How to write a semifactorial function that iterates up to the input?

Hello all,

I'm currently trying to write a function that calculates the semifactorial of an input statement whether it's odd or even, but I can't figure out how to make it iterate to the input statement.

The definition:

The semifactorial of n is the product of the integers between 1 and n which have the same parity (even or odd) as n. For example, 7‼ = 1 × 3 × 5 × 7 = 105, and 8‼ = 2 × 4 × 6 × 8 = 384.

Here's my code so far:

function [ factorial ] = FactorialPi( num )
i = 0;
factorial = [];
for i = 0:2:num
    if mod(num, 2) ~= 0            
        num = (2 * i) + 1;

      %else mod(num, 2) == 0
      %    i = (2 * i);
          factorial = [factorial;num]
      end 
  end

My output when I call FactorialPi(7) is:

 factorial =
     1

 factorial =
     1
     5

 factorial =
     1
     5
     9

 factorial =
     1
     5
     9
    13

 ans =
     1
     5
     9
    13

Any help would be greatly appreciated, thank you!

The semifactorial of

Answer 1

[Cedric]

This is a good start as you are trying, as a first step, to operate a bit how you would proceed by hand, element by element in a loop.

The next step is to realize that MATLAB can operate on arrays:

 >> x = 1 : 3 : 11
 x =
     1     4     7    10

defines a row vector, it is actually how you define the pool of values that your loop variable must take through iterations. Now say you have a vector of values, would you be able to compute their product without using a loop? You probably saw the function SUM, maybe there is an equivalent for products? [-> Google or Doc]

Here is an element-wise square and a sum to illustrate usual operations with arrays:

 >> x.^2        % Element-wise square.
 ans =
     1    16    49   100

 >> sum( x )    % Sum of all elements.
 ans =
    22

Once you understand this you'll know two things: how to build vectors of linearly spaced elements from a lower bound to an upper bound, and how to compute their product.

You will be in a situation where you know how to define the upper bound as it is the input of the function, but you will have to find a way to define the lower bound, which is a number that is either 1 or 2 depending the parity of the input. Maybe there is a way .. maybe you almost found it already (!)