numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
| Name | Size | Mode | |
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| lapack/TESTING/LIN/ddrvpb.f | 24622B | -rw-r--r-- |
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*> \brief \b DDRVPB * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE DDRVPB( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, * A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK, * RWORK, IWORK, NOUT ) * * .. Scalar Arguments .. * LOGICAL TSTERR * INTEGER NMAX, NN, NOUT, NRHS * DOUBLE PRECISION THRESH * .. * .. Array Arguments .. * LOGICAL DOTYPE( * ) * INTEGER IWORK( * ), NVAL( * ) * DOUBLE PRECISION A( * ), AFAC( * ), ASAV( * ), B( * ), * $ BSAV( * ), RWORK( * ), S( * ), WORK( * ), * $ X( * ), XACT( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DDRVPB tests the driver routines DPBSV 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 DOUBLE PRECISION array, dimension (NMAX*NMAX) *> \endverbatim *> *> \param[out] AFAC *> \verbatim *> AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX) *> \endverbatim *> *> \param[out] ASAV *> \verbatim *> ASAV is DOUBLE PRECISION array, dimension (NMAX*NMAX) *> \endverbatim *> *> \param[out] B *> \verbatim *> B is DOUBLE PRECISION array, dimension (NMAX*NRHS) *> \endverbatim *> *> \param[out] BSAV *> \verbatim *> BSAV is DOUBLE PRECISION array, dimension (NMAX*NRHS) *> \endverbatim *> *> \param[out] X *> \verbatim *> X is DOUBLE PRECISION array, dimension (NMAX*NRHS) *> \endverbatim *> *> \param[out] XACT *> \verbatim *> XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS) *> \endverbatim *> *> \param[out] S *> \verbatim *> S is DOUBLE PRECISION array, dimension (NMAX) *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension *> (NMAX*max(3,NRHS)) *> \endverbatim *> *> \param[out] RWORK *> \verbatim *> RWORK is DOUBLE PRECISION array, dimension (NMAX+2*NRHS) *> \endverbatim *> *> \param[out] IWORK *> \verbatim *> IWORK is INTEGER array, dimension (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 double_lin * * ===================================================================== SUBROUTINE DDRVPB( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, $ A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK, $ RWORK, IWORK, 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 IWORK( * ), NVAL( * ) DOUBLE PRECISION A( * ), AFAC( * ), ASAV( * ), B( * ), $ BSAV( * ), RWORK( * ), S( * ), WORK( * ), $ X( * ), XACT( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) INTEGER NTYPES, NTESTS PARAMETER ( NTYPES = 8, NTESTS = 6 ) INTEGER NBW PARAMETER ( NBW = 4 ) * .. * .. Local Scalars .. LOGICAL EQUIL, NOFACT, PREFAC, ZEROT CHARACTER DIST, EQUED, FACT, PACKIT, TYPE, UPLO, XTYPE CHARACTER*3 PATH INTEGER I, I1, I2, IEQUED, IFACT, IKD, IMAT, IN, INFO, $ IOFF, IUPLO, IW, IZERO, K, K1, KD, KL, KOFF, $ KU, LDA, LDAB, MODE, N, NB, NBMIN, NERRS, $ NFACT, NFAIL, NIMAT, NKD, NRUN, NT DOUBLE PRECISION AINVNM, AMAX, ANORM, CNDNUM, RCOND, RCONDC, $ ROLDC, SCOND * .. * .. Local Arrays .. CHARACTER EQUEDS( 2 ), FACTS( 3 ) INTEGER ISEED( 4 ), ISEEDY( 4 ), KDVAL( NBW ) DOUBLE PRECISION RESULT( NTESTS ) * .. * .. External Functions .. LOGICAL LSAME DOUBLE PRECISION DGET06, DLANGE, DLANSB EXTERNAL LSAME, DGET06, DLANGE, DLANSB * .. * .. External Subroutines .. EXTERNAL ALADHD, ALAERH, ALASVM, DCOPY, DERRVX, DGET04, $ DLACPY, DLAQSB, DLARHS, DLASET, DLATB4, DLATMS, $ DPBEQU, DPBSV, DPBSVX, DPBT01, DPBT02, DPBT05, $ DPBTRF, DPBTRS, DSWAP, XLAENV * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Scalars in Common .. LOGICAL LERR, OK CHARACTER*32 SRNAMT INTEGER INFOT, NUNIT * .. * .. Common blocks .. COMMON / INFOC / INFOT, NUNIT, OK, LERR COMMON / SRNAMC / SRNAMT * .. * .. Data statements .. DATA ISEEDY / 1988, 1989, 1990, 1991 / DATA FACTS / 'F', 'N', 'E' / DATA EQUEDS / 'N', 'Y' / * .. * .. Executable Statements .. * * Initialize constants and the random number seed. * PATH( 1: 1 ) = 'Double precision' PATH( 2: 3 ) = 'PB' NRUN = 0 NFAIL = 0 NERRS = 0 DO 10 I = 1, 4 ISEED( I ) = ISEEDY( I ) 10 CONTINUE * * Test the error exits * IF( TSTERR ) $ CALL DERRVX( PATH, NOUT ) INFOT = 0 KDVAL( 1 ) = 0 * * Set the block size and minimum block size for testing. * NB = 1 NBMIN = 2 CALL XLAENV( 1, NB ) CALL XLAENV( 2, NBMIN ) * * Do for each value of N in NVAL * DO 110 IN = 1, NN N = NVAL( IN ) LDA = MAX( N, 1 ) XTYPE = 'N' * * Set limits on the number of loop iterations. * NKD = MAX( 1, MIN( N, 4 ) ) NIMAT = NTYPES IF( N.EQ.0 ) $ NIMAT = 1 * KDVAL( 2 ) = N + ( N+1 ) / 4 KDVAL( 3 ) = ( 3*N-1 ) / 4 KDVAL( 4 ) = ( N+1 ) / 4 * DO 100 IKD = 1, NKD * * Do for KD = 0, (5*N+1)/4, (3N-1)/4, and (N+1)/4. This order * makes it easier to skip redundant values for small values * of N. * KD = KDVAL( IKD ) LDAB = KD + 1 * * Do first for UPLO = 'U', then for UPLO = 'L' * DO 90 IUPLO = 1, 2 KOFF = 1 IF( IUPLO.EQ.1 ) THEN UPLO = 'U' PACKIT = 'Q' KOFF = MAX( 1, KD+2-N ) ELSE UPLO = 'L' PACKIT = 'B' END IF * DO 80 IMAT = 1, NIMAT * * Do the tests only if DOTYPE( IMAT ) is true. * IF( .NOT.DOTYPE( IMAT ) ) $ GO TO 80 * * Skip types 2, 3, or 4 if the matrix size is too small. * ZEROT = IMAT.GE.2 .AND. IMAT.LE.4 IF( ZEROT .AND. N.LT.IMAT-1 ) $ GO TO 80 * IF( .NOT.ZEROT .OR. .NOT.DOTYPE( 1 ) ) THEN * * Set up parameters with DLATB4 and generate a test * matrix with DLATMS. * CALL DLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM, $ MODE, CNDNUM, DIST ) * SRNAMT = 'DLATMS' CALL DLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE, $ CNDNUM, ANORM, KD, KD, PACKIT, $ A( KOFF ), LDAB, WORK, INFO ) * * Check error code from DLATMS. * IF( INFO.NE.0 ) THEN CALL ALAERH( PATH, 'DLATMS', INFO, 0, UPLO, N, $ N, -1, -1, -1, IMAT, NFAIL, NERRS, $ NOUT ) GO TO 80 END IF ELSE IF( IZERO.GT.0 ) THEN * * Use the same matrix for types 3 and 4 as for type * 2 by copying back the zeroed out column, * IW = 2*LDA + 1 IF( IUPLO.EQ.1 ) THEN IOFF = ( IZERO-1 )*LDAB + KD + 1 CALL DCOPY( IZERO-I1, WORK( IW ), 1, $ A( IOFF-IZERO+I1 ), 1 ) IW = IW + IZERO - I1 CALL DCOPY( I2-IZERO+1, WORK( IW ), 1, $ A( IOFF ), MAX( LDAB-1, 1 ) ) ELSE IOFF = ( I1-1 )*LDAB + 1 CALL DCOPY( IZERO-I1, WORK( IW ), 1, $ A( IOFF+IZERO-I1 ), $ MAX( LDAB-1, 1 ) ) IOFF = ( IZERO-1 )*LDAB + 1 IW = IW + IZERO - I1 CALL DCOPY( I2-IZERO+1, WORK( IW ), 1, $ A( IOFF ), 1 ) END IF END IF * * For types 2-4, zero one row and column of the matrix * to test that INFO is returned correctly. * IZERO = 0 IF( ZEROT ) THEN IF( IMAT.EQ.2 ) THEN IZERO = 1 ELSE IF( IMAT.EQ.3 ) THEN IZERO = N ELSE IZERO = N / 2 + 1 END IF * * Save the zeroed out row and column in WORK(*,3) * IW = 2*LDA DO 20 I = 1, MIN( 2*KD+1, N ) WORK( IW+I ) = ZERO 20 CONTINUE IW = IW + 1 I1 = MAX( IZERO-KD, 1 ) I2 = MIN( IZERO+KD, N ) * IF( IUPLO.EQ.1 ) THEN IOFF = ( IZERO-1 )*LDAB + KD + 1 CALL DSWAP( IZERO-I1, A( IOFF-IZERO+I1 ), 1, $ WORK( IW ), 1 ) IW = IW + IZERO - I1 CALL DSWAP( I2-IZERO+1, A( IOFF ), $ MAX( LDAB-1, 1 ), WORK( IW ), 1 ) ELSE IOFF = ( I1-1 )*LDAB + 1 CALL DSWAP( IZERO-I1, A( IOFF+IZERO-I1 ), $ MAX( LDAB-1, 1 ), WORK( IW ), 1 ) IOFF = ( IZERO-1 )*LDAB + 1 IW = IW + IZERO - I1 CALL DSWAP( I2-IZERO+1, A( IOFF ), 1, $ WORK( IW ), 1 ) END IF END IF * * Save a copy of the matrix A in ASAV. * CALL DLACPY( 'Full', KD+1, N, A, LDAB, ASAV, LDAB ) * DO 70 IEQUED = 1, 2 EQUED = EQUEDS( IEQUED ) IF( IEQUED.EQ.1 ) THEN NFACT = 3 ELSE NFACT = 1 END IF * DO 60 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 60 RCONDC = ZERO * ELSE IF( .NOT.LSAME( FACT, 'N' ) ) THEN * * Compute the condition number for comparison * with the value returned by DPBSVX (FACT = * 'N' reuses the condition number from the * previous iteration with FACT = 'F'). * CALL DLACPY( 'Full', KD+1, N, ASAV, LDAB, $ AFAC, LDAB ) IF( EQUIL .OR. IEQUED.GT.1 ) THEN * * Compute row and column scale factors to * equilibrate the matrix A. * CALL DPBEQU( UPLO, N, KD, AFAC, LDAB, S, $ SCOND, AMAX, INFO ) IF( INFO.EQ.0 .AND. N.GT.0 ) THEN IF( IEQUED.GT.1 ) $ SCOND = ZERO * * Equilibrate the matrix. * CALL DLAQSB( UPLO, N, KD, AFAC, LDAB, $ S, SCOND, AMAX, EQUED ) END IF END IF * * Save the condition number of the * non-equilibrated system for use in DGET04. * IF( EQUIL ) $ ROLDC = RCONDC * * Compute the 1-norm of A. * ANORM = DLANSB( '1', UPLO, N, KD, AFAC, LDAB, $ RWORK ) * * Factor the matrix A. * CALL DPBTRF( UPLO, N, KD, AFAC, LDAB, INFO ) * * Form the inverse of A. * CALL DLASET( 'Full', N, N, ZERO, ONE, A, $ LDA ) SRNAMT = 'DPBTRS' CALL DPBTRS( UPLO, N, KD, N, AFAC, LDAB, A, $ LDA, INFO ) * * Compute the 1-norm condition number of A. * AINVNM = DLANGE( '1', N, N, A, LDA, 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 DLACPY( 'Full', KD+1, N, ASAV, LDAB, A, $ LDAB ) * * Form an exact solution and set the right hand * side. * SRNAMT = 'DLARHS' CALL DLARHS( PATH, XTYPE, UPLO, ' ', N, N, KD, $ KD, NRHS, A, LDAB, XACT, LDA, B, $ LDA, ISEED, INFO ) XTYPE = 'C' CALL DLACPY( 'Full', N, NRHS, B, LDA, BSAV, $ LDA ) * IF( NOFACT ) THEN * * --- Test DPBSV --- * * Compute the L*L' or U'*U factorization of the * matrix and solve the system. * CALL DLACPY( 'Full', KD+1, N, A, LDAB, AFAC, $ LDAB ) CALL DLACPY( 'Full', N, NRHS, B, LDA, X, $ LDA ) * SRNAMT = 'DPBSV ' CALL DPBSV( UPLO, N, KD, NRHS, AFAC, LDAB, X, $ LDA, INFO ) * * Check error code from DPBSV . * IF( INFO.NE.IZERO ) THEN CALL ALAERH( PATH, 'DPBSV ', INFO, IZERO, $ UPLO, N, N, KD, KD, NRHS, $ IMAT, NFAIL, NERRS, NOUT ) GO TO 40 ELSE IF( INFO.NE.0 ) THEN GO TO 40 END IF * * Reconstruct matrix from factors and compute * residual. * CALL DPBT01( UPLO, N, KD, A, LDAB, AFAC, $ LDAB, RWORK, RESULT( 1 ) ) * * Compute residual of the computed solution. * CALL DLACPY( 'Full', N, NRHS, B, LDA, WORK, $ LDA ) CALL DPBT02( UPLO, N, KD, NRHS, A, LDAB, X, $ LDA, WORK, LDA, RWORK, $ RESULT( 2 ) ) * * Check solution from generated exact solution. * CALL DGET04( N, NRHS, X, LDA, XACT, LDA, $ RCONDC, RESULT( 3 ) ) NT = 3 * * Print information about the tests that did * not pass the threshold. * DO 30 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 )'DPBSV ', $ UPLO, N, KD, IMAT, K, RESULT( K ) NFAIL = NFAIL + 1 END IF 30 CONTINUE NRUN = NRUN + NT 40 CONTINUE END IF * * --- Test DPBSVX --- * IF( .NOT.PREFAC ) $ CALL DLASET( 'Full', KD+1, N, ZERO, ZERO, $ AFAC, LDAB ) CALL DLASET( 'Full', N, NRHS, ZERO, ZERO, X, $ LDA ) IF( IEQUED.GT.1 .AND. N.GT.0 ) THEN * * Equilibrate the matrix if FACT='F' and * EQUED='Y' * CALL DLAQSB( UPLO, N, KD, A, LDAB, S, SCOND, $ AMAX, EQUED ) END IF * * Solve the system and compute the condition * number and error bounds using DPBSVX. * SRNAMT = 'DPBSVX' CALL DPBSVX( FACT, UPLO, N, KD, NRHS, A, LDAB, $ AFAC, LDAB, EQUED, S, B, LDA, X, $ LDA, RCOND, RWORK, RWORK( NRHS+1 ), $ WORK, IWORK, INFO ) * * Check the error code from DPBSVX. * IF( INFO.NE.IZERO ) THEN CALL ALAERH( PATH, 'DPBSVX', INFO, IZERO, $ FACT // UPLO, N, N, KD, KD, $ NRHS, IMAT, NFAIL, NERRS, NOUT ) GO TO 60 END IF * IF( INFO.EQ.0 ) THEN IF( .NOT.PREFAC ) THEN * * Reconstruct matrix from factors and * compute residual. * CALL DPBT01( UPLO, N, KD, A, LDAB, AFAC, $ LDAB, RWORK( 2*NRHS+1 ), $ RESULT( 1 ) ) K1 = 1 ELSE K1 = 2 END IF * * Compute residual of the computed solution. * CALL DLACPY( 'Full', N, NRHS, BSAV, LDA, $ WORK, LDA ) CALL DPBT02( UPLO, N, KD, NRHS, ASAV, LDAB, $ 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 DGET04( N, NRHS, X, LDA, XACT, LDA, $ RCONDC, RESULT( 3 ) ) ELSE CALL DGET04( N, NRHS, X, LDA, XACT, LDA, $ ROLDC, RESULT( 3 ) ) END IF * * Check the error bounds from iterative * refinement. * CALL DPBT05( UPLO, N, KD, NRHS, ASAV, LDAB, $ B, LDA, X, LDA, XACT, LDA, $ RWORK, RWORK( NRHS+1 ), $ RESULT( 4 ) ) ELSE K1 = 6 END IF * * Compare RCOND from DPBSVX with the computed * value in RCONDC. * RESULT( 6 ) = DGET06( RCOND, RCONDC ) * * Print information about the tests that did not * pass the threshold. * DO 50 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 )'DPBSVX', $ FACT, UPLO, N, KD, EQUED, IMAT, K, $ RESULT( K ) ELSE WRITE( NOUT, FMT = 9998 )'DPBSVX', $ FACT, UPLO, N, KD, IMAT, K, $ RESULT( K ) END IF NFAIL = NFAIL + 1 END IF 50 CONTINUE NRUN = NRUN + 7 - K1 60 CONTINUE 70 CONTINUE 80 CONTINUE 90 CONTINUE 100 CONTINUE 110 CONTINUE * * Print a summary of the results. * CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS ) * 9999 FORMAT( 1X, A, ', UPLO=''', A1, ''', N =', I5, ', KD =', I5, $ ', type ', I1, ', test(', I1, ')=', G12.5 ) 9998 FORMAT( 1X, A, '( ''', A1, ''', ''', A1, ''', ', I5, ', ', I5, $ ', ... ), type ', I1, ', test(', I1, ')=', G12.5 ) 9997 FORMAT( 1X, A, '( ''', A1, ''', ''', A1, ''', ', I5, ', ', I5, $ ', ... ), EQUED=''', A1, ''', type ', I1, ', test(', I1, $ ')=', G12.5 ) RETURN * * End of DDRVPB * END