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|
SUBROUTINE ZDRVPO( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
$ A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK,
$ RWORK, NOUT )
*
* -- LAPACK test routine (version 3.2) --
* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
* November 2006
*
* .. Scalar Arguments ..
LOGICAL TSTERR
INTEGER NMAX, NN, NOUT, NRHS
DOUBLE PRECISION THRESH
* ..
* .. Array Arguments ..
LOGICAL DOTYPE( * )
INTEGER NVAL( * )
DOUBLE PRECISION RWORK( * ), S( * )
COMPLEX*16 A( * ), AFAC( * ), ASAV( * ), B( * ),
$ BSAV( * ), WORK( * ), X( * ), XACT( * )
* ..
*
* Purpose
* =======
*
* ZDRVPO tests the driver routines ZPOSV, -SVX, and -SVXX.
*
* Note that this file is used only when the XBLAS are available,
* otherwise zdrvpo.f defines this subroutine.
*
* 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.
*
* 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 N, used in dimensioning the
* work arrays.
*
* A (workspace) COMPLEX*16 array, dimension (NMAX*NMAX)
*
* AFAC (workspace) COMPLEX*16 array, dimension (NMAX*NMAX)
*
* ASAV (workspace) COMPLEX*16 array, dimension (NMAX*NMAX)
*
* B (workspace) COMPLEX*16 array, dimension (NMAX*NRHS)
*
* BSAV (workspace) COMPLEX*16 array, dimension (NMAX*NRHS)
*
* X (workspace) COMPLEX*16 array, dimension (NMAX*NRHS)
*
* XACT (workspace) COMPLEX*16 array, dimension (NMAX*NRHS)
*
* S (workspace) DOUBLE PRECISION array, dimension (NMAX)
*
* WORK (workspace) COMPLEX*16 array, dimension
* (NMAX*max(3,NRHS))
*
* RWORK (workspace) DOUBLE PRECISION array, dimension (NMAX+2*NRHS)
*
* 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 = 9 )
INTEGER NTESTS
PARAMETER ( NTESTS = 6 )
* ..
* .. Local Scalars ..
LOGICAL EQUIL, NOFACT, PREFAC, ZEROT
CHARACTER DIST, EQUED, FACT, TYPE, UPLO, XTYPE
CHARACTER*3 PATH
INTEGER I, IEQUED, IFACT, IMAT, IN, INFO, IOFF, IUPLO,
$ IZERO, K, K1, KL, KU, LDA, MODE, N, NB, NBMIN,
$ NERRS, NFACT, NFAIL, NIMAT, NRUN, NT,
$ N_ERR_BNDS
DOUBLE PRECISION AINVNM, AMAX, ANORM, CNDNUM, RCOND, RCONDC,
$ ROLDC, SCOND, RPVGRW_SVXX
* ..
* .. Local Arrays ..
CHARACTER EQUEDS( 2 ), FACTS( 3 ), UPLOS( 2 )
INTEGER ISEED( 4 ), ISEEDY( 4 )
DOUBLE PRECISION RESULT( NTESTS ), BERR( NRHS ),
$ ERRBNDS_N( NRHS, 3 ), ERRBNDS_C( NRHS, 3 )
* ..
* .. External Functions ..
LOGICAL LSAME
DOUBLE PRECISION DGET06, ZLANHE
EXTERNAL LSAME, DGET06, ZLANHE
* ..
* .. External Subroutines ..
EXTERNAL ALADHD, ALAERH, ALASVM, XLAENV, ZERRVX, ZGET04,
$ ZLACPY, ZLAIPD, ZLAQHE, ZLARHS, ZLASET, ZLATB4,
$ ZLATMS, ZPOEQU, ZPOSV, ZPOSVX, ZPOT01, ZPOT02,
$ ZPOT05, ZPOTRF, ZPOTRI, ZPOSVXX
* ..
* .. Scalars in Common ..
LOGICAL LERR, OK
CHARACTER*32 SRNAMT
INTEGER INFOT, NUNIT
* ..
* .. Common blocks ..
COMMON / INFOC / INFOT, NUNIT, OK, LERR
COMMON / SRNAMC / SRNAMT
* ..
* .. Intrinsic Functions ..
INTRINSIC DCMPLX, MAX
* ..
* .. Data statements ..
DATA ISEEDY / 1988, 1989, 1990, 1991 /
DATA UPLOS / 'U', 'L' /
DATA FACTS / 'F', 'N', 'E' /
DATA EQUEDS / 'N', 'Y' /
* ..
* .. Executable Statements ..
*
* Initialize constants and the random number seed.
*
PATH( 1: 1 ) = 'Zomplex precision'
PATH( 2: 3 ) = 'PO'
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
*
* Set the block size and minimum block size for testing.
*
NB = 1
NBMIN = 2
CALL XLAENV( 1, NB )
CALL XLAENV( 2, NBMIN )
*
* Do for each value of N in NVAL
*
DO 130 IN = 1, NN
N = NVAL( IN )
LDA = MAX( N, 1 )
XTYPE = 'N'
NIMAT = NTYPES
IF( N.LE.0 )
$ NIMAT = 1
*
DO 120 IMAT = 1, NIMAT
*
* Do the tests only if DOTYPE( IMAT ) is true.
*
IF( .NOT.DOTYPE( IMAT ) )
$ GO TO 120
*
* Skip types 3, 4, or 5 if the matrix size is too small.
*
ZEROT = IMAT.GE.3 .AND. IMAT.LE.5
IF( ZEROT .AND. N.LT.IMAT-2 )
$ GO TO 120
*
* Do first for UPLO = 'U', then for UPLO = 'L'
*
DO 110 IUPLO = 1, 2
UPLO = UPLOS( IUPLO )
*
* Set up parameters with ZLATB4 and generate a test matrix
* with ZLATMS.
*
CALL ZLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM, MODE,
$ CNDNUM, DIST )
*
SRNAMT = 'ZLATMS'
CALL ZLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE,
$ CNDNUM, ANORM, KL, KU, UPLO, A, LDA, WORK,
$ INFO )
*
* Check error code from ZLATMS.
*
IF( INFO.NE.0 ) THEN
CALL ALAERH( PATH, 'ZLATMS', INFO, 0, UPLO, N, N, -1,
$ -1, -1, IMAT, NFAIL, NERRS, NOUT )
GO TO 110
END IF
*
* For types 3-5, zero one row and column of the matrix to
* test that INFO is returned correctly.
*
IF( ZEROT ) THEN
IF( IMAT.EQ.3 ) THEN
IZERO = 1
ELSE IF( IMAT.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 )
*
DO 100 IEQUED = 1, 2
EQUED = EQUEDS( IEQUED )
IF( IEQUED.EQ.1 ) THEN
NFACT = 3
ELSE
NFACT = 1
END IF
*
DO 90 IFACT = 1, NFACT
FACT = FACTS( IFACT )
PREFAC = LSAME( FACT, 'F' )
NOFACT = LSAME( FACT, 'N' )
EQUIL = LSAME( FACT, 'E' )
*
IF( ZEROT ) THEN
IF( PREFAC )
$ GO TO 90
RCONDC = ZERO
*
ELSE IF( .NOT.LSAME( FACT, 'N' ) ) THEN
*
* Compute the condition number for comparison with
* the value returned by ZPOSVX (FACT = 'N' reuses
* the condition number from the previous iteration
* with FACT = 'F').
*
CALL ZLACPY( UPLO, N, N, ASAV, LDA, AFAC, LDA )
IF( EQUIL .OR. IEQUED.GT.1 ) THEN
*
* Compute row and column scale factors to
* equilibrate the matrix A.
*
CALL ZPOEQU( N, AFAC, LDA, S, SCOND, AMAX,
$ INFO )
IF( INFO.EQ.0 .AND. N.GT.0 ) THEN
IF( IEQUED.GT.1 )
$ SCOND = ZERO
*
* Equilibrate the matrix.
*
CALL ZLAQHE( UPLO, N, AFAC, LDA, S, SCOND,
$ AMAX, EQUED )
END IF
END IF
*
* Save the condition number of the
* non-equilibrated system for use in ZGET04.
*
IF( EQUIL )
$ ROLDC = RCONDC
*
* Compute the 1-norm of A.
*
ANORM = ZLANHE( '1', UPLO, N, AFAC, LDA, RWORK )
*
* Factor the matrix A.
*
CALL ZPOTRF( UPLO, N, AFAC, LDA, INFO )
*
* Form the inverse of A.
*
CALL ZLACPY( UPLO, N, N, AFAC, LDA, A, LDA )
CALL ZPOTRI( UPLO, N, A, LDA, INFO )
*
* Compute the 1-norm condition number of A.
*
AINVNM = ZLANHE( '1', UPLO, N, A, LDA, RWORK )
IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
RCONDC = ONE
ELSE
RCONDC = ( ONE / ANORM ) / AINVNM
END IF
END IF
*
* Restore the matrix A.
*
CALL ZLACPY( UPLO, N, N, ASAV, LDA, A, LDA )
*
* Form an exact solution and set the right hand side.
*
SRNAMT = 'ZLARHS'
CALL ZLARHS( PATH, XTYPE, UPLO, ' ', N, N, KL, KU,
$ NRHS, A, LDA, XACT, LDA, B, LDA,
$ ISEED, INFO )
XTYPE = 'C'
CALL ZLACPY( 'Full', N, NRHS, B, LDA, BSAV, LDA )
*
IF( NOFACT ) THEN
*
* --- Test ZPOSV ---
*
* 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, LDA, X, LDA )
*
SRNAMT = 'ZPOSV '
CALL ZPOSV( UPLO, N, NRHS, AFAC, LDA, X, LDA,
$ INFO )
*
* Check error code from ZPOSV .
*
IF( INFO.NE.IZERO ) THEN
CALL ALAERH( PATH, 'ZPOSV ', INFO, IZERO,
$ UPLO, N, N, -1, -1, NRHS, IMAT,
$ NFAIL, NERRS, NOUT )
GO TO 70
ELSE IF( INFO.NE.0 ) THEN
GO TO 70
END IF
*
* Reconstruct matrix from factors and compute
* residual.
*
CALL ZPOT01( UPLO, N, A, LDA, AFAC, LDA, RWORK,
$ RESULT( 1 ) )
*
* Compute residual of the computed solution.
*
CALL ZLACPY( 'Full', N, NRHS, B, LDA, WORK,
$ LDA )
CALL ZPOT02( UPLO, N, NRHS, A, LDA, X, LDA,
$ WORK, LDA, RWORK, RESULT( 2 ) )
*
* Check solution from generated exact solution.
*
CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
$ RESULT( 3 ) )
NT = 3
*
* 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, PATH )
WRITE( NOUT, FMT = 9999 )'ZPOSV ', UPLO,
$ N, IMAT, K, RESULT( K )
NFAIL = NFAIL + 1
END IF
60 CONTINUE
NRUN = NRUN + NT
70 CONTINUE
END IF
*
* --- Test ZPOSVX ---
*
IF( .NOT.PREFAC )
$ CALL ZLASET( UPLO, N, N, DCMPLX( ZERO ),
$ DCMPLX( ZERO ), AFAC, LDA )
CALL ZLASET( 'Full', N, NRHS, DCMPLX( ZERO ),
$ DCMPLX( ZERO ), X, LDA )
IF( IEQUED.GT.1 .AND. N.GT.0 ) THEN
*
* Equilibrate the matrix if FACT='F' and
* EQUED='Y'.
*
CALL ZLAQHE( UPLO, N, A, LDA, S, SCOND, AMAX,
$ EQUED )
END IF
*
* Solve the system and compute the condition number
* and error bounds using ZPOSVX.
*
SRNAMT = 'ZPOSVX'
CALL ZPOSVX( FACT, UPLO, N, NRHS, A, LDA, AFAC,
$ LDA, EQUED, S, B, LDA, X, LDA, RCOND,
$ RWORK, RWORK( NRHS+1 ), WORK,
$ RWORK( 2*NRHS+1 ), INFO )
*
* Check the error code from ZPOSVX.
*
IF( INFO.NE.IZERO )
$ CALL ALAERH( PATH, 'ZPOSVX', INFO, IZERO,
$ FACT // UPLO, N, N, -1, -1, NRHS,
$ IMAT, NFAIL, NERRS, NOUT )
GO TO 90
*
IF( INFO.EQ.0 ) THEN
IF( .NOT.PREFAC ) THEN
*
* Reconstruct matrix from factors and compute
* residual.
*
CALL ZPOT01( UPLO, N, A, LDA, AFAC, LDA,
$ RWORK( 2*NRHS+1 ), RESULT( 1 ) )
K1 = 1
ELSE
K1 = 2
END IF
*
* Compute residual of the computed solution.
*
CALL ZLACPY( 'Full', N, NRHS, BSAV, LDA, WORK,
$ LDA )
CALL ZPOT02( UPLO, N, NRHS, ASAV, LDA, X, LDA,
$ WORK, LDA, RWORK( 2*NRHS+1 ),
$ RESULT( 2 ) )
*
* Check solution from generated exact solution.
*
IF( NOFACT .OR. ( PREFAC .AND. LSAME( EQUED,
$ 'N' ) ) ) THEN
CALL ZGET04( N, NRHS, X, LDA, XACT, LDA,
$ RCONDC, RESULT( 3 ) )
ELSE
CALL ZGET04( N, NRHS, X, LDA, XACT, LDA,
$ ROLDC, RESULT( 3 ) )
END IF
*
* Check the error bounds from iterative
* refinement.
*
CALL ZPOT05( UPLO, N, NRHS, ASAV, LDA, B, LDA,
$ X, LDA, XACT, LDA, RWORK,
$ RWORK( NRHS+1 ), RESULT( 4 ) )
ELSE
K1 = 6
END IF
*
* Compare RCOND from ZPOSVX with the computed value
* in RCONDC.
*
RESULT( 6 ) = DGET06( RCOND, RCONDC )
*
* Print information about the tests that did not pass
* the threshold.
*
DO 80 K = K1, 6
IF( RESULT( K ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALADHD( NOUT, PATH )
IF( PREFAC ) THEN
WRITE( NOUT, FMT = 9997 )'ZPOSVX', FACT,
$ UPLO, N, EQUED, IMAT, K, RESULT( K )
ELSE
WRITE( NOUT, FMT = 9998 )'ZPOSVX', FACT,
$ UPLO, N, IMAT, K, RESULT( K )
END IF
NFAIL = NFAIL + 1
END IF
80 CONTINUE
NRUN = NRUN + 7 - K1
*
* --- Test ZPOSVXX ---
*
* Restore the matrices A and B.
*
CALL ZLACPY( 'Full', N, N, ASAV, LDA, A, LDA )
CALL ZLACPY( 'Full', N, NRHS, BSAV, LDA, B, LDA )
IF( .NOT.PREFAC )
$ CALL ZLASET( UPLO, N, N, CMPLX( ZERO ),
$ CMPLX( ZERO ), AFAC, LDA )
CALL ZLASET( 'Full', N, NRHS, CMPLX( ZERO ),
$ CMPLX( ZERO ), X, LDA )
IF( IEQUED.GT.1 .AND. N.GT.0 ) THEN
*
* Equilibrate the matrix if FACT='F' and
* EQUED='Y'.
*
CALL ZLAQHE( UPLO, N, A, LDA, S, SCOND, AMAX,
$ EQUED )
END IF
*
* Solve the system and compute the condition number
* and error bounds using ZPOSVXX.
*
SRNAMT = 'ZPOSVXX'
CALL ZPOSVXX( FACT, UPLO, N, NRHS, A, LDA, AFAC,
$ LDA, EQUED, S, B, LDA, X,
$ LDA, rcond, rpvgrw_svxx, berr, n_err_bnds,
$ errbnds_n, errbnds_c, 0, ZERO, WORK,
$ RWORK( 2*NRHS+1 ), INFO )
*
* Check the error code from ZPOSVXX.
*
IF( INFO.EQ.N+1 ) GOTO 90
IF( INFO.NE.IZERO ) THEN
CALL ALAERH( PATH, 'ZPOSVXX', INFO, IZERO,
$ FACT // UPLO, N, N, -1, -1, NRHS,
$ IMAT, NFAIL, NERRS, NOUT )
GO TO 90
END IF
*
IF( INFO.EQ.0 ) THEN
IF( .NOT.PREFAC ) THEN
*
* Reconstruct matrix from factors and compute
* residual.
*
CALL ZPOT01( UPLO, N, A, LDA, AFAC, LDA,
$ RWORK( 2*NRHS+1 ), RESULT( 1 ) )
K1 = 1
ELSE
K1 = 2
END IF
*
* Compute residual of the computed solution.
*
CALL ZLACPY( 'Full', N, NRHS, BSAV, LDA, WORK,
$ LDA )
CALL ZPOT02( UPLO, N, NRHS, ASAV, LDA, X, LDA,
$ WORK, LDA, RWORK( 2*NRHS+1 ),
$ RESULT( 2 ) )
*
* Check solution from generated exact solution.
*
IF( NOFACT .OR. ( PREFAC .AND. LSAME( EQUED,
$ 'N' ) ) ) THEN
CALL ZGET04( N, NRHS, X, LDA, XACT, LDA,
$ RCONDC, RESULT( 3 ) )
ELSE
CALL ZGET04( N, NRHS, X, LDA, XACT, LDA,
$ ROLDC, RESULT( 3 ) )
END IF
*
* Check the error bounds from iterative
* refinement.
*
CALL ZPOT05( UPLO, N, NRHS, ASAV, LDA, B, LDA,
$ X, LDA, XACT, LDA, RWORK,
$ RWORK( NRHS+1 ), RESULT( 4 ) )
ELSE
K1 = 6
END IF
*
* Compare RCOND from ZPOSVXX with the computed value
* in RCONDC.
*
RESULT( 6 ) = DGET06( RCOND, RCONDC )
*
* Print information about the tests that did not pass
* the threshold.
*
DO 85 K = K1, 6
IF( RESULT( K ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALADHD( NOUT, PATH )
IF( PREFAC ) THEN
WRITE( NOUT, FMT = 9997 )'ZPOSVXX', FACT,
$ UPLO, N, EQUED, IMAT, K, RESULT( K )
ELSE
WRITE( NOUT, FMT = 9998 )'ZPOSVXX', FACT,
$ UPLO, N, IMAT, K, RESULT( K )
END IF
NFAIL = NFAIL + 1
END IF
85 CONTINUE
NRUN = NRUN + 7 - K1
90 CONTINUE
100 CONTINUE
110 CONTINUE
120 CONTINUE
130 CONTINUE
*
* Print a summary of the results.
*
CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS )
*
* Test Error Bounds for ZGESVXX
CALL ZEBCHVXX(THRESH, PATH)
9999 FORMAT( 1X, A, ', UPLO=''', A1, ''', N =', I5, ', type ', I1,
$ ', test(', I1, ')=', G12.5 )
9998 FORMAT( 1X, A, ', FACT=''', A1, ''', UPLO=''', A1, ''', N=', I5,
$ ', type ', I1, ', test(', I1, ')=', G12.5 )
9997 FORMAT( 1X, A, ', FACT=''', A1, ''', UPLO=''', A1, ''', N=', I5,
$ ', EQUED=''', A1, ''', type ', I1, ', test(', I1, ') =',
$ G12.5 )
RETURN
*
* End of ZDRVPO
*
END
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