refactor univariate gradient descent. confirming univariate version is simply a special case of multivariate version.

Author: everpeace

ex1/mlclass-ex1/computeCost.m

@@ -12,12 +12,18 @@
 % ====================== YOUR CODE HERE ======================
 % Instructions: Compute the cost of a particular choice of theta
 %               You should set J to the cost.
-for i=1:m
-  dif = (theta'*X(i, :)'-y(i));
-  J = J + dif*dif;
-endfor
-%
-J = J / (2*m);
+
+% initial version.
+% for i=1:m
+  % dif = (theta'*X(i, :)'-y(i));
+  % J = J + dif*dif;
+% endfor
+% J = J / (2*m);
+
+% vectorized version.
+% (exactly the same with multivariate version. )
+dif = X*theta -y;
+J = (dif'*dif)/(2*m);
 %
 % =========================================================================
 

ex1/mlclass-ex1/gradientDescent.m

@@ -21,16 +21,24 @@
     theta_prev = theta;
 
     % number of features.
-    p = length(X(1, :));
+    p = size(X, 2);
 
     % simultaneous update theta using theta_prev.
     for j = 1:p
+
+        % % calculate dJ/d(theta_j)
+        % % initial version
+        % deriv = 0;
+        % for i = 1:m
+          % deriv = deriv + (theta_prev'*X(i, :)'-y(i))*X(i, j);
+        % end
+        % deriv = deriv/m;
+
         % calculate dJ/d(theta_j)
-        deriv = 0;
-        for i = 1:m
-          deriv = deriv + (theta_prev'*X(i, :)'-y(i))*X(i, j);
-        end
-        deriv = deriv/m;
+        % vectorized version
+        % (exactly the same with multivariate version)
+        deriv = ((X*theta_prev - y)'*X(:, j))/m;
+
         % update theta_j
         theta(j) = theta_prev(j)-(alpha*deriv);
     end