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dpstf2.f(3) LAPACK dpstf2.f(3)NAMEdpstf2.f-SYNOPSISFunctions/Subroutines subroutine dpstf2 (UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO) DPSTF2 computes the Cholesky factorization with complete pivoting of a real symmetric or complex Hermitian positive semi-definite matrix.Function/Subroutine Documentation subroutine dpstf2 (characterUPLO, integerN, double precision, dimension( lda, * )A, integerLDA, integer, dimension( n )PIV, integerRANK, double precisionTOL, double precision, dimension( 2*n )WORK, integerINFO) DPSTF2 computes the Cholesky factorization with complete pivoting of a real symmetric or complex Hermitian positive semi-definite 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 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 =, 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. Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: September 2012 Definition at line 141 of file dpstf2.f.-KAuthorGenerated automatically by Doxygen for LAPACK from the source code.Version 3.4.2Tue Sep 25 2012 dpstf2.f(3)

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