Number of unique coordinates in an array

Dear all,

I am trying to solve the following problem as fast as possible. Consider a square matrix with coordinates (i,j) where i denotes the row and j the column. I would like to write a function that returns the number of unique elements for every coordinate pair. For instance, for a pair (6,2), the number unique elements is 2, while for the pair (4,4) the number of unique elements is 1. This is just the description of the basic problem.

More generally, I would like to be able to do the same not just for a matrix but also for a cube and for higher order arrays. To that end, I wrote the following function

function [dm,relvnt]=multiplicity(nz,degree)

ndx=1:nz^degree; % index for all the elements in the array

siz=[1,repmat(nz,1,degree)]; % size of the array : vector, matrix, cube, ... etc.

[varargout{1:degree+1}] = ind2sub(siz,ndx); % locating rows, columns, pages, etc.

varargout=cellfun(@(x)x(:),varargout,'UniformOutput',false); % turning into column vectors

relvnt=cell2mat(varargout); % collapsing coordinates into a matrix

[nrows,ncols]=size(relvnt); 

relvnt=mat2cell(relvnt(:,2:end),ones(1,nrows),ncols-1); % suppressing the first column and putting into a cell array

dm=cellfun(@(x)numel(unique(x)),relvnt); % counting the number of unique terms in each cell

end

This works well for any dimension nz and any degree. However, it becomes prohibitively slow as nz and degree increase. I wish I could just transform an index into the number of unique coordinates possibly in a vectorized fashion.

Answer 1

[Bruno Luong]

Is this what you want?

n=4; d=3;

c=cell(1,d);
[c{:}]=ndgrid(1:n);
relvnt=reshape(cat(d+1,c{:}),[],d);
dm = d-sum(diff(sort(relvnt,2),1,2)==0,2);
dm = reshape(dm,n+zeros(1,d));

[Patrick Mboma]

YES SIR !!!

Respects and gratitude !!!