def testGaussianSchellModel1DX(self):
x_coordinates = np.linspace(-12, 12, 1000)
y_coordinates = np.array([0.0])
gsm = GaussianSchellModel2D(A=1,
sigma_s_x=1.5,
sigma_g_x=1.5,
sigma_s_y=10000000,
sigma_g_y=10000000)
eigenmoder = SilentEigenmoder(x_coordinates, y_coordinates)
f = lambda r1, r2: gsm.evaluate(r1, r2)
twoform = eigenmoder.eigenmodes(f)
for n in range(min(len(twoform.eigenvalues()), 15)):
y = twoform.eigenvectors()[n, :, 0]
phi = gsm.phi_nm(n, 0, x_coordinates, [0.0])[:, 0]
phi /= np.linalg.norm(phi)
diff_norm_eig = np.sum(np.abs(phi - y))
diff_norm_neg = np.sum(np.abs(-1 * phi - y))
if diff_norm_eig > diff_norm_neg:
phi *= -1
diff_norm = np.sum(np.abs(phi - y))
self.assertLess(diff_norm, 1e-8)
def testGaussianSchellModel1DY(self):
x_coordinates = np.array([0.0])
y_coordinates = np.linspace(-15, 15, 100)
gsm = GaussianSchellModel2D(A=1,
sigma_s_x=10000000,
sigma_g_x=10000000,
sigma_s_y=2.0,
sigma_g_y=1.5)
eigenmoder = SilentEigenmoder(x_coordinates, y_coordinates)
f = lambda r1, r2: gsm.evaluate(r1, r2)
twoform = eigenmoder.eigenmodes(f)
for n in range(min(len(twoform.eigenvalues()), 15)):
x = twoform.eigenvectors()[n, 0, :]
x = x / np.sqrt(np.trapz(np.abs(x)**2, y_coordinates))
phi = np.array([gsm._mode_y.phi(n, y) for y in y_coordinates])
diff_norm_eig = np.sum(np.abs(phi - x))
diff_norm_neg = np.sum(np.abs(-1 * phi - x))
if diff_norm_eig > diff_norm_neg:
phi *= -1
diff_norm = np.sum(np.abs(phi - x))
self.assertLess(diff_norm, 1 * 1e-8)
def testEigenmodesNormalVsFast(self):
f = lambda r1, r2: np.exp(-(r1[0] - r2[0])**2 -
(r1[1] - r2[1])**2) + 0 * 1j
x_coordinates, y_coordinates = testCoordinates(n_x=30, n_y=30)
eigenmoder = SilentEigenmoder(x_coordinates, y_coordinates)
twoform_normal = eigenmoder.eigenmodes(f)
twoform_fast = eigenmoder.eigenmodes_fast(f, None)
number_samples = 5
for i_x_1 in np.random.randint(0, len(x_coordinates), number_samples):
x_1 = x_coordinates[i_x_1]
for i_y_1 in np.random.randint(0, len(y_coordinates),
number_samples):
y_1 = y_coordinates[i_y_1]
r_1 = (x_1, y_1)
for i_x_2 in np.random.randint(0, len(x_coordinates),
number_samples):
x_2 = x_coordinates[i_x_2]
for i_y_2 in np.random.randint(0, len(y_coordinates),
number_samples):
y_2 = y_coordinates[i_y_2]
r_2 = (x_2, y_2)
f_r = twoform_fast.evaluate(r_1, r_2)
t_r = twoform_normal.evaluate(r_1, r_2)
dr = f_r - t_r
if abs(f_r) > 10e-8:
self.assertLess(abs(dr), 1e-8)
def testGaussianSchellModel1D(self):
x_coordinates = np.linspace(-10, 10, 100)
y_coordinates = np.array([0.0])
gsm = GaussianSchellModel1D(1.0, 1.0, 1.0)
eigenmoder = SilentEigenmoder(x_coordinates, y_coordinates)
f = lambda r1, r2: gsm.evaluate(r1[0], r2[0])
twoform = eigenmoder.eigenmodes(f)
for n in range(min(len(twoform.eigenvalues()), 15)):
y = twoform.eigenvectors()[n, :, 0]
phi = [gsm.phi(n, x) for x in x_coordinates]
phi /= np.linalg.norm(phi)
diff_norm_eig = np.sum(np.abs(phi - y))
diff_norm_neg = np.sum(np.abs(-1 * phi - y))
if diff_norm_eig > diff_norm_neg:
phi *= -1
diff_norm = np.sum(np.abs(phi - y))
self.assertLess(diff_norm, 5 * 1e-10)
def testEigenmodesAllRandomNoSymmetry(self):
f = lambda r1, r2: np.exp(-((r1[0] - r2[0])**2) / 2.0 -
(r1[1] - r2[1])**2) + 0 * 1j
x_coordinates, y_coordinates = testCoordinates(n_x=30, n_y=30)
eigenmoder = SilentEigenmoder(x_coordinates, y_coordinates)
twoform = eigenmoder.eigenmodes(f)
number_samples = 8
for i_x_1 in np.random.randint(0, len(x_coordinates), number_samples):
x_1 = x_coordinates[i_x_1]
for i_y_1 in np.random.randint(0, len(y_coordinates),
number_samples):
y_1 = y_coordinates[i_y_1]
r_1 = (x_1, y_1)
for i_x_2 in np.random.randint(0, len(x_coordinates),
number_samples):
x_2 = x_coordinates[i_x_2]
for i_y_2 in np.random.randint(0, len(y_coordinates),
number_samples):
y_2 = y_coordinates[i_y_2]
r_2 = (x_2, y_2)
f_r = f(r_1, r_2)
t_r = twoform.evaluate(r_1, r_2)
dr = f_r - t_r
if abs(f_r) > 10e-6:
self.assertLess(abs(dr), 1e-12)
def testCreateWorkMatrixAllVsByUpperHalf(self):
f = lambda r1, r2: np.exp(-(r1[0] - r2[0])**2 - (r1[1] - r2[1])**2) + (
r1[0] - r2[0]) * 1j + (r1[1] - r2[1]) * 1j
x_coordinates, y_coordinates = testCoordinates(n_x=30, n_y=30)
eigenmoder = SilentEigenmoder(x_coordinates, y_coordinates)
work_matrix_all = eigenmoder._createWorkMatrixAll(f)
work_matrix_by_upp_half = eigenmoder._createWorkMatrixByUpperHalf(f)
diff = np.linalg.norm(work_matrix_all - work_matrix_by_upp_half)
self.assertLess(diff, 1e-10)
def testEigenmoder1DY(self):
x_coordinates = np.array([0.0])
y_coordinates = np.linspace(-3, 3, 100)
f = lambda r1, r2: np.exp(-(r1[0] - r2[0])**2)
eigenmoder = SilentEigenmoder(x_coordinates, y_coordinates)
twoform = eigenmoder.eigenmodes(f)
x = [twoform.evaluate([0.0, y], [0.0, 1.0]) for y in y_coordinates]
x_f = [f([0.0, y], [0.0, 1.0]) for y in y_coordinates]
d_x = np.array(x) - np.array(x_f)
self.assertLess(np.linalg.norm(d_x), 1e-8)
def testEigenmoder1DX(self):
x_coordinates = np.linspace(-3, 3, 100)
y_coordinates = np.array([0.0])
f = lambda r1, r2: np.exp(-(r1[0] - r2[0])**2)
eigenmoder = SilentEigenmoder(x_coordinates, y_coordinates)
twoform = eigenmoder.eigenmodes(f)
y = [twoform.evaluate([x, 0.0], [1, 0.0]) for x in x_coordinates]
y_f = [f([x, 0.0], [1, 0.0]) for x in x_coordinates]
d_y = np.array(y) - np.array(y_f)
self.assertLess(np.linalg.norm(d_y), 1e-8)
def testEigenmodesSavedIntensity(self):
f = lambda r1, r2: np.exp(-(r1[0] - r2[0])**2 -
(r1[1] - r2[1])**2) + 0 * 1j
x_coordinates, y_coordinates = testCoordinates(n_x=30, n_y=30)
eigenmoder = SilentEigenmoder(x_coordinates, y_coordinates)
twoform = eigenmoder.eigenmodes(f)
for i_x_1, x_1 in enumerate(x_coordinates):
for i_y_1, y_1 in enumerate(y_coordinates):
r_1 = (x_1, y_1)
f_r = f(r_1, r_1)
t_r = twoform.intensity()[i_x_1, i_y_1]
dr = f_r - t_r
self.assertLess(abs(dr), 1e-12)