NAG Toolbox: nag_lapack_zpotri (f07fw)

Purpose

Syntax

Description

References

Parameters

Compulsory Input Parameters

1:     $\mathrm{uplo}$ – string (length ≥ 1)

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 $\text{'L'}$.

2:     $\mathrm{a}\left(\mathit{lda},:\right)$ – complex array

The first dimension of the array a must be at least $\max \left(1,\mathbf{n}\right)$.

The second dimension of the array a must be at least $\max \left(1,\mathbf{n}\right)$.

The upper triangular matrix $U$ if $\mathbf{uplo}=\text{'U'}$ or the lower triangular matrix $L$ if $\mathbf{uplo}=\text{'L'}$, as returned by nag_lapack_zpotrf (f07fr).

Optional Input Parameters

1:     $\mathrm{n}$ – int64int32nag_int scalar

Default: the first dimension of the array a and the second dimension of the array a.

$n$, the order of the matrix $A$.

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

Output Parameters

1:     $\mathrm{a}\left(\mathit{lda},:\right)$ – complex array

The first dimension of the array a will be $\max \left(1,\mathbf{n}\right)$.

The second dimension of the array a will be $\max \left(1,\mathbf{n}\right)$.

$U$ stores the upper triangle of $A^{-1}$ if $\mathbf{uplo}=\text{'U'}$; $L$ stores the lower triangle of $A^{-1}$ if $\mathbf{uplo}=\text{'L'}$.

2:     $\mathrm{info}$ – int64int32nag_int scalar

$\mathbf{info}=0$ unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

Cases prefixed with W are classified as warnings and do not generate an error of type NAG:error_n. See nag_issue_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.

W  $\mathbf{info}>0$

Diagonal element $\_$ of the Cholesky factor is zero; the Cholesky factor is singular and the inverse of $A$ cannot be computed.

Accuracy

Further Comments

Example

Open in the MATLAB editor: f07fw_example

function f07fw_example


fprintf('f07fw example results\n\n');

% Lower triangular part of Hermitian matrix A
uplo = 'Lower';
a = [ 3.23 + 0i,     0    + 0i,     0    + 0i,     0    + 0i;
      1.51 + 1.92i,  3.58 + 0i,     0    + 0i,     0    + 0i;
      1.90 - 0.84i, -0.23 - 1.11i,  4.09 + 0i,     0    + 0i;
      0.42 - 2.50i, -1.18 - 1.37i,  2.33 + 0.14i,  4.29 + 0i];

% Factorize
[L, info] = f07fr( ...
                   uplo, a);

% Invert
[ainv, info] = f07fw( ...
                      uplo, L);

[ifail] = x04da( ...
                 uplo, 'Non-unit', ainv, 'Inverse');

f07fw example results

 Inverse
             1          2          3          4
 1      5.4691
        0.0000

 2     -1.2624     1.1024
       -1.5491     0.0000

 3     -2.9746     0.8989     2.1589
       -0.9616    -0.5672     0.0000

 4      1.1962    -0.9826    -1.3756     2.2934
        2.9772    -0.2566    -1.4550     0.0000