version 1.5, 2010/08/07 13:22:18
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version 1.14, 2016/08/27 15:34:29
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*> \brief \b DLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ. |
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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 DLAQGB + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaqgb.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/dlaqgb.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/dlaqgb.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 DLAQGB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, |
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* AMAX, EQUED ) |
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* |
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* .. Scalar Arguments .. |
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* CHARACTER EQUED |
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* INTEGER KL, KU, LDAB, M, N |
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* DOUBLE PRECISION AMAX, COLCND, ROWCND |
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* .. |
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* .. Array Arguments .. |
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* DOUBLE PRECISION AB( LDAB, * ), C( * ), R( * ) |
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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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*> DLAQGB equilibrates a general M by N band matrix A with KL |
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*> subdiagonals and KU superdiagonals using the row and scaling factors |
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*> in the vectors R and C. |
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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] M |
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*> \verbatim |
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*> M is INTEGER |
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*> The number of rows of the matrix A. M >= 0. |
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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 number of columns of the matrix A. N >= 0. |
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*> \endverbatim |
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*> |
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*> \param[in] KL |
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*> \verbatim |
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*> KL is INTEGER |
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*> The number of subdiagonals within the band of A. KL >= 0. |
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*> \endverbatim |
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*> |
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*> \param[in] KU |
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*> \verbatim |
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*> KU is INTEGER |
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*> The number of superdiagonals within the band of A. KU >= 0. |
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*> \endverbatim |
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*> |
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*> \param[in,out] AB |
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*> \verbatim |
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*> AB is DOUBLE PRECISION array, dimension (LDAB,N) |
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*> On entry, the matrix A in band storage, in rows 1 to KL+KU+1. |
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*> The j-th column of A is stored in the j-th column of the |
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*> array AB as follows: |
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*> AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl) |
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*> |
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*> On exit, the equilibrated matrix, in the same storage format |
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*> as A. See EQUED for the form of the equilibrated matrix. |
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*> \endverbatim |
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*> |
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*> \param[in] LDAB |
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*> \verbatim |
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*> LDAB is INTEGER |
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*> The leading dimension of the array AB. LDA >= KL+KU+1. |
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*> \endverbatim |
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*> |
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*> \param[in] R |
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*> \verbatim |
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*> R is DOUBLE PRECISION array, dimension (M) |
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*> The row scale factors for A. |
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*> \endverbatim |
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*> |
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*> \param[in] C |
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*> \verbatim |
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*> C is DOUBLE PRECISION array, dimension (N) |
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*> The column scale factors for A. |
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*> \endverbatim |
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*> |
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*> \param[in] ROWCND |
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*> \verbatim |
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*> ROWCND is DOUBLE PRECISION |
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*> Ratio of the smallest R(i) to the largest R(i). |
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*> \endverbatim |
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*> |
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*> \param[in] COLCND |
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*> \verbatim |
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*> COLCND is DOUBLE PRECISION |
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*> Ratio of the smallest C(i) to the largest C(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 the form of equilibration that was done. |
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*> = 'N': No equilibration |
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*> = 'R': Row equilibration, i.e., A has been premultiplied by |
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*> diag(R). |
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*> = 'C': Column equilibration, i.e., A has been postmultiplied |
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*> by diag(C). |
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*> = 'B': Both row and column equilibration, i.e., A has been |
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*> replaced by diag(R) * A * diag(C). |
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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 row or column scaling |
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*> should be done based on the ratio of the row or column scaling |
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*> factors. If ROWCND < THRESH, row scaling is done, and if |
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*> COLCND < THRESH, column scaling is done. |
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*> |
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*> LARGE and SMALL are threshold values used to decide if row scaling |
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*> should be done based on the absolute size of the largest matrix |
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*> element. If AMAX > LARGE or AMAX < SMALL, row 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 doubleGBauxiliary |
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* |
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* ===================================================================== |
SUBROUTINE DLAQGB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, |
SUBROUTINE DLAQGB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, |
$ AMAX, EQUED ) |
$ 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 |
CHARACTER EQUED |
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DOUBLE PRECISION AB( LDAB, * ), C( * ), R( * ) |
DOUBLE PRECISION AB( LDAB, * ), C( * ), R( * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* DLAQGB equilibrates a general M by N band matrix A with KL |
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* subdiagonals and KU superdiagonals using the row and scaling factors |
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* in the vectors R and C. |
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* |
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* Arguments |
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* ========= |
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* |
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* M (input) INTEGER |
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* The number of rows of the matrix A. M >= 0. |
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* |
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* N (input) INTEGER |
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* The number of columns of the matrix A. N >= 0. |
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* |
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* KL (input) INTEGER |
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* The number of subdiagonals within the band of A. KL >= 0. |
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* |
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* KU (input) INTEGER |
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* The number of superdiagonals within the band of A. KU >= 0. |
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* |
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* AB (input/output) DOUBLE PRECISION array, dimension (LDAB,N) |
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* On entry, the matrix A in band storage, in rows 1 to KL+KU+1. |
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* The j-th column of A is stored in the j-th column of the |
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* array AB as follows: |
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* AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl) |
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* |
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* On exit, the equilibrated matrix, in the same storage format |
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* as A. See EQUED for the form of the equilibrated matrix. |
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* |
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* LDAB (input) INTEGER |
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* The leading dimension of the array AB. LDA >= KL+KU+1. |
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* |
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* R (input) DOUBLE PRECISION array, dimension (M) |
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* The row scale factors for A. |
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* |
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* C (input) DOUBLE PRECISION array, dimension (N) |
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* The column scale factors for A. |
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* |
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* ROWCND (input) DOUBLE PRECISION |
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* Ratio of the smallest R(i) to the largest R(i). |
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* |
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* COLCND (input) DOUBLE PRECISION |
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* Ratio of the smallest C(i) to the largest C(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 the form of equilibration that was done. |
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* = 'N': No equilibration |
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* = 'R': Row equilibration, i.e., A has been premultiplied by |
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* diag(R). |
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* = 'C': Column equilibration, i.e., A has been postmultiplied |
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* by diag(C). |
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* = 'B': Both row and column equilibration, i.e., A has been |
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* replaced by diag(R) * A * diag(C). |
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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 row or column scaling |
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* should be done based on the ratio of the row or column scaling |
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* factors. If ROWCND < THRESH, row scaling is done, and if |
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* COLCND < THRESH, column scaling is done. |
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* |
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* LARGE and SMALL are threshold values used to decide if row scaling |
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* should be done based on the absolute size of the largest matrix |
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* element. If AMAX > LARGE or AMAX < SMALL, row scaling is done. |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |