SUBROUTINE DCHKTR( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL, \$ THRESH, TSTERR, NMAX, A, AINV, B, X, XACT, \$ 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, NNB, NNS, NOUT DOUBLE PRECISION THRESH * .. * .. Array Arguments .. LOGICAL DOTYPE( * ) INTEGER IWORK( * ), NBVAL( * ), NSVAL( * ), NVAL( * ) DOUBLE PRECISION A( * ), AINV( * ), B( * ), RWORK( * ), \$ WORK( * ), X( * ), XACT( * ) * .. * * Purpose * ======= * * DCHKTR tests DTRTRI, -TRS, -RFS, and -CON, and DLATRS * * 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 column dimension N. * * NNB (input) INTEGER * The number of values of NB contained in the vector NBVAL. * * NBVAL (input) INTEGER array, dimension (NNB) * The values of the blocksize NB. * * NNS (input) INTEGER * The number of values of NRHS contained in the vector NSVAL. * * NSVAL (input) INTEGER array, dimension (NNS) * The values of the number of right hand sides NRHS. * * 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 leading dimension of the work arrays. * NMAX >= the maximum value of N in NVAL. * * A (workspace) DOUBLE PRECISION array, dimension (NMAX*NMAX) * * AINV (workspace) DOUBLE PRECISION array, dimension (NMAX*NMAX) * * B (workspace) DOUBLE PRECISION array, dimension (NMAX*NSMAX) * where NSMAX is the largest entry in NSVAL. * * X (workspace) DOUBLE PRECISION array, dimension (NMAX*NSMAX) * * XACT (workspace) DOUBLE PRECISION array, dimension (NMAX*NSMAX) * * WORK (workspace) DOUBLE PRECISION array, dimension * (NMAX*max(3,NSMAX)) * * RWORK (workspace) DOUBLE PRECISION array, dimension * (max(NMAX,2*NSMAX)) * * IWORK (workspace) INTEGER array, dimension (NMAX) * * NOUT (input) INTEGER * The unit number for output. * * ===================================================================== * * .. Parameters .. INTEGER NTYPE1, NTYPES PARAMETER ( NTYPE1 = 10, NTYPES = 18 ) INTEGER NTESTS PARAMETER ( NTESTS = 9 ) INTEGER NTRAN PARAMETER ( NTRAN = 3 ) DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D0, ZERO = 0.0D0 ) * .. * .. Local Scalars .. CHARACTER DIAG, NORM, TRANS, UPLO, XTYPE CHARACTER*3 PATH INTEGER I, IDIAG, IMAT, IN, INB, INFO, IRHS, ITRAN, \$ IUPLO, K, LDA, N, NB, NERRS, NFAIL, NRHS, NRUN DOUBLE PRECISION AINVNM, ANORM, DUMMY, RCOND, RCONDC, RCONDI, \$ RCONDO, SCALE * .. * .. Local Arrays .. CHARACTER TRANSS( NTRAN ), UPLOS( 2 ) INTEGER ISEED( 4 ), ISEEDY( 4 ) DOUBLE PRECISION RESULT( NTESTS ) * .. * .. External Functions .. LOGICAL LSAME DOUBLE PRECISION DLANTR EXTERNAL LSAME, DLANTR * .. * .. External Subroutines .. EXTERNAL ALAERH, ALAHD, ALASUM, DCOPY, DERRTR, DGET04, \$ DLACPY, DLARHS, DLATRS, DLATTR, DTRCON, DTRRFS, \$ DTRT01, DTRT02, DTRT03, DTRT05, DTRT06, DTRTRI, \$ DTRTRS, XLAENV * .. * .. Scalars in Common .. LOGICAL LERR, OK CHARACTER*32 SRNAMT INTEGER INFOT, IOUNIT * .. * .. Common blocks .. COMMON / INFOC / INFOT, IOUNIT, OK, LERR COMMON / SRNAMC / SRNAMT * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Data statements .. DATA ISEEDY / 1988, 1989, 1990, 1991 / DATA UPLOS / 'U', 'L' / , TRANSS / 'N', 'T', 'C' / * .. * .. Executable Statements .. * * Initialize constants and the random number seed. * PATH( 1: 1 ) = 'Double precision' PATH( 2: 3 ) = 'TR' NRUN = 0 NFAIL = 0 NERRS = 0 DO 10 I = 1, 4 ISEED( I ) = ISEEDY( I ) 10 CONTINUE * * Test the error exits * IF( TSTERR ) \$ CALL DERRTR( PATH, NOUT ) INFOT = 0 CALL XLAENV( 2, 2 ) * DO 120 IN = 1, NN * * Do for each value of N in NVAL * N = NVAL( IN ) LDA = MAX( 1, N ) XTYPE = 'N' * DO 80 IMAT = 1, NTYPE1 * * Do the tests only if DOTYPE( IMAT ) is true. * IF( .NOT.DOTYPE( IMAT ) ) \$ GO TO 80 * DO 70 IUPLO = 1, 2 * * Do first for UPLO = 'U', then for UPLO = 'L' * UPLO = UPLOS( IUPLO ) * * Call DLATTR to generate a triangular test matrix. * SRNAMT = 'DLATTR' CALL DLATTR( IMAT, UPLO, 'No transpose', DIAG, ISEED, N, \$ A, LDA, X, WORK, INFO ) * * Set IDIAG = 1 for non-unit matrices, 2 for unit. * IF( LSAME( DIAG, 'N' ) ) THEN IDIAG = 1 ELSE IDIAG = 2 END IF * DO 60 INB = 1, NNB * * Do for each blocksize in NBVAL * NB = NBVAL( INB ) CALL XLAENV( 1, NB ) * *+ TEST 1 * Form the inverse of A. * CALL DLACPY( UPLO, N, N, A, LDA, AINV, LDA ) SRNAMT = 'DTRTRI' CALL DTRTRI( UPLO, DIAG, N, AINV, LDA, INFO ) * * Check error code from DTRTRI. * IF( INFO.NE.0 ) \$ CALL ALAERH( PATH, 'DTRTRI', INFO, 0, UPLO // DIAG, \$ N, N, -1, -1, NB, IMAT, NFAIL, NERRS, \$ NOUT ) * * Compute the infinity-norm condition number of A. * ANORM = DLANTR( 'I', UPLO, DIAG, N, N, A, LDA, RWORK ) AINVNM = DLANTR( 'I', UPLO, DIAG, N, N, AINV, LDA, \$ RWORK ) IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN RCONDI = ONE ELSE RCONDI = ( ONE / ANORM ) / AINVNM END IF * * Compute the residual for the triangular matrix times * its inverse. Also compute the 1-norm condition number * of A. * CALL DTRT01( UPLO, DIAG, N, A, LDA, AINV, LDA, RCONDO, \$ RWORK, RESULT( 1 ) ) * * Print the test ratio if it is .GE. THRESH. * IF( RESULT( 1 ).GE.THRESH ) THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) \$ CALL ALAHD( NOUT, PATH ) WRITE( NOUT, FMT = 9999 )UPLO, DIAG, N, NB, IMAT, \$ 1, RESULT( 1 ) NFAIL = NFAIL + 1 END IF NRUN = NRUN + 1 * * Skip remaining tests if not the first block size. * IF( INB.NE.1 ) \$ GO TO 60 * DO 40 IRHS = 1, NNS NRHS = NSVAL( IRHS ) XTYPE = 'N' * DO 30 ITRAN = 1, NTRAN * * Do for op(A) = A, A**T, or A**H. * TRANS = TRANSS( ITRAN ) IF( ITRAN.EQ.1 ) THEN NORM = 'O' RCONDC = RCONDO ELSE NORM = 'I' RCONDC = RCONDI END IF * *+ TEST 2 * Solve and compute residual for op(A)*x = b. * SRNAMT = 'DLARHS' CALL DLARHS( PATH, XTYPE, UPLO, TRANS, N, N, 0, \$ IDIAG, NRHS, A, LDA, XACT, LDA, B, \$ LDA, ISEED, INFO ) XTYPE = 'C' CALL DLACPY( 'Full', N, NRHS, B, LDA, X, LDA ) * SRNAMT = 'DTRTRS' CALL DTRTRS( UPLO, TRANS, DIAG, N, NRHS, A, LDA, \$ X, LDA, INFO ) * * Check error code from DTRTRS. * IF( INFO.NE.0 ) \$ CALL ALAERH( PATH, 'DTRTRS', INFO, 0, \$ UPLO // TRANS // DIAG, N, N, -1, \$ -1, NRHS, IMAT, NFAIL, NERRS, \$ NOUT ) * * This line is needed on a Sun SPARCstation. * IF( N.GT.0 ) \$ DUMMY = A( 1 ) * CALL DTRT02( UPLO, TRANS, DIAG, N, NRHS, A, LDA, \$ X, LDA, B, LDA, WORK, RESULT( 2 ) ) * *+ TEST 3 * Check solution from generated exact solution. * CALL DGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC, \$ RESULT( 3 ) ) * *+ TESTS 4, 5, and 6 * Use iterative refinement to improve the solution * and compute error bounds. * SRNAMT = 'DTRRFS' CALL DTRRFS( UPLO, TRANS, DIAG, N, NRHS, A, LDA, \$ B, LDA, X, LDA, RWORK, \$ RWORK( NRHS+1 ), WORK, IWORK, \$ INFO ) * * Check error code from DTRRFS. * IF( INFO.NE.0 ) \$ CALL ALAERH( PATH, 'DTRRFS', INFO, 0, \$ UPLO // TRANS // DIAG, N, N, -1, \$ -1, NRHS, IMAT, NFAIL, NERRS, \$ NOUT ) * CALL DGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC, \$ RESULT( 4 ) ) CALL DTRT05( UPLO, TRANS, DIAG, N, NRHS, A, LDA, \$ B, LDA, X, LDA, XACT, LDA, RWORK, \$ RWORK( NRHS+1 ), RESULT( 5 ) ) * * Print information about the tests that did not * pass the threshold. * DO 20 K = 2, 6 IF( RESULT( K ).GE.THRESH ) THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) \$ CALL ALAHD( NOUT, PATH ) WRITE( NOUT, FMT = 9998 )UPLO, TRANS, \$ DIAG, N, NRHS, IMAT, K, RESULT( K ) NFAIL = NFAIL + 1 END IF 20 CONTINUE NRUN = NRUN + 5 30 CONTINUE 40 CONTINUE * *+ TEST 7 * Get an estimate of RCOND = 1/CNDNUM. * DO 50 ITRAN = 1, 2 IF( ITRAN.EQ.1 ) THEN NORM = 'O' RCONDC = RCONDO ELSE NORM = 'I' RCONDC = RCONDI END IF SRNAMT = 'DTRCON' CALL DTRCON( NORM, UPLO, DIAG, N, A, LDA, RCOND, \$ WORK, IWORK, INFO ) * * Check error code from DTRCON. * IF( INFO.NE.0 ) \$ CALL ALAERH( PATH, 'DTRCON', INFO, 0, \$ NORM // UPLO // DIAG, N, N, -1, -1, \$ -1, IMAT, NFAIL, NERRS, NOUT ) * CALL DTRT06( RCOND, RCONDC, UPLO, DIAG, N, A, LDA, \$ RWORK, RESULT( 7 ) ) * * Print the test ratio if it is .GE. THRESH. * IF( RESULT( 7 ).GE.THRESH ) THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) \$ CALL ALAHD( NOUT, PATH ) WRITE( NOUT, FMT = 9997 )NORM, UPLO, N, IMAT, \$ 7, RESULT( 7 ) NFAIL = NFAIL + 1 END IF NRUN = NRUN + 1 50 CONTINUE 60 CONTINUE 70 CONTINUE 80 CONTINUE * * Use pathological test matrices to test DLATRS. * DO 110 IMAT = NTYPE1 + 1, NTYPES * * Do the tests only if DOTYPE( IMAT ) is true. * IF( .NOT.DOTYPE( IMAT ) ) \$ GO TO 110 * DO 100 IUPLO = 1, 2 * * Do first for UPLO = 'U', then for UPLO = 'L' * UPLO = UPLOS( IUPLO ) DO 90 ITRAN = 1, NTRAN * * Do for op(A) = A, A**T, and A**H. * TRANS = TRANSS( ITRAN ) * * Call DLATTR to generate a triangular test matrix. * SRNAMT = 'DLATTR' CALL DLATTR( IMAT, UPLO, TRANS, DIAG, ISEED, N, A, \$ LDA, X, WORK, INFO ) * *+ TEST 8 * Solve the system op(A)*x = b. * SRNAMT = 'DLATRS' CALL DCOPY( N, X, 1, B, 1 ) CALL DLATRS( UPLO, TRANS, DIAG, 'N', N, A, LDA, B, \$ SCALE, RWORK, INFO ) * * Check error code from DLATRS. * IF( INFO.NE.0 ) \$ CALL ALAERH( PATH, 'DLATRS', INFO, 0, \$ UPLO // TRANS // DIAG // 'N', N, N, \$ -1, -1, -1, IMAT, NFAIL, NERRS, NOUT ) * CALL DTRT03( UPLO, TRANS, DIAG, N, 1, A, LDA, SCALE, \$ RWORK, ONE, B, LDA, X, LDA, WORK, \$ RESULT( 8 ) ) * *+ TEST 9 * Solve op(A)*X = b again with NORMIN = 'Y'. * CALL DCOPY( N, X, 1, B( N+1 ), 1 ) CALL DLATRS( UPLO, TRANS, DIAG, 'Y', N, A, LDA, \$ B( N+1 ), SCALE, RWORK, INFO ) * * Check error code from DLATRS. * IF( INFO.NE.0 ) \$ CALL ALAERH( PATH, 'DLATRS', INFO, 0, \$ UPLO // TRANS // DIAG // 'Y', N, N, \$ -1, -1, -1, IMAT, NFAIL, NERRS, NOUT ) * CALL DTRT03( UPLO, TRANS, DIAG, N, 1, A, LDA, SCALE, \$ RWORK, ONE, B( N+1 ), LDA, X, LDA, WORK, \$ RESULT( 9 ) ) * * Print information about the tests that did not pass * the threshold. * IF( RESULT( 8 ).GE.THRESH ) THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) \$ CALL ALAHD( NOUT, PATH ) WRITE( NOUT, FMT = 9996 )'DLATRS', UPLO, TRANS, \$ DIAG, 'N', N, IMAT, 8, RESULT( 8 ) NFAIL = NFAIL + 1 END IF IF( RESULT( 9 ).GE.THRESH ) THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) \$ CALL ALAHD( NOUT, PATH ) WRITE( NOUT, FMT = 9996 )'DLATRS', UPLO, TRANS, \$ DIAG, 'Y', N, IMAT, 9, RESULT( 9 ) NFAIL = NFAIL + 1 END IF NRUN = NRUN + 2 90 CONTINUE 100 CONTINUE 110 CONTINUE 120 CONTINUE * * Print a summary of the results. * CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS ) * 9999 FORMAT( ' UPLO=''', A1, ''', DIAG=''', A1, ''', N=', I5, ', NB=', \$ I4, ', type ', I2, ', test(', I2, ')= ', G12.5 ) 9998 FORMAT( ' UPLO=''', A1, ''', TRANS=''', A1, ''', DIAG=''', A1, \$ ''', N=', I5, ', NB=', I4, ', type ', I2, ', \$ test(', I2, ')= ', G12.5 ) 9997 FORMAT( ' NORM=''', A1, ''', UPLO =''', A1, ''', N=', I5, ',', \$ 11X, ' type ', I2, ', test(', I2, ')=', G12.5 ) 9996 FORMAT( 1X, A, '( ''', A1, ''', ''', A1, ''', ''', A1, ''', ''', \$ A1, ''',', I5, ', ... ), type ', I2, ', test(', I2, ')=', \$ G12.5 ) RETURN * * End of DCHKTR * END