Writing a recursive matlab code that can perform column-oriented substitution

I'm trying to write a code that can perform forward substitution for the equation Ax=b where A is a lower triangular matrix and x and b are column vectors.

I have the pseudo code figured out, but I can't make the script work!! I'm new to Matlab, but i'm trying to write a program that takes a lower triangular matrix and a column vector (the b vector) and performs the necessary forward substitution, then outputs then solution. Here's the blueprint:

for k = 1,...,n
   [if g_jj = 0, set error flag (A is singular), exit
    b_(k,1) = b_(k.1)*a_(k,k)
    for m = k+1,...,n (but not executed when k=n)
         [b_(m,1) = b_(m,1) - g(m,k)*b_(k,1)

can somebody help me figure out how to get this code in a format where It can be ran as a matlab script? Thank you!

Answer 1

[Shubham Rawat]

Hi Michael,

I can't figure out the what are your variables for and working of your algorithm. But I have written a functional code for that. Before that you have to initialize the variables.

for k=1:n
    if g(k,k) == 0 %if this g(k,k) becomes 0 it will display and then exit
        disp('A is singular');
        return;
    end
    
    b(k) = b(k)*a(k,k);
    for m = k+1:n
        if(k == n) % if k becomes n it will exit
            return;
        end
        b(m) = b(m)-g(m,k)*b(k);
    end
end

If you are doing forward substitution. Here is the function for forward which take lower triangular matrix L and column vector b and give result vector x:

function x=forwardsubstitution(L,b)
    n = size(L,1);
for i=1:n 
    for j=1:i-1
        b(i)=b(i)-L(i,j)*b(j);
    end
    b(i) = b(i)/L(i,i);
end
    x=b;
end

Hope this helps!