LU Decomp without pivoting in Python

Question

I need to create the function [L,U] = lr(A) which will compute the LU decomp of matrix A without pivoting or the use of inv,lu,etc to solve the linear equation.

Just trying to work out the pseudo-code for now and understand it. Any ideas on how to get started?

Answer 1

"Numerical Methods in Engineering with Python 3" by Kiusalaas is a great resource. Below is the code for Doolittle's decomposition method from the book.

# [L][U] = LUdecomp([A])
def LUdecomp(a):
    n = len(a)
    for k in range(0,n-1):
        for i in range(k+1,n):
            if a[i,k] != 0.0:
                lam = a [i,k]/a[k,k]
                a[i,k+1:n] = a[i,k+1:n] - lam*a[k,k+1:n]
                a[i,k] = lam
    return a