*> \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. * *> \ingroup single_lin * * ===================================================================== SUBROUTINE SGET03( N, A, LDA, AINV, LDAINV, WORK, LDWORK, RWORK, $ RCOND, 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, 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