MULTI_NSUMK

Contents

function [g, g_comb,nv_un,nv_ic] = multi_nsumk(nv,v)
        

Combinatorics for vectors

This function finds all combinations of $nv$ positive integer vectors adding up to another positive integer vector $\mathbf{v}$ :

Let $\mathbf{v} \in \mathbf{N}^l$ . It finds all combinations consisting of $n$ positive, nonzero integer vectors such that they sum up to

$\mathbf{v}$ : $\sum_{i=1}^n \mathbf{g}_i = \mathbf{v}$ . All of those combinations are stored as 2D arrays, where the individual columns are filled with thevectors, in column $i$ the vector $\mathbf{g}_i$ is stored. The various combinations are stacked upon each other in a 3D array, which contains a third dimension with size equal to amount of combinations of vectors that sum up to $\mathbf{v}$ .

The result is then stored in a cell array, that contains these combinations for all tuples

$i,j$ , corresponding to $\texttt{v(:,i), nv(j)}$ .

%there can be multiple vectors in v
%
% This functionality is needed to construct the forcing contribution
% coefficients in fnl_intrusive.
%
% [g, g_comb,nv_un,nv_ic,varargout] = MULTI_NSUMK(nv,v,varargin)
%
% * nv:       number of integer vectors that should sum up to v
%           can be an array if v is a matrix, then the algorithm performs
%           the partition for each vector in v..
%
% * v:        vector which is partitioned into nv vectors, or matrix wich
%           contains vectors, for each of which the partitions are computed
%
% * varagin:  'rmzero' can be used to remove combinations that contain zero vectors
%           'unique' can be used to remove permutations of combinations
%
% * g:      cell array containing all the combos of nv vectors summing up
%           to v. If multiple input vectors are given, each of its z_k rows
%           contains permutations for one vector in v, each column (j) corresponds
%           to nv(j) combinations that sum up to said vector.
% * g_comb:   contains number of combinations that exist for a said tuple i,j
%
% * nv_un:    unique number of combinations that are requested.
%
% * nv_ic:    map nv_un back to positions in nv via this index array.
%
% * varargout:contains number of occurences of a permutation of combinations
%           for each tuple i,j
%
        

z_k = size(v,2);
l = size(v,1);
S = cell(1,l);
[nv_un,~,nv_ic] = unique(nv);
g = cell(z_k,size(nv_un,2));
g_comb = zeros(z_k,size(nv_un,2));
n_run = 1;
for n = nv_un
    for f = 1:z_k
        

        for i = 1:l
            %special case
            if v(i,f) == 1 && n == 1
                S{i} = 1;
            else
                S{i} = nsumk(n,v(i,f),'nonnegative').' ;
                %finds all combinations for each index in v
            end
        end
        

$\texttt{combvec}$ finds all possible combinations of the vectors in $\texttt{S}$ .

        g_fn = combvec(S{:});
        g_fn = reshape(g_fn,n,l,[]);
        g_fn = permute(g_fn,[2 1 3]);


        g{f,n_run}  = g_fn;
        g_comb(f,n_run) = size(g_fn,3);
        

    end

    n_run = n_run +1;
end
        

end
        

Published with MATLAB® R2023a