def do_choice(T, prefix, x, y, y_err):
fit_x = np.linspace(np.min(x), np.max(x), 100)
y_dist = []
popt_dist = []
for i in range(len(x)):
choice_x = bootstrap.generate_sample(x)
choice_y = bootstrap.generate_sample(y)
choice_y_err = bootstrap.generate_sample(y_err)
popt, pconv = op.curve_fit(linear, choice_x, choice_y, sigma=choice_y_err)
boot_fit_y = linear(fit_x, *popt)
y_dist.append(boot_fit_y)
popt_dist.append(popt)
fit_y_val, fit_y_err = bootstrap.average_and_std_arrays(y_dist)
np.savetxt('_build/xy/bootstrap-{}-band.tsv'.format(prefix),
bootstrap.pgfplots_error_band(fit_x, fit_y_val, fit_y_err))
np.savetxt('_build/xy/bootstrap-{}-final-fit.tsv'.format(prefix),
np.column_stack([fit_x, fit_y_val]))
popt_val, popt_err = bootstrap.average_and_std_arrays(popt_dist)
popt_val, pconv = op.curve_fit(linear, x, y, sigma=y_err)
T['bootstrap_{}_popt'.format(prefix)] = siunitx(popt_val, popt_err, error_digits=2)
T['bootstrap_{}_err'.format(prefix)] = siunitx(popt_err)
def do_choice(T, prefix, x, y, y_err):
fit_x = np.linspace(np.min(x), np.max(x), 100)
y_dist = []
popt_dist = []
for i in range(len(x)):
choice_x = bootstrap.generate_sample(x)
choice_y = bootstrap.generate_sample(y)
choice_y_err = bootstrap.generate_sample(y_err)
popt, pconv = op.curve_fit(linear,
choice_x,
choice_y,
sigma=choice_y_err)
boot_fit_y = linear(fit_x, *popt)
y_dist.append(boot_fit_y)
popt_dist.append(popt)
fit_y_val, fit_y_err = bootstrap.average_and_std_arrays(y_dist)
np.savetxt('_build/xy/bootstrap-{}-band.tsv'.format(prefix),
bootstrap.pgfplots_error_band(fit_x, fit_y_val, fit_y_err))
np.savetxt('_build/xy/bootstrap-{}-final-fit.tsv'.format(prefix),
np.column_stack([fit_x, fit_y_val]))
popt_val, popt_err = bootstrap.average_and_std_arrays(popt_dist)
popt_val, pconv = op.curve_fit(linear, x, y, sigma=y_err)
T['bootstrap_{}_popt'.format(prefix)] = siunitx(popt_val,
popt_err,
error_digits=2)
T['bootstrap_{}_err'.format(prefix)] = siunitx(popt_err)
def do_jackknife(T, prefix, x, y, y_err):
fit_x = np.linspace(np.min(x), np.max(x), 100)
y_dist = []
popt_dist = []
for i in range(len(x)):
jack_x = np.delete(x, i)
jack_y = np.delete(y, i)
popt, pconv = op.curve_fit(linear, jack_x, jack_y)
boot_fit_y = linear(fit_x, *popt)
y_dist.append(boot_fit_y)
popt_dist.append(popt)
np.savetxt('_build/xy/bootstrap-{}-{:d}-resampled.tsv'.format(prefix, i),
np.column_stack([jack_x, jack_y]))
np.savetxt('_build/xy/bootstrap-{}-{:d}-fit.tsv'.format(prefix, i),
np.column_stack([fit_x, boot_fit_y]))
fit_y_val, fit_y_err = bootstrap.average_and_std_arrays(y_dist)
np.savetxt('_build/xy/bootstrap-{}-band.tsv'.format(prefix),
bootstrap.pgfplots_error_band(fit_x, fit_y_val, fit_y_err))
np.savetxt('_build/xy/bootstrap-{}-final-fit.tsv'.format(prefix),
np.column_stack([fit_x, fit_y_val]))
popt_val, popt_err = bootstrap.average_and_std_arrays(popt_dist)
popt_val, pconv = op.curve_fit(linear, x, y, sigma=y_err)
T['bootstrap_{}_popt'.format(prefix)] = siunitx(popt_val, popt_err, error_digits=2)
T['bootstrap_{}_err'.format(prefix)] = siunitx(popt_err)
def do_jackknife(T, prefix, x, y, y_err):
fit_x = np.linspace(np.min(x), np.max(x), 100)
y_dist = []
popt_dist = []
for i in range(len(x)):
jack_x = np.delete(x, i)
jack_y = np.delete(y, i)
popt, pconv = op.curve_fit(linear, jack_x, jack_y)
boot_fit_y = linear(fit_x, *popt)
y_dist.append(boot_fit_y)
popt_dist.append(popt)
np.savetxt(
'_build/xy/bootstrap-{}-{:d}-resampled.tsv'.format(prefix, i),
np.column_stack([jack_x, jack_y]))
np.savetxt('_build/xy/bootstrap-{}-{:d}-fit.tsv'.format(prefix, i),
np.column_stack([fit_x, boot_fit_y]))
fit_y_val, fit_y_err = bootstrap.average_and_std_arrays(y_dist)
np.savetxt('_build/xy/bootstrap-{}-band.tsv'.format(prefix),
bootstrap.pgfplots_error_band(fit_x, fit_y_val, fit_y_err))
np.savetxt('_build/xy/bootstrap-{}-final-fit.tsv'.format(prefix),
np.column_stack([fit_x, fit_y_val]))
popt_val, popt_err = bootstrap.average_and_std_arrays(popt_dist)
popt_val, pconv = op.curve_fit(linear, x, y, sigma=y_err)
T['bootstrap_{}_popt'.format(prefix)] = siunitx(popt_val,
popt_err,
error_digits=2)
T['bootstrap_{}_err'.format(prefix)] = siunitx(popt_err)
def job_rayleigh_length(T):
beam_diameter_val = 3.5e-3
beam_diameter_err = 0.5e-3
refractive_index = 2.2
wavelength = 987e-9
length = 5e-3
distance = 60e-3
beam_radius_val = beam_diameter_val / 2
beam_radius_err = beam_diameter_err / 2
T['beam_radius'] = siunitx(beam_radius_val, beam_radius_err)
beam_radius_dist = bootstrap.make_dist(beam_radius_val, beam_diameter_err)
theta_dist = [
np.arctan(beam_radius / distance)
for beam_radius in beam_radius_dist
]
theta_val, theta_err = bootstrap.average_and_std_arrays(theta_dist)
T['theta'] = siunitx(theta_val, theta_err)
bootstrap.save_hist(theta_dist, '_build/dist-theta.pdf')
waist_dist = [
wavelength / (np.pi * theta)
for theta in theta_dist
]
waist_val, waist_err = bootstrap.average_and_std_arrays(waist_dist)
T['waist_mum'] = siunitx(waist_val / 1e-6, waist_err / 1e-6)
bootstrap.save_hist(waist_dist, '_build/dist-waist.pdf')
rayleigh_length_dist = list(itertools.filterfalse(np.isnan, [
refractive_index * np.pi * waist**2 / wavelength
for waist in waist_dist
]))
rayleigh_length_val, rayleigh_length_err = bootstrap.average_and_std_arrays(rayleigh_length_dist)
T['rayleigh_length_mm'] = siunitx(rayleigh_length_val / 1e-3, rayleigh_length_err / 1e-3, error_digits=2)
bootstrap.save_hist(rayleigh_length_dist, '_build/dist-rayleigh_length.pdf')
normalized_length_dist = list([
length / (2 * rayleigh_length)
for rayleigh_length in rayleigh_length_dist
])
normalized_length_val, normalized_length_err = bootstrap.average_and_std_arrays(normalized_length_dist)
T['normalized_length'] = siunitx(normalized_length_val, normalized_length_err, error_digits=2)
bootstrap.save_hist(normalized_length_dist, '_build/dist-normalized_length.pdf')
t = (normalized_length_val - 2.84) / normalized_length_err
T['boyd_kleinman_ttest_t'] = siunitx(t)
optimal_focal_length_dist = list([
get_optimal_focal_length(beam_radius, refractive_index, wavelength, length)
for beam_radius in beam_radius_dist
])
optimal_focal_length_val, optimal_focal_length_err = bootstrap.average_and_std_arrays(optimal_focal_length_dist)
T['optimal_focal_length_mm'] = siunitx(optimal_focal_length_val / 1e-3, optimal_focal_length_err / 1e-3, error_digits=2)
def job_variable_attenuator(T, extinction_dist):
data = np.loadtxt('Data/variable.tsv')
angle = data[:, 0]
power_val = data[:, 1] * 1e-6
power_err = np.ones(power_val.shape) * 1e-6
T['variable_attenuator_table'] = list(
zip(
siunitx(angle),
siunitx(power_val * 1e6, power_err * 1e6),
))
power_dist = bootstrap.make_dist(power_val,
power_err,
n=len(extinction_dist))
fit_x = np.linspace(np.min(angle), np.max(angle), 200)
fit_y_dist = []
angle_offset_dist = []
a_dist = []
b_dist = []
popt_dist = []
extinction_ratio_dist = []
for power in power_dist:
popt, pconv = op.curve_fit(cos_squared, angle, power, p0=[1.5, 0, 0])
fit_y_dist.append(cos_squared(fit_x, *popt))
angle_offset_dist.append(popt[1])
a = popt[0]
b = popt[2]
a_dist.append(a)
b_dist.append(b)
popt_dist.append(popt)
extinction_ratio_dist.append((a + b) / b)
fit_y_val, fit_y_err = bootstrap.average_and_std_arrays(fit_y_dist)
angle_offset_val, angle_offset_err = bootstrap.average_and_std_arrays(
angle_offset_dist)
a_val, a_err = bootstrap.average_and_std_arrays(a_dist)
b_val, b_err = bootstrap.average_and_std_arrays(b_dist)
extinction_ratio_val, extinction_ratio_err = bootstrap.average_and_std_arrays(
extinction_ratio_dist)
np.savetxt('_build/xy/variable-data.tsv',
np.column_stack([angle, power_val, power_err]))
np.savetxt('_build/xy/variable-fit.tsv',
np.column_stack([fit_x, fit_y_val]))
np.savetxt('_build/xy/variable-band.tsv',
bootstrap.pgfplots_error_band(fit_x, fit_y_val, fit_y_err))
T['variable_angle_offset'] = siunitx(angle_offset_val, angle_offset_err)
T['variable_a'] = siunitx(a_val, a_err)
T['variable_b'] = siunitx(b_val, b_err)
T['extinction_ratio'] = siunitx(extinction_ratio_val, extinction_ratio_err)
return popt_dist
def job_variable_attenuator(T, extinction_dist):
data = np.loadtxt('Data/variable.tsv')
angle = data[:, 0]
power_val = data[:, 1] * 1e-6
power_err = np.ones(power_val.shape) * 1e-6
T['variable_attenuator_table'] = list(zip(
siunitx(angle),
siunitx(power_val*1e6, power_err*1e6),
))
power_dist = bootstrap.make_dist(power_val, power_err, n=len(extinction_dist))
fit_x = np.linspace(np.min(angle), np.max(angle), 200)
fit_y_dist = []
angle_offset_dist = []
a_dist = []
b_dist = []
popt_dist = []
extinction_ratio_dist = []
for power in power_dist:
popt, pconv = op.curve_fit(cos_squared, angle, power, p0=[1.5, 0, 0])
fit_y_dist.append(cos_squared(fit_x, *popt))
angle_offset_dist.append(popt[1])
a = popt[0]
b = popt[2]
a_dist.append(a)
b_dist.append(b)
popt_dist.append(popt)
extinction_ratio_dist.append((a + b) / b)
fit_y_val, fit_y_err = bootstrap.average_and_std_arrays(fit_y_dist)
angle_offset_val, angle_offset_err = bootstrap.average_and_std_arrays(angle_offset_dist)
a_val, a_err = bootstrap.average_and_std_arrays(a_dist)
b_val, b_err = bootstrap.average_and_std_arrays(b_dist)
extinction_ratio_val, extinction_ratio_err = bootstrap.average_and_std_arrays(extinction_ratio_dist)
np.savetxt('_build/xy/variable-data.tsv',
np.column_stack([angle, power_val, power_err]))
np.savetxt('_build/xy/variable-fit.tsv',
np.column_stack([fit_x, fit_y_val]))
np.savetxt('_build/xy/variable-band.tsv',
bootstrap.pgfplots_error_band(fit_x, fit_y_val, fit_y_err))
T['variable_angle_offset'] = siunitx(angle_offset_val, angle_offset_err)
T['variable_a'] = siunitx(a_val, a_err)
T['variable_b'] = siunitx(b_val, b_err)
T['extinction_ratio'] = siunitx(extinction_ratio_val, extinction_ratio_err)
return popt_dist
def job_grating_resolution(T):
lines_per_m = 600e3
diameter_val = 3.5e-3 / 2
diameter_err = 0.5e-3 / 2
diameter_dist = bootstrap.make_dist(diameter_val, diameter_err)
illuminated_dist = [diameter * lines_per_m for diameter in diameter_dist]
illuminated_val, illuminated_err = bootstrap.average_and_std_arrays(
illuminated_dist)
T['illuminated'] = siunitx(illuminated_val, illuminated_err)
rel_error_dist = [1 / illuminated for illuminated in illuminated_dist]
rel_error_val, rel_error_err = bootstrap.average_and_std_arrays(
rel_error_dist)
T['rel_error'] = siunitx(rel_error_val, rel_error_err)
def job_input_polarization(T):
data = np.loadtxt('Data/harmonic_bare.tsv')
angle = data[:, 0]
power_val = data[:, 1] * 1e-6
power_err = data[:, 2] * 1e-6
power_dist = bootstrap.make_dist(power_val, power_err)
T['harmonic_bare_table'] = list(
zip(
siunitx(angle),
siunitx(power_val * 1e6, power_err * 1e6),
))
fit_x = np.linspace(np.min(angle), np.max(angle), 200)
fit_y_dist = []
angle_offset_dist = []
a_dist = []
b_dist = []
popt_dist = []
for power in power_dist:
popt, pconv = op.curve_fit(cos_quartic,
angle,
power,
p0=[1.5e-5, 0, 0])
fit_y_dist.append(cos_quartic(fit_x, *popt))
angle_offset_dist.append(popt[1])
a = popt[0]
b = popt[2]
a_dist.append(a)
b_dist.append(b)
popt_dist.append(popt)
fit_y_val, fit_y_err = bootstrap.average_and_std_arrays(fit_y_dist)
angle_offset_val, angle_offset_err = bootstrap.average_and_std_arrays(
angle_offset_dist)
a_val, a_err = bootstrap.average_and_std_arrays(a_dist)
b_val, b_err = bootstrap.average_and_std_arrays(b_dist)
np.savetxt('_build/xy/harmonic-bare-data.tsv',
np.column_stack([angle, power_val, power_err]))
np.savetxt('_build/xy/harmonic-bare-fit.tsv',
np.column_stack([fit_x, fit_y_val]))
np.savetxt('_build/xy/harmonic-bare-band.tsv',
bootstrap.pgfplots_error_band(fit_x, fit_y_val, fit_y_err))
T['bare_angle_offset'] = siunitx(angle_offset_val, angle_offset_err)
T['bare_a'] = siunitx(a_val, a_err)
T['bare_b'] = siunitx(b_val, b_err)
def job_grating_resolution(T):
lines_per_m = 600e3
diameter_val = 3.5e-3 / 2
diameter_err = 0.5e-3 / 2
diameter_dist = bootstrap.make_dist(diameter_val, diameter_err)
illuminated_dist = [
diameter * lines_per_m
for diameter in diameter_dist
]
illuminated_val, illuminated_err = bootstrap.average_and_std_arrays(illuminated_dist)
T['illuminated'] = siunitx(illuminated_val, illuminated_err)
rel_error_dist = [
1 / illuminated
for illuminated in illuminated_dist
]
rel_error_val, rel_error_err = bootstrap.average_and_std_arrays(rel_error_dist)
T['rel_error'] = siunitx(rel_error_val, rel_error_err)
def job_temperature_dependence(T):
data = np.loadtxt('Data/temperature.tsv')
temp = data[:, 0]
power_val = data[:, 1] * 1e-6
power_err = np.ones(power_val.shape) * 1e-6
power_dist = bootstrap.make_dist(power_val, power_err)
T['temperature_table'] = list(
zip(
siunitx(temp),
siunitx(power_val * 1e6, power_err * 1e6),
))
p0 = [36.5, 1, 36 - 6, 2e-6]
fit_x = np.linspace(np.min(temp), np.max(temp), 300)
popt_dist = []
fit_y_dist = []
for power in power_dist:
popt, pconv = op.curve_fit(sinc, temp, power, p0=p0)
fit_y_dist.append(sinc(fit_x, *popt))
popt_dist.append(popt)
center_dist, width_dist, amplitude_dist, offset_dist = zip(*popt_dist)
center_val, center_err = bootstrap.average_and_std_arrays(center_dist)
width_val, width_err = bootstrap.average_and_std_arrays(width_dist)
amplitude_val, amplitude_err = bootstrap.average_and_std_arrays(
amplitude_dist)
offset_val, offset_err = bootstrap.average_and_std_arrays(offset_dist)
fit_y_val, fit_y_err = bootstrap.average_and_std_arrays(fit_y_dist)
np.savetxt('_build/xy/temperature-data.tsv',
np.column_stack([temp, power_val, power_err]))
np.savetxt('_build/xy/temperature-fit.tsv',
np.column_stack([fit_x, fit_y_val]))
np.savetxt('_build/xy/temperature-band.tsv',
bootstrap.pgfplots_error_band(fit_x, fit_y_val, fit_y_err))
T['temp_center'] = siunitx(center_val, center_err)
T['temp_width'] = siunitx(width_val, width_err)
T['temp_amplitude'] = siunitx(amplitude_val, amplitude_err)
T['temp_offset'] = siunitx(offset_val, offset_err)
def job_input_polarization(T):
data = np.loadtxt('Data/harmonic_bare.tsv')
angle = data[:, 0]
power_val = data[:, 1] * 1e-6
power_err = data[:, 2] * 1e-6
power_dist = bootstrap.make_dist(power_val, power_err)
T['harmonic_bare_table'] = list(zip(
siunitx(angle),
siunitx(power_val*1e6, power_err*1e6),
))
fit_x = np.linspace(np.min(angle), np.max(angle), 200)
fit_y_dist = []
angle_offset_dist = []
a_dist = []
b_dist = []
popt_dist = []
for power in power_dist:
popt, pconv = op.curve_fit(cos_quartic, angle, power, p0=[1.5e-5, 0, 0])
fit_y_dist.append(cos_quartic(fit_x, *popt))
angle_offset_dist.append(popt[1])
a = popt[0]
b = popt[2]
a_dist.append(a)
b_dist.append(b)
popt_dist.append(popt)
fit_y_val, fit_y_err = bootstrap.average_and_std_arrays(fit_y_dist)
angle_offset_val, angle_offset_err = bootstrap.average_and_std_arrays(angle_offset_dist)
a_val, a_err = bootstrap.average_and_std_arrays(a_dist)
b_val, b_err = bootstrap.average_and_std_arrays(b_dist)
np.savetxt('_build/xy/harmonic-bare-data.tsv',
np.column_stack([angle, power_val, power_err]))
np.savetxt('_build/xy/harmonic-bare-fit.tsv',
np.column_stack([fit_x, fit_y_val]))
np.savetxt('_build/xy/harmonic-bare-band.tsv',
bootstrap.pgfplots_error_band(fit_x, fit_y_val, fit_y_err))
T['bare_angle_offset'] = siunitx(angle_offset_val, angle_offset_err)
T['bare_a'] = siunitx(a_val, a_err)
T['bare_b'] = siunitx(b_val, b_err)
def job_temperature_dependence(T):
data = np.loadtxt('Data/temperature.tsv')
temp = data[:, 0]
power_val = data[:, 1] * 1e-6
power_err = np.ones(power_val.shape) * 1e-6
power_dist = bootstrap.make_dist(power_val, power_err)
T['temperature_table'] = list(zip(
siunitx(temp),
siunitx(power_val*1e6, power_err*1e6),
))
p0 = [36.5, 1, 36-6, 2e-6]
fit_x = np.linspace(np.min(temp), np.max(temp), 300)
popt_dist = []
fit_y_dist = []
for power in power_dist:
popt, pconv = op.curve_fit(sinc, temp, power, p0=p0)
fit_y_dist.append(sinc(fit_x, *popt))
popt_dist.append(popt)
center_dist, width_dist, amplitude_dist, offset_dist = zip(*popt_dist)
center_val, center_err = bootstrap.average_and_std_arrays(center_dist)
width_val, width_err = bootstrap.average_and_std_arrays(width_dist)
amplitude_val, amplitude_err = bootstrap.average_and_std_arrays(amplitude_dist)
offset_val, offset_err = bootstrap.average_and_std_arrays(offset_dist)
fit_y_val, fit_y_err = bootstrap.average_and_std_arrays(fit_y_dist)
np.savetxt('_build/xy/temperature-data.tsv',
np.column_stack([temp, power_val, power_err]))
np.savetxt('_build/xy/temperature-fit.tsv',
np.column_stack([fit_x, fit_y_val]))
np.savetxt('_build/xy/temperature-band.tsv',
bootstrap.pgfplots_error_band(fit_x, fit_y_val, fit_y_err))
T['temp_center'] = siunitx(center_val, center_err)
T['temp_width'] = siunitx(width_val, width_err)
T['temp_amplitude'] = siunitx(amplitude_val, amplitude_err)
T['temp_offset'] = siunitx(offset_val, offset_err)
def job_harmonic_power(T, extinction_dist, input_popt_dist):
data = np.loadtxt('Data/harmonic_splitter.tsv')
angle = data[:, 0]
power_val = data[:, 1] * 1e-6
power_err = data[:, 2] * 1e-6
T['harmonic_splitter_table'] = list(zip(
siunitx(angle),
siunitx(power_val*1e6, power_err*1e6),
))
power_dist = bootstrap.make_dist(power_val, power_err)
fit_x = np.linspace(np.min(angle), np.max(angle), 200)
fit_y_dist = []
angle_offset_dist = []
a_dist = []
b_dist = []
popt_dist = []
for power in power_dist:
popt, pconv = op.curve_fit(cos_quartic, angle, power, p0=[1.5e-5, 0, 0])
fit_y_dist.append(cos_quartic(fit_x, *popt))
angle_offset_dist.append(popt[1])
a = popt[0]
b = popt[2]
a_dist.append(a)
b_dist.append(b)
popt_dist.append(popt)
fit_y_val, fit_y_err = bootstrap.average_and_std_arrays(fit_y_dist)
angle_offset_val, angle_offset_err = bootstrap.average_and_std_arrays(angle_offset_dist)
a_val, a_err = bootstrap.average_and_std_arrays(a_dist)
b_val, b_err = bootstrap.average_and_std_arrays(b_dist)
np.savetxt('_build/xy/harmonic-splitter-data.tsv',
np.column_stack([angle, power_val, power_err]))
np.savetxt('_build/xy/harmonic-splitter-fit.tsv',
np.column_stack([fit_x, fit_y_val]))
np.savetxt('_build/xy/harmonic-splitter-band.tsv',
bootstrap.pgfplots_error_band(fit_x, fit_y_val, fit_y_err))
T['splitter_angle_offset'] = siunitx(angle_offset_val, angle_offset_err)
T['splitter_a'] = siunitx(a_val, a_err)
T['splitter_b'] = siunitx(b_val, b_err)
efficiency_dist = []
efficiency_sq_dist = []
for extinction, input_popt, popt in zip(extinction_dist, input_popt_dist, popt_dist):
efficiency = popt[0] / (input_popt[0] * extinction)
efficiency_dist.append(efficiency)
efficiency_sq = popt[0] / (input_popt[0] * extinction)**2
efficiency_sq_dist.append(efficiency_sq)
efficiency_val, efficiency_err = bootstrap.average_and_std_arrays(efficiency_dist)
efficiency_sq_val, efficiency_sq_err = bootstrap.average_and_std_arrays(efficiency_sq_dist)
T['efficiency'] = siunitx(efficiency_val, efficiency_err)
T['efficiency_sq'] = siunitx(efficiency_sq_val, efficiency_sq_err)
def get_acryl_data(T, slope_val, width):
data = np.loadtxt('Data/longlong.txt')
channel = data[:, 0]
time = slope_val * channel
counts = data[:, 1]
x = np.linspace(np.min(time), np.max(time), 500)
fit_func = lambda t, mean, A_0, A_t, tau_0, tau_t, BG: \
np.log(models.lifetime_spectrum(t, mean, width, A_0, A_t, tau_0, tau_t, BG))
results = []
sel1 = (10.92 < time) & (time < 11.58)
sel2 = (13.11 < time) & (time < 22)
sels = [sel1, sel2]
x1 = np.linspace(np.min(time[sel1]), np.max(time[sel1]), 10)
x2 = np.linspace(np.min(time[sel2]), np.max(time[sel2]), 10)
for sample_id in range(BOOTSTRAP_SAMPLES):
print('Bootstrap sample', sample_id, 'running …')
boot_counts = bootstrap.redraw_count(counts)
lin_lifetimes = []
lin_results = []
for sel_lin, x_lin in zip(sels, [x1, x2]):
popt_lin, pconv_lin = op.curve_fit(exp_decay, time[sel_lin], boot_counts[sel_lin], p0=[1e5, 0.3])
y_lin = exp_decay(x_lin, *popt_lin)
lin_results.append(y_lin)
lin_results.append(popt_lin)
lin_results.append(1/popt_lin[1])
lin_lifetimes.append(1/popt_lin[1])
sel = (10 < time) & (time < 50) & (boot_counts > 0)
p0 = [10.5, 13e3, 34e2] + lin_lifetimes + [2]
popt, pconv = op.curve_fit(fit_func, time[sel], np.log(boot_counts[sel]), p0=p0)
mean, A_0, A_t, tau_0, tau_t, BG = popt
intens_0 = A_0 / (A_0 + A_t)
intens_t = A_t / (A_0 + A_t)
tau_bar = intens_0 * tau_0 + intens_t * tau_t
y = np.exp(fit_func(x, *popt))
tau_f = 1 / (intens_0 / tau_0 - intens_t / tau_t)
sigma_c = 1 / tau_0 - 1 / tau_f
results.append([
tau_0,
tau_bar,
tau_f,
tau_t,
intens_0,
intens_t,
y,
popt,
sigma_c,
] + lin_results)
tau_0_dist, tau_bar_dist, tau_f_dist, tau_t_dist, intens_0_dist, \
intens_t_dist, lifetime_y_dist, lifetime_popt_dist, sigma_c_dist, \
y_lin1_dist, popt_lin1_dist, tau_lin1_dist, \
y_lin2_dist, popt_lin2_dist, tau_lin2_dist, \
= zip(*results)
tau_0_val, tau_0_err = bootstrap.average_and_std_arrays(tau_0_dist)
tau_t_val, tau_t_err = bootstrap.average_and_std_arrays(tau_t_dist)
tau_f_val, tau_f_err = bootstrap.average_and_std_arrays(tau_f_dist)
tau_bar_val, tau_bar_err = bootstrap.average_and_std_arrays(tau_bar_dist)
popt_val, popt_err = bootstrap.average_and_std_arrays(lifetime_popt_dist)
y_val, y_err = bootstrap.average_and_std_arrays(lifetime_y_dist)
popt_lin1_val, popt_lin1_err = bootstrap.average_and_std_arrays(popt_lin1_dist)
y_lin1_val, y_lin1_err = bootstrap.average_and_std_arrays(y_lin1_dist)
tau_lin1_val, tau_lin1_err = bootstrap.average_and_std_arrays(tau_lin1_dist)
popt_lin2_val, popt_lin2_err = bootstrap.average_and_std_arrays(popt_lin2_dist)
y_lin2_val, y_lin2_err = bootstrap.average_and_std_arrays(y_lin2_dist)
tau_lin2_val, tau_lin2_err = bootstrap.average_and_std_arrays(tau_lin2_dist)
print('tau_0', siunitx(tau_0_val, tau_0_err))
print('tau_t', siunitx(tau_t_val, tau_t_err))
print('tau_f', siunitx(tau_f_val, tau_f_err))
print('tau_bar', siunitx(tau_bar_val, tau_bar_err))
T['acryl_tau_0'] = siunitx(tau_0_val, tau_0_err)
T['acryl_tau_t'] = siunitx(tau_t_val, tau_t_err)
T['acryl_tau_f'] = siunitx(tau_f_val, tau_f_err)
T['acryl_tau_bar'] = siunitx(tau_bar_val, tau_bar_err)
print('popt', siunitx(popt_val, popt_err))
print('popt_lin1', siunitx(popt_lin1_val, popt_lin1_err))
print('popt_lin2', siunitx(popt_lin2_val, popt_lin2_err))
print('tau_lin1', siunitx(tau_lin1_val, tau_lin1_err))
print('tau_lin2', siunitx(tau_lin2_val, tau_lin2_err))
T['acryl_tau_0_lin'] = siunitx(tau_lin1_val, tau_lin1_err)
T['acryl_tau_t_lin'] = siunitx(tau_lin2_val, tau_lin2_err)
print(x.shape)
print(y_lin1_val.shape)
pl.plot(time, counts, color='black', alpha=0.3)
counts_smooth = scipy.ndimage.filters.gaussian_filter1d(counts, 8)
pl.plot(time, counts_smooth, color='green')
pl.fill_between(x, y_val - y_err, y_val + y_err, alpha=0.5, color='red')
pl.plot(x, y_val, color='red')
pl.xlabel('Time / ns')
pl.ylabel('Counts')
dandify_plot()
#pl.xlim((8, 20))
pl.ylim((0.1, np.max(counts)*1.1))
pl.savefig('_build/mpl-lifetime-acryl.pdf')
pl.savefig('_build/mpl-lifetime-acryl.png')
pl.yscale('log')
pl.fill_between(x1, y_lin1_val - y_lin1_err, y_lin1_val + y_lin1_err, alpha=0.5, color='blue')
pl.fill_between(x2, y_lin2_val - y_lin2_err, y_lin2_val + y_lin2_err, alpha=0.5, color='blue')
pl.plot(x1, y_lin1_val, color='blue', alpha=0.5)
pl.plot(x2, y_lin2_val, color='blue', alpha=0.5)
dandify_plot()
pl.savefig('_build/mpl-lifetime-acryl-log.pdf')
pl.savefig('_build/mpl-lifetime-acryl-log.png')
#pl.show()
pl.clf()
np.savetxt('_build/xy/acryl-lifetime-data.tsv',
np.column_stack([time, counts]))
np.savetxt('_build/xy/acryl-lifetime-smoothed.tsv',
np.column_stack([time, counts_smooth]))
np.savetxt('_build/xy/acryl-lifetime-fit.tsv',
np.column_stack([x, y_val]))
np.savetxt('_build/xy/acryl-lifetime-band.tsv',
bootstrap.pgfplots_error_band(x, y_val, y_err))
np.savetxt('_build/xy/acryl-lifetime-fit-lin1.tsv',
np.column_stack([x1, y_lin1_val]))
np.savetxt('_build/xy/acryl-lifetime-band-lin1.tsv',
bootstrap.pgfplots_error_band(x1, y_lin1_val, y_lin1_err))
np.savetxt('_build/xy/acryl-lifetime-fit-lin2.tsv',
np.column_stack([x2, y_lin2_val]))
np.savetxt('_build/xy/acryl-lifetime-band-lin2.tsv',
bootstrap.pgfplots_error_band(x2, y_lin2_val, y_lin2_err))
def job_rayleigh_length(T):
beam_diameter_val = 3.5e-3
beam_diameter_err = 0.5e-3
refractive_index = 2.2
wavelength = 987e-9
length = 5e-3
distance = 60e-3
beam_radius_val = beam_diameter_val / 2
beam_radius_err = beam_diameter_err / 2
T['beam_radius'] = siunitx(beam_radius_val, beam_radius_err)
beam_radius_dist = bootstrap.make_dist(beam_radius_val, beam_diameter_err)
theta_dist = [
np.arctan(beam_radius / distance) for beam_radius in beam_radius_dist
]
theta_val, theta_err = bootstrap.average_and_std_arrays(theta_dist)
T['theta'] = siunitx(theta_val, theta_err)
bootstrap.save_hist(theta_dist, '_build/dist-theta.pdf')
waist_dist = [wavelength / (np.pi * theta) for theta in theta_dist]
waist_val, waist_err = bootstrap.average_and_std_arrays(waist_dist)
T['waist_mum'] = siunitx(waist_val / 1e-6, waist_err / 1e-6)
bootstrap.save_hist(waist_dist, '_build/dist-waist.pdf')
rayleigh_length_dist = list(
itertools.filterfalse(np.isnan, [
refractive_index * np.pi * waist**2 / wavelength
for waist in waist_dist
]))
rayleigh_length_val, rayleigh_length_err = bootstrap.average_and_std_arrays(
rayleigh_length_dist)
T['rayleigh_length_mm'] = siunitx(rayleigh_length_val / 1e-3,
rayleigh_length_err / 1e-3,
error_digits=2)
bootstrap.save_hist(rayleigh_length_dist,
'_build/dist-rayleigh_length.pdf')
normalized_length_dist = list([
length / (2 * rayleigh_length)
for rayleigh_length in rayleigh_length_dist
])
normalized_length_val, normalized_length_err = bootstrap.average_and_std_arrays(
normalized_length_dist)
T['normalized_length'] = siunitx(normalized_length_val,
normalized_length_err,
error_digits=2)
bootstrap.save_hist(normalized_length_dist,
'_build/dist-normalized_length.pdf')
t = (normalized_length_val - 2.84) / normalized_length_err
T['boyd_kleinman_ttest_t'] = siunitx(t)
optimal_focal_length_dist = list([
get_optimal_focal_length(beam_radius, refractive_index, wavelength,
length) for beam_radius in beam_radius_dist
])
optimal_focal_length_val, optimal_focal_length_err = bootstrap.average_and_std_arrays(
optimal_focal_length_dist)
T['optimal_focal_length_mm'] = siunitx(optimal_focal_length_val / 1e-3,
optimal_focal_length_err / 1e-3,
error_digits=2)
def main():
options = _parse_args()
R = 300
# Read in the data from the paper.
a_inv_val = 1616
a_inv_err = 20
a_inv_dist = bootstrap.make_dist(a_inv_val, a_inv_err, n=R)
aml, ams, l, t, trajectories, ampi_val, ampi_err, amk_val, amk_err, f_k_f_pi_val, f_k_f_pi_err = util.load_columns(
'physical_point/gmor.txt')
ampi_dist = bootstrap.make_dist(ampi_val, ampi_err, n=R)
amk_dist = bootstrap.make_dist(amk_val, amk_err, n=R)
mpi_dist = [ampi * a_inv for ampi, a_inv in zip(ampi_dist, a_inv_dist)]
mk_dist = [amk * a_inv for amk, a_inv in zip(amk_dist, a_inv_dist)]
# Convert the data in lattice units into physical units.
mpi_dist = [a_inv * ampi for ampi, a_inv in zip(ampi_dist, a_inv_dist)]
mpi_val, mpi_avg, mpi_err = bootstrap.average_and_std_arrays(mpi_dist)
mpi_sq_dist = [mpi**2 for mpi in mpi_dist]
mpi_sq_val, mpi_sq_avg, mpi_sq_err = bootstrap.average_and_std_arrays(
mpi_sq_dist)
ampi_sq_dist = [ampi**2 for ampi in ampi_dist]
ampi_sq_val, ampi_sq_avg, ampi_sq_err = bootstrap.average_and_std_arrays(
ampi_sq_dist)
# Do a GMOR fit in order to extract `a B` and `a m_cr`.
popt_dist = [
op.curve_fit(gmor_pion, aml, ampi_sq)[0] for ampi_sq in ampi_sq_dist
]
aB_dist = [popt[0] for popt in popt_dist]
amcr_dist = [popt[1] for popt in popt_dist]
aB_val, aB_avg, aB_err = bootstrap.average_and_std_arrays(aB_dist)
amcr_val, amcr_avg, amcr_err = bootstrap.average_and_std_arrays(amcr_dist)
print('aB =', siunitx(aB_val, aB_err))
print('am_cr =', siunitx(amcr_val, amcr_err))
ams_paper = -0.057
ams_phys = ams_paper - amcr_val
ams_red = 0.9 * ams_phys
ams_bare_red = ams_red + amcr_val
print(ams_paper, ams_phys, ams_red, ams_bare_red)
print()
print('Mass preconditioning masses:')
amlq = aml - amcr_val
for i in range(3):
amprec = amlq * 10**i + amcr_val
kappa = 1 / (amprec * 2 + 8)
print('a m_prec:', amprec)
print('κ', kappa)
exit()
diff_dist = [
np.sqrt(2) * np.sqrt(mk**2 - 0.5 * mpi**2)
for mpi, mk in zip(mpi_dist, mk_dist)
]
diff_val, diff_avg, diff_err = bootstrap.average_and_std_arrays(diff_dist)
popt_dist = [
op.curve_fit(linear, mpi, diff)[0]
for mpi, diff in zip(mpi_dist, diff_dist)
]
fit_x = np.linspace(np.min(mpi_dist), np.max(mpi_dist), 100)
fit_y_dist = [linear(fit_x, *popt) for popt in popt_dist]
fit_y_val, fit_y_avg, fit_y_err = bootstrap.average_and_std_arrays(
fit_y_dist)
# Physical meson masses from FLAG paper.
mpi_phys_dist = bootstrap.make_dist(134.8, 0.3, R)
mk_phys_dist = bootstrap.make_dist(494.2, 0.3, R)
mpi_phys_val, mpi_phys_avg, mpi_phys_err = bootstrap.average_and_std_arrays(
mpi_phys_dist)
ampi_phys_dist = [
mpi_phys / a_inv for a_inv, mpi_phys in zip(a_inv_dist, mpi_phys_dist)
]
amk_phys_dist = [
mk_phys / a_inv for a_inv, mk_phys in zip(a_inv_dist, mk_phys_dist)
]
ampi_phys_val, ampi_phys_avg, ampi_phys_err = bootstrap.average_and_std_arrays(
ampi_phys_dist)
amk_phys_val, amk_phys_avg, amk_phys_err = bootstrap.average_and_std_arrays(
amk_phys_dist)
print('aM_pi phys =', siunitx(ampi_phys_val, ampi_phys_err))
print('aM_k phys =', siunitx(amk_phys_val, amk_phys_err))
new_b_dist = [
np.sqrt(mk_phys**2 - 0.5 * mpi_phys**2) - popt[0] * mpi_phys for
mpi_phys, mk_phys, popt in zip(mpi_phys_dist, mk_phys_dist, popt_dist)
]
diff_sqrt_phys_dist = [
np.sqrt(mk_phys**2 - 0.5 * mpi_phys**2)
for mpi_phys, mk_phys in zip(mpi_phys_dist, mk_phys_dist)
]
diff_sqrt_phys_val, diff_sqrt_phys_avg, diff_sqrt_phys_err = bootstrap.average_and_std_arrays(
diff_sqrt_phys_dist)
ex_x = np.linspace(120, 700, 100)
ex_y_dist = [
linear(ex_x, popt[0], b) for popt, b in zip(popt_dist, new_b_dist)
]
ex_y_val, ex_y_avg, ex_y_err = bootstrap.average_and_std_arrays(ex_y_dist)
ams_art_dist = [
linear(mpi, popt[0], b)**2 / a_inv**2 / aB - amcr
for mpi, popt, b, a_inv, aB, amcr in zip(
mpi_dist, popt_dist, new_b_dist, a_inv_dist, aB_dist, amcr_dist)
]
ams_art_val, ams_art_avg, ams_art_err = bootstrap.average_and_std_arrays(
ams_art_dist)
print('a m_s with artifacts', siunitx(ams_art_val, ams_art_err))
fig, ax = util.make_figure()
ax.fill_between(fit_x,
fit_y_val + fit_y_err,
fit_y_val - fit_y_err,
color='red',
alpha=0.2)
ax.plot(fit_x, fit_y_val, label='Fit', color='red')
ax.fill_between(ex_x,
ex_y_val + ex_y_err,
ex_y_val - ex_y_err,
color='orange',
alpha=0.2)
ax.plot(ex_x, ex_y_val, label='Extrapolation', color='orange')
ax.errorbar(mpi_val,
diff_val,
xerr=mpi_err,
yerr=diff_err,
linestyle='none',
label='Data (Dürr 2010)')
ax.errorbar([mpi_phys_val], [diff_sqrt_phys_val],
xerr=[mpi_phys_err],
yerr=[diff_sqrt_phys_err],
label='Physical Point (Aoki)')
util.save_figure(fig, 'test')
np.savetxt('artifact-bmw-data.tsv',
np.column_stack([mpi_val, diff_val, mpi_err, diff_err]))
np.savetxt('artifact-bmw-fit.tsv', np.column_stack([fit_x, fit_y_val]))
np.savetxt('artifact-bmw-band.tsv',
bootstrap.pgfplots_error_band(fit_x, fit_y_val, fit_y_err))
np.savetxt(
'artifact-phys-data.tsv',
np.column_stack([[mpi_phys_val], [diff_sqrt_phys_val], [mpi_phys_err],
[diff_sqrt_phys_err]]))
np.savetxt('artifact-phys-fit.tsv', np.column_stack([ex_x, ex_y_val]))
np.savetxt('artifact-phys-band.tsv',
bootstrap.pgfplots_error_band(ex_x, ex_y_val, ex_y_err))
np.savetxt('artifact-ms.tsv',
np.column_stack([mpi_val, ams_art_val, mpi_err, ams_art_err]))
# Compute the strange quark mass that is needed to obtain a physical meson
# mass difference, ignoring lattice artifacts.
ams_phys_dist = [(amk_phys**2 - 0.5 * ampi_phys**2) / aB - amcr
for ampi_phys, amk_phys, aB, amcr in zip(
ampi_phys_dist, amk_phys_dist, aB_dist, amcr_dist)]
ams_phys_cen, ams_phys_val, ams_phys_err = bootstrap.average_and_std_arrays(
ams_phys_dist)
print('M_K = {} MeV <== am_s ='.format(siunitx(494.2, 0.3)),
siunitx(ams_phys_cen, ams_phys_err))
aml_phys_dist = [
op.newton(lambda aml: gmor_pion(aml, *popt) - ampi_phys**2,
np.min(aml))
for popt, ampi_phys in zip(popt_dist, ampi_phys_dist)
]
fit_x = np.linspace(np.min(aml_phys_dist), np.max(aml), 100)
fit_y_dist = [
np.sqrt(gmor_pion(fit_x, *popt)) * a_inv
for popt, a_inv in zip(popt_dist, a_inv_dist)
]
fit_y_cen, fit_y_val, fit_y_err = bootstrap.average_and_std_arrays(
fit_y_dist)
np.savetxt('physical_point/mpi-vs-aml-data.tsv',
np.column_stack([aml, mpi_val, mpi_err]))
np.savetxt('physical_point/mpi-vs-aml-fit.tsv',
np.column_stack([fit_x, fit_y_cen]))
np.savetxt('physical_point/mpi-vs-aml-band.tsv',
bootstrap.pgfplots_error_band(fit_x, fit_y_cen, fit_y_err))
aml_phys_val, aml_phys_avg, aml_phys_err = bootstrap.average_and_std_arrays(
aml_phys_dist)
mpi_cen, mpi_val, mpi_err = bootstrap.average_and_std_arrays(mpi_dist)
#aml_240_val, aml_240_avg, aml_240_err = bootstrap.average_and_std_arrays(aml_240_dist)
print('M_pi = {} MeV <== am_l ='.format(siunitx(134.8, 0.3)),
siunitx(aml_phys_val, aml_phys_err))
#print('M_pi = 240 MeV <== am_l =', siunitx(aml_240_val, aml_240_err))
fig = pl.figure()
ax = fig.add_subplot(2, 1, 1)
ax.fill_between(fit_x,
fit_y_val - fit_y_err,
fit_y_val + fit_y_err,
color='0.8')
ax.plot(fit_x, fit_y_val, color='black', label='GMOR Fit')
ax.errorbar(aml,
mpi_val,
yerr=mpi_err,
color='blue',
marker='+',
linestyle='none',
label='Data')
ax.errorbar([aml_phys_val], [135],
xerr=[aml_phys_err],
marker='+',
color='red',
label='Extrapolation')
#ax.errorbar([aml_240_val], [240], xerr=[aml_240_err], marker='+', color='red')
ax.set_title('Extrapolation to the Physical Point')
ax.set_xlabel(r'$a m_\mathrm{ud}$')
ax.set_ylabel(r'$M_\pi / \mathrm{MeV}$')
util.dandify_axes(ax)
ax = fig.add_subplot(2, 1, 2)
ax.hist(aml_phys_dist - aml_phys_val, bins=50)
ax.locator_params(nbins=6)
ax.set_title('Bootstrap Bias')
ax.set_xlabel(
r'$(a m_\mathrm{ud}^\mathrm{phys})^* - a m_\mathrm{ud}^\mathrm{phys}$')
util.dandify_axes(ax)
util.dandify_figure(fig)
fig.savefig('physical_point/GMOR.pdf')
np.savetxt('physical_point/ampi-sq-vs-aml.tsv',
np.column_stack([aml, ampi_sq_val, ampi_sq_err]))
np.savetxt('physical_point/mpi-sq-vs-aml.tsv',
np.column_stack([aml, mpi_sq_val, mpi_sq_err]))
def job_afb_analysis(T):
data = np.loadtxt('Data/radiative_corrections.tsv')
corrections = data[:, 1]
energies = np.loadtxt('Data/energies.txt')
data = np.loadtxt('Data/afb.txt')
negative = data[:, 0]
positive = data[:, 1]
results = []
for i in range(SAMPLES):
positive_boot = bootstrap.redraw_count(positive)
negative_boot = bootstrap.redraw_count(negative)
result = afb_kernel(positive_boot, negative_boot, corrections)
if result is not None:
results.append(result)
afb_corr_dist, sin_sq_dist = zip(*results)
afb_filt, sin_sq_filt = zip(*[(x[3], y)
for x, y in zip(afb_corr_dist, sin_sq_dist)
if not np.isnan(y)])
print('afb:', len(afb_corr_dist), len(afb_filt))
T['sin_sq_bootstrap_acceptance'] = siunitx(
(1 - len(sin_sq_filt) / len(sin_sq_dist)) * 100)
afb_val, afb_err = bootstrap.average_and_std_arrays(afb_corr_dist)
sin_sq_val, sin_sq_err = bootstrap.average_and_std_arrays(sin_sq_filt)
afb_val, sin_sq_val = afb_kernel(positive, negative, corrections)
sin_sq_up, sin_sq_down = bootstrap.percentile_arrays(
sin_sq_filt, sin_sq_val)
print('sin_sq:', sin_sq_val, sin_sq_err, sin_sq_up, sin_sq_down)
np.savetxt('_build/xy/afb.tsv',
np.column_stack([energies, afb_val, afb_err]))
T['afb_table'] = list(zip(
siunitx(energies),
siunitx(afb_val, afb_err),
))
T['sin_sq_afb'] = siunitx(sin_sq_val, sin_sq_err)
T['sin_sq_afb_asym'] = '{:.3f}^{{+{:.3f}}}_{{-{:.3f}}}'.format(
sin_sq_val, sin_sq_up, sin_sq_down)
counts, bins = np.histogram(sin_sq_filt)
counts = np.array(list(counts) + [counts[-1]])
print(bins.shape, counts.shape)
np.savetxt('_build/xy/sin_sq_hist.tsv', np.column_stack([bins, counts]))
counts, bins = np.histogram([x[3] for x in afb_corr_dist])
counts = np.array(list(counts) + [counts[-1]])
print(bins.shape, counts.shape)
np.savetxt('_build/xy/afb_hist.tsv', np.column_stack([bins, counts]))
counts, bins = np.histogram(afb_filt, bins=bins)
counts = np.array(list(counts) + [counts[-1]])
print(bins.shape, counts.shape)
np.savetxt('_build/xy/afb_filt_hist.tsv', np.column_stack([bins, counts]))
def bootstrap_driver(T):
# Load all the input data from the files.
lum_data = np.loadtxt('Data/luminosity.txt')
lum_val = lum_data[:, 0]
lum_err = lum_data[:, 3]
radiative_hadrons = np.loadtxt('Data/radiative-hadrons.tsv')
radiative_leptons = np.loadtxt('Data/radiative-leptons.tsv')
raw_matrix = np.loadtxt('Data/matrix.txt').T
mc_sizes = np.loadtxt('Data/monte-carlo-sizes.txt')
filtered = np.loadtxt('Data/filtered.txt')
# Some output into the template.
T['luminosities_table'] = list(zip(siunitx(energies), siunitx(lum_val, lum_err)))
T['radiative_cs_table'] = list(zip(
siunitx(energies),
siunitx(radiative_hadrons),
siunitx(radiative_leptons),
))
# Container for the results of each bootstrap run.
results = []
for r in range(SAMPLES):
# Draw new numbers for the matrix.
boot_matrix = bootstrap.redraw_count(raw_matrix)
# Draw new luminosities.
boot_lum_val = np.array([
random.gauss(val, err)
for val, err
in zip(lum_val, lum_err)])
# Draw new filtered readings.
boot_readings = bootstrap.redraw_count(filtered)
# Run the analysis on the resampled data and save the results.
results.append(bootstrap_kernel(mc_sizes, boot_matrix, boot_readings,
boot_lum_val, radiative_hadrons,
radiative_leptons))
# The `results` is a list which contains one entry per bootstrap run. This
# is not particularly helpful as the different interesting quantities are
# only on the second index on the list. The first index of the `results`
# list is the bootstrap run index. Therefore we use the `zip(*x)` trick to
# exchange the two indices. The result will be a list of quantities which
# are themselves lists of the bootstrap samples. Then using Python tuple
# assignments, we can split that (now) outer list into different
# quantities. Each of the new variables created here is a list of R
# bootstrap samples.
x_dist, masses_dist, widths_dist, cross_sections_dist, y_dist, corr_dist, \
matrix_dist, inverted_dist, readings_dist, peaks_dist, brs_dist, \
width_electron_dist, width_flavors_dist, missing_width_dist, \
width_lepton_dist, neutrino_families_dist, popts_dist, \
mean_mass_dist, mean_width_dist \
= zip(*results)
# We only need one of the lists of the x-values as they are all the same.
# So take the first and throw the others out.
x = x_dist[0]
# The masses and the widths that are given back from the `bootstrap_kernel`
# are a list of four elements (electrons, muons, tauons, hadrons) each. The
# variable `masses_dist` contains R copies of this four-list, one copy for
# each bootstrap sample. We now average along the bootstrap dimension, that
# is the outermost dimension. For each of the four masses, we take the
# average along the R copies. This will give us four masses and four
# masses-errors.
masses_val, masses_err = bootstrap.average_and_std_arrays(masses_dist)
widths_val, widths_err = bootstrap.average_and_std_arrays(widths_dist)
peaks_val, peaks_err = bootstrap.average_and_std_arrays(peaks_dist)
brs_val, brs_err = bootstrap.average_and_std_arrays(brs_dist)
T['brs'] = siunitx(brs_val[0:3], brs_err[0:3])
# Format masses and widths for the template.
T['lorentz_fits_table'] = list(zip(
display_names,
siunitx(masses_val, masses_err),
siunitx(widths_val, widths_err),
siunitx(peaks_val, peaks_err),
))
width_electron_val, width_electron_err = bootstrap.average_and_std_arrays(width_electron_dist)
width_flavors_val, width_flavors_err = bootstrap.average_and_std_arrays(width_flavors_dist)
T['width_electron_mev'] = siunitx(width_electron_val*1000, width_electron_err*1000)
T['width_flavors_mev'] = siunitx(width_flavors_val*1000, width_flavors_err*1000)
missing_width_val, missing_width_err = bootstrap.average_and_std_arrays(missing_width_dist)
width_lepton_val, width_lepton_err = bootstrap.average_and_std_arrays(width_lepton_dist)
neutrino_families_val, neutrino_families_err = bootstrap.average_and_std_arrays(neutrino_families_dist)
T['missing_width_mev'] = siunitx(missing_width_val*1000, missing_width_err*1000)
T['width_lepton_mev'] = siunitx(width_lepton_val*1000, width_lepton_err*1000)
T['neutrino_families'] = siunitx(neutrino_families_val, neutrino_families_err)
# Format original counts for the template.
val, err = bootstrap.average_and_std_arrays(readings_dist)
T['counts_table'] = []
for i in range(7):
T['counts_table'].append([siunitx(energies[i])] + siunitx(val[i, :], err[i, :], allowed_hang=10))
# Format corrected counts for the template.
val, err = bootstrap.average_and_std_arrays(corr_dist)
T['corrected_counts_table'] = []
for i in range(7):
T['corrected_counts_table'].append([siunitx(energies[i])] + siunitx(val[i, :], err[i, :], allowed_hang=10))
# Format matrix for the template.
matrix_val, matrix_err = bootstrap.average_and_std_arrays(matrix_dist)
T['matrix'] = []
for i in range(4):
T['matrix'].append([display_names[i]] + siunitx(matrix_val[i, :]*100, matrix_err[i, :]*100, allowed_hang=10))
# Format inverted matrix for the template.
inverted_val, inverted_err = bootstrap.average_and_std_arrays(inverted_dist)
T['inverted'] = []
for i in range(4):
T['inverted'].append([display_names[i]] +
list(map(number_padding,
siunitx(inverted_val[i, :], inverted_err[i, :], allowed_hang=10))))
# Format cross sections for the template.
cs_val, cs_err = bootstrap.average_and_std_arrays(cross_sections_dist)
T['cross_sections_table'] = []
for i in range(7):
T['cross_sections_table'].append([siunitx(energies[i])] + siunitx(cs_val[:, i], cs_err[:, i]))
# Build error band for pgfplots.
y_list_val, y_list_err = bootstrap.average_and_std_arrays(y_dist)
for i, name in zip(itertools.count(), names):
# Extract the y-values for the given decay type.
y_val = y_list_val[i, :]
y_err = y_list_err[i, :]
# Store the data for pgfplots.
np.savetxt('_build/xy/cross_section-{}s.tsv'.format(name),
np.column_stack([energies, cs_val[i, :], cs_err[i, :]]))
np.savetxt('_build/xy/cross_section-{}s-band.tsv'.format(name),
bootstrap.pgfplots_error_band(x, y_val, y_err))
np.savetxt('_build/xy/cross_section-{}s-fit.tsv'.format(name),
np.column_stack((x, y_val)))
popts_val, popts_err = bootstrap.average_and_std_arrays(popts_dist)
T['chi_sq'] = []
T['chi_sq_red'] = []
T['p'] = []
for i in range(4):
residuals = cs_val[i, :] - propagator(energies, *popts_val[i, :])
chi_sq = np.sum((residuals / cs_err[i, :])**2)
dof = len(residuals) - 1 - len(popts_val[i, :])
p = 1 - scipy.stats.chi2.cdf(chi_sq, dof)
print('chi_sq', chi_sq, chi_sq/dof, p)
T['chi_sq'].append(siunitx(chi_sq))
T['chi_sq_red'].append(siunitx(chi_sq/dof))
T['p'].append(siunitx(p))
T['confidence_table'] = list(zip(
display_names,
T['chi_sq'],
T['chi_sq_red'],
T['p'],
))
mean_mass_val, mean_mass_err = bootstrap.average_and_std_arrays(mean_mass_dist)
mean_width_val, mean_width_err = bootstrap.average_and_std_arrays(mean_width_dist)
T['mean_mass'] = siunitx(mean_mass_val, mean_mass_err)
T['mean_width'] = siunitx(mean_width_val, mean_width_err)
def time_gauge(T, show_gauss=False, show_lin=False):
time = []
channel_val = []
channel_err = []
# go through all six prompt-files
for i in range(1, 7):
time_raw = np.loadtxt('Data/prompt-{}.txt'.format(i))
channel = time_raw[:, 0]
counts = time_raw[:, 1]
if i == 1:
counts_tot = counts
elif i < 6:
counts_tot += counts
# bootstrap:
# - draw new counts from gaussian distribution with width of 'sqrt(N)'
# - fit gaussian distribution to drawn data
# - add mean to array
mean = []
width = []
amplitude = []
for a in range(BOOTSTRAP_SAMPLES):
boot_counts = redraw_count(counts)
popt, pconv = op.curve_fit(gauss,
channel,
boot_counts,
p0=[400 + i * 600, 200, 100])
mean.append(popt[0])
width.append(popt[1])
amplitude.append(popt[2])
# find average and standard deviation in arrays
mean_val, mean_err = bootstrap.average_and_std_arrays(mean)
width_val, width_err = bootstrap.average_and_std_arrays(width)
amplitude_val, amplitude_err = bootstrap.average_and_std_arrays(
amplitude)
# create files for prompt curve fits
x = np.linspace(mean_val - 200, mean_val + 200, 100)
y = gauss(x, mean_val, width_val, amplitude_val)
np.savetxt('_build/xy/prompt-{}-fit.txt'.format(i),
np.column_stack([x, y]))
# write result into new channel arrays
channel_val.append(mean_val)
channel_err.append(mean_err)
# write real time for gauging
time.append((i - 1) * 4)
# write files for prompt curve plotting
np.savetxt(
'_build/xy/prompts-short.txt',
bootstrap.pgfplots_error_band(channel[500:3500], counts_tot[500:3500],
np.sqrt(counts_tot[500:3500])))
np.savetxt(
'_build/xy/prompts-long.txt',
bootstrap.pgfplots_error_band(channel[3600:4200], counts[3600:4200],
np.sqrt(counts[3600:4200])))
# convert lists to arrays
channel_val = np.array(channel_val)
channel_err = np.array(channel_err)
time = np.array(time)
T['time_gauge_param'] = list(
zip(map(str, time), siunitx(channel_val, channel_err)))
# linear fit with delete-1-jackknife
slope = []
intercept = []
y_dist = []
x = np.linspace(750, 4000, 100)
for i in range(len(channel_val)):
channel_jackknife = np.delete(channel_val, i)
time_jackknife = np.delete(time, i)
popt, pconv = op.curve_fit(linear, channel_jackknife, time_jackknife)
slope.append(popt[0])
intercept.append(popt[1])
y = linear(x, *popt)
y_dist.append(y)
if show_lin:
x = np.linspace(0, 4000, 1000)
y = linear(x, *popt)
pl.plot(channel_val, time, linestyle="none", marker="o")
pl.plot(x, y)
pl.show()
pl.clf()
slope_val, slope_err = bootstrap.average_and_std_arrays(slope)
intercept_val, intercept_err = bootstrap.average_and_std_arrays(intercept)
y_val, y_err = bootstrap.average_and_std_arrays(y_dist)
# files for fit and plot of time gauge
np.savetxt('_build/xy/time_gauge_plot.txt',
np.column_stack([channel_val, time, channel_err]))
np.savetxt('_build/xy/time_gauge_fit.txt', np.column_stack([x, y_val]))
np.savetxt('_build/xy/time_gauge_band.txt',
bootstrap.pgfplots_error_band(x, y_val, y_err))
T['time_gauge_slope'] = siunitx(slope_val * 1e3, slope_err * 1e3)
T['time_gauge_intercept'] = siunitx(intercept_val, intercept_err)
# time resolution
T['width_6'] = siunitx(width_val, width_err)
FWHM_val = 2 * np.sqrt(2 * np.log(2)) * width_val
FWHM_err = 2 * np.sqrt(2 * np.log(2)) * width_err
T['FWHM_6'] = siunitx(FWHM_val, FWHM_err)
time_res = FWHM_val * slope_val
time_res_err = np.sqrt((FWHM_val * slope_err)**2 +
(FWHM_err * slope_val)**2)
T['time_resolution'] = siunitx(time_res, time_res_err)
return slope_val, width_val * slope_val
def job_harmonic_power(T, extinction_dist, input_popt_dist):
data = np.loadtxt('Data/harmonic_splitter.tsv')
angle = data[:, 0]
power_val = data[:, 1] * 1e-6
power_err = data[:, 2] * 1e-6
T['harmonic_splitter_table'] = list(
zip(
siunitx(angle),
siunitx(power_val * 1e6, power_err * 1e6),
))
power_dist = bootstrap.make_dist(power_val, power_err)
fit_x = np.linspace(np.min(angle), np.max(angle), 200)
fit_y_dist = []
angle_offset_dist = []
a_dist = []
b_dist = []
popt_dist = []
for power in power_dist:
popt, pconv = op.curve_fit(cos_quartic,
angle,
power,
p0=[1.5e-5, 0, 0])
fit_y_dist.append(cos_quartic(fit_x, *popt))
angle_offset_dist.append(popt[1])
a = popt[0]
b = popt[2]
a_dist.append(a)
b_dist.append(b)
popt_dist.append(popt)
fit_y_val, fit_y_err = bootstrap.average_and_std_arrays(fit_y_dist)
angle_offset_val, angle_offset_err = bootstrap.average_and_std_arrays(
angle_offset_dist)
a_val, a_err = bootstrap.average_and_std_arrays(a_dist)
b_val, b_err = bootstrap.average_and_std_arrays(b_dist)
np.savetxt('_build/xy/harmonic-splitter-data.tsv',
np.column_stack([angle, power_val, power_err]))
np.savetxt('_build/xy/harmonic-splitter-fit.tsv',
np.column_stack([fit_x, fit_y_val]))
np.savetxt('_build/xy/harmonic-splitter-band.tsv',
bootstrap.pgfplots_error_band(fit_x, fit_y_val, fit_y_err))
T['splitter_angle_offset'] = siunitx(angle_offset_val, angle_offset_err)
T['splitter_a'] = siunitx(a_val, a_err)
T['splitter_b'] = siunitx(b_val, b_err)
efficiency_dist = []
efficiency_sq_dist = []
for extinction, input_popt, popt in zip(extinction_dist, input_popt_dist,
popt_dist):
efficiency = popt[0] / (input_popt[0] * extinction)
efficiency_dist.append(efficiency)
efficiency_sq = popt[0] / (input_popt[0] * extinction)**2
efficiency_sq_dist.append(efficiency_sq)
efficiency_val, efficiency_err = bootstrap.average_and_std_arrays(
efficiency_dist)
efficiency_sq_val, efficiency_sq_err = bootstrap.average_and_std_arrays(
efficiency_sq_dist)
T['efficiency'] = siunitx(efficiency_val, efficiency_err)
T['efficiency_sq'] = siunitx(efficiency_sq_val, efficiency_sq_err)
def get_indium_data(T, slope_val, width):
files = glob.glob('Data/in-*.txt')
temps_val = []
temps_err = []
all_counts = []
all_tau_0_dist = []
all_tau_bar_dist = []
all_tau_f_dist = []
all_tau_t_dist = []
all_intens_0_dist = []
all_intens_t_dist = []
all_lifetime_y_dist = []
all_lifetime_popt_dist = []
all_sigma_c_dist = []
# Process lifetime curves with bootstrap.
for sample_id in range(BOOTSTRAP_SAMPLES):
print('Bootstrap sample', sample_id, 'running …')
results = []
for file_ in sorted(files):
print('Working on lifetime spectrum', file_)
if sample_id == 0:
temp_lower, temp_upper = get_temp(file_)
temp_mean = (temp_lower + temp_upper)/2
temp_err = temp_upper - temp_mean
temps_val.append(temp_mean)
temps_err.append(temp_err)
print('Mean temperature:', temp_mean)
data = np.loadtxt(file_)
channel = data[:, 0]
time = slope_val * channel
counts = data[:, 1]
boot_counts = bootstrap.redraw_count(counts)
if sample_id == 0:
all_counts.append(counts)
x = np.linspace(np.min(time), np.max(time), 2000)
sel = (9 < time) & (time < 15)
fit_func = lambda t, mean, A_0, A_t, tau_0, tau_t, BG: \
models.lifetime_spectrum(t, mean, width, A_0, A_t, tau_0, tau_t, BG)
p0 = [10.5, 210, 190, 0.07, 0.8, 0]
popt, pconv = op.curve_fit(fit_func, time[sel], boot_counts[sel], p0=p0)
mean, A_0, A_t, tau_0, tau_t, BG = popt
intens_0 = A_0 / (A_0 + A_t)
intens_t = A_t / (A_0 + A_t)
tau_bar = intens_0 * tau_0 + intens_t * tau_t
y = fit_func(x, *popt)
tau_f = 1 / (intens_0 / tau_0 - intens_t / tau_t)
sigma_c = 1 / tau_0 - 1 / tau_f
results.append([
tau_0,
tau_bar,
tau_f,
tau_t,
intens_0,
intens_t,
y,
popt,
sigma_c,
])
tau_0_list, tau_bar_list, tau_f_list, tau_t_list, intens_0_list, \
intens_t_list, lifetime_y_list, lifetime_popt_list, sigma_c_list \
= zip(*results)
all_tau_0_dist.append(tau_0_list)
all_tau_bar_dist.append(tau_bar_list)
all_tau_f_dist.append(tau_f_list)
all_tau_t_dist.append(tau_t_list)
all_intens_0_dist.append(intens_0_list)
all_intens_t_dist.append(intens_t_list)
all_lifetime_y_dist.append(lifetime_y_list)
all_lifetime_popt_dist.append(lifetime_popt_list)
all_sigma_c_dist.append(sigma_c_list)
T['temps_int'] = []
# Generate plots with lifetime curves and fits.
for temp, counts, lifetime_y_dist in zip(temps_val, all_counts, zip(*all_lifetime_y_dist)):
print('Creating lifetime plot with temp', temp)
y_val, y_err = bootstrap.average_and_std_arrays(lifetime_y_dist)
np.savetxt('_build/xy/lifetime-{}K-data.tsv'.format(int(temp)),
bootstrap.pgfplots_error_band(time[0:4000], counts[0:4000], np.sqrt(counts[0:4000])))
np.savetxt('_build/xy/lifetime-{}K-fit.tsv'.format(int(temp)),
np.column_stack([x, y_val]))
np.savetxt('_build/xy/lifetime-{}K-band.tsv'.format(int(temp)),
bootstrap.pgfplots_error_band(x, y_val, y_err))
T['temps_int'].append(int(temp))
if False:
pl.fill_between(x, y_val - y_err, y_val + y_err, alpha=0.5, color='red')
pl.plot(time, counts, color='black')
counts_smooth = scipy.ndimage.filters.gaussian_filter1d(counts, 8)
pl.plot(time, counts_smooth, color='green')
pl.plot(x, y_val, color='red')
pl.xlabel('Time / ns')
pl.ylabel('Counts')
dandify_plot()
pl.xlim((8, 20))
pl.savefig('_build/mpl-lifetime-{:04d}K.pdf'.format(int(temp)))
pl.savefig('_build/mpl-lifetime-{:04d}K.png'.format(int(temp)))
pl.yscale('log')
pl.savefig('_build/mpl-lifetime-{:04d}K-log.pdf'.format(int(temp)))
pl.savefig('_build/mpl-lifetime-{:04d}K-log.png'.format(int(temp)))
pl.clf()
T['temps_int'].sort()
# Plot the lifetimes.
taus_0_val, taus_0_err = bootstrap.average_and_std_arrays(all_tau_0_dist)
taus_t_val, taus_t_err = bootstrap.average_and_std_arrays(all_tau_t_dist)
taus_f_val, taus_f_err = bootstrap.average_and_std_arrays(all_tau_f_dist)
taus_bar_val, taus_bar_err = bootstrap.average_and_std_arrays(all_tau_bar_dist)
pl.errorbar(temps_val, taus_0_val, xerr=temps_err, yerr=taus_0_err,
label=r'$\tau_0$', linestyle='none', marker='+')
pl.errorbar(temps_val, taus_bar_val, xerr=temps_err, yerr=taus_bar_err,
label=r'$\bar\tau$', linestyle='none', marker='+')
pl.errorbar(temps_val, taus_t_val, xerr=temps_err, yerr=taus_t_err,
label=r'$\tau_\mathrm{t}$', linestyle='none', marker='+')
pl.errorbar(temps_val, taus_f_val, xerr=temps_err, yerr=taus_f_err,
label=r'$\tau_\mathrm{f}$', linestyle='none', marker='+')
pl.xlabel('T / K')
pl.ylabel(r'$\tau$ / ns')
dandify_plot()
pl.savefig('_build/mpl-tau_0-tau_t.pdf')
pl.savefig('_build/mpl-tau_0-tau_t.png')
pl.clf()
np.savetxt('_build/xy/tau_0.tsv',
np.column_stack([temps_val, taus_0_val, taus_0_err]))
np.savetxt('_build/xy/tau_t.tsv',
np.column_stack([temps_val, taus_t_val, taus_t_err]))
np.savetxt('_build/xy/tau_f.tsv',
np.column_stack([temps_val, taus_f_val, taus_f_err]))
np.savetxt('_build/xy/tau_bar.tsv',
np.column_stack([temps_val, taus_bar_val, taus_bar_err]))
T['taus_table'] = list(zip(
siunitx(temps_val, temps_err),
siunitx(taus_0_val, taus_0_err),
siunitx(taus_t_val, taus_t_err),
siunitx(taus_f_val, taus_f_err),
siunitx(taus_bar_val, taus_bar_err),
))
# Plot relative intensities.
all_intens_0_val, all_intens_0_err = bootstrap.average_and_std_arrays(all_intens_0_dist)
all_intens_t_val, all_intens_t_err = bootstrap.average_and_std_arrays(all_intens_t_dist)
pl.errorbar(temps_val, all_intens_0_val, xerr=temps_err, yerr=all_intens_0_err,
label=r'$A_0$', linestyle='none', marker='+')
pl.errorbar(temps_val, all_intens_t_val, xerr=temps_err, yerr=all_intens_t_err,
label=r'$A_\mathrm{t}$', linestyle='none', marker='+')
pl.xlabel('T / K')
pl.ylabel(r'Relative Intensity')
dandify_plot()
pl.savefig('_build/mpl-intensities.pdf')
pl.savefig('_build/mpl-intensities.png')
pl.clf()
np.savetxt('_build/xy/intensities-0.tsv',
np.column_stack([temps_val, all_intens_0_val, all_intens_0_err]))
np.savetxt('_build/xy/intensities-t.tsv',
np.column_stack([temps_val, all_intens_t_val, all_intens_t_err]))
T['intensities_table'] = list(zip(
siunitx(temps_val, temps_err),
siunitx(all_intens_0_val, all_intens_0_err),
siunitx(all_intens_t_val, all_intens_t_err),
))
inv_temps = 1 / np.array(temps_val)
results = []
x = np.linspace(np.min(inv_temps), np.max(inv_temps), 1000)
kelvin_to_eV = 8.621738e-5
for all_sigma_c in all_sigma_c_dist:
p0 = [11, 240]
print('inv_temps:', inv_temps)
print('all_sigma_c:', all_sigma_c)
for leave_out in range(len(all_sigma_c)):
inv_temps_jack = np.delete(inv_temps, leave_out)
all_sigma_c_jack = np.delete(all_sigma_c, leave_out)
popt, pconv = op.curve_fit(exp_decay, inv_temps_jack, all_sigma_c_jack, p0=p0)
y = exp_decay(x, *popt)
results.append([
popt,
popt[1] * kelvin_to_eV,
y,
])
popt_dist, Ht_eV_dist, arr_y_dist = zip(*results)
popt_val, popt_err = bootstrap.average_and_std_arrays(popt_dist)
print('popt:', siunitx(popt_val, popt_err))
Ht_eV_val, Ht_eV_err = bootstrap.average_and_std_arrays(Ht_eV_dist)
arr_y_val, arr_y_err = bootstrap.average_and_std_arrays(arr_y_dist)
sigma_c_val, sigma_c_err = bootstrap.average_and_std_arrays(all_sigma_c_dist)
pl.fill_between(x, arr_y_val - arr_y_err, arr_y_val + arr_y_err, alpha=0.5, color='red')
pl.plot(x, arr_y_val, color='red')
pl.errorbar(inv_temps, sigma_c_val, yerr=sigma_c_err, marker='+', linestyle='none', color='black')
pl.xlabel(r'$1 / T$')
pl.ylabel(r'$\sigma C_t(T)$')
pl.savefig('_build/mpl-arrhenius.pdf')
pl.savefig('_build/mpl-arrhenius.png')
pl.clf()
np.savetxt('_build/xy/arrhenius-data.tsv',
np.column_stack([inv_temps, sigma_c_val, sigma_c_err]))
np.savetxt('_build/xy/arrhenius-fit.tsv',
np.column_stack([x, arr_y_val]))
np.savetxt('_build/xy/arrhenius-band.tsv',
bootstrap.pgfplots_error_band(x, arr_y_val, arr_y_err))
T['arrhenius_table'] = list(zip(
siunitx(inv_temps),
siunitx(sigma_c_val, sigma_c_err),
))
print('Ht_eV:', siunitx(Ht_eV_val, Ht_eV_err))
T['Ht_eV'] = siunitx(Ht_eV_val, Ht_eV_err)
pl.errorbar(temps_val, taus_bar_val, xerr=temps_err, yerr=taus_bar_err,
label=r'$\bar\tau$', linestyle='none', marker='+')
dandify_plot()
pl.xlabel('T / K')
pl.ylabel(r'$\bar\tau$ / ns')
pl.savefig('_build/mpl-s_curve.pdf')
pl.savefig('_build/mpl-s_curve.png')
pl.clf()
np.savetxt('_build/xy/s_curve.tsv',
np.column_stack([temps_val, taus_bar_val, taus_bar_err]))
def michelson_resolution(T):
d_cm = np.sort(np.loadtxt('Data/lissajous_X.tsv'))
order = np.arange(0,len(d_cm))
wavelength = 987e-9
# get theoretical values
n_ground_theor = 1 + 1e-8 * (8342.13 + 2406030/(130-1/(wavelength*1e6)**2) + 15997/(38.9-1/(wavelength*1e6)**2))
T['n_ground_theor'] = siunitx(n_ground_theor - 1)
n_harm_theor = 1 + 1e-8 * (8342.13 + 2406030/(130-1/(wavelength*.5e6)**2) + 15997/(38.9-1/(wavelength*.5e6)**2))
T['n_harm_theor'] = siunitx(n_harm_theor - 1)
delta_n_theor = n_harm_theor - n_ground_theor
T['delta_n_theor'] = siunitx(delta_n_theor)
# prepare arrays
slope_dist_cm = []
offset_dist_cm = []
delta_n_dist = []
dev_ratio_dist = []
res_michelson_dist = []
fit_y_dist = []
# perform Jackknife
for i in range(len(d_cm)):
x = np.delete(order, i)
y = np.delete(d_cm, i)
popt, pconv = op.curve_fit(linear, x, y)
slope_dist_cm.append(popt[0])
offset_dist_cm.append(popt[1])
fit_y_dist.append(linear(order, *popt))
# experimental value for difference in refractive index
delta_n = wavelength/(8*popt[0]*1e-2)
delta_n_dist.append(delta_n)
# deviation from optimal 1/2 ratio
dev_ratio_dist.append(.5*delta_n/n_harm_theor)
# resolution of michelson interferometer
delta_wavelength = wavelength * (delta_n/n_ground_theor**2)
res_michelson_dist.append(wavelength/delta_wavelength)
# get averages and std
slope_val_cm, slope_err_cm = bootstrap.average_and_std_arrays(slope_dist_cm)
offset_val_cm, offset_err_cm = bootstrap.average_and_std_arrays(offset_dist_cm)
fit_y_val, fit_y_err = bootstrap.average_and_std_arrays(fit_y_dist)
delta_n_val, delta_n_err = bootstrap.average_and_std_arrays(delta_n_dist)
dev_ratio_val, dev_ratio_err = bootstrap.average_and_std_arrays(dev_ratio_dist)
dev_ratio_theor = .5*(delta_n_theor/n_harm_theor)
res_michelson_val, res_michelson_err = bootstrap.average_and_std_arrays(res_michelson_dist)
# write into T
T['distance_lissajous_X'] = siunitx(slope_val_cm, slope_err_cm)
T['delta_n'] = siunitx(delta_n_val, delta_n_err)
T['dev_ratio'] = siunitx(dev_ratio_val, dev_ratio_err)
T['dev_ratio_theor'] = siunitx(dev_ratio_theor)
T['res_michelson'] = siunitx(res_michelson_val, res_michelson_err)
# write data for plot
np.savetxt('_build/xy/michelson-line.tsv', np.column_stack([order, d_cm]))
np.savetxt('_build/xy/michelson-band.tsv', bootstrap.pgfplots_error_band(order, fit_y_val, fit_y_err))
T['mirror_position_table'] = list(zip(
siunitx(d_cm)
))
print(siunitx(dev_ratio_val, dev_ratio_err))
print(siunitx(dev_ratio_theor))
print(siunitx(res_michelson_val, res_michelson_err))
def job_power(T):
data = np.loadtxt('Data/diode.tsv')
norm_current = data[:, 0] * 1e-3
norm_power_val = data[:, 1] * 1e-3
norm_power_err = np.ones(norm_power_val.shape) * 1e-6
norm_power_dist = bootstrap.make_dist(norm_power_val, norm_power_err)
data = np.loadtxt('Data/diode_damped.tsv')
damp_current = data[:, 0] * 1e-3
damp_power_val = data[:, 1] * 1e-3
damp_power_err = data[:, 2] * 1e-3
damp_power_dist = bootstrap.make_dist(damp_power_val, damp_power_err)
np.savetxt('_build/xy/diode_normal-data.tsv',
np.column_stack([norm_current, norm_power_val, norm_power_err]))
np.savetxt('_build/xy/diode_damped-data.tsv',
np.column_stack([damp_current, damp_power_val, damp_power_err]))
T['diode_normal_table'] = list(
zip(
siunitx(norm_current * 1e3),
siunitx(norm_power_val * 1e6, norm_power_err * 1e6,
allowed_hang=6),
))
T['diode_damped_table'] = list(
zip(
siunitx(damp_current * 1e3),
siunitx(damp_power_val * 1e6, damp_power_err * 1e6),
))
hbar_omega = 6.626e-34 * 3e8 / 987e-9
electron_charge = 1.609e-19
# Find the threshold current.
sel = norm_power_val > 1e-3
slope_dist = []
quantum_efficiency_dist = []
threshold_dist = []
threshold_fit_x = np.linspace(0.05, 0.09, 100)
threshold_fit_y_dist = []
# Jackknife fit to find root.
for i in range(len(norm_power_val[sel])):
x = np.delete(norm_current[sel], i)
y_val = np.delete(norm_power_val[sel], i)
y_err = np.delete(norm_power_err[sel], i)
popt, pconv = op.curve_fit(linear, x, y_val, sigma=y_err)
a, b = popt
root = -b / a
threshold_dist.append(root)
threshold_fit_y_dist.append(linear(threshold_fit_x, *popt))
slope_dist.append(a)
quantum_efficiency_dist.append(a * electron_charge / hbar_omega)
threshold_val, threshold_err = bootstrap.average_and_std_arrays(
threshold_dist)
threshold_fit_y_val, threshold_fit_y_err = bootstrap.average_and_std_arrays(
threshold_fit_y_dist)
differential_efficiency_val, differential_efficiency_err = bootstrap.average_and_std_arrays(
slope_dist)
quantum_efficiency_val, quantum_efficiency_err = bootstrap.average_and_std_arrays(
quantum_efficiency_dist)
T['threshold'] = siunitx(threshold_val, threshold_err)
T['differential_efficiency'] = siunitx(differential_efficiency_val,
differential_efficiency_err)
T['quantum_efficiency'] = siunitx(quantum_efficiency_val,
quantum_efficiency_err)
np.savetxt(
'_build/xy/diode_normal-band.tsv',
bootstrap.pgfplots_error_band(threshold_fit_x, threshold_fit_y_val,
threshold_fit_y_err))
# Compare ratios of damped and normal power in the overlap range.
ratio_dist = []
x = np.linspace(70.1e-3, 86.9e-3, 20)
for norm_power, damp_power in zip(norm_power_dist, damp_power_dist):
norm_inter = scipy.interpolate.interp1d(norm_current, norm_power)
damp_inter = scipy.interpolate.interp1d(damp_current, damp_power)
a = norm_inter(x)
b = damp_inter(x)
ratio = a / b
ratio_dist.append(ratio)
ratio_val, ratio_err = bootstrap.average_and_std_arrays(ratio_dist)
extinction_dist = np.array(ratio_dist).flatten()
extinction_val, extinction_err = np.mean(ratio_dist), np.std(ratio_dist)
T['extinction'] = siunitx(extinction_val, extinction_err)
np.savetxt('_build/xy/diode-ratio-line.tsv',
np.column_stack([x, ratio_val]))
np.savetxt('_build/xy/diode-ratio-band.tsv',
bootstrap.pgfplots_error_band(x, ratio_val, ratio_err))
return extinction_dist
def job_power(T):
data = np.loadtxt('Data/diode.tsv')
norm_current = data[:, 0] * 1e-3
norm_power_val = data[:, 1] * 1e-3
norm_power_err = np.ones(norm_power_val.shape) * 1e-6
norm_power_dist = bootstrap.make_dist(norm_power_val, norm_power_err)
data = np.loadtxt('Data/diode_damped.tsv')
damp_current = data[:, 0] * 1e-3
damp_power_val = data[:, 1] * 1e-3
damp_power_err = data[:, 2] * 1e-3
damp_power_dist = bootstrap.make_dist(damp_power_val, damp_power_err)
np.savetxt('_build/xy/diode_normal-data.tsv',
np.column_stack([norm_current, norm_power_val, norm_power_err]))
np.savetxt('_build/xy/diode_damped-data.tsv',
np.column_stack([damp_current, damp_power_val, damp_power_err]))
T['diode_normal_table'] = list(zip(
siunitx(norm_current*1e3),
siunitx(norm_power_val*1e6, norm_power_err*1e6, allowed_hang=6),
))
T['diode_damped_table'] = list(zip(
siunitx(damp_current*1e3),
siunitx(damp_power_val*1e6, damp_power_err*1e6),
))
hbar_omega = 6.626e-34 * 3e8 / 987e-9
electron_charge = 1.609e-19
# Find the threshold current.
sel = norm_power_val > 1e-3
slope_dist = []
quantum_efficiency_dist = []
threshold_dist = []
threshold_fit_x = np.linspace(0.05, 0.09, 100)
threshold_fit_y_dist = []
# Jackknife fit to find root.
for i in range(len(norm_power_val[sel])):
x = np.delete(norm_current[sel], i)
y_val = np.delete(norm_power_val[sel], i)
y_err = np.delete(norm_power_err[sel], i)
popt, pconv = op.curve_fit(linear, x, y_val, sigma=y_err)
a, b = popt
root = -b / a
threshold_dist.append(root)
threshold_fit_y_dist.append(linear(threshold_fit_x, *popt))
slope_dist.append(a)
quantum_efficiency_dist.append(a * electron_charge / hbar_omega)
threshold_val, threshold_err = bootstrap.average_and_std_arrays(threshold_dist)
threshold_fit_y_val, threshold_fit_y_err = bootstrap.average_and_std_arrays(threshold_fit_y_dist)
differential_efficiency_val, differential_efficiency_err = bootstrap.average_and_std_arrays(slope_dist)
quantum_efficiency_val, quantum_efficiency_err = bootstrap.average_and_std_arrays(quantum_efficiency_dist)
T['threshold'] = siunitx(threshold_val, threshold_err)
T['differential_efficiency'] = siunitx(differential_efficiency_val, differential_efficiency_err)
T['quantum_efficiency'] = siunitx(quantum_efficiency_val, quantum_efficiency_err)
np.savetxt('_build/xy/diode_normal-band.tsv',
bootstrap.pgfplots_error_band(threshold_fit_x, threshold_fit_y_val, threshold_fit_y_err))
# Compare ratios of damped and normal power in the overlap range.
ratio_dist = []
x = np.linspace(70.1e-3, 86.9e-3, 20)
for norm_power, damp_power in zip(norm_power_dist, damp_power_dist):
norm_inter = scipy.interpolate.interp1d(norm_current, norm_power)
damp_inter = scipy.interpolate.interp1d(damp_current, damp_power)
a = norm_inter(x)
b = damp_inter(x)
ratio = a / b
ratio_dist.append(ratio)
ratio_val, ratio_err = bootstrap.average_and_std_arrays(ratio_dist)
extinction_dist = np.array(ratio_dist).flatten()
extinction_val, extinction_err = np.mean(ratio_dist), np.std(ratio_dist)
T['extinction'] = siunitx(extinction_val, extinction_err)
np.savetxt('_build/xy/diode-ratio-line.tsv',
np.column_stack([x, ratio_val]))
np.savetxt('_build/xy/diode-ratio-band.tsv',
bootstrap.pgfplots_error_band(x, ratio_val, ratio_err))
return extinction_dist
def time_gauge(T, show_gauss=False, show_lin=False):
time = []
channel_val = []
channel_err = []
# go through all six prompt-files
for i in range(1,7):
time_raw = np.loadtxt('Data/prompt-{}.txt'.format(i))
channel = time_raw[:,0]
counts = time_raw[:,1]
if i==1:
counts_tot = counts
elif i<6:
counts_tot += counts
# bootstrap:
# - draw new counts from gaussian distribution with width of 'sqrt(N)'
# - fit gaussian distribution to drawn data
# - add mean to array
mean = []
width = []
amplitude = []
for a in range(BOOTSTRAP_SAMPLES):
boot_counts = redraw_count(counts)
popt, pconv = op.curve_fit(gauss, channel, boot_counts, p0=[400+i*600, 200, 100])
mean.append(popt[0])
width.append(popt[1])
amplitude.append(popt[2])
# find average and standard deviation in arrays
mean_val, mean_err = bootstrap.average_and_std_arrays(mean)
width_val, width_err = bootstrap.average_and_std_arrays(width)
amplitude_val, amplitude_err = bootstrap.average_and_std_arrays(amplitude)
# create files for prompt curve fits
x = np.linspace(mean_val-200, mean_val+200, 100)
y = gauss(x, mean_val, width_val, amplitude_val)
np.savetxt('_build/xy/prompt-{}-fit.txt'.format(i), np.column_stack([x, y]))
# write result into new channel arrays
channel_val.append(mean_val)
channel_err.append(mean_err)
# write real time for gauging
time.append((i-1)*4)
# write files for prompt curve plotting
np.savetxt('_build/xy/prompts-short.txt',
bootstrap.pgfplots_error_band(channel[500:3500], counts_tot[500:3500], np.sqrt(counts_tot[500:3500])))
np.savetxt('_build/xy/prompts-long.txt',
bootstrap.pgfplots_error_band(channel[3600:4200], counts[3600:4200], np.sqrt(counts[3600:4200])))
# convert lists to arrays
channel_val = np.array(channel_val)
channel_err = np.array(channel_err)
time = np.array(time)
T['time_gauge_param'] = list(zip(
map(str, time),
siunitx(channel_val, channel_err)
))
# linear fit with delete-1-jackknife
slope = []
intercept = []
y_dist = []
x = np.linspace(750, 4000, 100)
for i in range(len(channel_val)):
channel_jackknife = np.delete(channel_val, i)
time_jackknife = np.delete(time, i)
popt, pconv = op.curve_fit(linear, channel_jackknife, time_jackknife)
slope.append(popt[0])
intercept.append(popt[1])
y = linear(x, *popt)
y_dist.append(y)
if show_lin:
x = np.linspace(0, 4000, 1000)
y = linear(x, *popt)
pl.plot(channel_val, time, linestyle="none", marker="o")
pl.plot(x, y)
pl.show()
pl.clf()
slope_val, slope_err = bootstrap.average_and_std_arrays(slope)
intercept_val, intercept_err = bootstrap.average_and_std_arrays(intercept)
y_val, y_err = bootstrap.average_and_std_arrays(y_dist)
# files for fit and plot of time gauge
np.savetxt('_build/xy/time_gauge_plot.txt',
np.column_stack([channel_val,time, channel_err]))
np.savetxt('_build/xy/time_gauge_fit.txt',
np.column_stack([x, y_val]))
np.savetxt('_build/xy/time_gauge_band.txt',
bootstrap.pgfplots_error_band(x, y_val, y_err))
T['time_gauge_slope'] = siunitx(slope_val*1e3, slope_err*1e3)
T['time_gauge_intercept'] = siunitx(intercept_val, intercept_err)
# time resolution
T['width_6'] = siunitx(width_val , width_err)
FWHM_val = 2*np.sqrt(2*np.log(2)) * width_val
FWHM_err = 2*np.sqrt(2*np.log(2)) * width_err
T['FWHM_6'] = siunitx(FWHM_val , FWHM_err)
time_res = FWHM_val * slope_val
time_res_err = np.sqrt((FWHM_val * slope_err)**2 + (FWHM_err * slope_val)**2)
T['time_resolution'] = siunitx(time_res , time_res_err)
return slope_val, width_val*slope_val
def get_acryl_data(T, slope_val, width):
data = np.loadtxt('Data/longlong.txt')
channel = data[:, 0]
time = slope_val * channel
counts = data[:, 1]
x = np.linspace(np.min(time), np.max(time), 500)
fit_func = lambda t, mean, A_0, A_t, tau_0, tau_t, BG: \
np.log(models.lifetime_spectrum(t, mean, width, A_0, A_t, tau_0, tau_t, BG))
results = []
sel1 = (10.92 < time) & (time < 11.58)
sel2 = (13.11 < time) & (time < 22)
sels = [sel1, sel2]
x1 = np.linspace(np.min(time[sel1]), np.max(time[sel1]), 10)
x2 = np.linspace(np.min(time[sel2]), np.max(time[sel2]), 10)
for sample_id in range(BOOTSTRAP_SAMPLES):
print('Bootstrap sample', sample_id, 'running …')
boot_counts = bootstrap.redraw_count(counts)
lin_lifetimes = []
lin_results = []
for sel_lin, x_lin in zip(sels, [x1, x2]):
popt_lin, pconv_lin = op.curve_fit(exp_decay,
time[sel_lin],
boot_counts[sel_lin],
p0=[1e5, 0.3])
y_lin = exp_decay(x_lin, *popt_lin)
lin_results.append(y_lin)
lin_results.append(popt_lin)
lin_results.append(1 / popt_lin[1])
lin_lifetimes.append(1 / popt_lin[1])
sel = (10 < time) & (time < 50) & (boot_counts > 0)
p0 = [10.5, 13e3, 34e2] + lin_lifetimes + [2]
popt, pconv = op.curve_fit(fit_func,
time[sel],
np.log(boot_counts[sel]),
p0=p0)
mean, A_0, A_t, tau_0, tau_t, BG = popt
intens_0 = A_0 / (A_0 + A_t)
intens_t = A_t / (A_0 + A_t)
tau_bar = intens_0 * tau_0 + intens_t * tau_t
y = np.exp(fit_func(x, *popt))
tau_f = 1 / (intens_0 / tau_0 - intens_t / tau_t)
sigma_c = 1 / tau_0 - 1 / tau_f
results.append([
tau_0,
tau_bar,
tau_f,
tau_t,
intens_0,
intens_t,
y,
popt,
sigma_c,
] + lin_results)
tau_0_dist, tau_bar_dist, tau_f_dist, tau_t_dist, intens_0_dist, \
intens_t_dist, lifetime_y_dist, lifetime_popt_dist, sigma_c_dist, \
y_lin1_dist, popt_lin1_dist, tau_lin1_dist, \
y_lin2_dist, popt_lin2_dist, tau_lin2_dist, \
= zip(*results)
tau_0_val, tau_0_err = bootstrap.average_and_std_arrays(tau_0_dist)
tau_t_val, tau_t_err = bootstrap.average_and_std_arrays(tau_t_dist)
tau_f_val, tau_f_err = bootstrap.average_and_std_arrays(tau_f_dist)
tau_bar_val, tau_bar_err = bootstrap.average_and_std_arrays(tau_bar_dist)
popt_val, popt_err = bootstrap.average_and_std_arrays(lifetime_popt_dist)
y_val, y_err = bootstrap.average_and_std_arrays(lifetime_y_dist)
popt_lin1_val, popt_lin1_err = bootstrap.average_and_std_arrays(
popt_lin1_dist)
y_lin1_val, y_lin1_err = bootstrap.average_and_std_arrays(y_lin1_dist)
tau_lin1_val, tau_lin1_err = bootstrap.average_and_std_arrays(
tau_lin1_dist)
popt_lin2_val, popt_lin2_err = bootstrap.average_and_std_arrays(
popt_lin2_dist)
y_lin2_val, y_lin2_err = bootstrap.average_and_std_arrays(y_lin2_dist)
tau_lin2_val, tau_lin2_err = bootstrap.average_and_std_arrays(
tau_lin2_dist)
print('tau_0', siunitx(tau_0_val, tau_0_err))
print('tau_t', siunitx(tau_t_val, tau_t_err))
print('tau_f', siunitx(tau_f_val, tau_f_err))
print('tau_bar', siunitx(tau_bar_val, tau_bar_err))
T['acryl_tau_0'] = siunitx(tau_0_val, tau_0_err)
T['acryl_tau_t'] = siunitx(tau_t_val, tau_t_err)
T['acryl_tau_f'] = siunitx(tau_f_val, tau_f_err)
T['acryl_tau_bar'] = siunitx(tau_bar_val, tau_bar_err)
print('popt', siunitx(popt_val, popt_err))
print('popt_lin1', siunitx(popt_lin1_val, popt_lin1_err))
print('popt_lin2', siunitx(popt_lin2_val, popt_lin2_err))
print('tau_lin1', siunitx(tau_lin1_val, tau_lin1_err))
print('tau_lin2', siunitx(tau_lin2_val, tau_lin2_err))
T['acryl_tau_0_lin'] = siunitx(tau_lin1_val, tau_lin1_err)
T['acryl_tau_t_lin'] = siunitx(tau_lin2_val, tau_lin2_err)
print(x.shape)
print(y_lin1_val.shape)
pl.plot(time, counts, color='black', alpha=0.3)
counts_smooth = scipy.ndimage.filters.gaussian_filter1d(counts, 8)
pl.plot(time, counts_smooth, color='green')
pl.fill_between(x, y_val - y_err, y_val + y_err, alpha=0.5, color='red')
pl.plot(x, y_val, color='red')
pl.xlabel('Time / ns')
pl.ylabel('Counts')
dandify_plot()
#pl.xlim((8, 20))
pl.ylim((0.1, np.max(counts) * 1.1))
pl.savefig('_build/mpl-lifetime-acryl.pdf')
pl.savefig('_build/mpl-lifetime-acryl.png')
pl.yscale('log')
pl.fill_between(x1,
y_lin1_val - y_lin1_err,
y_lin1_val + y_lin1_err,
alpha=0.5,
color='blue')
pl.fill_between(x2,
y_lin2_val - y_lin2_err,
y_lin2_val + y_lin2_err,
alpha=0.5,
color='blue')
pl.plot(x1, y_lin1_val, color='blue', alpha=0.5)
pl.plot(x2, y_lin2_val, color='blue', alpha=0.5)
dandify_plot()
pl.savefig('_build/mpl-lifetime-acryl-log.pdf')
pl.savefig('_build/mpl-lifetime-acryl-log.png')
#pl.show()
pl.clf()
np.savetxt('_build/xy/acryl-lifetime-data.tsv',
np.column_stack([time, counts]))
np.savetxt('_build/xy/acryl-lifetime-smoothed.tsv',
np.column_stack([time, counts_smooth]))
np.savetxt('_build/xy/acryl-lifetime-fit.tsv', np.column_stack([x, y_val]))
np.savetxt('_build/xy/acryl-lifetime-band.tsv',
bootstrap.pgfplots_error_band(x, y_val, y_err))
np.savetxt('_build/xy/acryl-lifetime-fit-lin1.tsv',
np.column_stack([x1, y_lin1_val]))
np.savetxt('_build/xy/acryl-lifetime-band-lin1.tsv',
bootstrap.pgfplots_error_band(x1, y_lin1_val, y_lin1_err))
np.savetxt('_build/xy/acryl-lifetime-fit-lin2.tsv',
np.column_stack([x2, y_lin2_val]))
np.savetxt('_build/xy/acryl-lifetime-band-lin2.tsv',
bootstrap.pgfplots_error_band(x2, y_lin2_val, y_lin2_err))
def main():
options = _parse_args()
# Read in the data.
data = np.genfromtxt('data.tsv')
y_val = data[:, 0]
y_err = data[:, 1]
x_val = data[:, 2]
x_err = data[:, 3]
rho = data[:, 4]
print('Data:')
print(data)
cov_xx = np.diag(x_err**2)
cov_yy = np.diag(y_err**2)
cov_xy = np.diag(rho * x_err * y_err)
cov = np.bmat([[cov_xx, cov_xy], [cov_xy, cov_yy]])
print('Covariance matrix:')
print(cov)
z_val = np.concatenate([x_val, y_val])
initial_guess = np.concatenate([x_val, [0.2]])
a_central = perform_fit(z_val, initial_guess, cov)
x = np.linspace(np.min(x_val), np.max(x_val), 100)
y = a_central * x**3
s = np.linalg.cholesky(cov).transpose()
a_dist = []
y_fit_dist = []
for sample in range(100):
r = np.random.normal(0, 1, 8)
z = s.dot(r) + z_val
a = perform_fit(z, initial_guess, cov)
y_fit = a * x**3
a_dist.append(a)
y_fit_dist.append(y_fit)
a_val, a_err = bootstrap.average_and_std_arrays(a_dist)
y_fit_val, y_fit_err = bootstrap.average_and_std_arrays(y_fit_dist)
print(a_central, a_val, a_err)
fig = pl.figure()
ax = fig.add_subplot(1, 1, 1)
ax.errorbar(x_val, y_val, xerr=x_err, yerr=y_err, marker='+', linestyle='none', color='blue')
ax.fill_between(x, y + y_fit_err, y - y_fit_err, color='black', alpha=0.2)
ax.plot(x, y, color='red')
ax.set_xlabel(r'$x$')
ax.set_ylabel(r'$y$')
dandify_axes(ax)
dandify_figure(fig)
fig.savefig('raw_data.pdf')
fig.savefig('raw_data.png')
print(conv)
def get_indium_data(T, slope_val, width):
files = glob.glob('Data/in-*.txt')
temps_val = []
temps_err = []
all_counts = []
all_tau_0_dist = []
all_tau_bar_dist = []
all_tau_f_dist = []
all_tau_t_dist = []
all_intens_0_dist = []
all_intens_t_dist = []
all_lifetime_y_dist = []
all_lifetime_popt_dist = []
all_sigma_c_dist = []
# Process lifetime curves with bootstrap.
for sample_id in range(BOOTSTRAP_SAMPLES):
print('Bootstrap sample', sample_id, 'running …')
results = []
for file_ in sorted(files):
print('Working on lifetime spectrum', file_)
if sample_id == 0:
temp_lower, temp_upper = get_temp(file_)
temp_mean = (temp_lower + temp_upper) / 2
temp_err = temp_upper - temp_mean
temps_val.append(temp_mean)
temps_err.append(temp_err)
print('Mean temperature:', temp_mean)
data = np.loadtxt(file_)
channel = data[:, 0]
time = slope_val * channel
counts = data[:, 1]
boot_counts = bootstrap.redraw_count(counts)
if sample_id == 0:
all_counts.append(counts)
x = np.linspace(np.min(time), np.max(time), 2000)
sel = (9 < time) & (time < 15)
fit_func = lambda t, mean, A_0, A_t, tau_0, tau_t, BG: \
models.lifetime_spectrum(t, mean, width, A_0, A_t, tau_0, tau_t, BG)
p0 = [10.5, 210, 190, 0.07, 0.8, 0]
popt, pconv = op.curve_fit(fit_func,
time[sel],
boot_counts[sel],
p0=p0)
mean, A_0, A_t, tau_0, tau_t, BG = popt
intens_0 = A_0 / (A_0 + A_t)
intens_t = A_t / (A_0 + A_t)
tau_bar = intens_0 * tau_0 + intens_t * tau_t
y = fit_func(x, *popt)
tau_f = 1 / (intens_0 / tau_0 - intens_t / tau_t)
sigma_c = 1 / tau_0 - 1 / tau_f
results.append([
tau_0,
tau_bar,
tau_f,
tau_t,
intens_0,
intens_t,
y,
popt,
sigma_c,
])
tau_0_list, tau_bar_list, tau_f_list, tau_t_list, intens_0_list, \
intens_t_list, lifetime_y_list, lifetime_popt_list, sigma_c_list \
= zip(*results)
all_tau_0_dist.append(tau_0_list)
all_tau_bar_dist.append(tau_bar_list)
all_tau_f_dist.append(tau_f_list)
all_tau_t_dist.append(tau_t_list)
all_intens_0_dist.append(intens_0_list)
all_intens_t_dist.append(intens_t_list)
all_lifetime_y_dist.append(lifetime_y_list)
all_lifetime_popt_dist.append(lifetime_popt_list)
all_sigma_c_dist.append(sigma_c_list)
T['temps_int'] = []
# Generate plots with lifetime curves and fits.
for temp, counts, lifetime_y_dist in zip(temps_val, all_counts,
zip(*all_lifetime_y_dist)):
print('Creating lifetime plot with temp', temp)
y_val, y_err = bootstrap.average_and_std_arrays(lifetime_y_dist)
np.savetxt(
'_build/xy/lifetime-{}K-data.tsv'.format(int(temp)),
bootstrap.pgfplots_error_band(time[0:4000], counts[0:4000],
np.sqrt(counts[0:4000])))
np.savetxt('_build/xy/lifetime-{}K-fit.tsv'.format(int(temp)),
np.column_stack([x, y_val]))
np.savetxt('_build/xy/lifetime-{}K-band.tsv'.format(int(temp)),
bootstrap.pgfplots_error_band(x, y_val, y_err))
T['temps_int'].append(int(temp))
if False:
pl.fill_between(x,
y_val - y_err,
y_val + y_err,
alpha=0.5,
color='red')
pl.plot(time, counts, color='black')
counts_smooth = scipy.ndimage.filters.gaussian_filter1d(counts, 8)
pl.plot(time, counts_smooth, color='green')
pl.plot(x, y_val, color='red')
pl.xlabel('Time / ns')
pl.ylabel('Counts')
dandify_plot()
pl.xlim((8, 20))
pl.savefig('_build/mpl-lifetime-{:04d}K.pdf'.format(int(temp)))
pl.savefig('_build/mpl-lifetime-{:04d}K.png'.format(int(temp)))
pl.yscale('log')
pl.savefig('_build/mpl-lifetime-{:04d}K-log.pdf'.format(int(temp)))
pl.savefig('_build/mpl-lifetime-{:04d}K-log.png'.format(int(temp)))
pl.clf()
T['temps_int'].sort()
# Plot the lifetimes.
taus_0_val, taus_0_err = bootstrap.average_and_std_arrays(all_tau_0_dist)
taus_t_val, taus_t_err = bootstrap.average_and_std_arrays(all_tau_t_dist)
taus_f_val, taus_f_err = bootstrap.average_and_std_arrays(all_tau_f_dist)
taus_bar_val, taus_bar_err = bootstrap.average_and_std_arrays(
all_tau_bar_dist)
pl.errorbar(temps_val,
taus_0_val,
xerr=temps_err,
yerr=taus_0_err,
label=r'$\tau_0$',
linestyle='none',
marker='+')
pl.errorbar(temps_val,
taus_bar_val,
xerr=temps_err,
yerr=taus_bar_err,
label=r'$\bar\tau$',
linestyle='none',
marker='+')
pl.errorbar(temps_val,
taus_t_val,
xerr=temps_err,
yerr=taus_t_err,
label=r'$\tau_\mathrm{t}$',
linestyle='none',
marker='+')
pl.errorbar(temps_val,
taus_f_val,
xerr=temps_err,
yerr=taus_f_err,
label=r'$\tau_\mathrm{f}$',
linestyle='none',
marker='+')
pl.xlabel('T / K')
pl.ylabel(r'$\tau$ / ns')
dandify_plot()
pl.savefig('_build/mpl-tau_0-tau_t.pdf')
pl.savefig('_build/mpl-tau_0-tau_t.png')
pl.clf()
np.savetxt('_build/xy/tau_0.tsv',
np.column_stack([temps_val, taus_0_val, taus_0_err]))
np.savetxt('_build/xy/tau_t.tsv',
np.column_stack([temps_val, taus_t_val, taus_t_err]))
np.savetxt('_build/xy/tau_f.tsv',
np.column_stack([temps_val, taus_f_val, taus_f_err]))
np.savetxt('_build/xy/tau_bar.tsv',
np.column_stack([temps_val, taus_bar_val, taus_bar_err]))
T['taus_table'] = list(
zip(
siunitx(temps_val, temps_err),
siunitx(taus_0_val, taus_0_err),
siunitx(taus_t_val, taus_t_err),
siunitx(taus_f_val, taus_f_err),
siunitx(taus_bar_val, taus_bar_err),
))
# Plot relative intensities.
all_intens_0_val, all_intens_0_err = bootstrap.average_and_std_arrays(
all_intens_0_dist)
all_intens_t_val, all_intens_t_err = bootstrap.average_and_std_arrays(
all_intens_t_dist)
pl.errorbar(temps_val,
all_intens_0_val,
xerr=temps_err,
yerr=all_intens_0_err,
label=r'$A_0$',
linestyle='none',
marker='+')
pl.errorbar(temps_val,
all_intens_t_val,
xerr=temps_err,
yerr=all_intens_t_err,
label=r'$A_\mathrm{t}$',
linestyle='none',
marker='+')
pl.xlabel('T / K')
pl.ylabel(r'Relative Intensity')
dandify_plot()
pl.savefig('_build/mpl-intensities.pdf')
pl.savefig('_build/mpl-intensities.png')
pl.clf()
np.savetxt(
'_build/xy/intensities-0.tsv',
np.column_stack([temps_val, all_intens_0_val, all_intens_0_err]))
np.savetxt(
'_build/xy/intensities-t.tsv',
np.column_stack([temps_val, all_intens_t_val, all_intens_t_err]))
T['intensities_table'] = list(
zip(
siunitx(temps_val, temps_err),
siunitx(all_intens_0_val, all_intens_0_err),
siunitx(all_intens_t_val, all_intens_t_err),
))
inv_temps = 1 / np.array(temps_val)
results = []
x = np.linspace(np.min(inv_temps), np.max(inv_temps), 1000)
kelvin_to_eV = 8.621738e-5
for all_sigma_c in all_sigma_c_dist:
p0 = [11, 240]
print('inv_temps:', inv_temps)
print('all_sigma_c:', all_sigma_c)
for leave_out in range(len(all_sigma_c)):
inv_temps_jack = np.delete(inv_temps, leave_out)
all_sigma_c_jack = np.delete(all_sigma_c, leave_out)
popt, pconv = op.curve_fit(exp_decay,
inv_temps_jack,
all_sigma_c_jack,
p0=p0)
y = exp_decay(x, *popt)
results.append([
popt,
popt[1] * kelvin_to_eV,
y,
])
popt_dist, Ht_eV_dist, arr_y_dist = zip(*results)
popt_val, popt_err = bootstrap.average_and_std_arrays(popt_dist)
print('popt:', siunitx(popt_val, popt_err))
Ht_eV_val, Ht_eV_err = bootstrap.average_and_std_arrays(Ht_eV_dist)
arr_y_val, arr_y_err = bootstrap.average_and_std_arrays(arr_y_dist)
sigma_c_val, sigma_c_err = bootstrap.average_and_std_arrays(
all_sigma_c_dist)
pl.fill_between(x,
arr_y_val - arr_y_err,
arr_y_val + arr_y_err,
alpha=0.5,
color='red')
pl.plot(x, arr_y_val, color='red')
pl.errorbar(inv_temps,
sigma_c_val,
yerr=sigma_c_err,
marker='+',
linestyle='none',
color='black')
pl.xlabel(r'$1 / T$')
pl.ylabel(r'$\sigma C_t(T)$')
pl.savefig('_build/mpl-arrhenius.pdf')
pl.savefig('_build/mpl-arrhenius.png')
pl.clf()
np.savetxt('_build/xy/arrhenius-data.tsv',
np.column_stack([inv_temps, sigma_c_val, sigma_c_err]))
np.savetxt('_build/xy/arrhenius-fit.tsv', np.column_stack([x, arr_y_val]))
np.savetxt('_build/xy/arrhenius-band.tsv',
bootstrap.pgfplots_error_band(x, arr_y_val, arr_y_err))
T['arrhenius_table'] = list(
zip(
siunitx(inv_temps),
siunitx(sigma_c_val, sigma_c_err),
))
print('Ht_eV:', siunitx(Ht_eV_val, Ht_eV_err))
T['Ht_eV'] = siunitx(Ht_eV_val, Ht_eV_err)
pl.errorbar(temps_val,
taus_bar_val,
xerr=temps_err,
yerr=taus_bar_err,
label=r'$\bar\tau$',
linestyle='none',
marker='+')
dandify_plot()
pl.xlabel('T / K')
pl.ylabel(r'$\bar\tau$ / ns')
pl.savefig('_build/mpl-s_curve.pdf')
pl.savefig('_build/mpl-s_curve.png')
pl.clf()
np.savetxt('_build/xy/s_curve.tsv',
np.column_stack([temps_val, taus_bar_val, taus_bar_err]))
def michelson_resolution(T):
d_cm = np.sort(np.loadtxt('Data/lissajous_X.tsv'))
order = np.arange(0, len(d_cm))
wavelength = 987e-9
# get theoretical values
n_ground_theor = 1 + 1e-8 * (8342.13 + 2406030 /
(130 - 1 / (wavelength * 1e6)**2) + 15997 /
(38.9 - 1 / (wavelength * 1e6)**2))
T['n_ground_theor'] = siunitx(n_ground_theor - 1)
n_harm_theor = 1 + 1e-8 * (8342.13 + 2406030 /
(130 - 1 / (wavelength * .5e6)**2) + 15997 /
(38.9 - 1 / (wavelength * .5e6)**2))
T['n_harm_theor'] = siunitx(n_harm_theor - 1)
delta_n_theor = n_harm_theor - n_ground_theor
T['delta_n_theor'] = siunitx(delta_n_theor)
# prepare arrays
slope_dist_cm = []
offset_dist_cm = []
delta_n_dist = []
dev_ratio_dist = []
res_michelson_dist = []
fit_y_dist = []
# perform Jackknife
for i in range(len(d_cm)):
x = np.delete(order, i)
y = np.delete(d_cm, i)
popt, pconv = op.curve_fit(linear, x, y)
slope_dist_cm.append(popt[0])
offset_dist_cm.append(popt[1])
fit_y_dist.append(linear(order, *popt))
# experimental value for difference in refractive index
delta_n = wavelength / (8 * popt[0] * 1e-2)
delta_n_dist.append(delta_n)
# deviation from optimal 1/2 ratio
dev_ratio_dist.append(.5 * delta_n / n_harm_theor)
# resolution of michelson interferometer
delta_wavelength = wavelength * (delta_n / n_ground_theor**2)
res_michelson_dist.append(wavelength / delta_wavelength)
# get averages and std
slope_val_cm, slope_err_cm = bootstrap.average_and_std_arrays(
slope_dist_cm)
offset_val_cm, offset_err_cm = bootstrap.average_and_std_arrays(
offset_dist_cm)
fit_y_val, fit_y_err = bootstrap.average_and_std_arrays(fit_y_dist)
delta_n_val, delta_n_err = bootstrap.average_and_std_arrays(delta_n_dist)
dev_ratio_val, dev_ratio_err = bootstrap.average_and_std_arrays(
dev_ratio_dist)
dev_ratio_theor = .5 * (delta_n_theor / n_harm_theor)
res_michelson_val, res_michelson_err = bootstrap.average_and_std_arrays(
res_michelson_dist)
# write into T
T['distance_lissajous_X'] = siunitx(slope_val_cm, slope_err_cm)
T['delta_n'] = siunitx(delta_n_val, delta_n_err)
T['dev_ratio'] = siunitx(dev_ratio_val, dev_ratio_err)
T['dev_ratio_theor'] = siunitx(dev_ratio_theor)
T['res_michelson'] = siunitx(res_michelson_val, res_michelson_err)
# write data for plot
np.savetxt('_build/xy/michelson-line.tsv', np.column_stack([order, d_cm]))
np.savetxt('_build/xy/michelson-band.tsv',
bootstrap.pgfplots_error_band(order, fit_y_val, fit_y_err))
T['mirror_position_table'] = list(zip(siunitx(d_cm)))
print(siunitx(dev_ratio_val, dev_ratio_err))
print(siunitx(dev_ratio_theor))
print(siunitx(res_michelson_val, res_michelson_err))
def job_afb_analysis(T):
data = np.loadtxt('Data/radiative_corrections.tsv')
corrections = data[:, 1]
energies = np.loadtxt('Data/energies.txt')
data = np.loadtxt('Data/afb.txt')
negative = data[:, 0]
positive = data[:, 1]
results = []
for i in range(SAMPLES):
positive_boot = bootstrap.redraw_count(positive)
negative_boot = bootstrap.redraw_count(negative)
result = afb_kernel(positive_boot, negative_boot, corrections)
if result is not None:
results.append(result)
afb_corr_dist, sin_sq_dist = zip(*results)
afb_filt, sin_sq_filt = zip(*[
(x[3], y)
for x, y in zip(afb_corr_dist, sin_sq_dist)
if not np.isnan(y)
])
print('afb:', len(afb_corr_dist), len(afb_filt))
T['sin_sq_bootstrap_acceptance'] = siunitx((1 - len(sin_sq_filt) / len(sin_sq_dist)) * 100)
afb_val, afb_err = bootstrap.average_and_std_arrays(afb_corr_dist)
sin_sq_val, sin_sq_err = bootstrap.average_and_std_arrays(sin_sq_filt)
afb_val, sin_sq_val = afb_kernel(positive, negative, corrections)
sin_sq_up, sin_sq_down = bootstrap.percentile_arrays(sin_sq_filt, sin_sq_val)
print('sin_sq:', sin_sq_val, sin_sq_err, sin_sq_up, sin_sq_down)
np.savetxt('_build/xy/afb.tsv', np.column_stack([energies, afb_val, afb_err]))
T['afb_table'] = list(zip(
siunitx(energies),
siunitx(afb_val, afb_err),
))
T['sin_sq_afb'] = siunitx(sin_sq_val, sin_sq_err)
T['sin_sq_afb_asym'] = '{:.3f}^{{+{:.3f}}}_{{-{:.3f}}}'.format(sin_sq_val, sin_sq_up, sin_sq_down)
counts, bins = np.histogram(sin_sq_filt)
counts = np.array(list(counts) + [counts[-1]])
print(bins.shape, counts.shape)
np.savetxt('_build/xy/sin_sq_hist.tsv', np.column_stack([bins, counts]))
counts, bins = np.histogram([x[3] for x in afb_corr_dist])
counts = np.array(list(counts) + [counts[-1]])
print(bins.shape, counts.shape)
np.savetxt('_build/xy/afb_hist.tsv', np.column_stack([bins, counts]))
counts, bins = np.histogram(afb_filt, bins=bins)
counts = np.array(list(counts) + [counts[-1]])
print(bins.shape, counts.shape)
np.savetxt('_build/xy/afb_filt_hist.tsv', np.column_stack([bins, counts]))
def bootstrap_driver(T):
# Load all the input data from the files.
lum_data = np.loadtxt('Data/luminosity.txt')
lum_val = lum_data[:, 0]
lum_err = lum_data[:, 3]
radiative_hadrons = np.loadtxt('Data/radiative-hadrons.tsv')
radiative_leptons = np.loadtxt('Data/radiative-leptons.tsv')
raw_matrix = np.loadtxt('Data/matrix.txt').T
mc_sizes = np.loadtxt('Data/monte-carlo-sizes.txt')
filtered = np.loadtxt('Data/filtered.txt')
# Some output into the template.
T['luminosities_table'] = list(
zip(siunitx(energies), siunitx(lum_val, lum_err)))
T['radiative_cs_table'] = list(
zip(
siunitx(energies),
siunitx(radiative_hadrons),
siunitx(radiative_leptons),
))
# Container for the results of each bootstrap run.
results = []
for r in range(SAMPLES):
# Draw new numbers for the matrix.
boot_matrix = bootstrap.redraw_count(raw_matrix)
# Draw new luminosities.
boot_lum_val = np.array(
[random.gauss(val, err) for val, err in zip(lum_val, lum_err)])
# Draw new filtered readings.
boot_readings = bootstrap.redraw_count(filtered)
# Run the analysis on the resampled data and save the results.
results.append(
bootstrap_kernel(mc_sizes, boot_matrix, boot_readings,
boot_lum_val, radiative_hadrons,
radiative_leptons))
# The `results` is a list which contains one entry per bootstrap run. This
# is not particularly helpful as the different interesting quantities are
# only on the second index on the list. The first index of the `results`
# list is the bootstrap run index. Therefore we use the `zip(*x)` trick to
# exchange the two indices. The result will be a list of quantities which
# are themselves lists of the bootstrap samples. Then using Python tuple
# assignments, we can split that (now) outer list into different
# quantities. Each of the new variables created here is a list of R
# bootstrap samples.
x_dist, masses_dist, widths_dist, cross_sections_dist, y_dist, corr_dist, \
matrix_dist, inverted_dist, readings_dist, peaks_dist, brs_dist, \
width_electron_dist, width_flavors_dist, missing_width_dist, \
width_lepton_dist, neutrino_families_dist, popts_dist, \
mean_mass_dist, mean_width_dist \
= zip(*results)
# We only need one of the lists of the x-values as they are all the same.
# So take the first and throw the others out.
x = x_dist[0]
# The masses and the widths that are given back from the `bootstrap_kernel`
# are a list of four elements (electrons, muons, tauons, hadrons) each. The
# variable `masses_dist` contains R copies of this four-list, one copy for
# each bootstrap sample. We now average along the bootstrap dimension, that
# is the outermost dimension. For each of the four masses, we take the
# average along the R copies. This will give us four masses and four
# masses-errors.
masses_val, masses_err = bootstrap.average_and_std_arrays(masses_dist)
widths_val, widths_err = bootstrap.average_and_std_arrays(widths_dist)
peaks_val, peaks_err = bootstrap.average_and_std_arrays(peaks_dist)
brs_val, brs_err = bootstrap.average_and_std_arrays(brs_dist)
T['brs'] = siunitx(brs_val[0:3], brs_err[0:3])
# Format masses and widths for the template.
T['lorentz_fits_table'] = list(
zip(
display_names,
siunitx(masses_val, masses_err),
siunitx(widths_val, widths_err),
siunitx(peaks_val, peaks_err),
))
width_electron_val, width_electron_err = bootstrap.average_and_std_arrays(
width_electron_dist)
width_flavors_val, width_flavors_err = bootstrap.average_and_std_arrays(
width_flavors_dist)
T['width_electron_mev'] = siunitx(width_electron_val * 1000,
width_electron_err * 1000)
T['width_flavors_mev'] = siunitx(width_flavors_val * 1000,
width_flavors_err * 1000)
missing_width_val, missing_width_err = bootstrap.average_and_std_arrays(
missing_width_dist)
width_lepton_val, width_lepton_err = bootstrap.average_and_std_arrays(
width_lepton_dist)
neutrino_families_val, neutrino_families_err = bootstrap.average_and_std_arrays(
neutrino_families_dist)
T['missing_width_mev'] = siunitx(missing_width_val * 1000,
missing_width_err * 1000)
T['width_lepton_mev'] = siunitx(width_lepton_val * 1000,
width_lepton_err * 1000)
T['neutrino_families'] = siunitx(neutrino_families_val,
neutrino_families_err)
# Format original counts for the template.
val, err = bootstrap.average_and_std_arrays(readings_dist)
T['counts_table'] = []
for i in range(7):
T['counts_table'].append(
[siunitx(energies[i])] +
siunitx(val[i, :], err[i, :], allowed_hang=10))
# Format corrected counts for the template.
val, err = bootstrap.average_and_std_arrays(corr_dist)
T['corrected_counts_table'] = []
for i in range(7):
T['corrected_counts_table'].append(
[siunitx(energies[i])] +
siunitx(val[i, :], err[i, :], allowed_hang=10))
# Format matrix for the template.
matrix_val, matrix_err = bootstrap.average_and_std_arrays(matrix_dist)
T['matrix'] = []
for i in range(4):
T['matrix'].append([display_names[i]] + siunitx(
matrix_val[i, :] * 100, matrix_err[i, :] * 100, allowed_hang=10))
# Format inverted matrix for the template.
inverted_val, inverted_err = bootstrap.average_and_std_arrays(
inverted_dist)
T['inverted'] = []
for i in range(4):
T['inverted'].append([display_names[i]] + list(
map(
number_padding,
siunitx(
inverted_val[i, :], inverted_err[i, :], allowed_hang=10))))
# Format cross sections for the template.
cs_val, cs_err = bootstrap.average_and_std_arrays(cross_sections_dist)
T['cross_sections_table'] = []
for i in range(7):
T['cross_sections_table'].append([siunitx(energies[i])] +
siunitx(cs_val[:, i], cs_err[:, i]))
# Build error band for pgfplots.
y_list_val, y_list_err = bootstrap.average_and_std_arrays(y_dist)
for i, name in zip(itertools.count(), names):
# Extract the y-values for the given decay type.
y_val = y_list_val[i, :]
y_err = y_list_err[i, :]
# Store the data for pgfplots.
np.savetxt('_build/xy/cross_section-{}s.tsv'.format(name),
np.column_stack([energies, cs_val[i, :], cs_err[i, :]]))
np.savetxt('_build/xy/cross_section-{}s-band.tsv'.format(name),
bootstrap.pgfplots_error_band(x, y_val, y_err))
np.savetxt('_build/xy/cross_section-{}s-fit.tsv'.format(name),
np.column_stack((x, y_val)))
popts_val, popts_err = bootstrap.average_and_std_arrays(popts_dist)
T['chi_sq'] = []
T['chi_sq_red'] = []
T['p'] = []
for i in range(4):
residuals = cs_val[i, :] - propagator(energies, *popts_val[i, :])
chi_sq = np.sum((residuals / cs_err[i, :])**2)
dof = len(residuals) - 1 - len(popts_val[i, :])
p = 1 - scipy.stats.chi2.cdf(chi_sq, dof)
print('chi_sq', chi_sq, chi_sq / dof, p)
T['chi_sq'].append(siunitx(chi_sq))
T['chi_sq_red'].append(siunitx(chi_sq / dof))
T['p'].append(siunitx(p))
T['confidence_table'] = list(
zip(
display_names,
T['chi_sq'],
T['chi_sq_red'],
T['p'],
))
mean_mass_val, mean_mass_err = bootstrap.average_and_std_arrays(
mean_mass_dist)
mean_width_val, mean_width_err = bootstrap.average_and_std_arrays(
mean_width_dist)
T['mean_mass'] = siunitx(mean_mass_val, mean_mass_err)
T['mean_width'] = siunitx(mean_width_val, mean_width_err)