There are two types of problem I need to solve, we have a function of two variables f(x,y): one is x, y are vector with same length, how to evaluate function at each (x_i,y_i). In first dimension, it is simply f(x). How to achieve this in two dimension.
The other is evaluate values for each point of the mesh formed by x and y i.e., evaluate at each point (x_i,y_j) for every (i,j)
For the first issue, can you clarify? I guess I see the first dimension case, but I don't get what you mean by 2 dimensions.
As for the mesh, it should be solved as follows. cartprod.m is my custom cartesian product function found here.
% Define Test Data
x = 1:5;
y = 2:4;
% Define Test Function
f = @(x,y) x*y;
% Permutate x/y as a grid
s = sortrows( cartprod(x,y) , 1 );
% Apply function for each permutation
a = arrayfun( f, s(:,1), s(:,2) );
% Reshape into matrix
M = reshape( a, 5, [] ) % Solution here
Please let me know if I misunderstood and please clarify the first half of the question for me!
1.
In addition to other solutions, If you define the function with vector properties, the rest would be easy.
example:
function f = myfunc(x)
%% x is a vector or matrix including y,z,.. vectors
%
f = (1 + ((x(:,1) + x(:,2) + 1).^2);
Then easily evaluate your function as follows:
X = [1 1;2 3;1 -1]; % consider this your input data
f(X);
2.
Additionally, if you do not want to define it separately, the function can be defined also in the spot:
f = @(x)(1 + ((x(:,1) + x(:,2) + 1).^2);
f(X)
.*, ./, .^, etc.) on both inputs? The same applies for a grid of values. - rayryeng