How to vectorize function with 3 input vectors and 3-dimensional matrix output?

Let f = @(X,Y,Z) ...; and length(X) = Nx; length(Y) = Ny; length(Z) = Nz; How to write f if I want a matrix (M) with size Nx x Ny x Nz as an output in which M(i,j,k) = f(X(i),Y(j),Z(k)) ?

Answer 1

[Walter Roberson]

[gX, gY, gZ] = ndgrid(X, Y, Z);
result = arrayfun(@f, gX, gY, gZ);

This assumes that the function f itself cannot be vectorized.

If f is receiving X, Y, Z as inputs, and the calculations it uses can be vectorized, then you can use ngrid, or you can use bsxfun(), or in R2016b and later you can use implicit expansion after having reshaped X to column vector, reshaped Y to row vector, and reshaped Z to "page vector" with reshape(Z, 1, 1, [])