%   call: run_dhdt_byfourier.m
%   Demo code for computing the matrix of the Hadamard transform 
%   by simplifying codes of the fast Fouirer transform.
%   List of codes used here:
%    fht_1d.m  - computing the DHdT by the paired-Foureir-transform
%    paired_1dFH.m  - computing the DHdT by the paired-Foureir-transform
%    dhd_matrix1.m  - computing the matrix of the DHdT by 'fht_1d.m'
%    dhd_matrix2.m  - computing the matrix of the DHdT by 'paired_1dFH.m'
%   Artyom M. Grigoryan, December 2008.

    clear all;    
    N=8; 

    HM8a=dhd_matrix1(N);
     1   -1   -1    1   -1    1    1   -1
     1    1   -1   -1   -1   -1    1    1
     1   -1    1   -1   -1    1   -1    1
     1    1    1    1   -1   -1   -1   -1
     1   -1   -1    1    1   -1   -1    1
     1    1   -1   -1    1    1   -1   -1
     1   -1    1   -1    1   -1    1   -1
     1    1    1    1    1    1    1    1
     
    HM8b=dhd_matrix2(N);     
    % In this case we have the complex Hadamard matrix: 
      [1    i   -1   -i   -1   -i    1    i
       1   -i   -1    i   -1    i    1   -i
       1   -1    1   -1   -1    1   -1    1 
       1    1    1    1   -1   -1   -1   -1 
       1   -1   -1    1    1   -1   -1    1 
       1    1   -1   -1    1    1   -1   -1 
       1   -1    1   -1    1   -1    1   -1 
       1    1    1    1    1    1    1    1];         
 
    % We can verify if this complex matrix is a unitary Hadamard matrix: 
     Hc8*Hc8'
      8   0   0   0   0   0   0   0
      0   8   0   0   0   0   0   0
      0   0   8   0   0   0   0   0
      0   0   0   8   0   0   0   0
      0   0   0   0   8   0   0   0
      0   0   0   0   0   8   0   0
      0   0   0   0   0   0   8   0  
      0   0   0   0   0   0   0   8   
    % Yes, is it.