version 1.5, 2010/08/07 13:22:12
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version 1.10, 2012/08/22 09:48:12
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*> \brief \b DGBTRF |
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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 DGBTRF + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgbtrf.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/dgbtrf.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/dgbtrf.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 DGBTRF( M, N, KL, KU, AB, LDAB, IPIV, INFO ) |
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* |
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* .. Scalar Arguments .. |
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* INTEGER INFO, KL, KU, LDAB, M, N |
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* .. |
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* .. Array Arguments .. |
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* INTEGER IPIV( * ) |
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* DOUBLE PRECISION AB( LDAB, * ) |
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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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*> DGBTRF computes an LU factorization of a real m-by-n band matrix A |
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*> using partial pivoting with row interchanges. |
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*> |
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*> This is the blocked version of the algorithm, calling Level 3 BLAS. |
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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 KL+1 to |
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*> 2*KL+KU+1; rows 1 to KL of the array need not be set. |
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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(kl+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, details of the factorization: U is stored as an |
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*> upper triangular band matrix with KL+KU superdiagonals in |
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*> rows 1 to KL+KU+1, and the multipliers used during the |
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*> factorization are stored in rows KL+KU+2 to 2*KL+KU+1. |
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*> See below for further details. |
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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 >= 2*KL+KU+1. |
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*> \endverbatim |
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*> |
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*> \param[out] IPIV |
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*> \verbatim |
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*> IPIV is INTEGER array, dimension (min(M,N)) |
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*> The pivot indices; for 1 <= i <= min(M,N), row i of the |
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*> matrix was interchanged with row IPIV(i). |
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*> \endverbatim |
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*> |
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*> \param[out] INFO |
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*> \verbatim |
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*> INFO is INTEGER |
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*> = 0: successful exit |
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*> < 0: if INFO = -i, the i-th argument had an illegal value |
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*> > 0: if INFO = +i, U(i,i) is exactly zero. The factorization |
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*> has been completed, but the factor U is exactly |
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*> singular, and division by zero will occur if it is used |
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*> to solve a system of equations. |
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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 doubleGBcomputational |
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* |
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*> \par Further Details: |
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* ===================== |
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*> |
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*> \verbatim |
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*> |
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*> The band storage scheme is illustrated by the following example, when |
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*> M = N = 6, KL = 2, KU = 1: |
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*> |
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*> On entry: On exit: |
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*> |
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*> * * * + + + * * * u14 u25 u36 |
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*> * * + + + + * * u13 u24 u35 u46 |
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*> * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56 |
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*> a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66 |
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*> a21 a32 a43 a54 a65 * m21 m32 m43 m54 m65 * |
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*> a31 a42 a53 a64 * * m31 m42 m53 m64 * * |
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*> |
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*> Array elements marked * are not used by the routine; elements marked |
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*> + need not be set on entry, but are required by the routine to store |
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*> elements of U because of fill-in resulting from the row interchanges. |
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*> \endverbatim |
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*> |
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* ===================================================================== |
SUBROUTINE DGBTRF( M, N, KL, KU, AB, LDAB, IPIV, INFO ) |
SUBROUTINE DGBTRF( M, N, KL, KU, AB, LDAB, IPIV, INFO ) |
* |
* |
* -- LAPACK routine (version 3.2) -- |
* -- LAPACK computational routine (version 3.4.0) -- |
* -- 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 |
* November 2011 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
INTEGER INFO, KL, KU, LDAB, M, N |
INTEGER INFO, KL, KU, LDAB, M, N |
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DOUBLE PRECISION AB( LDAB, * ) |
DOUBLE PRECISION AB( LDAB, * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* DGBTRF computes an LU factorization of a real m-by-n band matrix A |
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* using partial pivoting with row interchanges. |
|
* |
|
* This is the blocked version of the algorithm, calling Level 3 BLAS. |
|
* |
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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 KL+1 to |
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* 2*KL+KU+1; rows 1 to KL of the array need not be set. |
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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(kl+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, details of the factorization: U is stored as an |
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* upper triangular band matrix with KL+KU superdiagonals in |
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* rows 1 to KL+KU+1, and the multipliers used during the |
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* factorization are stored in rows KL+KU+2 to 2*KL+KU+1. |
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* See below for further details. |
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* |
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* LDAB (input) INTEGER |
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* The leading dimension of the array AB. LDAB >= 2*KL+KU+1. |
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* |
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* IPIV (output) INTEGER array, dimension (min(M,N)) |
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* The pivot indices; for 1 <= i <= min(M,N), row i of the |
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* matrix was interchanged with row IPIV(i). |
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* |
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* INFO (output) INTEGER |
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* = 0: successful exit |
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* < 0: if INFO = -i, the i-th argument had an illegal value |
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* > 0: if INFO = +i, U(i,i) is exactly zero. The factorization |
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* has been completed, but the factor U is exactly |
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* singular, and division by zero will occur if it is used |
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* to solve a system of equations. |
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* |
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* Further Details |
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* =============== |
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* |
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* The band storage scheme is illustrated by the following example, when |
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* M = N = 6, KL = 2, KU = 1: |
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* |
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* On entry: On exit: |
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* |
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* * * * + + + * * * u14 u25 u36 |
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* * * + + + + * * u13 u24 u35 u46 |
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* * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56 |
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* a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66 |
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* a21 a32 a43 a54 a65 * m21 m32 m43 m54 m65 * |
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* a31 a42 a53 a64 * * m31 m42 m53 m64 * * |
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* |
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* Array elements marked * are not used by the routine; elements marked |
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* + need not be set on entry, but are required by the routine to store |
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* elements of U because of fill-in resulting from the row interchanges. |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |