numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
| Name | Size | Mode | |
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| lapack/TESTING/LIN/zchktb.f | 19586B | -rw-r--r-- |
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*> \brief \b ZCHKTB * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE ZCHKTB( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, * NMAX, AB, AINV, B, X, XACT, WORK, RWORK, NOUT ) * * .. Scalar Arguments .. * LOGICAL TSTERR * INTEGER NMAX, NN, NNS, NOUT * DOUBLE PRECISION THRESH * .. * .. Array Arguments .. * LOGICAL DOTYPE( * ) * INTEGER NSVAL( * ), NVAL( * ) * DOUBLE PRECISION RWORK( * ) * COMPLEX*16 AB( * ), AINV( * ), B( * ), WORK( * ), X( * ), * $ XACT( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZCHKTB tests ZTBTRS, -RFS, and -CON, and ZLATBS. *> \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 column dimension N. *> \endverbatim *> *> \param[in] NNS *> \verbatim *> NNS is INTEGER *> The number of values of NRHS contained in the vector NSVAL. *> \endverbatim *> *> \param[in] NSVAL *> \verbatim *> NSVAL is INTEGER array, dimension (NNS) *> The values of the number of right hand sides NRHS. *> \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 leading dimension of the work arrays. *> NMAX >= the maximum value of N in NVAL. *> \endverbatim *> *> \param[out] AB *> \verbatim *> AB is COMPLEX*16 array, dimension (NMAX*NMAX) *> \endverbatim *> *> \param[out] AINV *> \verbatim *> AINV is COMPLEX*16 array, dimension (NMAX*NMAX) *> \endverbatim *> *> \param[out] B *> \verbatim *> B is COMPLEX*16 array, dimension (NMAX*NSMAX) *> where NSMAX is the largest entry in NSVAL. *> \endverbatim *> *> \param[out] X *> \verbatim *> X is COMPLEX*16 array, dimension (NMAX*NSMAX) *> \endverbatim *> *> \param[out] XACT *> \verbatim *> XACT is COMPLEX*16 array, dimension (NMAX*NSMAX) *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension *> (NMAX*max(3,NSMAX)) *> \endverbatim *> *> \param[out] RWORK *> \verbatim *> RWORK is DOUBLE PRECISION array, dimension *> (max(NMAX,2*NSMAX)) *> \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 ZCHKTB( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, $ NMAX, AB, AINV, B, X, XACT, 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, NNS, NOUT DOUBLE PRECISION THRESH * .. * .. Array Arguments .. LOGICAL DOTYPE( * ) INTEGER NSVAL( * ), NVAL( * ) DOUBLE PRECISION RWORK( * ) COMPLEX*16 AB( * ), AINV( * ), B( * ), WORK( * ), X( * ), $ XACT( * ) * .. * * ===================================================================== * * .. Parameters .. INTEGER NTYPE1, NTYPES PARAMETER ( NTYPE1 = 9, NTYPES = 17 ) INTEGER NTESTS PARAMETER ( NTESTS = 8 ) INTEGER NTRAN PARAMETER ( NTRAN = 3 ) DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+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 DOUBLE PRECISION AINVNM, ANORM, 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 ZLANTB, ZLANTR EXTERNAL LSAME, ZLANTB, ZLANTR * .. * .. External Subroutines .. EXTERNAL ALAERH, ALAHD, ALASUM, ZCOPY, ZERRTR, ZGET04, $ ZLACPY, ZLARHS, ZLASET, ZLATBS, ZLATTB, ZTBCON, $ ZTBRFS, ZTBSV, ZTBT02, ZTBT03, ZTBT05, ZTBT06, $ ZTBTRS * .. * .. 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 DCMPLX, 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 ) = 'Zomplex 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 ZERRTR( 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 ZLATTB to generate a triangular test matrix. * SRNAMT = 'ZLATTB' CALL ZLATTB( IMAT, UPLO, 'No transpose', DIAG, ISEED, $ N, KD, AB, LDAB, X, WORK, RWORK, 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 ZLASET( 'Full', N, N, DCMPLX( ZERO ), $ DCMPLX( ONE ), AINV, LDA ) IF( LSAME( UPLO, 'U' ) ) THEN DO 20 J = 1, N CALL ZTBSV( UPLO, 'No transpose', DIAG, J, KD, $ AB, LDAB, AINV( ( J-1 )*LDA+1 ), 1 ) 20 CONTINUE ELSE DO 30 J = 1, N CALL ZTBSV( 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 = ZLANTB( '1', UPLO, DIAG, N, KD, AB, LDAB, $ RWORK ) AINVNM = ZLANTR( '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 = ZLANTB( 'I', UPLO, DIAG, N, KD, AB, LDAB, $ RWORK ) AINVNM = ZLANTR( '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 = 'ZLARHS' CALL ZLARHS( PATH, XTYPE, UPLO, TRANS, N, N, KD, $ IDIAG, NRHS, AB, LDAB, XACT, LDA, $ B, LDA, ISEED, INFO ) XTYPE = 'C' CALL ZLACPY( 'Full', N, NRHS, B, LDA, X, LDA ) * SRNAMT = 'ZTBTRS' CALL ZTBTRS( UPLO, TRANS, DIAG, N, KD, NRHS, AB, $ LDAB, X, LDA, INFO ) * * Check error code from ZTBTRS. * IF( INFO.NE.0 ) $ CALL ALAERH( PATH, 'ZTBTRS', INFO, 0, $ UPLO // TRANS // DIAG, N, N, KD, $ KD, NRHS, IMAT, NFAIL, NERRS, $ NOUT ) * CALL ZTBT02( UPLO, TRANS, DIAG, N, KD, NRHS, AB, $ LDAB, X, LDA, B, LDA, WORK, RWORK, $ RESULT( 1 ) ) * *+ TEST 2 * Check solution from generated exact solution. * CALL ZGET04( 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 = 'ZTBRFS' CALL ZTBRFS( UPLO, TRANS, DIAG, N, KD, NRHS, AB, $ LDAB, B, LDA, X, LDA, RWORK, $ RWORK( NRHS+1 ), WORK, $ RWORK( 2*NRHS+1 ), INFO ) * * Check error code from ZTBRFS. * IF( INFO.NE.0 ) $ CALL ALAERH( PATH, 'ZTBRFS', INFO, 0, $ UPLO // TRANS // DIAG, N, N, KD, $ KD, NRHS, IMAT, NFAIL, NERRS, $ NOUT ) * CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC, $ RESULT( 3 ) ) CALL ZTBT05( 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 = 'ZTBCON' CALL ZTBCON( NORM, UPLO, DIAG, N, KD, AB, LDAB, $ RCOND, WORK, RWORK, INFO ) * * Check error code from ZTBCON. * IF( INFO.NE.0 ) $ CALL ALAERH( PATH, 'ZTBCON', INFO, 0, $ NORM // UPLO // DIAG, N, N, KD, KD, $ -1, IMAT, NFAIL, NERRS, NOUT ) * CALL ZTBT06( RCOND, RCONDC, UPLO, DIAG, N, KD, AB, $ LDAB, RWORK, RESULT( 6 ) ) * * Print the test ratio if it is .GE. THRESH. * IF( RESULT( 6 ).GE.THRESH ) THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) $ CALL ALAHD( NOUT, PATH ) WRITE( NOUT, FMT = 9998 ) 'ZTBCON', 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 ZLATBS. * 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 ZLATTB to generate a triangular test matrix. * SRNAMT = 'ZLATTB' CALL ZLATTB( IMAT, UPLO, TRANS, DIAG, ISEED, N, KD, $ AB, LDAB, X, WORK, RWORK, INFO ) * *+ TEST 7 * Solve the system op(A)*x = b * SRNAMT = 'ZLATBS' CALL ZCOPY( N, X, 1, B, 1 ) CALL ZLATBS( UPLO, TRANS, DIAG, 'N', N, KD, AB, $ LDAB, B, SCALE, RWORK, INFO ) * * Check error code from ZLATBS. * IF( INFO.NE.0 ) $ CALL ALAERH( PATH, 'ZLATBS', INFO, 0, $ UPLO // TRANS // DIAG // 'N', N, N, $ KD, KD, -1, IMAT, NFAIL, NERRS, $ NOUT ) * CALL ZTBT03( 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 ZCOPY( N, X, 1, B, 1 ) CALL ZLATBS( UPLO, TRANS, DIAG, 'Y', N, KD, AB, $ LDAB, B, SCALE, RWORK, INFO ) * * Check error code from ZLATBS. * IF( INFO.NE.0 ) $ CALL ALAERH( PATH, 'ZLATBS', INFO, 0, $ UPLO // TRANS // DIAG // 'Y', N, N, $ KD, KD, -1, IMAT, NFAIL, NERRS, $ NOUT ) * CALL ZTBT03( 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 )'ZLATBS', 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 )'ZLATBS', 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 ZCHKTB * END