Compare vector to two other vectors

I'm struggling with the following binning task:

I have three vectors of different sizes k, m and n. My goal is to get an -matrix in which the -th entry simply counts how many elements from the k-vector are simultaneously smaller than both and .

So basically I want to do something like but with one of the inputs as a matrix rather than a vector.

Is there an efficient way to do this?

Of course I can and have also done it with a loop, but that seems terribly inefficient especially since the k from my simplified example is actually really large. Trying to write everything in -Matrices results in too large arrays unfortunately.

Thanks in advance!

[Dyuman Joshi]

"Of course I can and have also done it with a loop..."

Can you show what have you tried?

Also, please attach your data using the paperclip button. It will be helpful in providing an answer to your problem.

Answer 1

[DucciVinci]

Ah I'm sorry, I completely forgot about matrix multiplication.

Solution actually is pretty simple:

Transpose the k-vector and compare with both other vectors using implicit Cartesian expansions, giving logical arrays of sizes and .

Now just transpose the -matrix and multiply, killing the k-dimension.

Not quite used to matrix multiplication with logical arrays, but it makes a lot of sense here.

Sorry to have bothered you.

Answer 2

[David Hill]

m=randi(100,1,20);
n=randi(100,1,30);
k=randi(100,1,10000);
[M,N]=meshgrid(m,n);
x=min(M,N);
z=zeros(size(x));
u=unique(x);
y=sum(k<u,2);
for j=1:length(u)
   z(x==u(j))=y(j);
end

Answer 3

[Steven Lord]

I think what you want is to use histcounts2 to calculate how many numbers fall into each bin between m(k) and m(k+1) [and between n(k) and n(k+1)] then call cumsum twice, once to sum across the rows and once to sum the matrix from the previous call down the columns.