Simplify the loop in steepest_descent().

diff --git a/optimization/steepest_descent.m b/optimization/steepest_descent.m
index c5bf0bca611d2d83747568ecbbc9c67506684650..1eea7bc1b13a5c39511608248f6ea8ece4490029 100644 (file)
--- a/optimization/steepest_descent.m
+++ b/optimization/steepest_descent.m
@@ -43,32 +43,33 @@ function [x, k] = steepest_descent(g, x0, step_size, tolerance, max_iterations)
   %
 
   % The initial gradient at x_{0} is not supplied, so we compute it
-  % here and begin the loop at k=1.
-  x = x0;
-  g_k = g(x);
+  % here and begin the loop at k=0.
+  k = 0;
+  xk = x0;
+  gk = g(xk);
 
-  if (norm(g_k) < tolerance)
-    % If x_0 is close enough to a solution, there's nothing for us to
-    % do! We use g_k (the gradient of f at x_k) instead of d_k because
-    % their 2-norms will be the same, and g_k is already stored.
-    return;
-  end
-
-  for k = [1 : max_iterations]
+  while (k <= max_iterations)
     % Loop until either of our stopping conditions are met. If the
     % loop finishes, we have implicitly met the second stopping
     % condition (number of iterations).
-    d_k = -g_k;
-    alpha_k = step_size(x);
-    x = x + (alpha_k * d_k);
-    g_k = g(x);
 
     if (norm(g_k) < tolerance)
+      # This catches the k=0 case, too.
+      x = xk;
       return;
     end
+
+    dk = -gk;
+    alpha_k = step_size(xk);
+    xk = xk + (alpha_k * dk);
+    gk = g(xk);
+
+    % We potentially just performed one more iteration than necessary
+    % in order to simplify the loop. Note that due to the structure of
+    % our loop, we will have k > max_iterations when we fail to
+    % converge.
+    k = k + 1;
   end
 
-  % If we make it to the end of the loop, that means we've executed the
-  % maximum allowed iterations. The caller should be able to examine the
-  % return value ``k`` to determine what happened.
+  x = xk;
 end