?pstrf

Syntax

FORTRAN 77:

call spstrf( uplo, n, a, lda, piv, rank, tol, work, info )

call dpstrf( uplo, n, a, lda, piv, rank, tol, work, info )

call cpstrf( uplo, n, a, lda, piv, rank, tol, work, info )

call zpstrf( uplo, n, a, lda, piv, rank, tol, work, info )

C:

lapack_int LAPACKE_spstrf( int matrix_order, char uplo, lapack_int n, float* a, lapack_int lda, lapack_int* piv, lapack_int* rank, float tol );

lapack_int LAPACKE_dpstrf( int matrix_order, char uplo, lapack_int n, double* a, lapack_int lda, lapack_int* piv, lapack_int* rank, double tol );

lapack_int LAPACKE_cpstrf( int matrix_order, char uplo, lapack_int n, lapack_complex_float* a, lapack_int lda, lapack_int* piv, lapack_int* rank, float tol );

lapack_int LAPACKE_zpstrf( int matrix_order, char uplo, lapack_int n, lapack_complex_double* a, lapack_int lda, lapack_int* piv, lapack_int* rank, double tol );

Include Files

The FORTRAN 77 interfaces are specified in the mkl_lapack.fi and mkl_lapack.h include files, the Fortran 95 interfaces are specified in the lapack.f90 include file, and the C interfaces are specified in the mkl_lapacke.h include file.

Description

The routine computes the Cholesky factorization with complete pivoting of a real symmetric (complex Hermitian) positive semidefinite matrix. The form of the factorization is:

where P is stored as vector piv, 'U' and 'L' are upper and lower triangular matrices respectively.

This algorithm does not attempt to check that A is positive semidefinite. This version of the algorithm calls level 3 BLAS.

Input Parameters

The data types are given for the Fortran interface. A <datatype> placeholder, if present, is used for the C interface data types in the C interface section above. See C Interface Conventions for the C interface principal conventions and type defintions.

uplo

CHARACTER*1. Must be 'U' or 'L'.

Indicates whether the upper or lower triangular part of A is stored:

If uplo = 'U', the array a stores the upper triangular part of the matrix A, and the strictly lower triangular part of the matrix is not referenced.

If uplo = 'L', the array a stores the lower triangular part of the matrix A, and the strictly upper triangular part of the matrix is not referenced.

n

INTEGER. The order of matrix A; n ≥ 0.

a, work

REAL for spstrf

DOUBLE PRECISION for dpstrf

COMPLEX for cpstrf

DOUBLE COMPLEX for zpstrf.

Array a, DIMENSION (lda,*). The array a contains either the upper or the lower triangular part of the matrix A (see uplo). The second dimension of a must be at least max(1, n).

work(*) is a workspace array. The dimension of work is at least max(1,2*n).

tol

REAL for single precision flavors

DOUBLE PRECISION for double precision flavors.

User difined tolerance. If tol < 0, then n*U*max(a(k,k)) will be used. The algorithm terminates at the (k-1)-th step, if the pivot ≤ tol.

lda

INTEGER. The first dimension of a; at least max(1, n).

Output Parameters

a

If info = 0, the factor U or L from the Cholesky factorization is as described in Description.

piv

INTEGER.

Array, DIMENSION at least max(1, n). The array piv is such that the nonzero entries are p( piv(k),k ) = 1.

rank

INTEGER.

The rank of a given by the number of steps the algorithm completed.

info

INTEGER. If info = 0, the execution is successful.

If info = -k, the k-th argument had an illegal value.

If info > 0, the matrix A is either rank deficient with a computed rank as returned in rank, or is indefinite.