*> \brief \b DDRVRF3
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE DDRVRF3( NOUT, NN, NVAL, THRESH, A, LDA, ARF, B1, B2,
* + D_WORK_DLANGE, D_WORK_DGEQRF, TAU )
*
* .. Scalar Arguments ..
* INTEGER LDA, NN, NOUT
* DOUBLE PRECISION THRESH
* ..
* .. Array Arguments ..
* INTEGER NVAL( NN )
* DOUBLE PRECISION A( LDA, * ), ARF( * ), B1( LDA, * ),
* + B2( LDA, * ), D_WORK_DGEQRF( * ),
* + D_WORK_DLANGE( * ), TAU( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DDRVRF3 tests the LAPACK RFP routines:
*> DTFSM
*> \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] 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 DOUBLE PRECISION array, dimension (LDA,NMAX)
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,NMAX).
*> \endverbatim
*>
*> \param[out] ARF
*> \verbatim
*> ARF is DOUBLE PRECISION array, dimension ((NMAX*(NMAX+1))/2).
*> \endverbatim
*>
*> \param[out] B1
*> \verbatim
*> B1 is DOUBLE PRECISION array, dimension (LDA,NMAX)
*> \endverbatim
*>
*> \param[out] B2
*> \verbatim
*> B2 is DOUBLE PRECISION array, dimension (LDA,NMAX)
*> \endverbatim
*>
*> \param[out] D_WORK_DLANGE
*> \verbatim
*> D_WORK_DLANGE is DOUBLE PRECISION array, dimension (NMAX)
*> \endverbatim
*>
*> \param[out] D_WORK_DGEQRF
*> \verbatim
*> D_WORK_DGEQRF is DOUBLE PRECISION array, dimension (NMAX)
*> \endverbatim
*>
*> \param[out] TAU
*> \verbatim
*> TAU 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 December 2016
*
*> \ingroup double_lin
*
* =====================================================================
SUBROUTINE DDRVRF3( NOUT, NN, NVAL, THRESH, A, LDA, ARF, B1, B2,
+ D_WORK_DLANGE, D_WORK_DGEQRF, TAU )
*
* -- 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 ..
INTEGER LDA, NN, NOUT
DOUBLE PRECISION THRESH
* ..
* .. Array Arguments ..
INTEGER NVAL( NN )
DOUBLE PRECISION A( LDA, * ), ARF( * ), B1( LDA, * ),
+ B2( LDA, * ), D_WORK_DGEQRF( * ),
+ D_WORK_DLANGE( * ), TAU( * )
* ..
*
* =====================================================================
* ..
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) ,
+ ONE = ( 1.0D+0, 0.0D+0 ) )
INTEGER NTESTS
PARAMETER ( NTESTS = 1 )
* ..
* .. Local Scalars ..
CHARACTER UPLO, CFORM, DIAG, TRANS, SIDE
INTEGER I, IFORM, IIM, IIN, INFO, IUPLO, J, M, N, NA,
+ NFAIL, NRUN, ISIDE, IDIAG, IALPHA, ITRANS
DOUBLE PRECISION EPS, ALPHA
* ..
* .. Local Arrays ..
CHARACTER UPLOS( 2 ), FORMS( 2 ), TRANSS( 2 ),
+ DIAGS( 2 ), SIDES( 2 )
INTEGER ISEED( 4 ), ISEEDY( 4 )
DOUBLE PRECISION RESULT( NTESTS )
* ..
* .. External Functions ..
DOUBLE PRECISION DLAMCH, DLANGE, DLARND
EXTERNAL DLAMCH, DLANGE, DLARND
* ..
* .. External Subroutines ..
EXTERNAL DTRTTF, DGEQRF, DGEQLF, DTFSM, DTRSM
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, SQRT
* ..
* .. 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', 'T' /
DATA SIDES / 'L', 'R' /
DATA TRANSS / 'N', 'T' /
DATA DIAGS / 'N', 'U' /
* ..
* .. Executable Statements ..
*
* Initialize constants and the random number seed.
*
NRUN = 0
NFAIL = 0
INFO = 0
DO 10 I = 1, 4
ISEED( I ) = ISEEDY( I )
10 CONTINUE
EPS = DLAMCH( 'Precision' )
*
DO 170 IIM = 1, NN
*
M = NVAL( IIM )
*
DO 160 IIN = 1, NN
*
N = NVAL( IIN )
*
DO 150 IFORM = 1, 2
*
CFORM = FORMS( IFORM )
*
DO 140 IUPLO = 1, 2
*
UPLO = UPLOS( IUPLO )
*
DO 130 ISIDE = 1, 2
*
SIDE = SIDES( ISIDE )
*
DO 120 ITRANS = 1, 2
*
TRANS = TRANSS( ITRANS )
*
DO 110 IDIAG = 1, 2
*
DIAG = DIAGS( IDIAG )
*
DO 100 IALPHA = 1, 3
*
IF ( IALPHA.EQ. 1) THEN
ALPHA = ZERO
ELSE IF ( IALPHA.EQ. 1) THEN
ALPHA = ONE
ELSE
ALPHA = DLARND( 2, ISEED )
END IF
*
* All the parameters are set:
* CFORM, SIDE, UPLO, TRANS, DIAG, M, N,
* and ALPHA
* READY TO TEST!
*
NRUN = NRUN + 1
*
IF ( ISIDE.EQ.1 ) THEN
*
* The case ISIDE.EQ.1 is when SIDE.EQ.'L'
* -> A is M-by-M ( B is M-by-N )
*
NA = M
*
ELSE
*
* The case ISIDE.EQ.2 is when SIDE.EQ.'R'
* -> A is N-by-N ( B is M-by-N )
*
NA = N
*
END IF
*
* Generate A our NA--by--NA triangular
* matrix.
* Our test is based on forward error so we
* do want A to be well conditionned! To get
* a well-conditionned triangular matrix, we
* take the R factor of the QR/LQ factorization
* of a random matrix.
*
DO J = 1, NA
DO I = 1, NA
A( I, J) = DLARND( 2, ISEED )
END DO
END DO
*
IF ( IUPLO.EQ.1 ) THEN
*
* The case IUPLO.EQ.1 is when SIDE.EQ.'U'
* -> QR factorization.
*
SRNAMT = 'DGEQRF'
CALL DGEQRF( NA, NA, A, LDA, TAU,
+ D_WORK_DGEQRF, LDA,
+ INFO )
ELSE
*
* The case IUPLO.EQ.2 is when SIDE.EQ.'L'
* -> QL factorization.
*
SRNAMT = 'DGELQF'
CALL DGELQF( NA, NA, A, LDA, TAU,
+ D_WORK_DGEQRF, LDA,
+ INFO )
END IF
*
* Store a copy of A in RFP format (in ARF).
*
SRNAMT = 'DTRTTF'
CALL DTRTTF( CFORM, UPLO, NA, A, LDA, ARF,
+ INFO )
*
* Generate B1 our M--by--N right-hand side
* and store a copy in B2.
*
DO J = 1, N
DO I = 1, M
B1( I, J) = DLARND( 2, ISEED )
B2( I, J) = B1( I, J)
END DO
END DO
*
* Solve op( A ) X = B or X op( A ) = B
* with DTRSM
*
SRNAMT = 'DTRSM'
CALL DTRSM( SIDE, UPLO, TRANS, DIAG, M, N,
+ ALPHA, A, LDA, B1, LDA )
*
* Solve op( A ) X = B or X op( A ) = B
* with DTFSM
*
SRNAMT = 'DTFSM'
CALL DTFSM( CFORM, SIDE, UPLO, TRANS,
+ DIAG, M, N, ALPHA, ARF, B2,
+ LDA )
*
* Check that the result agrees.
*
DO J = 1, N
DO I = 1, M
B1( I, J) = B2( I, J ) - B1( I, J )
END DO
END DO
*
RESULT(1) = DLANGE( 'I', M, N, B1, LDA,
+ D_WORK_DLANGE )
*
RESULT(1) = RESULT(1) / SQRT( EPS )
+ / MAX ( MAX( M, N), 1 )
*
IF( RESULT(1).GE.THRESH ) THEN
IF( NFAIL.EQ.0 ) THEN
WRITE( NOUT, * )
WRITE( NOUT, FMT = 9999 )
END IF
WRITE( NOUT, FMT = 9997 ) 'DTFSM',
+ CFORM, SIDE, UPLO, TRANS, DIAG, M,
+ N, RESULT(1)
NFAIL = NFAIL + 1
END IF
*
100 CONTINUE
110 CONTINUE
120 CONTINUE
130 CONTINUE
140 CONTINUE
150 CONTINUE
160 CONTINUE
170 CONTINUE
*
* Print a summary of the results.
*
IF ( NFAIL.EQ.0 ) THEN
WRITE( NOUT, FMT = 9996 ) 'DTFSM', NRUN
ELSE
WRITE( NOUT, FMT = 9995 ) 'DTFSM', NFAIL, NRUN
END IF
*
9999 FORMAT( 1X, ' *** Error(s) or Failure(s) while testing DTFSM
+ ***')
9997 FORMAT( 1X, ' Failure in ',A5,', CFORM=''',A1,''',',
+ ' SIDE=''',A1,''',',' UPLO=''',A1,''',',' TRANS=''',A1,''',',
+ ' DIAG=''',A1,''',',' M=',I3,', N =', I3,', test=',G12.5)
9996 FORMAT( 1X, 'All tests for ',A5,' auxiliary routine passed the ',
+ 'threshold ( ',I5,' tests run)')
9995 FORMAT( 1X, A6, ' auxiliary routine: ',I5,' out of ',I5,
+ ' tests failed to pass the threshold')
*
RETURN
*
* End of DDRVRF3
*
END