NAG Toolbox: nag_lapack_ztptri (f07uw)

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:     $\mathrm{ap}\left(:\right)$ – complex 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:     $\mathrm{ap}\left(:\right)$ – complex 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: f07uw_example

function f07uw_example


fprintf('f07uw example results\n\n');

% Invert A, where A is Complex Lower triangular and packed.
n = int64(4);
ap = [ 4.78 + 4.56i;  2.00 - 0.30i;  2.89 - 1.34i; -1.89 + 1.15i;
                     -4.11 + 1.25i;  2.36 - 4.25i;  0.04 - 3.69i;
                                     4.15 + 0.80i; -0.02 + 0.46i;
                                                    0.33 - 0.26i];

% Invert
uplo = 'L';
diag = 'N';
[ainv, info] = f07uw(uplo, diag, n, ap);

[ifail] = x04dc( ...
                 uplo, 'Non-unit', n, ainv, 'Inverse');

f07uw example results

 Inverse
             1          2          3          4
 1      0.1095
       -0.1045

 2      0.0582    -0.2227
       -0.0411    -0.0677

 3      0.0032     0.1538     0.2323
        0.1905    -0.2192    -0.0448

 4      0.7602     1.6184     0.1289     1.8697
        0.2814    -1.4346    -0.2250     1.4731