% CUR solution from ChatGPT for images.

clear
clc

A = double(imread('peppers.bmp'));

[m n]=size(A);
k=150;
[U,S,V]=svds(A);

row_lev = sum(U.^2,2);
col_lev = sum(V.^2,2);

row_prob = row_lev / sum(row_lev);
col_prob = col_lev / sum(col_lev);

row_idx = randsample(m,k,true,row_prob);
col_idx = randsample(n,k,true,col_prob);

C = A(:, col_idx);
R = A(row_idx, :);
W = A(row_idx, col_idx);

U_cur = pinv(W);

A_cur = C * U_cur * R;

subplot(1,2,1), imshow(uint8(A)), title('Original')
subplot(1,2,2), imshow(uint8(A_cur)), title('CUR approximation')

% suppose we want rank 3 approximation
% [U,S,V] = svd(A);
% k = 50;
% U_k = U(:, 1:k);
% S_k = S(1:k,1:k);
% V_k = V(:,1:k);
% 
% 
% 
% [~, row_idx] = maxk(row_lev,k);
% [~, col_idx] = maxk(col_lev,k);
% 
% C = A(:, col_idx);
% R = A(row_idx, :);
% W = A(row_idx, col_idx);
% 
% U_cur = pinv(W);
% 
% A_cur = C * U_cur * R;
% 
% % disp('Original A: '); disp(A);
% % disp('CUR approximation: '); disp(round(A_cur));
% 
% subplot(1,2,1), imshow(A,[])
% subplot(1,2,2), imshow(A_cur,[])