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Chapter Introduction
NAG Toolbox

# NAG Toolbox: nag_matop_dtfttr (f01vg)

## Purpose

nag_matop_dtfttr (f01vg) unpacks a real triangular matrix, stored in a Rectangular Full Packed (RFP) format array, to a full format array.

## Syntax

[a, info] = f01vg(transr, uplo, n, ar)
[a, info] = nag_matop_dtfttr(transr, uplo, n, ar)

## Description

nag_matop_dtfttr (f01vg) unpacks a real $n$ by $n$ triangular matrix $A$, stored in RFP format to conventional storage in a full format array. This function is intended for possible use in conjunction with functions from Chapters F07 and F16 where some functions that use triangular matrices store them in RFP format. The RFP storage format is described in Rectangular Full Packed (RFP) Storage in the F07 Chapter Introduction.

## References

Gustavson F G, Waśniewski J, Dongarra J J and Langou J (2010) Rectangular full packed format for Cholesky's algorithm: factorization, solution, and inversion ACM Trans. Math. Software 37, 2

## Parameters

### Compulsory Input Parameters

1:     $\mathrm{transr}$ – string (length ≥ 1)
Specifies whether the normal RFP representation of $A$ or its transpose is stored.
${\mathbf{transr}}=\text{'N'}$
The RFP representation of the matrix $A$ is stored.
${\mathbf{transr}}=\text{'T'}$
The transpose of the RFP representation of the matrix $A$ is stored.
Constraint: ${\mathbf{transr}}=\text{'N'}$ or $\text{'T'}$.
2:     $\mathrm{uplo}$ – 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 $\text{'L'}$.
3:     $\mathrm{n}$int64int32nag_int scalar
$n$, the order of the matrix $A$.
Constraint: ${\mathbf{n}}\ge 0$.
4:     $\mathrm{ar}\left({\mathbf{n}}×\left({\mathbf{n}}+1\right)/2\right)$ – double array
The upper or lower $n$ by $n$ triangular matrix $A$ (as specified by uplo) in either normal or transposed RFP format (as specified by transr). The storage format is described in Rectangular Full Packed (RFP) Storage in the F07 Chapter Introduction.

None.

### Output Parameters

1:     $\mathrm{a}\left(\mathit{lda},:\right)$ – double array
The first dimension of the array a will be $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$.
The second dimension of the array a will be ${\mathbf{n}}$.
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.
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 in RFP format and unpacks it to full format.
```function f01vg_example

fprintf('f01vg example results\n\n');

transr = 'n';
uplo   = 'u';
n      = int64(4);
ar = [1.30; 2.30; 3.30; 1.10; 1.20; 1.40; 2.40; 3.40; 4.40; 2.20];
% Print the Rectangular Full Packed array
fprintf('\n');
[ifail] = x04cb('g', 'x', ar, 'f5.2', 'RFP Packed Array ar:', 'i', ...
{''}, 'n', {''}, int64(80), int64(0));
% Convert to triangular form
[a, info] = f01vg(transr, uplo, n, ar);
% Print the unpacked matrix
fprintf('\n');
[ifail] = x04cb(uplo, 'n', a, 'f5.2', 'Unpacked matrix a:', 'i', ...
{''}, 'i', {''}, int64(80), int64(0));

```
```f01vg example results

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

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
```