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_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 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 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_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 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 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)