In this lecture, we talked about RECURSION. We wrote two recursive functions:
one to calculate the factorial of a given number (factorial.m) , the other one
to calculate the sum of the elements of a given vector of numbers (mysum.m).
See below to see how we wrote the functions and then how we called the fnctions.

Prof. Aydin 

>> !vim factorial.m

"factorial.m" 14L, 184C written
>>
>> type factorial.m

function result = factorial(n)
% inputs:
%  n = the number
% outputs:
%  result = the factorial of the number n
%


% Base case: if the number is less than equal to 1
if (n <=1)
   result = 1;
% the recursive case: if the number is greater than 1
else
   result = n * factorial(n-1);
end


>> clc
>> factorial(1)

ans =

     1

>> factorial(2)

ans =

     2

>> factorial(3)

ans =

     6

>> factorial(4)

ans =

    24

>> factorial(5)

ans =

   120

>> factorial(0)

ans =

     1

>> factorial(-1)

ans =

     1

>> clc
>> !vim mysum.m


"mysum.m" [New] 14L, 191C written
>> type mysum.m

function result = mysum(v)
%  inputs:
%     v: a vector of numbers
%  outputs:
%     sum: the sum of the numbers of vector v


% notes:
%  [1] the if statement for base case 1 (below), can also be written as: if
% (isempty(v) ==  true)
%  [2] note that there are two base cases in this recursive definition of the
%  sum (see below)

% base case #1: if the vector is empty
if (length(v) == 0)
   result = 0;
% base case #2: if the vector has one element in it
else if (length(v) == 1)
   result = v(1);
% the recursive case: self-calling the function, on a smaller part of the
% vector (i.e., from second element to the last element)
else
   result = v(1) + mysum(v(2:length(v)));
    end % if

end %function
>> mysum([])

ans =

     0

>> mysum([133])

ans =

   133

>> mysum([133 5])

ans =

   138

>> mysum([133 5 -5])

ans =

   133

>> V = [120 3 -2 1]

V =

   120     3    -2     1   

>> mysum(V)

ans =

   122
>>