dpstf2()

subroutine dpstf2	(	character	uplo,
		integer	n,
		double precision, dimension( lda, * )	a,
		integer	lda,
		integer, dimension( n )	piv,
		integer	rank,
		double precision	tol,
		double precision, dimension( 2*n )	work,
		integer	info )

DPSTF2 computes the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix.

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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

[in]	UPLO	!> 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 !>
[in]	N	!> N is INTEGER !> The order of the matrix A. N >= 0. !>
[in,out]	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. !>
[out]	PIV	!> PIV is INTEGER array, dimension (N) !> PIV is such that the nonzero entries are P( PIV(K), K ) = 1. !>
[out]	RANK	!> RANK is INTEGER !> The rank of A given by the number of steps the algorithm !> completed. !>
[in]	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. !>
[in]	LDA	!> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !>
[out]	WORK	!> WORK is DOUBLE PRECISION array, dimension (2*N) !> Work space. !>
[out]	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 Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.