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---
:name: dpstf2
:md5sum: a3c2b199ffdc016a07d33dd0e50b9821
:category: :subroutine
:arguments:
- uplo:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- a:
:type: doublereal
:intent: input/output
:dims:
- lda
- n
- lda:
:type: integer
:intent: input
- piv:
:type: integer
:intent: output
:dims:
- n
- rank:
:type: integer
:intent: output
- tol:
:type: doublereal
:intent: input
- work:
:type: doublereal
:intent: workspace
:dims:
- 2*n
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE DPSTF2( UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* DPSTF2 computes the Cholesky factorization with complete\n\
* pivoting of a real symmetric positive semidefinite matrix A.\n\
*\n\
* The factorization has the form\n\
* P' * A * P = U' * U , if UPLO = 'U',\n\
* P' * A * P = L * L', if UPLO = 'L',\n\
* where U is an upper triangular matrix and L is lower triangular, and\n\
* P is stored as vector PIV.\n\
*\n\
* This algorithm does not attempt to check that A is positive\n\
* semidefinite. This version of the algorithm calls level 2 BLAS.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* UPLO (input) CHARACTER*1\n\
* Specifies whether the upper or lower triangular part of the\n\
* symmetric matrix A is stored.\n\
* = 'U': Upper triangular\n\
* = 'L': Lower triangular\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrix A. N >= 0.\n\
*\n\
* A (input/output) DOUBLE PRECISION array, dimension (LDA,N)\n\
* On entry, the symmetric matrix A. If UPLO = 'U', the leading\n\
* n by n upper triangular part of A contains the upper\n\
* triangular part of the matrix A, and the strictly lower\n\
* triangular part of A is not referenced. If UPLO = 'L', the\n\
* leading n by n lower triangular part of A contains the lower\n\
* triangular part of the matrix A, and the strictly upper\n\
* triangular part of A is not referenced.\n\
*\n\
* On exit, if INFO = 0, the factor U or L from the Cholesky\n\
* factorization as above.\n\
*\n\
* PIV (output) INTEGER array, dimension (N)\n\
* PIV is such that the nonzero entries are P( PIV(K), K ) = 1.\n\
*\n\
* RANK (output) INTEGER\n\
* The rank of A given by the number of steps the algorithm\n\
* completed.\n\
*\n\
* TOL (input) DOUBLE PRECISION\n\
* User defined tolerance. If TOL < 0, then N*U*MAX( A( K,K ) )\n\
* will be used. The algorithm terminates at the (K-1)st step\n\
* if the pivot <= TOL.\n\
*\n\
* LDA (input) INTEGER\n\
* The leading dimension of the array A. LDA >= max(1,N).\n\
*\n\
* WORK (workspace) DOUBLE PRECISION array, dimension (2*N)\n\
* Work space.\n\
*\n\
* INFO (output) INTEGER\n\
* < 0: If INFO = -K, the K-th argument had an illegal value,\n\
* = 0: algorithm completed successfully, and\n\
* > 0: the matrix A is either rank deficient with computed rank\n\
* as returned in RANK, or is indefinite. See Section 7 of\n\
* LAPACK Working Note #161 for further information.\n\
*\n\n\
* =====================================================================\n\
*\n"
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