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SUBROUTINE ZDRVRFP( NOUT, NN, NVAL, NNS, NSVAL, NNT, NTVAL,
+ THRESH, A, ASAV, AFAC, AINV, B, + BSAV, XACT, X, ARF, ARFINV, + Z_WORK_ZLATMS, Z_WORK_ZPOT02, + Z_WORK_ZPOT03, D_WORK_ZLATMS, D_WORK_ZLANHE, + D_WORK_ZPOT01, D_WORK_ZPOT02, D_WORK_ZPOT03 ) * IMPLICIT NONE * * -- LAPACK test routine (version 3.2.0) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2008 * * .. Scalar Arguments .. INTEGER NN, NNS, NNT, NOUT DOUBLE PRECISION THRESH * .. * .. Array Arguments .. INTEGER NVAL( NN ), NSVAL( NNS ), NTVAL( NNT ) COMPLEX*16 A( * ) COMPLEX*16 AINV( * ) COMPLEX*16 ASAV( * ) COMPLEX*16 B( * ) COMPLEX*16 BSAV( * ) COMPLEX*16 AFAC( * ) COMPLEX*16 ARF( * ) COMPLEX*16 ARFINV( * ) COMPLEX*16 XACT( * ) COMPLEX*16 X( * ) COMPLEX*16 Z_WORK_ZLATMS( * ) COMPLEX*16 Z_WORK_ZPOT02( * ) COMPLEX*16 Z_WORK_ZPOT03( * ) DOUBLE PRECISION D_WORK_ZLATMS( * ) DOUBLE PRECISION D_WORK_ZLANHE( * ) DOUBLE PRECISION D_WORK_ZPOT01( * ) DOUBLE PRECISION D_WORK_ZPOT02( * ) DOUBLE PRECISION D_WORK_ZPOT03( * ) * .. * * Purpose * ======= * * ZDRVRFP tests the LAPACK RFP routines: * ZPFTRF, ZPFTRS, and ZPFTRI. * * This testing routine follow the same tests as ZDRVPO (test for the full * format Symmetric Positive Definite solver). * * The tests are performed in Full Format, convertion back and forth from * full format to RFP format are performed using the routines ZTRTTF and * ZTFTTR. * * 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 ZPFTRF, 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 ZPFTRF 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. * * Arguments * ========= * * NOUT (input) INTEGER * The unit number for output. * * 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. * * 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. * * NNT (input) INTEGER * The number of values of MATRIX TYPE contained in the vector NTVAL. * * NTVAL (input) INTEGER array, dimension (NNT) * The values of matrix type (between 0 and 9 for PO/PP/PF matrices). * * 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. * * A (workspace) COMPLEX*16 array, dimension (NMAX*NMAX) * * ASAV (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*MAXRHS) * * BSAV (workspace) COMPLEX*16 array, dimension (NMAX*MAXRHS) * * XACT (workspace) COMPLEX*16 array, dimension (NMAX*MAXRHS) * * X (workspace) COMPLEX*16 array, dimension (NMAX*MAXRHS) * * ARF (workspace) COMPLEX*16 array, dimension ((NMAX*(NMAX+1))/2) * * ARFINV (workspace) COMPLEX*16 array, dimension ((NMAX*(NMAX+1))/2) * * Z_WORK_ZLATMS (workspace) COMPLEX*16 array, dimension ( 3*NMAX ) * * Z_WORK_ZPOT02 (workspace) COMPLEX*16 array, dimension ( NMAX*MAXRHS ) * * Z_WORK_ZPOT03 (workspace) COMPLEX*16 array, dimension ( NMAX*NMAX ) * * D_WORK_ZLATMS (workspace) DOUBLE PRECISION array, dimension ( NMAX ) * * D_WORK_ZLANHE (workspace) DOUBLE PRECISION array, dimension ( NMAX ) * * D_WORK_ZPOT01 (workspace) DOUBLE PRECISION array, dimension ( NMAX ) * * D_WORK_ZPOT02 (workspace) DOUBLE PRECISION array, dimension ( NMAX ) * * D_WORK_ZPOT03 (workspace) DOUBLE PRECISION array, dimension ( NMAX ) * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+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 DOUBLE PRECISION ANORM, AINVNM, CNDNUM, RCONDC * .. * .. Local Arrays .. CHARACTER UPLOS( 2 ), FORMS( 2 ) INTEGER ISEED( 4 ), ISEEDY( 4 ) DOUBLE PRECISION RESULT( NTESTS ) * .. * .. External Functions .. DOUBLE PRECISION ZLANHE EXTERNAL ZLANHE * .. * .. External Subroutines .. EXTERNAL ALADHD, ALAERH, ALASVM, ZGET04, ZTFTTR, ZLACPY, + ZLAIPD, ZLARHS, ZLATB4, ZLATMS, ZPFTRI, ZPFTRF, + ZPFTRS, ZPOT01, ZPOT02, ZPOT03, ZPOTRI, ZPOTRF, + ZTRTTF * .. * .. 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.GT.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 ZLATB4 and generate a test * matrix with ZLATMS. * CALL ZLATB4( 'ZPO', IMAT, N, N, CTYPE, KL, KU, + ANORM, MODE, CNDNUM, DIST ) * SRNAMT = 'ZLATMS' CALL ZLATMS( N, N, DIST, ISEED, CTYPE, + D_WORK_ZLATMS, + MODE, CNDNUM, ANORM, KL, KU, UPLO, A, + LDA, Z_WORK_ZLATMS, INFO ) * * Check error code from ZLATMS. * IF( INFO.NE.0 ) THEN CALL ALAERH( 'ZPF', 'ZLATMS', 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 ZLAIPD( N, A, LDA+1, 0 ) * * Save a copy of the matrix A in ASAV. * CALL ZLACPY( 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 = ZLANHE( '1', UPLO, N, A, LDA, + D_WORK_ZLANHE ) * * Factor the matrix A. * CALL ZPOTRF( UPLO, N, A, LDA, INFO ) * * Form the inverse of A. * CALL ZPOTRI( UPLO, N, A, LDA, INFO ) * * Compute the 1-norm condition number of A. * AINVNM = ZLANHE( '1', UPLO, N, A, LDA, + D_WORK_ZLANHE ) RCONDC = ( ONE / ANORM ) / AINVNM * * Restore the matrix A. * CALL ZLACPY( UPLO, N, N, ASAV, LDA, A, LDA ) * END IF * * Form an exact solution and set the right hand side. * SRNAMT = 'ZLARHS' CALL ZLARHS( 'ZPO', 'N', UPLO, ' ', N, N, KL, KU, + NRHS, A, LDA, XACT, LDA, B, LDA, + ISEED, INFO ) CALL ZLACPY( 'Full', N, NRHS, B, LDA, BSAV, LDA ) * * Compute the L*L' or U'*U factorization of the * matrix and solve the system. * CALL ZLACPY( UPLO, N, N, A, LDA, AFAC, LDA ) CALL ZLACPY( 'Full', N, NRHS, B, LDB, X, LDB ) * SRNAMT = 'ZTRTTF' CALL ZTRTTF( CFORM, UPLO, N, AFAC, LDA, ARF, INFO ) SRNAMT = 'ZPFTRF' CALL ZPFTRF( CFORM, UPLO, N, ARF, INFO ) * * Check error code from ZPFTRF. * 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( 'ZPF', 'ZPFSV ', 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 = 'ZPFTRS' CALL ZPFTRS( CFORM, UPLO, N, NRHS, ARF, X, LDB, + INFO ) * SRNAMT = 'ZTFTTR' CALL ZTFTTR( CFORM, UPLO, N, ARF, AFAC, LDA, INFO ) * * Reconstruct matrix from factors and compute * residual. * CALL ZLACPY( UPLO, N, N, AFAC, LDA, ASAV, LDA ) CALL ZPOT01( UPLO, N, A, LDA, AFAC, LDA, + D_WORK_ZPOT01, RESULT( 1 ) ) CALL ZLACPY( UPLO, N, N, ASAV, LDA, AFAC, LDA ) * * Form the inverse and compute the residual. * IF(MOD(N,2).EQ.0)THEN CALL ZLACPY( 'A', N+1, N/2, ARF, N+1, ARFINV, + N+1 ) ELSE CALL ZLACPY( 'A', N, (N+1)/2, ARF, N, ARFINV, + N ) END IF * SRNAMT = 'ZPFTRI' CALL ZPFTRI( CFORM, UPLO, N, ARFINV , INFO ) * SRNAMT = 'ZTFTTR' CALL ZTFTTR( CFORM, UPLO, N, ARFINV, AINV, LDA, + INFO ) * * Check error code from ZPFTRI. * IF( INFO.NE.0 ) + CALL ALAERH( 'ZPO', 'ZPFTRI', INFO, 0, UPLO, N, + N, -1, -1, -1, IMAT, NFAIL, NERRS, + NOUT ) * CALL ZPOT03( UPLO, N, A, LDA, AINV, LDA, + Z_WORK_ZPOT03, LDA, D_WORK_ZPOT03, + RCONDC, RESULT( 2 ) ) * * Compute residual of the computed solution. * CALL ZLACPY( 'Full', N, NRHS, B, LDA, + Z_WORK_ZPOT02, LDA ) CALL ZPOT02( UPLO, N, NRHS, A, LDA, X, LDA, + Z_WORK_ZPOT02, LDA, D_WORK_ZPOT02, + RESULT( 3 ) ) * * Check solution from generated exact solution. * CALL ZGET04( 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, 'ZPF' ) WRITE( NOUT, FMT = 9999 )'ZPFSV ', 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( 'ZPF', NOUT, NFAIL, NRUN, NERRS ) * 9999 FORMAT( 1X, A6, ', UPLO=''', A1, ''', N =', I5, ', type ', I1, + ', test(', I1, ')=', G12.5 ) * RETURN * * End of ZDRVRFP * END |