*> \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. * *> \ingroup single_lin * * ===================================================================== SUBROUTINE SGET01( M, N, A, LDA, AFAC, LDAFAC, IPIV, RWORK, $ RESID ) * * -- LAPACK test routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. 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