X-Git-Url: http://gitweb.michael.orlitzky.com/?p=octave.git;a=blobdiff_plain;f=optimization%2Fsteepest_descent.m;h=7a437d36ad529c7f47bc1d2674bf75fb074e3beb;hp=32aad711457ec2d04aa5d0985cd4286769bb79cc;hb=8c8536a4a03dfdc5975b9f668305a89d1cd56e79;hpb=b1aa6fb5c819eb0ba94dd9dd65e7711202cddeac

diff --git a/optimization/steepest_descent.m b/optimization/steepest_descent.m
index 32aad71..7a437d3 100644
--- a/optimization/steepest_descent.m
+++ b/optimization/steepest_descent.m
@@ -35,34 +35,41 @@ function [x, k] = steepest_descent(g, x0, step_size, tolerance, max_iterations)
   %
   %   * ``k`` - the value of k when we stop; i.e. the number of
   %   iterations.
+  %
+  % NOTES:
+  %
+  % A specialized implementation for solving e.g. Qx=b can avoid one
+  % matrix-vector multiplication below.
+  %
 
   % 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)
+    if (norm(gk) < 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