"""
Ici, on implémente gauss
"""
import numpy as np
from ex1 import resolve_up


def gauss(A: np.array, b: np.array) -> (np.array, np.array):
    n = len(A)
    for k in range(n): # k = pivot
        for i in range(k+1, n): # i = ligne en dessous du pivot
            g = A[i, k] / A[k, k] # multiplication pour éliminer A[i, k]
            A[i, k:] -= g * A[k, k:] # row operation on A
            b[i] -= g * b[k] # same row operation on b

    return A, b # matrice triangularisé et le b modifié


def cholesky(A: np.array) -> np.array:
    L = np.zeros(A)
    L = np.sqrt(A[0, 0])
    m = len(A)
    # first column
    for i in range(1, m):
        L[i, 0] = A[i, 0] / L[0, 0]

    # généralisation k = 2, ..., m
    for k in range(1, m):
        # diagonale
        L[k, k] = np.sqrt(A[k, k] - np.sum(L[k, :k]**2))
        for i in range(k+1, m):
            for j in range(k-1):
                L[i,k] = (A[i,k] - np.sum(L[i, j] * L[k, j])) / L[k, k]
    return L


if __name__ == '__main__':
    A = np.array([
        [1, 1, 1, 1],
        [1, 5, 5, 5],
        [1, 5, 14, 14],
        [1, 5, 14, 15]
    ], dtype=np.float64)

    b = np.array([1, 0, 0, 0], dtype=np.float64)

    A_triangle, b_gauss = gauss(A, b)
    print(f"A triangulsarisée:\n {A_triangle}")

    x = resolve_up(A, b_gauss)
    print(f"x={x}")

    L = cholesky(A)
    print(f"L\n {L}")