### 5.52.5 LU decomposition (for TI compatibility) : LU

LU takes as argument a numeric square matrix A of size n and three variable names, var1, var2 and var3.
LU(A,var1,var2,var3) returns P, a permutation matrix, and stores :

- a lower triangular matrix L, with 1 on the diagonal, in var1,
- an upper triangular matrix U in var2,
- the permutation matrix P, result of the command LU, in var3.

These matrices are such that

the equation A*x=B is equivalent to L*U*x=P*B.

Input :

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

Output :

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

Input :

L

Output :

[[1,0],[0.75,1]]

Input :

U

Output :

[[4,5],[0,1.25]]

Input :

P

Output :

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