45 lines
733 B
Python
45 lines
733 B
Python
import numpy as np
|
|
|
|
def decompose(M):
|
|
n = len(M)
|
|
|
|
U = M.copy()
|
|
L = np.identity(n)
|
|
|
|
for i in range(0, n - 1):
|
|
for j in range(i + 1, n):
|
|
L[j, i] = U[j, i] / U[i, i]
|
|
U[j, i:n] -= L[j, i] * U[i, i:n]
|
|
|
|
assert np.allclose(M, L@U)
|
|
|
|
return L, U
|
|
|
|
def solve_lower(m, v):
|
|
x = np.zeros(len(v))
|
|
|
|
for i in range(0, len(v)):
|
|
x[i] = (v[i] - m[i, :i] @ x[:i]) / m[i, i]
|
|
|
|
assert np.allclose(m@x, v)
|
|
|
|
return x
|
|
|
|
def solve_upper(m, v):
|
|
x = np.zeros(len(v))
|
|
|
|
for i in reversed(range(0, len(m))):
|
|
x[i] = (v[i] - m[i, i+1:] @ x[i+1:]) / m[i, i]
|
|
|
|
assert np.allclose(m@x, v)
|
|
|
|
return x
|
|
|
|
def solve(m, v):
|
|
L, U = decompose(m)
|
|
x = solve_upper(U, solve_lower(L, v))
|
|
|
|
assert np.allclose(m@x, v)
|
|
|
|
return x
|