def show(data, arg_dict):
"""Display the mean value, estimated auto-correlaton and error
thereof."""
for label in sorted(data.keys()):
print "* label:", label
for o in arg_dict["orders"]:
print " * order:", o
mean, delta, tint, dtint = tauint(data[label].data, o, plots=arg_dict["uwplot"])
print " mean:", pretty_print(mean, delta)
print " tint:", pretty_print(tint, dtint)
def show(data, arg_dict):
"""Display the mean value, estimated auto-correlaton and error
thereof."""
for label in sorted(data.keys()):
print "* label:", label
for o in arg_dict["orders"]:
print " * order:", o
mean, delta, tint, dtint = tauint(data[label].data,
o,
plots=arg_dict['uwplot'])
print " mean:", pretty_print(mean, delta)
print " tint:", pretty_print(tint, dtint)
def therm(data, arg_dict):
"""Estimate thermalization effects, make a plot."""
for label in sorted(data.keys()):
print "* label:", label
for o in arg_dict["orders"]:
ydata = []
dydata = []
print " * order:", o
for nc in arg_dict["cutoffs"]:
mean, delta, tint, dtint = tauint(data[label].data[:, :, nc:], o)
ydata.append(mean)
dydata.append(delta)
plt.errorbar(arg_dict["cutoffs"], ydata, yerr=dydata)
plt.show()
def therm(data, arg_dict):
"""Estimate thermalization effects, make a plot."""
for label in sorted(data.keys()):
print "* label:", label
for o in arg_dict["orders"]:
ydata = []
dydata = []
print " * order:", o
for nc in arg_dict['cutoffs']:
mean, delta, tint, dtint = \
tauint(data[label].data[:,:,nc:], o)
ydata.append(mean)
dydata.append(delta)
plt.errorbar(arg_dict['cutoffs'], ydata, yerr=dydata)
plt.show()
def test_with_correlated_data_single_replicum(self):
r"""Check the :class:`puwr.tauint` method with the
:class:`puwr.correlated_data` method. Note that this is a
statistical test with random numbers. We test for a
:math:`3\sigma` deviation here, which is unlikely but not
impossible. If this test fails, re-run a few times before
making any conclusions."""
fails = 0
for known_tau in np.linspace(2, 20, 20):
data = correlated_data(known_tau)
mean, err, tau, dtau = tauint(data, 0)
if tau - 3*dtau > known_tau or \
tau + 3*dtau < known_tau:
print tau - known_tau, dtau
fails += 1
self.assertGreaterEqual(1, fails)
def test_secondary_multiple_replica_product(self):
"""Test using the product of two observables."""
fails = 0
for known_tau in np.linspace(2,20,10):
data = [[correlated_data(known_tau)[0][0],
correlated_data(known_tau)[0][0],
correlated_data(known_tau)[0][0]],
[correlated_data(known_tau)[0][0],
correlated_data(known_tau)[0][0],
correlated_data(known_tau)[0][0]]]
mean, err, tau, dtau = tauint(data, lambda x, y: x * y)
if tau - 3*dtau > known_tau or \
tau + 3*dtau < known_tau:
print tau - known_tau, dtau
fails += 1
self.assertGreaterEqual(0, fails)
def test_with_correlated_data_single_replicum(self):
r"""Check the :class:`puwr.tauint` method with the
:class:`puwr.correlated_data` method. Note that this is a
statistical test with random numbers. We test for a
:math:`3\sigma` deviation here, which is unlikely but not
impossible. If this test fails, re-run a few times before
making any conclusions."""
fails = 0
for known_tau in np.linspace(2,20,20):
data = correlated_data(known_tau)
mean, err, tau, dtau = tauint(data, 0)
if tau - 3*dtau > known_tau or \
tau + 3*dtau < known_tau:
print tau - known_tau, dtau
fails += 1
self.assertGreaterEqual(1, fails)
def extrapolate(data, arg_dict, f=(lambda x: 1., lambda x: x)):
"""Extrapolate data. Optionally make a plot."""
# check if target lattice sizes are given
# if not, do the extrapolation for all lattice sizes
if not arg_dict['L_sizes']:
arg_dict['L_sizes'] = sorted(set([d.L for d in data.values()]))
for o in arg_dict["orders"]:
print " * order = g^" + str(o)
x, y, dy, cl, dcl, ffn = [], [], [], [], [], []
for L in arg_dict['L_sizes']:
print " * L =", L
[i.append([]) for i in x, y, dy]
for label in data:
if data[label].L != L:
continue
print " ** label:", label
mean, delta, tint, dtint = \
tauint(data[label].data, o, plots=arg_dict['uwplot'])
x[-1].append(data[label].tau)
y[-1].append(mean)
dy[-1].append(delta)
print " mean:", pretty_print(mean, delta)
print " tint:", pretty_print(tint, dtint)
print " ** tau -> 0 limit"
coeffs, errors = extrapolate_cl(f, x[-1], y[-1], dy[-1])
ffn.append(
lambda x: np.sum(c[0, 0] * f(x) for c, f in zip(coeffs, f)))
cl.append(coeffs[0, 0])
dcl.append(errors[0, 0]**0.5)
sxsq = sum(xx**2 for xx in x[-1])
sx = sum(x[-1])
sa = np.sqrt(
sum(((sxsq - sx * xx) / (3 * sxsq - sx**2))**2 * yy**2
for xx, yy in zip(x[-1], dy[-1])))
assert (abs((dcl[-1] - sa) / sa) < 1e-12)
print " cl:", pretty_print(cl[-1], dcl[-1])
print " " + "*" * 50
for plt in (p for p in arg_dict["mk_plots"]
if L in p.L and o in p.orders):
plt.data.append((x[-1], y[-1], dy[-1]))
plt.cl.append((cl[-1], dcl[-1]))
fnx = np.linspace(0, max(x[-1]), 100)
plt.fit.append((fnx, [ffn[-1](i) for i in fnx]))
plt.labels.append("$L = {0}$".format(L))
for plt in arg_dict["mk_plots"]:
mk_plot(plt)
def extrapolate(data, arg_dict, f=(lambda x: 1.0, lambda x: x)):
"""Extrapolate data. Optionally make a plot."""
# check if target lattice sizes are given
# if not, do the extrapolation for all lattice sizes
if not arg_dict["L_sizes"]:
arg_dict["L_sizes"] = sorted(set([d.L for d in data.values()]))
for o in arg_dict["orders"]:
print " * order = g^" + str(o)
x, y, dy, cl, dcl, ffn = [], [], [], [], [], []
for L in arg_dict["L_sizes"]:
print " * L =", L
[i.append([]) for i in x, y, dy]
for label in data:
if data[label].L != L:
continue
print " ** label:", label
mean, delta, tint, dtint = tauint(data[label].data, o, plots=arg_dict["uwplot"])
x[-1].append(data[label].tau)
y[-1].append(mean)
dy[-1].append(delta)
print " mean:", pretty_print(mean, delta)
print " tint:", pretty_print(tint, dtint)
print " ** tau -> 0 limit"
coeffs, errors = extrapolate_cl(f, x[-1], y[-1], dy[-1])
ffn.append(lambda x: np.sum(c[0, 0] * f(x) for c, f in zip(coeffs, f)))
cl.append(coeffs[0, 0])
dcl.append(errors[0, 0] ** 0.5)
sxsq = sum(xx ** 2 for xx in x[-1])
sx = sum(x[-1])
sa = np.sqrt(sum(((sxsq - sx * xx) / (3 * sxsq - sx ** 2)) ** 2 * yy ** 2 for xx, yy in zip(x[-1], dy[-1])))
assert abs((dcl[-1] - sa) / sa) < 1e-12
print " cl:", pretty_print(cl[-1], dcl[-1])
print " " + "*" * 50
for plt in (p for p in arg_dict["mk_plots"] if L in p.L and o in p.orders):
plt.data.append((x[-1], y[-1], dy[-1]))
plt.cl.append((cl[-1], dcl[-1]))
fnx = np.linspace(0, max(x[-1]), 100)
plt.fit.append((fnx, [ffn[-1](i) for i in fnx]))
plt.labels.append("$L = {0}$".format(L))
for plt in arg_dict["mk_plots"]:
mk_plot(plt)
def test_secondary_multiple_replica_product(self):
"""Test using the product of two observables."""
fails = 0
for known_tau in np.linspace(2, 20, 10):
data = [[
correlated_data(known_tau)[0][0],
correlated_data(known_tau)[0][0],
correlated_data(known_tau)[0][0]
],
[
correlated_data(known_tau)[0][0],
correlated_data(known_tau)[0][0],
correlated_data(known_tau)[0][0]
]]
mean, err, tau, dtau = tauint(data, lambda x, y: x * y)
if tau - 3*dtau > known_tau or \
tau + 3*dtau < known_tau:
print tau - known_tau, dtau
fails += 1
self.assertGreaterEqual(0, fails)
if alpha < np.random.random(1): # reject
Z[i + 1, :] = Z[i, :]
lPex[i + 1] = lPex[i]
lPz[i + 1] = lPz[i]
num_of_rejects = num_of_rejects + 1
print('rejection rate = ' + repr((num_of_rejects * 100.0) / M))
# QoI = Quantile function
q = 0.05
theta1 = np.exp(Z[:, 0])
theta2 = Z[:, d + 1]
q_post = theta1 * ((-np.log(q))**(1.0 / theta2))
# IACT -- only works in python 2.7 due to bad print
try:
dumpmean, delta, tint, d_tint = puwr.tauint(
np.reshape(Z.T, [d + 2, 1, M]), 0)
tau[irun] = tint * 2.0
except:
pass
print('tau = ' + repr(tau[irun]))
q_post = np.mean(q_post)
print('Mean quantile = ' + repr(q_post))
Q_py[irun] = q_post
print('')
print('TT Shock absorber completed. Some average values:')
print('Q_py = ' + repr(np.mean(Q_py)) + ' +- ' +
repr(np.sqrt(np.sum((Q_py - np.mean(Q_py))**2) / (runs - 1))))
try:
print('tau = ' + repr(np.mean(tau)) + ' +- ' +