version 1.4, 2010/12/21 13:53:36
|
version 1.16, 2018/05/29 07:18:05
|
Line 1
|
Line 1
|
|
*> \brief \b DPSTF2 computes the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix. |
|
* |
|
* =========== DOCUMENTATION =========== |
|
* |
|
* Online html documentation available at |
|
* http://www.netlib.org/lapack/explore-html/ |
|
* |
|
*> \htmlonly |
|
*> Download DPSTF2 + dependencies |
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpstf2.f"> |
|
*> [TGZ]</a> |
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dpstf2.f"> |
|
*> [ZIP]</a> |
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dpstf2.f"> |
|
*> [TXT]</a> |
|
*> \endhtmlonly |
|
* |
|
* Definition: |
|
* =========== |
|
* |
|
* SUBROUTINE DPSTF2( UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO ) |
|
* |
|
* .. Scalar Arguments .. |
|
* DOUBLE PRECISION TOL |
|
* INTEGER INFO, LDA, N, RANK |
|
* CHARACTER UPLO |
|
* .. |
|
* .. Array Arguments .. |
|
* DOUBLE PRECISION A( LDA, * ), WORK( 2*N ) |
|
* INTEGER PIV( N ) |
|
* .. |
|
* |
|
* |
|
*> \par Purpose: |
|
* ============= |
|
*> |
|
*> \verbatim |
|
*> |
|
*> DPSTF2 computes the Cholesky factorization with complete |
|
*> pivoting of a real symmetric positive semidefinite matrix A. |
|
*> |
|
*> The factorization has the form |
|
*> P**T * A * P = U**T * U , if UPLO = 'U', |
|
*> P**T * A * P = L * L**T, if UPLO = 'L', |
|
*> where U is an upper triangular matrix and L is lower triangular, and |
|
*> P is stored as vector PIV. |
|
*> |
|
*> This algorithm does not attempt to check that A is positive |
|
*> semidefinite. This version of the algorithm calls level 2 BLAS. |
|
*> \endverbatim |
|
* |
|
* Arguments: |
|
* ========== |
|
* |
|
*> \param[in] UPLO |
|
*> \verbatim |
|
*> UPLO is CHARACTER*1 |
|
*> Specifies whether the upper or lower triangular part of the |
|
*> symmetric matrix A is stored. |
|
*> = 'U': Upper triangular |
|
*> = 'L': Lower triangular |
|
*> \endverbatim |
|
*> |
|
*> \param[in] N |
|
*> \verbatim |
|
*> N is INTEGER |
|
*> The order of the matrix A. N >= 0. |
|
*> \endverbatim |
|
*> |
|
*> \param[in,out] A |
|
*> \verbatim |
|
*> A is DOUBLE PRECISION array, dimension (LDA,N) |
|
*> On entry, the symmetric matrix A. If UPLO = 'U', the leading |
|
*> n by n upper triangular part of A contains the upper |
|
*> triangular part of the matrix A, and the strictly lower |
|
*> triangular part of A is not referenced. If UPLO = 'L', the |
|
*> leading n by n lower triangular part of A contains the lower |
|
*> triangular part of the matrix A, and the strictly upper |
|
*> triangular part of A is not referenced. |
|
*> |
|
*> On exit, if INFO = 0, the factor U or L from the Cholesky |
|
*> factorization as above. |
|
*> \endverbatim |
|
*> |
|
*> \param[out] PIV |
|
*> \verbatim |
|
*> PIV is INTEGER array, dimension (N) |
|
*> PIV is such that the nonzero entries are P( PIV(K), K ) = 1. |
|
*> \endverbatim |
|
*> |
|
*> \param[out] RANK |
|
*> \verbatim |
|
*> RANK is INTEGER |
|
*> The rank of A given by the number of steps the algorithm |
|
*> completed. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] TOL |
|
*> \verbatim |
|
*> TOL is DOUBLE PRECISION |
|
*> User defined tolerance. If TOL < 0, then N*U*MAX( A( K,K ) ) |
|
*> will be used. The algorithm terminates at the (K-1)st step |
|
*> if the pivot <= TOL. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] LDA |
|
*> \verbatim |
|
*> LDA is INTEGER |
|
*> The leading dimension of the array A. LDA >= max(1,N). |
|
*> \endverbatim |
|
*> |
|
*> \param[out] WORK |
|
*> \verbatim |
|
*> WORK is DOUBLE PRECISION array, dimension (2*N) |
|
*> Work space. |
|
*> \endverbatim |
|
*> |
|
*> \param[out] INFO |
|
*> \verbatim |
|
*> INFO is INTEGER |
|
*> < 0: If INFO = -K, the K-th argument had an illegal value, |
|
*> = 0: algorithm completed successfully, and |
|
*> > 0: the matrix A is either rank deficient with computed rank |
|
*> as returned in RANK, or is not positive semidefinite. See |
|
*> Section 7 of LAPACK Working Note #161 for further |
|
*> information. |
|
*> \endverbatim |
|
* |
|
* Authors: |
|
* ======== |
|
* |
|
*> \author Univ. of Tennessee |
|
*> \author Univ. of California Berkeley |
|
*> \author Univ. of Colorado Denver |
|
*> \author NAG Ltd. |
|
* |
|
*> \date December 2016 |
|
* |
|
*> \ingroup doubleOTHERcomputational |
|
* |
|
* ===================================================================== |
SUBROUTINE DPSTF2( UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO ) |
SUBROUTINE DPSTF2( UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO ) |
* |
* |
* -- LAPACK PROTOTYPE routine (version 3.2.2) -- |
* -- LAPACK computational routine (version 3.7.0) -- |
* 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..-- |
|
* December 2016 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
DOUBLE PRECISION TOL |
DOUBLE PRECISION TOL |
Line 14
|
Line 156
|
INTEGER PIV( N ) |
INTEGER PIV( N ) |
* .. |
* .. |
* |
* |
* Purpose |
|
* ======= |
|
* |
|
* DPSTF2 computes the Cholesky factorization with complete |
|
* pivoting of a real symmetric positive semidefinite matrix A. |
|
* |
|
* The factorization has the form |
|
* P' * A * P = U' * U , if UPLO = 'U', |
|
* P' * A * P = L * L', if UPLO = 'L', |
|
* where U is an upper triangular matrix and L is lower triangular, and |
|
* P is stored as vector PIV. |
|
* |
|
* This algorithm does not attempt to check that A is positive |
|
* semidefinite. This version of the algorithm calls level 2 BLAS. |
|
* |
|
* Arguments |
|
* ========= |
|
* |
|
* UPLO (input) CHARACTER*1 |
|
* Specifies whether the upper or lower triangular part of the |
|
* symmetric matrix A is stored. |
|
* = 'U': Upper triangular |
|
* = 'L': Lower triangular |
|
* |
|
* N (input) INTEGER |
|
* The order of the matrix A. N >= 0. |
|
* |
|
* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) |
|
* On entry, the symmetric matrix A. If UPLO = 'U', the leading |
|
* n by n upper triangular part of A contains the upper |
|
* triangular part of the matrix A, and the strictly lower |
|
* triangular part of A is not referenced. If UPLO = 'L', the |
|
* leading n by n lower triangular part of A contains the lower |
|
* triangular part of the matrix A, and the strictly upper |
|
* triangular part of A is not referenced. |
|
* |
|
* On exit, if INFO = 0, the factor U or L from the Cholesky |
|
* factorization as above. |
|
* |
|
* PIV (output) INTEGER array, dimension (N) |
|
* PIV is such that the nonzero entries are P( PIV(K), K ) = 1. |
|
* |
|
* RANK (output) INTEGER |
|
* The rank of A given by the number of steps the algorithm |
|
* completed. |
|
* |
|
* TOL (input) DOUBLE PRECISION |
|
* User defined tolerance. If TOL < 0, then N*U*MAX( A( K,K ) ) |
|
* will be used. The algorithm terminates at the (K-1)st step |
|
* if the pivot <= TOL. |
|
* |
|
* LDA (input) INTEGER |
|
* The leading dimension of the array A. LDA >= max(1,N). |
|
* |
|
* WORK (workspace) DOUBLE PRECISION array, dimension (2*N) |
|
* Work space. |
|
* |
|
* INFO (output) INTEGER |
|
* < 0: If INFO = -K, the K-th argument had an illegal value, |
|
* = 0: algorithm completed successfully, and |
|
* > 0: the matrix A is either rank deficient with computed rank |
|
* as returned in RANK, or is indefinite. See Section 7 of |
|
* LAPACK Working Note #161 for further information. |
|
* |
|
* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
Line 139
|
Line 217
|
AJJ = A( PVT, PVT ) |
AJJ = A( PVT, PVT ) |
END IF |
END IF |
END DO |
END DO |
IF( AJJ.EQ.ZERO.OR.DISNAN( AJJ ) ) THEN |
IF( AJJ.LE.ZERO.OR.DISNAN( AJJ ) ) THEN |
RANK = 0 |
RANK = 0 |
INFO = 1 |
INFO = 1 |
GO TO 170 |
GO TO 170 |
Line 161
|
Line 239
|
* |
* |
IF( UPPER ) THEN |
IF( UPPER ) THEN |
* |
* |
* Compute the Cholesky factorization P' * A * P = U' * U |
* Compute the Cholesky factorization P**T * A * P = U**T * U |
* |
* |
DO 130 J = 1, N |
DO 130 J = 1, N |
* |
* |
Line 224
|
Line 302
|
* |
* |
ELSE |
ELSE |
* |
* |
* Compute the Cholesky factorization P' * A * P = L * L' |
* Compute the Cholesky factorization P**T * A * P = L * L**T |
* |
* |
DO 150 J = 1, N |
DO 150 J = 1, N |
* |
* |