numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
| Name | Size | Mode | |
| .. | |||
| lapack/TESTING/LIN/cdrvge.f | 25328B | -rw-r--r-- |
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*> \brief \b CDRVGE * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE CDRVGE( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, * A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK, * RWORK, IWORK, NOUT ) * * .. Scalar Arguments .. * LOGICAL TSTERR * INTEGER NMAX, NN, NOUT, NRHS * REAL THRESH * .. * .. Array Arguments .. * LOGICAL DOTYPE( * ) * INTEGER IWORK( * ), NVAL( * ) * REAL RWORK( * ), S( * ) * COMPLEX A( * ), AFAC( * ), ASAV( * ), B( * ), * $ BSAV( * ), WORK( * ), X( * ), XACT( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> CDRVGE tests the driver routines CGESV and -SVX. *> \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] NRHS *> \verbatim *> NRHS is INTEGER *> The number of right hand side vectors to be generated for *> each linear system. *> \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[in] NMAX *> \verbatim *> NMAX is INTEGER *> The maximum value permitted for N, used in dimensioning the *> work arrays. *> \endverbatim *> *> \param[out] A *> \verbatim *> A is COMPLEX array, dimension (NMAX*NMAX) *> \endverbatim *> *> \param[out] AFAC *> \verbatim *> AFAC is COMPLEX array, dimension (NMAX*NMAX) *> \endverbatim *> *> \param[out] ASAV *> \verbatim *> ASAV is COMPLEX array, dimension (NMAX*NMAX) *> \endverbatim *> *> \param[out] B *> \verbatim *> B is COMPLEX array, dimension (NMAX*NRHS) *> \endverbatim *> *> \param[out] BSAV *> \verbatim *> BSAV is COMPLEX array, dimension (NMAX*NRHS) *> \endverbatim *> *> \param[out] X *> \verbatim *> X is COMPLEX array, dimension (NMAX*NRHS) *> \endverbatim *> *> \param[out] XACT *> \verbatim *> XACT is COMPLEX array, dimension (NMAX*NRHS) *> \endverbatim *> *> \param[out] S *> \verbatim *> S is REAL array, dimension (2*NMAX) *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX array, dimension *> (NMAX*max(3,NRHS)) *> \endverbatim *> *> \param[out] RWORK *> \verbatim *> RWORK is REAL array, dimension (2*NRHS+NMAX) *> \endverbatim *> *> \param[out] IWORK *> \verbatim *> IWORK is INTEGER array, dimension (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 complex_lin * * ===================================================================== SUBROUTINE CDRVGE( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, $ A, AFAC, ASAV, B, BSAV, X, XACT, S, 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 NMAX, NN, NOUT, NRHS REAL THRESH * .. * .. Array Arguments .. LOGICAL DOTYPE( * ) INTEGER IWORK( * ), NVAL( * ) REAL RWORK( * ), S( * ) COMPLEX A( * ), AFAC( * ), ASAV( * ), B( * ), $ BSAV( * ), WORK( * ), X( * ), XACT( * ) * .. * * ===================================================================== * * .. Parameters .. REAL ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) INTEGER NTYPES PARAMETER ( NTYPES = 11 ) INTEGER NTESTS PARAMETER ( NTESTS = 7 ) INTEGER NTRAN PARAMETER ( NTRAN = 3 ) * .. * .. Local Scalars .. LOGICAL EQUIL, NOFACT, PREFAC, TRFCON, ZEROT CHARACTER DIST, EQUED, FACT, TRANS, TYPE, XTYPE CHARACTER*3 PATH INTEGER I, IEQUED, IFACT, IMAT, IN, INFO, IOFF, ITRAN, $ IZERO, K, K1, KL, KU, LDA, LWORK, MODE, N, NB, $ NBMIN, NERRS, NFACT, NFAIL, NIMAT, NRUN, NT REAL AINVNM, AMAX, ANORM, ANORMI, ANORMO, CNDNUM, $ COLCND, RCOND, RCONDC, RCONDI, RCONDO, ROLDC, $ ROLDI, ROLDO, ROWCND, RPVGRW * .. * .. Local Arrays .. CHARACTER EQUEDS( 4 ), FACTS( 3 ), TRANSS( NTRAN ) INTEGER ISEED( 4 ), ISEEDY( 4 ) REAL RDUM( 1 ), RESULT( NTESTS ) * .. * .. External Functions .. LOGICAL LSAME REAL CLANGE, CLANTR, SGET06, SLAMCH EXTERNAL LSAME, CLANGE, CLANTR, SGET06, SLAMCH * .. * .. External Subroutines .. EXTERNAL ALADHD, ALAERH, ALASVM, CERRVX, CGEEQU, CGESV, $ CGESVX, CGET01, CGET02, CGET04, CGET07, CGETRF, $ CGETRI, CLACPY, CLAQGE, CLARHS, CLASET, CLATB4, $ CLATMS, XLAENV * .. * .. Intrinsic Functions .. INTRINSIC ABS, CMPLX, 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 TRANSS / 'N', 'T', 'C' / DATA FACTS / 'F', 'N', 'E' / DATA EQUEDS / 'N', 'R', 'C', 'B' / * .. * .. Executable Statements .. * * Initialize constants and the random number seed. * PATH( 1: 1 ) = 'Complex precision' PATH( 2: 3 ) = 'GE' NRUN = 0 NFAIL = 0 NERRS = 0 DO 10 I = 1, 4 ISEED( I ) = ISEEDY( I ) 10 CONTINUE * * Test the error exits * IF( TSTERR ) $ CALL CERRVX( 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 90 IN = 1, NN N = NVAL( IN ) LDA = MAX( N, 1 ) XTYPE = 'N' NIMAT = NTYPES IF( N.LE.0 ) $ NIMAT = 1 * DO 80 IMAT = 1, NIMAT * * Do the tests only if DOTYPE( IMAT ) is true. * IF( .NOT.DOTYPE( IMAT ) ) $ GO TO 80 * * Skip types 5, 6, or 7 if the matrix size is too small. * ZEROT = IMAT.GE.5 .AND. IMAT.LE.7 IF( ZEROT .AND. N.LT.IMAT-4 ) $ GO TO 80 * * Set up parameters with CLATB4 and generate a test matrix * with CLATMS. * CALL CLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM, MODE, $ CNDNUM, DIST ) RCONDC = ONE / CNDNUM * SRNAMT = 'CLATMS' CALL CLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE, CNDNUM, $ ANORM, KL, KU, 'No packing', A, LDA, WORK, $ INFO ) * * Check error code from CLATMS. * IF( INFO.NE.0 ) THEN CALL ALAERH( PATH, 'CLATMS', INFO, 0, ' ', N, N, -1, -1, $ -1, IMAT, NFAIL, NERRS, NOUT ) GO TO 80 END IF * * For types 5-7, zero one or more columns of the matrix to * test that INFO is returned correctly. * IF( ZEROT ) THEN IF( IMAT.EQ.5 ) THEN IZERO = 1 ELSE IF( IMAT.EQ.6 ) THEN IZERO = N ELSE IZERO = N / 2 + 1 END IF IOFF = ( IZERO-1 )*LDA IF( IMAT.LT.7 ) THEN DO 20 I = 1, N A( IOFF+I ) = ZERO 20 CONTINUE ELSE CALL CLASET( 'Full', N, N-IZERO+1, CMPLX( ZERO ), $ CMPLX( ZERO ), A( IOFF+1 ), LDA ) END IF ELSE IZERO = 0 END IF * * Save a copy of the matrix A in ASAV. * CALL CLACPY( 'Full', N, N, A, LDA, ASAV, LDA ) * DO 70 IEQUED = 1, 4 EQUED = EQUEDS( IEQUED ) IF( IEQUED.EQ.1 ) THEN NFACT = 3 ELSE NFACT = 1 END IF * DO 60 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 60 RCONDO = ZERO RCONDI = ZERO * ELSE IF( .NOT.NOFACT ) THEN * * Compute the condition number for comparison with * the value returned by CGESVX (FACT = 'N' reuses * the condition number from the previous iteration * with FACT = 'F'). * CALL CLACPY( 'Full', 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 CGEEQU( N, N, AFAC, LDA, S, S( N+1 ), $ ROWCND, COLCND, AMAX, INFO ) IF( INFO.EQ.0 .AND. N.GT.0 ) THEN IF( LSAME( EQUED, 'R' ) ) THEN ROWCND = ZERO COLCND = ONE ELSE IF( LSAME( EQUED, 'C' ) ) THEN ROWCND = ONE COLCND = ZERO ELSE IF( LSAME( EQUED, 'B' ) ) THEN ROWCND = ZERO COLCND = ZERO END IF * * Equilibrate the matrix. * CALL CLAQGE( N, N, AFAC, LDA, S, S( N+1 ), $ ROWCND, COLCND, AMAX, EQUED ) END IF END IF * * Save the condition number of the non-equilibrated * system for use in CGET04. * IF( EQUIL ) THEN ROLDO = RCONDO ROLDI = RCONDI END IF * * Compute the 1-norm and infinity-norm of A. * ANORMO = CLANGE( '1', N, N, AFAC, LDA, RWORK ) ANORMI = CLANGE( 'I', N, N, AFAC, LDA, RWORK ) * * Factor the matrix A. * SRNAMT = 'CGETRF' CALL CGETRF( N, N, AFAC, LDA, IWORK, INFO ) * * Form the inverse of A. * CALL CLACPY( 'Full', N, N, AFAC, LDA, A, LDA ) LWORK = NMAX*MAX( 3, NRHS ) SRNAMT = 'CGETRI' CALL CGETRI( N, A, LDA, IWORK, WORK, LWORK, INFO ) * * Compute the 1-norm condition number of A. * AINVNM = CLANGE( '1', N, N, A, LDA, 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 = CLANGE( 'I', N, N, A, LDA, RWORK ) IF( ANORMI.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN RCONDI = ONE ELSE RCONDI = ( ONE / ANORMI ) / AINVNM END IF END IF * DO 50 ITRAN = 1, NTRAN * * Do for each value of TRANS. * TRANS = TRANSS( ITRAN ) IF( ITRAN.EQ.1 ) THEN RCONDC = RCONDO ELSE RCONDC = RCONDI END IF * * Restore the matrix A. * CALL CLACPY( 'Full', N, N, ASAV, LDA, A, LDA ) * * Form an exact solution and set the right hand side. * SRNAMT = 'CLARHS' CALL CLARHS( PATH, XTYPE, 'Full', TRANS, N, N, KL, $ KU, NRHS, A, LDA, XACT, LDA, B, LDA, $ ISEED, INFO ) XTYPE = 'C' CALL CLACPY( 'Full', N, NRHS, B, LDA, BSAV, LDA ) * IF( NOFACT .AND. ITRAN.EQ.1 ) THEN * * --- Test CGESV --- * * Compute the LU factorization of the matrix and * solve the system. * CALL CLACPY( 'Full', N, N, A, LDA, AFAC, LDA ) CALL CLACPY( 'Full', N, NRHS, B, LDA, X, LDA ) * SRNAMT = 'CGESV ' CALL CGESV( N, NRHS, AFAC, LDA, IWORK, X, LDA, $ INFO ) * * Check error code from CGESV . * IF( INFO.NE.IZERO ) $ CALL ALAERH( PATH, 'CGESV ', INFO, IZERO, $ ' ', N, N, -1, -1, NRHS, IMAT, $ NFAIL, NERRS, NOUT ) * * Reconstruct matrix from factors and compute * residual. * CALL CGET01( N, N, A, LDA, AFAC, LDA, IWORK, $ RWORK, RESULT( 1 ) ) NT = 1 IF( IZERO.EQ.0 ) THEN * * Compute residual of the computed solution. * CALL CLACPY( 'Full', N, NRHS, B, LDA, WORK, $ LDA ) CALL CGET02( 'No transpose', N, N, NRHS, A, $ LDA, X, LDA, WORK, LDA, RWORK, $ RESULT( 2 ) ) * * Check solution from generated exact solution. * CALL CGET04( N, NRHS, X, LDA, XACT, LDA, $ RCONDC, RESULT( 3 ) ) NT = 3 END IF * * Print information about the tests that did not * pass the threshold. * DO 30 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 )'CGESV ', N, $ IMAT, K, RESULT( K ) NFAIL = NFAIL + 1 END IF 30 CONTINUE NRUN = NRUN + NT END IF * * --- Test CGESVX --- * IF( .NOT.PREFAC ) $ CALL CLASET( 'Full', N, N, CMPLX( ZERO ), $ CMPLX( ZERO ), AFAC, LDA ) CALL CLASET( 'Full', N, NRHS, CMPLX( ZERO ), $ CMPLX( ZERO ), X, LDA ) IF( IEQUED.GT.1 .AND. N.GT.0 ) THEN * * Equilibrate the matrix if FACT = 'F' and * EQUED = 'R', 'C', or 'B'. * CALL CLAQGE( N, N, A, LDA, S, S( N+1 ), ROWCND, $ COLCND, AMAX, EQUED ) END IF * * Solve the system and compute the condition number * and error bounds using CGESVX. * SRNAMT = 'CGESVX' CALL CGESVX( FACT, TRANS, N, NRHS, A, LDA, AFAC, $ LDA, IWORK, EQUED, S, S( N+1 ), B, $ LDA, X, LDA, RCOND, RWORK, $ RWORK( NRHS+1 ), WORK, $ RWORK( 2*NRHS+1 ), INFO ) * * Check the error code from CGESVX. * IF( INFO.NE.IZERO ) $ CALL ALAERH( PATH, 'CGESVX', INFO, IZERO, $ FACT // TRANS, N, N, -1, -1, NRHS, $ IMAT, NFAIL, NERRS, NOUT ) * * Compare RWORK(2*NRHS+1) from CGESVX with the * computed reciprocal pivot growth factor RPVGRW * IF( INFO.NE.0 .AND. INFO.LE.N) THEN RPVGRW = CLANTR( 'M', 'U', 'N', INFO, INFO, $ AFAC, LDA, RDUM ) IF( RPVGRW.EQ.ZERO ) THEN RPVGRW = ONE ELSE RPVGRW = CLANGE( 'M', N, INFO, A, LDA, $ RDUM ) / RPVGRW END IF ELSE RPVGRW = CLANTR( 'M', 'U', 'N', N, N, AFAC, LDA, $ RDUM ) IF( RPVGRW.EQ.ZERO ) THEN RPVGRW = ONE ELSE RPVGRW = CLANGE( 'M', N, N, A, LDA, RDUM ) / $ RPVGRW END IF END IF RESULT( 7 ) = ABS( RPVGRW-RWORK( 2*NRHS+1 ) ) / $ MAX( RWORK( 2*NRHS+1 ), RPVGRW ) / $ SLAMCH( 'E' ) * IF( .NOT.PREFAC ) THEN * * Reconstruct matrix from factors and compute * residual. * CALL CGET01( N, N, A, LDA, AFAC, LDA, IWORK, $ RWORK( 2*NRHS+1 ), RESULT( 1 ) ) K1 = 1 ELSE K1 = 2 END IF * IF( INFO.EQ.0 ) THEN TRFCON = .FALSE. * * Compute residual of the computed solution. * CALL CLACPY( 'Full', N, NRHS, BSAV, LDA, WORK, $ LDA ) CALL CGET02( TRANS, N, 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 CGET04( N, NRHS, X, LDA, XACT, LDA, $ RCONDC, RESULT( 3 ) ) ELSE IF( ITRAN.EQ.1 ) THEN ROLDC = ROLDO ELSE ROLDC = ROLDI END IF CALL CGET04( N, NRHS, X, LDA, XACT, LDA, $ ROLDC, RESULT( 3 ) ) END IF * * Check the error bounds from iterative * refinement. * CALL CGET07( TRANS, N, NRHS, ASAV, LDA, B, LDA, $ X, LDA, XACT, LDA, RWORK, .TRUE., $ RWORK( NRHS+1 ), RESULT( 4 ) ) ELSE TRFCON = .TRUE. END IF * * Compare RCOND from CGESVX with the computed value * in RCONDC. * RESULT( 6 ) = SGET06( RCOND, RCONDC ) * * Print information about the tests that did not pass * the threshold. * IF( .NOT.TRFCON ) THEN DO 40 K = K1, NTESTS 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 )'CGESVX', $ FACT, TRANS, N, EQUED, IMAT, K, $ RESULT( K ) ELSE WRITE( NOUT, FMT = 9998 )'CGESVX', $ FACT, TRANS, N, IMAT, K, RESULT( K ) END IF NFAIL = NFAIL + 1 END IF 40 CONTINUE NRUN = NRUN + NTESTS - K1 + 1 ELSE IF( RESULT( 1 ).GE.THRESH .AND. .NOT.PREFAC ) $ THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) $ CALL ALADHD( NOUT, PATH ) IF( PREFAC ) THEN WRITE( NOUT, FMT = 9997 )'CGESVX', FACT, $ TRANS, N, EQUED, IMAT, 1, RESULT( 1 ) ELSE WRITE( NOUT, FMT = 9998 )'CGESVX', FACT, $ TRANS, N, IMAT, 1, RESULT( 1 ) END IF NFAIL = NFAIL + 1 NRUN = NRUN + 1 END IF IF( RESULT( 6 ).GE.THRESH ) THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) $ CALL ALADHD( NOUT, PATH ) IF( PREFAC ) THEN WRITE( NOUT, FMT = 9997 )'CGESVX', FACT, $ TRANS, N, EQUED, IMAT, 6, RESULT( 6 ) ELSE WRITE( NOUT, FMT = 9998 )'CGESVX', FACT, $ TRANS, N, IMAT, 6, RESULT( 6 ) END IF NFAIL = NFAIL + 1 NRUN = NRUN + 1 END IF IF( RESULT( 7 ).GE.THRESH ) THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) $ CALL ALADHD( NOUT, PATH ) IF( PREFAC ) THEN WRITE( NOUT, FMT = 9997 )'CGESVX', FACT, $ TRANS, N, EQUED, IMAT, 7, RESULT( 7 ) ELSE WRITE( NOUT, FMT = 9998 )'CGESVX', FACT, $ TRANS, N, IMAT, 7, RESULT( 7 ) END IF NFAIL = NFAIL + 1 NRUN = NRUN + 1 END IF * END IF * 50 CONTINUE 60 CONTINUE 70 CONTINUE 80 CONTINUE 90 CONTINUE * * Print a summary of the results. * CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS ) * 9999 FORMAT( 1X, A, ', N =', I5, ', type ', I2, ', test(', I2, ') =', $ G12.5 ) 9998 FORMAT( 1X, A, ', FACT=''', A1, ''', TRANS=''', A1, ''', N=', I5, $ ', type ', I2, ', test(', I1, ')=', G12.5 ) 9997 FORMAT( 1X, A, ', FACT=''', A1, ''', TRANS=''', A1, ''', N=', I5, $ ', EQUED=''', A1, ''', type ', I2, ', test(', I1, ')=', $ G12.5 ) RETURN * * End of CDRVGE * END