Intersect many sets in MATLAB efficiently

Finding intersection of two sets in MATLAB is one of the most frequently used function if you are doing lots of data merging tasks.  This is achieved by intersect function. However if you would like to do the same for many sets,  there are not many alternatives.

Consider that you placed your arrays into a cell vector and would like to get all intersections of a given vector among other remaining arrays and its corresponding indices uniquely. The following function will do the job for you  efficiently. It is not O($N^2$) algorithm, so computational cost only grows linearly. I called this function intersectall, code is maintained in the mathworks file exchange; intersectall.

Matlab/Octave: imagesc with variable colorbar

Plotting a discrete matrix with a colour map is a common task that one would need in many different fields of sciences. To plot a discrete matrix with MATLAB, a possibility is to use imagesc, while it handles discrete points better then other density utilities, where it can handle (0,0) placement better. However, if there are limited number of values in the matrix entries, you may want to keep only existing ones on the color labels. One way to achieve this is to re-write your 'colormap' via 'jet', that maps existing colours on the current matrix. However, this is not sufficient, you need to re-write your matrix as well. See example code below. So called a variable 'colormap' situation is handled with this approach. (This is tested with MATLAB, on Octave, I think one needs to be careful on 'colormap', values behaviour of 'jet' is little different.)

% bare minimum - example -
clear all
close all
allLevelNames   = {'one', 'two', 'three', 'four'};
levelValues     = [1 2 3 4];
myMatrix        =  [3 3 3 3; 3 3 3 3; 4 4 1 1; 4 4 1 1];
% Now re-write colormap
aV              = length(levelValues);
jj              = jet(aV);
availableValues = unique(myMatrix);
getIndexes      = arrayfun(@(xx) find(levelValues == xx), availableValues); 
colormap(jj(getIndexes,:)); 
% Re-write myMatrix in the availableValues range 
myMatrix = arrayfun(@(x) find(availableValues == x), myMatrix);
% Now  Plot
h    = imagesc(myMatrix);
% Handle if there is more then one color is in use
maxV = max(availableValues); 
minV = min(availableValues); 
if(length(availableValues) > 1) caxis([minV maxV]); end; 
hcb=colorbar; 
set(hcb, 'YTick', availableValues); 
set(hcb, 'YTickLabel', allLevelNames(getIndexes));
set(gca,'YDir','normal') % Not to invert x-y but putting (0,0) on the bottom left 
xlabel('x values');
ylabel('y values (care on (0,0) location from imagesc)');
title({['Variable colormap handling'];['by msuzen at gmail']});