hist3 not returning expected output (weird range for indices etc)

I was trying to use hist3 to visually display a two-dimensional distribution, however the function behaves unexpectedly. I expected it to return a 2D histogram (a count) of how many times each pair of numbers in the input matrix occurs, and display that count at a position in the output matrix whose indices correspond to that number pair, scaled to a factor of 10 (by default) or some other square-matrix size. But this is not what my test examples showed:

For instance, if I define the following input matrix m:

1   1
2   2
3   3
4   4
5   5

then the command v=hist3(m, [5 5]) has the following expected output:

1   0   0   0   0
0   1   0   0   0
0   0   1   0   0
0   0   0   1   0
0   0   0   0   1

However for this input matrix:

4   1
4   2
4   3
4   4
4   5

the output is:

0   0   0   0   0
0   0   0   0   0
1   1   1   1   1
0   0   0   0   0
0   0   0   0   0

..rather than (as I would have expected):

0   0   0   0   0
0   0   0   0   0
0   0   0   0   0
1   1   1   1   1
0   0   0   0   0

Also, hist3(m,[5 5]) returns a plot where one of the 2 plane dimensions ranges from 2-6 rather than 1-5:

..while hist3(m) returns the even more unexpected plot:

Can anyone help clear the confusion? THanks!

Answer 1

[Massimo Zanetti]

The behaviour of hist3 is correct. Think about this: in the first dimension (say "x") you only have one coordinate number that repeats: 4. In the other dimension "y" you have a range of values from 1 to 5.

So, how Matlab decides to bin in the "x" dimension? It has to divide in 5 bins a range of values which only consists of one number :) Thus, it "earns" the scale of values from "y" dimension, and use that scale also in the "x" dimension, and it put the number 4 in the middle (this is the most reasonable choice). So, the final range of values in the "x" dimension is 2-6, because 4 is in the middle. Is that clear now?

To get it more clear, look the bin centers Matlab has computed in the first dimension:

X=[4,4,4,4,4;1,2,3,4,5]';
[N,C]=hist3(X,[5,5]);
%bin centers in the first dimension "x":
%C{1} = [2,3,4,5,6]
%bin centers in the second dimension "y":
%C{2} = [1.4,2.2,3.0 3.8 4.6]

You can see, the 4 number, falls in the middle bin :)

[z8080]

Thank you Massimo. That does make some sense, although I am wondering whether, in this case, there is a function other than hist3 that is better suited to what I am trying to do.

Again, what I would need is to obtain a 2D histogram (a count) of how many times each pair of numbers in the input matrix occurs, and have that count displayed at a position in the output matrix whose indices correspond to that number pair, as in the examples I gave.

Is there such a function, or will I just need to hack the output of hist3 (or perhaps use it with different input arguments) to make it fit for purpose?

Thanks again!

[Massimo Zanetti]

I think the best for you is to provide specifically the edges of the bins as argument of the hist3. This way you know the output, without "hacking" :)

Try this:

X=[4,4,4,4,4;1,2,3,4,5]';
edges = {.5:1:5.5,.5:1:5.5};
hist3(X,'Edges',edges);

If this answer helped you, please accept it.

[z8080]

Yes I think this is indeed the solution.

Grazie mille! :)