testdata/lapack/TESTING/LIN/zchktr.f
*> \brief \b ZCHKTR
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZCHKTR( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
* THRESH, TSTERR, NMAX, A, AINV, B, X, XACT,
* WORK, RWORK, NOUT )
*
* .. Scalar Arguments ..
* LOGICAL TSTERR
* INTEGER NMAX, NN, NNB, NNS, NOUT
* DOUBLE PRECISION THRESH
* ..
* .. Array Arguments ..
* LOGICAL DOTYPE( * )
* INTEGER NBVAL( * ), NSVAL( * ), NVAL( * )
* DOUBLE PRECISION RWORK( * )
* COMPLEX*16 A( * ), AINV( * ), B( * ), WORK( * ), X( * ),
* $ XACT( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZCHKTR tests ZTRTRI, -TRS, -RFS, and -CON, and ZLATRS
*> \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 column 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 leading dimension of the work arrays.
*> NMAX >= the maximum value of N in NVAL.
*> \endverbatim
*>
*> \param[out] A
*> \verbatim
*> A 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[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.
*
*> \date December 2016
*
*> \ingroup complex16_lin
*
* =====================================================================
SUBROUTINE ZCHKTR( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
$ THRESH, TSTERR, NMAX, A, AINV, B, X, XACT,
$ WORK, RWORK, NOUT )
*
* -- LAPACK test routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
*
* .. Scalar Arguments ..
LOGICAL TSTERR
INTEGER NMAX, NN, NNB, NNS, NOUT
DOUBLE PRECISION THRESH
* ..
* .. Array Arguments ..
LOGICAL DOTYPE( * )
INTEGER NBVAL( * ), NSVAL( * ), NVAL( * )
DOUBLE PRECISION RWORK( * )
COMPLEX*16 A( * ), AINV( * ), B( * ), WORK( * ), X( * ),
$ XACT( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
INTEGER NTYPE1, NTYPES
PARAMETER ( NTYPE1 = 10, NTYPES = 18 )
INTEGER NTESTS
PARAMETER ( NTESTS = 9 )
INTEGER NTRAN
PARAMETER ( NTRAN = 3 )
DOUBLE PRECISION ONE, ZERO
PARAMETER ( ONE = 1.0D0, ZERO = 0.0D0 )
* ..
* .. Local Scalars ..
CHARACTER DIAG, NORM, TRANS, UPLO, XTYPE
CHARACTER*3 PATH
INTEGER I, IDIAG, IMAT, IN, INB, INFO, IRHS, ITRAN,
$ IUPLO, K, LDA, N, NB, NERRS, NFAIL, NRHS, NRUN
DOUBLE PRECISION AINVNM, ANORM, DUMMY, RCOND, RCONDC, RCONDI,
$ RCONDO, SCALE
* ..
* .. Local Arrays ..
CHARACTER TRANSS( NTRAN ), UPLOS( 2 )
INTEGER ISEED( 4 ), ISEEDY( 4 )
DOUBLE PRECISION RESULT( NTESTS )
* ..
* .. External Functions ..
LOGICAL LSAME
DOUBLE PRECISION ZLANTR
EXTERNAL LSAME, ZLANTR
* ..
* .. External Subroutines ..
EXTERNAL ALAERH, ALAHD, ALASUM, XLAENV, ZCOPY, ZERRTR,
$ ZGET04, ZLACPY, ZLARHS, ZLATRS, ZLATTR, ZTRCON,
$ ZTRRFS, ZTRT01, ZTRT02, ZTRT03, ZTRT05, ZTRT06,
$ ZTRTRI, ZTRTRS
* ..
* .. Scalars in Common ..
LOGICAL LERR, OK
CHARACTER*32 SRNAMT
INTEGER INFOT, IOUNIT
* ..
* .. Common blocks ..
COMMON / INFOC / INFOT, IOUNIT, OK, LERR
COMMON / SRNAMC / SRNAMT
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Data statements ..
DATA ISEEDY / 1988, 1989, 1990, 1991 /
DATA UPLOS / 'U', 'L' / , TRANSS / 'N', 'T', 'C' /
* ..
* .. Executable Statements ..
*
* Initialize constants and the random number seed.
*
PATH( 1: 1 ) = 'Zomplex precision'
PATH( 2: 3 ) = 'TR'
NRUN = 0
NFAIL = 0
NERRS = 0
DO 10 I = 1, 4
ISEED( I ) = ISEEDY( I )
10 CONTINUE
*
* Test the error exits
*
IF( TSTERR )
$ CALL ZERRTR( PATH, NOUT )
INFOT = 0
*
DO 120 IN = 1, NN
*
* Do for each value of N in NVAL
*
N = NVAL( IN )
LDA = MAX( 1, N )
XTYPE = 'N'
*
DO 80 IMAT = 1, NTYPE1
*
* Do the tests only if DOTYPE( IMAT ) is true.
*
IF( .NOT.DOTYPE( IMAT ) )
$ GO TO 80
*
DO 70 IUPLO = 1, 2
*
* Do first for UPLO = 'U', then for UPLO = 'L'
*
UPLO = UPLOS( IUPLO )
*
* Call ZLATTR to generate a triangular test matrix.
*
SRNAMT = 'ZLATTR'
CALL ZLATTR( IMAT, UPLO, 'No transpose', DIAG, ISEED, N,
$ A, LDA, X, WORK, RWORK, INFO )
*
* Set IDIAG = 1 for non-unit matrices, 2 for unit.
*
IF( LSAME( DIAG, 'N' ) ) THEN
IDIAG = 1
ELSE
IDIAG = 2
END IF
*
DO 60 INB = 1, NNB
*
* Do for each blocksize in NBVAL
*
NB = NBVAL( INB )
CALL XLAENV( 1, NB )
*
*+ TEST 1
* Form the inverse of A.
*
CALL ZLACPY( UPLO, N, N, A, LDA, AINV, LDA )
SRNAMT = 'ZTRTRI'
CALL ZTRTRI( UPLO, DIAG, N, AINV, LDA, INFO )
*
* Check error code from ZTRTRI.
*
IF( INFO.NE.0 )
$ CALL ALAERH( PATH, 'ZTRTRI', INFO, 0, UPLO // DIAG,
$ N, N, -1, -1, NB, IMAT, NFAIL, NERRS,
$ NOUT )
*
* Compute the infinity-norm condition number of A.
*
ANORM = ZLANTR( 'I', UPLO, DIAG, N, N, A, LDA, RWORK )
AINVNM = ZLANTR( 'I', UPLO, DIAG, N, N, AINV, LDA,
$ RWORK )
IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
RCONDI = ONE
ELSE
RCONDI = ( ONE / ANORM ) / AINVNM
END IF
*
* Compute the residual for the triangular matrix times
* its inverse. Also compute the 1-norm condition number
* of A.
*
CALL ZTRT01( UPLO, DIAG, N, A, LDA, AINV, LDA, RCONDO,
$ 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, DIAG, N, NB, IMAT,
$ 1, RESULT( 1 )
NFAIL = NFAIL + 1
END IF
NRUN = NRUN + 1
*
* Skip remaining tests if not the first block size.
*
IF( INB.NE.1 )
$ GO TO 60
*
DO 40 IRHS = 1, NNS
NRHS = NSVAL( IRHS )
XTYPE = 'N'
*
DO 30 ITRAN = 1, NTRAN
*
* Do for op(A) = A, A**T, or A**H.
*
TRANS = TRANSS( ITRAN )
IF( ITRAN.EQ.1 ) THEN
NORM = 'O'
RCONDC = RCONDO
ELSE
NORM = 'I'
RCONDC = RCONDI
END IF
*
*+ TEST 2
* Solve and compute residual for op(A)*x = b.
*
SRNAMT = 'ZLARHS'
CALL ZLARHS( PATH, XTYPE, UPLO, TRANS, N, N, 0,
$ IDIAG, NRHS, A, LDA, XACT, LDA, B,
$ LDA, ISEED, INFO )
XTYPE = 'C'
CALL ZLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
*
SRNAMT = 'ZTRTRS'
CALL ZTRTRS( UPLO, TRANS, DIAG, N, NRHS, A, LDA,
$ X, LDA, INFO )
*
* Check error code from ZTRTRS.
*
IF( INFO.NE.0 )
$ CALL ALAERH( PATH, 'ZTRTRS', INFO, 0,
$ UPLO // TRANS // DIAG, N, N, -1,
$ -1, NRHS, IMAT, NFAIL, NERRS,
$ NOUT )
*
* This line is needed on a Sun SPARCstation.
*
IF( N.GT.0 )
$ DUMMY = A( 1 )
*
CALL ZTRT02( UPLO, TRANS, DIAG, N, NRHS, A, LDA,
$ X, LDA, B, LDA, WORK, RWORK,
$ RESULT( 2 ) )
*
*+ TEST 3
* Check solution from generated exact solution.
*
CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
$ RESULT( 3 ) )
*
*+ TESTS 4, 5, and 6
* Use iterative refinement to improve the solution
* and compute error bounds.
*
SRNAMT = 'ZTRRFS'
CALL ZTRRFS( UPLO, TRANS, DIAG, N, NRHS, A, LDA,
$ B, LDA, X, LDA, RWORK,
$ RWORK( NRHS+1 ), WORK,
$ RWORK( 2*NRHS+1 ), INFO )
*
* Check error code from ZTRRFS.
*
IF( INFO.NE.0 )
$ CALL ALAERH( PATH, 'ZTRRFS', INFO, 0,
$ UPLO // TRANS // DIAG, N, N, -1,
$ -1, NRHS, IMAT, NFAIL, NERRS,
$ NOUT )
*
CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
$ RESULT( 4 ) )
CALL ZTRT05( UPLO, TRANS, DIAG, N, NRHS, A, LDA,
$ B, LDA, X, LDA, XACT, LDA, RWORK,
$ RWORK( NRHS+1 ), RESULT( 5 ) )
*
* Print information about the tests that did not
* pass the threshold.
*
DO 20 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, TRANS,
$ DIAG, N, NRHS, IMAT, K, RESULT( K )
NFAIL = NFAIL + 1
END IF
20 CONTINUE
NRUN = NRUN + 5
30 CONTINUE
40 CONTINUE
*
*+ TEST 7
* Get an estimate of RCOND = 1/CNDNUM.
*
DO 50 ITRAN = 1, 2
IF( ITRAN.EQ.1 ) THEN
NORM = 'O'
RCONDC = RCONDO
ELSE
NORM = 'I'
RCONDC = RCONDI
END IF
SRNAMT = 'ZTRCON'
CALL ZTRCON( NORM, UPLO, DIAG, N, A, LDA, RCOND,
$ WORK, RWORK, INFO )
*
* Check error code from ZTRCON.
*
IF( INFO.NE.0 )
$ CALL ALAERH( PATH, 'ZTRCON', INFO, 0,
$ NORM // UPLO // DIAG, N, N, -1, -1,
$ -1, IMAT, NFAIL, NERRS, NOUT )
*
CALL ZTRT06( RCOND, RCONDC, UPLO, DIAG, N, A, LDA,
$ RWORK, RESULT( 7 ) )
*
* 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 )NORM, UPLO, N, IMAT,
$ 7, RESULT( 7 )
NFAIL = NFAIL + 1
END IF
NRUN = NRUN + 1
50 CONTINUE
60 CONTINUE
70 CONTINUE
80 CONTINUE
*
* Use pathological test matrices to test ZLATRS.
*
DO 110 IMAT = NTYPE1 + 1, NTYPES
*
* Do the tests only if DOTYPE( IMAT ) is true.
*
IF( .NOT.DOTYPE( IMAT ) )
$ GO TO 110
*
DO 100 IUPLO = 1, 2
*
* Do first for UPLO = 'U', then for UPLO = 'L'
*
UPLO = UPLOS( IUPLO )
DO 90 ITRAN = 1, NTRAN
*
* Do for op(A) = A, A**T, and A**H.
*
TRANS = TRANSS( ITRAN )
*
* Call ZLATTR to generate a triangular test matrix.
*
SRNAMT = 'ZLATTR'
CALL ZLATTR( IMAT, UPLO, TRANS, DIAG, ISEED, N, A,
$ LDA, X, WORK, RWORK, INFO )
*
*+ TEST 8
* Solve the system op(A)*x = b.
*
SRNAMT = 'ZLATRS'
CALL ZCOPY( N, X, 1, B, 1 )
CALL ZLATRS( UPLO, TRANS, DIAG, 'N', N, A, LDA, B,
$ SCALE, RWORK, INFO )
*
* Check error code from ZLATRS.
*
IF( INFO.NE.0 )
$ CALL ALAERH( PATH, 'ZLATRS', INFO, 0,
$ UPLO // TRANS // DIAG // 'N', N, N,
$ -1, -1, -1, IMAT, NFAIL, NERRS, NOUT )
*
CALL ZTRT03( UPLO, TRANS, DIAG, N, 1, A, LDA, SCALE,
$ RWORK, ONE, B, LDA, X, LDA, WORK,
$ RESULT( 8 ) )
*
*+ TEST 9
* Solve op(A)*X = b again with NORMIN = 'Y'.
*
CALL ZCOPY( N, X, 1, B( N+1 ), 1 )
CALL ZLATRS( UPLO, TRANS, DIAG, 'Y', N, A, LDA,
$ B( N+1 ), SCALE, RWORK, INFO )
*
* Check error code from ZLATRS.
*
IF( INFO.NE.0 )
$ CALL ALAERH( PATH, 'ZLATRS', INFO, 0,
$ UPLO // TRANS // DIAG // 'Y', N, N,
$ -1, -1, -1, IMAT, NFAIL, NERRS, NOUT )
*
CALL ZTRT03( UPLO, TRANS, DIAG, N, 1, A, LDA, SCALE,
$ RWORK, ONE, B( N+1 ), LDA, X, LDA, WORK,
$ RESULT( 9 ) )
*
* Print information about the tests that did not pass
* the threshold.
*
IF( RESULT( 8 ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALAHD( NOUT, PATH )
WRITE( NOUT, FMT = 9996 )'ZLATRS', UPLO, TRANS,
$ DIAG, 'N', N, IMAT, 8, RESULT( 8 )
NFAIL = NFAIL + 1
END IF
IF( RESULT( 9 ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALAHD( NOUT, PATH )
WRITE( NOUT, FMT = 9996 )'ZLATRS', UPLO, TRANS,
$ DIAG, 'Y', N, IMAT, 9, RESULT( 9 )
NFAIL = NFAIL + 1
END IF
NRUN = NRUN + 2
90 CONTINUE
100 CONTINUE
110 CONTINUE
120 CONTINUE
*
* Print a summary of the results.
*
CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS )
*
9999 FORMAT( ' UPLO=''', A1, ''', DIAG=''', A1, ''', N=', I5, ', NB=',
$ I4, ', type ', I2, ', test(', I2, ')= ', G12.5 )
9998 FORMAT( ' UPLO=''', A1, ''', TRANS=''', A1, ''', DIAG=''', A1,
$ ''', N=', I5, ', NB=', I4, ', type ', I2, ',
$ test(', I2, ')= ', G12.5 )
9997 FORMAT( ' NORM=''', A1, ''', UPLO =''', A1, ''', N=', I5, ',',
$ 11X, ' type ', I2, ', test(', I2, ')=', G12.5 )
9996 FORMAT( 1X, A, '( ''', A1, ''', ''', A1, ''', ''', A1, ''', ''',
$ A1, ''',', I5, ', ... ), type ', I2, ', test(', I2, ')=',
$ G12.5 )
RETURN
*
* End of ZCHKTR
*
END