call function for each combination of rows in A and columns in B

Xtrain = [1 2; 3 4; 5 6];

Xtest = [7 8 ; 9 10];

kernel = @(x1,x2) norm(x1 - x2);

m = size(Xtrain, 1);
n = size(Xtest,1);

kernels = kernel(Xtest, Xtrain);

I want "kernels" to be the following matrix:

kernels = [ kernel( [7 8] ,[ 1 2] ) kernel([7 8] ,[3 4] ) kernel([7 8] ,[5 6] )

kernel([9 10] , [1 2] ) kernel([9 10] ,[3 4]) kernel( [9 10] ,[5 6] )]

How can I call the kernel function properly so that I will get back this matrix?

Thank you.

Answer 1

[Ameer Hamza]

Try this

Xtrain = [1 2; 3 4; 5 6];
Xtest = [7 8 ; 9 10];
kernel = @(x1,x2) norm(x1 - x2);

m = size(Xtrain, 1);
n = size(Xtest, 1);

XtrainC = mat2cell(Xtrain, ones(m,1), 2);
XtestC = mat2cell(Xtest, ones(n,1), 2);

[R, C] = ndgrid(1:n, 1:m);
kernels = arrayfun(@(r, c) kernel(XtestC{r}, XtrainC{c}), R, C)

[danielle sisserman]

Beautiful! Thank you so much.

[Ameer Hamza]

I am glad to be of help!

Answer 2

[Bruno Luong]

Simple for-loop is 3-4 times faster than fancy MATLAB pseudo vectorization, and much more readable

Xtrain = rand(1000,2);
Xtest = rand(1000,2);
kernel = @(x1,x2) norm(x1 - x2);

m = size(Xtest,1);
n = size(Xtrain,1);

tic
kernels = zeros(m,n);
for i=1:m
    for j=1:n
        kernels(i,j) = kernel(Xtest(i,:),Xtrain(j,:));
    end
end
toc % Elapsed time is 1.389989 seconds.

tic
XtrainC = mat2cell(Xtrain, ones(m,1), 2);
XtestC = mat2cell(Xtest, ones(n,1), 2);
[R, C] = ndgrid(1:n, 1:m);
kernels = arrayfun(@(r, c) kernel(XtestC{r}, XtrainC{c}), R, C);
toc % Elapsed time is 5.821724 seconds.