X-Git-Url: http://gitweb.michael.orlitzky.com/?p=octave.git;a=blobdiff_plain;f=optimization%2Fstep_length_positive_definite.m;h=7e15a46513e7333a63f060385f353720745dbc29;hp=f6248f67b1dd40bf22ebdfed0947ddd6edbc47fa;hb=2a9c5d796e2f9d7b2b50739f61ef382623d977d6;hpb=b1a89e6359bfef7a07ffe49bc703b51ef47574a9

diff --git a/optimization/step_length_positive_definite.m b/optimization/step_length_positive_definite.m
index f6248f6..7e15a46 100644
--- a/optimization/step_length_positive_definite.m
+++ b/optimization/step_length_positive_definite.m
@@ -1,36 +1,44 @@
 function alpha = step_length_positive_definite(g, Q, p)
-  ##
-  ## Find the minimizer alpha of,
-  ##
-  ##   phi(alpha) = f(x + alpha*p)
-  ##
-  ## where ``p`` is a descent direction,
-  ##
-  ##   f(x) = (1/2)<Qx,x> - <b,x>
-  ##
-  ## and ``Q`` is positive-definite.
-  ##
-  ## The closed-form solution to this problem is given in Nocedal and
-  ## Wright, (3.55).
-  ##
-  ## 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).
-  ##
-  ## OUTPUT:
-  ##
-  ##   - ``alpha`` -- The value which causes ``f`` to decrease the
-  ##     most.
-  ##
-  ## NOTES:
-  ##
-  ## All vectors are assumed to be *column* vectors.
-  ##
-  alpha = -(g' * p)/(p' * Q * p);
+  %
+  % Find the minimizer alpha of,
+  %
+  %   phi(alpha) = f(x + alpha*p)
+  %
+  % where ``p`` is a descent direction,
+  %
+  %   f(x) = (1/2)<Qx,x> - <b,x>
+  %
+  % and ``Q`` is positive-definite.
+  %
+  % The closed-form solution to this problem is given in Nocedal and
+  % Wright, (3.55).
+  %
+  % 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).
+  %
+  % OUTPUT:
+  %
+  %   - ``alpha`` -- The value which causes ``f`` to decrease the
+  %     most.
+  %
+  % NOTES:
+  %
+  % All vectors are assumed to be *column* vectors.
+  %
+  denom = (p' * Q * p);
+
+  if (abs(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 = sign(denom)*eps;
+  end
+
+  alpha = -(g' * p)/denom;
 end