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Cloned library LAPACK-3.11.0 with extra build files for internal package management.
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LAPACK-3.11.0/TESTING/LIN/zchkhe.f

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*> \brief \b ZCHKHE
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZCHKHE( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
* THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X,
* XACT, WORK, RWORK, IWORK, NOUT )
*
* .. Scalar Arguments ..
* LOGICAL TSTERR
* INTEGER NMAX, NN, NNB, NNS, NOUT
* DOUBLE PRECISION THRESH
* ..
* .. Array Arguments ..
* LOGICAL DOTYPE( * )
* INTEGER IWORK( * ), NBVAL( * ), NSVAL( * ), NVAL( * )
* DOUBLE PRECISION RWORK( * )
* COMPLEX*16 A( * ), AFAC( * ), AINV( * ), B( * ),
* $ WORK( * ), X( * ), XACT( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZCHKHE tests ZHETRF, -TRI2, -TRS, -TRS2, -RFS, and -CON.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> DOTYPE is 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.
*> \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] NNB
*> \verbatim
*> NNB is INTEGER
*> The number of values of NB contained in the vector NBVAL.
*> \endverbatim
*>
*> \param[in] NBVAL
*> \verbatim
*> NBVAL is INTEGER array, dimension (NNB)
*> The values of the blocksize NB.
*> \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] 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[in] TSTERR
*> \verbatim
*> TSTERR is LOGICAL
*> Flag that indicates whether error exits are to be tested.
*> \endverbatim
*>
*> \param[in] NMAX
*> \verbatim
*> NMAX is INTEGER
*> The maximum value permitted for N, used in dimensioning the
*> work arrays.
*> \endverbatim
*>
*> \param[out] A
*> \verbatim
*> A 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*NSMAX)
*> where NSMAX is the largest entry in NSVAL.
*> \endverbatim
*>
*> \param[out] X
*> \verbatim
*> X is COMPLEX*16 array, dimension (NMAX*NSMAX)
*> \endverbatim
*>
*> \param[out] XACT
*> \verbatim
*> XACT is COMPLEX*16 array, dimension (NMAX*NSMAX)
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is COMPLEX*16 array, dimension (NMAX*max(3,NSMAX))
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*> RWORK is DOUBLE PRECISION array, dimension (max(NMAX,2*NSMAX))
*> \endverbatim
*>
*> \param[out] IWORK
*> \verbatim
*> IWORK is INTEGER array, dimension (NMAX)
*> \endverbatim
*>
*> \param[in] NOUT
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup complex16_lin
*
* =====================================================================
SUBROUTINE ZCHKHE( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
$ THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X,
$ XACT, WORK, RWORK, IWORK, NOUT )
*
* -- LAPACK test routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
LOGICAL TSTERR
INTEGER NMAX, NN, NNB, NNS, NOUT
DOUBLE PRECISION THRESH
* ..
* .. Array Arguments ..
LOGICAL DOTYPE( * )
INTEGER IWORK( * ), NBVAL( * ), NSVAL( * ), NVAL( * )
DOUBLE PRECISION RWORK( * )
COMPLEX*16 A( * ), AFAC( * ), AINV( * ), B( * ),
$ WORK( * ), X( * ), XACT( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO
PARAMETER ( ZERO = 0.0D+0 )
COMPLEX*16 CZERO
PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ) )
INTEGER NTYPES
PARAMETER ( NTYPES = 10 )
INTEGER NTESTS
PARAMETER ( NTESTS = 9 )
* ..
* .. Local Scalars ..
LOGICAL TRFCON, ZEROT
CHARACTER DIST, TYPE, UPLO, XTYPE
CHARACTER*3 PATH
INTEGER I, I1, I2, IMAT, IN, INB, INFO, IOFF, IRHS,
$ IUPLO, IZERO, J, K, KL, KU, LDA, LWORK, MODE,
$ N, NB, NERRS, NFAIL, NIMAT, NRHS, NRUN, NT
DOUBLE PRECISION ANORM, CNDNUM, RCOND, RCONDC
* ..
* .. Local Arrays ..
CHARACTER UPLOS( 2 )
INTEGER ISEED( 4 ), ISEEDY( 4 )
DOUBLE PRECISION RESULT( NTESTS )
* ..
* .. External Functions ..
DOUBLE PRECISION DGET06, ZLANHE
EXTERNAL DGET06, ZLANHE
* ..
* .. External Subroutines ..
EXTERNAL ALAERH, ALAHD, ALASUM, XLAENV, ZERRHE, ZGET04,
$ ZHECON, ZHERFS, ZHET01, ZHETRF, ZHETRI2,
$ ZHETRS, ZLACPY, ZLAIPD, ZLARHS, ZLATB4, ZLATMS,
$ ZPOT02, ZPOT03, ZPOT05
* ..
* .. 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 /
DATA UPLOS / 'U', 'L' /
* ..
* .. Executable Statements ..
*
* Initialize constants and the random number seed.
*
PATH( 1: 1 ) = 'Zomplex precision'
PATH( 2: 3 ) = 'HE'
NRUN = 0
NFAIL = 0
NERRS = 0
DO 10 I = 1, 4
ISEED( I ) = ISEEDY( I )
10 CONTINUE
*
* Test the error exits
*
IF( TSTERR )
$ CALL ZERRHE( PATH, NOUT )
INFOT = 0
*
* Set the minimum block size for which the block routine should
* be used, which will be later returned by ILAENV
*
CALL XLAENV( 2, 2 )
*
* Do for each value of N in NVAL
*
DO 180 IN = 1, NN
N = NVAL( IN )
LDA = MAX( N, 1 )
XTYPE = 'N'
NIMAT = NTYPES
IF( N.LE.0 )
$ NIMAT = 1
*
IZERO = 0
DO 170 IMAT = 1, NIMAT
*
* Do the tests only if DOTYPE( IMAT ) is true.
*
IF( .NOT.DOTYPE( IMAT ) )
$ GO TO 170
*
* Skip types 3, 4, 5, or 6 if the matrix size is too small.
*
ZEROT = IMAT.GE.3 .AND. IMAT.LE.6
IF( ZEROT .AND. N.LT.IMAT-2 )
$ GO TO 170
*
* Do first for UPLO = 'U', then for UPLO = 'L'
*
DO 160 IUPLO = 1, 2
UPLO = UPLOS( IUPLO )
*
* Set up parameters with ZLATB4 for the matrix generator
* based on the type of matrix to be generated.
*
CALL ZLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM, MODE,
$ CNDNUM, DIST )
*
* Generate a matrix with ZLATMS.
*
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 and handle error.
*
IF( INFO.NE.0 ) THEN
CALL ALAERH( PATH, 'ZLATMS', INFO, 0, UPLO, N, N, -1,
$ -1, -1, IMAT, NFAIL, NERRS, NOUT )
*
* Skip all tests for this generated matrix
*
GO TO 160
END IF
*
* For types 3-6, zero one or more rows and columns 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
*
IF( IMAT.LT.6 ) THEN
*
* Set row and column IZERO to zero.
*
IF( IUPLO.EQ.1 ) THEN
IOFF = ( IZERO-1 )*LDA
DO 20 I = 1, IZERO - 1
A( IOFF+I ) = CZERO
20 CONTINUE
IOFF = IOFF + IZERO
DO 30 I = IZERO, N
A( IOFF ) = CZERO
IOFF = IOFF + LDA
30 CONTINUE
ELSE
IOFF = IZERO
DO 40 I = 1, IZERO - 1
A( IOFF ) = CZERO
IOFF = IOFF + LDA
40 CONTINUE
IOFF = IOFF - IZERO
DO 50 I = IZERO, N
A( IOFF+I ) = CZERO
50 CONTINUE
END IF
ELSE
IF( IUPLO.EQ.1 ) THEN
*
* Set the first IZERO rows and columns to zero.
*
IOFF = 0
DO 70 J = 1, N
I2 = MIN( J, IZERO )
DO 60 I = 1, I2
A( IOFF+I ) = CZERO
60 CONTINUE
IOFF = IOFF + LDA
70 CONTINUE
ELSE
*
* Set the last IZERO rows and columns to zero.
*
IOFF = 0
DO 90 J = 1, N
I1 = MAX( J, IZERO )
DO 80 I = I1, N
A( IOFF+I ) = CZERO
80 CONTINUE
IOFF = IOFF + LDA
90 CONTINUE
END IF
END IF
ELSE
IZERO = 0
END IF
*
* End generate test matrix A.
*
*
* Set the imaginary part of the diagonals.
*
CALL ZLAIPD( N, A, LDA+1, 0 )
*
* Do for each value of NB in NBVAL
*
DO 150 INB = 1, NNB
*
* Set the optimal blocksize, which will be later
* returned by ILAENV.
*
NB = NBVAL( INB )
CALL XLAENV( 1, NB )
*
* Copy the test matrix A into matrix AFAC which
* will be factorized in place. This is needed to
* preserve the test matrix A for subsequent tests.
*
CALL ZLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
*
* Compute the L*D*L**T or U*D*U**T factorization of the
* matrix. IWORK stores details of the interchanges and
* the block structure of D. AINV is a work array for
* block factorization, LWORK is the length of AINV.
*
LWORK = MAX( 2, NB )*LDA
SRNAMT = 'ZHETRF'
CALL ZHETRF( UPLO, N, AFAC, LDA, IWORK, AINV, LWORK,
$ INFO )
*
* Adjust the expected value of INFO to account for
* pivoting.
*
K = IZERO
IF( K.GT.0 ) THEN
100 CONTINUE
IF( IWORK( K ).LT.0 ) THEN
IF( IWORK( K ).NE.-K ) THEN
K = -IWORK( K )
GO TO 100
END IF
ELSE IF( IWORK( K ).NE.K ) THEN
K = IWORK( K )
GO TO 100
END IF
END IF
*
* Check error code from ZHETRF and handle error.
*
IF( INFO.NE.K )
$ CALL ALAERH( PATH, 'ZHETRF', INFO, K, UPLO, N, N,
$ -1, -1, NB, IMAT, NFAIL, NERRS, NOUT )
*
* Set the condition estimate flag if the INFO is not 0.
*
IF( INFO.NE.0 ) THEN
TRFCON = .TRUE.
ELSE
TRFCON = .FALSE.
END IF
*
*+ TEST 1
* Reconstruct matrix from factors and compute residual.
*
CALL ZHET01( UPLO, N, A, LDA, AFAC, LDA, IWORK, AINV,
$ LDA, RWORK, RESULT( 1 ) )
NT = 1
*
*+ TEST 2
* Form the inverse and compute the residual.
*
IF( INB.EQ.1 .AND. .NOT.TRFCON ) THEN
CALL ZLACPY( UPLO, N, N, AFAC, LDA, AINV, LDA )
SRNAMT = 'ZHETRI2'
LWORK = (N+NB+1)*(NB+3)
CALL ZHETRI2( UPLO, N, AINV, LDA, IWORK, WORK,
$ LWORK, INFO )
*
* Check error code from ZHETRI and handle error.
*
IF( INFO.NE.0 )
$ CALL ALAERH( PATH, 'ZHETRI', INFO, -1, UPLO, N,
$ N, -1, -1, -1, IMAT, NFAIL, NERRS,
$ NOUT )
*
* Compute the residual for a symmetric matrix times
* its inverse.
*
CALL ZPOT03( UPLO, N, A, LDA, AINV, LDA, WORK, LDA,
$ RWORK, RCONDC, RESULT( 2 ) )
NT = 2
END IF
*
* Print information about the tests that did not pass
* the threshold.
*
DO 110 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 )UPLO, N, NB, IMAT, K,
$ RESULT( K )
NFAIL = NFAIL + 1
END IF
110 CONTINUE
NRUN = NRUN + NT
*
* Skip the other tests if this is not the first block
* size.
*
IF( INB.GT.1 )
$ GO TO 150
*
* Do only the condition estimate if INFO is not 0.
*
IF( TRFCON ) THEN
RCONDC = ZERO
GO TO 140
END IF
*
* Do for each value of NRHS in NSVAL.
*
DO 130 IRHS = 1, NNS
NRHS = NSVAL( IRHS )
*
*+ TEST 3 (Using TRS)
* Solve and compute residual for A * X = B.
*
* Choose a set of NRHS random solution vectors
* stored in XACT and set up the right hand side B
*
SRNAMT = 'ZLARHS'
CALL ZLARHS( PATH, XTYPE, UPLO, ' ', N, N, KL, KU,
$ NRHS, A, LDA, XACT, LDA, B, LDA,
$ ISEED, INFO )
CALL ZLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
*
SRNAMT = 'ZHETRS'
CALL ZHETRS( UPLO, N, NRHS, AFAC, LDA, IWORK, X,
$ LDA, INFO )
*
* Check error code from ZHETRS and handle error.
*
IF( INFO.NE.0 )
$ CALL ALAERH( PATH, 'ZHETRS', INFO, 0, UPLO, N,
$ N, -1, -1, NRHS, IMAT, NFAIL,
$ NERRS, NOUT )
*
CALL ZLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
*
* Compute the residual for the solution
*
CALL ZPOT02( UPLO, N, NRHS, A, LDA, X, LDA, WORK,
$ LDA, RWORK, RESULT( 3 ) )
*
*+ TEST 4 (Using TRS2)
* Solve and compute residual for A * X = B.
*
* Choose a set of NRHS random solution vectors
* stored in XACT and set up the right hand side B
*
SRNAMT = 'ZLARHS'
CALL ZLARHS( PATH, XTYPE, UPLO, ' ', N, N, KL, KU,
$ NRHS, A, LDA, XACT, LDA, B, LDA,
$ ISEED, INFO )
CALL ZLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
*
SRNAMT = 'ZHETRS2'
CALL ZHETRS2( UPLO, N, NRHS, AFAC, LDA, IWORK, X,
$ LDA, WORK, INFO )
*
* Check error code from ZHETRS2 and handle error.
*
IF( INFO.NE.0 )
$ CALL ALAERH( PATH, 'ZHETRS2', INFO, 0, UPLO, N,
$ N, -1, -1, NRHS, IMAT, NFAIL,
$ NERRS, NOUT )
*
CALL ZLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
*
* Compute the residual for the solution
*
CALL ZPOT02( UPLO, N, NRHS, A, LDA, X, LDA, WORK,
$ LDA, RWORK, RESULT( 4 ) )
*
*+ TEST 5
* Check solution from generated exact solution.
*
CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
$ RESULT( 5 ) )
*
*+ TESTS 6, 7, and 8
* Use iterative refinement to improve the solution.
*
SRNAMT = 'ZHERFS'
CALL ZHERFS( UPLO, 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 ZHERFS.
*
IF( INFO.NE.0 )
$ CALL ALAERH( PATH, 'ZHERFS', INFO, 0, UPLO, N,
$ N, -1, -1, NRHS, IMAT, NFAIL,
$ NERRS, NOUT )
*
CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
$ RESULT( 6 ) )
CALL ZPOT05( UPLO, N, NRHS, A, LDA, B, LDA, X, LDA,
$ XACT, LDA, RWORK, RWORK( NRHS+1 ),
$ RESULT( 7 ) )
*
* Print information about the tests that did not pass
* the threshold.
*
DO 120 K = 3, 8
IF( RESULT( K ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALAHD( NOUT, PATH )
WRITE( NOUT, FMT = 9998 )UPLO, N, NRHS,
$ IMAT, K, RESULT( K )
NFAIL = NFAIL + 1
END IF
120 CONTINUE
NRUN = NRUN + 6
*
* End do for each value of NRHS in NSVAL.
*
130 CONTINUE
*
*+ TEST 9
* Get an estimate of RCOND = 1/CNDNUM.
*
140 CONTINUE
ANORM = ZLANHE( '1', UPLO, N, A, LDA, RWORK )
SRNAMT = 'ZHECON'
CALL ZHECON( UPLO, N, AFAC, LDA, IWORK, ANORM, RCOND,
$ WORK, INFO )
*
* Check error code from ZHECON and handle error.
*
IF( INFO.NE.0 )
$ CALL ALAERH( PATH, 'ZHECON', INFO, 0, UPLO, N, N,
$ -1, -1, -1, IMAT, NFAIL, NERRS, NOUT )
*
RESULT( 9 ) = DGET06( RCOND, RCONDC )
*
* Print information about the tests that did not pass
* the threshold.
*
IF( RESULT( 9 ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALAHD( NOUT, PATH )
WRITE( NOUT, FMT = 9997 )UPLO, N, IMAT, 9,
$ RESULT( 9 )
NFAIL = NFAIL + 1
END IF
NRUN = NRUN + 1
150 CONTINUE
160 CONTINUE
170 CONTINUE
180 CONTINUE
*
* Print a summary of the results.
*
CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS )
*
9999 FORMAT( ' UPLO = ''', A1, ''', N =', I5, ', NB =', I4, ', type ',
$ I2, ', test ', I2, ', ratio =', G12.5 )
9998 FORMAT( ' UPLO = ''', A1, ''', N =', I5, ', NRHS=', I3, ', type ',
$ I2, ', test(', I2, ') =', G12.5 )
9997 FORMAT( ' UPLO = ''', A1, ''', N =', I5, ',', 10X, ' type ', I2,
$ ', test(', I2, ') =', G12.5 )
RETURN
*
* End of ZCHKHE
*
END