lu_tridiag.m

function [ud,uo,lo]=lu_tridiag(e,f,g);
%lu_tridiag The purpose of this function is to perform a LU-decomposition
%by creating a lower and upper matrix from three input vectors e,f,&g. This
%function is to provide a method that creates linear equations to compute
%the new matrix.
%Note: the inputs of the function must be vectors of the same length
%--------Linear equations-----------
ud = zeros(length(f), 1); %set up empty vector for new upper diagonal
uo = zeros(length(f)-1, 1); %empty vector for new upper-off diagonal matrix
lo = zeros(length(f)-1, 1); %empty vector for new lower-off diagonal matrix

lo = g;       %The value of the original upper matrix equals the new lower-off diagonal
ud(1)=f(1);   %first element in new upper diagonal equals first in original diagonal 
uo(1) = g(1); %first element in new upper-off diagonal equals that of first in g
k = 2;        %Set index to initialize while loop.

while k <= length(f)-1 %begin loop to assign values of generic vectors e f &g
    lo(k-1) = e(k-1)/(ud(k-1)); %compute values for new lower-off digaonal
    uo(k) = g(k); %assign values to new upper-off diagonal
    ud(k) = f(k)-(lo(k-1)*uo(k-1));
    k = k + 1; %repeat but shift to next column
end
lo(k-1) = e(k-1)/(ud(k-1)); %Due to indexing loop, equation is needed for final value of new lower-off diagonal
 ud(k) = f(k)-(lo(k-1)*uo(k-1)); %same reasoning, needed to find final value of new upper diagonal