LU decomposition (for TI compatibility): LU

The LU command finds the LU decomposition of a matrix.

LU takes four arguments:
- A, a numeric square matrix.
- l,u and p, three variable names.
LU(A) returns the matrix P from the LU decomposition of A, and assigns L, U and P to the variables l,u and p. Namely, P is a permutation matrix, L is lower triangular with 1s on the diagonal, and U is upper triangular with PA=LU.

Example.
Input:

LU([[3,5],[4,5]],L,U,P)

Output:

⎡
⎢
⎣

1	0
0	1

⎤
⎥
⎦

[[0,1],[1,0]]

Input:

Output:

⎡
⎢
⎢
⎢
⎢
⎣

⎤
⎥
⎥
⎥
⎥
⎦

Input:

Output:

⎡
⎢
⎢
⎢
⎢
⎣

−

⎤
⎥
⎥
⎥
⎥
⎦

Input:

Output:

⎡
⎢
⎣

1	0
0	1

⎤
⎥
⎦