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- *> \brief \b ZGET03
- *
- * =========== DOCUMENTATION ===========
- *
- * Online html documentation available at
- * http://www.netlib.org/lapack/explore-html/
- *
- * Definition:
- * ===========
- *
- * SUBROUTINE ZGET03( N, A, LDA, AINV, LDAINV, WORK, LDWORK, RWORK,
- * RCOND, RESID )
- *
- * .. Scalar Arguments ..
- * INTEGER LDA, LDAINV, LDWORK, N
- * DOUBLE PRECISION RCOND, RESID
- * ..
- * .. Array Arguments ..
- * DOUBLE PRECISION RWORK( * )
- * COMPLEX*16 A( LDA, * ), AINV( LDAINV, * ),
- * $ WORK( LDWORK, * )
- * ..
- *
- *
- *> \par Purpose:
- * =============
- *>
- *> \verbatim
- *>
- *> ZGET03 computes the residual for a general matrix times its inverse:
- *> norm( I - AINV*A ) / ( N * norm(A) * norm(AINV) * EPS ),
- *> where EPS is the machine epsilon.
- *> \endverbatim
- *
- * Arguments:
- * ==========
- *
- *> \param[in] N
- *> \verbatim
- *> N is INTEGER
- *> The number of rows and columns of the matrix A. N >= 0.
- *> \endverbatim
- *>
- *> \param[in] A
- *> \verbatim
- *> A is COMPLEX*16 array, dimension (LDA,N)
- *> The original N x N matrix A.
- *> \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)
- *> The inverse of the matrix A.
- *> \endverbatim
- *>
- *> \param[in] LDAINV
- *> \verbatim
- *> LDAINV is INTEGER
- *> The leading dimension of the array AINV. LDAINV >= max(1,N).
- *> \endverbatim
- *>
- *> \param[out] WORK
- *> \verbatim
- *> WORK is COMPLEX*16 array, dimension (LDWORK,N)
- *> \endverbatim
- *>
- *> \param[in] LDWORK
- *> \verbatim
- *> LDWORK is INTEGER
- *> The leading dimension of the array WORK. LDWORK >= max(1,N).
- *> \endverbatim
- *>
- *> \param[out] RWORK
- *> \verbatim
- *> RWORK is DOUBLE PRECISION array, dimension (N)
- *> \endverbatim
- *>
- *> \param[out] RCOND
- *> \verbatim
- *> RCOND is DOUBLE PRECISION
- *> The reciprocal of the condition number of A, computed as
- *> ( 1/norm(A) ) / norm(AINV).
- *> \endverbatim
- *>
- *> \param[out] RESID
- *> \verbatim
- *> RESID is DOUBLE PRECISION
- *> norm(I - AINV*A) / ( 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 December 2016
- *
- *> \ingroup complex16_lin
- *
- * =====================================================================
- SUBROUTINE ZGET03( N, A, LDA, AINV, LDAINV, WORK, LDWORK, RWORK,
- $ RCOND, RESID )
- *
- * -- 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, LDAINV, LDWORK, N
- DOUBLE PRECISION RCOND, RESID
- * ..
- * .. Array Arguments ..
- DOUBLE PRECISION RWORK( * )
- COMPLEX*16 A( LDA, * ), AINV( LDAINV, * ),
- $ WORK( LDWORK, * )
- * ..
- *
- * =====================================================================
- *
- * .. Parameters ..
- DOUBLE PRECISION ZERO, ONE
- PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
- COMPLEX*16 CZERO, CONE
- PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ),
- $ CONE = ( 1.0D+0, 0.0D+0 ) )
- * ..
- * .. Local Scalars ..
- INTEGER I
- DOUBLE PRECISION AINVNM, ANORM, EPS
- * ..
- * .. External Functions ..
- DOUBLE PRECISION DLAMCH, ZLANGE
- EXTERNAL DLAMCH, ZLANGE
- * ..
- * .. External Subroutines ..
- EXTERNAL ZGEMM
- * ..
- * .. 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 = ZLANGE( '1', N, N, A, LDA, RWORK )
- AINVNM = ZLANGE( '1', 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
- *
- * Compute I - A * AINV
- *
- CALL ZGEMM( 'No transpose', 'No transpose', N, N, N, -CONE, AINV,
- $ LDAINV, A, LDA, CZERO, WORK, LDWORK )
- DO 10 I = 1, N
- WORK( I, I ) = CONE + WORK( I, I )
- 10 CONTINUE
- *
- * Compute norm(I - AINV*A) / (N * norm(A) * norm(AINV) * EPS)
- *
- RESID = ZLANGE( '1', N, N, WORK, LDWORK, RWORK )
- *
- RESID = ( ( RESID*RCOND ) / EPS ) / DBLE( N )
- *
- RETURN
- *
- * End of ZGET03
- *
- END
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