subroutine dpstf2 (UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO)
DPSTF2 computes the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix.
DPSTF2 computes the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix.
Purpose:
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.
Parameters:
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
N
N is INTEGER The order of the matrix A. N >= 0.
A
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.
PIV
PIV is INTEGER array, dimension (N) PIV is such that the nonzero entries are P( PIV(K), K ) = 1.
RANK
RANK is INTEGER The rank of A given by the number of steps the algorithm completed.
TOL
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.
LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
WORK
WORK is DOUBLE PRECISION array, dimension (2*N) Work space.
INFO
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.
Author:
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
Definition at line 143 of file dpstf2.f.
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