%% Theory2:
% MSc MATLAB Crash Course: Cell-arrays, functions and programming.
%
% Originally written by Nick Hale, Oct 2013.
% Extended by Mohsin Javed, Oct 2014.
% Modified by Behnam Hashemi and Hadrien Montanelli, Sep. 2016.

rmpath functions

%% CELL ARRAYS
C = cell(3)
C{1} = 1
C{2} = 2
C{2,1} = zeros(2) % the same as C{2} here
C{2,2} = rand(3) % the same as C{5}
C{3,3} = [1; 2; 3]

%% RECAP: ANONYMOUS FUNCTIONS
% Anonymous function allowed us to write very simple functions in one line:
f = @(x) cos(pi*x) - exp(cos(x));

%% FUNCTIONS
% For more complicated functions, or those with more than one output, we
% typically write these in their own m-files. These then take the following
% format:

%  function [out1, out2, ...] = function_name(in1, in2, ...)
%  FUNCTION_NAME   <brief description>.
%  [OUT1, OUT2, ...] = FUNCTION_NAME(IN1, IN2, ...) returns <long description>.
%
%  Author name, Date.
%  
%  <CODE>
%
%  end

edit myfunc.m

%% Example
f(2)
f(3)
myfunc(2)
myfunc(3)

% In particular, we emphasize again that Matlab _isn't typed_, this means that
% any of the inputs can be a double, a string, a cell, etc., and that there is
% no need to declare variables (as you would in C or FORTRAN).

%% Example
% Let's look at an example by writing a short code to solve a quadratic:
edit functions/quadform.m

%% 
% Let's execute it: 
quadform(2, -1, -1)

% The script isn't in the same folder as the quadform code we just wrote, so I 
% can't acess it from here!

%% PATH, ADDPATH, PATHTOOL
% Matlab stores internally a 'path' which is a list of folders in which it will
% look for functions. 
path

%%
addpath functions

% 2*X^2 - X - 1 = 2 (X-1)(X + 0.5):
quadform(2, -1, -1)

%%
pathtool

%% NESTED FUNCTIONS
%
% Nested functions live somewhere between anonymous functions and m-files. They
% are useful when short snippets of code are used in a number of places, and
% you don't want to copy all the variables across to another m-file.

%  function y = function_name(x)
%  FUNCTION_NAME   <brief description>.
%  Y = FUNCTION_NAME(X) returns <long description>.
%
%  Author name, Date.
%  
%  <CODE>
%
%  y1 = nested_function(x1);
%
%  <CODE>
%
%
%       function y = nested_function(x)
%
%          <NESTED CODE>
%
%       end
%  end


%% Example
edit functions/quadform2.m

%% 
% Let's execute it: 
quadform2(2, -1, -1)

%% NARGIN() and NARGOUT()
%
% These commands tell you how many inputs or outputs were passed to a function.
% They can be used in conditional statements to alter the behavior of the
% function.

%% VARARGIN() and VARARGOUT()
%
% If you don't know how many inputs or outputs you expect to a function, you can
% declare them using VARARGIN() and VARARGOUT():
%
%   function varargout = function_name(varargin) 
%
edit functions/quadform3.m

%% 
% Let's execute it: 
x = quadform3(2, 1)

%%
x = quadform3(2, -1, -1)

%%
[x1, x2] = quadform3(2, -1, -1)