numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
| Name | Size | Mode | |
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| lapack/TESTING/LIN/cdrvrfp.f | 19685B | -rw-r--r-- |
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*> \brief \b CDRVRFP * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE CDRVRFP( NOUT, NN, NVAL, NNS, NSVAL, NNT, NTVAL, * + THRESH, A, ASAV, AFAC, AINV, B, * + BSAV, XACT, X, ARF, ARFINV, * + C_WORK_CLATMS, C_WORK_CPOT02, * + C_WORK_CPOT03, S_WORK_CLATMS, S_WORK_CLANHE, * + S_WORK_CPOT01, S_WORK_CPOT02, S_WORK_CPOT03 ) * * .. Scalar Arguments .. * INTEGER NN, NNS, NNT, NOUT * REAL THRESH * .. * .. Array Arguments .. * INTEGER NVAL( NN ), NSVAL( NNS ), NTVAL( NNT ) * COMPLEX A( * ) * COMPLEX AINV( * ) * COMPLEX ASAV( * ) * COMPLEX B( * ) * COMPLEX BSAV( * ) * COMPLEX AFAC( * ) * COMPLEX ARF( * ) * COMPLEX ARFINV( * ) * COMPLEX XACT( * ) * COMPLEX X( * ) * COMPLEX C_WORK_CLATMS( * ) * COMPLEX C_WORK_CPOT02( * ) * COMPLEX C_WORK_CPOT03( * ) * REAL S_WORK_CLATMS( * ) * REAL S_WORK_CLANHE( * ) * REAL S_WORK_CPOT01( * ) * REAL S_WORK_CPOT02( * ) * REAL S_WORK_CPOT03( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> CDRVRFP tests the LAPACK RFP routines: *> CPFTRF, CPFTRS, and CPFTRI. *> *> This testing routine follow the same tests as CDRVPO (test for the full *> format Symmetric Positive Definite solver). *> *> The tests are performed in Full Format, conversion back and forth from *> full format to RFP format are performed using the routines CTRTTF and *> CTFTTR. *> *> First, a specific matrix A of size N is created. There is nine types of *> different matrixes possible. *> 1. Diagonal 6. Random, CNDNUM = sqrt(0.1/EPS) *> 2. Random, CNDNUM = 2 7. Random, CNDNUM = 0.1/EPS *> *3. First row and column zero 8. Scaled near underflow *> *4. Last row and column zero 9. Scaled near overflow *> *5. Middle row and column zero *> (* - tests error exits from CPFTRF, no test ratios are computed) *> A solution XACT of size N-by-NRHS is created and the associated right *> hand side B as well. Then CPFTRF is called to compute L (or U), the *> Cholesky factor of A. Then L (or U) is used to solve the linear system *> of equations AX = B. This gives X. Then L (or U) is used to compute the *> inverse of A, AINV. The following four tests are then performed: *> (1) norm( L*L' - A ) / ( N * norm(A) * EPS ) or *> norm( U'*U - A ) / ( N * norm(A) * EPS ), *> (2) norm(B - A*X) / ( norm(A) * norm(X) * EPS ), *> (3) norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ), *> (4) ( norm(X-XACT) * RCOND ) / ( norm(XACT) * EPS ), *> where EPS is the machine precision, RCOND the condition number of A, and *> norm( . ) the 1-norm for (1,2,3) and the inf-norm for (4). *> Errors occur when INFO parameter is not as expected. Failures occur when *> a test ratios is greater than THRES. *> \endverbatim * * Arguments: * ========== * *> \param[in] NOUT *> \verbatim *> NOUT is INTEGER *> The unit number for output. *> \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 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] NNT *> \verbatim *> NNT is INTEGER *> The number of values of MATRIX TYPE contained in the vector NTVAL. *> \endverbatim *> *> \param[in] NTVAL *> \verbatim *> NTVAL is INTEGER array, dimension (NNT) *> The values of matrix type (between 0 and 9 for PO/PP/PF matrices). *> \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[out] A *> \verbatim *> A is COMPLEX array, dimension (NMAX*NMAX) *> \endverbatim *> *> \param[out] ASAV *> \verbatim *> ASAV is COMPLEX array, dimension (NMAX*NMAX) *> \endverbatim *> *> \param[out] AFAC *> \verbatim *> AFAC is COMPLEX array, dimension (NMAX*NMAX) *> \endverbatim *> *> \param[out] AINV *> \verbatim *> AINV is COMPLEX array, dimension (NMAX*NMAX) *> \endverbatim *> *> \param[out] B *> \verbatim *> B is COMPLEX array, dimension (NMAX*MAXRHS) *> \endverbatim *> *> \param[out] BSAV *> \verbatim *> BSAV is COMPLEX array, dimension (NMAX*MAXRHS) *> \endverbatim *> *> \param[out] XACT *> \verbatim *> XACT is COMPLEX array, dimension (NMAX*MAXRHS) *> \endverbatim *> *> \param[out] X *> \verbatim *> X is COMPLEX array, dimension (NMAX*MAXRHS) *> \endverbatim *> *> \param[out] ARF *> \verbatim *> ARF is COMPLEX array, dimension ((NMAX*(NMAX+1))/2) *> \endverbatim *> *> \param[out] ARFINV *> \verbatim *> ARFINV is COMPLEX array, dimension ((NMAX*(NMAX+1))/2) *> \endverbatim *> *> \param[out] C_WORK_CLATMS *> \verbatim *> C_WORK_CLATMS is COMPLEX array, dimension ( 3*NMAX ) *> \endverbatim *> *> \param[out] C_WORK_CPOT02 *> \verbatim *> C_WORK_CPOT02 is COMPLEX array, dimension ( NMAX*MAXRHS ) *> \endverbatim *> *> \param[out] C_WORK_CPOT03 *> \verbatim *> C_WORK_CPOT03 is COMPLEX array, dimension ( NMAX*NMAX ) *> \endverbatim *> *> \param[out] S_WORK_CLATMS *> \verbatim *> S_WORK_CLATMS is REAL array, dimension ( NMAX ) *> \endverbatim *> *> \param[out] S_WORK_CLANHE *> \verbatim *> S_WORK_CLANHE is REAL array, dimension ( NMAX ) *> \endverbatim *> *> \param[out] S_WORK_CPOT01 *> \verbatim *> S_WORK_CPOT01 is REAL array, dimension ( NMAX ) *> \endverbatim *> *> \param[out] S_WORK_CPOT02 *> \verbatim *> S_WORK_CPOT02 is REAL array, dimension ( NMAX ) *> \endverbatim *> *> \param[out] S_WORK_CPOT03 *> \verbatim *> S_WORK_CPOT03 is REAL array, dimension ( NMAX ) *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup complex_lin * * ===================================================================== SUBROUTINE CDRVRFP( NOUT, NN, NVAL, NNS, NSVAL, NNT, NTVAL, + THRESH, A, ASAV, AFAC, AINV, B, + BSAV, XACT, X, ARF, ARFINV, + C_WORK_CLATMS, C_WORK_CPOT02, + C_WORK_CPOT03, S_WORK_CLATMS, S_WORK_CLANHE, + S_WORK_CPOT01, S_WORK_CPOT02, S_WORK_CPOT03 ) * * -- 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 .. INTEGER NN, NNS, NNT, NOUT REAL THRESH * .. * .. Array Arguments .. INTEGER NVAL( NN ), NSVAL( NNS ), NTVAL( NNT ) COMPLEX A( * ) COMPLEX AINV( * ) COMPLEX ASAV( * ) COMPLEX B( * ) COMPLEX BSAV( * ) COMPLEX AFAC( * ) COMPLEX ARF( * ) COMPLEX ARFINV( * ) COMPLEX XACT( * ) COMPLEX X( * ) COMPLEX C_WORK_CLATMS( * ) COMPLEX C_WORK_CPOT02( * ) COMPLEX C_WORK_CPOT03( * ) REAL S_WORK_CLATMS( * ) REAL S_WORK_CLANHE( * ) REAL S_WORK_CPOT01( * ) REAL S_WORK_CPOT02( * ) REAL S_WORK_CPOT03( * ) * .. * * ===================================================================== * * .. Parameters .. REAL ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) INTEGER NTESTS PARAMETER ( NTESTS = 4 ) * .. * .. Local Scalars .. LOGICAL ZEROT INTEGER I, INFO, IUPLO, LDA, LDB, IMAT, NERRS, NFAIL, + NRHS, NRUN, IZERO, IOFF, K, NT, N, IFORM, IIN, + IIT, IIS CHARACTER DIST, CTYPE, UPLO, CFORM INTEGER KL, KU, MODE REAL ANORM, AINVNM, CNDNUM, RCONDC * .. * .. Local Arrays .. CHARACTER UPLOS( 2 ), FORMS( 2 ) INTEGER ISEED( 4 ), ISEEDY( 4 ) REAL RESULT( NTESTS ) * .. * .. External Functions .. REAL CLANHE EXTERNAL CLANHE * .. * .. External Subroutines .. EXTERNAL ALADHD, ALAERH, ALASVM, CGET04, CTFTTR, CLACPY, + CLAIPD, CLARHS, CLATB4, CLATMS, CPFTRI, CPFTRF, + CPFTRS, CPOT01, CPOT02, CPOT03, CPOTRI, CPOTRF, + CTRTTF * .. * .. Scalars in Common .. CHARACTER*32 SRNAMT * .. * .. Common blocks .. COMMON / SRNAMC / SRNAMT * .. * .. Data statements .. DATA ISEEDY / 1988, 1989, 1990, 1991 / DATA UPLOS / 'U', 'L' / DATA FORMS / 'N', 'C' / * .. * .. Executable Statements .. * * Initialize constants and the random number seed. * NRUN = 0 NFAIL = 0 NERRS = 0 DO 10 I = 1, 4 ISEED( I ) = ISEEDY( I ) 10 CONTINUE * DO 130 IIN = 1, NN * N = NVAL( IIN ) LDA = MAX( N, 1 ) LDB = MAX( N, 1 ) * DO 980 IIS = 1, NNS * NRHS = NSVAL( IIS ) * DO 120 IIT = 1, NNT * IMAT = NTVAL( IIT ) * * If N.EQ.0, only consider the first type * IF( N.EQ.0 .AND. IIT.GE.1 ) GO TO 120 * * Skip types 3, 4, or 5 if the matrix size is too small. * IF( IMAT.EQ.4 .AND. N.LE.1 ) GO TO 120 IF( IMAT.EQ.5 .AND. N.LE.2 ) GO TO 120 * * Do first for UPLO = 'U', then for UPLO = 'L' * DO 110 IUPLO = 1, 2 UPLO = UPLOS( IUPLO ) * * Do first for CFORM = 'N', then for CFORM = 'C' * DO 100 IFORM = 1, 2 CFORM = FORMS( IFORM ) * * Set up parameters with CLATB4 and generate a test * matrix with CLATMS. * CALL CLATB4( 'CPO', IMAT, N, N, CTYPE, KL, KU, + ANORM, MODE, CNDNUM, DIST ) * SRNAMT = 'CLATMS' CALL CLATMS( N, N, DIST, ISEED, CTYPE, + S_WORK_CLATMS, + MODE, CNDNUM, ANORM, KL, KU, UPLO, A, + LDA, C_WORK_CLATMS, INFO ) * * Check error code from CLATMS. * IF( INFO.NE.0 ) THEN CALL ALAERH( 'CPF', 'CLATMS', INFO, 0, UPLO, N, + N, -1, -1, -1, IIT, NFAIL, NERRS, + NOUT ) GO TO 100 END IF * * For types 3-5, zero one row and column of the matrix to * test that INFO is returned correctly. * ZEROT = IMAT.GE.3 .AND. IMAT.LE.5 IF( ZEROT ) THEN IF( IIT.EQ.3 ) THEN IZERO = 1 ELSE IF( IIT.EQ.4 ) THEN IZERO = N ELSE IZERO = N / 2 + 1 END IF IOFF = ( IZERO-1 )*LDA * * Set row and column IZERO of A to 0. * IF( IUPLO.EQ.1 ) THEN DO 20 I = 1, IZERO - 1 A( IOFF+I ) = ZERO 20 CONTINUE IOFF = IOFF + IZERO DO 30 I = IZERO, N A( IOFF ) = ZERO IOFF = IOFF + LDA 30 CONTINUE ELSE IOFF = IZERO DO 40 I = 1, IZERO - 1 A( IOFF ) = ZERO IOFF = IOFF + LDA 40 CONTINUE IOFF = IOFF - IZERO DO 50 I = IZERO, N A( IOFF+I ) = ZERO 50 CONTINUE END IF ELSE IZERO = 0 END IF * * Set the imaginary part of the diagonals. * CALL CLAIPD( N, A, LDA+1, 0 ) * * Save a copy of the matrix A in ASAV. * CALL CLACPY( UPLO, N, N, A, LDA, ASAV, LDA ) * * Compute the condition number of A (RCONDC). * IF( ZEROT ) THEN RCONDC = ZERO ELSE * * Compute the 1-norm of A. * ANORM = CLANHE( '1', UPLO, N, A, LDA, + S_WORK_CLANHE ) * * Factor the matrix A. * CALL CPOTRF( UPLO, N, A, LDA, INFO ) * * Form the inverse of A. * CALL CPOTRI( UPLO, N, A, LDA, INFO ) IF ( N .NE. 0 ) THEN * * Compute the 1-norm condition number of A. * AINVNM = CLANHE( '1', UPLO, N, A, LDA, + S_WORK_CLANHE ) RCONDC = ( ONE / ANORM ) / AINVNM * * Restore the matrix A. * CALL CLACPY( UPLO, N, N, ASAV, LDA, A, LDA ) END IF * END IF * * Form an exact solution and set the right hand side. * SRNAMT = 'CLARHS' CALL CLARHS( 'CPO', 'N', UPLO, ' ', N, N, KL, KU, + NRHS, A, LDA, XACT, LDA, B, LDA, + ISEED, INFO ) CALL CLACPY( 'Full', N, NRHS, B, LDA, BSAV, LDA ) * * Compute the L*L' or U'*U factorization of the * matrix and solve the system. * CALL CLACPY( UPLO, N, N, A, LDA, AFAC, LDA ) CALL CLACPY( 'Full', N, NRHS, B, LDB, X, LDB ) * SRNAMT = 'CTRTTF' CALL CTRTTF( CFORM, UPLO, N, AFAC, LDA, ARF, INFO ) SRNAMT = 'CPFTRF' CALL CPFTRF( CFORM, UPLO, N, ARF, INFO ) * * Check error code from CPFTRF. * IF( INFO.NE.IZERO ) THEN * * LANGOU: there is a small hick here: IZERO should * always be INFO however if INFO is ZERO, ALAERH does not * complain. * CALL ALAERH( 'CPF', 'CPFSV ', INFO, IZERO, + UPLO, N, N, -1, -1, NRHS, IIT, + NFAIL, NERRS, NOUT ) GO TO 100 END IF * * Skip the tests if INFO is not 0. * IF( INFO.NE.0 ) THEN GO TO 100 END IF * SRNAMT = 'CPFTRS' CALL CPFTRS( CFORM, UPLO, N, NRHS, ARF, X, LDB, + INFO ) * SRNAMT = 'CTFTTR' CALL CTFTTR( CFORM, UPLO, N, ARF, AFAC, LDA, INFO ) * * Reconstruct matrix from factors and compute * residual. * CALL CLACPY( UPLO, N, N, AFAC, LDA, ASAV, LDA ) CALL CPOT01( UPLO, N, A, LDA, AFAC, LDA, + S_WORK_CPOT01, RESULT( 1 ) ) CALL CLACPY( UPLO, N, N, ASAV, LDA, AFAC, LDA ) * * Form the inverse and compute the residual. * IF(MOD(N,2).EQ.0)THEN CALL CLACPY( 'A', N+1, N/2, ARF, N+1, ARFINV, + N+1 ) ELSE CALL CLACPY( 'A', N, (N+1)/2, ARF, N, ARFINV, + N ) END IF * SRNAMT = 'CPFTRI' CALL CPFTRI( CFORM, UPLO, N, ARFINV , INFO ) * SRNAMT = 'CTFTTR' CALL CTFTTR( CFORM, UPLO, N, ARFINV, AINV, LDA, + INFO ) * * Check error code from CPFTRI. * IF( INFO.NE.0 ) + CALL ALAERH( 'CPO', 'CPFTRI', INFO, 0, UPLO, N, + N, -1, -1, -1, IMAT, NFAIL, NERRS, + NOUT ) * CALL CPOT03( UPLO, N, A, LDA, AINV, LDA, + C_WORK_CPOT03, LDA, S_WORK_CPOT03, + RCONDC, RESULT( 2 ) ) * * Compute residual of the computed solution. * CALL CLACPY( 'Full', N, NRHS, B, LDA, + C_WORK_CPOT02, LDA ) CALL CPOT02( UPLO, N, NRHS, A, LDA, X, LDA, + C_WORK_CPOT02, LDA, S_WORK_CPOT02, + RESULT( 3 ) ) * * Check solution from generated exact solution. * CALL CGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC, + RESULT( 4 ) ) NT = 4 * * Print information about the tests that did not * pass the threshold. * DO 60 K = 1, NT IF( RESULT( K ).GE.THRESH ) THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) + CALL ALADHD( NOUT, 'CPF' ) WRITE( NOUT, FMT = 9999 )'CPFSV ', UPLO, + N, IIT, K, RESULT( K ) NFAIL = NFAIL + 1 END IF 60 CONTINUE NRUN = NRUN + NT 100 CONTINUE 110 CONTINUE 120 CONTINUE 980 CONTINUE 130 CONTINUE * * Print a summary of the results. * CALL ALASVM( 'CPF', NOUT, NFAIL, NRUN, NERRS ) * 9999 FORMAT( 1X, A6, ', UPLO=''', A1, ''', N =', I5, ', type ', I1, + ', test(', I1, ')=', G12.5 ) * RETURN * * End of CDRVRFP * END