Added "minimal" test case for costFunctionReg

- These tests use only 0s and 1s for the matrices, mainly, and allow you
  to find if you've got the very basics of the algorithm working. For a
  more detailed test of costFunctionReg see test_costFunctionReg.m from
  community TA Collin Beckingham which uses magic(3) and non-trival values
  for theta and y

ex2/test_costFunctionReg.m

@@ -8,7 +8,7 @@ function test_costFunctionReg ()
     lambda = 3;
 
     J_exp =  50.971;
-    grad_exp = [-6.1081 -7.1932 -12.3540];
+    grad_exp = [-6.1081 -7.1932 -12.3540]'; % vectors are typically vertical
 
     [J, grad] = costFunctionReg(theta, X, y, lambda);
 
@@ -19,10 +19,10 @@ function test_costFunctionReg ()
     % From TA Colin Beckingham, at https://class.coursera.org/ml-005/forum/thread?thread_id=943#post-4666
     theta =  [2; 1; -9];
     X = magic(3);
-    y = [1; -0.2; 3];    
+    y = [1; -0.2; 3];
     lambda = 0.1;
     J_exp_2 =  11.338;
-    grad_exp_2 = [-6.1081 -8.1598 -3.6540];
+    grad_exp_2 = [-6.1081 -8.1598 -3.6540]'; % vectors are typically vertical
 
     [J, grad] = costFunctionReg(theta, X, y, lambda);
 

ex2/test_costfunction_reg_minimal.m

@@ -0,0 +1,51 @@
+function test_costfunction_reg_minimal ()
+  % basically the same test as test_costfunction_minimal, but with 
+  % varying values for the lambda, and theta cannot be 0 (there would be
+  % nothing to penalize), and the x0 (ones) vector has been added
+
+  X = [1 1 1; 
+       1 2 2];      % minimal 2D feature matrix
+  y = [0 1]';       % at least one negative and one positive
+
+  theta = [0 1 1]';   % need non-zero values for theta
+
+  %
+  % lambda = 0 --> no regularization
+  %
+  [J0, grad0] = costFunctionReg(theta, X, y, 0.0);
+  [J1, grad1] = costFunctionReg(theta, X, y, 1.0);
+  [J2, grad2] = costFunctionReg(theta, X, y, 2.0);
+
+  J = [J0 J1 J2]  ;
+  assert(J, [1.0725 1.5725 2.0725], 1e-4);
+
+  grad_exp = [ 
+     0.43141   0.43141   0.43141;
+     0.42241   0.92241   1.42241;
+     0.42241   0.92241   1.42241; ];
+
+  grad = [grad0 grad1 grad2];
+
+  assert(grad, grad_exp, 1e-4);
+
+  % non-zero theta 0, validates that code isn't
+  % including theta 0 in the regularization term
+  theta = [1 1 1]'; 
+
+  [J0, grad0] = costFunctionReg(theta, X, y, 0.0);
+  [J1, grad1] = costFunctionReg(theta, X, y, 1.0);
+  [J2, grad2] = costFunctionReg(theta, X, y, 2.0);
+
+  J = [J0 J1 J2];
+  assert(J, [1.5277 2.0277 2.5277], 1e-4);
+
+  grad_exp = [
+     0.47294   0.47294   0.47294;
+     0.46959   0.96959   1.46959;
+     0.46959   0.96959   1.46959 ];
+
+  grad = [grad0 grad1 grad2];
+
+  assert(grad, grad_exp, 1e-4); 
+
+endfunction

ex2/test_ex2.m

@@ -8,4 +8,7 @@
 
 %!test test_predict()
 
-%!test test_costFunctionReg()
+%!test test_costfunction_reg_minimal()
+
+%!test test_costFunctionReg()
+