1 #!/usr/bin/octave --silent
5 unit_test_equals("sin[0] == 0", ...
7 divided_difference(@sin, 0));
9 unit_test_equals("sin[0, pi] == 0", ...
11 divided_difference(@sin, [0,pi]));
13 unit_test_equals("sin[0, pi, 2*pi] == 0", ...
15 divided_difference(@sin, [0,pi,2*pi]));
17 unit_test_equals("zero order divided_difference_coefficients", ...
19 divided_difference_coefficients([0]));
21 unit_test_equals("first order divided_difference_coefficients", ...
23 divided_difference_coefficients([0, pi]));
25 unit_test_equals("second order divided_difference_coefficients", ...
26 [1, -2, 1] / (2*pi^2), ...
27 divided_difference_coefficients([0, pi, 2*pi]));
30 unit_test_equals("1 is odd", ...
34 unit_test_equals("1 is not even", ...
38 unit_test_equals("2 is not odd", ...
42 unit_test_equals("2 is even", ...
46 expected_A = [1, 0, 0, 0, 0; ...
47 16, -32, 16, 0, 0; ...
48 0, 16, -32, 16, 0; ...
49 0, 0, 16, -32, 16; ...
51 unit_test_equals("Homework #1 problem #1 Poisson matrix is correct", ...
53 expected_A == poisson_matrix(4, 0, 1));
60 unit_test_equals("Homework #2 problem #5 fixed point is correct", ...
62 fixed_point_method(g, tol, x0));
66 g1 = @(u) 1 + h*exp(-u(1)^2)/(1+u(2)^2);
67 g2 = @(u) 0.5 + h*atan(u(1)^2 + u(2)^2);
68 my_g = @(u) [g1(u), g2(u)];
71 expected_fp = [1.0729, 1.0821];
72 unit_test_equals("Homework #3 problem #3i fixed point is correct", ...
74 fixed_point_method(my_g, tol, u0));
78 f_prime = @(x) 6*x^5 - 1;
81 expected_root = 1.1347;
82 unit_test_equals("Newton's method agrees with Haskell", ...
84 newtons_method(f, f_prime, tol, x0));
88 f1 = @(u) u(1)^2 + u(1)*u(2)^3 - 9;
89 f2 = @(u) 3*u(1)^2*u(2) - u(2)^3 - 4;
90 f = @(u) [f1(u); f2(u)];
91 ## The partials for the Jacobian.
92 f1x = @(u) 2*u(1) + u(2)^3;
93 f1y = @(u) 3*u(1)*u(2)^2;
94 f2x = @(u) 6*u(1)*u(2);
95 f2y = @(u) 3*u(1)^2 - 3*u(2)^2;
96 ## f_prime == Jacobian.
97 f_prime = @(u) [ f1x(u), f1y(u); f2x(u), f2y(u) ];
100 expected_root = [1.33635; 1.75424];
101 [actual_root, iterations] = newtons_method(f, f_prime, tol, u0);
102 unit_test_equals("Homework #3 problem #4 root is correct", ...