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|
*> \brief \b ZDRVRFP
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* 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 )
*
* .. 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( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> 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, conversion 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.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] NOUT
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \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] NNS
*> \verbatim
*> NNS is INTEGER
*> The number of values of NRHS contained in the vector NSVAL.
*> \endverbatim
*>
*> \param[in] NSVAL
*> \verbatim
*> NSVAL is INTEGER array, dimension (NNS)
*> The values of the number of right-hand sides NRHS.
*> \endverbatim
*>
*> \param[in] NNT
*> \verbatim
*> NNT is INTEGER
*> The number of values of MATRIX TYPE contained in the vector NTVAL.
*> \endverbatim
*>
*> \param[in] NTVAL
*> \verbatim
*> NTVAL is INTEGER array, dimension (NNT)
*> The values of matrix type (between 0 and 9 for PO/PP/PF matrices).
*> \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[out] A
*> \verbatim
*> A is COMPLEX*16 array, dimension (NMAX*NMAX)
*> \endverbatim
*>
*> \param[out] ASAV
*> \verbatim
*> ASAV is COMPLEX*16 array, dimension (NMAX*NMAX)
*> \endverbatim
*>
*> \param[out] AFAC
*> \verbatim
*> AFAC is COMPLEX*16 array, dimension (NMAX*NMAX)
*> \endverbatim
*>
*> \param[out] AINV
*> \verbatim
*> AINV is COMPLEX*16 array, dimension (NMAX*NMAX)
*> \endverbatim
*>
*> \param[out] B
*> \verbatim
*> B is COMPLEX*16 array, dimension (NMAX*MAXRHS)
*> \endverbatim
*>
*> \param[out] BSAV
*> \verbatim
*> BSAV is COMPLEX*16 array, dimension (NMAX*MAXRHS)
*> \endverbatim
*>
*> \param[out] XACT
*> \verbatim
*> XACT is COMPLEX*16 array, dimension (NMAX*MAXRHS)
*> \endverbatim
*>
*> \param[out] X
*> \verbatim
*> X is COMPLEX*16 array, dimension (NMAX*MAXRHS)
*> \endverbatim
*>
*> \param[out] ARF
*> \verbatim
*> ARF is COMPLEX*16 array, dimension ((NMAX*(NMAX+1))/2)
*> \endverbatim
*>
*> \param[out] ARFINV
*> \verbatim
*> ARFINV is COMPLEX*16 array, dimension ((NMAX*(NMAX+1))/2)
*> \endverbatim
*>
*> \param[out] Z_WORK_ZLATMS
*> \verbatim
*> Z_WORK_ZLATMS is COMPLEX*16 array, dimension ( 3*NMAX )
*> \endverbatim
*>
*> \param[out] Z_WORK_ZPOT02
*> \verbatim
*> Z_WORK_ZPOT02 is COMPLEX*16 array, dimension ( NMAX*MAXRHS )
*> \endverbatim
*>
*> \param[out] Z_WORK_ZPOT03
*> \verbatim
*> Z_WORK_ZPOT03 is COMPLEX*16 array, dimension ( NMAX*NMAX )
*> \endverbatim
*>
*> \param[out] D_WORK_ZLATMS
*> \verbatim
*> D_WORK_ZLATMS is DOUBLE PRECISION array, dimension ( NMAX )
*> \endverbatim
*>
*> \param[out] D_WORK_ZLANHE
*> \verbatim
*> D_WORK_ZLANHE is DOUBLE PRECISION array, dimension ( NMAX )
*> \endverbatim
*>
*> \param[out] D_WORK_ZPOT01
*> \verbatim
*> D_WORK_ZPOT01 is DOUBLE PRECISION array, dimension ( NMAX )
*> \endverbatim
*>
*> \param[out] D_WORK_ZPOT02
*> \verbatim
*> D_WORK_ZPOT02 is DOUBLE PRECISION array, dimension ( NMAX )
*> \endverbatim
*>
*> \param[out] D_WORK_ZPOT03
*> \verbatim
*> D_WORK_ZPOT03 is DOUBLE PRECISION array, dimension ( NMAX )
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2013
*
*> \ingroup complex16_lin
*
* =====================================================================
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 )
*
* -- LAPACK test routine (version 3.5.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2013
*
* .. 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( * )
* ..
*
* =====================================================================
*
* .. 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.GE.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 )
IF ( N .NE. 0 ) THEN
*
* 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
*
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
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