% This m-file is a tutorial on functions
clear
%% Anonymous' functions
% Single function with several inputs
sqr = @(x,y) x.^2+y.^2; % lhs is called the 'function handle'
sqr(1,2)
sqr([1 2], [3 4])
pause
% Arrays of function handles
S.a = @sin;  S.b = @cos;  S.c = @tan;
S.a(0.3)
S.b(0.3)
S.c(0.3)
%% Can pass function handles as input to other functions
f1 = @(x) 0.1*x.^3 - 3*x + 2;
fplot(f1,[-5, 5]); grid on; % Plot function
x0 = 1; % Starting point for root search
root = fzero(f1, x0) % Named function
root = fzero(@(x) sin(3*x),2) % Directly pass function definition to another function
%% Calling functions
help Simpson_rule % display help (all comment lines immediately after function definition line)
res=Simpson_rule(@(x) x.^2,[-5 1],100) % Integration by Simpson's rule using anonymous function
res=Simpson_rule(@ftest,[0 2],100)     % Using standard functions

%% Integrating a function with parameters using an anonymous function
a=1;b=-2;c=-5; % Define parameters
res=Simpson_rule(@(x) ftest2(x,a,b,c),[0 2],100)

%% Integrating a function with subfunctions
res=Simpson_rule(@ftest3,[0 2],100) 

%% Difference between nested functions and subfunctions
nested_fun % nested functions share variables with outer functions
pause
bad_subfunction_fun % subfunctions do not share variables with outer functions