X-Git-Url: http://gitweb.michael.orlitzky.com/?p=octave.git;a=blobdiff_plain;f=optimization%2Fconjugate_gradient_method.m;h=a6401e5ec21ff963883368576deb59ff0e1b36d0;hp=9b2ddac24377e5d02651f7b9e52a5ee3a4c0707c;hb=5ef96eb244b2a52886a31fc9873db479f52a6483;hpb=6e504c235e5e2ad1abc0a98b733ed2269936c17a

diff --git a/optimization/conjugate_gradient_method.m b/optimization/conjugate_gradient_method.m
index 9b2ddac..a6401e5 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 +8,7 @@ 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.
   %
   % INPUT:
   %
@@ -22,33 +22,28 @@ 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:
   %
   % All vectors are assumed to be *column* vectors.
   %
-  zero_vector = zeros(length(x0), 1);
-
-  k = 0;
-  xk = x0;
-  rk = A*xk - b; % The first residual must be computed the hard way.
-  pk = -rk;
-
-  while (norm(rk) > tolerance)
-    alpha_k = step_length_cgm(rk, A, pk);
-    x_next = xk + 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;
-    rk = r_next;
-    pk = p_next;
-  end
+  n = length(x0);
+  M = eye(n);
 
-  x_star = xk;
+  % The standard CGM is equivalent to the preconditioned CGM is you
+  % use the identity matrix as your preconditioner.
+  [x, k] = preconditioned_conjugate_gradient_method(A,
+ 						    M,
+						    b,
+						    x0,
+						    tolerance,
+						    max_iterations);
 end