How to generalized the formula in matlab - matlab

Question

I want to vary the condition for the n-th vector to cover a range of i-values (something like i=2:27).
N=51;
num =2;
W = 3;
i = 2;
string1 = '[';
for n = num:-1:1
string1 = [ string1 'a' num2str(n) ' '];
end
string1 = [ string1 '] = ndgrid(1:W);'];
string2 = 'ind = find(';
for n = 2:num
string2 = [ string2 'a' num2str(n) '>=a' num2str(n-1) '&' ];
end
for n = 1:num
string2 = [ string2 'a' num2str(n) '+'];
end
string2 = [ string2(1:end-1) '==i);' ];
string3 = 'C = [ ';
for n = 1:num
string3 = [ string3 'a' num2str(n) '(ind) ' ];
end
string3 = [ string3 ']' ];
eval(string1);
eval(string2);
eval(string3);
Unfortunately, I have difficulties in understanding how this is a generalization of my initial construct.
Ultimately, I need the matrix p2 (which selects combinations of a1, a2 to an) in a probability analysis.

Answer 1

Here's how you can do it:
N = 5; % number of columns, this was your a1 ... a5
W=3; % unchanged to first example in question
i=6; % unchanged to first example in question
% the following will create a matrix with N-1 columns
% because the last column is determined by the sum of the columns before it
% the a1 .. an-1 columns contains all possible permutations of 1:W
% (this code can be found on the internet)
for ii=1:N-1
dset{1,ii}=1:W;
end
n=numel(dset);
a=cell(n,1);
[a{1:n}]=ndgrid(dset{end:-1:1});
a=reshape(cat(n+1,a{:}),[],n);
a=a(:,end:-1:1);
% next, we sort the rows ascending
% because for you, 1-1-2 is the same as 1-2-1
% and after sorting, we pick the unique rows
a = unique(sort(a,2),'rows');
% next, we populate the last column
% and select those that match your criterion
% in a matrix p2n
p2n = [];
for ii=1:size(a,1)
a(ii,N) = i - sum(a(ii,1:N-1));
if(a(ii,N-1) <= a(ii,N) && a(ii,N)<=W)
p2n=[p2n;a(ii,:)];
end
end
See the comments in the code for explanations.
EDIT
If you want to vary N, i and W, use for-loops for example:
for N=2:4
for i=2:27
for W=3:7
% post code starting at line 11 here
% DO NOT DECLARE N, W, i inside the loops again
% Also, introduce a cell to store all `p2n` matrices:
% place this inside the loop but below the code given above
P2n{N,i,W} = p2n;
end
end
end