numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
| Name | Size | Mode | |
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| lapack/TESTING/LIN/zdrvpp.f | 20724B | -rw-r--r-- |
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*> \brief \b ZDRVPP * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE ZDRVPP( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, * A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK, * RWORK, NOUT ) * * .. Scalar Arguments .. * LOGICAL TSTERR * INTEGER NMAX, NN, NOUT, NRHS * DOUBLE PRECISION THRESH * .. * .. Array Arguments .. * LOGICAL DOTYPE( * ) * INTEGER NVAL( * ) * DOUBLE PRECISION RWORK( * ), S( * ) * COMPLEX*16 A( * ), AFAC( * ), ASAV( * ), B( * ), * $ BSAV( * ), WORK( * ), X( * ), XACT( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZDRVPP tests the driver routines ZPPSV and -SVX. *> \endverbatim * * Arguments: * ========== * *> \param[in] DOTYPE *> \verbatim *> DOTYPE is LOGICAL array, dimension (NTYPES) *> The matrix types to be used for testing. Matrices of type j *> (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = *> .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used. *> \endverbatim *> *> \param[in] 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 dimension N. *> \endverbatim *> *> \param[in] NRHS *> \verbatim *> NRHS is INTEGER *> The number of right hand side vectors to be generated for *> each linear system. *> \endverbatim *> *> \param[in] THRESH *> \verbatim *> THRESH is DOUBLE PRECISION *> 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[in] NMAX *> \verbatim *> NMAX is INTEGER *> The maximum value permitted for N, used in dimensioning the *> work arrays. *> \endverbatim *> *> \param[out] A *> \verbatim *> A is COMPLEX*16 array, dimension (NMAX*(NMAX+1)/2) *> \endverbatim *> *> \param[out] AFAC *> \verbatim *> AFAC is COMPLEX*16 array, dimension (NMAX*(NMAX+1)/2) *> \endverbatim *> *> \param[out] ASAV *> \verbatim *> ASAV is COMPLEX*16 array, dimension (NMAX*(NMAX+1)/2) *> \endverbatim *> *> \param[out] B *> \verbatim *> B is COMPLEX*16 array, dimension (NMAX*NRHS) *> \endverbatim *> *> \param[out] BSAV *> \verbatim *> BSAV is COMPLEX*16 array, dimension (NMAX*NRHS) *> \endverbatim *> *> \param[out] X *> \verbatim *> X is COMPLEX*16 array, dimension (NMAX*NRHS) *> \endverbatim *> *> \param[out] XACT *> \verbatim *> XACT is COMPLEX*16 array, dimension (NMAX*NRHS) *> \endverbatim *> *> \param[out] S *> \verbatim *> S is DOUBLE PRECISION array, dimension (NMAX) *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension *> (NMAX*max(3,NRHS)) *> \endverbatim *> *> \param[out] RWORK *> \verbatim *> RWORK is DOUBLE PRECISION array, dimension (NMAX+2*NRHS) *> \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 complex16_lin * * ===================================================================== SUBROUTINE ZDRVPP( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, $ A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK, $ RWORK, 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 NMAX, NN, NOUT, NRHS DOUBLE PRECISION THRESH * .. * .. Array Arguments .. LOGICAL DOTYPE( * ) INTEGER NVAL( * ) DOUBLE PRECISION RWORK( * ), S( * ) COMPLEX*16 A( * ), AFAC( * ), ASAV( * ), B( * ), $ BSAV( * ), WORK( * ), X( * ), XACT( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) INTEGER NTYPES PARAMETER ( NTYPES = 9 ) INTEGER NTESTS PARAMETER ( NTESTS = 6 ) * .. * .. Local Scalars .. LOGICAL EQUIL, NOFACT, PREFAC, ZEROT CHARACTER DIST, EQUED, FACT, PACKIT, TYPE, UPLO, XTYPE CHARACTER*3 PATH INTEGER I, IEQUED, IFACT, IMAT, IN, INFO, IOFF, IUPLO, $ IZERO, K, K1, KL, KU, LDA, MODE, N, NERRS, $ NFACT, NFAIL, NIMAT, NPP, NRUN, NT DOUBLE PRECISION AINVNM, AMAX, ANORM, CNDNUM, RCOND, RCONDC, $ ROLDC, SCOND * .. * .. Local Arrays .. CHARACTER EQUEDS( 2 ), FACTS( 3 ), PACKS( 2 ), UPLOS( 2 ) INTEGER ISEED( 4 ), ISEEDY( 4 ) DOUBLE PRECISION RESULT( NTESTS ) * .. * .. External Functions .. LOGICAL LSAME DOUBLE PRECISION DGET06, ZLANHP EXTERNAL LSAME, DGET06, ZLANHP * .. * .. External Subroutines .. EXTERNAL ALADHD, ALAERH, ALASVM, ZCOPY, ZERRVX, ZGET04, $ ZLACPY, ZLAIPD, ZLAQHP, ZLARHS, ZLASET, ZLATB4, $ ZLATMS, ZPPEQU, ZPPSV, ZPPSVX, ZPPT01, ZPPT02, $ ZPPT05, ZPPTRF, ZPPTRI * .. * .. Scalars in Common .. LOGICAL LERR, OK CHARACTER*32 SRNAMT INTEGER INFOT, NUNIT * .. * .. Common blocks .. COMMON / INFOC / INFOT, NUNIT, OK, LERR COMMON / SRNAMC / SRNAMT * .. * .. Intrinsic Functions .. INTRINSIC DCMPLX, MAX * .. * .. Data statements .. DATA ISEEDY / 1988, 1989, 1990, 1991 / DATA UPLOS / 'U', 'L' / , FACTS / 'F', 'N', 'E' / , $ PACKS / 'C', 'R' / , EQUEDS / 'N', 'Y' / * .. * .. Executable Statements .. * * Initialize constants and the random number seed. * PATH( 1: 1 ) = 'Zomplex precision' PATH( 2: 3 ) = 'PP' NRUN = 0 NFAIL = 0 NERRS = 0 DO 10 I = 1, 4 ISEED( I ) = ISEEDY( I ) 10 CONTINUE * * Test the error exits * IF( TSTERR ) $ CALL ZERRVX( PATH, NOUT ) INFOT = 0 * * Do for each value of N in NVAL * DO 140 IN = 1, NN N = NVAL( IN ) LDA = MAX( N, 1 ) NPP = N*( N+1 ) / 2 XTYPE = 'N' NIMAT = NTYPES IF( N.LE.0 ) $ NIMAT = 1 * DO 130 IMAT = 1, NIMAT * * Do the tests only if DOTYPE( IMAT ) is true. * IF( .NOT.DOTYPE( IMAT ) ) $ GO TO 130 * * Skip types 3, 4, or 5 if the matrix size is too small. * ZEROT = IMAT.GE.3 .AND. IMAT.LE.5 IF( ZEROT .AND. N.LT.IMAT-2 ) $ GO TO 130 * * Do first for UPLO = 'U', then for UPLO = 'L' * DO 120 IUPLO = 1, 2 UPLO = UPLOS( IUPLO ) PACKIT = PACKS( IUPLO ) * * Set up parameters with ZLATB4 and generate a test matrix * with ZLATMS. * CALL ZLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM, MODE, $ CNDNUM, DIST ) RCONDC = ONE / CNDNUM * SRNAMT = 'ZLATMS' CALL ZLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE, $ CNDNUM, ANORM, KL, KU, PACKIT, A, LDA, WORK, $ INFO ) * * Check error code from ZLATMS. * IF( INFO.NE.0 ) THEN CALL ALAERH( PATH, 'ZLATMS', INFO, 0, UPLO, N, N, -1, $ -1, -1, IMAT, NFAIL, NERRS, NOUT ) GO TO 120 END IF * * For types 3-5, zero one row and column of the matrix to * test that INFO is returned correctly. * IF( ZEROT ) THEN IF( IMAT.EQ.3 ) THEN IZERO = 1 ELSE IF( IMAT.EQ.4 ) THEN IZERO = N ELSE IZERO = N / 2 + 1 END IF * * Set row and column IZERO of A to 0. * IF( IUPLO.EQ.1 ) THEN IOFF = ( IZERO-1 )*IZERO / 2 DO 20 I = 1, IZERO - 1 A( IOFF+I ) = ZERO 20 CONTINUE IOFF = IOFF + IZERO DO 30 I = IZERO, N A( IOFF ) = ZERO IOFF = IOFF + I 30 CONTINUE ELSE IOFF = IZERO DO 40 I = 1, IZERO - 1 A( IOFF ) = ZERO IOFF = IOFF + N - I 40 CONTINUE IOFF = IOFF - IZERO DO 50 I = IZERO, N A( IOFF+I ) = ZERO 50 CONTINUE END IF ELSE IZERO = 0 END IF * * Set the imaginary part of the diagonals. * IF( IUPLO.EQ.1 ) THEN CALL ZLAIPD( N, A, 2, 1 ) ELSE CALL ZLAIPD( N, A, N, -1 ) END IF * * Save a copy of the matrix A in ASAV. * CALL ZCOPY( NPP, A, 1, ASAV, 1 ) * DO 110 IEQUED = 1, 2 EQUED = EQUEDS( IEQUED ) IF( IEQUED.EQ.1 ) THEN NFACT = 3 ELSE NFACT = 1 END IF * DO 100 IFACT = 1, NFACT FACT = FACTS( IFACT ) PREFAC = LSAME( FACT, 'F' ) NOFACT = LSAME( FACT, 'N' ) EQUIL = LSAME( FACT, 'E' ) * IF( ZEROT ) THEN IF( PREFAC ) $ GO TO 100 RCONDC = ZERO * ELSE IF( .NOT.LSAME( FACT, 'N' ) ) THEN * * Compute the condition number for comparison with * the value returned by ZPPSVX (FACT = 'N' reuses * the condition number from the previous iteration * with FACT = 'F'). * CALL ZCOPY( NPP, ASAV, 1, AFAC, 1 ) IF( EQUIL .OR. IEQUED.GT.1 ) THEN * * Compute row and column scale factors to * equilibrate the matrix A. * CALL ZPPEQU( UPLO, N, AFAC, S, SCOND, AMAX, $ INFO ) IF( INFO.EQ.0 .AND. N.GT.0 ) THEN IF( IEQUED.GT.1 ) $ SCOND = ZERO * * Equilibrate the matrix. * CALL ZLAQHP( UPLO, N, AFAC, S, SCOND, $ AMAX, EQUED ) END IF END IF * * Save the condition number of the * non-equilibrated system for use in ZGET04. * IF( EQUIL ) $ ROLDC = RCONDC * * Compute the 1-norm of A. * ANORM = ZLANHP( '1', UPLO, N, AFAC, RWORK ) * * Factor the matrix A. * CALL ZPPTRF( UPLO, N, AFAC, INFO ) * * Form the inverse of A. * CALL ZCOPY( NPP, AFAC, 1, A, 1 ) CALL ZPPTRI( UPLO, N, A, INFO ) * * Compute the 1-norm condition number of A. * AINVNM = ZLANHP( '1', UPLO, N, A, RWORK ) IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN RCONDC = ONE ELSE RCONDC = ( ONE / ANORM ) / AINVNM END IF END IF * * Restore the matrix A. * CALL ZCOPY( NPP, ASAV, 1, A, 1 ) * * Form an exact solution and set the right hand side. * SRNAMT = 'ZLARHS' CALL ZLARHS( PATH, XTYPE, UPLO, ' ', N, N, KL, KU, $ NRHS, A, LDA, XACT, LDA, B, LDA, $ ISEED, INFO ) XTYPE = 'C' CALL ZLACPY( 'Full', N, NRHS, B, LDA, BSAV, LDA ) * IF( NOFACT ) THEN * * --- Test ZPPSV --- * * Compute the L*L' or U'*U factorization of the * matrix and solve the system. * CALL ZCOPY( NPP, A, 1, AFAC, 1 ) CALL ZLACPY( 'Full', N, NRHS, B, LDA, X, LDA ) * SRNAMT = 'ZPPSV ' CALL ZPPSV( UPLO, N, NRHS, AFAC, X, LDA, INFO ) * * Check error code from ZPPSV . * IF( INFO.NE.IZERO ) THEN CALL ALAERH( PATH, 'ZPPSV ', INFO, IZERO, $ UPLO, N, N, -1, -1, NRHS, IMAT, $ NFAIL, NERRS, NOUT ) GO TO 70 ELSE IF( INFO.NE.0 ) THEN GO TO 70 END IF * * Reconstruct matrix from factors and compute * residual. * CALL ZPPT01( UPLO, N, A, AFAC, RWORK, $ RESULT( 1 ) ) * * Compute residual of the computed solution. * CALL ZLACPY( 'Full', N, NRHS, B, LDA, WORK, $ LDA ) CALL ZPPT02( UPLO, N, NRHS, A, X, LDA, WORK, $ LDA, RWORK, RESULT( 2 ) ) * * Check solution from generated exact solution. * CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC, $ RESULT( 3 ) ) NT = 3 * * Print information about the tests that did not * pass the threshold. * DO 60 K = 1, NT IF( RESULT( K ).GE.THRESH ) THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) $ CALL ALADHD( NOUT, PATH ) WRITE( NOUT, FMT = 9999 )'ZPPSV ', UPLO, $ N, IMAT, K, RESULT( K ) NFAIL = NFAIL + 1 END IF 60 CONTINUE NRUN = NRUN + NT 70 CONTINUE END IF * * --- Test ZPPSVX --- * IF( .NOT.PREFAC .AND. NPP.GT.0 ) $ CALL ZLASET( 'Full', NPP, 1, DCMPLX( ZERO ), $ DCMPLX( ZERO ), AFAC, NPP ) CALL ZLASET( 'Full', N, NRHS, DCMPLX( ZERO ), $ DCMPLX( ZERO ), X, LDA ) IF( IEQUED.GT.1 .AND. N.GT.0 ) THEN * * Equilibrate the matrix if FACT='F' and * EQUED='Y'. * CALL ZLAQHP( UPLO, N, A, S, SCOND, AMAX, EQUED ) END IF * * Solve the system and compute the condition number * and error bounds using ZPPSVX. * SRNAMT = 'ZPPSVX' CALL ZPPSVX( FACT, UPLO, N, NRHS, A, AFAC, EQUED, $ S, B, LDA, X, LDA, RCOND, RWORK, $ RWORK( NRHS+1 ), WORK, $ RWORK( 2*NRHS+1 ), INFO ) * * Check the error code from ZPPSVX. * IF( INFO.NE.IZERO ) THEN CALL ALAERH( PATH, 'ZPPSVX', INFO, IZERO, $ FACT // UPLO, N, N, -1, -1, NRHS, $ IMAT, NFAIL, NERRS, NOUT ) GO TO 90 END IF * IF( INFO.EQ.0 ) THEN IF( .NOT.PREFAC ) THEN * * Reconstruct matrix from factors and compute * residual. * CALL ZPPT01( UPLO, N, A, AFAC, $ RWORK( 2*NRHS+1 ), RESULT( 1 ) ) K1 = 1 ELSE K1 = 2 END IF * * Compute residual of the computed solution. * CALL ZLACPY( 'Full', N, NRHS, BSAV, LDA, WORK, $ LDA ) CALL ZPPT02( UPLO, N, NRHS, ASAV, X, LDA, WORK, $ LDA, RWORK( 2*NRHS+1 ), $ RESULT( 2 ) ) * * Check solution from generated exact solution. * IF( NOFACT .OR. ( PREFAC .AND. LSAME( EQUED, $ 'N' ) ) ) THEN CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, $ RCONDC, RESULT( 3 ) ) ELSE CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, $ ROLDC, RESULT( 3 ) ) END IF * * Check the error bounds from iterative * refinement. * CALL ZPPT05( UPLO, N, NRHS, ASAV, B, LDA, X, $ LDA, XACT, LDA, RWORK, $ RWORK( NRHS+1 ), RESULT( 4 ) ) ELSE K1 = 6 END IF * * Compare RCOND from ZPPSVX with the computed value * in RCONDC. * RESULT( 6 ) = DGET06( RCOND, RCONDC ) * * Print information about the tests that did not pass * the threshold. * DO 80 K = K1, 6 IF( RESULT( K ).GE.THRESH ) THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) $ CALL ALADHD( NOUT, PATH ) IF( PREFAC ) THEN WRITE( NOUT, FMT = 9997 )'ZPPSVX', FACT, $ UPLO, N, EQUED, IMAT, K, RESULT( K ) ELSE WRITE( NOUT, FMT = 9998 )'ZPPSVX', FACT, $ UPLO, N, IMAT, K, RESULT( K ) END IF NFAIL = NFAIL + 1 END IF 80 CONTINUE NRUN = NRUN + 7 - K1 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( 1X, A, ', UPLO=''', A1, ''', N =', I5, ', type ', I1, $ ', test(', I1, ')=', G12.5 ) 9998 FORMAT( 1X, A, ', FACT=''', A1, ''', UPLO=''', A1, ''', N=', I5, $ ', type ', I1, ', test(', I1, ')=', G12.5 ) 9997 FORMAT( 1X, A, ', FACT=''', A1, ''', UPLO=''', A1, ''', N=', I5, $ ', EQUED=''', A1, ''', type ', I1, ', test(', I1, ')=', $ G12.5 ) RETURN * * End of ZDRVPP * END