From 7e9b78da72817519f82477be5e9852ed04913aa9 Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Thu, 13 Sep 2012 22:54:15 -0400 Subject: [PATCH] Add the divided_difference Octave function. --- divided_difference.m | 27 +++++++++++++++++++++++++++ 1 file changed, 27 insertions(+) create mode 100755 divided_difference.m diff --git a/divided_difference.m b/divided_difference.m new file mode 100755 index 0000000..139fa47 --- /dev/null +++ b/divided_difference.m @@ -0,0 +1,27 @@ +#!/usr/bin/octave --silent + +function dd = divided_difference(f, xs) + ## Compute divided difference of `f` at points `xs`. The argument `xs` + ## is assumed to be a vector containing at least one element. If it + ## contains n elements, the (n-1)st divided difference will be + ## calculated. + order = length(xs); + + if (order < 1) + ## Can't do anything here. Return nothing. + dd = NA; + elseif (order == 1) + ## Our base case. + dd = f(xs(1)) + else + ## Order > 1, recurse. + + ## f[x0,...,x_n-1] + f0 = divided_difference(f, xs(1:end-1)); + ## f[x1,...,x_n] + f1 = divided_difference(f, xs(2:end)); + + # http://mathworld.wolfram.com/DividedDifference.html + dd = (f0 - f1)/(xs(1) - xs(end)) + end +end -- 2.44.2