Subscript to multi-index

function multi_index = sub2multiind(subs,r)

This function returns the multi-index corresponding to the input subscripts (subs) of a multidimensional array that acts on a vector of r variables. e.g. Monomial $x_1^2x_3$

subs: [1 1 3], [1 3 1] or [3 1 1]

multi_index: [2,0,1]

for r = 3, we have variables [x_1,x_2,x_3]. The monomial $x_1^2x_3$ may be represented in terms of multi-dimensional subscripts as [1 1 3], [1 3 1] or [3 1 1], but it has a unique representation in the multi-index notation in terms of exponents of each variable as [2 0 1].

[nSubs,d] = size(subs);
ne = numel(subs);
%
M = sparse(1:ne,reshape(subs.',1,[]),ones(1,ne),ne,r);
% summation operator
dSum = cell(1,nSubs);
dSum(:) = {sparse(ones(1,d))};
dSum = blkdiag(dSum{:});

% perform rowwise sum taken d rows at a time
multi_index = dSum * M;

end