NAG Toolbox: nag_lapack_dtrtri (f07tj)

Purpose

Syntax

Description

References

Parameters

Compulsory Input Parameters

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

Specifies whether $A$ is upper or lower triangular.

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

$A$ is upper triangular.

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

$A$ is lower triangular.

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

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

Indicates whether $A$ is a nonunit or unit triangular matrix.

$\mathbf{diag}=\text{'N'}$

$A$ is a nonunit triangular matrix.

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

$A$ is a unit triangular matrix; the diagonal elements are not referenced and are assumed to be $1$.

Constraint: $\mathbf{diag}=\text{'N'}$ or $\text{'U'}$.

3:     $\mathrm{a}\left(\mathit{lda},:\right)$ – 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 $n$ by $n$ triangular matrix $A$.

• If $\mathbf{uplo}=\text{'U'}$, $a$ is upper triangular and the elements of the array below the diagonal are not referenced.
• If $\mathbf{uplo}=\text{'L'}$, $a$ is lower triangular and the elements of the array above the diagonal are not referenced.
• If $\mathbf{diag}=\text{'U'}$, the diagonal elements of $a$ are assumed to be $1$, and are not referenced.

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

$A$ stores $A^{-1}$, using the same storage format as described above.

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. $A$ is singular its inverse cannot be computed.

Accuracy

Further Comments

Example

Open in the MATLAB editor: f07tj_example

function f07tj_example


fprintf('f07tj example results\n\n');

% Invert A, where A is Lower triangular
a = [ 4.30,  0,     0,    0;
     -3.96, -4.87,  0,    0;
      0.40,  0.31, -8.02, 0;
     -0.27,  0.07, -5.95, 0.12];

% Compute inverse
uplo = 'L';
diag = 'N';
[ainv, info] = f07tj(uplo, diag, a);

% Dispaly inverse
[ifail] = x04ca( ...
                 uplo, diag, ainv, 'Inverse');

f07tj example results

 Inverse
             1          2          3          4
 1      0.2326
 2     -0.1891    -0.2053
 3      0.0043    -0.0079    -0.1247
 4      0.8463    -0.2738    -6.1825     8.3333