numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
| Name | Size | Mode | |
| .. | |||
| lapack/TESTING/LIN/ddrvpt.f | 17865B | -rw-r--r-- |
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*> \brief \b DDRVPT * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE DDRVPT( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, D, * E, B, X, XACT, WORK, RWORK, NOUT ) * * .. Scalar Arguments .. * LOGICAL TSTERR * INTEGER NN, NOUT, NRHS * DOUBLE PRECISION THRESH * .. * .. Array Arguments .. * LOGICAL DOTYPE( * ) * INTEGER NVAL( * ) * DOUBLE PRECISION A( * ), B( * ), D( * ), E( * ), RWORK( * ), * $ WORK( * ), X( * ), XACT( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DDRVPT tests DPTSV 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 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 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[out] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (NMAX*2) *> \endverbatim *> *> \param[out] D *> \verbatim *> D is DOUBLE PRECISION array, dimension (NMAX*2) *> \endverbatim *> *> \param[out] E *> \verbatim *> E is DOUBLE PRECISION array, dimension (NMAX*2) *> \endverbatim *> *> \param[out] B *> \verbatim *> B is DOUBLE PRECISION array, dimension (NMAX*NRHS) *> \endverbatim *> *> \param[out] X *> \verbatim *> X is DOUBLE PRECISION array, dimension (NMAX*NRHS) *> \endverbatim *> *> \param[out] XACT *> \verbatim *> XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS) *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension *> (NMAX*max(3,NRHS)) *> \endverbatim *> *> \param[out] RWORK *> \verbatim *> RWORK is DOUBLE PRECISION array, dimension *> (max(NMAX,2*NRHS)) *> \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 double_lin * * ===================================================================== SUBROUTINE DDRVPT( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, D, $ E, 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 NN, NOUT, NRHS DOUBLE PRECISION THRESH * .. * .. Array Arguments .. LOGICAL DOTYPE( * ) INTEGER NVAL( * ) DOUBLE PRECISION A( * ), B( * ), D( * ), E( * ), RWORK( * ), $ WORK( * ), X( * ), XACT( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) INTEGER NTYPES PARAMETER ( NTYPES = 12 ) INTEGER NTESTS PARAMETER ( NTESTS = 6 ) * .. * .. Local Scalars .. LOGICAL ZEROT CHARACTER DIST, FACT, TYPE CHARACTER*3 PATH INTEGER I, IA, IFACT, IMAT, IN, INFO, IX, IZERO, J, K, $ K1, KL, KU, LDA, MODE, N, NERRS, NFAIL, NIMAT, $ NRUN, NT DOUBLE PRECISION AINVNM, ANORM, COND, DMAX, RCOND, RCONDC * .. * .. Local Arrays .. INTEGER ISEED( 4 ), ISEEDY( 4 ) DOUBLE PRECISION RESULT( NTESTS ), Z( 3 ) * .. * .. External Functions .. INTEGER IDAMAX DOUBLE PRECISION DASUM, DGET06, DLANST EXTERNAL IDAMAX, DASUM, DGET06, DLANST * .. * .. External Subroutines .. EXTERNAL ALADHD, ALAERH, ALASVM, DCOPY, DERRVX, DGET04, $ DLACPY, DLAPTM, DLARNV, DLASET, DLATB4, DLATMS, $ DPTSV, DPTSVX, DPTT01, DPTT02, DPTT05, DPTTRF, $ DPTTRS, DSCAL * .. * .. Intrinsic Functions .. INTRINSIC ABS, 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 / 0, 0, 0, 1 / * .. * .. Executable Statements .. * PATH( 1: 1 ) = 'Double precision' PATH( 2: 3 ) = 'PT' NRUN = 0 NFAIL = 0 NERRS = 0 DO 10 I = 1, 4 ISEED( I ) = ISEEDY( I ) 10 CONTINUE * * Test the error exits * IF( TSTERR ) $ CALL DERRVX( PATH, NOUT ) INFOT = 0 * DO 120 IN = 1, NN * * Do for each value of N in NVAL. * N = NVAL( IN ) LDA = MAX( 1, N ) NIMAT = NTYPES IF( N.LE.0 ) $ NIMAT = 1 * DO 110 IMAT = 1, NIMAT * * Do the tests only if DOTYPE( IMAT ) is true. * IF( N.GT.0 .AND. .NOT.DOTYPE( IMAT ) ) $ GO TO 110 * * Set up parameters with DLATB4. * CALL DLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM, MODE, $ COND, DIST ) * ZEROT = IMAT.GE.8 .AND. IMAT.LE.10 IF( IMAT.LE.6 ) THEN * * Type 1-6: generate a symmetric tridiagonal matrix of * known condition number in lower triangular band storage. * SRNAMT = 'DLATMS' CALL DLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE, COND, $ ANORM, KL, KU, 'B', A, 2, WORK, INFO ) * * Check the error code from DLATMS. * IF( INFO.NE.0 ) THEN CALL ALAERH( PATH, 'DLATMS', INFO, 0, ' ', N, N, KL, $ KU, -1, IMAT, NFAIL, NERRS, NOUT ) GO TO 110 END IF IZERO = 0 * * Copy the matrix to D and E. * IA = 1 DO 20 I = 1, N - 1 D( I ) = A( IA ) E( I ) = A( IA+1 ) IA = IA + 2 20 CONTINUE IF( N.GT.0 ) $ D( N ) = A( IA ) ELSE * * Type 7-12: generate a diagonally dominant matrix with * unknown condition number in the vectors D and E. * IF( .NOT.ZEROT .OR. .NOT.DOTYPE( 7 ) ) THEN * * Let D and E have values from [-1,1]. * CALL DLARNV( 2, ISEED, N, D ) CALL DLARNV( 2, ISEED, N-1, E ) * * Make the tridiagonal matrix diagonally dominant. * IF( N.EQ.1 ) THEN D( 1 ) = ABS( D( 1 ) ) ELSE D( 1 ) = ABS( D( 1 ) ) + ABS( E( 1 ) ) D( N ) = ABS( D( N ) ) + ABS( E( N-1 ) ) DO 30 I = 2, N - 1 D( I ) = ABS( D( I ) ) + ABS( E( I ) ) + $ ABS( E( I-1 ) ) 30 CONTINUE END IF * * Scale D and E so the maximum element is ANORM. * IX = IDAMAX( N, D, 1 ) DMAX = D( IX ) CALL DSCAL( N, ANORM / DMAX, D, 1 ) IF( N.GT.1 ) $ CALL DSCAL( N-1, ANORM / DMAX, E, 1 ) * ELSE IF( IZERO.GT.0 ) THEN * * Reuse the last matrix by copying back the zeroed out * elements. * IF( IZERO.EQ.1 ) THEN D( 1 ) = Z( 2 ) IF( N.GT.1 ) $ E( 1 ) = Z( 3 ) ELSE IF( IZERO.EQ.N ) THEN E( N-1 ) = Z( 1 ) D( N ) = Z( 2 ) ELSE E( IZERO-1 ) = Z( 1 ) D( IZERO ) = Z( 2 ) E( IZERO ) = Z( 3 ) END IF END IF * * For types 8-10, set one row and column of the matrix to * zero. * IZERO = 0 IF( IMAT.EQ.8 ) THEN IZERO = 1 Z( 2 ) = D( 1 ) D( 1 ) = ZERO IF( N.GT.1 ) THEN Z( 3 ) = E( 1 ) E( 1 ) = ZERO END IF ELSE IF( IMAT.EQ.9 ) THEN IZERO = N IF( N.GT.1 ) THEN Z( 1 ) = E( N-1 ) E( N-1 ) = ZERO END IF Z( 2 ) = D( N ) D( N ) = ZERO ELSE IF( IMAT.EQ.10 ) THEN IZERO = ( N+1 ) / 2 IF( IZERO.GT.1 ) THEN Z( 1 ) = E( IZERO-1 ) Z( 3 ) = E( IZERO ) E( IZERO-1 ) = ZERO E( IZERO ) = ZERO END IF Z( 2 ) = D( IZERO ) D( IZERO ) = ZERO END IF END IF * * Generate NRHS random solution vectors. * IX = 1 DO 40 J = 1, NRHS CALL DLARNV( 2, ISEED, N, XACT( IX ) ) IX = IX + LDA 40 CONTINUE * * Set the right hand side. * CALL DLAPTM( N, NRHS, ONE, D, E, XACT, LDA, ZERO, B, LDA ) * DO 100 IFACT = 1, 2 IF( IFACT.EQ.1 ) THEN FACT = 'F' ELSE FACT = 'N' END IF * * Compute the condition number for comparison with * the value returned by DPTSVX. * IF( ZEROT ) THEN IF( IFACT.EQ.1 ) $ GO TO 100 RCONDC = ZERO * ELSE IF( IFACT.EQ.1 ) THEN * * Compute the 1-norm of A. * ANORM = DLANST( '1', N, D, E ) * CALL DCOPY( N, D, 1, D( N+1 ), 1 ) IF( N.GT.1 ) $ CALL DCOPY( N-1, E, 1, E( N+1 ), 1 ) * * Factor the matrix A. * CALL DPTTRF( N, D( N+1 ), E( N+1 ), INFO ) * * Use DPTTRS to solve for one column at a time of * inv(A), computing the maximum column sum as we go. * AINVNM = ZERO DO 60 I = 1, N DO 50 J = 1, N X( J ) = ZERO 50 CONTINUE X( I ) = ONE CALL DPTTRS( N, 1, D( N+1 ), E( N+1 ), X, LDA, $ INFO ) AINVNM = MAX( AINVNM, DASUM( N, X, 1 ) ) 60 CONTINUE * * Compute the 1-norm condition number of A. * IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN RCONDC = ONE ELSE RCONDC = ( ONE / ANORM ) / AINVNM END IF END IF * IF( IFACT.EQ.2 ) THEN * * --- Test DPTSV -- * CALL DCOPY( N, D, 1, D( N+1 ), 1 ) IF( N.GT.1 ) $ CALL DCOPY( N-1, E, 1, E( N+1 ), 1 ) CALL DLACPY( 'Full', N, NRHS, B, LDA, X, LDA ) * * Factor A as L*D*L' and solve the system A*X = B. * SRNAMT = 'DPTSV ' CALL DPTSV( N, NRHS, D( N+1 ), E( N+1 ), X, LDA, $ INFO ) * * Check error code from DPTSV . * IF( INFO.NE.IZERO ) $ CALL ALAERH( PATH, 'DPTSV ', INFO, IZERO, ' ', N, $ N, 1, 1, NRHS, IMAT, NFAIL, NERRS, $ NOUT ) NT = 0 IF( IZERO.EQ.0 ) THEN * * Check the factorization by computing the ratio * norm(L*D*L' - A) / (n * norm(A) * EPS ) * CALL DPTT01( N, D, E, D( N+1 ), E( N+1 ), WORK, $ RESULT( 1 ) ) * * Compute the residual in the solution. * CALL DLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA ) CALL DPTT02( N, NRHS, D, E, X, LDA, WORK, LDA, $ RESULT( 2 ) ) * * Check solution from generated exact solution. * CALL DGET04( 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 70 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 )'DPTSV ', N, IMAT, K, $ RESULT( K ) NFAIL = NFAIL + 1 END IF 70 CONTINUE NRUN = NRUN + NT END IF * * --- Test DPTSVX --- * IF( IFACT.GT.1 ) THEN * * Initialize D( N+1:2*N ) and E( N+1:2*N ) to zero. * DO 80 I = 1, N - 1 D( N+I ) = ZERO E( N+I ) = ZERO 80 CONTINUE IF( N.GT.0 ) $ D( N+N ) = ZERO END IF * CALL DLASET( 'Full', N, NRHS, ZERO, ZERO, X, LDA ) * * Solve the system and compute the condition number and * error bounds using DPTSVX. * SRNAMT = 'DPTSVX' CALL DPTSVX( FACT, N, NRHS, D, E, D( N+1 ), E( N+1 ), B, $ LDA, X, LDA, RCOND, RWORK, RWORK( NRHS+1 ), $ WORK, INFO ) * * Check the error code from DPTSVX. * IF( INFO.NE.IZERO ) $ CALL ALAERH( PATH, 'DPTSVX', INFO, IZERO, FACT, N, N, $ 1, 1, NRHS, IMAT, NFAIL, NERRS, NOUT ) IF( IZERO.EQ.0 ) THEN IF( IFACT.EQ.2 ) THEN * * Check the factorization by computing the ratio * norm(L*D*L' - A) / (n * norm(A) * EPS ) * K1 = 1 CALL DPTT01( N, D, E, D( N+1 ), E( N+1 ), WORK, $ RESULT( 1 ) ) ELSE K1 = 2 END IF * * Compute the residual in the solution. * CALL DLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA ) CALL DPTT02( N, NRHS, D, E, X, LDA, WORK, LDA, $ RESULT( 2 ) ) * * Check solution from generated exact solution. * CALL DGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC, $ RESULT( 3 ) ) * * Check error bounds from iterative refinement. * CALL DPTT05( N, NRHS, D, E, B, LDA, X, LDA, XACT, LDA, $ RWORK, RWORK( NRHS+1 ), RESULT( 4 ) ) ELSE K1 = 6 END IF * * Check the reciprocal of the condition number. * RESULT( 6 ) = DGET06( RCOND, RCONDC ) * * Print information about the tests that did not pass * the threshold. * DO 90 K = K1, 6 IF( RESULT( K ).GE.THRESH ) THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) $ CALL ALADHD( NOUT, PATH ) WRITE( NOUT, FMT = 9998 )'DPTSVX', FACT, N, IMAT, $ K, RESULT( K ) NFAIL = NFAIL + 1 END IF 90 CONTINUE NRUN = NRUN + 7 - K1 100 CONTINUE 110 CONTINUE 120 CONTINUE * * Print a summary of the results. * CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS ) * 9999 FORMAT( 1X, A, ', N =', I5, ', type ', I2, ', test ', I2, $ ', ratio = ', G12.5 ) 9998 FORMAT( 1X, A, ', FACT=''', A1, ''', N =', I5, ', type ', I2, $ ', test ', I2, ', ratio = ', G12.5 ) RETURN * * End of DDRVPT * END