# zpstf2.f man page

zpstf2.f

## Synopsis

### Functions/Subroutines

subroutine zpstf2 (UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO)
ZPSTF2 computes the Cholesky factorization with complete pivoting of a complex Hermitian positive semidefinite matrix.

## Function/Subroutine Documentation

### subroutine zpstf2 (character UPLO, integer N, complex*16, dimension( lda, * ) A, integer LDA, integer, dimension( n ) PIV, integer RANK, double precision TOL, double precision, dimension( 2*n ) WORK, integer INFO)

ZPSTF2 computes the Cholesky factorization with complete pivoting of a complex Hermitian positive semidefinite matrix.

Purpose:

``` ZPSTF2 computes the Cholesky factorization with complete
pivoting of a complex Hermitian positive semidefinite matrix A.

The factorization has the form
P**T * A * P = U**H * U ,  if UPLO = 'U',
P**T * A * P = L  * L**H,  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 COMPLEX*16 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 Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:

December 2016

Definition at line 144 of file zpstf2.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zpstf2(3) is an alias of zpstf2.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK