From: Michael Orlitzky <michael@orlitzky.com>
Date: Tue, 19 Mar 2013 13:28:17 +0000 (-0400)
Subject: Allow CGM to take a maximum number of iterations, return the amount needed.
X-Git-Url: https://gitweb.michael.orlitzky.com/?a=commitdiff_plain;h=6c0b2e3b90fad51bbbb14f4755127a7920fd59c4;p=octave.git

Allow CGM to take a maximum number of iterations, return the amount needed.
---

diff --git a/optimization/conjugate_gradient_method.m b/optimization/conjugate_gradient_method.m
index 9b2ddac..2c94487 100644
--- a/optimization/conjugate_gradient_method.m
+++ b/optimization/conjugate_gradient_method.m
@@ -1,4 +1,4 @@
-function x_star = conjugate_gradient_method(A, b, x0, tolerance)
+function [x, k] = conjugate_gradient_method(A, b, x0, tolerance, max_iterations)
   %
   % Solve,
   %
@@ -8,7 +8,8 @@ function x_star = conjugate_gradient_method(A, b, x0, tolerance)
   %
   %   min [phi(x) = (1/2)*<Ax,x> + <b,x>]
   %
-  % using Algorithm 5.2 in Nocedal and Wright.
+  % using the conjugate_gradient_method (Algorithm 5.2 in Nocedal and
+  % Wright).
   %
   % INPUT:
   %
@@ -22,9 +23,14 @@ function x_star = conjugate_gradient_method(A, b, x0, tolerance)
   %   - ``tolerance`` -- How close ``Ax`` has to be to ``b`` (in
   %     magnitude) before we stop.
   %
+  %   - ``max_iterations`` -- The maximum number of iterations to perform.
+  %
   % OUTPUT:
   %
-  %   - ``x_star`` - The solution to Ax=b.
+  %   - ``x`` - The solution to Ax=b.
+  %
+  %   - ``k`` - The ending value of k; that is, the number of iterations that
+  %     were performed.
   %
   % NOTES:
   %
@@ -33,22 +39,25 @@ function x_star = conjugate_gradient_method(A, b, x0, tolerance)
   zero_vector = zeros(length(x0), 1);
 
   k = 0;
-  xk = x0;
-  rk = A*xk - b; % The first residual must be computed the hard way.
+  x = x0; % Eschew the 'k' suffix on 'x' for simplicity.
+  rk = A*x - b; % The first residual must be computed the hard way.
   pk = -rk;
 
-  while (norm(rk) > tolerance)
+  for k = [ 0 : max_iterations ]
+    if (norm(rk) < tolerance)
+       % Success.
+       return;
+    end
+
     alpha_k = step_length_cgm(rk, A, pk);
-    x_next = xk + alpha_k*pk;
+    x_next = x + alpha_k*pk;
     r_next = rk + alpha_k*A*pk;
     beta_next = (r_next' * r_next)/(rk' * rk);
     p_next = -r_next + beta_next*pk;
 
     k = k + 1;
-    xk = x_next;
+    x = x_next;
     rk = r_next;
     pk = p_next;
   end
-
-  x_star = xk;
 end