?pftrf

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 )

C:

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

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

A = UT*U for real data, A = UH*U for complex data	if uplo='U'
A = L*LT for real data, A = L*LH 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 defintions.

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

a

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.