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partint.cc

/*
## Copyright (C) 2006   Torsten Finke   <fi@igh-essen.com>
##
## This program is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 2 of the License, or
## (at your option) any later version.
##
## This program is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
## GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with this program; If not, see <http://www.gnu.org/licenses/>.

$Revision: 5847 $
$Date: 2009-05-18 22:13:16 +0200 (man, 18 maj 2009) $
$RCSfile$

*/


#include <octave/oct.h>
#include <octave/lo-ieee.h>

#include "partint.h"

unsigned long * pcnt(unsigned long n) 
{
    unsigned long *s = new unsigned long[n];
    unsigned long *x = new unsigned long[n*n];
    unsigned long **p = new unsigned long*[n];
    for (unsigned long k=0; k<n; ++k)  {
      p[k] = x + (k*n);
      s[k] = 0;
    }
    for (unsigned long k=0; k<n*n; ++k)  x[k] = 0;
    p[0][0] = 1;
    for (unsigned long k=1; k<n; ++k)
    { 
        // p[N][j] == numpart of N with max summand j
      for (unsigned long j=1; j<=k; ++j) {
          p[k][j] = p[k-1][j-1] + p[k-j][j];
      }
      for (unsigned long j=1; j<=k; ++j) { 
          s[k] += p[k][j]; // S(k) = numpart(n)
      }
    }
    return s; 
}

DEFUN_DLD (partcnt, args, ,
"-*- texinfo -*-\n\
@deftypefn{Loadable Function} {@var{p} =} partcnt(@var{n})\n\
\n\
@cindex partition count\n\
\n\
Calculate integer partition count. Argument @var{n} be scalar, vector\n\
or matrix of non-negative numbers. A partition is the sum decomposition \n\
of integers. \n\
\n\
Example:\n\
@example \n\
partcnt([1, 5; 17 -3])\n\
@end example\n\
@noindent\n\
returns\n\
@example\n\
ans =\n\
    1     7\n\
  297   NaN\n\
@end example\n\
\n\
Reference:\n\
Joerg Arndt: Algorithms for programmers (http://www.jjj.de), 2006.\n\n\
@end deftypefn\n\
@seealso{partint}\n\
")
{    
    octave_value r;
    
    int nargin = args.length ();
    if (nargin != 1) {
      error("partcnt accepts exactly one argument"); 
      return r; 
    }
    if ( ! args(0).is_numeric_type()) {
      error("partcnt only accepts a numeric argument"); 
      return r;
    }

    NDArray f(args(0).matrix_value());
    RowVector m(f.max()); 
    double mmax = m.max();
    if ( mmax < 1 ) {
      error("partcnt is only defined for non-negative arguments"); 
      return r;
    }

    unsigned long n = (unsigned long) mmax + 1; 
    unsigned long *s = pcnt(n); 
    unsigned long fr = (unsigned long) f.rows();
    unsigned long fc = (unsigned long) f.columns();
    for (unsigned long i=0; i<fr; i++) {
      for (unsigned long k=0; k<fc; k++) {
          unsigned long idx = (unsigned long) f(i, k); 
          if (0 < idx && idx < n) {
            f(i, k) = s[idx];
          } else {
            f(i, k) = lo_ieee_nan_value(); 
          }
      }
    }
    r = f; 
    return r;
}

/*

%!assert(partcnt(1), 1);
%!assert(partcnt(17), 297);
%!fail("partcnt()", "partcnt");
%!fail("partcnt(1,2)", "partcnt");
%!fail("partcnt('xyz')", "partcnt");
%!demo
%! p = partcnt([1, 5; 17 -5])

*/

DEFUN_DLD (partint, args, ,
"-*- texinfo -*-\n\
@deftypefn{Loadable Function} {@var{p} =} partint(@var{n})\n\
\n\
@cindex partition\n\
\n\
Calculate all integer partitions. Argument @var{n} be \n\
a positive number. A partition is the sum decomposition \n\
of integers. \n\
\n\
Example:\n\
@example \n\
partint(4)\n\
@end example\n\
@noindent\n\
returns\n\
@example\n\
ans =\n\
  4  0  0  0\n\
  2  1  0  0\n\
  0  2  0  0\n\
  1  0  1  0\n\
  0  0  0  1\n\
@end example\n\
\n\
This means\n\n\
@iftex\n\
@tex\n\
$$\eqalign{4 & = 4 \\cdot 1 \\cr\n\
 & = 2 \\cdot 1 + 1 \\cdot 2 \\cr\n\
 & = 2 \\cdot 2 \\cr\n\
 & = 1 \\cdot 1 + 1 \\cdot 3 \\cr\n\
 & = 1 \\cdot 1 \\cr\n\
\\cr}$$\n\
@end tex\n\
@end iftex\n\
@ifinfo\n\
@example\n\
4 = 4 * 1\n\
  = 2 * 1 + 1 * 2\n\
  =         2 * 2\n\
  = 1 * 1         + 1 * 3\n\
  =                 1 * 4\n\
@end example\n\
@end ifinfo\n\
\n\
Note:\n\
\n\
partint(n) * [1:n]' == n\n\
\n\
Reference:\n\
Joerg Arndt: Algorithms for programmers (http://www.jjj.de), 2006.\n\n\
@end deftypefn\n\
@seealso{partcnt}\n\
")
{    
    octave_value r;
    
    int nargin = args.length ();
    if (nargin != 1 || 
      ! args(0).is_scalar_type() ||
      ! args(0).is_numeric_type()
      ) {
      error("partint only accepts one scalar positive integer argument"); 
      return r;
    }
    double arg0 = args(0).double_value();
    if ( arg0 < 1 ) {
      error("partint is only defined for positive integer arguments"); 
      return r;
    }

    unsigned long n = (unsigned long) arg0;
    unsigned long *s = pcnt(n+1); 
    unsigned long k = s[n]; 
    Matrix pa(k, n, 0);
    int_partition p(n); 
    unsigned long i = 0; 
    do {
      const unsigned long *d = p.data(); 
      for (unsigned long j=0; j<n; j++) {
          pa(i, j) = (unsigned long)d[j+1];  
      }     
      i ++; 
    } while (p.next()); 
    r = pa; 
    return r;
}

/*

%!assert(partint(1), 1);
%!assert(all(partint(n=17) * [1:n]' == n) - 1, 0); 
%!fail("partint()", "partint");
%!fail("partint(1,2)", "partint");
%!fail("partint('xyz')", "partint");
%!demo
%! p = partint(4)

*/

/*
  ;;; Local Variables: ***
  ;;; mode: C++ ***
  ;;; End: ***
*/
    

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