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+function [L U] = LU (A)
+  [n n1] = size (A);
+  [L U] = deal (eye (n), A);
+  for k = 1:n
+    for i = k + 1 : n
+      L(i, k) = U(i, k) / U(k, k);
+      U(i, :) = U(i, :) - L(i, k)*U(k, :);
+    end
+  end
+end