NAG Toolbox: nag_lapack_dpotri (f07fj)

Purpose

Syntax

Description

References

Parameters

Compulsory Input Parameters

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

Specifies how $A$ has been factorized.

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

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

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

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

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

2:     $\mathrm{a}\left(\mathit{lda},:\right)$ – double 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_dpotrf (f07fd).

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:     $\mathrm{a}\left(\mathit{lda},:\right)$ – double 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: f07fj_example

function f07fj_example


fprintf('f07fj example results\n\n');

% Lower triangular part of symmetric matrix A
uplo = 'Lower';
a = [ 4.16,  0,    0,    0;
     -3.12,  5.03, 0,    0;
      0.56, -0.83, 0.76, 0;
     -0.10,  1.18, 0.34, 1.18];

% Factorize A
[L, info] = f07fd( ...
                   uplo, a);

% Invert A using L.

[ainv, info] = f07fj( ...
                      uplo, L);

[ifail] = x04ca( ...
                 uplo, 'N', ainv, 'Inverse');

f07fj example results

 Inverse
             1          2          3          4
 1      0.6995
 2      0.7769     1.4239
 3      0.7508     1.8255     4.0688
 4     -0.9340    -1.8841    -2.9342     3.4978