X-Git-Url: http://gitweb.michael.orlitzky.com/?p=octave.git;a=blobdiff_plain;f=run-tests.m;h=2ad4c2462b06f1203134c5576aaecde217db9f98;hp=aa285c32e38fb3f70747a75402e57ef6a8515ed2;hb=99b641383e285ba62808678be74077485a61e024;hpb=13bba59d9d3cc9a508deef1e0f6176cfab73fbcd

diff --git a/run-tests.m b/run-tests.m
index aa285c3..2ad4c24 100755
--- a/run-tests.m
+++ b/run-tests.m
@@ -43,11 +43,11 @@ 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];
+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));
@@ -72,3 +72,46 @@ 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);
+
+
+
+f = @(x,y) y;
+x0 = 0;
+y0 = 1;
+h = 1;
+actual_y = forward_euler1(x0, y0, f, h);
+expected_y = 2;
+
+unit_test_equals("Forward Euler works for one step", ...
+		 expected_y, ...
+		 actual_y);