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version 1.16, 2018/05/29 07:18:03
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*> \brief \b DPBSTF |
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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 DPBSTF + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpbstf.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/dpbstf.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/dpbstf.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 DPBSTF( UPLO, N, KD, AB, LDAB, INFO ) |
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* |
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* .. Scalar Arguments .. |
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* CHARACTER UPLO |
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* INTEGER INFO, KD, LDAB, N |
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* .. |
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* .. Array Arguments .. |
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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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*> DPBSTF computes a split Cholesky factorization of a real |
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*> symmetric positive definite band matrix A. |
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*> |
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*> This routine is designed to be used in conjunction with DSBGST. |
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*> |
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*> The factorization has the form A = S**T*S where S is a band matrix |
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*> of the same bandwidth as A and the following structure: |
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*> |
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*> S = ( U ) |
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*> ( M L ) |
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*> |
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*> where U is upper triangular of order m = (n+kd)/2, and L is lower |
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*> triangular of order n-m. |
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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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*> = 'U': Upper triangle of A is stored; |
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*> = 'L': Lower triangle of A is stored. |
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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] KD |
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*> \verbatim |
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*> KD is INTEGER |
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*> The number of superdiagonals of the matrix A if UPLO = 'U', |
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*> or the number of subdiagonals if UPLO = 'L'. KD >= 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 upper or lower triangle of the symmetric band |
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*> matrix A, stored in the first kd+1 rows of the array. The |
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*> j-th column of A is stored in the j-th column of the array AB |
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*> as follows: |
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*> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; |
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*> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). |
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*> |
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*> On exit, if INFO = 0, the factor S from the split Cholesky |
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*> factorization A = S**T*S. See 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 >= KD+1. |
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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, the factorization could not be completed, |
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*> because the updated element a(i,i) was negative; the |
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*> matrix A is not positive definite. |
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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 December 2016 |
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* |
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*> \ingroup doubleOTHERcomputational |
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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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*> N = 7, KD = 2: |
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*> |
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*> S = ( s11 s12 s13 ) |
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*> ( s22 s23 s24 ) |
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*> ( s33 s34 ) |
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*> ( s44 ) |
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*> ( s53 s54 s55 ) |
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*> ( s64 s65 s66 ) |
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*> ( s75 s76 s77 ) |
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*> |
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*> If UPLO = 'U', the array AB holds: |
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*> |
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*> on entry: on exit: |
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*> |
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*> * * a13 a24 a35 a46 a57 * * s13 s24 s53 s64 s75 |
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*> * a12 a23 a34 a45 a56 a67 * s12 s23 s34 s54 s65 s76 |
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*> a11 a22 a33 a44 a55 a66 a77 s11 s22 s33 s44 s55 s66 s77 |
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*> |
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*> If UPLO = 'L', the array AB holds: |
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*> |
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*> on entry: on exit: |
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*> |
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*> a11 a22 a33 a44 a55 a66 a77 s11 s22 s33 s44 s55 s66 s77 |
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*> a21 a32 a43 a54 a65 a76 * s12 s23 s34 s54 s65 s76 * |
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*> a31 a42 a53 a64 a64 * * s13 s24 s53 s64 s75 * * |
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*> |
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*> Array elements marked * are not used by the routine. |
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*> \endverbatim |
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*> |
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* ===================================================================== |
SUBROUTINE DPBSTF( UPLO, N, KD, AB, LDAB, INFO ) |
SUBROUTINE DPBSTF( UPLO, N, KD, AB, LDAB, INFO ) |
* |
* |
* -- LAPACK routine (version 3.2) -- |
* -- LAPACK computational routine (version 3.7.0) -- |
* -- 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 |
* December 2016 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER UPLO |
CHARACTER UPLO |
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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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* DPBSTF computes a split Cholesky factorization of a real |
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* symmetric positive definite band matrix A. |
|
* |
|
* This routine is designed to be used in conjunction with DSBGST. |
|
* |
|
* The factorization has the form A = S**T*S where S is a band matrix |
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* of the same bandwidth as A and the following structure: |
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* |
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* S = ( U ) |
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* ( M L ) |
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* |
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* where U is upper triangular of order m = (n+kd)/2, and L is lower |
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* triangular of order n-m. |
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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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* = 'U': Upper triangle of A is stored; |
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* = 'L': Lower triangle of A is stored. |
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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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* KD (input) INTEGER |
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* The number of superdiagonals of the matrix A if UPLO = 'U', |
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* or the number of subdiagonals if UPLO = 'L'. KD >= 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 upper or lower triangle of the symmetric band |
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* matrix A, stored in the first kd+1 rows of the array. The |
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* j-th column of A is stored in the j-th column of the array AB |
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* as follows: |
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* if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; |
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* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). |
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* |
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* On exit, if INFO = 0, the factor S from the split Cholesky |
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* factorization A = S**T*S. See 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 >= KD+1. |
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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, the factorization could not be completed, |
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* because the updated element a(i,i) was negative; the |
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* matrix A is not positive definite. |
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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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* N = 7, KD = 2: |
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* |
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* S = ( s11 s12 s13 ) |
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* ( s22 s23 s24 ) |
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* ( s33 s34 ) |
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* ( s44 ) |
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* ( s53 s54 s55 ) |
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* ( s64 s65 s66 ) |
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* ( s75 s76 s77 ) |
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* |
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* If UPLO = 'U', the array AB holds: |
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* |
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* on entry: on exit: |
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* |
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* * * a13 a24 a35 a46 a57 * * s13 s24 s53 s64 s75 |
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* * a12 a23 a34 a45 a56 a67 * s12 s23 s34 s54 s65 s76 |
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* a11 a22 a33 a44 a55 a66 a77 s11 s22 s33 s44 s55 s66 s77 |
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* |
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* If UPLO = 'L', the array AB holds: |
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* |
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* on entry: on exit: |
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* |
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* a11 a22 a33 a44 a55 a66 a77 s11 s22 s33 s44 s55 s66 s77 |
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* a21 a32 a43 a54 a65 a76 * s12 s23 s34 s54 s65 s76 * |
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* a31 a42 a53 a64 a64 * * s13 s24 s53 s64 s75 * * |
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* |
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* Array elements marked * are not used by the routine. |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |