1: $m$ – int64int32nag_int scalar: $m$ , the number of Hermitian sequences to be conjugated.

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: $x (m \times n)$ – double array: The imaginary parts $y_{j}^{p}$ are negated. The real parts $x_{j}^{p}$ are not referenced.
2: $ifail$ – 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 expanded into full complex form using nag_sum_convert_herm2complex_sep (c06gs) and printed. The sequences are then conjugated (using nag_sum_conjugate_hermitian_mult_rfmt (c06gq)) and the conjugated sequences are expanded into complex form using nag_sum_convert_herm2complex_sep (c06gs) and printed out.

Open in the MATLAB editor: c06gq_example

function c06gq_example


fprintf('c06gq 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);

% Conjugate values
[xc, ifail] = c06gq(m, n, x);
disp(' ');
disp('Conjugated data in compact Hermitian form:');
disp(xc);

[u, v, ifail] = c06gs(m, n, xc);
zc = reshape(u + i*v,nd);
disp(' ');
title = 'Conjugated data in full complex form';
[ifail] = x04da('General','Non-unit', zc, title);

c06gq 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
 
Conjugated data 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

 
 Conjugated 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