Complex step example

complex_step_example.m

% Complex step example.  Requires Symbolic Math Toolbox.

format long
syms x; f = atan(x)/(1+exp(-x^2))

% Derivative at $a = 2$:
a = 2; fd = double(subs( diff(f), a))

% Convert symbolic function to MATLAB function.
f = matlabFunction(f);  
% Complex step approximation is 
fd_cs = complex_step(f,a)

% Finite difference approximations with step $u$ and $u^{1/2}$:
u = 4*eps;
fd_fd1 = (f(a+u)-f(a))/u
fd_fd2 = (f(a+u^(1/2))-f(a))/u^(1/2)