NAG FL Interface
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: $\mathbf{n}$ – Integer Input

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

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

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

On entry: the upper or lower triangular part (as specified by uplo) of the $n\times n$ 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: $\mathbf{info}$ – Integer Output

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.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results