version 1.4, 2010/08/06 15:32:37
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version 1.8, 2011/11/21 20:43:08
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*> \brief <b> ZGBSV computes the solution to system of linear equations A * X = B for GB matrices</b> (simple driver) |
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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 ZGBSV + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgbsv.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/zgbsv.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/zgbsv.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 ZGBSV( N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO ) |
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* |
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* .. Scalar Arguments .. |
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* INTEGER INFO, KL, KU, LDAB, LDB, N, NRHS |
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* .. |
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* .. Array Arguments .. |
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* INTEGER IPIV( * ) |
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* COMPLEX*16 AB( LDAB, * ), B( LDB, * ) |
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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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*> ZGBSV computes the solution to a complex system of linear equations |
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*> A * X = B, where A is a band matrix of order N with KL subdiagonals |
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*> and KU superdiagonals, and X and B are N-by-NRHS matrices. |
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*> |
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*> The LU decomposition with partial pivoting and row interchanges is |
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*> used to factor A as A = L * U, where L is a product of permutation |
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*> and unit lower triangular matrices with KL subdiagonals, and U is |
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*> upper triangular with KL+KU superdiagonals. The factored form of A |
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*> is then used to solve the system of equations A * X = B. |
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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] NRHS |
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*> \verbatim |
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*> NRHS is INTEGER |
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*> The number of right hand sides, i.e., the number of columns |
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*> of the matrix B. NRHS >= 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 COMPLEX*16 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(N,j+KL) |
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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 (N) |
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*> The pivot indices that define the permutation matrix P; |
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*> row i of the matrix was interchanged with row IPIV(i). |
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*> \endverbatim |
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*> |
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*> \param[in,out] B |
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*> \verbatim |
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*> B is COMPLEX*16 array, dimension (LDB,NRHS) |
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*> On entry, the N-by-NRHS right hand side matrix B. |
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*> On exit, if INFO = 0, the N-by-NRHS solution matrix X. |
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*> \endverbatim |
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*> |
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*> \param[in] LDB |
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*> \verbatim |
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*> LDB is INTEGER |
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*> The leading dimension of the array B. LDB >= max(1,N). |
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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 the solution has not been computed. |
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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 complex16GBsolve |
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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 ZGBSV( N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO ) |
SUBROUTINE ZGBSV( N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO ) |
* |
* |
* -- LAPACK driver routine (version 3.2) -- |
* -- LAPACK driver 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, LDB, N, NRHS |
INTEGER INFO, KL, KU, LDAB, LDB, N, NRHS |
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COMPLEX*16 AB( LDAB, * ), B( LDB, * ) |
COMPLEX*16 AB( LDAB, * ), B( LDB, * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* ZGBSV computes the solution to a complex system of linear equations |
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* A * X = B, where A is a band matrix of order N with KL subdiagonals |
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* and KU superdiagonals, and X and B are N-by-NRHS matrices. |
|
* |
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* The LU decomposition with partial pivoting and row interchanges is |
|
* used to factor A as A = L * U, where L is a product of permutation |
|
* and unit lower triangular matrices with KL subdiagonals, and U is |
|
* upper triangular with KL+KU superdiagonals. The factored form of A |
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* is then used to solve the system of equations A * X = B. |
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* |
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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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* NRHS (input) INTEGER |
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* The number of right hand sides, i.e., the number of columns |
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* of the matrix B. NRHS >= 0. |
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* |
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* AB (input/output) COMPLEX*16 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(N,j+KL) |
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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 (N) |
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* The pivot indices that define the permutation matrix P; |
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* row i of the matrix was interchanged with row IPIV(i). |
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* |
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* B (input/output) COMPLEX*16 array, dimension (LDB,NRHS) |
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* On entry, the N-by-NRHS right hand side matrix B. |
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* On exit, if INFO = 0, the N-by-NRHS solution matrix X. |
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* |
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* LDB (input) INTEGER |
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* The leading dimension of the array B. LDB >= max(1,N). |
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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 the solution has not been computed. |
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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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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. External Subroutines .. |
* .. External Subroutines .. |