NAG Library Routine Document

F07GRF (ZPPTRF)

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     UPLO – CHARACTER(1)Input

On entry: specifies whether the upper or lower triangular part of A is stored and how A is to be factorized.

UPLO='U'

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

UPLO='L'

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

Constraint: UPLO='U' or 'L'.

2:     N – INTEGERInput

On entry: n, the order of the matrix A.

Constraint: N≥0.

3:     AP(*) – COMPLEX (KIND=nag_wp) arrayInput/Output

Note: the dimension of the array AP must be at least max1,N×N+1/2.

On entry: the n by n Hermitian matrix A, packed by columns.

More precisely,

• if UPLO='U', the upper triangle of A must be stored with element Aij in APi+jj-1/2 for i≤j;
• if UPLO='L', the lower triangle of A must be stored with element Aij in APi+2n-jj-1/2 for i≥j.

On exit: if INFO=0, the factor U or L from the Cholesky factorization A=UHU or A=LLT, in the same storage format as A.

4:     INFO – INTEGEROutput

On exit: INFO=0 unless the routine detects an error (see Section 6).

6  Error Indicators and Warnings

INFO<0

If INFO=-i, the ith parameter had an illegal value. An explanatory message is output, and execution of the program is terminated.

INFO>0

If INFO=i, the leading minor of order i is not positive definite and the factorization could not be completed. Hence A itself is not positive definite. This may indicate an error in forming the matrix A. To factorize a matrix which is not positive definite, call F07PRF (ZHPTRF) instead.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (f07grfe.f90)

9.2  Program Data

Program Data (f07grfe.d)

9.3  Program Results

Program Results (f07grfe.r)