Add Newton's method and some tests.

[octave.git] / run-tests.m

diff --git a/run-tests.m b/run-tests.m
index aa285c32e38fb3f70747a75402e57ef6a8515ed2..2892ba0e84f916571960177c62bb297068d7b448 100755 (executable)
--- a/run-tests.m
+++ b/run-tests.m
@@ -72,3 +72,33 @@ 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);