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*> \brief \b SGET01
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE SGET01( M, N, A, LDA, AFAC, LDAFAC, IPIV, RWORK,
* RESID )
*
* .. Scalar Arguments ..
* INTEGER LDA, LDAFAC, M, N
* REAL RESID
* ..
* .. Array Arguments ..
* INTEGER IPIV( * )
* REAL A( LDA, * ), AFAC( LDAFAC, * ), RWORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> SGET01 reconstructs a matrix A from its L*U factorization and
*> computes the residual
*> norm(L*U - A) / ( N * norm(A) * EPS ),
*> where EPS is the machine epsilon.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The number of rows of the matrix A. M >= 0.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of columns of the matrix A. N >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is REAL array, dimension (LDA,N)
*> The original M x N matrix A.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,M).
*> \endverbatim
*>
*> \param[in,out] AFAC
*> \verbatim
*> AFAC is REAL array, dimension (LDAFAC,N)
*> The factored form of the matrix A. AFAC contains the factors
*> L and U from the L*U factorization as computed by SGETRF.
*> Overwritten with the reconstructed matrix, and then with the
*> difference L*U - A.
*> \endverbatim
*>
*> \param[in] LDAFAC
*> \verbatim
*> LDAFAC is INTEGER
*> The leading dimension of the array AFAC. LDAFAC >= max(1,M).
*> \endverbatim
*>
*> \param[in] IPIV
*> \verbatim
*> IPIV is INTEGER array, dimension (N)
*> The pivot indices from SGETRF.
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*> RWORK is REAL array, dimension (M)
*> \endverbatim
*>
*> \param[out] RESID
*> \verbatim
*> RESID is REAL
*> norm(L*U - A) / ( N * norm(A) * 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 SGET01( M, N, A, LDA, AFAC, LDAFAC, IPIV, RWORK,
$ 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, LDAFAC, M, N
REAL RESID
* ..
* .. Array Arguments ..
INTEGER IPIV( * )
REAL A( LDA, * ), AFAC( LDAFAC, * ), RWORK( * )
* ..
*
* =====================================================================
*
*
* .. Parameters ..
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
* ..
* .. Local Scalars ..
INTEGER I, J, K
REAL ANORM, EPS, T
* ..
* .. External Functions ..
REAL SDOT, SLAMCH, SLANGE
EXTERNAL SDOT, SLAMCH, SLANGE
* ..
* .. External Subroutines ..
EXTERNAL SGEMV, SLASWP, SSCAL, STRMV
* ..
* .. Intrinsic Functions ..
INTRINSIC MIN, REAL
* ..
* .. Executable Statements ..
*
* Quick exit if M = 0 or N = 0.
*
IF( M.LE.0 .OR. N.LE.0 ) THEN
RESID = ZERO
RETURN
END IF
*
* Determine EPS and the norm of A.
*
EPS = SLAMCH( 'Epsilon' )
ANORM = SLANGE( '1', M, N, A, LDA, RWORK )
*
* Compute the product L*U and overwrite AFAC with the result.
* A column at a time of the product is obtained, starting with
* column N.
*
DO 10 K = N, 1, -1
IF( K.GT.M ) THEN
CALL STRMV( 'Lower', 'No transpose', 'Unit', M, AFAC,
$ LDAFAC, AFAC( 1, K ), 1 )
ELSE
*
* Compute elements (K+1:M,K)
*
T = AFAC( K, K )
IF( K+1.LE.M ) THEN
CALL SSCAL( M-K, T, AFAC( K+1, K ), 1 )
CALL SGEMV( 'No transpose', M-K, K-1, ONE,
$ AFAC( K+1, 1 ), LDAFAC, AFAC( 1, K ), 1, ONE,
$ AFAC( K+1, K ), 1 )
END IF
*
* Compute the (K,K) element
*
AFAC( K, K ) = T + SDOT( K-1, AFAC( K, 1 ), LDAFAC,
$ AFAC( 1, K ), 1 )
*
* Compute elements (1:K-1,K)
*
CALL STRMV( 'Lower', 'No transpose', 'Unit', K-1, AFAC,
$ LDAFAC, AFAC( 1, K ), 1 )
END IF
10 CONTINUE
CALL SLASWP( N, AFAC, LDAFAC, 1, MIN( M, N ), IPIV, -1 )
*
* Compute the difference L*U - A and store in AFAC.
*
DO 30 J = 1, N
DO 20 I = 1, M
AFAC( I, J ) = AFAC( I, J ) - A( I, J )
20 CONTINUE
30 CONTINUE
*
* Compute norm( L*U - A ) / ( N * norm(A) * EPS )
*
RESID = SLANGE( '1', M, N, AFAC, LDAFAC, RWORK )
*
IF( ANORM.LE.ZERO ) THEN
IF( RESID.NE.ZERO )
$ RESID = ONE / EPS
ELSE
RESID = ( ( RESID / REAL( N ) ) / ANORM ) / EPS
END IF
*
RETURN
*
* End of SGET01
*
END
|
