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

Univ. of Colorado Denver

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