Add performance notes to steepest descent stuff.

[octave.git] / divided_difference.m

diff --git a/divided_difference.m b/divided_difference.m
old mode 100755 (executable)
new mode 100644 (file)
index 139fa47..4705f0a
--- a/divided_difference.m
+++ b/divided_difference.m
@@ -1,27 +1,33 @@
-#!/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)
+  ##
+  ## 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 < 0)
     ## Can't do anything here. Return nothing.
     dd = NA;
-  elseif (order == 1)
+  elseif (order == 0)
     ## Our base case.
-    dd = f(xs(1))
+    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))
+    ## Order >= 1.
+    cs = divided_difference_coefficients(xs);
+    dd = dot(cs, f(xs));
   end
 end