Add Newton's method and some tests.

[octave.git] / run-tests.m

diff --git a/run-tests.m b/run-tests.m
index ef72b10731fecb8f6f324d4b25150153140af948..2892ba0e84f916571960177c62bb297068d7b448 100755 (executable)
--- a/run-tests.m
+++ b/run-tests.m
@@ -13,3 +13,92 @@ unit_test_equals("sin[0, pi] == 0", ...
 unit_test_equals("sin[0, pi, 2*pi] == 0", ...
                 0, ...
                 divided_difference(@sin, [0,pi,2*pi]));
+
+unit_test_equals("zero order divided_difference_coefficients", ...
+                [1], ...
+                divided_difference_coefficients([0]));
+
+unit_test_equals("first order divided_difference_coefficients", ...
+                [-1, 1] / pi, ...
+                divided_difference_coefficients([0, pi]));
+
+unit_test_equals("second order divided_difference_coefficients", ...
+                [1, -2, 1] / (2*pi^2), ...
+                divided_difference_coefficients([0, pi, 2*pi]));
+
+
+unit_test_equals("1 is odd", ...
+                true, ...
+                odd(1));
+
+unit_test_equals("1 is not even", ...
+                false, ...
+                even(1));
+
+unit_test_equals("2 is not odd", ...
+                false, ...
+                odd(2));
+
+unit_test_equals("2 is even", ...
+                true, ...
+                even(2));
+
+expected_A = [1, 0, 0, 0, 0; ...
+              16, -32,  16,  0,  0; ...
+             0,   16, -32,  16, 0; ...
+             0,   0,   16, -32, 16; ...
+             0,   0,   0,   0,  1];
+unit_test_equals("Homework #1 problem #1 Poisson matrix is correct", ...
+                true, ...
+                expected_A == poisson_matrix(4, 0, 1));
+
+
+g = @(x) 1 + atan(x);
+expected_fp = 2.1323;
+tol = 1 / 10^10;
+x0 = 2.4;
+unit_test_equals("Homework #2 problem #5 fixed point is correct", ...
+                expected_fp, ...
+                fixed_point_method(g, tol, x0));
+
+
+h = 0.5;
+g1 = @(u) 1 + h*exp(-u(1)^2)/(1+u(2)^2);
+g2 = @(u) 0.5 + h*atan(u(1)^2 + u(2)^2);
+my_g = @(u) [g1(u), g2(u)];
+tol = 1 / 10^9;
+u0 = [1,1];
+expected_fp = [1.0729, 1.0821];
+unit_test_equals("Homework #3 problem #3i fixed point is correct", ...
+                expected_fp, ...
+                fixed_point_method(my_g, tol, u0));
+
+
+f = @(x) x^6 - x - 1;
+f_prime = @(x) 6*x^5 - 1;
+tol = 1/1000000;
+x0 = 2;
+expected_root = 1.1347;
+unit_test_equals("Newton's method agrees with Haskell", ...
+                expected_root, ...
+                newtons_method(f, f_prime, tol, x0));
+
+
+
+f1 = @(u) u(1)^2 + u(1)*u(2)^3 - 9;
+f2 = @(u) 3*u(1)^2*u(2) - u(2)^3 - 4;
+f = @(u) [f1(u); f2(u)];
+## The partials for the Jacobian.
+f1x = @(u) 2*u(1) + u(2)^3;
+f1y = @(u) 3*u(1)*u(2)^2;
+f2x = @(u) 6*u(1)*u(2);
+f2y = @(u) 3*u(1)^2 - 3*u(2)^2;
+## f_prime == Jacobian.
+f_prime = @(u) [ f1x(u), f1y(u); f2x(u), f2y(u) ];
+tol = 1 / 10^12;
+u0 = [1.2; 2.5];
+expected_root = [1.33635; 1.75424];
+[actual_root, iterations] = newtons_method(f, f_prime, tol, u0);
+unit_test_equals("Homework #3 problem #4 root is correct", ...
+                expected_root, ...
+                actual_root);