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*> \brief \b SGET03
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE SGET03( N, A, LDA, AINV, LDAINV, WORK, LDWORK, RWORK,
* RCOND, RESID )
*
* .. Scalar Arguments ..
* INTEGER LDA, LDAINV, LDWORK, N
* REAL RCOND, RESID
* ..
* .. Array Arguments ..
* REAL A( LDA, * ), AINV( LDAINV, * ), RWORK( * ),
* $ WORK( LDWORK, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> SGET03 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 REAL 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 REAL 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 REAL 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 REAL array, dimension (N)
*> \endverbatim
*>
*> \param[out] RCOND
*> \verbatim
*> RCOND is REAL
*> The reciprocal of the condition number of A, computed as
*> ( 1/norm(A) ) / norm(AINV).
*> \endverbatim
*>
*> \param[out] RESID
*> \verbatim
*> RESID is REAL
*> 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 single_lin
*
* =====================================================================
SUBROUTINE SGET03( 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
REAL RCOND, RESID
* ..
* .. Array Arguments ..
REAL A( LDA, * ), AINV( LDAINV, * ), RWORK( * ),
$ WORK( LDWORK, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
* ..
* .. Local Scalars ..
INTEGER I
REAL AINVNM, ANORM, EPS
* ..
* .. External Functions ..
REAL SLAMCH, SLANGE
EXTERNAL SLAMCH, SLANGE
* ..
* .. External Subroutines ..
EXTERNAL SGEMM
* ..
* .. Intrinsic Functions ..
INTRINSIC REAL
* ..
* .. 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 = SLAMCH( 'Epsilon' )
ANORM = SLANGE( '1', N, N, A, LDA, RWORK )
AINVNM = SLANGE( '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 SGEMM( 'No transpose', 'No transpose', N, N, N, -ONE,
$ AINV, LDAINV, A, LDA, ZERO, WORK, LDWORK )
DO 10 I = 1, N
WORK( I, I ) = ONE + WORK( I, I )
10 CONTINUE
*
* Compute norm(I - AINV*A) / (N * norm(A) * norm(AINV) * EPS)
*
RESID = SLANGE( '1', N, N, WORK, LDWORK, RWORK )
*
RESID = ( ( RESID*RCOND ) / EPS ) / REAL( N )
*
RETURN
*
* End of SGET03
*
END
|
