dpstf2 man page on Scientific

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```DPSTF2(1)	    LAPACK PROTOTYPE routine (version 3.2)	     DPSTF2(1)

NAME
DPSTF2  - computes the Cholesky factorization with complete pivoting of
a real symmetric positive semidefinite matrix A

SYNOPSIS
SUBROUTINE DPSTF2( UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO )

DOUBLE	  PRECISION TOL

INTEGER	  INFO, LDA, N, RANK

CHARACTER	  UPLO

DOUBLE	  PRECISION A( LDA, * ), WORK( 2*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 semidefi‐
nite. 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  com‐
pleted.

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    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.

LAPACK PROTOTYPE routine (versioNovember 2008			     DPSTF2(1)
```
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