numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
| Name | Size | Mode | |
| .. | |||
| lapack/TESTING/LIN/schkgb.f | 25309B | -rw-r--r-- |
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*> \brief \b SCHKGB * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE SCHKGB( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NNS, * NSVAL, THRESH, TSTERR, A, LA, AFAC, LAFAC, B, * X, XACT, WORK, RWORK, IWORK, NOUT ) * * .. Scalar Arguments .. * LOGICAL TSTERR * INTEGER LA, LAFAC, NM, NN, NNB, NNS, NOUT * REAL THRESH * .. * .. Array Arguments .. * LOGICAL DOTYPE( * ) * INTEGER IWORK( * ), MVAL( * ), NBVAL( * ), NSVAL( * ), * $ NVAL( * ) * REAL A( * ), AFAC( * ), B( * ), RWORK( * ), * $ WORK( * ), X( * ), XACT( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> SCHKGB tests SGBTRF, -TRS, -RFS, and -CON *> \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] NM *> \verbatim *> NM is INTEGER *> The number of values of M contained in the vector MVAL. *> \endverbatim *> *> \param[in] MVAL *> \verbatim *> MVAL is INTEGER array, dimension (NM) *> The values of the matrix row dimension M. *> \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] NNB *> \verbatim *> NNB is INTEGER *> The number of values of NB contained in the vector NBVAL. *> \endverbatim *> *> \param[in] NBVAL *> \verbatim *> NBVAL is INTEGER array, dimension (NNB) *> The values of the blocksize NB. *> \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 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. *> \endverbatim *> *> \param[in] TSTERR *> \verbatim *> TSTERR is LOGICAL *> Flag that indicates whether error exits are to be tested. *> \endverbatim *> *> \param[out] A *> \verbatim *> A is REAL array, dimension (LA) *> \endverbatim *> *> \param[in] LA *> \verbatim *> LA is INTEGER *> The length of the array A. LA >= (KLMAX+KUMAX+1)*NMAX *> where KLMAX is the largest entry in the local array KLVAL, *> KUMAX is the largest entry in the local array KUVAL and *> NMAX is the largest entry in the input array NVAL. *> \endverbatim *> *> \param[out] AFAC *> \verbatim *> AFAC is REAL array, dimension (LAFAC) *> \endverbatim *> *> \param[in] LAFAC *> \verbatim *> LAFAC is INTEGER *> The length of the array AFAC. LAFAC >= (2*KLMAX+KUMAX+1)*NMAX *> where KLMAX is the largest entry in the local array KLVAL, *> KUMAX is the largest entry in the local array KUVAL and *> NMAX is the largest entry in the input array NVAL. *> \endverbatim *> *> \param[out] B *> \verbatim *> B is REAL array, dimension (NMAX*NSMAX) *> where NSMAX is the largest entry in NSVAL. *> \endverbatim *> *> \param[out] X *> \verbatim *> X is REAL array, dimension (NMAX*NSMAX) *> \endverbatim *> *> \param[out] XACT *> \verbatim *> XACT is REAL array, dimension (NMAX*NSMAX) *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is REAL array, dimension *> (NMAX*max(3,NSMAX,NMAX)) *> \endverbatim *> *> \param[out] RWORK *> \verbatim *> RWORK is REAL array, dimension *> (NMAX+2*NSMAX) *> \endverbatim *> *> \param[out] IWORK *> \verbatim *> IWORK is INTEGER array, dimension (2*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 single_lin * * ===================================================================== SUBROUTINE SCHKGB( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NNS, $ NSVAL, THRESH, TSTERR, A, LA, AFAC, LAFAC, B, $ X, XACT, 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 LA, LAFAC, NM, NN, NNB, NNS, NOUT REAL THRESH * .. * .. Array Arguments .. LOGICAL DOTYPE( * ) INTEGER IWORK( * ), MVAL( * ), NBVAL( * ), NSVAL( * ), $ NVAL( * ) REAL A( * ), AFAC( * ), B( * ), RWORK( * ), $ WORK( * ), X( * ), XACT( * ) * .. * * ===================================================================== * * .. Parameters .. REAL ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) INTEGER NTYPES, NTESTS PARAMETER ( NTYPES = 8, NTESTS = 7 ) INTEGER NBW, NTRAN PARAMETER ( NBW = 4, NTRAN = 3 ) * .. * .. Local Scalars .. LOGICAL TRFCON, ZEROT CHARACTER DIST, NORM, TRANS, TYPE, XTYPE CHARACTER*3 PATH INTEGER I, I1, I2, IKL, IKU, IM, IMAT, IN, INB, INFO, $ IOFF, IRHS, ITRAN, IZERO, J, K, KL, KOFF, KU, $ LDA, LDAFAC, LDB, M, MODE, N, NB, NERRS, NFAIL, $ NIMAT, NKL, NKU, NRHS, NRUN REAL AINVNM, ANORM, ANORMI, ANORMO, CNDNUM, RCOND, $ RCONDC, RCONDI, RCONDO * .. * .. Local Arrays .. CHARACTER TRANSS( NTRAN ) INTEGER ISEED( 4 ), ISEEDY( 4 ), KLVAL( NBW ), $ KUVAL( NBW ) REAL RESULT( NTESTS ) * .. * .. External Functions .. REAL SGET06, SLANGB, SLANGE EXTERNAL SGET06, SLANGB, SLANGE * .. * .. External Subroutines .. EXTERNAL ALAERH, ALAHD, ALASUM, SCOPY, SERRGE, SGBCON, $ SGBRFS, SGBT01, SGBT02, SGBT05, SGBTRF, SGBTRS, $ SGET04, SLACPY, SLARHS, SLASET, SLATB4, SLATMS, $ 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 / , $ TRANSS / 'N', 'T', 'C' / * .. * .. Executable Statements .. * * Initialize constants and the random number seed. * PATH( 1: 1 ) = 'Single precision' PATH( 2: 3 ) = 'GB' NRUN = 0 NFAIL = 0 NERRS = 0 DO 10 I = 1, 4 ISEED( I ) = ISEEDY( I ) 10 CONTINUE * * Test the error exits * IF( TSTERR ) $ CALL SERRGE( PATH, NOUT ) INFOT = 0 CALL XLAENV( 2, 2 ) * * Initialize the first value for the lower and upper bandwidths. * KLVAL( 1 ) = 0 KUVAL( 1 ) = 0 * * Do for each value of M in MVAL * DO 160 IM = 1, NM M = MVAL( IM ) * * Set values to use for the lower bandwidth. * KLVAL( 2 ) = M + ( M+1 ) / 4 * * KLVAL( 2 ) = MAX( M-1, 0 ) * KLVAL( 3 ) = ( 3*M-1 ) / 4 KLVAL( 4 ) = ( M+1 ) / 4 * * Do for each value of N in NVAL * DO 150 IN = 1, NN N = NVAL( IN ) XTYPE = 'N' * * Set values to use for the upper bandwidth. * KUVAL( 2 ) = N + ( N+1 ) / 4 * * KUVAL( 2 ) = MAX( N-1, 0 ) * KUVAL( 3 ) = ( 3*N-1 ) / 4 KUVAL( 4 ) = ( N+1 ) / 4 * * Set limits on the number of loop iterations. * NKL = MIN( M+1, 4 ) IF( N.EQ.0 ) $ NKL = 2 NKU = MIN( N+1, 4 ) IF( M.EQ.0 ) $ NKU = 2 NIMAT = NTYPES IF( M.LE.0 .OR. N.LE.0 ) $ NIMAT = 1 * DO 140 IKL = 1, NKL * * Do for KL = 0, (5*M+1)/4, (3M-1)/4, and (M+1)/4. This * order makes it easier to skip redundant values for small * values of M. * KL = KLVAL( IKL ) DO 130 IKU = 1, NKU * * Do for KU = 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. * KU = KUVAL( IKU ) * * Check that A and AFAC are big enough to generate this * matrix. * LDA = KL + KU + 1 LDAFAC = 2*KL + KU + 1 IF( ( LDA*N ).GT.LA .OR. ( LDAFAC*N ).GT.LAFAC ) THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) $ CALL ALAHD( NOUT, PATH ) IF( N*( KL+KU+1 ).GT.LA ) THEN WRITE( NOUT, FMT = 9999 )LA, M, N, KL, KU, $ N*( KL+KU+1 ) NERRS = NERRS + 1 END IF IF( N*( 2*KL+KU+1 ).GT.LAFAC ) THEN WRITE( NOUT, FMT = 9998 )LAFAC, M, N, KL, KU, $ N*( 2*KL+KU+1 ) NERRS = NERRS + 1 END IF GO TO 130 END IF * DO 120 IMAT = 1, NIMAT * * Do the tests only if DOTYPE( IMAT ) is true. * IF( .NOT.DOTYPE( IMAT ) ) $ GO TO 120 * * 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 120 * IF( .NOT.ZEROT .OR. .NOT.DOTYPE( 1 ) ) THEN * * Set up parameters with SLATB4 and generate a * test matrix with SLATMS. * CALL SLATB4( PATH, IMAT, M, N, TYPE, KL, KU, $ ANORM, MODE, CNDNUM, DIST ) * KOFF = MAX( 1, KU+2-N ) DO 20 I = 1, KOFF - 1 A( I ) = ZERO 20 CONTINUE SRNAMT = 'SLATMS' CALL SLATMS( M, N, DIST, ISEED, TYPE, RWORK, $ MODE, CNDNUM, ANORM, KL, KU, 'Z', $ A( KOFF ), LDA, WORK, INFO ) * * Check the error code from SLATMS. * IF( INFO.NE.0 ) THEN CALL ALAERH( PATH, 'SLATMS', INFO, 0, ' ', M, $ N, KL, KU, -1, IMAT, NFAIL, $ NERRS, NOUT ) GO TO 120 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. * CALL SCOPY( I2-I1+1, B, 1, A( IOFF+I1 ), 1 ) END IF * * For types 2, 3, and 4, zero one or more columns 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 = MIN( M, N ) ELSE IZERO = MIN( M, N ) / 2 + 1 END IF IOFF = ( IZERO-1 )*LDA IF( IMAT.LT.4 ) THEN * * Store the column to be zeroed out in B. * I1 = MAX( 1, KU+2-IZERO ) I2 = MIN( KL+KU+1, KU+1+( M-IZERO ) ) CALL SCOPY( I2-I1+1, A( IOFF+I1 ), 1, B, 1 ) * DO 30 I = I1, I2 A( IOFF+I ) = ZERO 30 CONTINUE ELSE DO 50 J = IZERO, N DO 40 I = MAX( 1, KU+2-J ), $ MIN( KL+KU+1, KU+1+( M-J ) ) A( IOFF+I ) = ZERO 40 CONTINUE IOFF = IOFF + LDA 50 CONTINUE END IF END IF * * These lines, if used in place of the calls in the * loop over INB, cause the code to bomb on a Sun * SPARCstation. * * ANORMO = SLANGB( 'O', N, KL, KU, A, LDA, RWORK ) * ANORMI = SLANGB( 'I', N, KL, KU, A, LDA, RWORK ) * * Do for each blocksize in NBVAL * DO 110 INB = 1, NNB NB = NBVAL( INB ) CALL XLAENV( 1, NB ) * * Compute the LU factorization of the band matrix. * IF( M.GT.0 .AND. N.GT.0 ) $ CALL SLACPY( 'Full', KL+KU+1, N, A, LDA, $ AFAC( KL+1 ), LDAFAC ) SRNAMT = 'SGBTRF' CALL SGBTRF( M, N, KL, KU, AFAC, LDAFAC, IWORK, $ INFO ) * * Check error code from SGBTRF. * IF( INFO.NE.IZERO ) $ CALL ALAERH( PATH, 'SGBTRF', INFO, IZERO, $ ' ', M, N, KL, KU, NB, IMAT, $ NFAIL, NERRS, NOUT ) TRFCON = .FALSE. * *+ TEST 1 * Reconstruct matrix from factors and compute * residual. * CALL SGBT01( M, N, KL, KU, A, LDA, AFAC, LDAFAC, $ IWORK, WORK, RESULT( 1 ) ) * * Print information about the tests so far that * did not pass the threshold. * IF( RESULT( 1 ).GE.THRESH ) THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) $ CALL ALAHD( NOUT, PATH ) WRITE( NOUT, FMT = 9997 )M, N, KL, KU, NB, $ IMAT, 1, RESULT( 1 ) NFAIL = NFAIL + 1 END IF NRUN = NRUN + 1 * * Skip the remaining tests if this is not the * first block size or if M .ne. N. * IF( INB.GT.1 .OR. M.NE.N ) $ GO TO 110 * ANORMO = SLANGB( 'O', N, KL, KU, A, LDA, RWORK ) ANORMI = SLANGB( 'I', N, KL, KU, A, LDA, RWORK ) * IF( INFO.EQ.0 ) THEN * * Form the inverse of A so we can get a good * estimate of CNDNUM = norm(A) * norm(inv(A)). * LDB = MAX( 1, N ) CALL SLASET( 'Full', N, N, ZERO, ONE, WORK, $ LDB ) SRNAMT = 'SGBTRS' CALL SGBTRS( 'No transpose', N, KL, KU, N, $ AFAC, LDAFAC, IWORK, WORK, LDB, $ INFO ) * * Compute the 1-norm condition number of A. * AINVNM = SLANGE( 'O', N, N, WORK, LDB, $ RWORK ) IF( ANORMO.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN RCONDO = ONE ELSE RCONDO = ( ONE / ANORMO ) / AINVNM END IF * * Compute the infinity-norm condition number of * A. * AINVNM = SLANGE( 'I', N, N, WORK, LDB, $ RWORK ) IF( ANORMI.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN RCONDI = ONE ELSE RCONDI = ( ONE / ANORMI ) / AINVNM END IF ELSE * * Do only the condition estimate if INFO.NE.0. * TRFCON = .TRUE. RCONDO = ZERO RCONDI = ZERO END IF * * Skip the solve tests if the matrix is singular. * IF( TRFCON ) $ GO TO 90 * DO 80 IRHS = 1, NNS NRHS = NSVAL( IRHS ) XTYPE = 'N' * DO 70 ITRAN = 1, NTRAN TRANS = TRANSS( ITRAN ) IF( ITRAN.EQ.1 ) THEN RCONDC = RCONDO NORM = 'O' ELSE RCONDC = RCONDI NORM = 'I' END IF * *+ TEST 2: * Solve and compute residual for op(A) * X = B. * SRNAMT = 'SLARHS' CALL SLARHS( PATH, XTYPE, ' ', TRANS, N, $ N, KL, KU, NRHS, A, LDA, $ XACT, LDB, B, LDB, ISEED, $ INFO ) XTYPE = 'C' CALL SLACPY( 'Full', N, NRHS, B, LDB, X, $ LDB ) * SRNAMT = 'SGBTRS' CALL SGBTRS( TRANS, N, KL, KU, NRHS, AFAC, $ LDAFAC, IWORK, X, LDB, INFO ) * * Check error code from SGBTRS. * IF( INFO.NE.0 ) $ CALL ALAERH( PATH, 'SGBTRS', INFO, 0, $ TRANS, N, N, KL, KU, -1, $ IMAT, NFAIL, NERRS, NOUT ) * CALL SLACPY( 'Full', N, NRHS, B, LDB, $ WORK, LDB ) CALL SGBT02( TRANS, M, N, KL, KU, NRHS, A, $ LDA, X, LDB, WORK, LDB, $ RWORK, RESULT( 2 ) ) * *+ TEST 3: * Check solution from generated exact * solution. * CALL SGET04( N, NRHS, X, LDB, XACT, LDB, $ RCONDC, RESULT( 3 ) ) * *+ TESTS 4, 5, 6: * Use iterative refinement to improve the * solution. * SRNAMT = 'SGBRFS' CALL SGBRFS( TRANS, N, KL, KU, NRHS, A, $ LDA, AFAC, LDAFAC, IWORK, B, $ LDB, X, LDB, RWORK, $ RWORK( NRHS+1 ), WORK, $ IWORK( N+1 ), INFO ) * * Check error code from SGBRFS. * IF( INFO.NE.0 ) $ CALL ALAERH( PATH, 'SGBRFS', INFO, 0, $ TRANS, N, N, KL, KU, NRHS, $ IMAT, NFAIL, NERRS, NOUT ) * CALL SGET04( N, NRHS, X, LDB, XACT, LDB, $ RCONDC, RESULT( 4 ) ) CALL SGBT05( TRANS, N, KL, KU, NRHS, A, $ LDA, B, LDB, X, LDB, XACT, $ LDB, RWORK, RWORK( NRHS+1 ), $ RESULT( 5 ) ) DO 60 K = 2, 6 IF( RESULT( K ).GE.THRESH ) THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) $ CALL ALAHD( NOUT, PATH ) WRITE( NOUT, FMT = 9996 )TRANS, N, $ KL, KU, NRHS, IMAT, K, $ RESULT( K ) NFAIL = NFAIL + 1 END IF 60 CONTINUE NRUN = NRUN + 5 70 CONTINUE 80 CONTINUE * *+ TEST 7: * Get an estimate of RCOND = 1/CNDNUM. * 90 CONTINUE DO 100 ITRAN = 1, 2 IF( ITRAN.EQ.1 ) THEN ANORM = ANORMO RCONDC = RCONDO NORM = 'O' ELSE ANORM = ANORMI RCONDC = RCONDI NORM = 'I' END IF SRNAMT = 'SGBCON' CALL SGBCON( NORM, N, KL, KU, AFAC, LDAFAC, $ IWORK, ANORM, RCOND, WORK, $ IWORK( N+1 ), INFO ) * * Check error code from SGBCON. * IF( INFO.NE.0 ) $ CALL ALAERH( PATH, 'SGBCON', INFO, 0, $ NORM, N, N, KL, KU, -1, IMAT, $ NFAIL, NERRS, NOUT ) * RESULT( 7 ) = SGET06( RCOND, RCONDC ) * * 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 = 9995 )NORM, N, KL, KU, $ IMAT, 7, RESULT( 7 ) NFAIL = NFAIL + 1 END IF NRUN = NRUN + 1 100 CONTINUE * 110 CONTINUE 120 CONTINUE 130 CONTINUE 140 CONTINUE 150 CONTINUE 160 CONTINUE * * Print a summary of the results. * CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS ) * 9999 FORMAT( ' *** In SCHKGB, LA=', I5, ' is too small for M=', I5, $ ', N=', I5, ', KL=', I4, ', KU=', I4, $ / ' ==> Increase LA to at least ', I5 ) 9998 FORMAT( ' *** In SCHKGB, LAFAC=', I5, ' is too small for M=', I5, $ ', N=', I5, ', KL=', I4, ', KU=', I4, $ / ' ==> Increase LAFAC to at least ', I5 ) 9997 FORMAT( ' M =', I5, ', N =', I5, ', KL=', I5, ', KU=', I5, $ ', NB =', I4, ', type ', I1, ', test(', I1, ')=', G12.5 ) 9996 FORMAT( ' TRANS=''', A1, ''', N=', I5, ', KL=', I5, ', KU=', I5, $ ', NRHS=', I3, ', type ', I1, ', test(', I1, ')=', G12.5 ) 9995 FORMAT( ' NORM =''', A1, ''', N=', I5, ', KL=', I5, ', KU=', I5, $ ',', 10X, ' type ', I1, ', test(', I1, ')=', G12.5 ) * RETURN * * End of SCHKGB * END