solve_tridiag.m

function [ x ] = solve_tridiag(dU,odL,odU,b)
%UNTITLED2 Summary of this function goes here
%   Detailed explanation goes here
%   dU:  upper matrix diagonal
%   odU: upper matrix diagonals, order 4, 8, 7
%   odL: diagonal of lower matrix, order: 2, 6, 3
%   b:   3x1 matrix

% for general case

upper_diag = diag(dU);
width = length(upper_diag);

if width == 3 % for function we made
    
    L = eye(3) + diag(odL(1:2),-1) + diag(odL(3),-2); % creates L matrix
    U = upper_diag + diag(odU(1:2),1) + diag(odU(3),2); % creates U matrix

    
    % for forward substitution 
    
    for i = 1:width
        x(i) = b(i);
            for k = 1:i-1
                x(i) = x(i) - L(i,k)*x(k);
            end
        x(i) = x(i)/L(i,i);
    end
    
    b = x';
    
    % for backwards substitution 

    for i = width:-1:1
        x(i) = b(i);
            for k = i+1:width
                x(i) = x(i) - U(i,k)*x(k);
            end
        x(i) = x(i)/U(i,i);
    end
    
    x = x';
    
else % for A matrices
    U = diag(dU);
    k = 1;

    for i = 1:width-1
    
        ofd = odU(k:k+width-i-1);
        U = U + diag(ofd, i);
        k = k + width - i;
    
    end

% makign L matrix

    L = eye(width);

    k = 1;


    for i = 1:width-1
    
        ofdL = odL(k:k+width-i-1);
        L = L + diag(ofdL, -i);
        k = k + width - i;
    
end
    
        % for forward substitution 
    
    for i = 1:width
        
        x(i) = b(i);
        
        for k = 1:i-1
            x(i) = x(i) - L(i,k)*x(k);
        end
        
        x(i) = x(i)/L(i,i);
        
    end
    
    b = x';
    
    % for backwards substitution 

    for i = width:-1:1
        x(i) = b(i);
            for k = i+1:width
                x(i) = x(i) - U(i,k)*x(k);
            end
        x(i) = x(i)/U(i,i);
    end
    
    x = x';
    
    
end


end