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SUBROUTINE DDRVPO( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
$ A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK, $ RWORK, IWORK, NOUT ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. 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( * ) * .. * * Purpose * ======= * * DDRVPO tests the driver routines DPOSV and -SVX. * * Arguments * ========= * * DOTYPE (input) 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. * * NN (input) INTEGER * The number of values of N contained in the vector NVAL. * * NVAL (input) INTEGER array, dimension (NN) * The values of the matrix dimension N. * * NRHS (input) INTEGER * The number of right hand side vectors to be generated for * each linear system. * * THRESH (input) 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. * * TSTERR (input) LOGICAL * Flag that indicates whether error exits are to be tested. * * NMAX (input) INTEGER * The maximum value permitted for N, used in dimensioning the * work arrays. * * A (workspace) DOUBLE PRECISION array, dimension (NMAX*NMAX) * * AFAC (workspace) DOUBLE PRECISION array, dimension (NMAX*NMAX) * * ASAV (workspace) DOUBLE PRECISION array, dimension (NMAX*NMAX) * * B (workspace) DOUBLE PRECISION array, dimension (NMAX*NRHS) * * BSAV (workspace) DOUBLE PRECISION array, dimension (NMAX*NRHS) * * X (workspace) DOUBLE PRECISION array, dimension (NMAX*NRHS) * * XACT (workspace) DOUBLE PRECISION array, dimension (NMAX*NRHS) * * S (workspace) DOUBLE PRECISION array, dimension (NMAX) * * WORK (workspace) DOUBLE PRECISION array, dimension * (NMAX*max(3,NRHS)) * * RWORK (workspace) DOUBLE PRECISION array, dimension (NMAX+2*NRHS) * * IWORK (workspace) INTEGER array, dimension (NMAX) * * NOUT (input) INTEGER * The unit number for output. * * ===================================================================== * * .. 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, TYPE, UPLO, XTYPE CHARACTER*3 PATH INTEGER I, IEQUED, IFACT, IMAT, IN, INFO, IOFF, IUPLO, $ IZERO, K, K1, KL, KU, LDA, MODE, N, NB, NBMIN, $ NERRS, NFACT, NFAIL, NIMAT, NRUN, NT DOUBLE PRECISION AINVNM, AMAX, ANORM, CNDNUM, RCOND, RCONDC, $ ROLDC, SCOND * .. * .. Local Arrays .. CHARACTER EQUEDS( 2 ), FACTS( 3 ), UPLOS( 2 ) INTEGER ISEED( 4 ), ISEEDY( 4 ) DOUBLE PRECISION RESULT( NTESTS ) * .. * .. External Functions .. LOGICAL LSAME DOUBLE PRECISION DGET06, DLANSY EXTERNAL LSAME, DGET06, DLANSY * .. * .. External Subroutines .. EXTERNAL ALADHD, ALAERH, ALASVM, DERRVX, DGET04, DLACPY, $ DLAQSY, DLARHS, DLASET, DLATB4, DLATMS, DPOEQU, $ DPOSV, DPOSVX, DPOT01, DPOT02, DPOT05, DPOTRF, $ DPOTRI, XLAENV * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. 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 UPLOS / 'U', 'L' / 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 ) = 'PO' 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 * * 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 130 IN = 1, NN N = NVAL( IN ) LDA = MAX( N, 1 ) XTYPE = 'N' NIMAT = NTYPES IF( N.LE.0 ) $ NIMAT = 1 * DO 120 IMAT = 1, NIMAT * * Do the tests only if DOTYPE( IMAT ) is true. * IF( .NOT.DOTYPE( IMAT ) ) $ GO TO 120 * * 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 120 * * Do first for UPLO = 'U', then for UPLO = 'L' * DO 110 IUPLO = 1, 2 UPLO = UPLOS( IUPLO ) * * 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, KL, KU, UPLO, A, LDA, 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 110 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 IOFF = ( IZERO-1 )*LDA * * Set row and column IZERO of A to 0. * IF( IUPLO.EQ.1 ) THEN 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 + LDA 30 CONTINUE ELSE IOFF = IZERO DO 40 I = 1, IZERO - 1 A( IOFF ) = ZERO IOFF = IOFF + LDA 40 CONTINUE IOFF = IOFF - IZERO DO 50 I = IZERO, N A( IOFF+I ) = ZERO 50 CONTINUE END IF ELSE IZERO = 0 END IF * * Save a copy of the matrix A in ASAV. * CALL DLACPY( UPLO, N, N, A, LDA, ASAV, LDA ) * DO 100 IEQUED = 1, 2 EQUED = EQUEDS( IEQUED ) IF( IEQUED.EQ.1 ) THEN NFACT = 3 ELSE NFACT = 1 END IF * DO 90 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 90 RCONDC = ZERO * ELSE IF( .NOT.LSAME( FACT, 'N' ) ) THEN * * Compute the condition number for comparison with * the value returned by DPOSVX (FACT = 'N' reuses * the condition number from the previous iteration * with FACT = 'F'). * CALL DLACPY( UPLO, N, N, ASAV, LDA, AFAC, LDA ) IF( EQUIL .OR. IEQUED.GT.1 ) THEN * * Compute row and column scale factors to * equilibrate the matrix A. * CALL DPOEQU( N, AFAC, LDA, S, SCOND, AMAX, $ INFO ) IF( INFO.EQ.0 .AND. N.GT.0 ) THEN IF( IEQUED.GT.1 ) $ SCOND = ZERO * * Equilibrate the matrix. * CALL DLAQSY( UPLO, N, AFAC, LDA, 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 = DLANSY( '1', UPLO, N, AFAC, LDA, RWORK ) * * Factor the matrix A. * CALL DPOTRF( UPLO, N, AFAC, LDA, INFO ) * * Form the inverse of A. * CALL DLACPY( UPLO, N, N, AFAC, LDA, A, LDA ) CALL DPOTRI( UPLO, N, A, LDA, INFO ) * * Compute the 1-norm condition number of A. * AINVNM = DLANSY( '1', UPLO, 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( UPLO, N, N, ASAV, LDA, A, LDA ) * * Form an exact solution and set the right hand side. * SRNAMT = 'DLARHS' CALL DLARHS( PATH, XTYPE, UPLO, ' ', N, N, KL, KU, $ NRHS, A, LDA, XACT, LDA, B, LDA, $ ISEED, INFO ) XTYPE = 'C' CALL DLACPY( 'Full', N, NRHS, B, LDA, BSAV, LDA ) * IF( NOFACT ) THEN * * --- Test DPOSV --- * * Compute the L*L' or U'*U factorization of the * matrix and solve the system. * CALL DLACPY( UPLO, N, N, A, LDA, AFAC, LDA ) CALL DLACPY( 'Full', N, NRHS, B, LDA, X, LDA ) * SRNAMT = 'DPOSV ' CALL DPOSV( UPLO, N, NRHS, AFAC, LDA, X, LDA, $ INFO ) * * Check error code from DPOSV . * IF( INFO.NE.IZERO ) THEN CALL ALAERH( PATH, 'DPOSV ', 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 DPOT01( UPLO, N, A, LDA, AFAC, LDA, RWORK, $ RESULT( 1 ) ) * * Compute residual of the computed solution. * CALL DLACPY( 'Full', N, NRHS, B, LDA, WORK, $ LDA ) CALL DPOT02( UPLO, N, NRHS, A, LDA, 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 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 )'DPOSV ', UPLO, $ N, IMAT, K, RESULT( K ) NFAIL = NFAIL + 1 END IF 60 CONTINUE NRUN = NRUN + NT 70 CONTINUE END IF * * --- Test DPOSVX --- * IF( .NOT.PREFAC ) $ CALL DLASET( UPLO, N, N, ZERO, ZERO, AFAC, LDA ) 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 DLAQSY( UPLO, N, A, LDA, S, SCOND, AMAX, $ EQUED ) END IF * * Solve the system and compute the condition number * and error bounds using DPOSVX. * SRNAMT = 'DPOSVX' CALL DPOSVX( FACT, UPLO, N, NRHS, A, LDA, AFAC, $ LDA, EQUED, S, B, LDA, X, LDA, RCOND, $ RWORK, RWORK( NRHS+1 ), WORK, IWORK, $ INFO ) * * Check the error code from DPOSVX. * IF( INFO.NE.IZERO ) THEN CALL ALAERH( PATH, 'DPOSVX', 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 DPOT01( UPLO, N, A, LDA, AFAC, LDA, $ 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 DPOT02( UPLO, N, NRHS, ASAV, LDA, 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 DPOT05( UPLO, N, NRHS, ASAV, LDA, B, LDA, $ X, LDA, XACT, LDA, RWORK, $ RWORK( NRHS+1 ), RESULT( 4 ) ) ELSE K1 = 6 END IF * * Compare RCOND from DPOSVX 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 )'DPOSVX', FACT, $ UPLO, N, EQUED, IMAT, K, RESULT( K ) ELSE WRITE( NOUT, FMT = 9998 )'DPOSVX', 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 * * 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 DDRVPO * END |