NAG Library Routine Document

F07MWF (ZHETRI)

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     $\mathrm{UPLO}$ – CHARACTER(1)Input

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

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

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

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

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

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

2:     $\mathrm{N}$ – INTEGERInput

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

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

3:     $\mathrm{A}\left(\mathbf{LDA},*\right)$ – COMPLEX (KIND=nag_wp) arrayInput/Output

Note: the second dimension of the array A must be at least $\max \left(1,\mathbf{N}\right)$.

On entry: details of the factorization of $A$, as returned by F07MRF (ZHETRF).

On exit: the factorization is overwritten by the $n$ by $n$ Hermitian matrix $A^{-1}$.

If $\mathbf{UPLO}=\text{'U'}$, the upper triangle of $A^{-1}$ is stored in the upper triangular part of the array.

If $\mathbf{UPLO}=\text{'L'}$, the lower triangle of $A^{-1}$ is stored in the lower triangular part of the array.

4:     $\mathrm{LDA}$ – INTEGERInput

On entry: the first dimension of the array A as declared in the (sub)program from which F07MWF (ZHETRI) is called.

Constraint: $\mathbf{LDA}\ge \max \left(1,\mathbf{N}\right)$.

5:     $\mathrm{IPIV}\left(*\right)$ – INTEGER arrayInput

Note: the dimension of the array IPIV must be at least $\max \left(1,\mathbf{N}\right)$.

On entry: details of the interchanges and the block structure of $D$, as returned by F07MRF (ZHETRF).

6:     $\mathrm{WORK}\left(\mathbf{N}\right)$ – COMPLEX (KIND=nag_wp) arrayWorkspace

7:     $\mathrm{INFO}$ – 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.

$\mathbf{INFO}>0$

Element $〈\mathit{\text{value}}〉$ of the diagonal is exactly zero. $D$ is singular and the inverse of $A$ cannot be computed.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (f07mwfe.f90)

10.2  Program Data

Program Data (f07mwfe.d)

10.3  Program Results

Program Results (f07mwfe.r)