X-Git-Url: http://gitweb.michael.orlitzky.com/?p=octave.git;a=blobdiff_plain;f=divided_difference.m;h=2b8f8df0d5e75ca126b618acb8e81257235e79c2;hp=139fa478384254d90dfdd44336e3b88fb1dd758a;hb=66a777a08fdad85ff6f07e98e144ba87602eb0e3;hpb=7e9b78da72817519f82477be5e9852ed04913aa9

diff --git a/divided_difference.m b/divided_difference.m
old mode 100755
new mode 100644
index 139fa47..2b8f8df
--- a/divided_difference.m
+++ b/divided_difference.m
@@ -1,20 +1,31 @@
-#!/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);
+  ##
+  ## INPUTS:
+  ##
+  ##   * ``f`` - The function whose divided differences we want.
+  ##
+  ##   * ``xs`` - A vector containing x-coordinates. The length of `xs`
+  ##   determines the order of the divided difference.
+  ##
+  ##
+  ## OUTPUTS:
+  ##
+  ##   * ``dd`` - The divided difference f[xs(1), xs(2),...]
+  ##
+  order = length(xs) - 1;
   
-  if (order < 1)
+  if (order < 0)
     ## Can't do anything here. Return nothing.
     dd = NA;
-  elseif (order == 1)
+  elseif (order == 0)
     ## Our base case.
     dd = f(xs(1))
   else
-    ## Order > 1, recurse.
+    ## Order >= 1, recurse.
 
     ## f[x0,...,x_n-1]
     f0 = divided_difference(f, xs(1:end-1));
@@ -22,6 +33,6 @@ function dd = divided_difference(f, xs)
     f1 = divided_difference(f, xs(2:end));
 
     # http://mathworld.wolfram.com/DividedDifference.html
-    dd = (f0 - f1)/(xs(1) - xs(end))
+    dd = (f0 - f1)/(xs(1) - xs(end));
   end
 end