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SUBROUTINE SCHKTB( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
$ NMAX, AB, 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, NNS, NOUT REAL THRESH * .. * .. Array Arguments .. LOGICAL DOTYPE( * ) INTEGER IWORK( * ), NSVAL( * ), NVAL( * ) REAL AB( * ), AINV( * ), B( * ), RWORK( * ), $ WORK( * ), X( * ), XACT( * ) * .. * * Purpose * ======= * * SCHKTB tests STBTRS, -RFS, and -CON, and SLATBS. * * 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. * * 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) 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. * * 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. * * AB (workspace) REAL array, dimension (NMAX*NMAX) * * AINV (workspace) REAL array, dimension (NMAX*NMAX) * * B (workspace) REAL array, dimension (NMAX*NSMAX) * where NSMAX is the largest entry in NSVAL. * * X (workspace) REAL array, dimension (NMAX*NSMAX) * * XACT (workspace) REAL array, dimension (NMAX*NSMAX) * * WORK (workspace) REAL array, dimension * (NMAX*max(3,NSMAX)) * * RWORK (workspace) REAL 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 = 9, NTYPES = 17 ) INTEGER NTESTS PARAMETER ( NTESTS = 8 ) INTEGER NTRAN PARAMETER ( NTRAN = 3 ) REAL ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) * .. * .. Local Scalars .. CHARACTER DIAG, NORM, TRANS, UPLO, XTYPE CHARACTER*3 PATH INTEGER I, IDIAG, IK, IMAT, IN, INFO, IRHS, ITRAN, $ IUPLO, J, K, KD, LDA, LDAB, N, NERRS, NFAIL, $ NIMAT, NIMAT2, NK, NRHS, NRUN REAL AINVNM, ANORM, RCOND, RCONDC, RCONDI, RCONDO, $ SCALE * .. * .. Local Arrays .. CHARACTER TRANSS( NTRAN ), UPLOS( 2 ) INTEGER ISEED( 4 ), ISEEDY( 4 ) REAL RESULT( NTESTS ) * .. * .. External Functions .. LOGICAL LSAME REAL SLANTB, SLANTR EXTERNAL LSAME, SLANTB, SLANTR * .. * .. External Subroutines .. EXTERNAL ALAERH, ALAHD, ALASUM, SCOPY, SERRTR, SGET04, $ SLACPY, SLARHS, SLASET, SLATBS, SLATTB, STBCON, $ STBRFS, STBSV, STBT02, STBT03, STBT05, STBT06, $ STBTRS * .. * .. 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, MIN * .. * .. 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 ) = 'Single precision' PATH( 2: 3 ) = 'TB' NRUN = 0 NFAIL = 0 NERRS = 0 DO 10 I = 1, 4 ISEED( I ) = ISEEDY( I ) 10 CONTINUE * * Test the error exits * IF( TSTERR ) $ CALL SERRTR( PATH, NOUT ) INFOT = 0 * DO 140 IN = 1, NN * * Do for each value of N in NVAL * N = NVAL( IN ) LDA = MAX( 1, N ) XTYPE = 'N' NIMAT = NTYPE1 NIMAT2 = NTYPES IF( N.LE.0 ) THEN NIMAT = 1 NIMAT2 = NTYPE1 + 1 END IF * NK = MIN( N+1, 4 ) DO 130 IK = 1, NK * * Do for KD = 0, N, (3N-1)/4, and (N+1)/4. This order makes * it easier to skip redundant values for small values of N. * IF( IK.EQ.1 ) THEN KD = 0 ELSE IF( IK.EQ.2 ) THEN KD = MAX( N, 0 ) ELSE IF( IK.EQ.3 ) THEN KD = ( 3*N-1 ) / 4 ELSE IF( IK.EQ.4 ) THEN KD = ( N+1 ) / 4 END IF LDAB = KD + 1 * DO 90 IMAT = 1, NIMAT * * Do the tests only if DOTYPE( IMAT ) is true. * IF( .NOT.DOTYPE( IMAT ) ) $ GO TO 90 * DO 80 IUPLO = 1, 2 * * Do first for UPLO = 'U', then for UPLO = 'L' * UPLO = UPLOS( IUPLO ) * * Call SLATTB to generate a triangular test matrix. * SRNAMT = 'SLATTB' CALL SLATTB( IMAT, UPLO, 'No transpose', DIAG, ISEED, $ N, KD, AB, LDAB, 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 * * Form the inverse of A so we can get a good estimate * of RCONDC = 1/(norm(A) * norm(inv(A))). * CALL SLASET( 'Full', N, N, ZERO, ONE, AINV, LDA ) IF( LSAME( UPLO, 'U' ) ) THEN DO 20 J = 1, N CALL STBSV( UPLO, 'No transpose', DIAG, J, KD, $ AB, LDAB, AINV( ( J-1 )*LDA+1 ), 1 ) 20 CONTINUE ELSE DO 30 J = 1, N CALL STBSV( UPLO, 'No transpose', DIAG, N-J+1, $ KD, AB( ( J-1 )*LDAB+1 ), LDAB, $ AINV( ( J-1 )*LDA+J ), 1 ) 30 CONTINUE END IF * * Compute the 1-norm condition number of A. * ANORM = SLANTB( '1', UPLO, DIAG, N, KD, AB, LDAB, $ RWORK ) AINVNM = SLANTR( '1', UPLO, DIAG, N, N, AINV, LDA, $ RWORK ) IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN RCONDO = ONE ELSE RCONDO = ( ONE / ANORM ) / AINVNM END IF * * Compute the infinity-norm condition number of A. * ANORM = SLANTB( 'I', UPLO, DIAG, N, KD, AB, LDAB, $ RWORK ) AINVNM = SLANTR( '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 * DO 60 IRHS = 1, NNS NRHS = NSVAL( IRHS ) XTYPE = 'N' * DO 50 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 1 * Solve and compute residual for op(A)*x = b. * SRNAMT = 'SLARHS' CALL SLARHS( PATH, XTYPE, UPLO, TRANS, N, N, KD, $ IDIAG, NRHS, AB, LDAB, XACT, LDA, $ B, LDA, ISEED, INFO ) XTYPE = 'C' CALL SLACPY( 'Full', N, NRHS, B, LDA, X, LDA ) * SRNAMT = 'STBTRS' CALL STBTRS( UPLO, TRANS, DIAG, N, KD, NRHS, AB, $ LDAB, X, LDA, INFO ) * * Check error code from STBTRS. * IF( INFO.NE.0 ) $ CALL ALAERH( PATH, 'STBTRS', INFO, 0, $ UPLO // TRANS // DIAG, N, N, KD, $ KD, NRHS, IMAT, NFAIL, NERRS, $ NOUT ) * CALL STBT02( UPLO, TRANS, DIAG, N, KD, NRHS, AB, $ LDAB, X, LDA, B, LDA, WORK, $ RESULT( 1 ) ) * *+ TEST 2 * Check solution from generated exact solution. * CALL SGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC, $ RESULT( 2 ) ) * *+ TESTS 3, 4, and 5 * Use iterative refinement to improve the solution * and compute error bounds. * SRNAMT = 'STBRFS' CALL STBRFS( UPLO, TRANS, DIAG, N, KD, NRHS, AB, $ LDAB, B, LDA, X, LDA, RWORK, $ RWORK( NRHS+1 ), WORK, IWORK, $ INFO ) * * Check error code from STBRFS. * IF( INFO.NE.0 ) $ CALL ALAERH( PATH, 'STBRFS', INFO, 0, $ UPLO // TRANS // DIAG, N, N, KD, $ KD, NRHS, IMAT, NFAIL, NERRS, $ NOUT ) * CALL SGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC, $ RESULT( 3 ) ) CALL STBT05( UPLO, TRANS, DIAG, N, KD, NRHS, AB, $ LDAB, B, LDA, X, LDA, XACT, LDA, $ RWORK, RWORK( NRHS+1 ), $ RESULT( 4 ) ) * * Print information about the tests that did not * pass the threshold. * DO 40 K = 1, 5 IF( RESULT( K ).GE.THRESH ) THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) $ CALL ALAHD( NOUT, PATH ) WRITE( NOUT, FMT = 9999 )UPLO, TRANS, $ DIAG, N, KD, NRHS, IMAT, K, RESULT( K ) NFAIL = NFAIL + 1 END IF 40 CONTINUE NRUN = NRUN + 5 50 CONTINUE 60 CONTINUE * *+ TEST 6 * Get an estimate of RCOND = 1/CNDNUM. * DO 70 ITRAN = 1, 2 IF( ITRAN.EQ.1 ) THEN NORM = 'O' RCONDC = RCONDO ELSE NORM = 'I' RCONDC = RCONDI END IF SRNAMT = 'STBCON' CALL STBCON( NORM, UPLO, DIAG, N, KD, AB, LDAB, $ RCOND, WORK, IWORK, INFO ) * * Check error code from STBCON. * IF( INFO.NE.0 ) $ CALL ALAERH( PATH, 'STBCON', INFO, 0, $ NORM // UPLO // DIAG, N, N, KD, KD, $ -1, IMAT, NFAIL, NERRS, NOUT ) * CALL STBT06( RCOND, RCONDC, UPLO, DIAG, N, KD, AB, $ LDAB, RWORK, RESULT( 6 ) ) * * Print information about the tests that did not pass * the threshold. * IF( RESULT( 6 ).GE.THRESH ) THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) $ CALL ALAHD( NOUT, PATH ) WRITE( NOUT, FMT = 9998 ) 'STBCON', NORM, UPLO, $ DIAG, N, KD, IMAT, 6, RESULT( 6 ) NFAIL = NFAIL + 1 END IF NRUN = NRUN + 1 70 CONTINUE 80 CONTINUE 90 CONTINUE * * Use pathological test matrices to test SLATBS. * DO 120 IMAT = NTYPE1 + 1, NIMAT2 * * Do the tests only if DOTYPE( IMAT ) is true. * IF( .NOT.DOTYPE( IMAT ) ) $ GO TO 120 * DO 110 IUPLO = 1, 2 * * Do first for UPLO = 'U', then for UPLO = 'L' * UPLO = UPLOS( IUPLO ) DO 100 ITRAN = 1, NTRAN * * Do for op(A) = A, A**T, and A**H. * TRANS = TRANSS( ITRAN ) * * Call SLATTB to generate a triangular test matrix. * SRNAMT = 'SLATTB' CALL SLATTB( IMAT, UPLO, TRANS, DIAG, ISEED, N, KD, $ AB, LDAB, X, WORK, INFO ) * *+ TEST 7 * Solve the system op(A)*x = b * SRNAMT = 'SLATBS' CALL SCOPY( N, X, 1, B, 1 ) CALL SLATBS( UPLO, TRANS, DIAG, 'N', N, KD, AB, $ LDAB, B, SCALE, RWORK, INFO ) * * Check error code from SLATBS. * IF( INFO.NE.0 ) $ CALL ALAERH( PATH, 'SLATBS', INFO, 0, $ UPLO // TRANS // DIAG // 'N', N, N, $ KD, KD, -1, IMAT, NFAIL, NERRS, $ NOUT ) * CALL STBT03( UPLO, TRANS, DIAG, N, KD, 1, AB, LDAB, $ SCALE, RWORK, ONE, B, LDA, X, LDA, $ WORK, RESULT( 7 ) ) * *+ TEST 8 * Solve op(A)*x = b again with NORMIN = 'Y'. * CALL SCOPY( N, X, 1, B, 1 ) CALL SLATBS( UPLO, TRANS, DIAG, 'Y', N, KD, AB, $ LDAB, B, SCALE, RWORK, INFO ) * * Check error code from SLATBS. * IF( INFO.NE.0 ) $ CALL ALAERH( PATH, 'SLATBS', INFO, 0, $ UPLO // TRANS // DIAG // 'Y', N, N, $ KD, KD, -1, IMAT, NFAIL, NERRS, $ NOUT ) * CALL STBT03( UPLO, TRANS, DIAG, N, KD, 1, AB, LDAB, $ SCALE, RWORK, ONE, B, LDA, X, LDA, $ WORK, RESULT( 8 ) ) * * Print information about the tests that did not pass * the threshold. * IF( RESULT( 7 ).GE.THRESH ) THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) $ CALL ALAHD( NOUT, PATH ) WRITE( NOUT, FMT = 9997 )'SLATBS', UPLO, TRANS, $ DIAG, 'N', N, KD, IMAT, 7, RESULT( 7 ) NFAIL = NFAIL + 1 END IF IF( RESULT( 8 ).GE.THRESH ) THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) $ CALL ALAHD( NOUT, PATH ) WRITE( NOUT, FMT = 9997 )'SLATBS', UPLO, TRANS, $ DIAG, 'Y', N, KD, IMAT, 8, RESULT( 8 ) NFAIL = NFAIL + 1 END IF NRUN = NRUN + 2 100 CONTINUE 110 CONTINUE 120 CONTINUE 130 CONTINUE 140 CONTINUE * * Print a summary of the results. * CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS ) * 9999 FORMAT( ' UPLO=''', A1, ''', TRANS=''', A1, ''', $ DIAG=''', A1, ''', N=', I5, ', KD=', I5, ', NRHS=', I5, $ ', type ', I2, ', test(', I2, ')=', G12.5 ) 9998 FORMAT( 1X, A, '( ''', A1, ''', ''', A1, ''', ''', A1, ''',', $ I5, ',', I5, ', ... ), type ', I2, ', test(', I2, ')=', $ G12.5 ) 9997 FORMAT( 1X, A, '( ''', A1, ''', ''', A1, ''', ''', A1, ''', ''', $ A1, ''',', I5, ',', I5, ', ... ), type ', I2, ', test(', $ I1, ')=', G12.5 ) RETURN * * End of SCHKTB * END |