NAG Library Routine Document

f07wrf (zpftrf)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{transr}$ – Character(1)Input

On entry: specifies whether the normal RFP representation of $A$ or its conjugate transpose is stored.

$\mathbf{transr}=\text{'N'}$

The matrix $A$ is stored in normal RFP format.

$\mathbf{transr}=\text{'C'}$

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

Constraint: $\mathbf{transr}=\text{'N'}$ or $\text{'C'}$.

2:     $\mathbf{uplo}$ – Character(1)Input

On entry: specifies whether the upper or lower triangular part of $A$ is stored.

$\mathbf{uplo}=\text{'U'}$

The upper triangular part of $A$ is stored, and $A$ is factorized as $U^{\mathrm{H}}U$, where $U$ is upper triangular.

$\mathbf{uplo}=\text{'L'}$

The lower triangular part of $A$ is stored, and $A$ is factorized as $L{L}^{\mathrm{H}}$, where $L$ is lower triangular.

Constraint: $\mathbf{uplo}=\text{'U'}$ or $\text{'L'}$.

3:     $\mathbf{n}$ – IntegerInput

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

Constraint: $\mathbf{n}\ge 0$.

4:     $\mathbf{ar}\left(\mathbf{n}\times \left(\mathbf{n}+1\right)/2\right)$ – Complex (Kind=nag_wp) arrayInput/Output

On entry: the upper or lower triangular part (as specified by uplo) of the $n$ by $n$ Hermitian matrix $A$, in either normal or transposed RFP format (as specified by transr). The storage format is described in detail in Section 3.3.3 in the F07 Chapter Introduction.

On exit: if $\mathbf{info}=\mathbf{0}$, the factor $U$ or $L$ from the Cholesky factorization $A=U^{\mathrm{H}}U$ or $A=L{L}^{\mathrm{H}}$, in the same storage format as $A$.

5:     $\mathbf{info}$ – IntegerOutput

On exit: $\mathbf{info}=0$ unless the routine detects an error (see Section 6).

6

Error Indicators and Warnings

$\mathbf{info}<0$

If $\mathbf{info}=-i$, argument $i$ had an illegal value. An explanatory message is output, and execution of the program is terminated.

$\mathbf{info}>0$

The leading minor of order $〈\mathit{\text{value}}〉$ 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 $A$. There is no routine 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 f07mrf (zhetrf).

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (f07wrfe.f90)

10.2

Program Data

Program Data (f07wrfe.d)

10.3

Program Results

Program Results (f07wrfe.r)