tests/newtons_method_tests.m

   1 f = @(x) x^6 - x - 1;
   2 f_prime = @(x) 6*x^5 - 1;
   3 tol = 1/1000000;
   4 x0 = 2;
   5 expected_root = 1.1347;
   6 unit_test_equals("Newton's method agrees with Haskell", ...
   7                  expected_root, ...
   8                  newtons_method(f, f_prime, tol, x0));
   9
  10
  11 f1 = @(u) u(1)^2 + u(1)*u(2)^3 - 9;
  12 f2 = @(u) 3*u(1)^2*u(2) - u(2)^3 - 4;
  13 f = @(u) [f1(u); f2(u)];
  14 ## The partials for the Jacobian.
  15 f1x = @(u) 2*u(1) + u(2)^3;
  16 f1y = @(u) 3*u(1)*u(2)^2;
  17 f2x = @(u) 6*u(1)*u(2);
  18 f2y = @(u) 3*u(1)^2 - 3*u(2)^2;
  19 ## f_prime == Jacobian.
  20 f_prime = @(u) [ f1x(u), f1y(u); f2x(u), f2y(u) ];
  21 tol = 1 / 10^12;
  22 u0 = [1.2; 2.5];
  23 expected_root = [1.33635; 1.75424];
  24 [actual_root, iterations] = newtons_method(f, f_prime, tol, u0);
  25 unit_test_equals("Homework #3 problem #4 root is correct", ...
  26                  expected_root, ...
  27                  actual_root);