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SUBROUTINE SCHKPB( DOTYPE, 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) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. LOGICAL TSTERR INTEGER NMAX, NN, NNB, NNS, NOUT REAL THRESH * .. * .. Array Arguments .. LOGICAL DOTYPE( * ) INTEGER IWORK( * ), NBVAL( * ), NSVAL( * ), NVAL( * ) REAL A( * ), AFAC( * ), AINV( * ), B( * ), $ RWORK( * ), WORK( * ), X( * ), XACT( * ) * .. * * Purpose * ======= * * SCHKPB tests SPBTRF, -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. * * 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 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. * * THRESH (input) 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. * * TSTERR (input) LOGICAL * Flag that indicates whether error exits are to be tested. * * NMAX (input) INTEGER * The maximum value permitted for N, used in dimensioning the * work arrays. * * A (workspace) REAL array, dimension (NMAX*NMAX) * * AFAC (workspace) REAL array, dimension (NMAX*NMAX) * * AINV (workspace) REAL array, dimension (NMAX*NMAX) * * B (workspace) REAL array, dimension (NMAX*NSMAX) * where NSMAX is the largest entry in NSVAL. * * X (workspace) REAL array, dimension (NMAX*NSMAX) * * XACT (workspace) REAL array, dimension (NMAX*NSMAX) * * WORK (workspace) REAL array, dimension * (NMAX*max(3,NSMAX)) * * RWORK (workspace) REAL array, dimension * (max(NMAX,2*NSMAX)) * * IWORK (workspace) INTEGER array, dimension (NMAX) * * NOUT (input) INTEGER * The unit number for output. * * ===================================================================== * * .. Parameters .. REAL ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) INTEGER NTYPES, NTESTS PARAMETER ( NTYPES = 8, NTESTS = 7 ) INTEGER NBW PARAMETER ( NBW = 4 ) * .. * .. Local Scalars .. LOGICAL ZEROT CHARACTER DIST, PACKIT, TYPE, UPLO, XTYPE CHARACTER*3 PATH INTEGER I, I1, I2, IKD, IMAT, IN, INB, INFO, IOFF, $ IRHS, IUPLO, IW, IZERO, K, KD, KL, KOFF, KU, $ LDA, LDAB, MODE, N, NB, NERRS, NFAIL, NIMAT, $ NKD, NRHS, NRUN REAL AINVNM, ANORM, CNDNUM, RCOND, RCONDC * .. * .. Local Arrays .. INTEGER ISEED( 4 ), ISEEDY( 4 ), KDVAL( NBW ) REAL RESULT( NTESTS ) * .. * .. External Functions .. REAL SGET06, SLANGE, SLANSB EXTERNAL SGET06, SLANGE, SLANSB * .. * .. External Subroutines .. EXTERNAL ALAERH, ALAHD, ALASUM, SCOPY, SERRPO, SGET04, $ SLACPY, SLARHS, SLASET, SLATB4, SLATMS, SPBCON, $ SPBRFS, SPBT01, SPBT02, SPBT05, SPBTRF, SPBTRS, $ SSWAP, XLAENV * .. * .. Intrinsic Functions .. INTRINSIC 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 / * .. * .. Executable Statements .. * * Initialize constants and the random number seed. * PATH( 1: 1 ) = 'Single precision' PATH( 2: 3 ) = 'PB' NRUN = 0 NFAIL = 0 NERRS = 0 DO 10 I = 1, 4 ISEED( I ) = ISEEDY( I ) 10 CONTINUE * * Test the error exits * IF( TSTERR ) $ CALL SERRPO( PATH, NOUT ) INFOT = 0 CALL XLAENV( 2, 2 ) KDVAL( 1 ) = 0 * * Do for each value of N in NVAL * DO 90 IN = 1, NN N = NVAL( IN ) LDA = MAX( N, 1 ) XTYPE = 'N' * * Set limits on the number of loop iterations. * NKD = MAX( 1, MIN( N, 4 ) ) NIMAT = NTYPES IF( N.EQ.0 ) $ NIMAT = 1 * KDVAL( 2 ) = N + ( N+1 ) / 4 KDVAL( 3 ) = ( 3*N-1 ) / 4 KDVAL( 4 ) = ( N+1 ) / 4 * DO 80 IKD = 1, NKD * * Do for KD = 0, (5*N+1)/4, (3N-1)/4, and (N+1)/4. This order * makes it easier to skip redundant values for small values * of N. * KD = KDVAL( IKD ) LDAB = KD + 1 * * Do first for UPLO = 'U', then for UPLO = 'L' * DO 70 IUPLO = 1, 2 KOFF = 1 IF( IUPLO.EQ.1 ) THEN UPLO = 'U' KOFF = MAX( 1, KD+2-N ) PACKIT = 'Q' ELSE UPLO = 'L' PACKIT = 'B' END IF * DO 60 IMAT = 1, NIMAT * * Do the tests only if DOTYPE( IMAT ) is true. * IF( .NOT.DOTYPE( IMAT ) ) $ GO TO 60 * * Skip types 2, 3, or 4 if the matrix size is too small. * ZEROT = IMAT.GE.2 .AND. IMAT.LE.4 IF( ZEROT .AND. N.LT.IMAT-1 ) $ GO TO 60 * IF( .NOT.ZEROT .OR. .NOT.DOTYPE( 1 ) ) THEN * * Set up parameters with SLATB4 and generate a test * matrix with SLATMS. * CALL SLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM, $ MODE, CNDNUM, DIST ) * SRNAMT = 'SLATMS' CALL SLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE, $ CNDNUM, ANORM, KD, KD, PACKIT, $ A( KOFF ), LDAB, WORK, INFO ) * * Check error code from SLATMS. * IF( INFO.NE.0 ) THEN CALL ALAERH( PATH, 'SLATMS', INFO, 0, UPLO, N, $ N, KD, KD, -1, IMAT, NFAIL, NERRS, $ NOUT ) GO TO 60 END IF ELSE IF( IZERO.GT.0 ) THEN * * Use the same matrix for types 3 and 4 as for type * 2 by copying back the zeroed out column, * IW = 2*LDA + 1 IF( IUPLO.EQ.1 ) THEN IOFF = ( IZERO-1 )*LDAB + KD + 1 CALL SCOPY( IZERO-I1, WORK( IW ), 1, $ A( IOFF-IZERO+I1 ), 1 ) IW = IW + IZERO - I1 CALL SCOPY( I2-IZERO+1, WORK( IW ), 1, $ A( IOFF ), MAX( LDAB-1, 1 ) ) ELSE IOFF = ( I1-1 )*LDAB + 1 CALL SCOPY( IZERO-I1, WORK( IW ), 1, $ A( IOFF+IZERO-I1 ), $ MAX( LDAB-1, 1 ) ) IOFF = ( IZERO-1 )*LDAB + 1 IW = IW + IZERO - I1 CALL SCOPY( I2-IZERO+1, WORK( IW ), 1, $ A( IOFF ), 1 ) END IF END IF * * For types 2-4, zero one row and column of the matrix * to test that INFO is returned correctly. * IZERO = 0 IF( ZEROT ) THEN IF( IMAT.EQ.2 ) THEN IZERO = 1 ELSE IF( IMAT.EQ.3 ) THEN IZERO = N ELSE IZERO = N / 2 + 1 END IF * * Save the zeroed out row and column in WORK(*,3) * IW = 2*LDA DO 20 I = 1, MIN( 2*KD+1, N ) WORK( IW+I ) = ZERO 20 CONTINUE IW = IW + 1 I1 = MAX( IZERO-KD, 1 ) I2 = MIN( IZERO+KD, N ) * IF( IUPLO.EQ.1 ) THEN IOFF = ( IZERO-1 )*LDAB + KD + 1 CALL SSWAP( IZERO-I1, A( IOFF-IZERO+I1 ), 1, $ WORK( IW ), 1 ) IW = IW + IZERO - I1 CALL SSWAP( I2-IZERO+1, A( IOFF ), $ MAX( LDAB-1, 1 ), WORK( IW ), 1 ) ELSE IOFF = ( I1-1 )*LDAB + 1 CALL SSWAP( IZERO-I1, A( IOFF+IZERO-I1 ), $ MAX( LDAB-1, 1 ), WORK( IW ), 1 ) IOFF = ( IZERO-1 )*LDAB + 1 IW = IW + IZERO - I1 CALL SSWAP( I2-IZERO+1, A( IOFF ), 1, $ WORK( IW ), 1 ) END IF END IF * * Do for each value of NB in NBVAL * DO 50 INB = 1, NNB NB = NBVAL( INB ) CALL XLAENV( 1, NB ) * * Compute the L*L' or U'*U factorization of the band * matrix. * CALL SLACPY( 'Full', KD+1, N, A, LDAB, AFAC, LDAB ) SRNAMT = 'SPBTRF' CALL SPBTRF( UPLO, N, KD, AFAC, LDAB, INFO ) * * Check error code from SPBTRF. * IF( INFO.NE.IZERO ) THEN CALL ALAERH( PATH, 'SPBTRF', INFO, IZERO, UPLO, $ N, N, KD, KD, NB, IMAT, NFAIL, $ NERRS, NOUT ) GO TO 50 END IF * * Skip the tests if INFO is not 0. * IF( INFO.NE.0 ) $ GO TO 50 * *+ TEST 1 * Reconstruct matrix from factors and compute * residual. * CALL SLACPY( 'Full', KD+1, N, AFAC, LDAB, AINV, $ LDAB ) CALL SPBT01( UPLO, N, KD, A, LDAB, AINV, LDAB, $ RWORK, RESULT( 1 ) ) * * Print the test ratio if it is .GE. THRESH. * IF( RESULT( 1 ).GE.THRESH ) THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) $ CALL ALAHD( NOUT, PATH ) WRITE( NOUT, FMT = 9999 )UPLO, N, KD, NB, IMAT, $ 1, RESULT( 1 ) NFAIL = NFAIL + 1 END IF NRUN = NRUN + 1 * * Only do other tests if this is the first blocksize. * IF( INB.GT.1 ) $ GO TO 50 * * Form the inverse of A so we can get a good estimate * of RCONDC = 1/(norm(A) * norm(inv(A))). * CALL SLASET( 'Full', N, N, ZERO, ONE, AINV, LDA ) SRNAMT = 'SPBTRS' CALL SPBTRS( UPLO, N, KD, N, AFAC, LDAB, AINV, LDA, $ INFO ) * * Compute RCONDC = 1/(norm(A) * norm(inv(A))). * ANORM = SLANSB( '1', UPLO, N, KD, A, LDAB, RWORK ) AINVNM = SLANGE( '1', N, N, AINV, LDA, RWORK ) IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN RCONDC = ONE ELSE RCONDC = ( ONE / ANORM ) / AINVNM END IF * DO 40 IRHS = 1, NNS NRHS = NSVAL( IRHS ) * *+ TEST 2 * Solve and compute residual for A * X = B. * SRNAMT = 'SLARHS' CALL SLARHS( PATH, XTYPE, UPLO, ' ', N, N, KD, $ KD, NRHS, A, LDAB, XACT, LDA, B, $ LDA, ISEED, INFO ) CALL SLACPY( 'Full', N, NRHS, B, LDA, X, LDA ) * SRNAMT = 'SPBTRS' CALL SPBTRS( UPLO, N, KD, NRHS, AFAC, LDAB, X, $ LDA, INFO ) * * Check error code from SPBTRS. * IF( INFO.NE.0 ) $ CALL ALAERH( PATH, 'SPBTRS', INFO, 0, UPLO, $ N, N, KD, KD, NRHS, IMAT, NFAIL, $ NERRS, NOUT ) * CALL SLACPY( 'Full', N, NRHS, B, LDA, WORK, $ LDA ) CALL SPBT02( UPLO, N, KD, NRHS, A, LDAB, X, LDA, $ WORK, LDA, RWORK, RESULT( 2 ) ) * *+ TEST 3 * Check solution from generated exact solution. * CALL SGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC, $ RESULT( 3 ) ) * *+ TESTS 4, 5, and 6 * Use iterative refinement to improve the solution. * SRNAMT = 'SPBRFS' CALL SPBRFS( UPLO, N, KD, NRHS, A, LDAB, AFAC, $ LDAB, B, LDA, X, LDA, RWORK, $ RWORK( NRHS+1 ), WORK, IWORK, $ INFO ) * * Check error code from SPBRFS. * IF( INFO.NE.0 ) $ CALL ALAERH( PATH, 'SPBRFS', INFO, 0, UPLO, $ N, N, KD, KD, NRHS, IMAT, NFAIL, $ NERRS, NOUT ) * CALL SGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC, $ RESULT( 4 ) ) CALL SPBT05( UPLO, N, KD, NRHS, A, LDAB, B, LDA, $ X, LDA, XACT, LDA, RWORK, $ RWORK( NRHS+1 ), RESULT( 5 ) ) * * Print information about the tests that did not * pass the threshold. * DO 30 K = 2, 6 IF( RESULT( K ).GE.THRESH ) THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) $ CALL ALAHD( NOUT, PATH ) WRITE( NOUT, FMT = 9998 )UPLO, N, KD, $ NRHS, IMAT, K, RESULT( K ) NFAIL = NFAIL + 1 END IF 30 CONTINUE NRUN = NRUN + 5 40 CONTINUE * *+ TEST 7 * Get an estimate of RCOND = 1/CNDNUM. * SRNAMT = 'SPBCON' CALL SPBCON( UPLO, N, KD, AFAC, LDAB, ANORM, RCOND, $ WORK, IWORK, INFO ) * * Check error code from SPBCON. * IF( INFO.NE.0 ) $ CALL ALAERH( PATH, 'SPBCON', INFO, 0, UPLO, N, $ N, KD, KD, -1, IMAT, NFAIL, NERRS, $ NOUT ) * RESULT( 7 ) = SGET06( RCOND, RCONDC ) * * Print the test ratio if it is .GE. THRESH. * IF( RESULT( 7 ).GE.THRESH ) THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) $ CALL ALAHD( NOUT, PATH ) WRITE( NOUT, FMT = 9997 )UPLO, N, KD, IMAT, 7, $ RESULT( 7 ) NFAIL = NFAIL + 1 END IF NRUN = NRUN + 1 50 CONTINUE 60 CONTINUE 70 CONTINUE 80 CONTINUE 90 CONTINUE * * Print a summary of the results. * CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS ) * 9999 FORMAT( ' UPLO=''', A1, ''', N=', I5, ', KD=', I5, ', NB=', I4, $ ', type ', I2, ', test ', I2, ', ratio= ', G12.5 ) 9998 FORMAT( ' UPLO=''', A1, ''', N=', I5, ', KD=', I5, ', NRHS=', I3, $ ', type ', I2, ', test(', I2, ') = ', G12.5 ) 9997 FORMAT( ' UPLO=''', A1, ''', N=', I5, ', KD=', I5, ',', 10X, $ ' type ', I2, ', test(', I2, ') = ', G12.5 ) RETURN * * End of SCHKPB * END |