def testStaticElectronDensity(self):
sigma_x = 3e-6
sigma_y = 1e-6
sigma_matrix = SigmaWaist(sigma_x=sigma_x,
sigma_y=sigma_y,
sigma_x_prime=5e-6,
sigma_y_prime=4e-6)
wavenumber = 1e+11
density = PhaseSpaceDensity(sigma_matrix, wavenumber)
x_coordinates = np.linspace(-10e-6, 10e-6, 100)
y_coordinates = np.linspace(-10e-6, 10e-6, 100)
prefactor = 1.0 / (2 * np.pi * sigma_matrix.sigma_x()**2 *
sigma_matrix.sigma_y()**2 *
sigma_matrix.sigma_d()**2)
#TODO prefactor not correct!
prefactor = density.staticPart(np.array([0, 0]))
diff_prefactor = prefactor / density.staticPart(np.array([0, 0]))
self.assertLess(np.abs(1 - diff_prefactor), 1e-12)
dy = 0.0
for dx in x_coordinates:
dr = np.array([dx, dy])
diff = density.staticPart(delta_r=dr) / \
(prefactor * np.exp(-(dx-dy)**2 * (0.5*wavenumber**2*sigma_matrix.sigma_x_prime()**2)))
self.assertLess(np.abs(1 - diff), 1e-12)
dx = 0.0
for dy in y_coordinates:
dr = np.array([dx, dy])
diff = density.staticPart(delta_r=dr) / \
(prefactor * np.exp(-(dx-dy)**2 * (0.5*wavenumber**2*sigma_matrix.sigma_y_prime()**2)))
self.assertLess(np.abs(1 - diff), 1e-12)
def testIntegrationPartGaussian(self):
sigma_x = 3e-6
sigma_y = 1e-6
sigma_matrix = SigmaWaist(sigma_x=sigma_x,
sigma_y=sigma_y,
sigma_x_prime=5e-6,
sigma_y_prime=4e-6)
wavenumber = 1e+11
density = PhaseSpaceDensity(sigma_matrix, wavenumber)
x_coordinates = np.linspace(-15e-6, 15e-6, 200)
y_coordinates = np.linspace(-7e-6, 7e-6, 200)
for dx in x_coordinates:
diff = density.integrationPartGaussian(
delta=0.0, z=0.0, x=dx, y=0.0) - np.exp(
-dx**2 / (2 * sigma_matrix.sigma_x()**2))
self.assertLess(diff, 1e-12)
for dy in y_coordinates:
diff = density.integrationPartGaussian(
delta=0.0, z=0.0, x=0.0, y=dy) - np.exp(
-dy**2 / (2 * sigma_matrix.sigma_y()**2))
self.assertLess(diff, 1e-12)
rho = np.zeros((x_coordinates.size, y_coordinates.size),
dtype=np.complex128)
for i_x, dx in enumerate(x_coordinates):
for i_y, dy in enumerate(y_coordinates):
rho[i_x, i_y] = density.integrationPartGaussian(delta=0.0,
z=0.0,
x=dx,
y=dy)
norm_1 = np.trapz(np.trapz(np.abs(rho), y_coordinates), x_coordinates)
self.assertLess(1 - norm_1 / (2 * np.pi * sigma_x * sigma_y), 1e-6)
def testStaticElectronDensity(self):
sigma_x = 3e-6
sigma_y = 1e-6
sigma_matrix = SigmaWaist(sigma_x=sigma_x,
sigma_y=sigma_y,
sigma_x_prime=5e-6,
sigma_y_prime=4e-6)
wavenumber = 1e+11
density = PhaseSpaceDensity(sigma_matrix, wavenumber)
x_coordinates = np.linspace(-10e-6, 10e-6, 100)
y_coordinates = np.linspace(-10e-6, 10e-6, 100)
prefactor = 1.0 / (2 * np.pi * sigma_matrix.sigma_x()**2 * sigma_matrix.sigma_y()**2 * sigma_matrix.sigma_d()**2)
#TODO prefactor not correct!
prefactor = density.staticPart(np.array([0,0]))
diff_prefactor = prefactor / density.staticPart(np.array([0,0]))
self.assertLess(np.abs(1-diff_prefactor), 1e-12)
dy = 0.0
for dx in x_coordinates:
dr = np.array([dx, dy])
diff = density.staticPart(delta_r=dr) / \
(prefactor * np.exp(-(dx-dy)**2 * (0.5*wavenumber**2*sigma_matrix.sigma_x_prime()**2)))
self.assertLess(np.abs(1-diff), 1e-12)
dx = 0.0
for dy in y_coordinates:
dr = np.array([dx, dy])
diff = density.staticPart(delta_r=dr) / \
(prefactor * np.exp(-(dx-dy)**2 * (0.5*wavenumber**2*sigma_matrix.sigma_y_prime()**2)))
self.assertLess(np.abs(1-diff), 1e-12)
def testNumerical_f_dzSimgple(self):
sigma_matrix = SigmaWaist(sigma_x=3e-6,
sigma_y=1e-6,
sigma_x_prime=5e-6,
sigma_y_prime=4e-6)
wavenumber = 1e+11
x_coordinates = np.linspace(-10e-6, 10e-6, 15)
y_coordinates = np.linspace(-10e-6, 10e-6, 10)
tester = Numerical_f_dz(sigma_matrix, z=0.0, delta=0.0)
prefactor = 2 * np.pi * sigma_matrix.sigma_x_prime(
) * sigma_matrix.sigma_y_prime()
for x in x_coordinates:
for y in y_coordinates:
vec_x_y = np.array([x, y])
for dx in x_coordinates:
for dy in y_coordinates:
vec_dr = np.array([dx, dy])
result_tester = tester.evaluateAnalytical(
k=wavenumber, vec_x_y=vec_x_y, vec_dr=vec_dr)
result_analytic = prefactor * \
np.exp(-0.5 * ((x**2/sigma_matrix.sigma_x()**2)+(y**2/sigma_matrix.sigma_y()**2))) * \
np.exp(-0.5 * wavenumber**2 * ((dx**2 * sigma_matrix.sigma_x_prime()**2)+(dy**2 * sigma_matrix.sigma_y_prime()**2)))
diff = np.abs(1 - (result_tester / result_analytic))
self.assertLess(diff, 1e-12)
def testNumerical_f_dzSimgple(self):
sigma_matrix = SigmaWaist(sigma_x=3e-6,
sigma_y=1e-6,
sigma_x_prime=5e-6,
sigma_y_prime=4e-6)
wavenumber = 1e+11
x_coordinates = np.linspace(-10e-6, 10e-6, 15)
y_coordinates = np.linspace(-10e-6, 10e-6, 10)
tester = Numerical_f_dz(sigma_matrix, z=0.0, delta=0.0)
prefactor = 2 * np.pi * sigma_matrix.sigma_x_prime() * sigma_matrix.sigma_y_prime()
for x in x_coordinates:
for y in y_coordinates:
vec_x_y = np.array([x, y])
for dx in x_coordinates:
for dy in y_coordinates:
vec_dr = np.array([dx, dy])
result_tester = tester.evaluateAnalytical(k=wavenumber,
vec_x_y=vec_x_y,
vec_dr=vec_dr)
result_analytic = prefactor * \
np.exp(-0.5 * ((x**2/sigma_matrix.sigma_x()**2)+(y**2/sigma_matrix.sigma_y()**2))) * \
np.exp(-0.5 * wavenumber**2 * ((dx**2 * sigma_matrix.sigma_x_prime()**2)+(dy**2 * sigma_matrix.sigma_y_prime()**2)))
diff = np.abs(1 - (result_tester / result_analytic))
self.assertLess(diff, 1e-12)
def testIntegrationPartGaussian(self):
sigma_x = 3e-6
sigma_y = 1e-6
sigma_matrix = SigmaWaist(sigma_x=sigma_x,
sigma_y=sigma_y,
sigma_x_prime=5e-6,
sigma_y_prime=4e-6)
wavenumber = 1e+11
density = PhaseSpaceDensity(sigma_matrix, wavenumber)
x_coordinates = np.linspace(-15e-6, 15e-6, 200)
y_coordinates = np.linspace(-7e-6, 7e-6, 200)
for dx in x_coordinates:
diff = density.integrationPartGaussian(delta=0.0, z=0.0, x=dx, y=0.0) - np.exp(-dx**2/(2*sigma_matrix.sigma_x()**2))
self.assertLess(diff, 1e-12)
for dy in y_coordinates:
diff = density.integrationPartGaussian(delta=0.0, z=0.0, x=0.0, y=dy) - np.exp(-dy**2/(2*sigma_matrix.sigma_y()**2))
self.assertLess(diff, 1e-12)
rho = np.zeros((x_coordinates.size, y_coordinates.size), dtype=np.complex128)
for i_x, dx in enumerate(x_coordinates):
for i_y, dy in enumerate(y_coordinates):
rho[i_x, i_y] = density.integrationPartGaussian(delta=0.0, z=0.0, x=dx, y=dy)
norm_1 = np.trapz(np.trapz(np.abs(rho), y_coordinates), x_coordinates)
self.assertLess(1-norm_1/(2*np.pi*sigma_x*sigma_y), 1e-6)