fast way of filing up a matrix with function calls

i have a 2-D matrix m(i,j). for each (i,j) some function f(i,j) has to be evaluated and that fills up the matrix m(i,j). presently i am using a loop for i=1:N for j=1:N mat(i,j) = f(i,j); to fill up the matrix. Is there a faster implementation of this piece of code.

[Matt J]

What does f() look like?

Answer 1

[Matt J]

 If f() is element-wise vectorized, you could do this

 [I,J]=ndgrid(1:N,1:N);
 mat=f(I,J)

but more optimal approaches might still be possible depending on the form of f().

Answer 2

[Azzi Abdelmalek]

M=rand(4);                % your matrix
f=@(x) sin(x)*x           % your function
out=arrayfun(@(x) f(x),M)

Or you can use operation element by elemment (Faster)

 out=sin(M).*M

[Matt J]

Well ... but the OP asked for a "faster" approach. We know arrayfun is unlikely to execute faster than a for-loop.

[Azzi Abdelmalek]

You are right. The for loop is faster then arrayfun, but I think the op element/element is faster then the for loop

[Kaushik]

thank you for your answer. well my grid is something like x_grid (has length M) y_grid (has length N). and my output matrix will have size M*N. and output(i,j) = f(x_grid(i),y_grid(j),other parameters) inside f(x_i,y_i,other param) { i do integration of some kind on splines}. so you see the function has to take in two different values x,y in from two different vector and compute.

[Azzi Abdelmalek]

x_grid=1:5;
y_grid=1:4;
[M1,M2]=meshgrid(x_grid,y_grid)

Then calculate using M1 and M2