% trigimage.m displays an intensity plot of a trig field as an image, as a way of understanding the differences between matrices and images.  Then it changes the colormaps.

gridsize = [80 80];                           % number of grid points in x, y
gridrange= [0 10 0 10];                       % default [xmin xmax ymin ymax]
[x,y]    = easygrid(gridrange, gridsize);     % matrices of x and y values
Z        = zeros(gridsize);

m        = 100;                               % number of Fourier modes

A        = randn(1,m)*sqrt(2/m);                % amplitudes of Fourier modes
phi      = 2 * pi * rand(m,1);                  % random phase
norm     = sqrt(-2*log(rand(m,1)));             % magnitudes of wave numbers
norm     = 1 + 2*round(rand(m,1)) + 0.1*rand(m,1); % magnitudes of wave numbers
theta    = 2 * pi * rand(m,1);                  % arguments of wave numbers
K        = [norm.*cos(theta) norm.*sin(theta)]; % isotropic wave numbers

for i=1:gridsize(1),                            % step through grid points
  for j=1:gridsize(2),
    Z(i,j) = A * cos(K*[x(i,j); y(i,j)] + phi); % compute field value at x,y
  end
end

clf
colormap('default')
subplot(2,2,1)
imagesc(Z);                                     % scale Z values into [0,1]
title('Matrix Z plotted as an image, automatically scaled')
colorbar

subplot(2,2,2)
W = Z-min(min(Z));
W = 64*W/max(max((W)));
image(W);
title('Matrix Z plotted as an image, manually scaled')

subplot(2,2,3)
pcolor(Z);
shading flat
title('Matrix Z plotted with pcolor');

jet

fprintf('Now we will look at different colormaps.\n');
fprintf('The matrix Z has real entries, which get scaled from 1 to 64.\n');
fprintf('Whatever the value of Z, Matlab looks at the corresponding row\n');
fprintf('of the 64 by 3 matrix colormap to see with what intensity it\n');
fprintf('should give to blue, green, and red.\n');
fprintf('In the default colormap jet, low Z values go with blue, medium\n');
fprintf('with green, and high with red.\n');

pause

fprintf('In the gray colormap you see here, all colors have equal\n');
fprintf('intensities, and the result is varying intensities of white.\n');

colormap(gray)

pause

colormap('default')

pause

colormap(hot)

pause

colormap(copper)

pause

colormap(cool)

pause

colormap(winter)

pause

colormap(hsv)