numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
| Name | Size | Mode | |
| .. | |||
| lapack/TESTING/LIN/cdrvls.f | 41495B | -rw-r--r-- |
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*> \brief \b CDRVLS * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE CDRVLS( DOTYPE, NM, MVAL, NN, NVAL, NNS, NSVAL, NNB, * NBVAL, NXVAL, THRESH, TSTERR, A, COPYA, B, * COPYB, C, S, COPYS, NOUT ) * * .. Scalar Arguments .. * LOGICAL TSTERR * INTEGER NM, NN, NNB, NNS, NOUT * REAL THRESH * .. * .. Array Arguments .. * LOGICAL DOTYPE( * ) * INTEGER MVAL( * ), NBVAL( * ), NSVAL( * ), * $ NVAL( * ), NXVAL( * ) * REAL COPYS( * ), S( * ) * COMPLEX A( * ), B( * ), C( * ), COPYA( * ), COPYB( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> CDRVLS tests the least squares driver routines CGELS, CGELST, *> CGETSLS, CGELSS, CGELSY *> and CGELSD. *> \endverbatim * * Arguments: * ========== * *> \param[in] DOTYPE *> \verbatim *> DOTYPE is LOGICAL array, dimension (NTYPES) *> The matrix types to be used for testing. Matrices of type j *> (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = *> .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used. *> The matrix of type j is generated as follows: *> j=1: A = U*D*V where U and V are random unitary matrices *> and D has random entries (> 0.1) taken from a uniform *> distribution (0,1). A is full rank. *> j=2: The same of 1, but A is scaled up. *> j=3: The same of 1, but A is scaled down. *> j=4: A = U*D*V where U and V are random unitary matrices *> and D has 3*min(M,N)/4 random entries (> 0.1) taken *> from a uniform distribution (0,1) and the remaining *> entries set to 0. A is rank-deficient. *> j=5: The same of 4, but A is scaled up. *> j=6: The same of 5, but A is scaled down. *> \endverbatim *> *> \param[in] NM *> \verbatim *> NM is INTEGER *> The number of values of M contained in the vector MVAL. *> \endverbatim *> *> \param[in] MVAL *> \verbatim *> MVAL is INTEGER array, dimension (NM) *> The values of the matrix row dimension M. *> \endverbatim *> *> \param[in] NN *> \verbatim *> NN is INTEGER *> The number of values of N contained in the vector NVAL. *> \endverbatim *> *> \param[in] NVAL *> \verbatim *> NVAL is INTEGER array, dimension (NN) *> The values of the matrix column dimension N. *> \endverbatim *> *> \param[in] NNB *> \verbatim *> NNB is INTEGER *> The number of values of NB and NX contained in the *> vectors NBVAL and NXVAL. The blocking parameters are used *> in pairs (NB,NX). *> \endverbatim *> *> \param[in] NBVAL *> \verbatim *> NBVAL is INTEGER array, dimension (NNB) *> The values of the blocksize NB. *> \endverbatim *> *> \param[in] NXVAL *> \verbatim *> NXVAL is INTEGER array, dimension (NNB) *> The values of the crossover point NX. *> \endverbatim *> *> \param[in] NNS *> \verbatim *> NNS is INTEGER *> The number of values of NRHS contained in the vector NSVAL. *> \endverbatim *> *> \param[in] NSVAL *> \verbatim *> NSVAL is INTEGER array, dimension (NNS) *> The values of the number of right hand sides NRHS. *> \endverbatim *> *> \param[in] THRESH *> \verbatim *> THRESH is REAL *> The threshold value for the test ratios. A result is *> included in the output file if RESULT >= THRESH. To have *> every test ratio printed, use THRESH = 0. *> \endverbatim *> *> \param[in] TSTERR *> \verbatim *> TSTERR is LOGICAL *> Flag that indicates whether error exits are to be tested. *> \endverbatim *> *> \param[out] A *> \verbatim *> A is COMPLEX array, dimension (MMAX*NMAX) *> where MMAX is the maximum value of M in MVAL and NMAX is the *> maximum value of N in NVAL. *> \endverbatim *> *> \param[out] COPYA *> \verbatim *> COPYA is COMPLEX array, dimension (MMAX*NMAX) *> \endverbatim *> *> \param[out] B *> \verbatim *> B is COMPLEX array, dimension (MMAX*NSMAX) *> where MMAX is the maximum value of M in MVAL and NSMAX is the *> maximum value of NRHS in NSVAL. *> \endverbatim *> *> \param[out] COPYB *> \verbatim *> COPYB is COMPLEX array, dimension (MMAX*NSMAX) *> \endverbatim *> *> \param[out] C *> \verbatim *> C is COMPLEX array, dimension (MMAX*NSMAX) *> \endverbatim *> *> \param[out] S *> \verbatim *> S is REAL array, dimension *> (min(MMAX,NMAX)) *> \endverbatim *> *> \param[out] COPYS *> \verbatim *> COPYS is REAL array, dimension *> (min(MMAX,NMAX)) *> \endverbatim *> *> \param[in] NOUT *> \verbatim *> NOUT is INTEGER *> The unit number for output. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup complex_lin * * ===================================================================== SUBROUTINE CDRVLS( DOTYPE, NM, MVAL, NN, NVAL, NNS, NSVAL, NNB, $ NBVAL, NXVAL, THRESH, TSTERR, A, COPYA, B, $ COPYB, C, S, COPYS, NOUT ) * * -- LAPACK test routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. LOGICAL TSTERR INTEGER NM, NN, NNB, NNS, NOUT REAL THRESH * .. * .. Array Arguments .. LOGICAL DOTYPE( * ) INTEGER MVAL( * ), NBVAL( * ), NSVAL( * ), $ NVAL( * ), NXVAL( * ) REAL COPYS( * ), S( * ) COMPLEX A( * ), B( * ), C( * ), COPYA( * ), COPYB( * ) * .. * * ===================================================================== * * .. Parameters .. INTEGER NTESTS PARAMETER ( NTESTS = 18 ) INTEGER SMLSIZ PARAMETER ( SMLSIZ = 25 ) REAL ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) COMPLEX CONE, CZERO PARAMETER ( CONE = ( 1.0E+0, 0.0E+0 ), $ CZERO = ( 0.0E+0, 0.0E+0 ) ) * .. * .. Local Scalars .. CHARACTER TRANS CHARACTER*3 PATH INTEGER CRANK, I, IM, IMB, IN, INB, INFO, INS, IRANK, $ ISCALE, ITRAN, ITYPE, J, K, LDA, LDB, LDWORK, $ LWLSY, LWORK, M, MNMIN, N, NB, NCOLS, NERRS, $ NFAIL, NRHS, NROWS, NRUN, RANK, MB, $ MMAX, NMAX, NSMAX, LIWORK, LRWORK, $ LWORK_CGELS, LWORK_CGELST, LWORK_CGETSLS, $ LWORK_CGELSS, LWORK_CGELSY, LWORK_CGELSD, $ LRWORK_CGELSY, LRWORK_CGELSS, LRWORK_CGELSD REAL EPS, NORMA, NORMB, RCOND * .. * .. Local Arrays .. INTEGER ISEED( 4 ), ISEEDY( 4 ), IWQ( 1 ) REAL RESULT( NTESTS ), RWQ( 1 ) COMPLEX WQ( 1 ) * .. * .. Allocatable Arrays .. COMPLEX, ALLOCATABLE :: WORK (:) REAL, ALLOCATABLE :: RWORK (:), WORK2 (:) INTEGER, ALLOCATABLE :: IWORK (:) * .. * .. External Functions .. REAL CQRT12, CQRT14, CQRT17, SASUM, SLAMCH EXTERNAL CQRT12, CQRT14, CQRT17, SASUM, SLAMCH * .. * .. External Subroutines .. EXTERNAL ALAERH, ALAHD, ALASVM, CERRLS, CGELS, CGELSD, $ CGELSS, CGELST, CGELSY, CGEMM, CGETSLS, CLACPY, $ CLARNV, CQRT13, CQRT15, CQRT16, CSSCAL, $ SAXPY, XLAENV * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN, INT, REAL, SQRT * .. * .. Scalars in Common .. LOGICAL LERR, OK CHARACTER*32 SRNAMT INTEGER INFOT, IOUNIT * .. * .. Common blocks .. COMMON / INFOC / INFOT, IOUNIT, OK, LERR COMMON / SRNAMC / SRNAMT * .. * .. Data statements .. DATA ISEEDY / 1988, 1989, 1990, 1991 / * .. * .. Executable Statements .. * * Initialize constants and the random number seed. * PATH( 1: 1 ) = 'Complex precision' PATH( 2: 3 ) = 'LS' NRUN = 0 NFAIL = 0 NERRS = 0 DO 10 I = 1, 4 ISEED( I ) = ISEEDY( I ) 10 CONTINUE EPS = SLAMCH( 'Epsilon' ) * * Threshold for rank estimation * RCOND = SQRT( EPS ) - ( SQRT( EPS )-EPS ) / 2 * * Test the error exits * CALL XLAENV( 9, SMLSIZ ) IF( TSTERR ) $ CALL CERRLS( PATH, NOUT ) * * Print the header if NM = 0 or NN = 0 and THRESH = 0. * IF( ( NM.EQ.0 .OR. NN.EQ.0 ) .AND. THRESH.EQ.ZERO ) $ CALL ALAHD( NOUT, PATH ) INFOT = 0 * * Compute maximal workspace needed for all routines * NMAX = 0 MMAX = 0 NSMAX = 0 DO I = 1, NM IF ( MVAL( I ).GT.MMAX ) THEN MMAX = MVAL( I ) END IF ENDDO DO I = 1, NN IF ( NVAL( I ).GT.NMAX ) THEN NMAX = NVAL( I ) END IF ENDDO DO I = 1, NNS IF ( NSVAL( I ).GT.NSMAX ) THEN NSMAX = NSVAL( I ) END IF ENDDO M = MMAX N = NMAX NRHS = NSMAX MNMIN = MAX( MIN( M, N ), 1 ) * * Compute workspace needed for routines * CQRT14, CQRT17 (two side cases), CQRT15 and CQRT12 * LWORK = MAX( 1, ( M+N )*NRHS, $ ( N+NRHS )*( M+2 ), ( M+NRHS )*( N+2 ), $ MAX( M+MNMIN, NRHS*MNMIN,2*N+M ), $ MAX( M*N+4*MNMIN+MAX(M,N), M*N+2*MNMIN+4*N ) ) LRWORK = 1 LIWORK = 1 * * Iterate through all test cases and compute necessary workspace * sizes for ?GELS, ?GELST, ?GETSLS, ?GELSY, ?GELSS and ?GELSD * routines. * DO IM = 1, NM M = MVAL( IM ) LDA = MAX( 1, M ) DO IN = 1, NN N = NVAL( IN ) MNMIN = MAX(MIN( M, N ),1) LDB = MAX( 1, M, N ) DO INS = 1, NNS NRHS = NSVAL( INS ) DO IRANK = 1, 2 DO ISCALE = 1, 3 ITYPE = ( IRANK-1 )*3 + ISCALE IF( DOTYPE( ITYPE ) ) THEN IF( IRANK.EQ.1 ) THEN DO ITRAN = 1, 2 IF( ITRAN.EQ.1 ) THEN TRANS = 'N' ELSE TRANS = 'C' END IF * * Compute workspace needed for CGELS CALL CGELS( TRANS, M, N, NRHS, A, LDA, $ B, LDB, WQ, -1, INFO ) LWORK_CGELS = INT( WQ( 1 ) ) * Compute workspace needed for CGELST CALL CGELST( TRANS, M, N, NRHS, A, LDA, $ B, LDB, WQ, -1, INFO ) LWORK_CGELST = INT ( WQ ( 1 ) ) * Compute workspace needed for CGETSLS CALL CGETSLS( TRANS, M, N, NRHS, A, LDA, $ B, LDB, WQ, -1, INFO ) LWORK_CGETSLS = INT( WQ( 1 ) ) ENDDO END IF * Compute workspace needed for CGELSY CALL CGELSY( M, N, NRHS, A, LDA, B, LDB, $ IWQ, RCOND, CRANK, WQ, -1, RWQ, $ INFO ) LWORK_CGELSY = INT( WQ( 1 ) ) LRWORK_CGELSY = 2*N * Compute workspace needed for CGELSS CALL CGELSS( M, N, NRHS, A, LDA, B, LDB, S, $ RCOND, CRANK, WQ, -1, RWQ, INFO ) LWORK_CGELSS = INT( WQ( 1 ) ) LRWORK_CGELSS = 5*MNMIN * Compute workspace needed for CGELSD CALL CGELSD( M, N, NRHS, A, LDA, B, LDB, S, $ RCOND, CRANK, WQ, -1, RWQ, IWQ, $ INFO ) LWORK_CGELSD = INT( WQ( 1 ) ) LRWORK_CGELSD = INT( RWQ ( 1 ) ) * Compute LIWORK workspace needed for CGELSY and CGELSD LIWORK = MAX( LIWORK, N, IWQ ( 1 ) ) * Compute LRWORK workspace needed for CGELSY, CGELSS and CGELSD LRWORK = MAX( LRWORK, LRWORK_CGELSY, $ LRWORK_CGELSS, LRWORK_CGELSD ) * Compute LWORK workspace needed for all functions LWORK = MAX( LWORK, LWORK_CGELS, LWORK_CGETSLS, $ LWORK_CGELSY, LWORK_CGELSS, $ LWORK_CGELSD ) END IF ENDDO ENDDO ENDDO ENDDO ENDDO * LWLSY = LWORK * ALLOCATE( WORK( LWORK ) ) ALLOCATE( IWORK( LIWORK ) ) ALLOCATE( RWORK( LRWORK ) ) ALLOCATE( WORK2( 2 * LWORK ) ) * DO 140 IM = 1, NM M = MVAL( IM ) LDA = MAX( 1, M ) * DO 130 IN = 1, NN N = NVAL( IN ) MNMIN = MAX(MIN( M, N ),1) LDB = MAX( 1, M, N ) MB = (MNMIN+1) * DO 120 INS = 1, NNS NRHS = NSVAL( INS ) * DO 110 IRANK = 1, 2 DO 100 ISCALE = 1, 3 ITYPE = ( IRANK-1 )*3 + ISCALE IF( .NOT.DOTYPE( ITYPE ) ) $ GO TO 100 * ===================================================== * Begin test CGELS * ===================================================== IF( IRANK.EQ.1 ) THEN * * Generate a matrix of scaling type ISCALE * CALL CQRT13( 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 = 'C' NROWS = N NCOLS = M END IF LDWORK = MAX( 1, NCOLS ) * * Set up a consistent rhs * IF( NCOLS.GT.0 ) THEN CALL CLARNV( 2, ISEED, NCOLS*NRHS, $ WORK ) CALL CSSCAL( NCOLS*NRHS, $ ONE / REAL( NCOLS ), WORK, $ 1 ) END IF CALL CGEMM( TRANS, 'No transpose', NROWS, $ NRHS, NCOLS, CONE, COPYA, LDA, $ WORK, LDWORK, CZERO, B, LDB ) CALL CLACPY( 'Full', NROWS, NRHS, B, LDB, $ COPYB, LDB ) * * Solve LS or overdetermined system * IF( M.GT.0 .AND. N.GT.0 ) THEN CALL CLACPY( 'Full', M, N, COPYA, LDA, $ A, LDA ) CALL CLACPY( 'Full', NROWS, NRHS, $ COPYB, LDB, B, LDB ) END IF SRNAMT = 'CGELS ' CALL CGELS( TRANS, M, N, NRHS, A, LDA, B, $ LDB, WORK, LWORK, INFO ) * IF( INFO.NE.0 ) $ CALL ALAERH( PATH, 'CGELS ', INFO, 0, $ TRANS, M, N, NRHS, -1, NB, $ ITYPE, NFAIL, NERRS, $ NOUT ) * * Test 1: Check correctness of results * for CGELS, 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 CLACPY( 'Full', NROWS, NRHS, $ COPYB, LDB, C, LDB ) CALL CQRT16( TRANS, M, N, NRHS, COPYA, $ LDA, B, LDB, C, LDB, RWORK, $ RESULT( 1 ) ) * * Test 2: Check correctness of results * for CGELS. * IF( ( ITRAN.EQ.1 .AND. M.GE.N ) .OR. $ ( ITRAN.EQ.2 .AND. M.LT.N ) ) THEN * * Solving LS system * RESULT( 2 ) = CQRT17( TRANS, 1, M, N, $ NRHS, COPYA, LDA, B, LDB, $ COPYB, LDB, C, WORK, $ LWORK ) ELSE * * Solving overdetermined system * RESULT( 2 ) = CQRT14( 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 CGELS * ===================================================== * ===================================================== * Begin test CGELST * ===================================================== IF( IRANK.EQ.1 ) THEN * * Generate a matrix of scaling type ISCALE * CALL CQRT13( 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 = 'C' NROWS = N NCOLS = M END IF LDWORK = MAX( 1, NCOLS ) * * Set up a consistent rhs * IF( NCOLS.GT.0 ) THEN CALL CLARNV( 2, ISEED, NCOLS*NRHS, $ WORK ) CALL CSSCAL( NCOLS*NRHS, $ ONE / REAL( NCOLS ), WORK, $ 1 ) END IF CALL CGEMM( TRANS, 'No transpose', NROWS, $ NRHS, NCOLS, CONE, COPYA, LDA, $ WORK, LDWORK, CZERO, B, LDB ) CALL CLACPY( 'Full', NROWS, NRHS, B, LDB, $ COPYB, LDB ) * * Solve LS or overdetermined system * IF( M.GT.0 .AND. N.GT.0 ) THEN CALL CLACPY( 'Full', M, N, COPYA, LDA, $ A, LDA ) CALL CLACPY( 'Full', NROWS, NRHS, $ COPYB, LDB, B, LDB ) END IF SRNAMT = 'CGELST' CALL CGELST( TRANS, M, N, NRHS, A, LDA, B, $ LDB, WORK, LWORK, INFO ) * IF( INFO.NE.0 ) $ CALL ALAERH( PATH, 'CGELST', INFO, 0, $ TRANS, M, N, NRHS, -1, NB, $ ITYPE, NFAIL, NERRS, $ NOUT ) * * Test 3: Check correctness of results * for CGELST, 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 CLACPY( 'Full', NROWS, NRHS, $ COPYB, LDB, C, LDB ) CALL CQRT16( TRANS, M, N, NRHS, COPYA, $ LDA, B, LDB, C, LDB, RWORK, $ RESULT( 3 ) ) * * Test 4: Check correctness of results * for CGELST. * IF( ( ITRAN.EQ.1 .AND. M.GE.N ) .OR. $ ( ITRAN.EQ.2 .AND. M.LT.N ) ) THEN * * Solving LS system * RESULT( 4 ) = CQRT17( TRANS, 1, M, N, $ NRHS, COPYA, LDA, B, LDB, $ COPYB, LDB, C, WORK, $ LWORK ) ELSE * * Solving overdetermined system * RESULT( 4 ) = CQRT14( 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 CGELST * ===================================================== * ===================================================== * Begin test CGELSTSLS * ===================================================== IF( IRANK.EQ.1 ) THEN * * Generate a matrix of scaling type ISCALE * CALL CQRT13( ISCALE, M, N, COPYA, LDA, NORMA, $ ISEED ) * * Loop for testing different block sizes MB. * DO INB = 1, NNB MB = NBVAL( INB ) CALL XLAENV( 1, MB ) * * Loop for testing different block sizes NB. * DO IMB = 1, NNB NB = NBVAL( IMB ) 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 = 'C' NROWS = N NCOLS = M END IF LDWORK = MAX( 1, NCOLS ) * * Set up a consistent rhs * IF( NCOLS.GT.0 ) THEN CALL CLARNV( 2, ISEED, NCOLS*NRHS, $ WORK ) CALL CSCAL( NCOLS*NRHS, $ CONE / REAL( NCOLS ), $ WORK, 1 ) END IF CALL CGEMM( TRANS, 'No transpose', $ NROWS, NRHS, NCOLS, CONE, $ COPYA, LDA, WORK, LDWORK, $ CZERO, B, LDB ) CALL CLACPY( 'Full', NROWS, NRHS, $ B, LDB, COPYB, LDB ) * * Solve LS or overdetermined system * IF( M.GT.0 .AND. N.GT.0 ) THEN CALL CLACPY( 'Full', M, N, $ COPYA, LDA, A, LDA ) CALL CLACPY( 'Full', NROWS, NRHS, $ COPYB, LDB, B, LDB ) END IF SRNAMT = 'CGETSLS ' CALL CGETSLS( TRANS, M, N, NRHS, A, $ LDA, B, LDB, WORK, LWORK, $ INFO ) IF( INFO.NE.0 ) $ CALL ALAERH( PATH, 'CGETSLS ', INFO, $ 0, TRANS, M, N, NRHS, $ -1, NB, ITYPE, NFAIL, $ NERRS, NOUT ) * * Test 5: Check correctness of results * for CGETSLS, 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 CLACPY( 'Full', NROWS, NRHS, $ COPYB, LDB, C, LDB ) CALL CQRT16( TRANS, M, N, NRHS, $ COPYA, LDA, B, LDB, $ C, LDB, WORK2, $ RESULT( 5 ) ) * * Test 6: Check correctness of results * for CGETSLS. * 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 ) = CQRT17( TRANS, 1, M, $ N, NRHS, COPYA, LDA, $ B, LDB, COPYB, LDB, $ C, WORK, LWORK ) ELSE * * Solving overdetermined system * RESULT( 6 ) = CQRT14( 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 CGELSTSLS * ==================================================== * * Generate a matrix of scaling type ISCALE and rank * type IRANK. * CALL CQRT15( 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 90 INB = 1, NNB NB = NBVAL( INB ) CALL XLAENV( 1, NB ) CALL XLAENV( 3, NXVAL( INB ) ) * * Test CGELSY * * CGELSY: Compute the minimum-norm solution * X to min( norm( A * X - B ) ) * using the rank-revealing orthogonal * factorization. * CALL CLACPY( 'Full', M, N, COPYA, LDA, A, LDA ) CALL CLACPY( 'Full', M, NRHS, COPYB, LDB, B, $ LDB ) * * Initialize vector IWORK. * DO 70 J = 1, N IWORK( J ) = 0 70 CONTINUE * SRNAMT = 'CGELSY' CALL CGELSY( M, N, NRHS, A, LDA, B, LDB, IWORK, $ RCOND, CRANK, WORK, LWLSY, RWORK, $ INFO ) IF( INFO.NE.0 ) $ CALL ALAERH( PATH, 'CGELSY', INFO, 0, ' ', M, $ N, NRHS, -1, NB, ITYPE, NFAIL, $ NERRS, NOUT ) * * workspace used: 2*MNMIN+NB*NB+NB*MAX(N,NRHS) * * Test 7: Compute relative error in svd * workspace: M*N + 4*MIN(M,N) + MAX(M,N) * RESULT( 7 ) = CQRT12( CRANK, CRANK, A, LDA, $ COPYS, WORK, LWORK, RWORK ) * * Test 8: Compute error in solution * workspace: M*NRHS + M * CALL CLACPY( 'Full', M, NRHS, COPYB, LDB, WORK, $ LDWORK ) CALL CQRT16( 'No transpose', M, N, NRHS, COPYA, $ LDA, B, LDB, WORK, LDWORK, RWORK, $ RESULT( 8 ) ) * * Test 9: Check norm of r'*A * workspace: NRHS*(M+N) * RESULT( 9 ) = ZERO IF( M.GT.CRANK ) $ RESULT( 9 ) = CQRT17( '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 ) = CQRT14( 'No transpose', M, N, $ NRHS, COPYA, LDA, B, LDB, $ WORK, LWORK ) * * Test CGELSS * * CGELSS: Compute the minimum-norm solution * X to min( norm( A * X - B ) ) * using the SVD. * CALL CLACPY( 'Full', M, N, COPYA, LDA, A, LDA ) CALL CLACPY( 'Full', M, NRHS, COPYB, LDB, B, $ LDB ) SRNAMT = 'CGELSS' CALL CGELSS( M, N, NRHS, A, LDA, B, LDB, S, $ RCOND, CRANK, WORK, LWORK, RWORK, $ INFO ) * IF( INFO.NE.0 ) $ CALL ALAERH( PATH, 'CGELSS', 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 SAXPY( MNMIN, -ONE, COPYS, 1, S, 1 ) RESULT( 11 ) = SASUM( MNMIN, S, 1 ) / $ SASUM( MNMIN, COPYS, 1 ) / $ ( EPS*REAL( MNMIN ) ) ELSE RESULT( 11 ) = ZERO END IF * * Test 12: Compute error in solution * CALL CLACPY( 'Full', M, NRHS, COPYB, LDB, WORK, $ LDWORK ) CALL CQRT16( 'No transpose', M, N, NRHS, COPYA, $ LDA, B, LDB, WORK, LDWORK, RWORK, $ RESULT( 12 ) ) * * Test 13: Check norm of r'*A * RESULT( 13 ) = ZERO IF( M.GT.CRANK ) $ RESULT( 13 ) = CQRT17( '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 ) = CQRT14( 'No transpose', M, N, $ NRHS, COPYA, LDA, B, LDB, $ WORK, LWORK ) * * Test CGELSD * * CGELSD: Compute the minimum-norm solution X * to min( norm( A * X - B ) ) using a * divide and conquer SVD. * CALL XLAENV( 9, 25 ) * CALL CLACPY( 'Full', M, N, COPYA, LDA, A, LDA ) CALL CLACPY( 'Full', M, NRHS, COPYB, LDB, B, $ LDB ) * SRNAMT = 'CGELSD' CALL CGELSD( M, N, NRHS, A, LDA, B, LDB, S, $ RCOND, CRANK, WORK, LWORK, RWORK, $ IWORK, INFO ) IF( INFO.NE.0 ) $ CALL ALAERH( PATH, 'CGELSD', INFO, 0, ' ', M, $ N, NRHS, -1, NB, ITYPE, NFAIL, $ NERRS, NOUT ) * * Test 15: Compute relative error in svd * IF( RANK.GT.0 ) THEN CALL SAXPY( MNMIN, -ONE, COPYS, 1, S, 1 ) RESULT( 15 ) = SASUM( MNMIN, S, 1 ) / $ SASUM( MNMIN, COPYS, 1 ) / $ ( EPS*REAL( MNMIN ) ) ELSE RESULT( 15 ) = ZERO END IF * * Test 16: Compute error in solution * CALL CLACPY( 'Full', M, NRHS, COPYB, LDB, WORK, $ LDWORK ) CALL CQRT16( 'No transpose', M, N, NRHS, COPYA, $ LDA, B, LDB, WORK, LDWORK, RWORK, $ RESULT( 16 ) ) * * Test 17: Check norm of r'*A * RESULT( 17 ) = ZERO IF( M.GT.CRANK ) $ RESULT( 17 ) = CQRT17( '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 ) = CQRT14( 'No transpose', M, N, $ NRHS, COPYA, LDA, B, LDB, $ WORK, LWORK ) * * Print information about the tests that did not * pass the threshold. * DO 80 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 80 CONTINUE NRUN = NRUN + 12 * 90 CONTINUE 100 CONTINUE 110 CONTINUE 120 CONTINUE 130 CONTINUE 140 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( RWORK ) DEALLOCATE( IWORK ) RETURN * * End of CDRVLS * END