MATLAB: Find indices of row subsets

Question

I am trying to find vectorized matlab function ind = item2ind(item,t) to solve following problem: I have a list of row vectors

item = [2 3 1; 2 1 2; 3 1 1; 1 3 3]

and vector of all possible item elements at each item row vector

t = [1 1 2 2 2 3 3];

I need to find indexes of of separate item rows elements corresponding to the vector t in this way:

ind = [3 6 1; 3 1 4; 6 1 2; 1 6 7]

But

item = [1 1 1]

does not correspond to the vector t, because there are 3 "1" elements, and t contains only 2 "1" elements.

Note: Serial version is inefficient for large item (10000 x 100) and t (1 x 200).

function ind = item2ind(item,t)
[nlp,N] = size(item);
ind = zeros(nlp,N);
for i = 1:nlp
    auxitem = item(i,:);
    auxt = t;
    for j = 1:N
        I = find(auxitem(j) == auxt,1,'first');
        if ~isempty(I)
            auxt(I) = 0;
            ind(i,j) = I;
        else
            error('Incompatible content of item and t.');
        end
    end
end
end

Additional remarks:

Most of the time is spent on the line:

I = find(auxitem(j) == auxt,1,'first');

Is there any clever trick how to speed up this line of code? I tried this, for example, but without any speedup:

I = ipos(auxitem(j) == auxt); I = I(1);

where ipos is preallocated as:

ipos = 1:length(t);

Thanks in advance for any help …

Answer 1

So far best solution:

function ind = item2ind_new(item,t)
t = t(:);
[m,n] = size(item);
mct = max(accumarray(t,1));
G = accumarray(t,1:length(t),[],@(x) {sort(x)});
G = cellfun(@(x) padarray(x.',[0 mct-length(x)],0,'post'), G, 'UniformOutput', false);
G = vertcat(G{:});
C = cumsum(reshape(item,m,1,n)==item,3);
ia = C(sub2ind(size(C),repelem((1:m).',1,n),repelem(1:n,m,1),repelem(1:n,m,1)));
ind = G(sub2ind(size(G),item,ia));

Any idea how to improve it?