192 lines
4.9 KiB
Fortran
192 lines
4.9 KiB
Fortran
*> \brief \b ZGET03
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE ZGET03( N, A, LDA, AINV, LDAINV, WORK, LDWORK, RWORK,
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* RCOND, RESID )
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*
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* .. Scalar Arguments ..
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* INTEGER LDA, LDAINV, LDWORK, N
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* DOUBLE PRECISION RCOND, RESID
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* ..
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* .. Array Arguments ..
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* DOUBLE PRECISION RWORK( * )
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* COMPLEX*16 A( LDA, * ), AINV( LDAINV, * ),
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* $ WORK( LDWORK, * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> ZGET03 computes the residual for a general matrix times its inverse:
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*> norm( I - AINV*A ) / ( N * norm(A) * norm(AINV) * EPS ),
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*> where EPS is the machine epsilon.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The number of rows and columns of the matrix A. N >= 0.
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*> \endverbatim
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*>
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*> \param[in] A
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*> \verbatim
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*> A is COMPLEX*16 array, dimension (LDA,N)
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*> The original N x N matrix A.
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is INTEGER
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*> The leading dimension of the array A. LDA >= max(1,N).
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*> \endverbatim
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*>
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*> \param[in] AINV
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*> \verbatim
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*> AINV is COMPLEX*16 array, dimension (LDAINV,N)
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*> The inverse of the matrix A.
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*> \endverbatim
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*>
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*> \param[in] LDAINV
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*> \verbatim
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*> LDAINV is INTEGER
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*> The leading dimension of the array AINV. LDAINV >= max(1,N).
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is COMPLEX*16 array, dimension (LDWORK,N)
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*> \endverbatim
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*>
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*> \param[in] LDWORK
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*> \verbatim
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*> LDWORK is INTEGER
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*> The leading dimension of the array WORK. LDWORK >= max(1,N).
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*> \endverbatim
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*>
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*> \param[out] RWORK
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*> \verbatim
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*> RWORK is DOUBLE PRECISION array, dimension (N)
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*> \endverbatim
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*>
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*> \param[out] RCOND
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*> \verbatim
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*> RCOND is DOUBLE PRECISION
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*> The reciprocal of the condition number of A, computed as
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*> ( 1/norm(A) ) / norm(AINV).
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*> \endverbatim
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*>
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*> \param[out] RESID
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*> \verbatim
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*> RESID is DOUBLE PRECISION
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*> norm(I - AINV*A) / ( N * norm(A) * norm(AINV) * EPS )
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \date November 2011
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*
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*> \ingroup complex16_lin
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*
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* =====================================================================
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SUBROUTINE ZGET03( N, A, LDA, AINV, LDAINV, WORK, LDWORK, RWORK,
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$ RCOND, RESID )
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*
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* -- LAPACK test routine (version 3.4.0) --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* November 2011
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*
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* .. Scalar Arguments ..
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INTEGER LDA, LDAINV, LDWORK, N
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DOUBLE PRECISION RCOND, RESID
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION RWORK( * )
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COMPLEX*16 A( LDA, * ), AINV( LDAINV, * ),
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$ WORK( LDWORK, * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ZERO, ONE
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PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
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COMPLEX*16 CZERO, CONE
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PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ),
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$ CONE = ( 1.0D+0, 0.0D+0 ) )
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* ..
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* .. Local Scalars ..
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INTEGER I
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DOUBLE PRECISION AINVNM, ANORM, EPS
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* ..
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* .. External Functions ..
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DOUBLE PRECISION DLAMCH, ZLANGE
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EXTERNAL DLAMCH, ZLANGE
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* ..
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* .. External Subroutines ..
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EXTERNAL ZGEMM
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC DBLE
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* ..
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* .. Executable Statements ..
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*
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* Quick exit if N = 0.
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*
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IF( N.LE.0 ) THEN
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RCOND = ONE
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RESID = ZERO
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RETURN
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END IF
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*
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* Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
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*
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EPS = DLAMCH( 'Epsilon' )
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ANORM = ZLANGE( '1', N, N, A, LDA, RWORK )
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AINVNM = ZLANGE( '1', N, N, AINV, LDAINV, RWORK )
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IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
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RCOND = ZERO
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RESID = ONE / EPS
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RETURN
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END IF
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RCOND = ( ONE / ANORM ) / AINVNM
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*
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* Compute I - A * AINV
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*
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CALL ZGEMM( 'No transpose', 'No transpose', N, N, N, -CONE, AINV,
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$ LDAINV, A, LDA, CZERO, WORK, LDWORK )
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DO 10 I = 1, N
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WORK( I, I ) = CONE + WORK( I, I )
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10 CONTINUE
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*
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* Compute norm(I - AINV*A) / (N * norm(A) * norm(AINV) * EPS)
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*
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RESID = ZLANGE( '1', N, N, WORK, LDWORK, RWORK )
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*
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RESID = ( ( RESID*RCOND ) / EPS ) / DBLE( N )
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*
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RETURN
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*
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* End of ZGET03
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*
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END
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