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 test_negative_error(self):
unitprint.siunitx(1.0, -0.5)
def test_siunitx_array_loop(self):
x = np.array([1, 2, 3])
out = unitprint.siunitx(x)
def test_zero_error(self):
unitprint.siunitx(1.0, 0.0)
def test_to_siunitx_3(self):
self.assertEqual("12 +- 1", unitprint.siunitx(12.3, 1.23))