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version 1.10, 2014/01/27 09:28:26
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*> \brief \b DPSTRF |
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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 DPSTRF + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpstrf.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/dpstrf.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/dpstrf.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 DPSTRF( UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO ) |
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* |
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* .. Scalar Arguments .. |
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* DOUBLE PRECISION TOL |
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* INTEGER INFO, LDA, N, RANK |
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* CHARACTER UPLO |
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* .. |
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* .. Array Arguments .. |
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* DOUBLE PRECISION A( LDA, * ), WORK( 2*N ) |
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* INTEGER PIV( N ) |
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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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*> DPSTRF computes the Cholesky factorization with complete |
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*> pivoting of a real symmetric positive semidefinite matrix A. |
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*> |
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*> The factorization has the form |
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*> P**T * A * P = U**T * U , if UPLO = 'U', |
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*> P**T * A * P = L * L**T, if UPLO = 'L', |
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*> where U is an upper triangular matrix and L is lower triangular, and |
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*> P is stored as vector PIV. |
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*> |
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*> This algorithm does not attempt to check that A is positive |
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*> semidefinite. This version of the algorithm calls 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] UPLO |
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*> \verbatim |
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*> UPLO is CHARACTER*1 |
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*> Specifies whether the upper or lower triangular part of the |
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*> symmetric matrix A is stored. |
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*> = 'U': Upper triangular |
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*> = 'L': Lower triangular |
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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,out] A |
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*> \verbatim |
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*> A is DOUBLE PRECISION array, dimension (LDA,N) |
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*> On entry, the symmetric matrix A. If UPLO = 'U', the leading |
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*> n by n upper triangular part of A contains the upper |
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*> triangular part of the matrix A, and the strictly lower |
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*> triangular part of A is not referenced. If UPLO = 'L', the |
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*> leading n by n lower triangular part of A contains the lower |
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*> triangular part of the matrix A, and the strictly upper |
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*> triangular part of A is not referenced. |
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*> |
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*> On exit, if INFO = 0, the factor U or L from the Cholesky |
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*> factorization as above. |
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*> \endverbatim |
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*> |
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*> \param[in] LDA |
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*> \verbatim |
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*> LDA is INTEGER |
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*> The leading dimension of the array A. LDA >= max(1,N). |
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*> \endverbatim |
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*> |
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*> \param[out] PIV |
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*> \verbatim |
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*> PIV is INTEGER array, dimension (N) |
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*> PIV is such that the nonzero entries are P( PIV(K), K ) = 1. |
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*> \endverbatim |
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*> |
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*> \param[out] RANK |
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*> \verbatim |
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*> RANK is INTEGER |
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*> The rank of A given by the number of steps the algorithm |
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*> completed. |
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*> \endverbatim |
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*> |
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*> \param[in] TOL |
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*> \verbatim |
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*> TOL is DOUBLE PRECISION |
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*> User defined tolerance. If TOL < 0, then N*U*MAX( A(K,K) ) |
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*> will be used. The algorithm terminates at the (K-1)st step |
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*> if the pivot <= TOL. |
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*> \endverbatim |
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*> |
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*> \param[out] WORK |
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*> \verbatim |
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*> WORK is DOUBLE PRECISION array, dimension (2*N) |
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*> Work space. |
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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: If INFO = -K, the K-th argument had an illegal value, |
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*> = 0: algorithm completed successfully, and |
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*> > 0: the matrix A is either rank deficient with computed rank |
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*> as returned in RANK, or is indefinite. See Section 7 of |
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*> LAPACK Working Note #161 for further information. |
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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 doubleOTHERcomputational |
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* |
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* ===================================================================== |
SUBROUTINE DPSTRF( UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO ) |
SUBROUTINE DPSTRF( UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO ) |
* |
* |
* -- LAPACK routine (version 3.2.2) -- |
* -- LAPACK computational routine (version 3.4.0) -- |
* Craig Lucas, University of Manchester / NAG Ltd. |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* October, 2008 |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
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* November 2011 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
DOUBLE PRECISION TOL |
DOUBLE PRECISION TOL |
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INTEGER PIV( N ) |
INTEGER PIV( N ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* DPSTRF computes the Cholesky factorization with complete |
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* pivoting of a real symmetric positive semidefinite matrix A. |
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* |
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* The factorization has the form |
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* P' * A * P = U' * U , if UPLO = 'U', |
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* P' * A * P = L * L', if UPLO = 'L', |
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* where U is an upper triangular matrix and L is lower triangular, and |
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* P is stored as vector PIV. |
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* |
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* This algorithm does not attempt to check that A is positive |
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* semidefinite. This version of the algorithm calls level 3 BLAS. |
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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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* Specifies whether the upper or lower triangular part of the |
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* symmetric matrix A is stored. |
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* = 'U': Upper triangular |
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* = 'L': Lower triangular |
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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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* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) |
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* On entry, the symmetric matrix A. If UPLO = 'U', the leading |
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* n by n upper triangular part of A contains the upper |
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* triangular part of the matrix A, and the strictly lower |
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* triangular part of A is not referenced. If UPLO = 'L', the |
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* leading n by n lower triangular part of A contains the lower |
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* triangular part of the matrix A, and the strictly upper |
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* triangular part of A is not referenced. |
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* |
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* On exit, if INFO = 0, the factor U or L from the Cholesky |
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* factorization as above. |
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* |
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* LDA (input) INTEGER |
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* The leading dimension of the array A. LDA >= max(1,N). |
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* |
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* PIV (output) INTEGER array, dimension (N) |
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* PIV is such that the nonzero entries are P( PIV(K), K ) = 1. |
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* |
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* RANK (output) INTEGER |
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* The rank of A given by the number of steps the algorithm |
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* completed. |
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* |
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* TOL (input) DOUBLE PRECISION |
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* User defined tolerance. If TOL < 0, then N*U*MAX( A(K,K) ) |
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* will be used. The algorithm terminates at the (K-1)st step |
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* if the pivot <= TOL. |
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* |
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* WORK (workspace) DOUBLE PRECISION array, dimension (2*N) |
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* Work space. |
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* |
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* INFO (output) INTEGER |
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* < 0: If INFO = -K, the K-th argument had an illegal value, |
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* = 0: algorithm completed successfully, and |
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* > 0: the matrix A is either rank deficient with computed rank |
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* as returned in RANK, or is indefinite. See Section 7 of |
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* LAPACK Working Note #161 for further information. |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
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* |
* |
IF( UPPER ) THEN |
IF( UPPER ) THEN |
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* Compute the Cholesky factorization P' * A * P = U' * U |
* Compute the Cholesky factorization P**T * A * P = U**T * U |
* |
* |
DO 140 K = 1, N, NB |
DO 140 K = 1, N, NB |
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* |
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* |
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ELSE |
ELSE |
* |
* |
* Compute the Cholesky factorization P' * A * P = L * L' |
* Compute the Cholesky factorization P**T * A * P = L * L**T |
* |
* |
DO 180 K = 1, N, NB |
DO 180 K = 1, N, NB |
* |
* |