Please explain for me this code , and what does each function do in detail ?

function s=lagrangeP(x,X,Y) %This creates the function lagrangeP. s is the output. x, X, and Y are the inputs.
format long %This allows the display of numbers in the command window to appear long (many decimal places)
%This section preallocates the variable L before it goes through the for loop. This reduces computation time, so you don't an array changing sizes
%after every loop. Now, you will just be replacing values in an array of a set size.
n=size(X);%This finds the size of X and saves the dimensions as a vector array with the variable name n.
L=ones(n);%This creates a n by n matrix of ones equal to the dimensions of X. 
%This section calculates values within the matrix L
for i=1:n %This creates a for loop by giving values for i that starts with 1 and then increases by 1 until it reaches an element size of n
    for j=1:n %This does the same think but for variable j
        if (i~=j) %This if condition states that the line below only applies when the value of i does not equal the value of j
            L(i)=L(i).*(x-X(j))./(X(i)-X(j));%These calculations can be found in the equation below. L(i) goes through each element of the matrix L when in the for loop from L(1) to L(n).
        end
    end
end
s=0;
for i=1:n
    s=s+Y(i)*L(i);
end