'
|
||
|
|
CALL DGELSY( M, N, NRHS, A, LDA, B, LDB, IWORK,
|
||
|
|
$ RCOND, CRANK, WORK, LWLSY, INFO )
|
||
|
|
IF( INFO.NE.0 )
|
||
|
|
$ CALL ALAERH( PATH, 'DGELSY', INFO, 0, ' ', M,
|
||
|
|
$ N, NRHS, -1, NB, ITYPE, NFAIL,
|
||
|
|
$ NERRS, NOUT )
|
||
|
|
*
|
||
|
|
* Test 7: Compute relative error in svd
|
||
|
|
* workspace: M*N + 4*MIN(M,N) + MAX(M,N)
|
||
|
|
*
|
||
|
|
RESULT( 7 ) = DQRT12( CRANK, CRANK, A, LDA,
|
||
|
|
$ COPYS, WORK, LWORK )
|
||
|
|
*
|
||
|
|
* Test 8: Compute error in solution
|
||
|
|
* workspace: M*NRHS + M
|
||
|
|
*
|
||
|
|
CALL DLACPY( 'Full', M, NRHS, COPYB, LDB, WORK,
|
||
|
|
$ LDWORK )
|
||
|
|
CALL DQRT16( 'No transpose', M, N, NRHS, COPYA,
|
||
|
|
$ LDA, B, LDB, WORK, LDWORK,
|
||
|
|
$ WORK( M*NRHS+1 ), RESULT( 8 ) )
|
||
|
|
*
|
||
|
|
* Test 9: Check norm of r'*A
|
||
|
|
* workspace: NRHS*(M+N)
|
||
|
|
*
|
||
|
|
RESULT( 9 ) = ZERO
|
||
|
|
IF( M.GT.CRANK )
|
||
|
|
$ RESULT( 9 ) = DQRT17( 'No transpose', 1, M,
|
||
|
|
$ N, NRHS, COPYA, LDA, B, LDB,
|
||
|
|
$ COPYB, LDB, C, WORK, LWORK )
|
||
|
|
*
|
||
|
|
* Test 10: Check if x is in the rowspace of A
|
||
|
|
* workspace: (M+NRHS)*(N+2)
|
||
|
|
*
|
||
|
|
RESULT( 10 ) = ZERO
|
||
|
|
*
|
||
|
|
IF( N.GT.CRANK )
|
||
|
|
$ RESULT( 10 ) = DQRT14( 'No transpose', M, N,
|
||
|
|
$ NRHS, COPYA, LDA, B, LDB,
|
||
|
|
$ WORK, LWORK )
|
||
|
|
*
|
||
|
|
* Test DGELSS
|
||
|
|
*
|
||
|
|
* DGELSS: Compute the minimum-norm solution X
|
||
|
|
* to min( norm( A * X - B ) )
|
||
|
|
* using the SVD.
|
||
|
|
*
|
||
|
|
CALL DLACPY( 'Full', M, N, COPYA, LDA, A, LDA )
|
||
|
|
CALL DLACPY( 'Full', M, NRHS, COPYB, LDB, B,
|
||
|
|
$ LDB )
|
||
|
|
SRNAMT = 'DGELSS'
|
||
|
|
CALL DGELSS( M, N, NRHS, A, LDA, B, LDB, S,
|
||
|
|
$ RCOND, CRANK, WORK, LWORK, INFO )
|
||
|
|
IF( INFO.NE.0 )
|
||
|
|
$ CALL ALAERH( PATH, 'DGELSS', INFO, 0, ' ', M,
|
||
|
|
$ N, NRHS, -1, NB, ITYPE, NFAIL,
|
||
|
|
$ NERRS, NOUT )
|
||
|
|
*
|
||
|
|
* workspace used: 3*min(m,n) +
|
||
|
|
* max(2*min(m,n),nrhs,max(m,n))
|
||
|
|
*
|
||
|
|
* Test 11: Compute relative error in svd
|
||
|
|
*
|
||
|
|
IF( RANK.GT.0 ) THEN
|
||
|
|
CALL DAXPY( MNMIN, -ONE, COPYS, 1, S, 1 )
|
||
|
|
RESULT( 11 ) = DASUM( MNMIN, S, 1 ) /
|
||
|
|
$ DASUM( MNMIN, COPYS, 1 ) /
|
||
|
|
$ ( EPS*DBLE( MNMIN ) )
|
||
|
|
ELSE
|
||
|
|
RESULT( 11 ) = ZERO
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Test 12: Compute error in solution
|
||
|
|
*
|
||
|
|
CALL DLACPY( 'Full', M, NRHS, COPYB, LDB, WORK,
|
||
|
|
$ LDWORK )
|
||
|
|
CALL DQRT16( 'No transpose', M, N, NRHS, COPYA,
|
||
|
|
$ LDA, B, LDB, WORK, LDWORK,
|
||
|
|
$ WORK( M*NRHS+1 ), RESULT( 12 ) )
|
||
|
|
*
|
||
|
|
* Test 13: Check norm of r'*A
|
||
|
|
*
|
||
|
|
RESULT( 13 ) = ZERO
|
||
|
|
IF( M.GT.CRANK )
|
||
|
|
$ RESULT( 13 ) = DQRT17( 'No transpose', 1, M,
|
||
|
|
$ N, NRHS, COPYA, LDA, B, LDB,
|
||
|
|
$ COPYB, LDB, C, WORK, LWORK )
|
||
|
|
*
|
||
|
|
* Test 14: Check if x is in the rowspace of A
|
||
|
|
*
|
||
|
|
RESULT( 14 ) = ZERO
|
||
|
|
IF( N.GT.CRANK )
|
||
|
|
$ RESULT( 14 ) = DQRT14( 'No transpose', M, N,
|
||
|
|
$ NRHS, COPYA, LDA, B, LDB,
|
||
|
|
$ WORK, LWORK )
|
||
|
|
*
|
||
|
|
* Test DGELSD
|
||
|
|
*
|
||
|
|
* DGELSD: Compute the minimum-norm solution X
|
||
|
|
* to min( norm( A * X - B ) ) using a
|
||
|
|
* divide and conquer SVD.
|
||
|
|
*
|
||
|
|
* Initialize vector IWORK.
|
||
|
|
*
|
||
|
|
DO 80 J = 1, N
|
||
|
|
IWORK( J ) = 0
|
||
|
|
80 CONTINUE
|
||
|
|
*
|
||
|
|
CALL DLACPY( 'Full', M, N, COPYA, LDA, A, LDA )
|
||
|
|
CALL DLACPY( 'Full', M, NRHS, COPYB, LDB, B,
|
||
|
|
$ LDB )
|
||
|
|
*
|
||
|
|
SRNAMT = 'DGELSD'
|
||
|
|
CALL DGELSD( M, N, NRHS, A, LDA, B, LDB, S,
|
||
|
|
$ RCOND, CRANK, WORK, LWORK, IWORK,
|
||
|
|
$ INFO )
|
||
|
|
IF( INFO.NE.0 )
|
||
|
|
$ CALL ALAERH( PATH, 'DGELSD', INFO, 0, ' ', M,
|
||
|
|
$ N, NRHS, -1, NB, ITYPE, NFAIL,
|
||
|
|
$ NERRS, NOUT )
|
||
|
|
*
|
||
|
|
* Test 15: Compute relative error in svd
|
||
|
|
*
|
||
|
|
IF( RANK.GT.0 ) THEN
|
||
|
|
CALL DAXPY( MNMIN, -ONE, COPYS, 1, S, 1 )
|
||
|
|
RESULT( 15 ) = DASUM( MNMIN, S, 1 ) /
|
||
|
|
$ DASUM( MNMIN, COPYS, 1 ) /
|
||
|
|
$ ( EPS*DBLE( MNMIN ) )
|
||
|
|
ELSE
|
||
|
|
RESULT( 15 ) = ZERO
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Test 16: Compute error in solution
|
||
|
|
*
|
||
|
|
CALL DLACPY( 'Full', M, NRHS, COPYB, LDB, WORK,
|
||
|
|
$ LDWORK )
|
||
|
|
CALL DQRT16( 'No transpose', M, N, NRHS, COPYA,
|
||
|
|
$ LDA, B, LDB, WORK, LDWORK,
|
||
|
|
$ WORK( M*NRHS+1 ), RESULT( 16 ) )
|
||
|
|
*
|
||
|
|
* Test 17: Check norm of r'*A
|
||
|
|
*
|
||
|
|
RESULT( 17 ) = ZERO
|
||
|
|
IF( M.GT.CRANK )
|
||
|
|
$ RESULT( 17 ) = DQRT17( 'No transpose', 1, M,
|
||
|
|
$ N, NRHS, COPYA, LDA, B, LDB,
|
||
|
|
$ COPYB, LDB, C, WORK, LWORK )
|
||
|
|
*
|
||
|
|
* Test 18: Check if x is in the rowspace of A
|
||
|
|
*
|
||
|
|
RESULT( 18 ) = ZERO
|
||
|
|
IF( N.GT.CRANK )
|
||
|
|
$ RESULT( 18 ) = DQRT14( 'No transpose', M, N,
|
||
|
|
$ NRHS, COPYA, LDA, B, LDB,
|
||
|
|
$ WORK, LWORK )
|
||
|
|
*
|
||
|
|
* Print information about the tests that did not
|
||
|
|
* pass the threshold.
|
||
|
|
*
|
||
|
|
DO 90 K = 7, 18
|
||
|
|
IF( RESULT( K ).GE.THRESH ) THEN
|
||
|
|
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
|
||
|
|
$ CALL ALAHD( NOUT, PATH )
|
||
|
|
WRITE( NOUT, FMT = 9998 )M, N, NRHS, NB,
|
||
|
|
$ ITYPE, K, RESULT( K )
|
||
|
|
NFAIL = NFAIL + 1
|
||
|
|
END IF
|
||
|
|
90 CONTINUE
|
||
|
|
NRUN = NRUN + 12
|
||
|
|
*
|
||
|
|
100 CONTINUE
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
110 CONTINUE
|
||
|
|
120 CONTINUE
|
||
|
|
130 CONTINUE
|
||
|
|
140 CONTINUE
|
||
|
|
150 CONTINUE
|
||
|
|
*
|
||
|
|
* Print a summary of the results.
|
||
|
|
*
|
||
|
|
CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS )
|
||
|
|
*
|
||
|
|
9999 FORMAT( ' TRANS=''', A1, ''', M=', I5, ', N=', I5, ', NRHS=', I4,
|
||
|
|
$ ', NB=', I4, ', type', I2, ', test(', I2, ')=', G12.5 )
|
||
|
|
9998 FORMAT( ' M=', I5, ', N=', I5, ', NRHS=', I4, ', NB=', I4,
|
||
|
|
$ ', type', I2, ', test(', I2, ')=', G12.5 )
|
||
|
|
9997 FORMAT( ' TRANS=''', A1,' M=', I5, ', N=', I5, ', NRHS=', I4,
|
||
|
|
$ ', MB=', I4,', NB=', I4,', type', I2,
|
||
|
|
$ ', test(', I2, ')=', G12.5 )
|
||
|
|
*
|
||
|
|
DEALLOCATE( WORK )
|
||
|
|
DEALLOCATE( IWORK )
|
||
|
|
RETURN
|
||
|
|
*
|
||
|
|
* End of DDRVLS
|
||
|
|
*
|
||
|
|
END
|