nchoosek warning, checks and tests

[Francesco Potortì]

Here is a new version of my previous patch, this time against Jaroslav's
non recursive implementation.  

Discussion:
- help string now mentions some differences between this and bincoeff
- many sanity checks are done on the arguments
- log of sum is used instead of product so that overflow is further away
- handle k==0
- correct k==n case, when a column vector was output
- add error and warning tests
- when testing against bincoeff, use a case where no precision is lost

Jaroslav, should I send you this as an attachment?

# HG changeset patch
# User Francesco Potortì <address@hidden>
# Date 1228919345 -3600
# Node ID 089d2f5463453acca07a0888fa9b6b52cf5cec86
# Parent  c8a785d0e867a2f2c735a8f7b828c00e05204e59
nchoosek warning, checks and tests

diff -r c8a785d0e867 -r 089d2f546345 scripts/ChangeLog
--- a/scripts/ChangeLog Wed Dec 10 13:20:24 2008 +0100
+++ b/scripts/ChangeLog Wed Dec 10 15:29:05 2008 +0100
@@ -1,3 +1,8 @@ 2008-12-10  Jaroslav Hajek  <address@hidden
+2008-12-10  Francesco Potortì  <address@hidden>
+
+       * specfun/nchoosek.m: Check for input arguments, signal loss of
+       precision, correctly handle k==0 and k==n cases, add proper tests.
+
 2008-12-10  Jaroslav Hajek  <address@hidden>
 
        * script/linear-algebra/expm.m: New source.
diff -r c8a785d0e867 -r 089d2f546345 scripts/specfun/nchoosek.m
--- a/scripts/specfun/nchoosek.m        Wed Dec 10 13:20:24 2008 +0100
+++ b/scripts/specfun/nchoosek.m        Wed Dec 10 15:29:05 2008 +0100
@@ -1,5 +1,5 @@
 ## Copyright (C) 2001, 2006, 2007 Rolf Fabian and Paul Kienzle
-## Copyright (C) 2008 Jaroslav Hajek
+## Copyright (C) 2008 Jaroslav Hajek and Francesco Potortì
 ##
 ## This file is part of Octave.
 ##
@@ -49,31 +49,45 @@
 ## of @var{n}, taken @var{k} at a time, one row per combination. The 
 ## resulting @var{c} has size @code{[nchoosek (length (@var{n}), 
 ## @var{k}), @var{k}]}.
+##
+## @code{nchoosek} works only for nonnegative integer arguments; use
+## @code{bincoeff} for non-integer scalar arguments and for using vector
+## arguments to compute many coefficients at once.
 ##
 ## @seealso{bincoeff}
 ## @end deftypefn
 
 ## Author: Rolf Fabian  <address@hidden>
 ## Author: Paul Kienzle <address@hidden>
-
-## FIXME -- This function is identical to bincoeff for scalar
-## values, and so should probably be combined with bincoeff.
+## Author: Jaroslav Hajek
+## Author: Francesco Potortì <address@hidden>
 
 function A = nchoosek (v, k)
 
-  if (nargin != 2)
+  if (nargin != 2
+      || !isnumeric(k) || !isnumeric(v)
+      || !isscalar(k) || (!isscalar(v) && !isvector(v)))
     print_usage ();
+  endif
+  if ((isscalar(v) && v < k) || k < 0
+      || k != round(k) || any (v < 0 || v != round(v)))
+    error ("nchoosek: args are nonnegative integers with V not less than K");
   endif
 
   n = length (v);
 
   if (n == 1)
-    if (k > v/2)
-      k = v - k;
+    k = min (k, v-k);          # improve precision at next step
+    A = round (exp (sum (log (v-k+1:v)) - sum (log (2:k))));
+    if (A > 1/(exp (2*k*eps) - 1))
+      warning ("nchoosek", "nchoosek: possible loss of precision");
     endif
-    A = round (prod ((v-k+1:v)./(1:k)));
+  elseif (k == 0)
+    A = [];
   elseif (k == 1)
     A = v(:);
+  elseif (k == n)
+    A = v(:).';
   elseif (k > n)
     A = zeros (0, k, class (v));
   else
@@ -110,6 +124,8 @@ function A = nchoosek (v, k)
   endif
 endfunction
 
-# nchoosek seems to be slightly more accurate (but only allowing scalar inputs)
-%!assert (nchoosek(100,45), bincoeff(100,45), -1e2*eps)
+%!warning (nchoosek(100,45));
+%!error (nchoosek(100,45.5));
+%!error (nchoosek(100,145));
+%!assert (nchoosek(80,10), bincoeff(80,10))
 %!assert 
(nchoosek(1:5,3),[1:3;1,2,4;1,2,5;1,3,4;1,3,5;1,4,5;2:4;2,3,5;2,4,5;3:5])

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