partitionNk.m

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%% WSINDy_PDE: generate all monomials over k variables with total
%%%%%%%%%%%% degree less than or equal to N
%%%%%%%%%%%% 
%%%%%%%%%%%% Copyright 2020, All Rights Reserved
%%%%%%%%%%%% Code by Daniel A. Messenger
%%%%%%%%%%%% For Paper, "Weak SINDy for Partial Differential Equations"
%%%%%%%%%%%% by D. A. Messenger and D. M. Bortz
%%%%%%%%%%%% 
%%%%%%%%%%%% utilizes 'partitions.m' by John D'Errico (e-mail:
%%%%%%%%%%%% woodchips@rochester.rr.com, Release: 2, Release date: 7/15/08)

function total_parts = partitionNk(N,k) 
    if N>1
%         A = partitions(N,0:N,N,k);
%         num_unique_parts = size(A,1);
%         unique_parts = zeros(num_unique_parts,k);
%         for j=1:num_unique_parts
%             temp_part = [];
%             for m= 1:N+1
%                 if A(j,m)>0
%                     for l = 1:A(j,m)
%                         temp_part = [temp_part m-1];
%                     end
%                 end
%             end
%             unique_parts(j,:) = temp_part;
%         end
%         total_parts = [];
%         for j=1:num_unique_parts
%             total_parts = [total_parts;unique(perms(unique_parts(j,:)),'rows')];
%         end
%        total_parts = flipud(total_parts);
       total_parts = partitions(N,ones(1,k));
    elseif N==1
        total_parts = eye(k);
    elseif N==0
        total_parts = zeros(1,k);
    end
end