version 1.3, 2010/08/13 21:03:47
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version 1.9, 2012/12/14 14:22:31
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*> \brief \b DLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix. |
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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_GBRPVGRW + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dla_gbrpvgrw.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_gbrpvgrw.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_gbrpvgrw.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_GBRPVGRW( N, KL, KU, NCOLS, AB, |
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* LDAB, AFB, LDAFB ) |
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* |
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* .. Scalar Arguments .. |
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* INTEGER N, KL, KU, NCOLS, LDAB, LDAFB |
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* .. |
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* .. Array Arguments .. |
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* DOUBLE PRECISION AB( LDAB, * ), AFB( LDAFB, * ) |
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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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*> DLA_GBRPVGRW 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] 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] 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] 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(N,j+kl) |
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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. LDAB >= KL+KU+1. |
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*> \endverbatim |
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*> |
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*> \param[in] AFB |
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*> \verbatim |
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*> AFB is DOUBLE PRECISION array, dimension (LDAFB,N) |
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*> Details of the LU factorization of the band matrix A, as |
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*> computed by DGBTRF. U is stored as an upper triangular |
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*> band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, |
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*> and the multipliers used during the factorization are stored |
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*> in rows KL+KU+2 to 2*KL+KU+1. |
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*> \endverbatim |
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*> |
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*> \param[in] LDAFB |
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*> \verbatim |
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*> LDAFB is INTEGER |
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*> The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1. |
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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 doubleGBcomputational |
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* |
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* ===================================================================== |
DOUBLE PRECISION FUNCTION DLA_GBRPVGRW( N, KL, KU, NCOLS, AB, |
DOUBLE PRECISION FUNCTION DLA_GBRPVGRW( N, KL, KU, NCOLS, AB, |
$ LDAB, AFB, LDAFB ) |
$ LDAB, AFB, LDAFB ) |
* |
* |
* -- LAPACK routine (version 3.2.2) -- |
* -- LAPACK computational routine (version 3.4.2) -- |
* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- Jason Riedy of Univ. of California Berkeley. -- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- June 2010 -- |
* September 2012 |
* |
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* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
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* -- Univ. of California Berkeley and NAG Ltd. -- |
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* |
* |
IMPLICIT NONE |
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* .. |
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* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
INTEGER N, KL, KU, NCOLS, LDAB, LDAFB |
INTEGER N, KL, KU, NCOLS, LDAB, LDAFB |
* .. |
* .. |
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DOUBLE PRECISION AB( LDAB, * ), AFB( LDAFB, * ) |
DOUBLE PRECISION AB( LDAB, * ), AFB( LDAFB, * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* DLA_GBRPVGRW 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 |
|
* solution X, estimated condition numbers, and error bounds could be |
|
* unreliable. |
|
* |
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* Arguments |
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* ========= |
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* |
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* N (input) 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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* |
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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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* NCOLS (input) INTEGER |
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* The number of columns of the matrix A. NCOLS >= 0. |
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* |
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* AB (input) 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(N,j+kl) |
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* |
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* LDAB (input) INTEGER |
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* The leading dimension of the array AB. LDAB >= KL+KU+1. |
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* |
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* AFB (input) DOUBLE PRECISION array, dimension (LDAFB,N) |
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* Details of the LU factorization of the band matrix A, as |
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* computed by DGBTRF. U is stored as an upper triangular |
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* band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, |
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* and the multipliers used during the factorization are stored |
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* in rows KL+KU+2 to 2*KL+KU+1. |
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* |
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* LDAFB (input) INTEGER |
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* The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1. |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Local Scalars .. |
* .. Local Scalars .. |