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*> \brief \b ZTRT01
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZTRT01( UPLO, DIAG, N, A, LDA, AINV, LDAINV, RCOND,
* RWORK, RESID )
*
* .. Scalar Arguments ..
* CHARACTER DIAG, UPLO
* INTEGER LDA, LDAINV, N
* DOUBLE PRECISION RCOND, RESID
* ..
* .. Array Arguments ..
* DOUBLE PRECISION RWORK( * )
* COMPLEX*16 A( LDA, * ), AINV( LDAINV, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZTRT01 computes the residual for a triangular matrix A times its
*> inverse:
*> RESID = norm( A*AINV - I ) / ( N * norm(A) * norm(AINV) * EPS ),
*> where EPS is the machine epsilon.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> Specifies whether the matrix A is upper or lower triangular.
*> = 'U': Upper triangular
*> = 'L': Lower triangular
*> \endverbatim
*>
*> \param[in] DIAG
*> \verbatim
*> DIAG is CHARACTER*1
*> Specifies whether or not the matrix A is unit triangular.
*> = 'N': Non-unit triangular
*> = 'U': Unit triangular
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrix A. N >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is COMPLEX*16 array, dimension (LDA,N)
*> The triangular matrix A. If UPLO = 'U', the leading n by n
*> upper triangular part of the array A contains the upper
*> triangular matrix, and the strictly lower triangular part of
*> A is not referenced. If UPLO = 'L', the leading n by n lower
*> triangular part of the array A contains the lower triangular
*> matrix, and the strictly upper triangular part of A is not
*> referenced. If DIAG = 'U', the diagonal elements of A are
*> also not referenced and are assumed to be 1.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,N).
*> \endverbatim
*>
*> \param[in] AINV
*> \verbatim
*> AINV is COMPLEX*16 array, dimension (LDAINV,N)
*> On entry, the (triangular) inverse of the matrix A, in the
*> same storage format as A.
*> On exit, the contents of AINV are destroyed.
*> \endverbatim
*>
*> \param[in] LDAINV
*> \verbatim
*> LDAINV is INTEGER
*> The leading dimension of the array AINV. LDAINV >= max(1,N).
*> \endverbatim
*>
*> \param[out] RCOND
*> \verbatim
*> RCOND is DOUBLE PRECISION
*> The reciprocal condition number of A, computed as
*> 1/(norm(A) * norm(AINV)).
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*> RWORK is DOUBLE PRECISION array, dimension (N)
*> \endverbatim
*>
*> \param[out] RESID
*> \verbatim
*> RESID is DOUBLE PRECISION
*> norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS )
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup complex16_lin
*
* =====================================================================
SUBROUTINE ZTRT01( UPLO, DIAG, N, A, LDA, AINV, LDAINV, RCOND,
$ RWORK, RESID )
*
* -- LAPACK test routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
CHARACTER DIAG, UPLO
INTEGER LDA, LDAINV, N
DOUBLE PRECISION RCOND, RESID
* ..
* .. Array Arguments ..
DOUBLE PRECISION RWORK( * )
COMPLEX*16 A( LDA, * ), AINV( LDAINV, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
* ..
* .. Local Scalars ..
INTEGER J
DOUBLE PRECISION AINVNM, ANORM, EPS
* ..
* .. External Functions ..
LOGICAL LSAME
DOUBLE PRECISION DLAMCH, ZLANTR
EXTERNAL LSAME, DLAMCH, ZLANTR
* ..
* .. External Subroutines ..
EXTERNAL ZTRMV
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE
* ..
* .. Executable Statements ..
*
* Quick exit if N = 0
*
IF( N.LE.0 ) THEN
RCOND = ONE
RESID = ZERO
RETURN
END IF
*
* Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
*
EPS = DLAMCH( 'Epsilon' )
ANORM = ZLANTR( '1', UPLO, DIAG, N, N, A, LDA, RWORK )
AINVNM = ZLANTR( '1', UPLO, DIAG, N, N, AINV, LDAINV, RWORK )
IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
RCOND = ZERO
RESID = ONE / EPS
RETURN
END IF
RCOND = ( ONE / ANORM ) / AINVNM
*
* Set the diagonal of AINV to 1 if AINV has unit diagonal.
*
IF( LSAME( DIAG, 'U' ) ) THEN
DO 10 J = 1, N
AINV( J, J ) = ONE
10 CONTINUE
END IF
*
* Compute A * AINV, overwriting AINV.
*
IF( LSAME( UPLO, 'U' ) ) THEN
DO 20 J = 1, N
CALL ZTRMV( 'Upper', 'No transpose', DIAG, J, A, LDA,
$ AINV( 1, J ), 1 )
20 CONTINUE
ELSE
DO 30 J = 1, N
CALL ZTRMV( 'Lower', 'No transpose', DIAG, N-J+1, A( J, J ),
$ LDA, AINV( J, J ), 1 )
30 CONTINUE
END IF
*
* Subtract 1 from each diagonal element to form A*AINV - I.
*
DO 40 J = 1, N
AINV( J, J ) = AINV( J, J ) - ONE
40 CONTINUE
*
* Compute norm(A*AINV - I) / (N * norm(A) * norm(AINV) * EPS)
*
RESID = ZLANTR( '1', UPLO, 'Non-unit', N, N, AINV, LDAINV, RWORK )
*
RESID = ( ( RESID*RCOND ) / DBLE( N ) ) / EPS
*
RETURN
*
* End of ZTRT01
*
END
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