close all
clear all
n1=40;
n2 = 60;
n3 = 100;
q(1:n1) = linspace(1/n1,1,n1);
q(n1+1:n1+n2) = linspace(1-2/n2,-1,n2);
q(1+n1+n2:n1+n2+n3) = linspace(-1+1/n3,0,n3);
qx = repmat(q, [200,1]);
qy = repmat(q, [200,1])';

[n,m]=size(qx);
singleChannelXderivative = createSparseMatrixFrom1dSeperableKernel(1, [0 -1 1],n,m);
singleChannelYderivative = createSparseMatrixFrom1dSeperableKernel([0 -1 1],1,n,m);
K = [singleChannelXderivative;singleChannelYderivative];
u = reshape(K'*[qy(:);qx(:)], [n,m]);

ushow = u - min(u(:));
ushow = ushow ./max(ushow(:));
figure, imshow(ushow)
imwrite(ushow, 'type2a.png', 'png');
img = u;
temp = K*img(:);
dy = reshape(temp(1:n*m), [n,m]);
dx = reshape(temp(1+n*m:end), [n,m]);

tv2a = sum(sum(max(abs(dx),[],3)+max(abs(dy),[],3)))
sum(dx(:).*qx(:) + dy(:).*qy(:))