1: $m$ – int64int32nag_int scalar: $m$ , the number of Hermitian sequences to be converted into complex form.

Constraint: $m \geq 1$ .
2: $n$ – int64int32nag_int scalar: $n$ , the number of data values in each Hermitian sequence.

Constraint: $n \geq 1$ .
3: $x (m \times n)$ – double array: The data must be stored in x as if in a two-dimensional array of dimension $(1 : m, 0 : n - 1)$ ; each of the $m$ sequences is stored in a row of the array in Hermitian form. If the $n$ data values $z_{j}^{p}$ are written as $x_{j}^{p} + i y_{j}^{p}$ , then for $0 \leq j \leq n / 2$ , $x_{j}^{p}$ is contained in $x (p, j)$ , and for $1 \leq j \leq (n - 1) / 2$ , $y_{j}^{p}$ is contained in $x (p, n - j)$ . (See also Real transforms in the C06 Chapter Introduction.)

Optional Input Parameters

None.

Output Parameters

1: $u (m \times n)$ – double array

2: $v (m \times n)$ – double array

The real and imaginary parts of the

m

sequences of length

n

, are stored in u and v respectively, as if in two-dimensional arrays of dimension

(1 : m, 0 : n - 1)

; each of the

m

sequences is stored as if in a row of each array. In other words, if the real parts of the

p

th sequence are denoted by

x_{j}^{p}

, for

j = 0, 1, \dots, n - 1

then the

m n

elements of the array u contain the values

x_{0}^{1}, x_{0}^{2}, \dots, x_{0}^{m}, x_{1}^{1}, x_{1}^{2}, \dots, x_{1}^{m}, \dots, x_{n - 1}^{1}, x_{n - 1}^{2}, \dots, x_{n - 1}^{m}

3: $ifail$ – int64int32nag_int scalar

ifail = 0

unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

Errors or warnings detected by the function:

$ifail = 1$

On entry,

m < 1

$ifail = 2$

On entry,

n < 1

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.

$ifail = - 999$: Dynamic memory allocation failed.

Accuracy

Exact.

Further Comments

None.

Example

This example reads in sequences of real data values which are assumed to be Hermitian sequences of complex data stored in Hermitian form. The sequences are then expanded into full complex form using nag_sum_convert_herm2complex_sep (c06gs) and printed.

Open in the MATLAB editor: c06gs_example

function c06gs_example


fprintf('c06gs example results\n\n');

% 3 Hermitian sequences stored as rows in compact form
m = int64(3);
n = int64(6);
x = [0.3854  0.6772  0.1138  0.6751  0.6362  0.1424;
     0.5417  0.2983  0.1181  0.7255  0.8638  0.8723;
     0.9172  0.0644  0.6037  0.6430  0.0428  0.4815];

disp('Original values in compact Hermitian form:');
disp(x);

% Put x in full complex form
[u, v, ifail] = c06gs(m, n, x);

nd = [m,n];
z = reshape(u + i*v,nd);
disp(' ');
title = 'Original data in full complex form';
[ifail] = x04da('General','Non-unit', z, title);

c06gs example results

Original values in compact Hermitian form:
    0.3854    0.6772    0.1138    0.6751    0.6362    0.1424
    0.5417    0.2983    0.1181    0.7255    0.8638    0.8723
    0.9172    0.0644    0.6037    0.6430    0.0428    0.4815

 
 Original data in full complex form
          1       2       3       4       5       6
 1   0.3854  0.6772  0.1138  0.6751  0.1138  0.6772
     0.0000  0.1424  0.6362  0.0000 -0.6362 -0.1424

 2   0.5417  0.2983  0.1181  0.7255  0.1181  0.2983
     0.0000  0.8723  0.8638  0.0000 -0.8638 -0.8723

 3   0.9172  0.0644  0.6037  0.6430  0.6037  0.0644
     0.0000  0.4815  0.0428  0.0000 -0.0428 -0.4815

PDF version (NAG web site, 64-bit version, 64-bit version)

Chapter Contents

Chapter Introduction

NAG Toolbox