NAG Toolbox: nag_lapack_dsytri (f07mj)

Purpose

Syntax

Description

References

Parameters

Compulsory Input Parameters

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

Specifies how $A$ has been factorized.

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

$A=PUD{U}^{\mathrm{T}}{P}^{\mathrm{T}}$, 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:     $\mathrm{a}\left(\mathit{lda},:\right)$ – 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 $\max \left(1,\mathbf{n}\right)$.

Details of the factorization of $A$, as returned by nag_lapack_dsytrf (f07md).

3:     $\mathrm{ipiv}\left(:\right)$ – int64int32nag_int array

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

Details of the interchanges and the block structure of $D$, as returned by nag_lapack_dsytrf (f07md).

Optional Input Parameters

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

Default: the first dimension of the array a and the second dimension of the arrays a, ipiv.

$n$, 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 $\max \left(1,\mathbf{n}\right)$.

The factorization stores 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.

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  $\mathbf{info}>0$

Element $\_$ of the diagonal is exactly zero. $D$ is singular and the inverse of $A$ cannot be computed.

Accuracy

Further Comments

Example

Open in the MATLAB editor: f07mj_example

function f07mj_example


fprintf('f07mj example results\n\n');

% Indefinite matrix A (lower triangular part stored)
uplo = 'L';
a = [ 2.07,  0,    0,     0; 
      3.87, -0.21, 0,     0;
      4.20,  1.87, 1.15,  0;
     -1.15,  0.63, 2.06, -1.81];

% Factorize
[af, ipiv, info] = f07md( ...
                          uplo, a);

% Invert
[ainv, info] = f07mj( ...
                      uplo, af, ipiv);

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

f07mj example results

 Inverse
             1          2          3          4
 1      0.7485
 2      0.5221    -0.1605
 3     -1.0058    -0.3131     1.3501
 4     -1.4386    -0.7440     2.0667     2.4547