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 testCalculateRhoPhase(self):
sigma_matrix = SigmaWaist(sigma_x=3e-6,
sigma_y=1e-6,
sigma_x_prime=5e-6,
sigma_y_prime=5e-6)
x_coordinates = np.linspace(-1e-5, 1e-5, 50)
y_coordinates = np.linspace(-1e-5, 1e-5, 50)
wavenumber = 1e+11
density = PhaseSpaceDensity(sigma_matrix, wavenumber)
e_field = createGaussian2D(sigma_x=1.0e-6,
sigma_y=1.0e-6,
x_coordinates=x_coordinates,
y_coordinates=y_coordinates)
e_field = e_field + 0j
strategy = BuilderStrategyPython(x_coordinates, y_coordinates, density,
x_coordinates, y_coordinates,
e_field[np.newaxis, :, :])
for x in x_coordinates[::5]:
for y in y_coordinates[::2]:
norm_diff = np.linalg.norm(
strategy.calculateRhoPhase((x, y)) -
strategy.calculateRhoPhaseSlow((x, y)))
self.assertLess(norm_diff, 1e-10)
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 testNumerical_f_dz(self):
sigma_matrix = SigmaWaist(sigma_x=3e-6,
sigma_y=1e-6,
sigma_x_prime=5e-6,
sigma_y_prime=4e-6)
sigma_matrix = sigma_matrix.SigmaMatrix()
sigma_matrix[0, 1] = sigma_matrix[0, 0] * 0.0001
sigma_matrix[1, 0] = sigma_matrix[0, 1]
sigma_matrix[2, 3] = sigma_matrix[2, 2] * 0.00003
sigma_matrix[3, 2] = sigma_matrix[2, 3]
sigma_matrix[4, 4] = 90000
sigma_matrix[5, 5] = 60000
sigma_matrix[4, 5] = 11000
sigma_matrix[5, 4] = 11000
sigma_matrix = SigmaMatrix(sigma_matrix)
x_coordinates = np.linspace(-1e-6, 1e-6, 3)
y_coordinates = np.linspace(-1e-6, 1e-6, 2)
tester = Numerical_f_dz(sigma_matrix,
z=0.01,
delta=0.005,
integration_points=100)
# It is very expansive to converge for high frequency...
for wavenumber in [1e9, 1e1, 1e11, 5e11]:
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_analytic = tester.evaluateAnalytical(
k=wavenumber, vec_x_y=vec_x_y, vec_dr=vec_dr)
result_numerical = tester.evaluateNumerical(
k=wavenumber, vec_x_y=vec_x_y, vec_dr=vec_dr)
diff = np.abs(1 -
(result_analytic / result_numerical))
#print(diff,wavenumber/10e10,x,y,dx,dy)
self.assertLess(diff, 2e-3)
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)
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 testConvolutionVisual(self):
sigma_matrix = SigmaWaist(sigma_x=3e-6,
sigma_y=1e-6,
sigma_x_prime=5e-6,
sigma_y_prime=5e-6)
x_coordinates = np.linspace(-1e-5, 1e-5, 50)
y_coordinates = np.linspace(-1e-5, 1e-5, 50)
wavenumber = 1e+11
e_field = createGaussian2D(sigma_x=1.0e-6,
sigma_y=1.0e-6,
x_coordinates=x_coordinates,
y_coordinates=y_coordinates)
e_field = e_field + 0j
af = AutocorrelationBuilder(N_e=0.0000001,
sigma_matrix=sigma_matrix,
field=e_field,
x_coordinates=x_coordinates,
y_coordinates=y_coordinates,
k=wavenumber)
f = np.zeros((x_coordinates.shape[0], y_coordinates.shape[0]),
dtype=np.complex128)
# damping along y should be higher than along x because sigma_x > sigma_y for the density.
for y in (0.0, 1.5e-6, -1.5e-6):
for i_x_1, x_1 in enumerate(x_coordinates):
for i_x_2, x_2 in enumerate(x_coordinates):
r_1 = np.array([x_1 + x_2, y])
r_2 = np.array([x_1 - x_2, y])
f[i_x_1, i_x_2] = af.evaluate(r_1, r_2)
plotSurface(x_coordinates, x_coordinates, f, False)
for x in (0.0, 1.5e-6, -1.5e-6):
for i_y_1, y_1 in enumerate(y_coordinates):
for i_y_2, y_2 in enumerate(y_coordinates):
r_1 = np.array([x, y_1 + y_2])
r_2 = np.array([x, y_1 - y_2])
f[i_y_1, i_y_2] = af.evaluate(r_1, r_2)
plotSurface(y_coordinates, y_coordinates, f, False)
def testFredholm(self):
Sigma_x = 0.75e-6
Sigma_y = 1e-6
sigma_matrix = SigmaWaist(sigma_x=Sigma_x,
sigma_y=Sigma_y,
sigma_x_prime=1e-6,
sigma_y_prime=1e-6)
x_coordinates = np.linspace(-1e-5, 1e-5, 60)
y_coordinates = np.linspace(-1e-5, 1e-5, 60)
wavenumber = 1e+11
sigma_x = 1.0e-6
sigma_y = 1.0e-6
e_field = createGaussian2D(sigma_x=sigma_x,
sigma_y=sigma_y,
x_coordinates=x_coordinates,
y_coordinates=y_coordinates)
e_field = e_field + 0j
af = AutocorrelationBuilder(N_e=0.0000001,
sigma_matrix=sigma_matrix,
field=e_field,
x_coordinates=x_coordinates,
y_coordinates=y_coordinates,
k=wavenumber)
x_coordinates = af._field_x_coordinates
y_coordinates = af._field_y_coordinates
f2d = np.zeros((x_coordinates.shape[0], y_coordinates.shape[0]),
dtype=np.complex128)
f = np.zeros((x_coordinates.shape[0] * y_coordinates.shape[0]),
dtype=np.complex128)
r_1 = np.array([x_coordinates[0], y_coordinates[0]])
r_2 = np.array([x_coordinates[0], y_coordinates[0]])
res = af.evaluate(r_1, r_2)
f2d[0, 0] = 1.0
res_f = af.fredholmAction(f2d)
print(res)
print(res_f[0, 0])
def testStaticPartFixedR1(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
density = PhaseSpaceDensity(sigma_matrix, wavenumber)
x_coordinates = np.linspace(-10e-6, 10e-6, 100)
y_coordinates = np.linspace(-10e-6, 10e-6, 100)
r_1 = np.array([0.0, 0.0])
density.setAllStaticPartCoordinates(x_coordinates, y_coordinates)
values = density.staticPartFixedR1(r_1)
for i_x, x in enumerate(x_coordinates):
for i_y, y in enumerate(y_coordinates):
dr = r_1 - np.array([x, y])
diff = np.abs(1 - values[i_x, i_y] / density.staticPart(dr))
self.assertLess(diff, 1e-12)
def testNumerical(self):
x_coordinates_gaussian = np.linspace(-3e-7, 3e-7, 100)
y_coordinates_gaussian = np.linspace(-3e-7, 3e-7, 100)
field = createGaussian2D(sigma_x=1e-7,
sigma_y=1e-7,
x_coordinates=x_coordinates_gaussian,
y_coordinates=y_coordinates_gaussian)
sigma_matrix = SigmaWaist(sigma_x=3e-6,
sigma_y=1e-6,
sigma_x_prime=5e-6,
sigma_y_prime=4e-6)
wavenumber = 1e+11
tester = NumericalPhaseSpaceDensity(
N_e=1,
field_x_coordinates=x_coordinates_gaussian,
field_y_coordinates=y_coordinates_gaussian,
efield=field,
sigma_matrix=sigma_matrix,
z=0.0,
delta=0.0,
wavenumber=wavenumber)
x_coordinates = np.linspace(-10e-6, 10e-6, 15)
y_coordinates = np.linspace(-10e-6, 10e-6, 15)
work_buff = np.zeros((x_coordinates.shape[0], y_coordinates.shape[0]),
dtype=np.complex128)
for i_x, x in enumerate(x_coordinates):
for i_y, y in enumerate(y_coordinates):
r_1 = np.array([x, y])
r_2 = r_1
work_buff[i_x, i_y] = tester.evaluate(r_1, r_2)
plotSurface(x_coordinates, y_coordinates, work_buff, True)
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 testConvolution(self):
Sigma_x = 0.75e-6
Sigma_y = 1e-6
sigma_matrix = SigmaWaist(sigma_x=Sigma_x,
sigma_y=Sigma_y,
sigma_x_prime=1e-60,
sigma_y_prime=1e-60,
sigma_dd=0.89e-03)
x_coordinates = np.linspace(-0.5e-5, 0.5e-5, 200)
y_coordinates = np.linspace(-0.5e-5, 0.5e-5, 200)
wavenumber = 1e+11
sigma_x = 1.0e-6
sigma_y = 1.0e-6
e_field = createGaussian2D(sigma_x=sigma_x,
sigma_y=sigma_y,
x_coordinates=x_coordinates,
y_coordinates=y_coordinates)
e_field = e_field + 0j
e_field = e_field[np.newaxis, :, :]
tester_x = ConvolutionTester(Sigma_x=Sigma_x, A=2.0, sigma_x=sigma_x)
tester_y = ConvolutionTester(Sigma_x=Sigma_y, A=2.0, sigma_x=sigma_y)
af = AutocorrelationBuilder(N_e=0.0000001,
sigma_matrix=sigma_matrix,
weighted_fields=e_field,
x_coordinates=x_coordinates,
y_coordinates=y_coordinates,
k=wavenumber)
f = np.zeros((x_coordinates.shape[0], y_coordinates.shape[0]),
dtype=np.complex128)
t = np.zeros_like(f)
# Test along y slices
for y in y_coordinates:
for i_x_1, x_1 in enumerate(x_coordinates):
for i_x_2, x_2 in enumerate(x_coordinates):
r_1 = np.array([x_1 + x_2, y])
r_2 = np.array([x_1 - x_2, y])
f[i_x_1, i_x_2] = af.evaluate(r_1, r_2)
t[i_x_1, i_x_2] = tester_x.evaluateAnalytical(
r_1[0], r_2[0]) * tester_y.evaluateAnalytical(
r_1[1], r_2[1])
f /= norm2D(x_coordinates, x_coordinates, f)
t /= norm2D(x_coordinates, x_coordinates, t)
diff = norm2D(x_coordinates, x_coordinates, f - t)
plotSurface(x_coordinates, x_coordinates, f)
plotSurface(x_coordinates, x_coordinates, t)
self.assertLess(diff, 1e-10)
# Test along x slices
for x in x_coordinates:
for i_y_1, y_1 in enumerate(y_coordinates):
for i_y_2, y_2 in enumerate(y_coordinates):
r_1 = np.array([x, y_1 + y_2])
r_2 = np.array([x, y_1 - y_2])
f[i_y_1, i_y_2] = af.evaluate(r_1, r_2)
t[i_y_1, i_y_2] = tester_x.evaluateAnalytical(
r_1[0], r_2[0]) * tester_y.evaluateAnalytical(
r_1[1], r_2[1])
f /= norm2D(y_coordinates, y_coordinates, f)
t /= norm2D(y_coordinates, y_coordinates, t)
diff = norm2D(y_coordinates, y_coordinates, f - t)
print(diff)
self.assertLess(diff, 1e-10)
def createStraightSectionTestMatrix():
sigma_matrix = SigmaWaist(sigma_x=3e-6,
sigma_y=1e-6,
sigma_x_prime=5e-6,
sigma_y_prime=4e-6)
return sigma_matrix