SUBROUTINE ZCHKGE( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NNS, \$ NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, \$ X, XACT, WORK, RWORK, IWORK, NOUT ) * * -- LAPACK test routine (version 3.1.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * January 2007 * * .. Scalar Arguments .. LOGICAL TSTERR INTEGER NM, NMAX, NN, NNB, NNS, NOUT DOUBLE PRECISION THRESH * .. * .. Array Arguments .. LOGICAL DOTYPE( * ) INTEGER IWORK( * ), MVAL( * ), NBVAL( * ), NSVAL( * ), \$ NVAL( * ) DOUBLE PRECISION RWORK( * ) COMPLEX*16 A( * ), AFAC( * ), AINV( * ), B( * ), \$ WORK( * ), X( * ), XACT( * ) * .. * * Purpose * ======= * * ZCHKGE tests ZGETRF, -TRI, -TRS, -RFS, and -CON. * * Arguments * ========= * * DOTYPE (input) 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. * * NM (input) INTEGER * The number of values of M contained in the vector MVAL. * * MVAL (input) INTEGER array, dimension (NM) * The values of the matrix row dimension M. * * NN (input) INTEGER * The number of values of N contained in the vector NVAL. * * NVAL (input) INTEGER array, dimension (NN) * The values of the matrix column dimension N. * * NNB (input) INTEGER * The number of values of NB contained in the vector NBVAL. * * NBVAL (input) INTEGER array, dimension (NBVAL) * The values of the blocksize NB. * * NNS (input) INTEGER * The number of values of NRHS contained in the vector NSVAL. * * NSVAL (input) INTEGER array, dimension (NNS) * The values of the number of right hand sides NRHS. * * NRHS (input) INTEGER * The number of right hand side vectors to be generated for * each linear system. * * THRESH (input) 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. * * TSTERR (input) LOGICAL * Flag that indicates whether error exits are to be tested. * * NMAX (input) INTEGER * The maximum value permitted for M or N, used in dimensioning * the work arrays. * * A (workspace) COMPLEX*16 array, dimension (NMAX*NMAX) * * AFAC (workspace) COMPLEX*16 array, dimension (NMAX*NMAX) * * AINV (workspace) COMPLEX*16 array, dimension (NMAX*NMAX) * * B (workspace) COMPLEX*16 array, dimension (NMAX*NSMAX) * where NSMAX is the largest entry in NSVAL. * * X (workspace) COMPLEX*16 array, dimension (NMAX*NSMAX) * * XACT (workspace) COMPLEX*16 array, dimension (NMAX*NSMAX) * * WORK (workspace) COMPLEX*16 array, dimension * (NMAX*max(3,NSMAX)) * * RWORK (workspace) DOUBLE PRECISION array, dimension * (max(2*NMAX,2*NSMAX+NWORK)) * * IWORK (workspace) INTEGER array, dimension (NMAX) * * NOUT (input) INTEGER * The unit number for output. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) INTEGER NTYPES PARAMETER ( NTYPES = 11 ) INTEGER NTESTS PARAMETER ( NTESTS = 8 ) INTEGER NTRAN PARAMETER ( NTRAN = 3 ) * .. * .. Local Scalars .. LOGICAL TRFCON, ZEROT CHARACTER DIST, NORM, TRANS, TYPE, XTYPE CHARACTER*3 PATH INTEGER I, IM, IMAT, IN, INB, INFO, IOFF, IRHS, ITRAN, \$ IZERO, K, KL, KU, LDA, LWORK, M, MODE, N, NB, \$ NERRS, NFAIL, NIMAT, NRHS, NRUN, NT DOUBLE PRECISION AINVNM, ANORM, ANORMI, ANORMO, CNDNUM, DUMMY, \$ RCOND, RCONDC, RCONDI, RCONDO * .. * .. Local Arrays .. CHARACTER TRANSS( NTRAN ) INTEGER ISEED( 4 ), ISEEDY( 4 ) DOUBLE PRECISION RESULT( NTESTS ) * .. * .. External Functions .. DOUBLE PRECISION DGET06, ZLANGE EXTERNAL DGET06, ZLANGE * .. * .. External Subroutines .. EXTERNAL ALAERH, ALAHD, ALASUM, XLAENV, ZERRGE, ZGECON, \$ ZGERFS, ZGET01, ZGET02, ZGET03, ZGET04, ZGET07, \$ ZGETRF, ZGETRI, ZGETRS, ZLACPY, ZLARHS, ZLASET, \$ ZLATB4, ZLATMS * .. * .. Intrinsic Functions .. INTRINSIC DCMPLX, 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 ) = 'Zomplex 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 * CALL XLAENV( 1, 1 ) IF( TSTERR ) \$ CALL ZERRGE( PATH, NOUT ) INFOT = 0 CALL XLAENV( 2, 2 ) * * Do for each value of M in MVAL * DO 120 IM = 1, NM M = MVAL( IM ) LDA = MAX( 1, M ) * * Do for each value of N in NVAL * DO 110 IN = 1, NN N = NVAL( IN ) XTYPE = 'N' NIMAT = NTYPES IF( M.LE.0 .OR. N.LE.0 ) \$ NIMAT = 1 * DO 100 IMAT = 1, NIMAT * * Do the tests only if DOTYPE( IMAT ) is true. * IF( .NOT.DOTYPE( IMAT ) ) \$ GO TO 100 * * 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 100 * * Set up parameters with ZLATB4 and generate a test matrix * with ZLATMS. * CALL ZLATB4( PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE, \$ CNDNUM, DIST ) * SRNAMT = 'ZLATMS' CALL ZLATMS( M, N, DIST, ISEED, TYPE, RWORK, MODE, \$ CNDNUM, ANORM, KL, KU, 'No packing', A, LDA, \$ WORK, INFO ) * * Check error code from ZLATMS. * IF( INFO.NE.0 ) THEN CALL ALAERH( PATH, 'ZLATMS', INFO, 0, ' ', M, N, -1, \$ -1, -1, IMAT, NFAIL, NERRS, NOUT ) GO TO 100 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 = MIN( M, N ) ELSE IZERO = MIN( M, N ) / 2 + 1 END IF IOFF = ( IZERO-1 )*LDA IF( IMAT.LT.7 ) THEN DO 20 I = 1, M A( IOFF+I ) = ZERO 20 CONTINUE ELSE CALL ZLASET( 'Full', M, N-IZERO+1, DCMPLX( ZERO ), \$ DCMPLX( ZERO ), A( IOFF+1 ), LDA ) END IF ELSE IZERO = 0 END IF * * These lines, if used in place of the calls in the DO 60 * loop, cause the code to bomb on a Sun SPARCstation. * * ANORMO = ZLANGE( 'O', M, N, A, LDA, RWORK ) * ANORMI = ZLANGE( 'I', M, N, A, LDA, RWORK ) * * Do for each blocksize in NBVAL * DO 90 INB = 1, NNB NB = NBVAL( INB ) CALL XLAENV( 1, NB ) * * Compute the LU factorization of the matrix. * CALL ZLACPY( 'Full', M, N, A, LDA, AFAC, LDA ) SRNAMT = 'ZGETRF' CALL ZGETRF( M, N, AFAC, LDA, IWORK, INFO ) * * Check error code from ZGETRF. * IF( INFO.NE.IZERO ) \$ CALL ALAERH( PATH, 'ZGETRF', INFO, IZERO, ' ', M, \$ N, -1, -1, NB, IMAT, NFAIL, NERRS, \$ NOUT ) TRFCON = .FALSE. * *+ TEST 1 * Reconstruct matrix from factors and compute residual. * CALL ZLACPY( 'Full', M, N, AFAC, LDA, AINV, LDA ) CALL ZGET01( M, N, A, LDA, AINV, LDA, IWORK, RWORK, \$ RESULT( 1 ) ) NT = 1 * *+ TEST 2 * Form the inverse if the factorization was successful * and compute the residual. * IF( M.EQ.N .AND. INFO.EQ.0 ) THEN CALL ZLACPY( 'Full', N, N, AFAC, LDA, AINV, LDA ) SRNAMT = 'ZGETRI' NRHS = NSVAL( 1 ) LWORK = NMAX*MAX( 3, NRHS ) CALL ZGETRI( N, AINV, LDA, IWORK, WORK, LWORK, \$ INFO ) * * Check error code from ZGETRI. * IF( INFO.NE.0 ) \$ CALL ALAERH( PATH, 'ZGETRI', INFO, 0, ' ', N, N, \$ -1, -1, NB, IMAT, NFAIL, NERRS, \$ NOUT ) * * Compute the residual for the matrix times its * inverse. Also compute the 1-norm condition number * of A. * CALL ZGET03( N, A, LDA, AINV, LDA, WORK, LDA, \$ RWORK, RCONDO, RESULT( 2 ) ) ANORMO = ZLANGE( 'O', M, N, A, LDA, RWORK ) * * Compute the infinity-norm condition number of A. * ANORMI = ZLANGE( 'I', M, N, A, LDA, RWORK ) AINVNM = ZLANGE( 'I', N, N, AINV, LDA, RWORK ) IF( ANORMI.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN RCONDI = ONE ELSE RCONDI = ( ONE / ANORMI ) / AINVNM END IF NT = 2 ELSE * * Do only the condition estimate if INFO > 0. * TRFCON = .TRUE. ANORMO = ZLANGE( 'O', M, N, A, LDA, RWORK ) ANORMI = ZLANGE( 'I', M, N, A, LDA, RWORK ) RCONDO = ZERO RCONDI = ZERO END IF * * Print information about the tests so far 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 ALAHD( NOUT, PATH ) WRITE( NOUT, FMT = 9999 )M, N, NB, IMAT, K, \$ RESULT( K ) NFAIL = NFAIL + 1 END IF 30 CONTINUE NRUN = NRUN + NT * * Skip the remaining tests if this is not the first * block size or if M .ne. N. Skip the solve tests if * the matrix is singular. * IF( INB.GT.1 .OR. M.NE.N ) \$ GO TO 90 IF( TRFCON ) \$ GO TO 70 * DO 60 IRHS = 1, NNS NRHS = NSVAL( IRHS ) XTYPE = 'N' * DO 50 ITRAN = 1, NTRAN TRANS = TRANSS( ITRAN ) IF( ITRAN.EQ.1 ) THEN RCONDC = RCONDO ELSE RCONDC = RCONDI END IF * *+ TEST 3 * Solve and compute residual for A * X = B. * SRNAMT = 'ZLARHS' CALL ZLARHS( PATH, XTYPE, ' ', TRANS, N, N, KL, \$ KU, NRHS, A, LDA, XACT, LDA, B, \$ LDA, ISEED, INFO ) XTYPE = 'C' * CALL ZLACPY( 'Full', N, NRHS, B, LDA, X, LDA ) SRNAMT = 'ZGETRS' CALL ZGETRS( TRANS, N, NRHS, AFAC, LDA, IWORK, \$ X, LDA, INFO ) * * Check error code from ZGETRS. * IF( INFO.NE.0 ) \$ CALL ALAERH( PATH, 'ZGETRS', INFO, 0, TRANS, \$ N, N, -1, -1, NRHS, IMAT, NFAIL, \$ NERRS, NOUT ) * CALL ZLACPY( 'Full', N, NRHS, B, LDA, WORK, \$ LDA ) CALL ZGET02( TRANS, N, N, NRHS, A, LDA, X, LDA, \$ WORK, LDA, RWORK, RESULT( 3 ) ) * *+ TEST 4 * Check solution from generated exact solution. * CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC, \$ RESULT( 4 ) ) * *+ TESTS 5, 6, and 7 * Use iterative refinement to improve the * solution. * SRNAMT = 'ZGERFS' CALL ZGERFS( TRANS, N, NRHS, A, LDA, AFAC, LDA, \$ IWORK, B, LDA, X, LDA, RWORK, \$ RWORK( NRHS+1 ), WORK, \$ RWORK( 2*NRHS+1 ), INFO ) * * Check error code from ZGERFS. * IF( INFO.NE.0 ) \$ CALL ALAERH( PATH, 'ZGERFS', INFO, 0, TRANS, \$ N, N, -1, -1, NRHS, IMAT, NFAIL, \$ NERRS, NOUT ) * CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC, \$ RESULT( 5 ) ) CALL ZGET07( TRANS, N, NRHS, A, LDA, B, LDA, X, \$ LDA, XACT, LDA, RWORK, .TRUE., \$ RWORK( NRHS+1 ), RESULT( 6 ) ) * * Print information about the tests that did not * pass the threshold. * DO 40 K = 3, 7 IF( RESULT( K ).GE.THRESH ) THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) \$ CALL ALAHD( NOUT, PATH ) WRITE( NOUT, FMT = 9998 )TRANS, N, NRHS, \$ IMAT, K, RESULT( K ) NFAIL = NFAIL + 1 END IF 40 CONTINUE NRUN = NRUN + 5 50 CONTINUE 60 CONTINUE * *+ TEST 8 * Get an estimate of RCOND = 1/CNDNUM. * 70 CONTINUE DO 80 ITRAN = 1, 2 IF( ITRAN.EQ.1 ) THEN ANORM = ANORMO RCONDC = RCONDO NORM = 'O' ELSE ANORM = ANORMI RCONDC = RCONDI NORM = 'I' END IF SRNAMT = 'ZGECON' CALL ZGECON( NORM, N, AFAC, LDA, ANORM, RCOND, \$ WORK, RWORK, INFO ) * * Check error code from ZGECON. * IF( INFO.NE.0 ) \$ CALL ALAERH( PATH, 'ZGECON', INFO, 0, NORM, N, \$ N, -1, -1, -1, IMAT, NFAIL, NERRS, \$ NOUT ) * * This line is needed on a Sun SPARCstation. * DUMMY = RCOND * RESULT( 8 ) = DGET06( RCOND, RCONDC ) * * Print information about the tests that did not pass * the threshold. * IF( RESULT( 8 ).GE.THRESH ) THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) \$ CALL ALAHD( NOUT, PATH ) WRITE( NOUT, FMT = 9997 )NORM, N, IMAT, 8, \$ RESULT( 8 ) NFAIL = NFAIL + 1 END IF NRUN = NRUN + 1 80 CONTINUE 90 CONTINUE 100 CONTINUE * 110 CONTINUE 120 CONTINUE * * Print a summary of the results. * CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS ) * 9999 FORMAT( ' M = ', I5, ', N =', I5, ', NB =', I4, ', type ', I2, \$ ', test(', I2, ') =', G12.5 ) 9998 FORMAT( ' TRANS=''', A1, ''', N =', I5, ', NRHS=', I3, ', type ', \$ I2, ', test(', I2, ') =', G12.5 ) 9997 FORMAT( ' NORM =''', A1, ''', N =', I5, ',', 10X, ' type ', I2, \$ ', test(', I2, ') =', G12.5 ) RETURN * * End of ZCHKGE * END