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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 to packed format. The RFP storage format is described in Section [Rectangular Full Packed (RFP) Storage] in the F07 Chapter Introduction and the packed storage format is described in Section [Packed storage] in the F07 Chapter Introduction.

## Syntax

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

## Description

nag_matop_ztfttp (f01vm) packs a complex n$n$ by n$n$ triangular matrix A$A$ stored in RFP format to packed format. This function is intended for possible use in conjunction with functions from Chapter F07 where some functions that use triangular matrices store them in RFP format.

None.

## Parameters

### Compulsory Input Parameters

1:     transr – string (length ≥ 1)
Specifies whether the normal RFP representation of A$A$ or its conjugate transpose is stored.
transr = 'N'${\mathbf{transr}}=\text{'N'}$
The matrix A$A$ is stored in normal RFP format.
transr = 'C'${\mathbf{transr}}=\text{'C'}$
The conjugate transpose of the RFP representation of the matrix A$A$ is stored.
Constraint: transr = 'N'${\mathbf{transr}}=\text{'N'}$ or 'C'$\text{'C'}$.
2:     uplo – string (length ≥ 1)
Specifies whether A$A$ is upper or lower triangular.
uplo = 'U'${\mathbf{uplo}}=\text{'U'}$
A$A$ is upper triangular.
uplo = 'L'${\mathbf{uplo}}=\text{'L'}$
A$A$ is lower triangular.
Constraint: uplo = 'U'${\mathbf{uplo}}=\text{'U'}$ or 'L'$\text{'L'}$.
3:     n – int64int32nag_int scalar
n$n$, the order of the matrix A$A$.
Constraint: n0${\mathbf{n}}\ge 0$.
4:     arf(n × (n + 1) / 2${\mathbf{n}}×\left({\mathbf{n}}+1\right)/2$) – complex array
The triangular matrix A$A$ in RFP format, as described in Section [Rectangular Full Packed (RFP) Storage] in the F07 Chapter Introduction.

None.

None.

### Output Parameters

1:     ap(n × (n + 1) / 2${\mathbf{n}}×\left({\mathbf{n}}+1\right)/2$) – complex array
The n$n$ by n$n$ triangular matrix A$A$, packed by columns.
More precisely,
• if uplo = 'U'${\mathbf{uplo}}=\text{'U'}$, the upper triangle of A$A$ is stored with element Aij${A}_{ij}$ in ap(i + j(j1) / 2)${\mathbf{ap}}\left(i+j\left(j-1\right)/2\right)$ for ij$i\le j$;
• if uplo = 'L'${\mathbf{uplo}}=\text{'L'}$, the lower triangle of A$A$ is stored with element Aij${A}_{ij}$ in ap(i + (2nj)(j1) / 2)${\mathbf{ap}}\left(i+\left(2n-j\right)\left(j-1\right)/2\right)$ for ij$i\ge j$.
2:     info – int64int32nag_int scalar
info = 0${\mathbf{info}}=0$ unless the function detects an error (see Section [Error Indicators and Warnings]).

## Error Indicators and Warnings

info = i${\mathbf{info}}=-i$
If info = i${\mathbf{info}}=-i$, parameter i$i$ had an illegal value on entry. The parameters are numbered as follows:
1: transr, 2: uplo, 3: n, 4: arf, 5: ap, 6: info.

Not applicable.

None.

## Example

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

RFP Packed Array arf:
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)

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

ifail =

0

```
```function f01vm_example
transr = 'n';
uplo   = 'u';
n      = int64(4);
arf = [1.1 + 1.1i;
1.2 + 1.2i;
2.2 + 2.2i;
1.3 + 1.3i;
2.3 + 2.3i;
3.3 + 3.3i;
1.4 + 1.4i;
2.4 + 2.4i;
3.4 + 3.4i;
4.4 + 4.4i];
% Print the Rectangular Full Packed array
fprintf('\n');
[ifail] = x04db('g', 'x', arf, 'b', 'f5.2', 'RFP Packed Array arf:', 'i', ...
'n', int64(80), int64(0));
% Convert to packed vector form
[ap, info] = f01vm(transr, uplo, n, arf);
% Print the packed vector
fprintf('\n');
[ifail] = x04db('g', 'x', ap, 'b', 'f5.2', 'Packed Array ap:', 'i', ...
'n', int64(80), int64(0))
```
```

RFP Packed Array arf:
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)

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

ifail =

0

```