def test_riemann_matrix(self):
# the transformed period matrices should still result in a Riemann
# matrix after normalization
Pa, Pb = symmetrize_periods(self.atrott.T, self.btrott.T)
Omega = Pa.inverse() * Pb
Y = Omega.apply_map(imag)
symmetric_error = (Omega - Omega.T).norm()
eigenvalues = Y.eigenvalues()
self.assertLess(symmetric_error,
3e-3) # the example itself has low precision
for eig in eigenvalues:
self.assertGreater(eig, 0)
Pa, Pb = symmetrize_periods(self.aklein.T, self.bklein.T, tol=1e-3)
Omega = Pa.inverse() * Pb
Y = Omega.apply_map(imag)
symmetric_error = (Omega - Omega.T).norm()
eigenvalues = Y.eigenvalues()
self.assertLess(symmetric_error, 1e-3)
for eig in eigenvalues:
self.assertGreater(eig, 0)
Pa, Pb = symmetrize_periods(self.afermat.T, self.bfermat.T, tol=1e-3)
Omega = Pa.inverse() * Pb
Y = Omega.apply_map(imag)
symmetric_error = (Omega - Omega.T).norm()
eigenvalues = Y.eigenvalues()
self.assertLess(symmetric_error, 1e-3)
for eig in eigenvalues:
self.assertGreater(eig, 0)
Pa, Pb = symmetrize_periods(self.a6.T, self.b6.T)
Omega = Pa.inverse() * Pb
Y = Omega.apply_map(imag)
symmetric_error = (Omega - Omega.T).norm()
eigenvalues = Y.eigenvalues()
self.assertLess(symmetric_error, 1e-3)
for eig in eigenvalues:
self.assertGreater(eig, 0)
def test_riemann_matrix(self):
# the transformed period matrices should still result in a Riemann
# matrix after normalization
Pa, Pb = symmetrize_periods(self.atrott.T, self.btrott.T)
Omega = Pa.inverse()*Pb
Y = Omega.apply_map(imag)
symmetric_error = (Omega - Omega.T).norm()
eigenvalues = Y.eigenvalues()
self.assertLess(symmetric_error, 3e-3) # the example itself has low precision
for eig in eigenvalues:
self.assertGreater(eig, 0)
Pa, Pb = symmetrize_periods(self.aklein.T, self.bklein.T, tol=1e-3)
Omega = Pa.inverse()*Pb
Y = Omega.apply_map(imag)
symmetric_error = (Omega - Omega.T).norm()
eigenvalues = Y.eigenvalues()
self.assertLess(symmetric_error, 1e-3)
for eig in eigenvalues:
self.assertGreater(eig, 0)
Pa, Pb = symmetrize_periods(self.afermat.T, self.bfermat.T, tol=1e-3)
Omega = Pa.inverse()*Pb
Y = Omega.apply_map(imag)
symmetric_error = (Omega - Omega.T).norm()
eigenvalues = Y.eigenvalues()
self.assertLess(symmetric_error, 1e-3)
for eig in eigenvalues:
self.assertGreater(eig, 0)
Pa, Pb = symmetrize_periods(self.a6.T, self.b6.T)
Omega = Pa.inverse()*Pb
Y = Omega.apply_map(imag)
symmetric_error = (Omega - Omega.T).norm()
eigenvalues = Y.eigenvalues()
self.assertLess(symmetric_error, 1e-3)
for eig in eigenvalues:
self.assertGreater(eig, 0)
def test_integral(self):
# symmetrize_periods already tests if Gamma is integral
Pa, Pb = symmetrize_periods(self.atrott.T, self.btrott.T)
Pa, Pb = symmetrize_periods(self.aklein.T, self.bklein.T, tol=1e-3)
Pa, Pb = symmetrize_periods(self.afermat.T, self.bfermat.T, tol=1e-3)
Pa, Pb = symmetrize_periods(self.a6.T, self.b6.T)
def test_integral(self):
# symmetrize_periods already tests if Gamma is integral
Pa, Pb = symmetrize_periods(self.atrott.T, self.btrott.T)
Pa, Pb = symmetrize_periods(self.aklein.T, self.bklein.T, tol=1e-3)
Pa, Pb = symmetrize_periods(self.afermat.T, self.bfermat.T, tol=1e-3)
Pa, Pb = symmetrize_periods(self.a6.T, self.b6.T)
