intpart.m

%    Author      : Senol Korkmaz < senol.korkmaz@gmail.com >
%    Filename    : intpart.m
%    Requires    : partitions.m  < http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=12009&objectType=file >
%    Description : A Matlab Function to calculate partitions of an integer
%    Usage       : intpart(n,m,k)
%
%    Input       : n is an integer to find out its partitions
%                : m is a vector which indicates that how many numbers can be used
%                : k is a vector which indicates that which numbers can be used
%
%    Output      : This function returns a matrice that includes partitions of n
%                
%    Version     : 1.0
%
%    License     : GNU/GPL v3
%    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 3 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/>.

function iparts = intpart(n,m,k) % Declare function and its arguments

if (nargin==1)       % There is only one input (n)
    m = 1:n;     % Consider that m is a vector that contains all integers from 1 to n
    k = m;       % Consider that k is a vector that contains all integers from 1 to n
end

if (nargin==2)       % There are two inputs ( n & m)
    k = 1:n;     % Consider that k is a vector that contains all integers from 1 to n
end

partlist = partitions(n,k);   % Calculate the partitions of n with the numbers whis is in the vector k

% Code explanations will be written as soon as possible

partlist =  partlist(find(ismember(sum(partlist,2),m)==1),:);

iparts = zeros(size(partlist,1),max(m));

for i = 1:size(partlist,1)

    tmpROW = [];

    for j = 1 : size(partlist,2)
        tmpROW = horzcat(tmpROW,repmat(k(j),1,partlist(i,j)));
    end

    tmpROW = horzcat(tmpROW,repmat(0,1,size(iparts,2)-size(tmpROW,2)));
    iparts(i,:) = sort(tmpROW,'descend') ;
end