General method to find submatrix in matlab matrix

Question

I am looking for a \'good\' way to find a matrix (pattern) in a larger matrix (arbitrary number of dimensions).

Example:

total = rand(3,4,5);
sub = t         


        

Answer 1

This is based on doing all possible shifts of the original matrix total and comparing the upper-leftmost-etc sub-matrix of the shifted total with the sought pattern subs. Shifts are generated using strings, and are applied using circshift.

Most of the work is done vectorized. Only one level of loops is used.

The function finds all matchings, not just the first. For example:

>> total = ones(3,4,5,6);
>> sub = ones(3,3,5,6);
>> matrixFind(total, sub)
ans =

     1     1     1     1
     1     2     1     1

Here is the function:

function sol = matrixFind(total, sub)

nd = ndims(total);
sizt = size(total).';
max_sizt = max(sizt);
sizs = [ size(sub) ones(1,nd-ndims(sub)) ].'; % in case there are
% trailing singletons

if any(sizs>sizt)
    error('Incorrect dimensions')
end

allowed_shift = (sizt-sizs);
max_allowed_shift = max(allowed_shift);
if max_allowed_shift>0
    shifts = dec2base(0:(max_allowed_shift+1)^nd-1,max_allowed_shift+1).'-'0';
    filter = all(bsxfun(@le,shifts,allowed_shift));
    shifts = shifts(:,filter); % possible shifts of matrix "total", along 
    % all dimensions
else
    shifts = zeros(nd,1);
end

for dim = 1:nd
    d{dim} = 1:sizt(dim); % vectors with subindices per dimension
end
g = cell(1,nd);
[g{:}] = ndgrid(d{:}); % grid of subindices per dimension
gc = cat(nd+1,g{:}); % concatenated grid
accept = repmat(permute(sizs,[2:nd+1 1]), [sizt; 1]); % acceptable values
% of subindices in order to compare with matrix "sub"
ind_filter = find(all(gc<=accept,nd+1));

sol = [];
for shift = shifts
    total_shifted = circshift(total,-shift);
    if all(total_shifted(ind_filter)==sub(:))
        sol = [ sol; shift.'+1 ];
    end
end