% copyright J K blah blah blah
% display original picture and PCA approximated pictures using an arbitrary basis
%
% assume featureNormalize() function has been modified to accept optional mu,sigma arguments
% see ex4->displaydata.m->example_width variable how to do this.
%
% start with a fresh octave.  run ex7_pca, press <ctrl> - c after done training but before it goes back to k-means stuff
% you want the variables to be set up properly
%
% function accepts identical picture dimension as U was created by. 32x32
% typical calls to the function:
% jmkPCA_Picture(reshape(double(imread('name.png'))/255,1,1024),mu,sigma,U,1:30:300)
% jmkPCA_Picture(X(<pick any row for a face>,:),mu,sigma,U,1:30:300)


% K is a vector for the # of features you want for that picture, for example K = 1:20:200
%
% here is a function which can give you nice results warping to one side or other
% paste the following two lines at the prompt
% maxfeatures = 1024;
% abc = @(x,a) uint32(1+(maxfeatures-1).*(1-nthroot(1-((0:(x-1))/(x-1)).^a,a)))
%
% K = abc(8,1)    % this is 8 reconstructions linear from 1:maxfeatures
% K = abc(8,2)    % this is a perfect circle
% K = abc(8,3.5)  % you can use real #s for warp factor
% K = abc(8,0.5)  % as well as values < 1 (not useful for this application)
% typical call with abc function, (typical range for a is is in 1 to 3.5 or so)
% jmkPCA_Picture(X(<pick any row for a face>,:),mu,sigma,U,abc(8,3.5))

%
% X_norm  has N original features(pixels of original image)
% Z is a K feature vector(weights of face like feature pictures) 1 <= K <= N
%

function [w h] = jmkPCA_Picture(A,mu,sigma,U,K)

[w h] = size(A);

% if a one color channel image, of proper dimensions of U vectors.
if (w == 1 && (w*h) == size(U,1))
  X_norm = featureNormalize(A,mu,sigma);

  subplot(1, size(K,2)+1, 1);
  imagesc(reshape(A,32,32,1));
  title('Original');

  count = 1;

  for k = K
    Z = projectData(X_norm,U,k);
    X_rec = recoverData(Z,U,k);

    % unnormalize the recovered features
    X_rec = featureNormalize(X_rec,-mu./sigma,1./sigma);

    subplot(1, size(K,2)+1, count+1);
    imagesc(reshape(X_rec,32,32,1));
    title(sprintf('%d',k));

    count = count + 1;
  end


  fprintf("Taaadaaa!\n");
end

end