Don't take a redundant parameter in step_length_positive_definite().

[octave.git] / optimization / step_length_positive_definite.m

diff --git a/optimization/step_length_positive_definite.m b/optimization/step_length_positive_definite.m
index ad63956cfa603c097084d15291962c552d6c9d7a..5d3e8a0b2e92a1d4d4b54606ab9453b5a96be215 100644 (file)
--- a/optimization/step_length_positive_definite.m
+++ b/optimization/step_length_positive_definite.m
@@ -1,4 +1,4 @@
-function alpha = step_length_positive_definite(g, Q, p)
+function alpha = step_length_positive_definite(g, Q)
   %
   % Find the minimizer alpha of,
   %
@@ -11,26 +11,33 @@ function alpha = step_length_positive_definite(g, Q, p)
   % and ``Q`` is positive-definite.
   %
   % The closed-form solution to this problem is given in Nocedal and
-  % Wright, (3.55).
+  % Wright, (3.55). The direction of steepest descent will always be
+  % the negative gradient direction; this simplified form is given in
+  % Guler.
   %
   % INPUT:
   %
   %   - ``g`` -- The gradient of f at x.
   %
   %   - ``Q`` -- The positive-definite matrix in the definition of
-  %     ``f`` above.
-  %
-  %   - ``p`` -- The direction in which ``f`` decreases. The line
-  %     along which we minimize f(x + alpha*p).
+  %   ``f`` above.
   %
   % OUTPUT:
   %
-  %   - ``alpha`` -- The value which causes ``f`` to decrease the
-  %     most.
+  %   - ``alpha`` -- The value which decreases ``f`` the most.
   %
   % NOTES:
   %
   % All vectors are assumed to be *column* vectors.
   %
-  alpha = -(g' * p)/(p' * Q * p);
+  denom = (g' * Q * g);
+
+  % denom is non-negative, since it's a Q-norm. No need to abs() it.
+  if (denom < eps)
+    % Catch divide-by-zeros. If denom is effectively zero, set it to
+    % something tiny instead. This trick is also used in the PCGM.
+    denom = eps;
+  end
+
+  alpha = (g' * g)/denom;
 end