version 1.6, 2010/08/13 21:03:50
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version 1.11, 2012/12/14 12:30:24
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*> \brief \b DLAQSY scales a symmetric/Hermitian matrix, using scaling factors computed by spoequ. |
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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 DLAQSY + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaqsy.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/dlaqsy.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/dlaqsy.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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* SUBROUTINE DLAQSY( UPLO, N, A, LDA, S, SCOND, AMAX, EQUED ) |
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* |
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* .. Scalar Arguments .. |
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* CHARACTER EQUED, UPLO |
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* INTEGER LDA, N |
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* DOUBLE PRECISION AMAX, SCOND |
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* .. |
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* .. Array Arguments .. |
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* DOUBLE PRECISION A( LDA, * ), S( * ) |
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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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*> DLAQSY equilibrates a symmetric matrix A using the scaling factors |
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*> in the vector S. |
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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] UPLO |
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*> \verbatim |
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*> UPLO is CHARACTER*1 |
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*> Specifies whether the upper or lower triangular part of the |
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*> symmetric matrix A is stored. |
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*> = 'U': Upper triangular |
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*> = 'L': Lower triangular |
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*> \endverbatim |
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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 order of the matrix A. N >= 0. |
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*> \endverbatim |
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*> |
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*> \param[in,out] 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 symmetric matrix A. If UPLO = 'U', the leading |
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*> n by n upper triangular part of A contains the upper |
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*> triangular part of the matrix A, and the strictly lower |
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*> triangular part of A is not referenced. If UPLO = 'L', the |
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*> leading n by n lower triangular part of A contains the lower |
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*> triangular part of the matrix A, and the strictly upper |
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*> triangular part of A is not referenced. |
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*> |
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*> On exit, if EQUED = 'Y', the equilibrated matrix: |
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*> diag(S) * A * diag(S). |
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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(N,1). |
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*> \endverbatim |
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*> |
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*> \param[in] S |
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*> \verbatim |
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*> S is DOUBLE PRECISION array, dimension (N) |
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*> The scale factors for A. |
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*> \endverbatim |
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*> |
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*> \param[in] SCOND |
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*> \verbatim |
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*> SCOND is DOUBLE PRECISION |
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*> Ratio of the smallest S(i) to the largest S(i). |
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*> \endverbatim |
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*> |
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*> \param[in] AMAX |
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*> \verbatim |
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*> AMAX is DOUBLE PRECISION |
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*> Absolute value of largest matrix entry. |
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*> \endverbatim |
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*> |
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*> \param[out] EQUED |
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*> \verbatim |
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*> EQUED is CHARACTER*1 |
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*> Specifies whether or not equilibration was done. |
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*> = 'N': No equilibration. |
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*> = 'Y': Equilibration was done, i.e., A has been replaced by |
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*> diag(S) * A * diag(S). |
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*> \endverbatim |
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* |
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*> \par Internal Parameters: |
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* ========================= |
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*> |
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*> \verbatim |
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*> THRESH is a threshold value used to decide if scaling should be done |
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*> based on the ratio of the scaling factors. If SCOND < THRESH, |
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*> scaling is done. |
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*> |
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*> LARGE and SMALL are threshold values used to decide if scaling should |
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*> be done based on the absolute size of the largest matrix element. |
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*> If AMAX > LARGE or AMAX < SMALL, scaling is done. |
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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 September 2012 |
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* |
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*> \ingroup doubleSYauxiliary |
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* |
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* ===================================================================== |
SUBROUTINE DLAQSY( UPLO, N, A, LDA, S, SCOND, AMAX, EQUED ) |
SUBROUTINE DLAQSY( UPLO, N, A, LDA, S, SCOND, AMAX, EQUED ) |
* |
* |
* -- LAPACK auxiliary routine (version 3.2) -- |
* -- LAPACK auxiliary routine (version 3.4.2) -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* November 2006 |
* September 2012 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER EQUED, UPLO |
CHARACTER EQUED, UPLO |
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DOUBLE PRECISION A( LDA, * ), S( * ) |
DOUBLE PRECISION A( LDA, * ), S( * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* DLAQSY equilibrates a symmetric matrix A using the scaling factors |
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* in the vector S. |
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* |
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* Arguments |
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* ========= |
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* |
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* UPLO (input) CHARACTER*1 |
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* Specifies whether the upper or lower triangular part of the |
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* symmetric matrix A is stored. |
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* = 'U': Upper triangular |
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* = 'L': Lower triangular |
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* |
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* N (input) INTEGER |
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* The order of the matrix A. N >= 0. |
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* |
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* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) |
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* On entry, the symmetric matrix A. If UPLO = 'U', the leading |
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* n by n upper triangular part of A contains the upper |
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* triangular part of the matrix A, and the strictly lower |
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* triangular part of A is not referenced. If UPLO = 'L', the |
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* leading n by n lower triangular part of A contains the lower |
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* triangular part of the matrix A, and the strictly upper |
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* triangular part of A is not referenced. |
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* |
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* On exit, if EQUED = 'Y', the equilibrated matrix: |
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* diag(S) * A * diag(S). |
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* |
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* LDA (input) INTEGER |
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* The leading dimension of the array A. LDA >= max(N,1). |
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* |
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* S (input) DOUBLE PRECISION array, dimension (N) |
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* The scale factors for A. |
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* |
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* SCOND (input) DOUBLE PRECISION |
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* Ratio of the smallest S(i) to the largest S(i). |
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* |
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* AMAX (input) DOUBLE PRECISION |
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* Absolute value of largest matrix entry. |
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* |
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* EQUED (output) CHARACTER*1 |
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* Specifies whether or not equilibration was done. |
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* = 'N': No equilibration. |
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* = 'Y': Equilibration was done, i.e., A has been replaced by |
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* diag(S) * A * diag(S). |
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* |
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* Internal Parameters |
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* =================== |
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* |
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* THRESH is a threshold value used to decide if scaling should be done |
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* based on the ratio of the scaling factors. If SCOND < THRESH, |
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* scaling is done. |
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* |
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* LARGE and SMALL are threshold values used to decide if scaling should |
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* be done based on the absolute size of the largest matrix element. |
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* If AMAX > LARGE or AMAX < SMALL, scaling is done. |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |