import numpy as np

rng = np.random.default_rng(0)
# ----------------- Input  -----------------------------------
#   !!!! Aceasta sectiune nu se modifica !!!!
n = 5;
A = np.diagflat(rng.integers(1,10, size=(n,1)), k=0)
A[:, n-1] = rng.integers(1,20, size=(1,n))
A[:, 0] = rng.integers(1,20, size=(1,n))
for i  in range (0,n-1):
    A[i+1,i] = rng.integers(1,10, size=(1,1))

b = rng.integers(1,10, size=(n,1)).astype(float)
#-----------------------------------------------------
L = np.zeros((n,n))
U = np.zeros((n,n))
def crout(A,L,U,n):
    for i in range(n):
        U[i,i]=1
        for j in range(i+1):
            sum0 = sum(L[i][k]*U[k][j] for k in range(j))
            L[i][j] = A[i][j]-sum0
        for j in range(i,n):
            sum0 = sum(L[i][k]*U[k][j] for k in range(i))
            U[i][j]=(A[i][j]-sum0)/L[i][i]
def bksub(b,L,U,n):
    x = b
    y = b
    for r in range(0,n):
        sum0 = sum(L[r][c]*y[c] for c in range(0,r))
        y[r] = (b[r] - sum0)/L[r][r]

    x[n-1] = y[n-1]/U[n-1][n-1]
    for r in range(n-2,-1,-1):
        sum0 = sum(x[c]*U[r][c] for c in range(n-1,r,-1))
        x[r] = (y[r]-sum0)/U[r][r]
    print("x = ",x)
crout(A,L,U,n)
print(L)
print(U)
bksub(b,L,U,n)