NAG Toolbox: nag_lapack_ztrtri (f07tw)

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:     $\mathrm{a}\left(\mathit{lda},:\right)$ – complex 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:     $\mathrm{a}\left(\mathit{lda},:\right)$ – complex 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: f07tw_example

function f07tw_example


fprintf('f07tw example results\n\n');

% Invert A, where A is Lower triangular
a = [  4.78 +  4.56i,   0    +  0i,     0    + 0i,    0    + 0i;
       2.00 -  0.30i,  -4.11 +  1.25i,  0    + 0i,    0    + 0i;
       2.89 -  1.34i,   2.36 -  4.25i,  4.15 + 0.8i,  0    + 0i;
      -1.89 +  1.15i,   0.04 -  3.69i, -0.02 + 0.46i, 0.33 - 0.26i];

% Invert
uplo = 'L';
diag = 'N';
[ainv, info] = f07tw(uplo, diag, a);

% Display inverse
disp('Inverse');
disp(ainv);

f07tw example results

Inverse
   0.1095 - 0.1045i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i
   0.0582 - 0.0411i  -0.2227 - 0.0677i   0.0000 + 0.0000i   0.0000 + 0.0000i
   0.0032 + 0.1905i   0.1538 - 0.2192i   0.2323 - 0.0448i   0.0000 + 0.0000i
   0.7602 + 0.2814i   1.6184 - 1.4346i   0.1289 - 0.2250i   1.8697 + 1.4731i