NAG Toolbox: nag_matop_dtrttp (f01va)

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:     $\mathrm{a}\left(\mathit{lda},:\right)$ – 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 $\mathbf{n}$.

The 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.

Optional Input Parameters

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

Default: the second dimension of the array a.

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

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

Output Parameters

1:     $\mathrm{ap}\left(\mathbf{n}\times \left(\mathbf{n}+1\right)/2\right)$ – double array

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

More precisely,

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

2:     $\mathrm{info}$ – int64int32nag_int scalar

$\mathbf{info}=0$ unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and 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.

Accuracy

Further Comments

Example

Open in the MATLAB editor: f01va_example

function f01va_example


fprintf('f01va example results\n\n');

uplo = 'u';
a = [1.1, 1.2, 1.3, 1.4;
     0.0, 2.2, 2.3, 2.4;
     0.0, 0.0, 3.3, 3.4;
     0.0, 0.0, 0.0, 4.4];
% Print the unpacked matrix
fprintf('\n');
[ifail] = x04cb(uplo, 'n', a, 'f5.2', 'Unpacked matrix a:', 'i', ...
                {''}, 'i', {''}, int64(80), int64(0));
% Convert to packed vector form
[ap, info] = f01va(uplo, a);
% Print the packed vector
fprintf('\n');
[ifail] = x04cb('g', 'x', ap, 'f5.2', 'Packed matrix ap:', 'i', ...
                {''}, 'n', {''}, int64(80), int64(0));

f01va example results


 Unpacked matrix a:
       1    2    3    4
 1  1.10 1.20 1.30 1.40
 2       2.20 2.30 2.40
 3            3.30 3.40
 4                 4.40

 Packed matrix ap:
  1  1.10
  2  1.20
  3  2.20
  4  1.30
  5  2.30
  6  3.30
  7  1.40
  8  2.40
  9  3.40
 10  4.40