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dla_gerpvgrw.f
Go to the documentation of this file.
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*> \brief \b DLA_GERPVGRW
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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*> \htmlonly
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*> Download DLA_GERPVGRW + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dla_gerpvgrw.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dla_gerpvgrw.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dla_gerpvgrw.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* DOUBLE PRECISION FUNCTION DLA_GERPVGRW( N, NCOLS, A, LDA, AF,
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* LDAF )
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*
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* .. Scalar Arguments ..
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* INTEGER N, NCOLS, LDA, LDAF
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* ..
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* .. Array Arguments ..
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* DOUBLE PRECISION A( LDA, * ), AF( LDAF, * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*>
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*> DLA_GERPVGRW computes the reciprocal pivot growth factor
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*> norm(A)/norm(U). The "max absolute element" norm is used. If this is
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*> much less than 1, the stability of the LU factorization of the
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*> (equilibrated) matrix A could be poor. This also means that the
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*> solution X, estimated condition numbers, and error bounds could be
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*> unreliable.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The number of linear equations, i.e., the order of the
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*> matrix A. N >= 0.
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*> \endverbatim
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*>
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*> \param[in] NCOLS
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*> \verbatim
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*> NCOLS is INTEGER
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*> The number of columns of the matrix A. NCOLS >= 0.
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*> \endverbatim
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*>
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*> \param[in] A
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*> \verbatim
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*> A is DOUBLE PRECISION array, dimension (LDA,N)
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*> On entry, the N-by-N matrix A.
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is INTEGER
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*> The leading dimension of the array A. LDA >= max(1,N).
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*> \endverbatim
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*>
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*> \param[in] AF
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*> \verbatim
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*> AF is DOUBLE PRECISION array, dimension (LDAF,N)
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*> The factors L and U from the factorization
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*> A = P*L*U as computed by DGETRF.
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*> \endverbatim
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*>
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*> \param[in] LDAF
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*> \verbatim
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*> LDAF is INTEGER
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*> The leading dimension of the array AF. LDAF >= max(1,N).
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \date November 2011
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*
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*> \ingroup doubleGEcomputational
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*
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* =====================================================================
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DOUBLE PRECISION
FUNCTION
dla_gerpvgrw
( N, NCOLS, A, LDA, AF,
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$ ldaf )
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*
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* -- LAPACK computational routine (version 3.4.0) --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* November 2011
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*
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* .. Scalar Arguments ..
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INTEGER
n, ncols, lda, ldaf
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION
a( lda, * ), af( ldaf, * )
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* ..
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*
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* =====================================================================
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*
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* .. Local Scalars ..
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INTEGER
i,
j
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DOUBLE PRECISION
amax, umax, rpvgrw
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC
abs, max, min
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* ..
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* .. Executable Statements ..
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*
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rpvgrw = 1.0d+0
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DO
j
= 1, ncols
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amax = 0.0d+0
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umax = 0.0d+0
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DO
i = 1, n
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amax = max( abs( a( i,
j
) ), amax )
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END DO
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DO
i = 1,
j
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umax = max( abs( af( i,
j
) ), umax )
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END DO
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IF
( umax /= 0.0d+0 )
THEN
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rpvgrw = min( amax / umax, rpvgrw )
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END IF
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END DO
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dla_gerpvgrw
= rpvgrw
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END
src
dla_gerpvgrw.f
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