?pstrf

Computes the Cholesky factorization with complete pivoting of a real symmetric (complex Hermitian) positive semidefinite matrix.

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 )

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

Fortran: mkl_lapack.fi and mkl_lapack.h
Fortran 95: lapack.f90
C: mkl_lapacke.h

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:

P^T * A * P = U^T * U, if uplo ='U' for real flavors,

P^H * A * P = U^H * U, if uplo ='U' for complex flavors,

P^T * A * P = L * L^T, if uplo ='L' for real flavors,

P^H * A * P = L * L^H, if uplo ='L' for complex flavors,

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 definitions.

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 `nUmax(a(k,k))` will be used. The algorithm terminates at the `(k-1)`-th step, if the pivot ≤ tol.
lda	INTEGER. The leading 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.