naginterfaces.library.lapacklin.zpftrf

naginterfaces.library.lapacklin.zpftrf(transr, uplo, n, ar)[source]

zpftrf computes the Cholesky factorization of a complex Hermitian positive definite matrix stored in Rectangular Full Packed (RFP) format.

For full information please refer to the NAG Library document for f07wr

https://www.nag.com/numeric/nl/nagdoc_27.3/flhtml/f07/f07wrf.html

Parameters
transrstr, length 1

Specifies whether the normal RFP representation of or its conjugate transpose is stored.

The matrix is stored in normal RFP format.

The conjugate transpose of the RFP representation of the matrix is stored.

uplostr, length 1

Specifies whether the upper or lower triangular part of is stored.

The upper triangular part of is stored, and is factorized as , where is upper triangular.

The lower triangular part of is stored, and is factorized as , where is lower triangular.

nint

, the order of the matrix .

arcomplex, array-like, shape

The upper or lower triangular part (as specified by ) of the Hermitian matrix , in either normal or transposed RFP format (as specified by ). The storage format is described in detail in the F07 Introduction.

Returns
arcomplex, ndarray, shape

If no exception or warning is raised, the factor or from the Cholesky factorization or , in the same storage format as .

Raises
NagValueError
(errno )

On entry, error in parameter .

Constraint: or .

(errno )

On entry, error in parameter .

Constraint: or .

(errno )

On entry, error in parameter .

Constraint: .

(errno )

The leading minor of order is not positive definite and the factorization could not be completed. Hence itself is not positive definite. This may indicate an error in forming the matrix . There is no function specifically designed to factorize a Hermitian matrix stored in RFP format which is not positive definite; the matrix must be treated as a full Hermitian matrix, by calling zhetrf().

Notes

zpftrf forms the Cholesky factorization of a complex Hermitian positive definite matrix either as if or if , where is an upper triangular matrix and is a lower triangular, stored in RFP format. The RFP storage format is described in the F07 Introduction.

References

Demmel, J W, 1989, On floating-point errors in Cholesky, LAPACK Working Note No. 14, University of Tennessee, Knoxville, https://www.netlib.org/lapack/lawnspdf/lawn14.pdf

Gustavson, F G, Waśniewski, J, Dongarra, J J and Langou, J, 2010, Rectangular full packed format for Cholesky’s algorithm: factorization, solution, and inversion, ACM Trans. Math. Software (37, 2)