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Chapter Contents
Chapter Introduction
NAG Toolbox

# NAG Toolbox: nag_matop_ztpttr (f01vd)

## Purpose

nag_matop_ztpttr (f01vd) unpacks a complex triangular matrix, stored in packed format in a one-dimensional array, to full format in a two-dimensional array. Packed storage format is described in Section [Packed storage] in the F07 Chapter Introduction.

## Syntax

[a, info] = f01vd(uplo, n, ap)
[a, info] = nag_matop_ztpttr(uplo, n, ap)

## Description

nag_matop_ztpttr (f01vd) unpacks a complex n$n$ by n$n$ triangular matrix A$A$, stored in a one-dimensional array of length n(n + 1) / 2$n\left(n+1\right)/2$ to conventional storage in a two-dimensional array. This function is intended for possible use in conjunction with functions from Chapters F07 and F08 where some functions use triangular matrices stored in the packed form.

None.

## Parameters

### Compulsory Input Parameters

1:     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'$\text{'L'}$.
2:     n – int64int32nag_int scalar
n$n$, the order of the matrix A$A$.
Constraint: n1${\mathbf{n}}\ge 1$.
3:     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$A$ must be 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$A$ must be 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$i\ge j$.

None.

lda

### Output Parameters

1:     a(lda, : $:$) – complex array
The first dimension of the array a will be max (1,n)$\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$
The second dimension of the array will be n${\mathbf{n}}$
ldamax (1,n)$\mathit{lda}\ge \mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$.
The triangular matrix A$A$.
• If uplo = 'U'${\mathbf{uplo}}=\text{'U'}$, a$a$ is upper triangular and the elements of the array below the diagonal are not referenced.
• If uplo = 'L'${\mathbf{uplo}}=\text{'L'}$, a$a$ is lower triangular and the elements of the array above the diagonal are not referenced.
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: uplo, 2: n, 3: ap, 4: a, 5: lda, 6: info.
It is possible that info refers to a parameter that is omitted from the MATLAB interface. This usually indicates that an error in one of the other input parameters has caused an incorrect value to be inferred.

Not applicable.

None.

## Example

```function nag_matop_ztpttr_example
uplo = 'u';
n = int64(4);
ap = [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 packed vector
fprintf('\n');
[ifail] = ...
nag_file_print_matrix_complex_gen_comp('g', 'x', ap, 'b', 'f5.2', 'Packed matrix ap:', 'i', ...
'n', int64(80), int64(0));
% Convert to triangular form
[a, info] = nag_matop_ztpttr(uplo, n, ap);
% Print the unpacked matrix
fprintf('\n');
[ifail] = ...
nag_file_print_matrix_complex_gen_comp(uplo, 'n', a, 'b', 'f5.2', 'Unpacked matrix a:', 'i', ...
'i', int64(80), int64(0))
```
```

Packed matrix 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)

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

ifail =

0

```
```function f01vd_example
uplo = 'u';
n = int64(4);
ap = [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 packed vector
fprintf('\n');
[ifail] = x04db('g', 'x', ap, 'b', 'f5.2', 'Packed matrix ap:', 'i', ...
'n', int64(80), int64(0));
% Convert to triangular form
[a, info] = f01vd(uplo, n, ap);
% Print the unpacked matrix
fprintf('\n');
[ifail] = x04db(uplo, 'n', a, 'b', 'f5.2', 'Unpacked matrix a:', 'i', ...
'i', int64(80), int64(0))
```
```

Packed matrix 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)

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

ifail =

0

```