mene

%task1heiheihei
function A_k = task1(image, k)
  %TODO
  A = double(imread(image));
  [U, S, V] = svd (A);
  U = U(:,1:k);
  S = S(1:k,1:k);
  V = V(:,1:k);
  V = V';
  A_k = U * S * V;
end

%task2heiheihei

function task2(k,image)
   %TODO
  A = double(imread(image));
  [m n] = size(A);
  [U, S, V] = svd (A);
  x = diag(S);
  s=0;
  sort(x,"descend");
  subplot(2,2,1);
  plot(x)

  for i = 1 : k
    s = s + S(i,i);
    v(i) = s;
  endfor
  s1 = sum(diag(S));
  v = v / s1;
  subplot(2,2,2);
  plot(v)

  for z = 1 : k
    A_k = task1(image, z);
    s2 = 0;
    for i = 1 : m
      for j = 1 : n
      s2 = s2 + (A(i,j) - A_k(i,j))^2;
      endfor
  endfor
      v1(z) = s2;
  endfor
  v1 = v1 / (m*n);
  subplot(2,2,3);
  plot(v1)

  for i = 1 : k
    qq(i) = (m*i + n*i + i)/(m*n);
  endfor
  subplot(2,2,4)
  plot(qq)

  end

%task3heiheihei

function [A_k S] = task3(image, k)
  %TODO
  A = double(imread(image));
  [m n] = size(A);
  for j = 1 : m
    u(j) = mean(A(j,:),2);
    A(j,:) = A(j,:) - u(j);
  endfor
  Z = A' / sqrt(n-1);
  [U, S, V] = svd(Z);
  W = V(:,1:k);
  Y = W' * A;
  A_k = W * Y + u';
endfunction


%task4heiheihei

function [A_k S] = task4(image, k)
   %TODO
   A = double(imread(image));
  [m n] = size(A);
  for j = 1 : m
    u(j) = mean(A(j,:),2);
    A(j,:) = A(j,:) - u(j);
  endfor
  Z = 1/(n-1) * A * A';
  [V S] = eig(Z);
  W = V(:,1:k);
  Y = W' * A;
  A_k = W * Y + u';
 endfunction