NAG Toolbox: nag_lapack_dtptri (f07uj)

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:     $\mathrm{n}$ – int64int32nag_int scalar

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

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

4:     $\mathrm{ap}\left(:\right)$ – double array

The dimension of the array ap must be at least $\max \left(1,\mathbf{n}\times \left(\mathbf{n}+1\right)/2\right)$

The $n$ by $n$ triangular matrix $A$, packed by columns.

More precisely,

• if $\mathbf{uplo}=\text{'U'}$, the upper triangle of $A$ must be stored with element $A_{ij}$ in $\mathbf{ap}\left(i+j\left(j-1\right)/2\right)$ for $i\le j$;
• if $\mathbf{uplo}=\text{'L'}$, the lower triangle of $A$ must be stored with element $A_{ij}$ in $\mathbf{ap}\left(i+\left(2n-j\right)\left(j-1\right)/2\right)$ for $i\ge j$.

If $\mathbf{diag}=\text{'U'}$, the diagonal elements of $A$ are assumed to be $1$, and are not referenced; the same storage scheme is used whether $\mathbf{diag}=\text{'N'}$ or ‘U’.

Optional Input Parameters

None.

Output Parameters

1:     $\mathrm{ap}\left(:\right)$ – double array

The dimension of the array ap will be $\max \left(1,\mathbf{n}\times \left(\mathbf{n}+1\right)/2\right)$

$A$ 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: f07uj_example

function f07uj_example


fprintf('f07uj example results\n\n');

% Invert A, where A is Lower triangular and packed
n = int64(4);
ap = [ 4.30; -3.96;  0.40; -0.27;
             -4.87;  0.31;  0.07;
                    -8.02; -5.95;
                            0.12];
uplo = 'L';
diag = 'N';

% Invert
[ainv, info] = f07uj(uplo, diag, n, ap);

[ifail] = x04cc( ...
                 uplo, 'Non-unit', n, ainv, 'Inverse');

f07uj 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