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

[octave.git] / optimization / conjugate_gradient_method.m

diff --git a/optimization/conjugate_gradient_method.m b/optimization/conjugate_gradient_method.m
index 5b07e1c183f88f5f0764975a23edc1c27dad446e..2c94487a65508e876903343abf457cda853bb929 100644 (file)
--- a/optimization/conjugate_gradient_method.m
+++ b/optimization/conjugate_gradient_method.m
@@ -1,54 +1,63 @@
-function x_star = conjugate_gradient_method(A, b, x0, tolerance)
-  ##
-  ## Solve,
-  ##
-  ##   Ax = b
-  ##
-  ## or equivalently,
-  ##
-  ##   min [phi(x) = (1/2)*<Ax,x> + <b,x>]
-  ##
-  ## using Algorithm 5.2 in Nocedal and Wright.
-  ##
-  ## INPUT:
-  ##
-  ##   - ``A`` -- The coefficient matrix of the system to solve. Must
-  ##     be positive definite.
-  ##
-  ##   - ``b`` -- The right-hand-side of the system to solve.
-  ##
-  ##   - ``x0`` -- The starting point for the search.
-  ##
-  ##   - ``tolerance`` -- How close ``Ax`` has to be to ``b`` (in
-  ##     magnitude) before we stop.
-  ##
-  ## OUTPUT:
-  ##
-  ##   - ``x_star`` - The solution to Ax=b.
-  ##
-  ## NOTES:
-  ##
-  ## All vectors are assumed to be *column* vectors.
-  ##
+function [x, k] = conjugate_gradient_method(A, b, x0, tolerance, max_iterations)
+  %
+  % Solve,
+  %
+  %   Ax = b
+  %
+  % or equivalently,
+  %
+  %   min [phi(x) = (1/2)*<Ax,x> + <b,x>]
+  %
+  % using the conjugate_gradient_method (Algorithm 5.2 in Nocedal and
+  % Wright).
+  %
+  % INPUT:
+  %
+  %   - ``A`` -- The coefficient matrix of the system to solve. Must
+  %     be positive definite.
+  %
+  %   - ``b`` -- The right-hand-side of the system to solve.
+  %
+  %   - ``x0`` -- The starting point for the search.
+  %
+  %   - ``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`` - 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.
+  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