# Seals - Program made for educational intent, can be freely distributed
# and can be used for economical intent. I will not take legal actions
# unless my intelectual propperty, the code, is stolen or change without permission.  

# Copyright (C) 2020  VItor Hideyoshi Nakazone Batista

# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License version 2 as published by
# the Free Software Foundation.

# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.

# You should have received a copy of the GNU General Public License along
# with this program; if not, write to the Free Software Foundation, Inc.,
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.

import numpy as np


def eigen(a: np.ndarray) -> np.ndarray:
    l = np.ones((a.shape[0]))

    at = a  # variavel temporaria para A
    b = np.random.rand(a.shape[0], a.shape[1])

    for k in range(at.shape[0]):

        u = np.random.rand(at.shape[0], 1)
        u = u / max(u.min(), u.max(), key=abs)

        ctrl = 0

        while ctrl != l[k]:
            ctrl = l[k]
            u = at.dot(u)
            l[k] = max(u.min(), u.max(), key=abs)
            u = u / l[k]

        alpha = 0.999 * l[k]

        t = np.random.rand(a.shape[0], 1)

        b[k] = b[k] / max(b[k].min(), b[k].max(), key=abs)
        t = l / max(l.min(), l.max(), key=abs)

        while not (np.allclose(b[k], t, atol=10 ** (-17))):
            t = b[k].copy()
            b[k] = np.linalg.solve((a - alpha * np.identity(a.shape[0])), ((l[k] - alpha) * t))
            b[k] = b[k] / max(b[k].min(), b[k].max(), key=abs)

        i = 0

        while u[i] == 0:
            i += 1

        at = at - (1 / u[i]) * u * at[i]

    return l, b