?pftrf

Computes the Cholesky factorization of a symmetric (Hermitian) positive-definite matrix using the Rectangular Full Packed (RFP) format .

Syntax

FORTRAN 77:

call spftrf( transr, uplo, n, a, info )

call dpftrf( transr, uplo, n, a, info )

call cpftrf( transr, uplo, n, a, info )

call zpftrf( transr, uplo, n, a, info )

lapack_int LAPACKE_<?>pftrf( int matrix_order, char transr, char uplo, lapack_int n, <datatype>* a );

Include Files

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

Description

The routine forms the Cholesky factorization of a symmetric positive-definite or, for complex data, a Hermitian positive-definite matrix A:

`A = U^TU` for real data, `A = U^HU` for complex data	if `uplo='U'`
`A = LL^T` for real data, `A = LL^H` for complex data	if `uplo='L'`

where L is a lower triangular matrix and U is upper triangular.

The matrix A is in the Rectangular Full Packed (RFP) format. For the description of the RFP format, see Matrix Storage Schemes.

This is the block version of the algorithm, calling 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.

transr	CHARACTER*1. Must be 'N', 'T' (for real data) or 'C' (for complex data). If transr = 'N', the Normal transr of RFP `A` is stored. If transr = 'T', the Transpose transr of RFP `A` is stored. If transr = 'C', the Conjugate-Transpose transr of RFP `A` is stored.
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`. If uplo = 'L', the array a stores the lower triangular part of the matrix `A`.
n	INTEGER. The order of the matrix `A`; n ≥ 0.
a	REAL for spftrf DOUBLE PRECISION for dpftrf COMPLEX for cpftrf DOUBLE COMPLEX for zpftrf. Array, DIMENSION `(n*(n+1)/2)`. The array a contains the matrix `A` in the RFP format.

Output Parameters

The upper or lower triangular part of a is overwritten by the Cholesky factor U or L, as specified by info.

info

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

If info = -i, the i-th parameter had an illegal value.

If info = i, the leading minor of order i (and therefore the matrix A itself) is not positive-definite, and the factorization could not be completed. This may indicate an error in forming the matrix A.