NAG Library Routine Document

F07WWF (ZPFTRI)

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     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:     UPLO – CHARACTER(1)Input

On entry: specifies how $A$ has been factorized.

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

$A=U^{\mathrm{H}}U$, where $U$ is upper triangular.

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

$A=L{L}^{\mathrm{H}}$, where $L$ is lower triangular.

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

3:     N – INTEGERInput

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

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

4:     A($\mathbf{N}\times \left(\mathbf{N}+1\right)/2$) – COMPLEX (KIND=nag_wp) arrayInput/Output

On entry: the Cholesky factorization of $A$ stored in RFP format, as returned by F07WRF (ZPFTRF).

On exit: the factorization is overwritten by the $n$ by $n$ matrix $A^{-1}$ stored in RFP format.

5:     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 $\mathbf{INFO}=-i$, the $i$th parameter had an illegal value. An explanatory message is output, and execution of the program is terminated.

$\mathbf{INFO}>0$

If $\mathbf{INFO}=i$, the $i$th diagonal element of the Cholesky factor is zero; the Cholesky factor is singular and the inverse of $A$ cannot be computed.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (f07wwfe.f90)

9.2  Program Data

Program Data (f07wwfe.d)

9.3  Program Results

Program Results (f07wwfe.r)