41 lines
805 B
Python
41 lines
805 B
Python
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#! /usr/bin/env python3
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import numpy as np
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A = np.array([[0, 0, 0], [0, 0, -1], [0, -1, 0]])
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B = np.array([[0, 1, 0], [1, 0, 0], [0, 0, 0]])
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def similarity_transform(matrix):
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L, S = np.linalg.eig(matrix)
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L = np.diag(L)
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S = S.transpose()
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assert np.allclose(np.matmul(S.transpose(), np.matmul(L, S)), matrix)
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return L, S
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def plusminus(matrix):
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L, S = similarity_transform(matrix)
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def signed(op):
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return 0.5 * np.matmul(S.transpose(), np.matmul(op(L, np.abs(L)), S))
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plus = signed(np.add)
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minus = signed(np.subtract)
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assert np.allclose(matrix, plus + minus)
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return plus, minus
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Aplus, Aminus = plusminus(A)
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Bplus, Bminus = plusminus(B)
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print("A+")
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print(Aplus)
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print("A-")
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print(Aminus)
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print()
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print("B+")
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print(Bplus)
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print("B-")
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print(Bminus)
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