SummationByParts/maxwell/misc/eigenvalues.py

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2020-06-14 20:02:28 +00:00
#! /usr/bin/env python3
import numpy as np
A = np.array([[0, 0, 0], [0, 0, -1], [0, -1, 0]])
B = np.array([[0, 1, 0], [1, 0, 0], [0, 0, 0]])
def similarity_transform(matrix):
L, S = np.linalg.eig(matrix)
L = np.diag(L)
S = S.transpose()
assert np.allclose(np.matmul(S.transpose(), np.matmul(L, S)), matrix)
return L, S
def plusminus(matrix):
L, S = similarity_transform(matrix)
def signed(op):
return 0.5 * np.matmul(S.transpose(), np.matmul(op(L, np.abs(L)), S))
plus = signed(np.add)
minus = signed(np.subtract)
assert np.allclose(matrix, plus + minus)
return plus, minus
Aplus, Aminus = plusminus(A)
Bplus, Bminus = plusminus(B)
print("A+")
print(Aplus)
print("A-")
print(Aminus)
print()
print("B+")
print(Bplus)
print("B-")
print(Bminus)
2020-06-15 20:28:53 +00:00
print()
print("SA = Aplus - Aminus")
print(Aplus - Aminus)
print("SB = Bplus - Bminus")
print(Bplus - Bminus)