From d2a898d4e9937c00b1a81e35c0492a8ed80c8950 Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Fri, 22 Mar 2013 15:48:26 -0400 Subject: [PATCH] Simplify the loop in steepest_descent(). --- optimization/steepest_descent.m | 37 +++++++++++++++++---------------- 1 file changed, 19 insertions(+), 18 deletions(-) diff --git a/optimization/steepest_descent.m b/optimization/steepest_descent.m index c5bf0bc..1eea7bc 100644 --- a/optimization/steepest_descent.m +++ b/optimization/steepest_descent.m @@ -43,32 +43,33 @@ function [x, k] = steepest_descent(g, x0, step_size, tolerance, max_iterations) % % The initial gradient at x_{0} is not supplied, so we compute it - % here and begin the loop at k=1. - x = x0; - g_k = g(x); + % here and begin the loop at k=0. + k = 0; + xk = x0; + gk = g(xk); - if (norm(g_k) < tolerance) - % If x_0 is close enough to a solution, there's nothing for us to - % do! We use g_k (the gradient of f at x_k) instead of d_k because - % their 2-norms will be the same, and g_k is already stored. - return; - end - - for k = [1 : max_iterations] + while (k <= max_iterations) % Loop until either of our stopping conditions are met. If the % loop finishes, we have implicitly met the second stopping % condition (number of iterations). - d_k = -g_k; - alpha_k = step_size(x); - x = x + (alpha_k * d_k); - g_k = g(x); if (norm(g_k) < tolerance) + # This catches the k=0 case, too. + x = xk; return; end + + dk = -gk; + alpha_k = step_size(xk); + xk = xk + (alpha_k * dk); + gk = g(xk); + + % We potentially just performed one more iteration than necessary + % in order to simplify the loop. Note that due to the structure of + % our loop, we will have k > max_iterations when we fail to + % converge. + k = k + 1; end - % If we make it to the end of the loop, that means we've executed the - % maximum allowed iterations. The caller should be able to examine the - % return value ``k`` to determine what happened. + x = xk; end -- 2.33.1