*> \brief \b DLA_GERPVGRW * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLA_GERPVGRW + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * DOUBLE PRECISION FUNCTION DLA_GERPVGRW( N, NCOLS, A, LDA, AF, * LDAF ) * * .. Scalar Arguments .. * INTEGER N, NCOLS, LDA, LDAF * .. * .. Array Arguments .. * DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> *> DLA_GERPVGRW computes the reciprocal pivot growth factor *> norm(A)/norm(U). The "max absolute element" norm is used. If this is *> much less than 1, the stability of the LU factorization of the *> (equilibrated) matrix A could be poor. This also means that the *> solution X, estimated condition numbers, and error bounds could be *> unreliable. *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> The number of linear equations, i.e., the order of the *> matrix A. N >= 0. *> \endverbatim *> *> \param[in] NCOLS *> \verbatim *> NCOLS is INTEGER *> The number of columns of the matrix A. NCOLS >= 0. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA,N) *> On entry, the N-by-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] AF *> \verbatim *> AF is DOUBLE PRECISION array, dimension (LDAF,N) *> The factors L and U from the factorization *> A = P*L*U as computed by DGETRF. *> \endverbatim *> *> \param[in] LDAF *> \verbatim *> LDAF is INTEGER *> The leading dimension of the array AF. LDAF >= max(1,N). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup doubleGEcomputational * * ===================================================================== DOUBLE PRECISION FUNCTION DLA_GERPVGRW( N, NCOLS, A, LDA, AF, $ LDAF ) * * -- LAPACK computational 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 N, NCOLS, LDA, LDAF * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ) * .. * * ===================================================================== * * .. Local Scalars .. INTEGER I, J DOUBLE PRECISION AMAX, UMAX, RPVGRW * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, MIN * .. * .. Executable Statements .. * RPVGRW = 1.0D+0 DO J = 1, NCOLS AMAX = 0.0D+0 UMAX = 0.0D+0 DO I = 1, N AMAX = MAX( ABS( A( I, J ) ), AMAX ) END DO DO I = 1, J UMAX = MAX( ABS( AF( I, J ) ), UMAX ) END DO IF ( UMAX /= 0.0D+0 ) THEN RPVGRW = MIN( AMAX / UMAX, RPVGRW ) END IF END DO DLA_GERPVGRW = RPVGRW END