NAG Library Routine Document

f07nwf (zsytri)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

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

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

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

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

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

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

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

2:     $\mathbf{n}$ – IntegerInput

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) 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 f07nrf (zsytrf).

On exit: the factorization is overwritten by the $n$ by $n$ symmetric 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:     $\mathbf{lda}$ – IntegerInput

On entry: the first dimension of the array a as declared in the (sub)program from which f07nwf (zsytri) is called.

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

5:     $\mathbf{ipiv}\left(*\right)$ – 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 f07nrf (zsytrf).

6:     $\mathbf{work}\left(2\times \mathbf{n}\right)$ – Complex (Kind=nag_wp) arrayWorkspace

7:     $\mathbf{info}$ – IntegerOutput

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 3.7 in How to Use the NAG Library and its Documentation 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

Program Text (f07nwfe.f90)

10.2

Program Data

Program Data (f07nwfe.d)

10.3

Program Results

Program Results (f07nwfe.r)