% Test code for the fast quaternion Fourier transform.
% This code tests the following functions:
%
%  fft  fft2
% ifft ifft2

% Copyright © 2005 Stephen J. Sangwine and Nicolas Le Bihan.
% See the file : Copyright.m for further details.

% We have to test the 1D and 2D functions separately because they do not
% call each other. In addition, we need to verify the results of the FFTs
% against the DFT code in the corresponding qdft functions.

% Test 1. Real data, and therefore real axis, 1D and 2D.
% Check that the transform inverts correctly and then that it agrees with
% the DFT code.

T = 1e-12;

q = quaternion(randn(10,10), randn(10,10), randn(10,10), randn(10,10));

RA = unit(quaternion(1,1,1)); % Real axis.

compare(q,  ifft(fft(q)),            T, 'fft/ifft failed test 1.');
compare(q, iqdft(fft(q), RA, 'L'),   T, 'fft/iqdft failed test 1.');
compare(q, ifft2(fft2(q)),           T, 'fft2/ifft2 failed test 1.');
compare(q, iqdft2(fft2(q), RA, 'L'), T, 'fft2/iqfft2 failed test 1.');

clear q RA

% Test 2. Complex data, and therefore complex axis, 1D and 2D.
% Check that the transform inverts correctly and then that it agrees with
% the DFT code.

b = quaternion(complex(randn(10,10),randn(10,10)),...
               complex(randn(10,10),randn(10,10)),...
               complex(randn(10,10),randn(10,10)),...
               complex(randn(10,10),randn(10,10)));

CA = quaternion(1,1,1) + quaternion(0,1,-1).*i; % Complex axis.

compare(b, ifft(fft(b)),             T, 'fft/ifft failed test 2.');
compare(b, iqdft(fft(b), CA, 'L'),   T, 'fft/iqdft failed test 2.');
compare(b, ifft2(fft2(b)),           T, 'fft2/ifft2 failed test 2.');
compare(b, iqdft2(fft2(b), CA, 'L'), T, 'fft2/iqfft2 failed test 2.');

clear CA b T