SummationByParts/maxwell/misc/eigenvalues_rotated.py

56 lines
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Python
Executable File

#! /usr/bin/env python3
import sympy as sp
A = sp.Matrix([[0, 0, 0], [0, 0, -1], [0, -1, 0]])
B = sp.Matrix([[0, 1, 0], [1, 0, 0], [0, 0, 0]])
kx, ky = sp.symbols("kx ky")
A = kx * A + ky * B
print("flux")
sp.pprint(A)
eigenvalues = A.eigenvals()
# sp.pprint(eigenvalues)
eigenvectors = A.eigenvects()
# sp.pprint(eigenvectors)
S, L = A.diagonalize()
Labs = (L*L)**0.5
plus = S*(L + Labs)*S.inv()/2
minus = S*(L - Labs)*S.inv()/2
Ahat = plus + minus
plus.simplify()
minus.simplify()
print("Positive flux")
r = sp.symbols("r")
sp.pprint(plus.subs((kx*kx + ky*ky)**0.5, r))
print("Negative flux")
sp.pprint(minus.subs((kx*kx + ky*ky)**0.5, r))
print("r = ")
sp.pprint((kx*kx + ky*ky)**0.5)
print("Evaluations:")
print("plus (1, 0)")
sp.pprint(plus.subs(kx, 1).subs(ky, 0))
print("plus (0, 1)")
sp.pprint(plus.subs(kx, 0).subs(ky, 1))
print("plus (1/sqrt(2), 1/sqrt(2)")
sp.pprint(plus.subs(kx, 1/2**0.5).subs(ky, 1/2**0.5))
print("positive flux - negative flux")
S = plus - minus
S.simplify
sp.pprint(S.subs((kx*kx + ky*ky)**0.5, r))