I am trying to build the following function in a three dimensional domain.
where k is a constant vector, X is the position vector, c is a constant number, and t is time.
k is a vector of size [1 3], X is an array of size [NX*NY*NZ 3] that represents the points in the three-dimensional domain, c is a constant, and t is an array of size [1 NT].
The following is the setup of the problem.
dx = 0.1;
dy = 0.5;
dz = 0.1;
[x, y, z] = meshgrid( (1:100)*dx, (1:100)*dy, (1:100)*dz );
X = [x(:) y(:) z(:)];
k = [1 2 3];
c = 0.5;
t = 0:0.1:1;
I thought about using arrayfun and repeating the vector k using repmat and dot it with X in the second dimension but I don't know what I should do for the multiplication of c and t.
In fact, the following loop works but it is very slow (takes 200 seconds on my machine).
f = zeros(numel(X)/3, numel(t));
for n = 1:numel(t)
for i = 1:numel(X)/3
f(i, n) = tan(dot(k, X(i,:)+c*t(n)));
What would be an efficient way of defining the function for all the points and all the times? The output of this function, for example, looks like an array of size [NX*NY*NZ NT].