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Chapter Contents
Chapter Introduction
NAG Toolbox

# NAG Toolbox: nag_matop_ztfttp (f01vm)

## Purpose

nag_matop_ztfttp (f01vm) copies a complex triangular matrix, stored in a Rectangular Full Packed (RFP) format array, to a standard packed format array.

## Syntax

[ap, info] = f01vm(transr, uplo, n, ar)
[ap, info] = nag_matop_ztfttp(transr, uplo, n, ar)

## Description

nag_matop_ztfttp (f01vm) packs a complex $n$ by $n$ triangular matrix $A$, stored in RFP format, to packed format. 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 and the packed storage format is described in Packed 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 conjugate transpose is stored.
${\mathbf{transr}}=\text{'N'}$
The RFP representation of the matrix $A$ is stored.
${\mathbf{transr}}=\text{'C'}$
The conjugate transpose of the RFP representation of the matrix $A$ is stored.
Constraint: ${\mathbf{transr}}=\text{'N'}$ or $\text{'C'}$.
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:     $\mathrm{ar}\left({\mathbf{n}}×\left({\mathbf{n}}+1\right)/2\right)$ – complex 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:     $\mathrm{ap}\left({\mathbf{n}}×\left({\mathbf{n}}+1\right)/2\right)$ – complex 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

$-999<{\mathbf{info}}<0$
If ${\mathbf{info}}=-i$, argument $i$ had an illegal value. An explanatory message is output, and execution of the program is terminated.
${\mathbf{info}}=-999$
Dynamic memory allocation failed.

Not applicable.

None.

## Example

This example reads in a triangular matrix in RFP format and copies it to packed format.
```function f01vm_example

fprintf('f01vm example results\n\n');

transr = 'n';
uplo   = 'u';
n      = int64(4);
ar = [1.3 + 1.3i;
2.3 + 2.3i;
3.3 + 3.3i;
1.1 - 1.1i;
1.2 - 1.2i;
1.4 + 1.4i;
2.4 + 2.4i;
3.4 + 3.4i;
4.4 + 4.4i;
2.2 - 2.2i];
% Print the Rectangular Full Packed array
fprintf('\n');
[ifail] = x04db('g', 'x', ar, 'b', 'f5.2', 'RFP Packed Array ar:', 'i', ...
'n', int64(80), int64(0));
% Convert to packed vector form
[ap, info] = f01vm(transr, uplo, n, ar);
% Print the packed vector
fprintf('\n');
[ifail] = x04db('g', 'x', ap, 'b', 'f5.2', 'Packed Array ap:', 'i', ...
'n', int64(80), int64(0));

```
```f01vm example results

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

Packed Array ap:
1  ( 1.10, 1.10)
2  ( 1.20, 1.20)
3  ( 2.20, 2.20)
4  ( 1.30, 1.30)
5  ( 2.30, 2.30)
6  ( 3.30, 3.30)
7  ( 1.40, 1.40)
8  ( 2.40, 2.40)
9  ( 3.40, 3.40)
10  ( 4.40, 4.40)
```