NAG FL Interface
f07mwf (zhetri)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{uplo}$ – 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: $\mathbf{n}$ – Integer Input

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

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

3: $\mathbf{a}\left(\mathbf{lda},*\right)$ – Complex (Kind=nag_wp) array Input/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.

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: $\mathbf{lda}$ – Integer Input

On entry: the first dimension of the array a as declared in the (sub)program from which f07mwf is called.

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

5: $\mathbf{ipiv}\left(*\right)$ – Integer array Input

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.

6: $\mathbf{work}\left(\mathbf{n}\right)$ – Complex (Kind=nag_wp) array Workspace

7: $\mathbf{info}$ – Integer Output

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

6 Error Indicators and Warnings

$-999<\mathbf{info}<0$

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

$\mathbf{info}=-999$

Dynamic memory allocation failed.

See Section 9 in the Introduction to the NAG Library FL Interface for further information.

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

10.2 Program Data

10.3 Program Results