*> \brief \b ZDRVGT * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE ZDRVGT( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, AF, * B, X, XACT, WORK, RWORK, IWORK, NOUT ) * * .. Scalar Arguments .. * LOGICAL TSTERR * INTEGER NN, NOUT, NRHS * DOUBLE PRECISION THRESH * .. * .. Array Arguments .. * LOGICAL DOTYPE( * ) * INTEGER IWORK( * ), NVAL( * ) * DOUBLE PRECISION RWORK( * ) * COMPLEX*16 A( * ), AF( * ), B( * ), WORK( * ), X( * ), * \$ XACT( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZDRVGT tests ZGTSV 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 sides, NRHS >= 0. *> \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 COMPLEX*16 array, dimension (NMAX*4) *> \endverbatim *> *> \param[out] AF *> \verbatim *> AF is COMPLEX*16 array, dimension (NMAX*4) *> \endverbatim *> *> \param[out] B *> \verbatim *> B is COMPLEX*16 array, dimension (NMAX*NRHS) *> \endverbatim *> *> \param[out] X *> \verbatim *> X is COMPLEX*16 array, dimension (NMAX*NRHS) *> \endverbatim *> *> \param[out] XACT *> \verbatim *> XACT is COMPLEX*16 array, dimension (NMAX*NRHS) *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension *> (NMAX*max(3,NRHS)) *> \endverbatim *> *> \param[out] RWORK *> \verbatim *> RWORK is DOUBLE PRECISION array, dimension (NMAX+2*NRHS) *> \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 complex16_lin * * ===================================================================== SUBROUTINE ZDRVGT( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, AF, \$ 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 NN, NOUT, NRHS DOUBLE PRECISION THRESH * .. * .. Array Arguments .. LOGICAL DOTYPE( * ) INTEGER IWORK( * ), NVAL( * ) DOUBLE PRECISION RWORK( * ) COMPLEX*16 A( * ), AF( * ), B( * ), 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 TRFCON, ZEROT CHARACTER DIST, FACT, TRANS, TYPE CHARACTER*3 PATH INTEGER I, IFACT, IMAT, IN, INFO, ITRAN, IX, IZERO, J, \$ K, K1, KL, KOFF, KU, LDA, M, MODE, N, NERRS, \$ NFAIL, NIMAT, NRUN, NT DOUBLE PRECISION AINVNM, ANORM, ANORMI, ANORMO, COND, RCOND, \$ RCONDC, RCONDI, RCONDO * .. * .. Local Arrays .. CHARACTER TRANSS( 3 ) INTEGER ISEED( 4 ), ISEEDY( 4 ) DOUBLE PRECISION RESULT( NTESTS ), Z( 3 ) * .. * .. External Functions .. DOUBLE PRECISION DGET06, DZASUM, ZLANGT EXTERNAL DGET06, DZASUM, ZLANGT * .. * .. External Subroutines .. EXTERNAL ALADHD, ALAERH, ALASVM, ZCOPY, ZDSCAL, ZERRVX, \$ ZGET04, ZGTSV, ZGTSVX, ZGTT01, ZGTT02, ZGTT05, \$ ZGTTRF, ZGTTRS, ZLACPY, ZLAGTM, ZLARNV, ZLASET, \$ ZLATB4, ZLATMS * .. * .. Intrinsic Functions .. INTRINSIC DCMPLX, 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 / , TRANSS / 'N', 'T', \$ 'C' / * .. * .. Executable Statements .. * PATH( 1: 1 ) = 'Zomplex precision' PATH( 2: 3 ) = 'GT' NRUN = 0 NFAIL = 0 NERRS = 0 DO 10 I = 1, 4 ISEED( I ) = ISEEDY( I ) 10 CONTINUE * * Test the error exits * IF( TSTERR ) \$ CALL ZERRVX( PATH, NOUT ) INFOT = 0 * DO 140 IN = 1, NN * * Do for each value of N in NVAL. * N = NVAL( IN ) M = MAX( N-1, 0 ) LDA = MAX( 1, N ) NIMAT = NTYPES IF( N.LE.0 ) \$ NIMAT = 1 * DO 130 IMAT = 1, NIMAT * * Do the tests only if DOTYPE( IMAT ) is true. * IF( .NOT.DOTYPE( IMAT ) ) \$ GO TO 130 * * Set up parameters with ZLATB4. * CALL ZLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM, MODE, \$ COND, DIST ) * ZEROT = IMAT.GE.8 .AND. IMAT.LE.10 IF( IMAT.LE.6 ) THEN * * Types 1-6: generate matrices of known condition number. * KOFF = MAX( 2-KU, 3-MAX( 1, N ) ) SRNAMT = 'ZLATMS' CALL ZLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE, COND, \$ ANORM, KL, KU, 'Z', AF( KOFF ), 3, WORK, \$ INFO ) * * Check the error code from ZLATMS. * IF( INFO.NE.0 ) THEN CALL ALAERH( PATH, 'ZLATMS', INFO, 0, ' ', N, N, KL, \$ KU, -1, IMAT, NFAIL, NERRS, NOUT ) GO TO 130 END IF IZERO = 0 * IF( N.GT.1 ) THEN CALL ZCOPY( N-1, AF( 4 ), 3, A, 1 ) CALL ZCOPY( N-1, AF( 3 ), 3, A( N+M+1 ), 1 ) END IF CALL ZCOPY( N, AF( 2 ), 3, A( M+1 ), 1 ) ELSE * * Types 7-12: generate tridiagonal matrices with * unknown condition numbers. * IF( .NOT.ZEROT .OR. .NOT.DOTYPE( 7 ) ) THEN * * Generate a matrix with elements from [-1,1]. * CALL ZLARNV( 2, ISEED, N+2*M, A ) IF( ANORM.NE.ONE ) \$ CALL ZDSCAL( N+2*M, ANORM, A, 1 ) ELSE IF( IZERO.GT.0 ) THEN * * Reuse the last matrix by copying back the zeroed out * elements. * IF( IZERO.EQ.1 ) THEN A( N ) = Z( 2 ) IF( N.GT.1 ) \$ A( 1 ) = Z( 3 ) ELSE IF( IZERO.EQ.N ) THEN A( 3*N-2 ) = Z( 1 ) A( 2*N-1 ) = Z( 2 ) ELSE A( 2*N-2+IZERO ) = Z( 1 ) A( N-1+IZERO ) = Z( 2 ) A( IZERO ) = Z( 3 ) END IF END IF * * If IMAT > 7, set one column of the matrix to 0. * IF( .NOT.ZEROT ) THEN IZERO = 0 ELSE IF( IMAT.EQ.8 ) THEN IZERO = 1 Z( 2 ) = A( N ) A( N ) = ZERO IF( N.GT.1 ) THEN Z( 3 ) = A( 1 ) A( 1 ) = ZERO END IF ELSE IF( IMAT.EQ.9 ) THEN IZERO = N Z( 1 ) = A( 3*N-2 ) Z( 2 ) = A( 2*N-1 ) A( 3*N-2 ) = ZERO A( 2*N-1 ) = ZERO ELSE IZERO = ( N+1 ) / 2 DO 20 I = IZERO, N - 1 A( 2*N-2+I ) = ZERO A( N-1+I ) = ZERO A( I ) = ZERO 20 CONTINUE A( 3*N-2 ) = ZERO A( 2*N-1 ) = ZERO END IF END IF * DO 120 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 ZGTSVX. * IF( ZEROT ) THEN IF( IFACT.EQ.1 ) \$ GO TO 120 RCONDO = ZERO RCONDI = ZERO * ELSE IF( IFACT.EQ.1 ) THEN CALL ZCOPY( N+2*M, A, 1, AF, 1 ) * * Compute the 1-norm and infinity-norm of A. * ANORMO = ZLANGT( '1', N, A, A( M+1 ), A( N+M+1 ) ) ANORMI = ZLANGT( 'I', N, A, A( M+1 ), A( N+M+1 ) ) * * Factor the matrix A. * CALL ZGTTRF( N, AF, AF( M+1 ), AF( N+M+1 ), \$ AF( N+2*M+1 ), IWORK, INFO ) * * Use ZGTTRS to solve for one column at a time of * inv(A), computing the maximum column sum as we go. * AINVNM = ZERO DO 40 I = 1, N DO 30 J = 1, N X( J ) = ZERO 30 CONTINUE X( I ) = ONE CALL ZGTTRS( 'No transpose', N, 1, AF, AF( M+1 ), \$ AF( N+M+1 ), AF( N+2*M+1 ), IWORK, X, \$ LDA, INFO ) AINVNM = MAX( AINVNM, DZASUM( N, X, 1 ) ) 40 CONTINUE * * Compute the 1-norm condition number of A. * IF( ANORMO.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN RCONDO = ONE ELSE RCONDO = ( ONE / ANORMO ) / AINVNM END IF * * Use ZGTTRS 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 ZGTTRS( 'Conjugate transpose', N, 1, AF, \$ AF( M+1 ), AF( N+M+1 ), AF( N+2*M+1 ), \$ IWORK, X, LDA, INFO ) AINVNM = MAX( AINVNM, DZASUM( N, X, 1 ) ) 60 CONTINUE * * Compute the infinity-norm condition number of A. * IF( ANORMI.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN RCONDI = ONE ELSE RCONDI = ( ONE / ANORMI ) / AINVNM END IF END IF * DO 110 ITRAN = 1, 3 TRANS = TRANSS( ITRAN ) IF( ITRAN.EQ.1 ) THEN RCONDC = RCONDO ELSE RCONDC = RCONDI END IF * * Generate NRHS random solution vectors. * IX = 1 DO 70 J = 1, NRHS CALL ZLARNV( 2, ISEED, N, XACT( IX ) ) IX = IX + LDA 70 CONTINUE * * Set the right hand side. * CALL ZLAGTM( TRANS, N, NRHS, ONE, A, A( M+1 ), \$ A( N+M+1 ), XACT, LDA, ZERO, B, LDA ) * IF( IFACT.EQ.2 .AND. ITRAN.EQ.1 ) THEN * * --- Test ZGTSV --- * * Solve the system using Gaussian elimination with * partial pivoting. * CALL ZCOPY( N+2*M, A, 1, AF, 1 ) CALL ZLACPY( 'Full', N, NRHS, B, LDA, X, LDA ) * SRNAMT = 'ZGTSV ' CALL ZGTSV( N, NRHS, AF, AF( M+1 ), AF( N+M+1 ), X, \$ LDA, INFO ) * * Check error code from ZGTSV . * IF( INFO.NE.IZERO ) \$ CALL ALAERH( PATH, 'ZGTSV ', INFO, IZERO, ' ', \$ N, N, 1, 1, NRHS, IMAT, NFAIL, \$ NERRS, NOUT ) NT = 1 IF( IZERO.EQ.0 ) THEN * * Check residual of computed solution. * CALL ZLACPY( 'Full', N, NRHS, B, LDA, WORK, \$ LDA ) CALL ZGTT02( TRANS, N, NRHS, A, A( M+1 ), \$ A( N+M+1 ), X, LDA, WORK, LDA, \$ RESULT( 2 ) ) * * Check solution from generated exact solution. * CALL ZGET04( 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 80 K = 2, NT IF( RESULT( K ).GE.THRESH ) THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) \$ CALL ALADHD( NOUT, PATH ) WRITE( NOUT, FMT = 9999 )'ZGTSV ', N, IMAT, \$ K, RESULT( K ) NFAIL = NFAIL + 1 END IF 80 CONTINUE NRUN = NRUN + NT - 1 END IF * * --- Test ZGTSVX --- * IF( IFACT.GT.1 ) THEN * * Initialize AF to zero. * DO 90 I = 1, 3*N - 2 AF( I ) = ZERO 90 CONTINUE END IF CALL ZLASET( 'Full', N, NRHS, DCMPLX( ZERO ), \$ DCMPLX( ZERO ), X, LDA ) * * Solve the system and compute the condition number and * error bounds using ZGTSVX. * SRNAMT = 'ZGTSVX' CALL ZGTSVX( FACT, TRANS, N, NRHS, A, A( M+1 ), \$ A( N+M+1 ), AF, AF( M+1 ), AF( N+M+1 ), \$ AF( N+2*M+1 ), IWORK, B, LDA, X, LDA, \$ RCOND, RWORK, RWORK( NRHS+1 ), WORK, \$ RWORK( 2*NRHS+1 ), INFO ) * * Check the error code from ZGTSVX. * IF( INFO.NE.IZERO ) \$ CALL ALAERH( PATH, 'ZGTSVX', INFO, IZERO, \$ FACT // TRANS, N, N, 1, 1, NRHS, IMAT, \$ NFAIL, NERRS, NOUT ) * IF( IFACT.GE.2 ) THEN * * Reconstruct matrix from factors and compute * residual. * CALL ZGTT01( N, A, A( M+1 ), A( N+M+1 ), AF, \$ AF( M+1 ), AF( N+M+1 ), AF( N+2*M+1 ), \$ IWORK, WORK, LDA, RWORK, RESULT( 1 ) ) K1 = 1 ELSE K1 = 2 END IF * IF( INFO.EQ.0 ) THEN TRFCON = .FALSE. * * Check residual of computed solution. * CALL ZLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA ) CALL ZGTT02( TRANS, N, NRHS, A, A( M+1 ), \$ A( N+M+1 ), X, LDA, WORK, LDA, \$ RESULT( 2 ) ) * * Check solution from generated exact solution. * CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC, \$ RESULT( 3 ) ) * * Check the error bounds from iterative refinement. * CALL ZGTT05( TRANS, N, NRHS, A, A( M+1 ), \$ A( N+M+1 ), B, LDA, X, LDA, XACT, LDA, \$ RWORK, RWORK( NRHS+1 ), RESULT( 4 ) ) NT = 5 END IF * * Print information about the tests that did not pass * the threshold. * DO 100 K = K1, NT IF( RESULT( K ).GE.THRESH ) THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) \$ CALL ALADHD( NOUT, PATH ) WRITE( NOUT, FMT = 9998 )'ZGTSVX', FACT, TRANS, \$ N, IMAT, K, RESULT( K ) NFAIL = NFAIL + 1 END IF 100 CONTINUE * * Check the reciprocal of the condition number. * RESULT( 6 ) = DGET06( RCOND, RCONDC ) IF( RESULT( 6 ).GE.THRESH ) THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) \$ CALL ALADHD( NOUT, PATH ) WRITE( NOUT, FMT = 9998 )'ZGTSVX', FACT, TRANS, N, \$ IMAT, K, RESULT( K ) NFAIL = NFAIL + 1 END IF NRUN = NRUN + NT - K1 + 2 * 110 CONTINUE 120 CONTINUE 130 CONTINUE 140 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, ''', TRANS=''', A1, ''', N =', \$ I5, ', type ', I2, ', test ', I2, ', ratio = ', G12.5 ) RETURN * * End of ZDRVGT * END