62 lines
1.9 KiB
Python
62 lines
1.9 KiB
Python
# Seals - Program made for educational intent, can be freely distributed
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# and can be used for economical intent. I will not take legal actions
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# unless my intelectual propperty, the code, is stolen or change without permission.
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# Copyright (C) 2020 VItor Hideyoshi Nakazone Batista
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# This program is free software; you can redistribute it and/or modify
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# it under the terms of the GNU General Public License version 2 as published by
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# the Free Software Foundation.
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# This program is distributed in the hope that it will be useful,
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# but WITHOUT ANY WARRANTY; without even the implied warranty of
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# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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# GNU General Public License for more details.
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# You should have received a copy of the GNU General Public License along
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# with this program; if not, write to the Free Software Foundation, Inc.,
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# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
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import numpy as np
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def eigen(a: np.ndarray) -> np.ndarray:
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l = np.ones((a.shape[0]))
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at = a # variavel temporaria para A
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b = np.random.rand(a.shape[0], a.shape[1])
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for k in range(at.shape[0]):
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u = np.random.rand(at.shape[0], 1)
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u = u / max(u.min(), u.max(), key=abs)
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ctrl = 0
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while ctrl != l[k]:
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ctrl = l[k]
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u = at.dot(u)
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l[k] = max(u.min(), u.max(), key=abs)
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u = u / l[k]
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alpha = 0.999 * l[k]
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t = np.random.rand(a.shape[0], 1)
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b[k] = b[k] / max(b[k].min(), b[k].max(), key=abs)
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t = l / max(l.min(), l.max(), key=abs)
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while not (np.allclose(b[k], t, atol=10 ** (-17))):
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t = b[k].copy()
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b[k] = np.linalg.solve((a - alpha * np.identity(a.shape[0])), ((l[k] - alpha) * t))
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b[k] = b[k] / max(b[k].min(), b[k].max(), key=abs)
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i = 0
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while u[i] == 0:
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i += 1
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at = at - (1 / u[i]) * u * at[i]
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return l, b
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