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Chapter Contents
Chapter Introduction
NAG Toolbox

# NAG Toolbox: nag_matop_dtrttp (f01va)

## Purpose

nag_matop_dtrttp (f01va) copies a real triangular matrix, stored in a full format array, to a standard packed format array.

## Syntax

[ap, info] = f01va(uplo, a, 'n', n)
[ap, info] = nag_matop_dtrttp(uplo, a, 'n', n)

## Description

nag_matop_dtrttp (f01va) packs a real $n$ by $n$ triangular matrix $A$, stored conventionally in a full format array, into an array of length $n\left(n+1\right)/2$. The matrix is packed by columns. This function is intended for possible use in conjunction with functions from Chapters F07, F08 and F16 where some functions use triangular matrices stored in the packed form. Packed storage format is described in Packed storage in the F07 Chapter Introduction.

None.

## 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 $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$.
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:     $\mathrm{ap}\left({\mathbf{n}}×\left({\mathbf{n}}+1\right)/2\right)$ – 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.

Not applicable.

None.

## Example

This example reads in a triangular matrix and copies it to packed format.
```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
```