diff --git a/.gitlab-ci.yml b/.gitlab-ci.yml
index cd255bdb33ce9b6d8611a2d9a15494f7d7018c9f..a18a9bd7ce9c701fe9c0e78311bcf647bdbf5a76 100644
--- a/.gitlab-ci.yml
+++ b/.gitlab-ci.yml
@@ -21,10 +21,11 @@ exitcode-jessie:
- pip install -r requirements.txt
- pip install coverage
- pip install coverage-badge
- - coverage run test/prior_tests.py
- - coverage run test/tests.py
- - coverage run test/waveform_generator_tests.py
- - coverage run test/noise_realisation_tests.py
+ - coverage erase
+ - coverage run -a test/prior_tests.py
+ - coverage run -a test/tests.py
+ - coverage run -a test/waveform_generator_tests.py
+ - coverage run -a test/noise_realisation_tests.py
- coverage html --include=peyote/*
- coverage-badge -o coverage.svg
artifacts:
diff --git a/README.md b/README.md
index 1810ef8fa76835c97070f88fa8cc4abc43e627ff..dddf36210d530553da698ab9e4d0d3e419d5dff3 100644
--- a/README.md
+++ b/README.md
@@ -6,25 +6,26 @@ https://monash.docs.ligo.org/peyote/)
Fulfilling all your GW dreams.
+## Installation
+
In the following, we assume you have installed
[pip](https://pip.pypa.io/en/stable/installing/) and [git](https://git-scm.com/).
-First, clone the repository, install the requirements, and then install `Peyote`.
+### Install peyote
+Clone the repository, install the requirements, and then install `peyote`.
```bash
$ git clone git@git.ligo.org:Monash/peyote.git
+$ cd peyote/
$ pip install -r requirements.txt
$ python setup.py install
```
-Once you have run these three steps, you have `Peyote installed`. However, you
-aren't quite yet ready to run anything. First,
-`pymultinest` needs the MultiNest library to be installed to work properly. The
-full instructions can be found
-[here](https://johannesbuchner.github.io/PyMultiNest/install.html). We have
-also written [a shortened tl;dr here](./TLDR_MULTINEST.md).
+Once you have run these steps, you have `peyote` installed.
-Second, you need `lalsimulation` from `lalsuite` installed. To do this head
-to [https://git.ligo.org/lscsoft/lalsuite](https://git.ligo.org/lscsoft/lalsuite)
+### Install lalsuite
+Many of the `peyote` features rely on having a swig-wrapped `lalsuite`
+installation. To install this head to
+[https://git.ligo.org/lscsoft/lalsuite](https://git.ligo.org/lscsoft/lalsuite)
to check you have an account and SSH keys set up. Then,
```bash
@@ -36,10 +37,18 @@ $ ./configure --prefix=${HOME}/lalsuite-install --disable-all-lal --enable-swig
$ make; make install
```
-** warning **: in the configure line here, we have disabled everything except lalsimulation. If you need other modules, see `./configure --help`.
+Warning: in the configure line here, we have disabled everything except
+lalsimulation. If you need other modules, see `./configure --help`.
You could also `pip install lal, lalsuite`.
+### Install lalsuite (optional)
+
+If you want to use the `pymultinest` sampler, you first need the
+MultiNest library to be installed to work properly. The full instructions can
+be found [here](https://johannesbuchner.github.io/PyMultiNest/install.html). We
+have also written [a shortened tl;dr here](./TLDR_MULTINEST.md).
+
## Tests and coverage
To locally test the code
diff --git a/peyote/detector.py b/peyote/detector.py
index 9bf1f84def42f5c71970b0ee093dfbb92154bdeb..4315615dccfb278c726a8d5192023693ac89535a 100644
--- a/peyote/detector.py
+++ b/peyote/detector.py
@@ -1,5 +1,6 @@
from __future__ import division, print_function, absolute_import
import numpy as np
+import peyote
import logging
import os
from scipy.interpolate import interp1d
@@ -210,7 +211,16 @@ class Interferometer(object):
:param waveform_polarizations: dict, polarizations of the waveform
:param parameters: dict, parameters describing position and time of arrival of the signal
"""
- self.data += self.get_detector_response(waveform_polarizations, parameters)
+ signal_ifo = self.get_detector_response(waveform_polarizations, parameters)
+ self.data += signal_ifo
+ opt_snr = np.sqrt(peyote.utils.optimal_snr_squared(signal=signal_ifo, interferometer=self,
+ time_duration=1 / (self.frequency_array[1]
+ - self.frequency_array[0])).real)
+ mf_snr = np.sqrt(peyote.utils.matched_filter_snr_squared(signal=signal_ifo, interferometer=self,
+ time_duration=1 / (self.frequency_array[1]
+ - self.frequency_array[0])).real)
+ logging.info("Injection found with optimal SNR = {:.2f} and matched filter SNR = {:.2f} in {}".format(
+ opt_snr, mf_snr, self.name))
def unit_vector_along_arm(self, arm):
"""
@@ -323,6 +333,14 @@ class Interferometer(object):
def whitened_data(self):
return self.data / self.amplitude_spectral_density_array
+ def save_data(self, outdir):
+ np.savetxt('{}/{}_frequency_domain_data.dat'.format(outdir, self.name), [self.frequency_array,
+ self.data.real, self.data.imag],
+ header='f real_h(f) imag_h(f)')
+ np.savetxt('{}/{}_psd.dat'.format(outdir, self.name), [self.frequency_array,
+ self.amplitude_spectral_density_array],
+ header='f h(f)')
+
class PowerSpectralDensity:
@@ -458,7 +476,8 @@ GEO600 = get_empty_interferometer('GEO600')
def get_inteferometer(
name, center_time, T=4, alpha=0.25, psd_offset=-1024, psd_duration=100,
- cache=True, outdir='outdir', plot=True, filter_freq=1024, **kwargs):
+ cache=True, outdir='outdir', plot=True, filter_freq=1024,
+ raw_data_file=None, **kwargs):
"""
Helper function to obtain an Interferometer instance with appropriate
PSD and data, given an center_time
@@ -497,10 +516,11 @@ def get_inteferometer(
strain = get_open_strain_data(
name, center_time-T/2, center_time+T/2, outdir=outdir, cache=cache,
- **kwargs)
+ raw_data_file=raw_data_file, **kwargs)
strain_psd = get_open_strain_data(
name, center_time+psd_offset, center_time+psd_offset+psd_duration,
+ raw_data_file=raw_data_file,
outdir=outdir, cache=cache, **kwargs)
sampling_frequency = int(strain.sample_rate.value)
@@ -555,9 +575,80 @@ def get_inteferometer(
return interferometer, sampling_frequency, time_duration
-def get_open_strain_data(name, t1, t2, outdir, cache=False, **kwargs):
+def get_inteferometer_with_fake_noise_and_injection(
+ name, injection_polarizations, injection_parameters, sampling_frequency=4096, time_duration=4,
+ outdir='outdir', plot=True, save=True):
+ """
+ Helper function to obtain an Interferometer instance with appropriate
+ PSD and data, given an center_time
+
+ Parameters
+ ----------
+ name: str
+ Detector name, e.g., 'H1'.
+ injection_polarizations: dict
+ polarizations of waveform to inject, output of waveform_generator.get_frequency_domain_signal
+ injection_parameters: dict
+ injection parameters, needed for sky position and timing
+ sampling_frequency: float
+ sampling frequency for data, should match injection signal
+ time_duration: float
+ length of data, should be the same as used for signal generation
+ outdir: str
+ directory in which to store output
+ plot: bool
+ If true, create an ASD + strain plot
+ save: bool
+ If true, save frequency domain data and PSD to file
+
+ Returns
+ -------
+ interferometer: `peyote.detector.Interferometer`
+ An Interferometer instance with a PSD and frequency-domain strain data.
+ """
+
+ utils.check_directory_exists_and_if_not_mkdir(outdir)
+
+ interferometer = get_empty_interferometer(name)
+ interferometer.set_data(sampling_frequency=sampling_frequency, duration=time_duration,
+ from_power_spectral_density=True)
+ interferometer.inject_signal(waveform_polarizations=injection_polarizations, parameters=injection_parameters)
+
+ interferometer_signal = interferometer.get_detector_response(injection_polarizations, injection_parameters)
+
+ if plot:
+ fig, ax = plt.subplots()
+ ax.loglog(interferometer.frequency_array, np.abs(interferometer.data),
+ '-C0', label=name)
+ ax.loglog(interferometer.frequency_array,
+ interferometer.amplitude_spectral_density_array,
+ '-C1', lw=0.5, label=name+' ASD')
+ ax.loglog(interferometer.frequency_array, abs(interferometer_signal), label='Signal')
+ ax.grid('on')
+ ax.set_ylabel(r'strain [strain/$\sqrt{\rm Hz}$]')
+ ax.set_xlabel(r'frequency [Hz]')
+ ax.set_xlim(20, 2000)
+ ax.legend(loc='best')
+ fig.savefig('{}/{}_frequency_domain_data.png'.format(outdir, name))
+
+ if save:
+ interferometer.save_data(outdir)
+
+ return interferometer
+
+
+def get_open_strain_data(name, t1, t2, outdir, cache=False, raw_data_file=None,
+ **kwargs):
filename = '{}/{}_{}_{}.txt'.format(outdir, name, t1, t2)
- if os.path.isfile(filename) and cache:
+ if raw_data_file:
+ logging.info('Attempting to use raw_data_file {}'.format(raw_data_file))
+ strain = TimeSeries.read(raw_data_file)
+ if (t1 > strain.times[0].value) and (t2 < strain.times[-1].value):
+ logging.info('Using supplied raw data file')
+ strain = strain.crop(t1, t2)
+ else:
+ raise ValueError('Supplied file does not contain requested data')
+ elif os.path.isfile(filename) and cache:
logging.info('Using cached data from {}'.format(filename))
strain = TimeSeries.read(filename)
else:
@@ -566,4 +657,3 @@ def get_open_strain_data(name, t1, t2, outdir, cache=False, **kwargs):
logging.info('Saving data to {}'.format(filename))
strain.write(filename)
return strain
-
diff --git a/peyote/likelihood.py b/peyote/likelihood.py
index d1bbbb62515960b2e641325989a1c7f812ee7d6f..2208f21db69be1c0db29542ea57622273147bcf2 100644
--- a/peyote/likelihood.py
+++ b/peyote/likelihood.py
@@ -1,4 +1,13 @@
+from __future__ import division, print_function
import numpy as np
+try:
+ from scipy.special import logsumexp
+except ImportError:
+ from scipy.misc import logsumexp
+from scipy.special import i0, i0e
+from scipy.interpolate import interp1d
+import peyote
+import logging
class Likelihood(object):
@@ -30,3 +39,120 @@ class Likelihood(object):
def log_likelihood_ratio(self):
return self.log_likelihood() - self.noise_log_likelihood()
+
+
+class MarginalizedLikelihood(Likelihood):
+ def __init__(self, interferometers, waveform_generator, distance_marginalization=False, phase_marginalization=False,
+ time_marginalization=False, prior=None):
+ Likelihood.__init__(self, interferometers, waveform_generator)
+ self.distance_marginalization = distance_marginalization
+ self.phase_marginalization = phase_marginalization
+ self.time_marginalization = time_marginalization
+ self.prior = prior
+
+ if self.distance_marginalization:
+ self.distance_array = np.array([])
+ self.delta_distance = 0
+ self.distance_prior_array = np.array([])
+ self.setup_distance_marginalization()
+ prior['luminosity_distance'] = 1
+
+ if self.phase_marginalization:
+ self.bessel_function_interped = None
+ self.setup_phase_marginalization()
+ prior['psi'] = 0
+
+ if self.time_marginalization:
+ logging.warning('Time marginalisation not yet implemented.')
+ self.time_marginalization = False
+
+ def setup_distance_marginalization(self):
+ if 'luminosity_distance' not in self.prior.keys():
+ logging.info('No prior provided for distance, using default prior.')
+ self.prior['luminosity_distance'] = peyote.prior.create_default_prior('luminosity_distance')
+ self.distance_array = np.linspace(self.prior['luminosity_distance'].minimum,
+ self.prior['luminosity_distance'].maximum, 1e4)
+ self.delta_distance = self.distance_array[1] - self.distance_array[0]
+ self.distance_prior_array = np.array([self.prior['luminosity_distance'].prob(distance)
+ for distance in self.distance_array])
+
+ def setup_phase_marginalization(self):
+ if 'psi' not in self.prior.keys() or not isinstance(prior['psi'], peyote.prior.Prior):
+ logging.info('No prior provided for polarization, using default prior.')
+ self.prior['psi'] = peyote.prior.create_default_prior('psi')
+ self.bessel_function_interped = interp1d(np.linspace(0, 1e6, 1e5),
+ np.log([i0e(snr) for snr in np.linspace(0, 1e6, 1e5)])
+ + np.linspace(0, 1e6, 1e5),
+ bounds_error=False, fill_value=-np.inf)
+
+ def noise_log_likelihood(self):
+ log_l = 0
+ for interferometer in self.interferometers:
+ log_l -= peyote.utils.noise_weighted_inner_product(interferometer.data, interferometer.data,
+ interferometer.power_spectral_density_array,
+ self.waveform_generator.time_duration) / 2
+ return log_l.real
+
+ def log_likelihood_ratio(self):
+ waveform_polarizations = self.waveform_generator.frequency_domain_strain()
+
+ if waveform_polarizations is None:
+ return np.nan_to_num(-np.inf)
+
+ if self.time_marginalization:
+ signal_times_data = 0 * 1j
+ else:
+ matched_filter_snr_squared = 0
+ optimal_snr_squared = 0
+
+ for interferometer in self.interferometers:
+ signal_ifo = interferometer.get_detector_response(waveform_polarizations,
+ self.waveform_generator.parameters)
+ if self.time_marginalization:
+ signal_times_data += np.conj(signal_ifo) * interferometer.data\
+ / interferometer.power_spectral_density_array
+ else:
+ matched_filter_snr_squared += peyote.utils.matched_filter_snr_squared(
+ signal_ifo, interferometer, self.waveform_generator.time_duration)
+ optimal_snr_squared += peyote.utils.optimal_snr_squared(signal_ifo, interferometer,
+ self.waveform_generator.time_duration)
+
+ if self.time_marginalization:
+ matched_filter_snr_squared = np.abs(np.fft.ifft(signal_times_data))\
+ * 4 / self.waveform_generator.time_duration
+
+ if self.phase_marginalization and not self.distance_marginalization and not self.time_marginalization:
+ matched_filter_snr_squared = self.bessel_function_interped(abs(matched_filter_snr_squared))
+
+ log_l = matched_filter_snr_squared - optimal_snr_squared / 2
+
+ elif self.distance_marginalization and not self.phase_marginalization and not self.time_marginalization:
+ log_l = logsumexp(matched_filter_snr_squared * self.waveform_generator.parameters['luminosity_distance']
+ / self.distance_array
+ - optimal_snr_squared * self.waveform_generator.parameters['luminosity_distance']**2
+ / self.distance_array**2 / 2, b=self.distance_prior_array * self.delta_distance)
+
+ elif self.distance_marginalization and self.phase_marginalization and not self.time_marginalization:
+ log_l = logsumexp(self.bessel_function_interped(abs(matched_filter_snr_squared)
+ * self.waveform_generator.parameters['luminosity_distance']
+ / self.distance_array)
+ - optimal_snr_squared * self.waveform_generator.parameters['luminosity_distance']**2
+ / self.distance_array**2 / 2, b=self.distance_prior_array * self.delta_distance)
+
+ elif self.distance_marginalization and self.phase_marginalization and self.time_marginalization:
+ log_l = logsumexp(np.array([sum(self.bessel_function_interped(
+ matched_filter_snr_squared * self.waveform_generator.parameters['luminosity_distance']
+ / distance)) for distance in self.distance_array])
+ - optimal_snr_squared * self.waveform_generator.parameters['luminosity_distance']**2
+ / self.distance_array**2 / 2, b=self.distance_prior_array * self.delta_distance)\
+ - np.log(self.waveform_generator.sampling_frequency)
+ print(log_l)
+ else:
+ log_l = matched_filter_snr_squared - optimal_snr_squared / 2
+
+ return log_l.real
+
+ def log_likelihood(self):
+ return self.log_likelihood() + self.noise_log_likelihood()
+
+
diff --git a/peyote/prior.py b/peyote/prior.py
index 3d8d7d34550fc5b7e2526410f04da08bdc3a7a3a..69f47dffd1d4dcfc8d12cdfbe39a2fa9e6b1fc0b 100644
--- a/peyote/prior.py
+++ b/peyote/prior.py
@@ -5,6 +5,8 @@ import numpy as np
from scipy.interpolate import interp1d
from scipy.integrate import cumtrapz
from scipy.special import erf, erfinv
+import logging
+import os
class Prior(object):
@@ -23,11 +25,17 @@ class Prior(object):
def rescale(self, val):
"""
- 'Rescale' a sample from the unit line element to the prior, does nothing.
+ 'Rescale' a sample from the unit line element to the prior.
- This maps to the inverse CDF.
+ This should be overwritten by each subclass.
"""
- return val
+ return None
+
+ @staticmethod
+ def test_valid_for_rescaling(val):
+ """Test if 0 < val < 1"""
+ if (val < 0) or (val > 1):
+ raise ValueError("Number to be rescaled should be in [0, 1]")
def __repr__(self):
prior_name = self.__class__.__name__
@@ -68,10 +76,10 @@ class Prior(object):
return '$\\theta_1$'
elif self.name == 'tilt_2':
return '$\\theta_2$'
- elif self.name == 'phi_1':
- return '$\phi_1$'
- elif self.name == 'phi_2':
- return '$\phi_2$'
+ elif self.name == 'phi_12':
+ return '$\Delta\phi$'
+ elif self.name == 'phi_jl':
+ return '$\phi_{JL}$'
elif self.name == 'luminosity_distance':
return '$d_L$'
elif self.name == 'dec':
@@ -95,18 +103,19 @@ class Prior(object):
class Uniform(Prior):
"""Uniform prior"""
- def __init__(self, lower, upper, name=None, latex_label=None):
+ def __init__(self, minimum, maximum, name=None, latex_label=None):
Prior.__init__(self, name, latex_label)
- self.lower = lower
- self.upper = upper
- self.support = upper - lower
+ self.minimum = minimum
+ self.maximum = maximum
+ self.support = maximum - minimum
def rescale(self, val):
- return self.lower + val * self.support
+ Prior.test_valid_for_rescaling(val)
+ return self.minimum + val * self.support
def prob(self, val):
"""Return the prior probability of val"""
- if (self.lower < val) and (val < self.upper):
+ if (self.minimum < val) and (val < self.maximum):
return 1 / self.support
else:
return 0
@@ -121,6 +130,7 @@ class DeltaFunction(Prior):
def rescale(self, val):
"""Rescale everything to the peak with the correct shape."""
+ Prior.test_valid_for_rescaling(val)
return self.peak * val ** 0
def prob(self, val):
@@ -134,11 +144,12 @@ class DeltaFunction(Prior):
class PowerLaw(Prior):
"""Power law prior distribution"""
- def __init__(self, alpha, bounds, name=None, latex_label=None):
+ def __init__(self, alpha, minimum, maximum, name=None, latex_label=None):
"""Power law with bounds and alpha, spectral index"""
Prior.__init__(self, name, latex_label)
self.alpha = alpha
- self.low, self.high = bounds
+ self.minimum = minimum
+ self.maximum = maximum
def rescale(self, val):
"""
@@ -146,20 +157,21 @@ class PowerLaw(Prior):
This maps to the inverse CDF. This has been analytically solved for this case.
"""
+ Prior.test_valid_for_rescaling(val)
if self.alpha == -1:
- return self.low * np.exp(val * np.log(self.high / self.low))
+ return self.minimum * np.exp(val * np.log(self.maximum / self.minimum))
else:
- return (self.low ** (1 + self.alpha) + val *
- (self.high ** (1 + self.alpha) - self.low ** (1 + self.alpha))) ** (1. / (1 + self.alpha))
+ return (self.minimum ** (1 + self.alpha) + val *
+ (self.maximum ** (1 + self.alpha) - self.minimum ** (1 + self.alpha))) ** (1. / (1 + self.alpha))
def prob(self, val):
"""Return the prior probability of val"""
- if (val > self.low) and (val < self.high):
+ if (val > self.minimum) and (val < self.maximum):
if self.alpha == -1:
- return 1 / val / np.log(self.high / self.low)
+ return 1 / val / np.log(self.maximum / self.minimum)
else:
- return val ** self.alpha * (1 + self.alpha) / (self.high ** (1 + self.alpha)
- - self.low ** (1 + self.alpha))
+ return val ** self.alpha * (1 + self.alpha) / (self.maximum ** (1 + self.alpha)
+ - self.minimum ** (1 + self.alpha))
else:
return 0
@@ -175,12 +187,16 @@ class Cosine(Prior):
This maps to the inverse CDF. This has been analytically solved for this case.
"""
+ Prior.test_valid_for_rescaling(val)
return np.arcsin(-1 + val * 2)
@staticmethod
def prob(val):
- """Return the prior probability of val"""
- return np.cos(val) / 2
+ """Return the prior probability of val, defined over [-pi/2, pi/2]"""
+ if (val > -np.pi / 2) and (val < np.pi / 2):
+ return np.cos(val) / 2
+ else:
+ return 0
class Sine(Prior):
@@ -194,12 +210,16 @@ class Sine(Prior):
This maps to the inverse CDF. This has been analytically solved for this case.
"""
+ Prior.test_valid_for_rescaling(val)
return np.arccos(-1 + val * 2)
@staticmethod
def prob(val):
- """Return the prior probability of val"""
- return np.sin(val) / 2
+ """Return the prior probability of val, defined over [0, pi]"""
+ if (val > 0) and (val < np.pi):
+ return np.sin(val) / 2
+ else:
+ return 0
class Gaussian(Prior):
@@ -217,6 +237,7 @@ class Gaussian(Prior):
This maps to the inverse CDF. This has been analytically solved for this case.
"""
+ Prior.test_valid_for_rescaling(val)
return self.mu + erfinv(2 * val - 1) * 2**0.5 * self.sigma
def prob(self, val):
@@ -231,16 +252,16 @@ class TruncatedGaussian(Prior):
https://en.wikipedia.org/wiki/Truncated_normal_distribution
"""
- def __init__(self, mu, sigma, low, high, name=None, latex_label=None):
+ def __init__(self, mu, sigma, minimum, maximum, name=None, latex_label=None):
"""Power law with bounds and alpha, spectral index"""
Prior.__init__(self, name, latex_label)
self.mu = mu
self.sigma = sigma
- self.low = low
- self.high = high
+ self.minimum = minimum
+ self.maximum = maximum
- self.normalisation = (erf((self.high - self.mu) / 2 ** 0.5 / self.sigma) - erf(
- (self.low - self.mu) / 2 ** 0.5 / self.sigma)) / 2
+ self.normalisation = (erf((self.maximum - self.mu) / 2 ** 0.5 / self.sigma) - erf(
+ (self.minimum - self.mu) / 2 ** 0.5 / self.sigma)) / 2
def rescale(self, val):
"""
@@ -248,101 +269,133 @@ class TruncatedGaussian(Prior):
This maps to the inverse CDF. This has been analytically solved for this case.
"""
+ Prior.test_valid_for_rescaling(val)
return erfinv(2 * val * self.normalisation + erf(
- (self.low - self.mu) / 2 ** 0.5 / self.sigma)) * 2 ** 0.5 * self.sigma + self.mu
+ (self.minimum - self.mu) / 2 ** 0.5 / self.sigma)) * 2 ** 0.5 * self.sigma + self.mu
def prob(self, val):
"""Return the prior probability of val"""
- return np.exp(-(self.mu - val) ** 2 / (2 * self.sigma ** 2)) / (
- 2 * np.pi) ** 0.5 / self.sigma / self.normalisation
+ if (val > self.minimum) & (val < self.maximum):
+ return np.exp(-(self.mu - val) ** 2 / (2 * self.sigma ** 2)) / (
+ 2 * np.pi) ** 0.5 / self.sigma / self.normalisation
+ else:
+ return 0
class Interped(Prior):
- def __init__(self, xx, yy, name=None, latex_label=None):
+ def __init__(self, xx, yy, minimum=None, maximum=None, name=None, latex_label=None):
"""Initialise object from arrays of x and y=p(x)"""
Prior.__init__(self, name, latex_label)
- self.xx = xx
- self.low = min(self.xx)
- self.high = max(self.xx)
- self.yy = yy
- if np.trapz(self.yy, self.xx) != 0:
- print('Supplied PDF is not normalised, normalising.')
+ if minimum is None or minimum < min(xx):
+ self.minimum = min(xx)
+ else:
+ self.minimum = minimum
+ if maximum is None or maximum > max(xx):
+ self.maximum = max(xx)
+ else:
+ self.maximum = maximum
+ self.xx = xx[(xx > self.minimum) & (xx < self.maximum)]
+ self.yy = yy[(xx > self.minimum) & (xx < self.maximum)]
+ if np.trapz(self.yy, self.xx) != 1:
+ logging.info('Supplied PDF is not normalised, normalising.')
self.yy /= np.trapz(self.yy, self.xx)
self.YY = cumtrapz(self.yy, self.xx, initial=0)
- self.probability_density = interp1d(x=self.xx, y=self.yy, bounds_error=False, fill_value=min(self.yy))
+ self.probability_density = interp1d(x=self.xx, y=self.yy, bounds_error=False, fill_value=0)
self.cumulative_distribution = interp1d(x=self.xx, y=self.YY, bounds_error=False, fill_value=0)
- self.invervse_cumulative_distribution = interp1d(x=self.YY, y=self.xx, bounds_error=False,
- fill_value=(min(self.xx), max(self.xx)))
+ self.inverse_cumulative_distribution = interp1d(x=self.YY, y=self.xx, bounds_error=True)
def prob(self, val):
"""Return the prior probability of val"""
- return self.probability_density(val)
+ if (val > self.minimum) & (val < self.maximum):
+ return self.probability_density(val)
+ else:
+ return 0
- def rescale(self, x):
+ def rescale(self, val):
"""
'Rescale' a sample from the unit line element to the prior.
This maps to the inverse CDF. This is done using interpolation.
"""
- return self.invervse_cumulative_distribution(x)
+ Prior.test_valid_for_rescaling(val)
+ return self.inverse_cumulative_distribution(val)
+
+ def __repr__(self):
+ prior_name = self.__class__.__name__
+ prior_args = ', '.join(
+ ['{}={}'.format(key, self.__dict__[key]) for key in ['xx', 'yy', '_Prior__latex_label']])
+ return "{}({})".format(prior_name, prior_args)
class FromFile(Interped):
- def __init__(self, file_name):
+ def __init__(self, file_name, minimum=None, maximum=None, name=None, latex_label=None):
try:
self.id = file_name
- xx, yy = np.genfromtxt(file_name).T
- Interped.__init__(self, xx, yy)
+ if '/' not in self.id:
+ self.id = '{}/peyote/prior_files/{}'.format(os.getcwd(), self.id)
+ xx, yy = np.genfromtxt(self.id).T
+ Interped.__init__(self, xx=xx, yy=yy, minimum=minimum, maximum=maximum, name=name, latex_label=latex_label)
except IOError:
- print("Can't load {}.".format(file_name))
- print("Format should be:")
- print(r"x\tp(x)")
+ logging.warning("Can't load {}.".format(self.id))
+ logging.warning("Format should be:")
+ logging.warning(r"x\tp(x)")
+
+ def __repr__(self):
+ prior_name = self.__class__.__name__
+ prior_args = ', '.join(
+ ['{}={}'.format(key, self.__dict__[key]) for key in ['id', 'minimum', 'maximum', '_Prior__latex_label']])
+ return "{}({})".format(prior_name, prior_args)
+
+
+class UniformComovingVolume(FromFile):
+
+ def __init__(self, minimum=None, maximum=None, name=None, latex_label=None):
+ FromFile.__init__(self, file_name='comoving.txt', minimum=minimum, maximum=maximum, name=name,
+ latex_label=latex_label)
def fix(prior, value=None):
if value is None or np.isnan(value):
raise ValueError("You can't fix the value to be np.nan. You need to assign it a legal value")
- prior = DeltaFunction(name=prior.name,
- latex_label=prior.latex_label,
- peak=value)
+ prior = DeltaFunction(name=prior.name, latex_label=prior.latex_label, peak=value)
return prior
def create_default_prior(name):
if name == 'mass_1':
- prior = PowerLaw(name=name, alpha=0, bounds=(5, 100))
+ prior = PowerLaw(name=name, alpha=0, minimum=5, maximum=100)
elif name == 'mass_2':
- prior = PowerLaw(name=name, alpha=0, bounds=(5, 100))
+ prior = PowerLaw(name=name, alpha=0, minimum=5, maximum=100)
elif name == 'mchirp':
- prior = PowerLaw(name=name, alpha=0, bounds=(5, 100))
+ prior = Uniform(name=name, minimum=5, maximum=100)
elif name == 'q':
- prior = PowerLaw(name=name, alpha=0, bounds=(0, 1))
+ prior = Uniform(name=name, minimum=0, maximum=1)
elif name == 'a_1':
- prior = PowerLaw(name=name, alpha=0, bounds=(0, 0.8))
+ prior = Uniform(name=name, minimum=0, maximum=0.8)
elif name == 'a_2':
- prior = PowerLaw(name=name, alpha=0, bounds=(0, 0.8))
+ prior = Uniform(name=name, minimum=0, maximum=0.8)
elif name == 'tilt_1':
prior = Sine(name=name)
elif name == 'tilt_2':
prior = Sine(name=name)
- elif name == 'phi_1':
- prior = PowerLaw(name=name, alpha=0, bounds=(0, 2 * np.pi))
- elif name == 'phi_2':
- prior = PowerLaw(name=name, alpha=0, bounds=(0, 2 * np.pi))
+ elif name == 'phi_12':
+ prior = Uniform(name=name, minimum=0, maximum=2 * np.pi)
+ elif name == 'phi_jl':
+ prior = Uniform(name=name, minimum=0, maximum=2 * np.pi)
elif name == 'luminosity_distance':
- prior = PowerLaw(name=name, alpha=2, bounds=(1e2, 5e3))
+ prior = PowerLaw(name=name, alpha=2, minimum=1e2, maximum=5e3)
elif name == 'dec':
prior = Cosine(name=name)
elif name == 'ra':
- prior = PowerLaw(name=name, alpha=0, bounds=(0, 2 * np.pi))
+ prior = Uniform(name=name, minimum=0, maximum=2 * np.pi)
elif name == 'iota':
prior = Sine(name=name)
elif name == 'psi':
- prior = PowerLaw(name=name, alpha=0, bounds=(0, 2 * np.pi))
+ prior = Uniform(name=name, minimum=0, maximum=2 * np.pi)
elif name == 'phase':
- prior = PowerLaw(name=name, alpha=0, bounds=(0, 2 * np.pi))
+ prior = Uniform(name=name, minimum=0, maximum=2 * np.pi)
else:
prior = None
return prior
@@ -353,8 +406,8 @@ def parse_floats_to_fixed_priors(old_parameters):
for key in parameters:
if type(parameters[key]) is not float and type(parameters[key]) is not int \
and type(parameters[key]) is not Prior:
- print("Expected parameter " + str(key) + " to be a float or int but was " + str(type(parameters[key]))
- + " instead. Will not be converted.")
+ logging.info("Expected parameter " + str(key) + " to be a float or int but was "
+ + str(type(parameters[key])) + " instead. Will not be converted.")
continue
elif type(parameters[key]) is Prior:
continue
@@ -367,3 +420,61 @@ def parse_keys_to_parameters(keys):
for key in keys:
parameters[key] = create_default_prior(key)
return parameters
+
+
+def fill_priors(prior, waveform_generator):
+ """
+ Fill dictionary of priors based on required parameters for waveform generator
+
+ Any floats in prior will be converted to delta function prior.
+ Any required, non-specified parameters will use the default.
+ Parameters
+ ----------
+ prior: dict
+ dictionary of prior objects and floats
+ waveform_generator: WaveformGenerator
+ waveform generator to be used for inference
+ """
+ bad_keys = []
+ for key in prior:
+ if isinstance(prior[key], Prior):
+ continue
+ elif isinstance(prior[key], float) or isinstance(prior[key], int):
+ prior[key] = DeltaFunction(prior[key])
+ logging.info("{} converted to delta function prior.".format(key))
+ else:
+ logging.warning("{} cannot be converted to delta function prior.".format(key))
+ logging.warning("If required the default prior will be used.")
+ bad_keys.append(key)
+
+ missing_keys = set(waveform_generator.parameters) - set(prior.keys())
+
+ for missing_key in missing_keys:
+ prior[missing_key] = create_default_prior(missing_key)
+ if prior[missing_key] is None:
+ logging.warning("No default prior found for unspecified variable {}.".format(missing_key))
+ logging.warning("This variable will NOT be sampled.")
+ bad_keys.append(missing_key)
+
+ for key in bad_keys:
+ prior.pop(key)
+
+
+def write_priors_to_file(priors, outdir):
+ """
+ Write the prior distribtuion to file.
+
+ Parameters
+ ----------
+ priors: dict
+ priors used
+ outdir: str
+ output directory
+ """
+ if outdir[-1] != "/":
+ outdir += "/"
+ prior_file = outdir + "prior.txt"
+ print("Writing priors to {}".format(prior_file))
+ with open(prior_file, "w") as outfile:
+ for key in priors:
+ outfile.write("prior['{}'] = {}\n".format(key, priors[key]))
diff --git a/peyote/prior_files/comoving.txt b/peyote/prior_files/comoving.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6ee3bea215e0803a12d86840df3e2bf3c9f163bf
--- /dev/null
+++ b/peyote/prior_files/comoving.txt
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+2.999399939993999214e+04 4.511677898929728874e-05
+2.999699969996999789e+04 4.511702547339091561e-05
+3.000000000000000000e+04 4.511727195748453569e-05
diff --git a/peyote/sampler.py b/peyote/sampler.py
index a9757dde2e81f58df0dfbb13ff7662c90884a1c7..ea28b389294b1d70cc6ceeefafc466b3f1494fd7 100644
--- a/peyote/sampler.py
+++ b/peyote/sampler.py
@@ -5,11 +5,14 @@ import logging
import os
import sys
import numpy as np
+from chainconsumer import ChainConsumer
+import matplotlib.pyplot as plt
from .result import Result
-from .prior import Prior
+from .prior import Prior, fill_priors
from . import utils
from . import prior
+import peyote
class Sampler(object):
@@ -140,6 +143,11 @@ class Sampler(object):
def prior_transform(self, theta):
return [self.priors[key].rescale(t) for key, t in zip(self.__search_parameter_keys, theta)]
+ def log_prior(self, theta):
+ return np.sum(
+ [np.log(self.priors[key].prob(t)) for key, t in
+ zip(self.__search_parameter_keys, theta)])
+
def log_likelihood(self, theta):
for i, k in enumerate(self.__search_parameter_keys):
self.likelihood.waveform_generator.parameters[k] = theta[i]
@@ -148,6 +156,24 @@ class Sampler(object):
else:
return self.likelihood.log_likelihood()
+ def get_random_draw_from_prior(self):
+ """ Get a random draw from the prior distribution
+
+ Returns
+ draw: array_like
+ An ndim-length array of values drawn from the prior. Parameters
+ with delta-function (or fixed) priors are not returned
+
+ """
+
+ draw = np.array([self.priors[key].sample()
+ for key in self.__search_parameter_keys])
+ if np.isinf(self.log_likelihood(draw)):
+ logging.info('Prior draw {} has inf likelihood'.format(draw))
+ if np.isinf(self.log_prior(draw)):
+ logging.info('Prior draw {} has inf prior'.format(draw))
+ return draw
+
def run_sampler(self):
pass
@@ -192,13 +218,29 @@ class Nestle(Sampler):
class Dynesty(Sampler):
+
+ @property
+ def kwargs(self):
+ return self.__kwargs
+
+ @kwargs.setter
+ def kwargs(self, kwargs):
+ self.__kwargs = dict(dlogz=0.1, sample='rwalk', walks=100, bound='multi', update_interval=6000)
+ self.__kwargs.update(kwargs)
+ if 'npoints' not in self.__kwargs:
+ for equiv in ['nlive', 'nlives', 'n_live_points', 'npoint']:
+ if equiv in self.__kwargs:
+ self.__kwargs['npoints'] = self.__kwargs.pop(equiv)
+ if 'npoints' not in self.__kwargs:
+ self.__kwargs['npoints'] = 10000
+
def run_sampler(self):
dynesty = self.external_sampler
nested_sampler = dynesty.NestedSampler(
loglikelihood=self.log_likelihood,
prior_transform=self.prior_transform,
ndim=self.ndim, **self.kwargs)
- nested_sampler.run_nested()
+ nested_sampler.run_nested(dlogz=self.kwargs['dlogz'])
out = nested_sampler.results
self.result.sampler_output = out
@@ -218,7 +260,7 @@ class Pymultinest(Sampler):
@kwargs.setter
def kwargs(self, kwargs):
- outputfiles_basename = self.outdir + '/pymultinest_{}_out/'.format(self.label)
+ outputfiles_basename = self.outdir + '/pymultinest_{}/'.format(self.label)
utils.check_directory_exists_and_if_not_mkdir(outputfiles_basename)
self.__kwargs = dict(importance_nested_sampling=False, resume=True,
verbose=True, sampling_efficiency='parameter',
@@ -251,8 +293,55 @@ class Pymultinest(Sampler):
return self.result
-def run_sampler(likelihood, priors, label='label', outdir='outdir',
- sampler='nestle', use_ratio=False, injection_parameters=None,
+class Ptemcee(Sampler):
+
+ def run_sampler(self):
+ ntemps = self.kwargs.pop('ntemps', 2)
+ nwalkers = self.kwargs.pop('nwalkers', 100)
+ nsteps = self.kwargs.pop('nsteps', 100)
+ nburn = self.kwargs.pop('nburn', 50)
+ ptemcee = self.external_sampler
+ tqdm = utils.get_progress_bar(self.kwargs.pop('tqdm', 'tqdm'))
+
+ sampler = ptemcee.Sampler(
+ ntemps=ntemps, nwalkers=nwalkers, dim=self.ndim,
+ logl=self.log_likelihood, logp=self.log_prior,
+ **self.kwargs)
+ pos0 = [[self.get_random_draw_from_prior()
+ for i in range(nwalkers)]
+ for j in range(ntemps)]
+
+ for result in tqdm(
+ sampler.sample(pos0, iterations=nsteps, adapt=True), total=nsteps):
+ pass
+
+ self.result.sampler_output = np.nan
+ self.result.samples = sampler.chain[0, :, nburn:, :].reshape(
+ (-1, self.ndim))
+ self.result.walkers = sampler.chain[0, :, :, :]
+ self.result.logz = np.nan
+ self.result.logzerr = np.nan
+ self.plot_walkers()
+ logging.info("Max autocorr time = {}".format(np.max(sampler.get_autocorr_time())))
+ logging.info("Tswap frac = {}".format(sampler.tswap_acceptance_fraction))
+ return self.result
+
+ def plot_walkers(self, save=True, **kwargs):
+ nwalkers, nsteps, ndim = self.result.walkers.shape
+ idxs = np.arange(nsteps)
+ fig, axes = plt.subplots(nrows=ndim, figsize=(6, 3*self.ndim))
+ for i, ax in enumerate(axes):
+ ax.plot(idxs, self.result.walkers[:, :, i].T, lw=0.1, color='k')
+ ax.set_ylabel(self.result.parameter_labels[i])
+
+ fig.tight_layout()
+ filename = '{}/{}_walkers.png'.format(self.outdir, self.label)
+ logging.info('Saving walkers plot to {}'.format('filename'))
+ fig.savefig(filename)
+
+
+def run_sampler(likelihood, priors=None, label='label', outdir='outdir',
+ sampler='nestle', use_ratio=True, injection_parameters=None,
**sampler_kwargs):
"""
The primary interface to easy parameter estimation
@@ -263,8 +352,10 @@ def run_sampler(likelihood, priors, label='label', outdir='outdir',
A `Likelihood` instance
priors: dict
A dictionary of the priors for each parameter - missing parameters will
- use default priors
- label, outdir: str
+ use default priors, if None, all priors will be default
+ label: str
+ Name for the run, used in output files
+ outdir: str
A string used in defining output files
sampler: str
The name of the sampler to use - see
@@ -288,6 +379,11 @@ def run_sampler(likelihood, priors, label='label', outdir='outdir',
utils.check_directory_exists_and_if_not_mkdir(outdir)
implemented_samplers = get_implemented_samplers()
+ if priors is None:
+ priors = dict()
+ fill_priors(priors, likelihood.waveform_generator)
+ peyote.prior.write_priors_to_file(priors, outdir)
+
if implemented_samplers.__contains__(sampler.title()):
sampler_class = globals()[sampler.title()]
sampler = sampler_class(likelihood, priors, sampler, outdir=outdir,
diff --git a/peyote/source.py b/peyote/source.py
index c4e777b0244a16d0e9e9b43bfe8a5c2a69332f6b..230f876eb9548129768b32efaffe41fc16bf8717 100644
--- a/peyote/source.py
+++ b/peyote/source.py
@@ -10,19 +10,20 @@ from . import utils
def lal_binary_black_hole(
- frequency_array, mass_1, mass_2, luminosity_distance, a_1, tilt_1, phi_1, a_2, tilt_2, phi_2,
+ frequency_array, mass_1, mass_2, luminosity_distance, a_1, tilt_1, phi_12, a_2, tilt_2, phi_jl,
iota, phase, waveform_approximant, reference_frequency, ra, dec,
geocent_time, psi):
""" A Binary Black Hole waveform model using lalsimulation """
if mass_2 > mass_1:
- return {'plus': 0, 'cross': 0}
+ return None
luminosity_distance = luminosity_distance * 1e6 * utils.parsec
mass_1 = mass_1 * utils.solar_mass
mass_2 = mass_2 * utils.solar_mass
- spin_1x, spin_1y, spin_1z = utils.spherical_to_cartesian(a_1, tilt_1, phi_1)
- spin_2x, spin_2y, spin_2z = utils.spherical_to_cartesian(a_2, tilt_2, phi_2)
+ iota, spin_1x, spin_1y, spin_1z, spin_2x, spin_2y, spin_2z = \
+ lalsim.SimInspiralTransformPrecessingNewInitialConditions(iota, phi_jl, tilt_1, tilt_2, phi_12, a_1, a_2,
+ mass_1, mass_2, reference_frequency, phase)
longitude_ascending_nodes = 0.0
eccentricity = 0.0
diff --git a/peyote/utils.py b/peyote/utils.py
index c8632e333e0f1ac1f724807658252c571095ff1c..bf3fa6283048f50cda9ad06b9900e47fa23a58e1 100644
--- a/peyote/utils.py
+++ b/peyote/utils.py
@@ -284,6 +284,23 @@ def setup_logger(log_level='info'):
logger.addHandler(stream_handler)
+def get_progress_bar(module='tqdm'):
+ if module in ['tqdm']:
+ try:
+ from tqdm import tqdm
+ except ImportError:
+ def tqdm(x, *args, **kwargs):
+ return x
+ return tqdm
+ elif module in ['tqdm_notebook']:
+ try:
+ from tqdm import tqdm_notebook as tqdm
+ except ImportError:
+ def tqdm(x, *args, **kwargs):
+ return x
+ return tqdm
+
+
def spherical_to_cartesian(radius, theta, phi):
"""
Convert from spherical coordinates to cartesian.
@@ -327,3 +344,38 @@ def inner_product(aa, bb, frequency, PSD):
product = 4. * np.real(integral)
return product
+
+
+def noise_weighted_inner_product(aa, bb, power_spectral_density, time_duration):
+ """
+ Calculate the noise weighted inner product between two arrays.
+
+ Parameters
+ ----------
+ aa: array
+ Array to be complex conjugated
+ bb: array
+ Array not to be complex conjugated
+ power_spectral_density: array
+ Power spectral density
+ time_duration: float
+ time_duration of the data
+
+ Return
+ ------
+ Noise-weighted inner product.
+ """
+
+ # caluclate the inner product
+ integrand = np.conj(aa) * bb / power_spectral_density
+ product = 4 / time_duration * np.sum(integrand)
+ return product
+
+
+def matched_filter_snr_squared(signal, interferometer, time_duration):
+ return noise_weighted_inner_product(signal, interferometer.data, interferometer.power_spectral_density_array,
+ time_duration)
+
+
+def optimal_snr_squared(signal, interferometer, time_duration):
+ return noise_weighted_inner_product(signal, signal, interferometer.power_spectral_density_array, time_duration)
diff --git a/requirements.txt b/requirements.txt
index 31cb609d557582f664e393911d1756f5cbf8b7d4..84f9ee6099b35774a6bf8dc48be39f639807c177 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -13,3 +13,4 @@ NRSur7dq2
chainconsumer
nestle
deepdish
+ptemcee
diff --git a/test/noise_realisation_tests.py b/test/noise_realisation_tests.py
index 730fc73086d9ac98c6edd77acc6defa80022884a..812629184874f06c1e263f40f3413c04642ff3a7 100644
--- a/test/noise_realisation_tests.py
+++ b/test/noise_realisation_tests.py
@@ -8,40 +8,40 @@ class TestNoiseRealisation(unittest.TestCase):
time_duration = 1.
sampling_frequency = 4096.
factor = np.sqrt(2./time_duration)
- navg = 1000
+ n_avg = 1000
psd_avg = 0
- H1 = peyote.detector.H1
- for x in range(0, navg):
- H1_hf_noise, frequencies = H1.power_spectral_density.get_noise_realisation(sampling_frequency,
- time_duration)
- H1.set_data(sampling_frequency, time_duration, frequency_domain_strain=H1_hf_noise)
- hf_tmp = H1.data
- psd_avg += abs(hf_tmp)**2
-
- psd_avg = psd_avg/navg
+ interferometer = peyote.detector.H1
+ for x in range(0, n_avg):
+ interferometer.set_data(sampling_frequency, time_duration, from_power_spectral_density=True)
+ psd_avg += abs(interferometer.data)**2
+
+ psd_avg = psd_avg/n_avg
asd_avg = np.sqrt(abs(psd_avg))
- a = H1.amplitude_spectral_density_array/factor
+ a = interferometer.amplitude_spectral_density_array/factor
b = asd_avg
self.assertTrue(np.isclose(a[2]/b[2], 1.00, atol=1e-1))
def test_noise_normalisation(self):
time_duration = 1.
sampling_frequency = 4096.
- number_of_samples = int(np.round(time_duration*sampling_frequency))
- time_array = (1./sampling_frequency) * np.linspace(0, number_of_samples, number_of_samples)
+ time_array = peyote.utils.create_time_series(sampling_frequency=sampling_frequency, duration=time_duration)
# generate some toy-model signal for matched filtering SNR testing
- navg = 10000
- snr = np.zeros(navg)
+ n_avg = 10000
+ snr = np.zeros(n_avg)
mu = np.exp(-(time_array-time_duration/2.)**2 / (2.*0.1**2)) * np.sin(2*np.pi*100*time_array)
muf, frequency_array = peyote.utils.nfft(mu, sampling_frequency)
- for x in range(0, navg):
- H1 = peyote.detector.H1
- H1_hf_noise, frequencies = H1.power_spectral_density.get_noise_realisation(sampling_frequency, time_duration)
- H1.set_data(sampling_frequency, time_duration,frequency_domain_strain=H1_hf_noise)
- hf_tmp = H1.data
- Sh = H1.power_spectral_density
- snr[x] = peyote.utils.inner_product(hf_tmp, muf, frequency_array, Sh) / np.sqrt(peyote.utils.inner_product(muf, muf, frequency_array, Sh))
+ for x in range(0, n_avg):
+ interferometer = peyote.detector.H1
+ interferometer.set_data(sampling_frequency, time_duration, from_power_spectral_density=True)
+ hf_tmp = interferometer.data
+ psd = interferometer.power_spectral_density
+ snr[x] = peyote.utils.inner_product(hf_tmp, muf, frequency_array, psd) \
+ / np.sqrt(peyote.utils.inner_product(muf, muf, frequency_array, psd))
self.assertTrue(np.isclose(np.std(snr), 1.00, atol=1e-2))
+
+
+if __name__ == '__main__':
+ unittest.main()
diff --git a/test/prior_tests.py b/test/prior_tests.py
index d310d54056cb6bc2ac7debce0f2484175ae35ead..a61afa78b93e4cc6eb60fff124ae49f154585450 100644
--- a/test/prior_tests.py
+++ b/test/prior_tests.py
@@ -79,7 +79,7 @@ class TestPriorIsFixed(unittest.TestCase):
self.assertTrue(self.prior.is_fixed)
def test_is_fixed_uniform_class(self):
- self.prior = peyote.prior.Uniform(lower=0, upper=10)
+ self.prior = peyote.prior.Uniform(minimum=0, maximum=10)
self.assertFalse(self.prior.is_fixed)
diff --git a/test/tests.py b/test/tests.py
index d5c3b555baef70ca05c197761259510018a765cf..9c28c31a3fc48e2f057cd8f5ceb13c19a88a7069 100644
--- a/test/tests.py
+++ b/test/tests.py
@@ -49,10 +49,13 @@ class Test(unittest.TestCase):
likelihood = peyote.likelihood.Likelihood(
[self.msd['IFO']], self.msd['waveform_generator'])
+ priors = {}
+ for key in self.msd['simulation_parameters']:
+ priors[key] = self.msd['simulation_parameters'][key]
+
dL = self.msd['simulation_parameters']['luminosity_distance']
- priors = {'luminosity_distance' : peyote.prior.Uniform(
- name='luminosity_distance', lower=dL - 10, upper=dL + 10)
-}
+ priors['luminosity_distance'] = peyote.prior.Uniform(
+ name='luminosity_distance', minimum=dL - 10, maximum=dL + 10)
result = peyote.sampler.run_sampler(likelihood, priors, sampler='nestle', verbose=False)
self.assertAlmostEqual(np.mean(result.samples), dL, delta=np.std(result.samples))
diff --git a/tutorials/BasicTutorial.py b/tutorials/BasicTutorial.py
index b17769c04b1bf627b42d8e742154b8165c94de12..fcdeed337c231101838693b3c0282dd60157aeef 100644
--- a/tutorials/BasicTutorial.py
+++ b/tutorials/BasicTutorial.py
@@ -1,58 +1,48 @@
-import numpy as np
-import pylab as plt
+#!/bin/python
+"""
+Tutorial to demonstrate running parameter estimation on a reduced parameter space for an injected signal.
+
+This example estimates the masses using a uniform prior in both component masses and distance using a uniform in
+comoving volume prior on luminosity distance, the cosmology is WMAP7.
+"""
+from __future__ import division, print_function
import peyote
-peyote.utils.setup_logger()
+peyote.utils.setup_logger(log_level="info")
-time_duration = 1.
-sampling_frequency = 4096.
+time_duration = 4.
+sampling_frequency = 2048.
+outdir = 'outdir'
-injection_parameters = dict(mass_1=36., mass_2=29., a_1=0, a_2=0, tilt_1=0, tilt_2=0, phi_1=0, phi_2=0,
- luminosity_distance=2500., iota=0.4, psi=2.659, phase=1.3, geocent_time=1126259642.413,
+np.random.seed(170809)
+
+injection_parameters = dict(mass_1=36., mass_2=29., a_1=0.4, a_2=0.3, tilt_1=0.5, tilt_2=1.0, phi_12=1.7, phi_jl=0.3,
+ luminosity_distance=4000., iota=0.4, psi=2.659, phase=1.3, geocent_time=1126259642.413,
waveform_approximant='IMRPhenomPv2', reference_frequency=50., ra=1.375, dec=-1.2108)
# Create the waveform_generator using a LAL BinaryBlackHole source function
waveform_generator = peyote.waveform_generator.WaveformGenerator(
- sampling_frequency=sampling_frequency,
- time_duration=time_duration,
+ sampling_frequency=sampling_frequency, time_duration=time_duration,
frequency_domain_source_model=peyote.source.lal_binary_black_hole,
parameters=injection_parameters)
hf_signal = waveform_generator.frequency_domain_strain()
# Set up interferometers.
-IFOs = [peyote.detector.get_empty_interferometer(name) for name in ['H1', 'L1', 'V1']]
-
-for IFO in IFOs:
- IFO.set_data(sampling_frequency=sampling_frequency, duration=time_duration, from_power_spectral_density=True)
- IFO.inject_signal(waveform_polarizations=hf_signal, parameters=injection_parameters)
-
-# Plot the noise and signal
-fig, ax = plt.subplots()
-for IFO in IFOs:
- plt.loglog(IFO.frequency_array, np.abs(IFO.data), lw=1.5, label='{} noise+signal'.format(IFO.name))
- plt.loglog(IFO.frequency_array, IFO.amplitude_spectral_density_array, lw=1.5, label='{} ASD'.format(IFO.name))
-plt.xlim(10, 1000)
-plt.legend()
-plt.xlabel(r'frequency')
-plt.ylabel(r'strain')
-fig.savefig('data')
-
-# Set up likelihood
-likelihood = peyote.likelihood.Likelihood(IFOs, waveform_generator)
+IFOs = [peyote.detector.get_inteferometer_with_fake_noise_and_injection(
+ name, injection_polarizations=hf_signal, injection_parameters=injection_parameters, time_duration=time_duration,
+ sampling_frequency=sampling_frequency, outdir=outdir) for name in ['H1', 'L1', 'V1']]
# Set up prior
-priors = {}
-priors['mass_1'] = peyote.prior.Uniform(
- lower=35, upper=37, name='mass_1', latex_label='$m_1$')
-priors['luminosity_distance'] = peyote.prior.create_default_prior('luminosity_distance')
-for key in ['mass_2', 'a_1', 'a_2', 'tilt_1', 'tilt_2', 'phi_1', 'phi_2', 'phase', 'psi', 'iota', 'ra',
- 'dec', 'geocent_time']:
+priors = dict()
+# These parameters will not be sampled
+for key in ['a_1', 'a_2', 'tilt_1', 'tilt_2', 'phi_12', 'phi_jl', 'phase', 'psi', 'iota', 'ra', 'dec', 'geocent_time']:
priors[key] = injection_parameters[key]
+priors['luminosity_distance'] = peyote.prior.FromFile(file_name='comoving.txt', minimum=500, maximum=5000,
+ name='luminosity_distance')
# Run sampler
-result = peyote.sampler.run_sampler(likelihood=likelihood, priors=priors, sampler='dynesty',
- label='BasicTutorial', use_ratio=True, npoints=500, verbose=True,
- injection_parameters=injection_parameters)
+result = peyote.sampler.run_sampler(likelihood=likelihood, priors=priors, sampler='dynesty', npoints=500,
+ injection_parameters=injection_parameters, outdir=outdir, label='BasicTutorial')
result.plot_corner()
result.plot_walks()
result.plot_distributions()
diff --git a/tutorials/Compare_samplers.ipynb b/tutorials/Compare_samplers.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..c4a84bd30e16110a838468d7cdabc9f2b1fafdd3
--- /dev/null
+++ b/tutorials/Compare_samplers.ipynb
@@ -0,0 +1,429 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Compare samplers\n",
+ "\n",
+ "In this notebook, we'll compare the different samplers implemented in `tupak`. As of this version, we don't compare the outputs, only how to run them and the timings for their default setup.\n",
+ "\n",
+ "## Setup"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "09:49 INFO : Setting H1 data using noise realization from providedpower_spectal_density\n"
+ ]
+ }
+ ],
+ "source": [
+ "import numpy as np\n",
+ "import pylab as plt\n",
+ "\n",
+ "%matplotlib inline\n",
+ "\n",
+ "import peyote\n",
+ "\n",
+ "peyote.utils.setup_logger()\n",
+ "\n",
+ "time_duration = 1.\n",
+ "sampling_frequency = 4096.\n",
+ "\n",
+ "injection_parameters = dict(mass_1=36., mass_2=29., a_1=0, a_2=0, tilt_1=0, tilt_2=0, phi_12=0, phi_jl=0,\n",
+ " luminosity_distance=100., iota=0.4, phase=1.3, waveform_approximant='IMRPhenomPv2',\n",
+ " reference_frequency=50., ra=1.375, dec=-1.2108, geocent_time=1126259642.413,\n",
+ " psi=2.659)\n",
+ "\n",
+ "waveform_generator = peyote.waveform_generator.WaveformGenerator(\n",
+ " sampling_frequency=sampling_frequency,\n",
+ " time_duration=time_duration,\n",
+ " frequency_domain_source_model=peyote.source.lal_binary_black_hole,\n",
+ " parameters=injection_parameters)\n",
+ "\n",
+ "hf_signal = waveform_generator.frequency_domain_strain()\n",
+ "\n",
+ "H1 = peyote.detector.H1\n",
+ "H1.set_data(sampling_frequency=sampling_frequency, duration=time_duration,\n",
+ " from_power_spectral_density=True)\n",
+ "H1.inject_signal(waveform_polarizations=hf_signal, parameters=injection_parameters)\n",
+ "\n",
+ "IFOs = [H1]\n",
+ "\n",
+ "likelihood = peyote.likelihood.Likelihood(IFOs, waveform_generator)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Prior\n",
+ "\n",
+ "For this test, we will simply search of the sky position, setting the other parameters to their simulated values."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "09:49 INFO : Expected parameter waveform_approximant to be a float or int but was <type 'str'> instead. Will not be converted.\n"
+ ]
+ }
+ ],
+ "source": [
+ "priors = peyote.prior.parse_floats_to_fixed_priors(injection_parameters)\n",
+ "priors['ra'] = peyote.prior.Uniform(0, 2*np.pi, 'ra')\n",
+ "priors['dec'] = peyote.prior.Uniform(-np.pi/2, np.pi/2, 'dec')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## PyMultinest"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "09:49 WARNING : waveform_approximant cannot be converted to delta function prior.\n",
+ "09:49 WARNING : If required the default prior will be used.\n",
+ "09:49 INFO : Search parameters:\n",
+ "09:49 INFO : ra ~ Uniform(support=6.28318530718, minimum=0, name=ra, maximum=6.28318530718, _Prior__latex_label=$\\mathrm{RA}$)\n",
+ "09:49 INFO : dec ~ Uniform(support=3.14159265359, minimum=-1.57079632679, name=dec, maximum=1.57079632679, _Prior__latex_label=$\\mathrm{DEC}$)\n",
+ "09:49 INFO : psi = 2.659\n",
+ "09:49 INFO : a_2 = 0\n",
+ "09:49 INFO : a_1 = 0\n",
+ "09:49 INFO : geocent_time = 1126259642.41\n",
+ "09:49 INFO : reference_frequency = 50.0\n",
+ "09:49 INFO : phi_jl = 0\n",
+ "09:49 INFO : phase = 1.3\n",
+ "09:49 INFO : mass_2 = 29.0\n",
+ "09:49 INFO : mass_1 = 36.0\n",
+ "09:49 INFO : phi_12 = 0\n",
+ "09:49 INFO : luminosity_distance = 100.0\n",
+ "09:49 INFO : tilt_2 = 0\n",
+ "09:49 INFO : iota = 0.4\n",
+ "09:49 INFO : tilt_1 = 0\n",
+ "09:49 INFO : Using sampler Pymultinest with kwargs {'importance_nested_sampling': False, 'verbose': False, 'resume': False, 'sampling_efficiency': 'parameter', 'outputfiles_basename': 'outdir/pymultinest_pymultinest/', 'n_live_points': 200}\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Writing priors to outdir/prior.txt\n"
+ ]
+ },
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "09:49 INFO : Renaming existing file outdir/pymultinest_result.h5 to outdir/pymultinest_result.h5.old\n",
+ "09:49 INFO : Saving result to outdir/pymultinest_result.h5\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " analysing data from outdir/pymultinest_pymultinest/.txt\n"
+ ]
+ },
+ {
+ "data": {
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Fz/3uAP+5tpNvXlN4zGv+/vFmblkQ4JIq71ns7dmh+WADP7r/n2hubOBLX/1muqyxgeKy\nci5d8TEA6uvrue+++6ivr+fb3/72obL777+ftz5o5a//1AjA2rVr2bx5M5WVlQQCAXJycli9ejX3\n/st3+MqfGvnVZydzcaWXRzb2cs+aZp7/m+oTXlQPsGbNGm699dZTus+MS7dYSvngkLKVmT+XABul\nlGuOdf4x6gkAt5EWmsojrxntWiFEJTAoPIuEEDkAg8ellPVCiAeEEI9JKQ/d+GjlQ46vFUK8Aqw9\nsadzfI7x/IJAAKiXUm4+gaoWAxuPd5IlaCfA41uChGIG/+/mdDLEX905met+vJ8lU9xcOd034jWP\n1PTR3Jfiwc9MPsu9PTuUTang2o+u5N11r7Lixk8cKv/1T/+Tpx75DZf809eprKxkxYoVbNq0iZUr\nVx46Z+HChbhirYRiBg/818/obT/IAw88cOh4fX09a9euxVjyNT4+P8DFlekvhNsXZ7N6Ux+P1PTx\nmQuP+UU9jFWrVvHKK6+c9D1mrJW7GfJBynxAgxmLZ40Qok8IsTbjsh11/mj1ZHhMSrkic85jwFGC\nNtK1Usr6wXOFECuPENQHgFUZ8ao8XvkI1AshKjNtfChGeX6VwAop5d2Z148Bx/y2yTzzEV3lIznv\nXM5QzDipVDf9MYPvPN/O/Z84nNk136fxk09N4m8fa6a9/+gdyt+tD/OdF9r5ye2Tjpkm+1zk8391\nDz///r+OejwYDLJ8+XL6+0NcOc3Ht+756jAxA6isrOSK62/hld0D/MOKw1awEIJ/u6mYH7zcQeQs\nTChkROtIJawEVgx53ZspG+38EcszH/bgkHNG/FCPVucxWA1UCiHuBe4TQgz+Paz8GNfXMYpwDE4s\nHFFWeeTExHH6Puy+M3UszPxeecTPYFuVpC20JRy2TEfk/Pq0AR39Oj9c23nC5//glQ6Wz/SxYJJ7\nWPklVV4+f1EOX324adj+ly/v6ufLf2zk53dMZmbx+blI25eVTX390V/w9fX1h8oXLlxIfmgT3vyj\nLVgpJW3ld/CNq/OPmlCYV+ZmWbWXn715YokmT/fMppRyjZTyPjjkMuacoMt0JJWZOpYPfoBPsUvD\nHrSUcrOUcq2U8nuZ3/WZv4eVH6e+ES04KWUQCAz2NWNtrTzJ+w8APUNeD/1CWHPEz9rBctIW2nFn\nYs87l7My384fNvSyfKaPeWXuY567szXGk9tCvH7P1BGPf/0jBbzXcIBvP9nCl5bl8cjGXp7ZHuJ/\nP1/OoinHrvtcZ6iQ1NfXs2bNGlatWjXMGptX5iKeMokkDDxDQlf+vDVEWyjFnUe4lcFgkEcffZRJ\nEZ3/eqgTdheS5VIxTYkhJddfew2VlcM/i729vQQCZywi4QFg0SleG4BDVgxCiFeEEJtP1tU7RTE9\nFvUMt0CPbG9NRoDvzbwebYLhtJIR01H7Nch5J2g2RfDN64r49p9beearVaMOLid0k394vIV7rykk\n1zPyY1IVwc/vmMR/PN/Ol35/kEurvbz8jakjbkpyPjEQ6mPhwsNeSGVlJStXrmT58uX09qazcdTX\n1/OxG69FDzbz1LYQd2TEq6k3yb8+08rXpjZgt00bVm8gEOCuu9KRBWJWOy/uGuCCgJO1tQNEEyat\nO5z8e7kc9p7m5OSMaKU9+OCDR5YXDn5IgQczH6BRyVgpqz7EWFM9kDvkdZC0q/ehxq4yVuNiYKGU\n8nuZ13dl6j00AD9a+QmyGbidtBt7sgxOBgySw4e856Gcl5+8WxcGeGxTHz97s4uvXZWOAzNMyZam\nKMGogVNTWLWum0nZGp+5MPuYdeV4bPzXrWVno9sTgv/9xQ/57N33jHgsEAgcspYGZzW/9Z0f87df\n+2s+vu5hmnqTfOH3B7l7qYNK9ehwlkELDSBLSmaH4oTaDe4scuLKUXh2+3T+26Nyz/LCYW0OiuhQ\nBoVxkPvuu6/jRK2NzNjO5swA+6DbebIfyrWkRWGQStJC8aHITE4MtbLuIiPQmYmBzccpzyE9jjYi\nQ9zMWwdd5aGTEifAo6Qt20ECp9PKPC8FTVEEP7qtjJt+WkdLMEVfNL2lW3GWRqHPRjRlcmmVl69d\nlX/MPTLPZ5oPNvDSM2tobmzglef+nC5rbMDnD3DDrX8BpK2wV1555ZDLCWkXcNWqVfzyl78E4P5/\n/Br74nlMvflehL+Uv7iinBmqb8SYsaEW2kjc3p/iuh/vZ1mVl6UVng99jxnhWkF63GhzJqxhIbAK\nCGb+NyqllNmjnT9aeUZIVg8JZr1/UBSFEJuAq4fMnB5V50mwZIhQV55A+UJGEdaMeK8cvG6I+7lw\nJFE6xn0/NmTA/4Ejr/swiPNtc4vFixfLwYjx5r4kT20Lkee1cflUL8VZY5OTbP3+MC67clKxVeMV\n3ZDEUyaXVJ947J2Ukt3tccoCdvyuD7cMbO3ufr79ZCuvfGMqAXe6rvvuu4+7776bssnl/HZ9D2/u\nC1OR5+DrV+VT6E+/50KITVLKxceqe6KQsaLullLelwmL+HJGSF45IkxkxPLRZlwnAuelhTZIWbad\nr16ZP9bdOO8RIr1V3ulg+Uw/b+wN87XVTaz6zGTcdoW7776b//jBT2me/lcUeG38xcW5bDgQYfmP\n9nHvNYUnFdM2XhhhVjQ4ivW2kbQbGWR4uMRR5RkL7LSNZ40F57WgWZyb/PONRdz7eAuXfX8PS8o9\ndA7AhnrB/11p40tXlSOE4JpZfj65IMC3/tzKj1/vGusunzTHGbdaDizMWGoPAncJIYLA/YNjYEeW\nZ667a8jfE5LzzuUUQnQBB8e6H0MRdo8HoapwLrwXAqRhyGTkxFaen118wGg5wKdIKc9bc31w9cDp\nWCEwlpx3gmZhYXHuct6tFLCwsDh3sQTNwsLinMESNAsLi3OG826WMy8vT5aXl491NyxOAwNJnQP9\ncZASVBtIEwwDodmZFXCgnERQ9KZNm7qPnBRwZ+XIWVOPlWln/DHSfZxPnHeCVl5efq6mYj6vmPr0\nAVKtByivmo007OgdvShuJ1phgGTzPvqiA2y5cwkBp/2E6hNCHDXz7cwunXD/KyPdx/mE5XJaTDg2\ntwVJtdTjmLaI8Pp9hJ5fT6q9l+j2/fSsfg1seaj+HBY+9sGHaieWkuztiJ+mXlucDSxBs5hwrHx5\nH/bJ04m8txvF7cReugyZLEX1zMNeMJ+BN7eg+EswowNs7zj17fIKfDb+7dm2k0oIajG2WIJmMaGI\npQyMgSDC4SPZ0gVGFYm6dfSv+x8G3vk5KAqu2ZXEdx/AllPIJ98ZvgogaZg0BCP0J47ONHwkeV4b\nbaEUr9aOFotrMd4478bQLCY29cEIisOF0RdBy0+ndorXv41WMB0UlWTrDjRjBjLViWvmdFLdbQDs\n6urnppfqMEI9CJuGTCVRXF60oknU3lA6YlsCuHNpDi/s7B+2UbLF+MUSNIsJRZ7LjplKYPM4MUJh\nFJeCLbcSI9yJTMVwlF+ETEZRfG6knkKoKtOeaSTRtA97WTX24mqM/hjC7UQoSZKNe6n+4+gp2cMJ\nk2z3ubUR9LmMJWgW4xrdNIkkDVyail1VKPQ6ETYNxaWAqmAv6wNzJXpfI4rTj+IKkOraiHvRPPS+\nFu6c5OT3tfW4Zi4hUrOfRP0ObLl+jFAExePEd+UCzIG2Udvf1Rbnmpkj7+xlMf6wBM1i3CGl5Nl9\n7XxjQytGsAcUBUwDxe1D9WcjFBW9vRH/1UsIPb8erSQPYQ+glSaJ7dqAs7oM1a+id4b4/Z4BnFPn\nEn63FgDH5GWg2FB9oJX0EnruXXJWXnXM/pzAntIW4wRL0CzGFXHdYNYj25HxKFpxOWpOBTKWBFVB\ncZjIZBRpGmAaaHlZ5Nz2EeL7mkm1dWNGnfivXoywJUjs285/fWQ6f/fGXkxDI9Xajb1sGcmmGmJ7\nX8OWV4nH/CSO8mKiO0dPMHHDHD8PruvmkwsCKOdAAs5zHUvQLMYNUkpmP/oBQgjUwukMvLkdmdJR\nszxI3UDv6UcrzsU9fzb24lyMSD+Jug9Q/TloBSWY8Sipjt0IofDcrYtpHYijuP3oHb1opflII0ls\n72toeVWYySipjl2oWaXIvtFjUT96QRa/fqeHX77dzd2Xn7cB+BMGS9AsTpm4biAluLTTM2j+TlMP\nRjiEVjqH0PPvYsueDppJqq0OhIKaXY0Zh/6XN+C5cBaOqiLMSD9AegLA7uTxm+awoCiAIgQpw0Qm\nYqjZdsxoHNXrQHGmZyvNaC+KNx+pJ1BcR2/IMoiiCH5y+yRu/Ol+LpvqPW2ZdS3ODBNS0IQQQlrR\njmNCyjCZ9exB9O52zFg6PktxebHlFvHBTeU4PsRO8X/xbidaQRnRzXuw+SsxQq3E697EXnwB0jRI\n7ngSxZuPa+Z1RGq2I2wqrtkXEt+/A0yDt6+dRJH38ObOFxRkYSYTOPJ86L39KLYBvEs+S6pjD47y\ni1C9BaR6anDPm3nMfk3JtfMvNxbz1YebeP5r1bg0K3xzvDLh3hkhhAr8jRDCsv/PMh2RONN++y5G\nsAf75Kk4pl2EY9pS7FNmYAwEmfHb9bQOxE65fmOgD8WXQ7K5C8VXRHzvq9j8JchkBPQ4aqAModpI\n1L+Nlr+A8Ls7iNW246heiHB6uOgP7/JBZ/+h+lRFoBWUkmqtw3f5fJKdW7Hlh9AKpoKiofdtQssL\nYCs5/p4Cty4MMK3AyU/fmHjpus8nJpygSSkN0huVrhJCFIx1f84XDFNy0eqtqNkFCHcJoRe3EHp2\nPaHn3iX4XA3CXogtv4Rlj24hZZinpU0pDVAOu7NCCJCQbNuB0NxohUuQ8SR9j7+J3m1iL5/BTU9s\nIhhPHrpm+8erMaMDCGWAwI2XYMaTGNF9CGcP7vnTcC2YTHzH+uP2RQjBfdcV8tv1PdZSqHHMhBK0\njHUG8BSwF3hQCFEyhl06b3hmXxsgQcki/NZWVO807KXLsJcsw5Y1k/Db2zF1N0K1MfuFllNqQ/Vl\nYw70Yi/Jwwx34JhyIWZiAKknDp8kTZASaepII4GMl2EvvYhEXQupljBqdgGLnzk8a+nWbGz6zIWY\n8QjJpu3YJznxXzUT9wWFyGQbyfqdPHTTvBPqX2VeeqytJ2Kc0v1ZnHkmhKAJIRxCCOeQol1Sym8B\nDwE/E0IUjnLp4PV3CSFqhBA1XV2Wy3Aq3LOxA61wMtFNtahZ00CahN/9FQPrVyH1BLbsGUQ37kYr\nmoze035Kbfzu4gJSnc24F01HD9WhlcxDy5+KHmwm1XsAPdSC3nsAZ/UVxD54mvB7v6H/rZ+g99Sh\n+mcT2bIXW24JRrB7WL05Ljv1n13EEzfPA0Uh1d2GTMT4ySWT2P2ly1g2KfeE+jdomVkW2vhl3E8K\nCCHswB2AH2gXQuwBtgkhrpVSPiaE8AK/E0L8CnhipMkCKeWDpLftYvHixeftf+NAQmfhC40YwW6M\n6ACK3YHqz+HF5ZOpzjn2xsBmOIgyaRqpzj6clfOJbH0UrWgmQrUTq30J75LPker8AOHwYQwEj1nX\naFw6OQ/VG8AINuJfvoSBV2uwT8lHK/oCUpoI00Bx54CiEnr5O2hFs5F6nNjuF8m66u9RXA7MJJiJ\nGAMJHZ9j+L/3wuIA+28JnFLfAN6tjxBwqeR5x/3H5rxlXFtoQggB3AS8ADxGep+3O4DpwLrMadsA\nDfgG4B6Dbk4ItnWEuOC3b2NGB9BKynHNvgh75WyEzc7Vj2xg6lMNx65AUUEamXEsA8XuwRjowBho\nR7GnH7uUEhSRXtV9iuy8bTZIiRFsIHDzRWgF2RiRvRh9uxCaE6Ha0nFqvkJUby627EkoTj9SSmQy\nhbApgERTT28QbDRpcu8TLfzj9UXpZ2AxLhnXgpaxtjqBOUAb8CppAfsCsEII8QnSey3+E/AZKeV4\n3AtyzGkbiPOxJzZhL5+B1LMIvbydnofW0rfmHRIHIzhnXEiqo4lpz7eOWofqz8Ho78U+uRBbfjeu\n6SsQmhskuGbegEwMoPrcCEyENnpc1/Fw2lT237kAW24R8f1bcFTkkXvb1dhy/NiKw4fOc8/9BHqo\nFb2vCffcT2JGuhF2DUiiePw4bad3QfnP3+xibpmLGy/IOq31WpxeJoLtbCO9E3SLlHK3EOJlwAEY\nwI6JvjEb+/FvAAAgAElEQVTq2eDSZ/ZgK5hE8kCQRH0rqnc6Wn4AqceRehP9L9fgXzGfxN4thJMF\neO1H/1v88qJCvvTKHtyL5xJ8eh324sW4Z11/6LgR7U3vlexwIfUULQMxSn0u4rrBzq5+wkmdbKed\n2fl+1OMsIVKEYN/NU6haHcYIB9F7Yuh9AyiOWQxOC6nePLwLP3Wo7VT3LvzLl6C3NqDlnf55oq6w\njsOmYJrSWgI1jhmXFpoQYp4Q4rMAUso3gB7gc0KImVLKLuA9YBrQmDnf+g8bhaRhovd2YsspJrpt\nP7bAPMxYH5GNfyDZWIM0qhEOO6nWEIrbz+sHRp40uWpKHgiBouq4ZlWg+Ian3FFcAaRhkKxvRSuc\nxKWPbaVq9U5m/PItVj6/my+8cYCPPb2DqgffpPrxvcT1Y88UxlIGRrAb1RsgsnEXtsAMzGgf/W//\njNBrP0DvawQyYta1A//yJZBKh1TsvnHS6Xl4Q7jv2kLquhJ8/dFmkvrpCUuxOP2MS0EDyoF/FkL8\nJYCU8vtAL3CnEOIWIEVazJyZ4+ftQP/x2NnVj+J0k+oMoRXlAILo1seR0iTZvgu9aw8YBSQOtGPL\nLeBva0YWNCEEaiAPY6APoSoMfoUkWrYR3fU8ZjSIzT+LgXe2oxVXYMsrQXF60EpnIo1c9F470szH\nVjgVGY8y83fv0RlJDGsjrhs8uquZyt/XMOPB11H9OYAdIxJHcecS3fU8jslLUDx5xPa9DoA0G/Et\nm4sQAxj9vWz99MLjWoCnQrbbxuovVxBOGHzx9wdJWKI2Lhk3gpaZzQRASvkUcBFwgxDirkzZ90nH\nn/UBlwAvSynDI9VlcZhhH20Jh5TINAYLEEIBKVH9uei9HVSv3sWrDZ1EU/qwuqSeQmgaqY5e9C4P\nqa59JOrWIVQ7kU1/Qji82HKzSDV3oRVNJtkcJfTSJsxoglS7ghlPMvDadvQeBTU7n6WPbCKWSltq\n2ztCzPjNO3yrph1bfgmeBZfjrL4AIxzFluVND8QLBTMRQfUXo9jdSNNA7+pDK84l2XKAdbctJMup\nnbFn6dIUfnXnFDRV4bsvdpyxdixOnXExhiaEcAH/RwhRTHrg/1UpZYcQ4ivAL4QQSCkflFK+nznf\nJqXUj1WnRZrZ+X7MRAxHVRYDb/TiKDPwLLiNxMENqFmlaAXTkWYtWn4eisuDa85SjGAPf/lGA2Z0\nB/bJ1ey9aXJaUAwdFBsypSNUFSPcjZpVjBkLYibD6Xi0gBcjHCO6bR/JxnYUdwn9r72IGe1D7PDg\nrL6SVGcQyEbNdjL3uYM8d1k+Nz++CXvFTIw+nYF1+9B7alBcDlSvC+FIi5R79o3Eal9CKDZcs27A\n6G9DK8zFjPai+gOU+c/8wnGbKrj/EyV85If7+MoVeeT7zpyAWpw8Y26hZaL/Pwf8N/AScClQCSCl\nbAfuBq4QQvxACDEY0m2Fap8gmqpgyy5A723FvWAqqb6tCIcP9/xbcUxZguJpRO/qwzF1EvG9jUTe\n30estgdhK8Q5YzF6ZwtVv69he0cI4XBhxsJoRbmoOf3YS+dhxoKkOnbjrFiGsDlJtnajeF1EN+8F\nUUhsx9MoDj9a0WxUXyGJhnfQ+3Tie5tQs0pINu9nxer3sZdPJ1HXS2TLXhTbZJzll6PlzQdZjFCr\nAVA9uXgX3YFnwW0gVPRQHe7FM0h1NvPfS8/egpEiv8anL8zmKw830Re1vlfHE2MuaJm1mVuAHCnl\no8AB4LOQFjspZQewCrgZCGauscbMToL1H5uG3tmCfZIf9/ypmLF9xOteI3HwHYyBKFnXX0z/SxuI\n1R7ECHowB3wkGtoIPbsBW+F01JwCbn5yK6m2AwjVhmtWBfG9jchUFO/SL5K14h9xVC5DaHWHUvFo\nBdmk2nbgqLgExelDCIFid6N68kjUvYVj6iSSB7vRiivQ8ktA8xPbfQAtZwFmfIDoB0+j9zRgyyo+\nFOc2FMXbhmtmOTafHZmMc0N10Vl9pt+6tojZxU5u+Ekdmw5Gz2rbFqMzLlxOoBi4VAixH/gh8NVM\n+WwhRBOwFbhEStk9WgUWo1PocfLsJxdx0xObUf3Z+K+Zj3D6UDQNoQj6X9uEmu1D6pWk2nYgkxHs\nxXPwXAihF97DWVmKc/b8dD4xR3oFWta1S+l/tQbV9GDLC5BsbEf1ucm6dinJ5i6EZsOM9mFGgyjO\nwzn5heZEOLwkm1Ionhjei5YBEN22D2dlKWY4SnT7EyjubOL7XkfYHGj5U4+6J8XtxOjrRxo6wmY/\nIxMBx0JTBf/20RIurAjxxd8f5MuX5fE3V1oJYMaaMbfQMjwD/CxjrSkcFtorgdlSyn5LzD4ccwr8\nbP/CMhSPn2TDbuI730XqSfTgAInGdmSqgujmh0m178JMhBl499dEatpwlF2McGiEnnuHgTe2YcbS\nM5P24jxyP70C1+xKFJcd72XzyLrhEhSHHdXrwuiPIOwepDnK/pdCgHl4ptBM6giHhpmKgaqhOP2o\nvkKMcFfmeJTI9icZeO83pHrqMXrySRxoB0XDjEVInqYMHyfLDXOyeOkb1Txa08eazX1j0geLw4yZ\noAkhDrUtpTSllPGMi5kE3hJC3An8O2CtJj9N+B0a+z5WwXt3LEamkkhDJ7JhF+45Veidu5FGCmH3\ngJ5AzSohvvc1wht+R2zHQWw5s1H9HvqefAsjEgfACMdINLQSqakl9MJ79L+8gVRHL7bcLPTgALb8\nqWCawxZzSz2OTEZwVrmw5fjRQz3ooR7sJXkkDrSheAuxF19AqrseKU3spfMBiO99FaEoCMVGdOvj\nAGiFOeidIRSniz09Y7cZcJFf4x+vL+KxTae2htXi9HHWXU4hxHygT0p5UAihSCkPfbVmLDSAy4B/\nBC6XUu452308l9FNk4tWb8FeWklsx0GMgShSLyW2dw2qr+DQOkXF7kZoLmQygpmMEt7wW1wzr8M5\nfTLBp9fhnDaJ6I463BdUI0gP2tuKegm98j720ny0whykkYNweNIiZpogDcxEGEfFpcT3NuG9fB7x\n2s1gGrguuATF5UDY6nBWX4Fr2keGd1y1I1NREAKJBClBDM2AcVYf41FcVOHh7x5rorY9zowi5/Ev\nsDgjjIWF9nHgeSFEhZTSHGqpDeFhYIGUcvtZ7tuEJqGbbG4LsrG171B815HMfLIeodpI9UGivgXh\nKCdS80cc5UtR7J5h5wohUBzetMUWKCNW+zLJAzqKuwIzlsBeuID43n763/45ode+T/C5l1Bck0FR\nMPojGP11uGZci+orTGedlRJH+cU4qnNRs30o9hSqL4Cjei7xvVvwf2QBMpki2bIebPsx44etLlf1\nFSAlZjKKe87NgCTV3ouWn4WZiDMzb2z3zgy4Vb7zsVI+uaqeH67toGtgFFfb4owyFpMCD5Ae5P+x\nEOLrUsqGQUtNCPEx4Hop5V+NQb8mLB3hOJc8vRe9rwvF6QIEZjyC6svmhRunMT03/WFv6o+SbD+I\ns2ohfU+vR8u/gEjNn3BMuRCjf/TNdgEUzQXeAiLbnsC75E5IVWHGGontfhHVX4iwTcKMh4huW4Nr\n+nIcU4ox+sOkurZjn5yPVjANhAJqJ3pnkMBNl6D3tSH1FOuvzOXil2IkGnaQteJi9J4QoZffR/VH\ngblAejLBM+8WID2epvfvwDWnEiPYji2Qj6aO/XDwLQsCzJ/k4udvdnH5f+7lymk+Pn9RLksr3FaG\njrPEWf8vkFLGpJRPAn8E/kcIUTnodmZWCHz3bPdpIrO3Z4Clf3wX4XDhqJgPFCD1HGz5M1ADeVyz\n+v1DWTQ+8kYXtuwCYrubcM2YQuLAe9jyqo4rZoMoTh+u6csJb/wjeqiVeN1bKO5sFLsHoSio7mxs\nWaXEal9G7/OS6ugj57arcUwpQvENoLj70ApzcE6fTKKhFeHIRs3KZdHv3uafqzTMcD/SNEl1BZG6\ngVArh7UvjSSmsZtk20YclSU4qvNIdTTy1s3TTvdjPWUq8xx8/5NlvHffDBZNcfPNJ1q46of7+NU7\n3UST1nKpM81ZF7TBheRSytXA74HvCiFuyKwSQEp54Gz3abxwIBjhoR2NVD+6i6lPNbCjM3TM7Kid\nkQTXPFaDfdI0kgejhJ7fgBEMI5Mpopv3EX67DvukOSQP7uH1A10YwS5s2fkkD7ZjBPNIdexGJk9u\n9ZjeU4/qySW88Q/oPQ0ozuHpdITmxD5pEamWbah+D2Y4hmtmOf6rFqG4ncR21qN39ZFs6Sb41Dri\ne4I4q+bzr5vb0EorMPojhN/7AK1gAWakh/j+t0j1Hki3HWpDJlPkfmo59hIXyfoPWPPxBZT6xt/W\nclkulb9clsdbfz+V+z9Rwob6CJd8bw+ra6yZ0DPJWXc5hwbFSilXCyFmAD8BLj7bfRkvDCR05j+x\nK51dIisPxePDjEf56JNNCM3OG5+Yy5TA8ODSvT1hrn1qB7aCMhJ1vejBARRfJZHN7yOTEWz5U/Es\nqaD/5c1kXTefL7ywA4SCsDvTIikEQnWkZzZVeyZBYgTF4UsPtqfiCNvIec0UVxaa5kpfqxz9nWgE\nm0GxpTf3TabHksLrd6D39aN6pxDbsR2px1Fzq1BcDvpf20b2x69A2FQG1m3DNbuSxP6DxGpfxl48\nh+iOp3BVX4nqLwJlAMwUyaZ9vP7ppVQEPEe1P54QQnBxpZeLK71sb4nx1YebiKdMPn/xiaX9tjg5\nxsJCyztiD4BHgSullJ2jXXMuE0sZzP3jRhAKjurF6EGN6LZ2Um0GWukcbDlFXPHwBvb1hgkndaY+\n2UD5qje45tGN2HKKEI5c4vuakalcoltWYwukU+foXfvpf3U9jupS4rUdqDmFyGQcM9KPvSQPW0EI\n59QrMfrbkUiMcCdmPITqL0Jx56AHm9IxYaMgTR29py69WckRVqQaKENx5yATSYRDQ+/tJ1HXjBlx\nEt3+BEakCzMVI9W6jej2vah+D9Ht+wFIdfehd3pJNtagenKRyQiqr4jYnldAc6N39mEmYihu37gX\nsyOZW+pi5cIA79ZbeUjPFGdV0IQQZaSXMB1KJyql3C2lbDqb/RhPXPB0HcLhBC2PvifXpS2aVAGK\nw07/ixvQO1PYp0xjxSPvM+c36zDCQexls8BWSqIuRP9L7+NZOovkgfdQ3NkY/a0oTj/C7kHvayLV\nqhCva0YrKAMg1dWCa2410W37UP3FeJd8Flt2Oc5pK/As/ixqoAx76XxcM2/ACLUNm2kcREqJ1BM4\np69AGilkIozUk0gpMWMhkk2b0YrnYEQT2LL9xPc3p8fN6tahegtQPXmorgCKK0CqoxYjkkV8Tzq/\nGaZECAUzFQU1vfBb0Zwo7mzMSE/6lJTEjE+s5Ua17XH+7rFm/vR+L/cst3ZfPFOcNUETQpQC1wFv\nSSlHz/V8HmGYklR7I/ayqQy8vhktfy5muAg91Eqqw4O9eEnGcvHgnLUYx7QF6L02gs+9jxGKoHc7\nsOXMRm/NxYh0I4aseRSKgpZXiRHuQiZ1UO0gBGa4H8UuyVpxIXrvLlDbcFT4EHSi92xH8QRJtm/C\nOSML15yPYsaC6AMdYHNgRHowon2Y8RDC5sAx5UI882/Dlj2JVG8Dqc5aTD2Oe94toDfjvXAWwqZi\nRuOk2mzprLZ215A+qiievIzlmLYGVa8bMxlNh5AYhxd+K67sdJrvbB9mzESmkoQS4zs0ImVIntsR\n4rYH6/n0rxqYnK3x4termVZoxamdKc7KGJoQYjLpNNpvSCn3n402JwIfdPWj2J3onf3YcvwoTj8D\n61ehuLKJ73sN38VfxjWnknjtQXyXzWNg3dZ0KmpnAeH31mPGQtiySg4tAJepGGhpwZBSYgRbcBbO\nwEiGEA4HWtEUpJ5CcbpRfXZyPr2C+J5GzFgC7yVz0UryEEJghKOEXtyA6nXgWfp5ZLQPPdgCRhJp\npLDlVWEvnpvOoybAWX0FjqrLkMkY2uQo0ZpanNMno5UFMCID2LJ9IPux+Yux5VZiZLLNSj2Z3mRF\ncyKy/QDYJxeSbO7EljMFM9YPmVhrmYqDqiFUiZASodqIpQyyHOMvfU9PROdXb3fz8MY+KvLsfO6i\nXG6c48duG/vQknOdMy5oQggb6TWZ71hiNpy2cBzhdGEMRNN5xPr7MRNhVF8xiisbPdSC1PNA6SHV\nHSLR0ApaHvHal1E9Odj8Rdhyyols+hOumdcTq30R1VuQDsNQ7SiuLFyz/CTqclEUBfuU6aRau4lu\nbyDV2UuqtTu9plJKkgfacC+cjqOyBNXrJvsTlxPbUU9k62bsRYtwZk8+5r3IVJxU12akDOBfvggz\n1klizxakoeOoXkBky16cVZcT2f5EOiZN0dJ7bFZdjhTtuGZVAGAvKyC8YSda6ULCG36DVjADxe4m\n1V2PLWcKqfYaFJ8D2aGT47Ifs09jwQs7Q9z7eAs3zMni0S9XWNbYWeaMf2VkEjE+fLqWMAkh3EKI\nbwkhrhZCjG14+Idkdr4PcyCELT9AsqULxRXAXjiLVPsHIBS0vGrU3DC2XD+JumacM8pJHtyA6slF\ncWYhbA6MUAv2krmYsT58l9yF4slF9RdjL5mLs/oqIht341s2F71vgL41rxNevx2ZSiETuajZVQgt\nC+HIAbWISM1uwm9vR0qJUFVc86pRszzpJUdDkNIk1XuA+IENpLr2H5ohVbO8BK6/GDPcCqbBti9e\niqN8BqnWfXgumo0Ra8I9fyXCnYvi9OGe/VG0fBeq24ktz050+3qkGcMxuRDV24F3yecRiooZD+G9\n8HNohUHUgBfMGGpWLvZMMG1jKMrqnc1UP7GPF+s66Islx+LtBOBrjzTz289P4YFbSi0xGwPOissp\npTwtgx2ZzLa3k9405U5grhDiJxM1e+0kvxs0DcUpEXYNxdeEa/aNuGasANWOGekm1dxIzsqPENlU\ni9HrxIwPYPMPz/0lTR2h2ECCsyoPM5mF3tuPGasn69qlKG4nvWtew7NoBvF6lcjGd0h27EZx+LBl\nlSLNFHpPA85pV5Nq7yG+pxHXjCno3UHMSAJbSR7J1h3E69chExGkNFDdOaiBSSSbarCXzsMxZSmJ\ngx8gDRM92M3WL15OlkOj9sYyqh/qBtmD99K5RGv2oNh0hNOOEW7EUVGFY3oJidpN/P2SKfznpu14\nliwm9NJGFFcUe8lcUBQUTzfRHV0EbryYxIFt/HrFDFoGYlz2xAeY0QFUfw7C6eErbzdihHegFU5i\n58en4jjLbt78Mhd72hMsnjKxZmDPFSaaU58H1Egpfwn8lPS4XNXYdunDseoj00gc2I3/6oWkWrtJ\ntq0HtQE9tAk9uIfAdRehel0oTjtST2ELlKJmlR66XuoJUu27sWVPJtmxGcXrwjG5CP/l88m5bTn2\n4jxitQexlxWQqBdE3v8titOPlluJLasEkAjFhi0wifi+10HkEXl/J9IwSTS04ZxahhntJbbnZRRn\nAFteJVr+NFRfIRhJFE8uyeYtCFVLi9RAFDi81ZsiBLWfnoew2TEHDhK45XICH7sM/0cWkfe56/Es\nnokZCYKqMiffj5qVS7xuK4GbL8NRUQxqG9JsSlt/N19CsmU3tqw8puV6WfbQBlR/DvaqxeghB4m6\nfqSZg2vWUsxYhJkPbSJ1ltMKffu6In78eucxA6ItzhwTTdAEsEwIcaeUsoZ0HrUFAEKIUb8ShRB3\nCSFqhBA1XV3jKxvRtVWF2HKLSNRtwXvZDPzXXIhWnId38Sxy77gGrSgXqRvoXUGcMzw4p15FonEj\n0kiCqqH3NeGYehXINtzzp2Iv82LGm0g2byO2Yz1mMk6qowdzIECyeSv2sgWYsSBCHT6YLjQnjopL\nSLZuR/V5SDZ3IuNJUi0CMz6AsHvSM5RCQaZimLEQZmIAxeFD9Ren61AVMNMbDXeE44fqtqsKtbfN\nxozHkIkYqs+DjCeJ7T5IoqkDW14JWnE5X3qjAaO/D4FA2FQcVcX4LpuJb9k01KwU8T0bsWXlsfe2\nmVz++Ha0oinoQUHwqXWg6xhBD6n2XvoeX4camAJSMuu5xrP6fk4tcNAV1kkZlqCNBRNC0IQQkwCk\nlI3AduC5zKEtwOBeaDdnJiCOIrPBymIp5eL8/PGXVXT/J6fx62tmkmraR+rgFlD60hHxisCMJeh7\n6q10gGpnHqo7B9/FX8aWV43izsGz+A5sWaD43GglHpLN+3jomuls+NwlCKcbo7cTxa6lo/o1F2a0\nb1Trweg9iNHXjKOihOTBdrSiXNB6UbMno3rySHXtI9W1D6nHEZoznbPHNHDNvA4AxeNK50HLyuOG\n15qH1T3zqTpUbxZmzKT30bWE39uJ3hMiuqmWnt+/RHx3F8JRgqN8Aa55y0AIopvfILbzfVKdzQjV\nxou3Xci+W6p5v6UvvQOVI5voplrsJRdiBPMwE2EE1diyZ9C/tgb75OmkWhrOqrW0tnaAS6u91ozm\nGDFeUnCPSkakfiGE2CSl/Bcp5frBY1LKDUKISUKITwD/Slro+seqrx+GqysKaPjLAhpDUbZ1hPib\nF7eh5pXS/9IGtNJ84rVdJBt/gUzF0Irn4Jq+AkyDZPsGXLMqcC+YTmzX+yhOD5FMOMMPFhXwD5s6\nsU8uIrb7AI7JSwhv/EM6Xk0oaVEais2BmYyQOKgg9T68y+YS2boXrbAF97xbkMkoCGXEHP8AglLC\n735A9seWEa99n9ruMmbk+RhI6KTaDuKcfRHBP7+NZ/FMks0BjGAXirsMh0fBlh8kUddM+L0gituJ\nb9lcnDMWkWjYiRHqwQgHue6RJhSHC6knsU+Znh7rm12B3plg4L3foLgCJBrW4136BRS9kVRfDIRg\nf1+EqTnek35PTAnhxMntx6ObJq3BFD3hFLne8RdScq4z7gWNtBX5XeBuIcQ3pJT/DYeETgN+AcwE\nVkopJ6SYDWVylhubIhA2O6m2XqRuEt/dQbJlC4o7B6Gmc/XHal9Ob7rrdeNZNAMAR8VMjN5O7nqz\nATOyDYTAXlKBVlxMeP0OlIIk3qWfJ9G4kUT9elyzb0Dv3HuobSEEqq8AMxnGHIiAgMBNyxh4fROp\n7gPYi3JAUZCKBolJCM2JGe8nXv82ijMrnessq5Do1joc5VO4ce1B6j41hzcPdqF6s0g1dmPLC5Bq\n8hHZ+LtM9tooWslcHNF5CPtktOJZmOEOgi+8S9aKC3EvuAJp6MhYirSdlURIE8WXjfH+QQyzGD10\nENVXhLC7SHXUIhMD2HL8yIEYistDS3/slAQtmjTZeODkViTkeWxU5Nq59Af7uGd5AV+4OBebaqUO\nOluMe0HLpOReJ4TYBPxOCCGklD/KzGzqQoj1wH1Syg/GtqenTjCe5PUD3XxzZ4RvVtj43r4oij+b\nVGMnzqll9P75MVRfQTonGYBQSLZux1l9JUZPmP7XN6UzuSZToKpohXm45s5DKBJhc6RXG8j04L9Q\nbDjLL07Hr9U8hC23atgCc9Wdi4z3o/rdpNp6sJfmE7hxGUZ/hFRXMB2z1tQB9kaQ04jufA7F6SfV\nvR9ppnBMuYhky3t4Fi8n9sF6pv65DqO/DzW7gPieHmQ0i1R8L0LVUDy5YOoIIYhs/zMyFUVoLjwL\nP4WWN4fQK+/jKC9OtydBmiaKy4H3wlk4/AI14EXY4wj7NBIN72D2HkArnoVw+Ei178Q5fTLJ5nqm\n5Z68mEHao871nPxH5GtXFXDFtCi/Xd/DHzf08uPby5hXNrJVa3F6GZeCltl/8wIp5R8zrzUpZVQI\n8SXgV0KIMPAnKWUU+O6Q1N0TikhSZ+4Tteg97aj+bFRPFt/fH09ndq2YSaJhK3qfF5kYQGRPOnSd\nUGyonhzMaC/24gsxguk1jkLVkKZByvz/2Xvz8Diu88z3d2rtvRuNfScBAlxAEtwpklosyVqpLY4l\ny3scO7Eniyd3bjLJJDeZmzxzM84kca6TmSx2HDv2JJYsb5IsW5K1Ubsp7jtIgiAIEjvQ6L2ru6rO\n/FFNiBQ3kKJEysL7PHgIVHWdc6q7+dY53/m+950gW87WLw6Mogb9aJVdZRkeiRquQ4vUI4wA0rEQ\nyinyO5qJtIv4F88j9ewb+Oa3YjTVoDdU4Yt4+y5K0E/m1V3ocXBzk9P6105iAGXeB1CCfpxkDn/X\nGoqDR5HFAlq8BsWfQWl0sUdrcLJjqEhvmWul0aINSClRQ9XkDzxNaMWDoHTjTCTRq5ejmCGvVjQ3\nSfrlnUgp8S+cQ+KxlzBqI4TXfx5ZyiOMIGrFIHZCQwl4M92GKyAvtLQxwF9+yMdju5M88LU+PrMu\nzu/dWveuu1O933BVEhowB/iTMpF9Q0pZKv+eFkJ8FNgGbBRCfLxMau85jOcsVv/7FpRgGKOlm8K+\nYxQyQygBH77OFoRuokYCKKaDGqnHLaRQ/TGgXBzulMqzsgz2+BGczAjSLqL4IhgtqzHqWlD0BKpv\nDnZyjML+b6LGvHQPJ/mkNzPyR8+QCBKagSzlsYcq0auXg0iQfnknQtcIrVuMUV+FXh3DSWbRIgV8\n824gt+dxEIJg94cB8HU0k3zqdfSGanztjfiXdiEUgdneRPInr2DUryWw+B6s/je83dJCEqN+CTI/\nhbQLXvUCePfrj+Fkx0nveAQQBBbfgxbvIrt5H5UP3kLkhuWkNm1Hr65AjQYpnhjDnlSJfHAlxb5d\nGM1XLqtHUxU+tKyCNa1B/vqZEZ7ryfCnd9ezru3SZoyzuDDE1ZIvI4QwysvLk3/HgX8GnpBSfr18\nzJRSWkKITwOvX0r1wapVq+SWLVsu27gvBbbr0vGtN1CDUaz+HMVjI/iXzqPY5yXJytIJ1EgQ/6I5\nZH6+D6E1ktvxMHrdYpyp4x7pSBc1XEdpeC9G/RLs1CBCqGjV7V5gfPWnUEPV2MlBstseQo02TC9Z\npZTg2qBoZ0hDu1YGO3kCXAekgxKIo9cuQq9qx8kexWipI7h6Ibkdh3CSGRSzq1xELk8jR9fK4Oan\nkPnHn1oAACAASURBVHIYhCB25zoU0yC79QCFnmMowTbUUBVC0XCtDFb/ZkqjB1B8UQKL70bxRabb\nymz5N7SKFqR0cVJDBJd/BKt/E5UP3oLiN5ElG6t/GDebR62OoQZVin37UKOVHLp/wYzkr8ubTqtO\nPTZ/8Qr5yJOvvJ2Pehq26/LoziSP7kxSE9b40PIY93bHqI9e3o2Ds93H+wlXBaGVKwD+CM9w+Fng\nWSnliBCiDi/o//hJUiu/Xr3UZebVQGgdj/XjTI7gpHyUJtLYEyWsIy8jbQuh+/F13oxRp+JaJdxs\nAaE1IjQfpeE9uFYGLdaMGp9L+pW/R6+ah1DU09oXvghIib/zJjLbH0avbMNJnl/gREqJtDJlNYxy\nTO2k0KPhx57s90qVGqFwcIDAknmUxhLYkynMOfXYYz7UcC0nPW/sqRNIp4ha0Ypi9uGkskTvWIcQ\nAqt/mNzOQ5RGJlGDfsy2BpzJiulxu/lJ1HgaZyKEGqomu+uHIF3vR9UJdN2N1beJyk/dgXV4B056\nCiUYQegGbnoKFIW/vbGTuzvqZqzl/04T2klkCg4/P5rl50dzbD+Wo7PW5L5lMe5ZGqU6/PbJ7f1O\naFd8ySmEUIFPAV8BbsQrZO8DRqSUw0KIzwNfFkIsBL4tpdz5Xo2ZAZQcl9JgH3pdB5ktO8HVKZ7Y\niRqpQ2g+ZClH4cDTCOM+1EARe3yK8PVzsEfiqO3XT7fjFlII1TiDzADsyX6QDvmeZ3BSIwjFOKuy\n7KlQ/BGsod0YLWvAfjMp9qQkkRqIk9vzGNpgK+bcDRQHBtDiUYLLO70kXHcQ1Ay4HVjHt1M4vAmh\nmWixJvxdG3HzW0k/vxWjuRY1FiZ217UgwJ5IYvWewE7vxxnMgZRoVVE0vRY7ccAj5oV3YPW+BEJg\ntl2LVjuOa1XhpMaRjs32z97AvrEUSctmUXUnc6JXrylJyKdy84IIH+gMk8w7vNGf5ad7U3zpyREW\n1fu4a2mUu5ZEL/vM7f2CK05oUkpHCLEdiEspvyuEmAN8EnitPBMbEUL8E97y8++u4FAvCw4nsqCq\nWEcn8HU0kfzpD9AqWqaXa8IIIoNxrIPPErrms/g6F2OPnElGQjWQtnXGcQDFF/Hs58AL/l+AzKR0\nKQ1sw991t1cp4I+e8ZqTopGKP0Z2y/8msOx+rGP9mB1NBFcuwJzbQPKpn2PUdXgEHaxEmCFKYwfx\nFa5Hi3ajxsaw+gaxE2ncbAF/11yCqxair40RWtuFYxURruMl7voCmK11TP3kVQJL2oFrAYFWNUF2\nay+xjespHd/D3984j7jf4NqWqov7IK4wVEUQD2rctijKLQsjTGZttvbn+dm+FH/59Ajt1SZ3LYlw\n15IYrZVXn6rI1YoLEpoQ4kvAzcDDUsq/Kh+7Gc8e4LnLNI564FohxGHgy8Bvlo93CSEG8Gzv1ksp\nxy9Tf1cM/ckcii+AdXgCaZmokfozAvOKL4qbnyK77SEv8F9IowTjmK3XoJ0M7OcT06T1VghF9bTR\n8IL8F4K0sij+GHpNJ/kDT3nkdZYZjlBUL6UjWEVu1w+o+NAD5HYexqivQgkHcDI5pJRosUZv08Ip\noVd3kt31QxRfBDc3ibQtFF8UrXoe9kSSqZ+8SuyOdVj9+7FHj4OqofiCuIUsWlU9sXs2kN91hOLQ\nES/1RKvzLPDGjqAEQtzeXnuWO3pvQRGCqpDObV06tywKk8o7bD2W45XeLP/rhXEqgyq3Lopw5+Io\ny5v903WyszgTM5mhPQz8k5Sy7+QBKeWzQoioEOKmy0RqjwNGebZmnDKuDwDbpJQvX4Y+rgoUbMdb\nJkoXKV04y5JRCOERQCGFEArCDKFVtJDd/jCBrrvQazopDe5Gr12ItM6UyL4YSClBuhjNK1GMAGqo\nGllIIc4ySzsJxR8F3SS3YwjsFE62gCwWEZqKEAJz7rWkX/0nL6am+xBCePdiBFDMMNIpYk8coTRq\nE1i6nOwb+1ErLP6/GxfxiSWe7lrKKrH8+/spHt2Jb14TwZWeXpqTnKB4dAdqrIq9H1541S4tLxWK\nEMQCGjcviHDT/DCZosvewTxbj+X5zYeOkbFcbl8U4bMbKllYf/W5XV1pzITQKqSU2996UEqZFG/j\n23TSXLjclgsUykvMohDiRSHEJ4A/A9Zeah9XIxrDflwrj1oRwagIUjgwgIjPOWMmJRQVNVAx/beT\nHESN1JHb+wThWBOl0R6UUA3KW8uXLgJSStRAnFJ2HKOhGwBfx43kdv8IoZsI7dxty2IOJ9FPaO1y\nEt9/Huk4hNZ0URqR2BNHPKVZITxCLqebTN+bXnaekjlKwzlKwxNEb1/Cf909NU1oEVOn92NLef34\nJJ94dQSrbz8AaiTO9+7tZlV9xRlj+kWDEIKwqXLN3BDXzA1RtF16xyxeOpzl/q/2cUNniL/7SPPs\njO0UzITQYuc5d+7H+DkghFgGJKSU/aeSGnjxtPKv1wF/CFx/uYQhrxbMrwzh5rP45neRfmk3Zvt1\nFI9tQQnEEEbovDMOxQiiNi4l8/rXvWLzc9jMnQtaVTuF3pcQut+bAeancDOjBFd8dDrOplfOxddx\nI4WeZ/B13jwtl/1WCM2HkxzEyd6DXl0JQiG3q59C7w88Mg7XvVnZcLbrhUBKh9JoD755C5EFB1ks\nnPG6a5riHH4gflH3+YsKQ1NYWO+ns9ZHY0zjqy9P8F9uK9IUv7jvwS8yZkJobZd47ly4D7hfCHGX\nlLLvraRWxneAR34R3aAipo4Wr0FoRbSKMEZTDYo/RuHwC7iJAYzGbqRdPCexuYW0p5qRn8ItJD3l\nWiHKaho+ioO7CXTd5c2STr3OSpM/8DTB7l8up2ikEUYALT7ntJ1St5BGKF5ZUv7A0xi1C846jpOk\nmN38ryAUnMwoWqQeRfcjzhGDOydk+ecXbPl4ueG4kk2HMnznjUlMTfCfb60lGrji+3pXFWbybmwX\nQvx3KeV/OfWgEOIfgEcuoc+/wAvy/60Q4ounkpoQ4l7gDinlFy6h3fcMfn9+mP9xOIdvfguF/Ucx\narsxahfglgpkNv8rihFE+M6uLi6EAEVFCcTBtjz3cjOIk5/CbFxGcNn95Pf/FO0UDwDplHDSowSW\nfsgjsWgSJ9WAGvTMbt1SgeKxzRRP7ETaRdRYo6flr5+7/lAIAUYQitmyXHi7p5o7Q0gpPTPiyjac\ndBZhCoQ7K1l9NkjpEdm3Xp8k5FP4+Jo4d3aFaYqb+PRZmaJTccFvYHkDoF0I4QK95cNtwOcvZUNA\nSpkHfiSEMIH/KYT4bSnlkfK5R4UQOy+2zfca/mJ/CiUcxTo0il5biZOSlAZ34aRHPRVZoXiZ/OeA\nFm1E6D587dfj5KeQxTxqMI7QTKRj4xbeIjoiFIzGZajhaqy+V1FSAdx0H76Om3AzY2S2P4wWn4MS\nqkZo5SB+ZvRMeSHe2qzqJcNeJLyyLU8oUq/1o8VrKY0c4zsbF190W7/o6Bku8A8vjlGwJZ/bEGfj\nkii1EX1Wb+0cmNEjVUr5VeCr5XQNpJTPXmqHZbUMKaV8uLws+ZIQ4pvAdinlkJTy6KW2faWRtErs\nHE6iq4LldTF82uk7mOM5i3VPDeCkJjHmLMR6cg9G4zUUB16hNLwPvXYh1vFtCN2PGqlFoJyxWSCl\nxB7tIbDMq5s8We94EtbA1tMluksF7ORxItf9NlK66I3VKKYO8SXIUo7M9ofxd96MPd6LOE/Ma7o9\nu4hrpQGJ4o9fMMdt+jrHxrW85bKd6MdsWo6vcx7SdtDrDdyMn2saZ2NlJ5EuOPzzK+NsPprj/hUx\nfnVDJQ1RY1aK6AKYEaGVk11jJ4lMCDEXT/r6iJRyx8V0KE+ptSqT2gK8hNl1F9PO1YQD42nu/PF+\nnEwSNRRFug5uLoMareTR27zi6HufOoyTmkSL1+FbtAp7LIkaDqDoPopDe1F8Yc8sWFEJrf4kpcHd\nWMc2Y7auxclOTMekpJVG6D7U8OlGKW4+Sf7gMzipYdTQKUmmqobZuhahGQhA0Zd5np25IXJ7HsNs\nWoE93sv5IKVEi8+heHwbbi6BVj0PWUh5gugXgHRthGpiTxxEi7eiVbUTXL0c6/AgakUIo97Anhzm\njU+s/YVLwbhU7DqR50tPDbO8OcA3P93Kkkb/7NJyhphJYu0EcP+py8tyTlqfEOINYPXFdCiEqAJU\nKeVI+dB3gX+RUo5eTDtXC+Y/NYLVuxejeR5640JKQxMouoI5txInNcbdP9wJAvTaZtRIM4XDJ8jv\n34k9NkVo/WLsIdDic7zdRCnRKlpRAxWo867HaFxKdsf30Wvn42Y9iSCEgptPUjj0HGq4FmkXsSeP\nYk8cwWhe6SnRlusppV3ETvQTWHzP9Hid7ATZ7Q+D62LOXYedGLggkWgVzVj9r+Pr/KCXW4YLmo/0\nK/+IGqxGMc+0c5Cui1vwlDT0mvmE1n0O1BOUhidQ9Aqit3djj/bjZg22fGItVYHZnTqAqbzDnz0x\nxBdvrOZja+LEL0GP7f2MmbxbX5JSPieEiAJzy8emykvDr15MZ0KIJuBW4MmTx6SU+y+mjasJ/VM5\nCr178M1fSW5rL1b/bsyWWqTtkH55F4HuDgIrrgMpSb+8k+KxHgJL2nESIYz6edhDXqa/v/MmisN7\nwbExGpdNty98URR/BOm+WbqqmCGINYFQKY32IFQdNz+FVjnXS4gVbz7JXSuNXtN5miFKbu+PMZtX\nYieHPOWOC5CZlJLCkZcJLnsArSqHdWQHwtBQgn58HTdh9b2K0P3TS0/pFBF6AHt0H2q0nsCSe/Ev\njpB5bReBpfMIrGjBHj6KPZ7hazd3cvPc6tmZ2SkQ5R9DE8T8ZyZdz+L8mAmhnQzYJ4UQSTz1i/vL\n5yZn2pEQohG4HXhBSnl+6Yf3CG568ghGfSuFfcdx8xZm87VIKweqjtncjnVkF9K2cbN5nJyFMOtJ\nPP4Ybj7hlfEYQbRoPWqsBbNp2enyO/kpCr0v4+ZTILTTYlWK7kcWkmUvTjm9W/lWKIEK1EiDR4jl\ntA6cIqXRQyjn2EU9A9JFlvIo4Vrye5+l6jN3ITSVxKMvElhajzNZj5MaAUVFizVTGjuE0bSc0Ppf\nA6eE5AS57UPE7lyLnRigdGKEf7ipk9vba2eJ7CyI+lX+ZGM9X315nO+8keDP72uY1U+7CMyE0E6N\nefUJIb56inb/jLSHhBAteB6aL0gpD1/8MK8cRjIFrn1mECeV8FIaglH+ZnkF17dWYU+O4F+0lvzT\nL2A2XUPx+Hbyh55DIAgs+zBabCnFY7sQfhOcevK7vo0arvE8LQGcIq6VhakB0sc2YzSvxM0lKI0d\nAtdGr+tCCVTMOPB+KqRtYSeO4eu4ieLxV3CtImbzGnzt15Pb91Mv9eMcZienQSgoRhBnagDFZ+Jm\nC2gVYSI3riTx6EsYrWtx06PYk0dB1Qit+RW06gz5/TvQ4lF885vR6yNYvbvR4jXsf7D7XTf/fa9h\nSaOfv/7lRp7al+Kz3zrGr19Xye/c/N6vWX03MBNC+0MhxC2n/N0mhPhg+fdVwA/Od3HZzOQDwCvv\nNTLrfOI4Vn8PWrwWvaYRoZs4mSn+46sDOE/tQo3EkZaLEjARuo/CkZc9IULbwup9CX3Np9Cr1gCQ\n2/sEZusaT7L6JDQTtTwrUwIVuPkkSjCOVmwA1QCneFZ5oAtBShfXSmO2XYvQjuOb34JWXUHmlR3o\nVd0EFt1Bbs+PIdpwQVITQiDMMIXDm4hcfz2FQwOE1ixCDQeI3nENqad+7hHXghU46SxW3x7UaBMV\n912HLCYpjRzHOtTH//rgQjZ21J23r1mcAiFoiRu0VxtsOpjhc9dWETJnl6AXwkyXnNtO+fvU38++\n1jkFUkpbCPEdKWXpYgd3NgghfMCvAK8AR6WUb686+xzo/MkgxeO9+OevpHBohNy2vbh5C72uEv+S\neZhtPoRuIG0XN1dAug5aRTPSsVEDFUi7eFp7dqIfJRA/ZzmQYoa9GVt69KwlTVLKGS/RtFgTpWIe\no3E5xeOvUfWpVV7huCJIbdpOoLsD17kD69Bz3u7nBRJiFX+M0thBioMKaiiNPTFM4eAO1Fg1Ffdt\noDScxJ5IosUjBJa34yRHsQ5vRY3G+cbNHVzbUol2CbPM9xNcKekds9gxkGf7QI59wwUaozorWgJ8\ncm0c3+ysdkaYCaH9/qlKG6dCCPHMTDq5jGRmAOuB3UA38CEhxNcud0xuqlCkePQAZudyks/uQA36\nUYLzUaMmRlOG1M9+TmhDN772RoQGem0lauUIga67sPp/jpubwr/wjun2vOTXHCLScNb+LkRWbiGN\nnTyOGqzEaFyOneg/Lwk52Um0yjlvpnq4LgIVc24D8aqY56bUEsdNzseeGvDkgtTzCwoKoXgF50ic\ndILfXdfB354QFHq2gKqhxSO4hTEKB/rQKmt5/mNrmRs7p5n9LIBU3uH1o1l+3pdl14k8YVOlq8HH\nDZ0h/uD2WuZWmsQCKsHZmdmMMZNKgWkyOyUfbcdbz71LqAFqpJQPCSH2ALcA/0kI8ddSyqHL1clT\nvaMokQqKxyZRTAPUhdiDb+CkRpDWevTqbjIv78ScU4dQVcLXdZP40YtoFTq+sqqsPXUc69hmhKJS\nHN6P0bIKmU+e1o9bLhuyJ4+iGCHUaP1ZiUqrnAuKgtmyhuLgTkpjh7xaSjOMVtWGm5s6jRDdjBfT\n8s1djzmvkalHX8JorvHcmxqriW1cz+R3n8NoXQOqTvHEDrRo/TnVNbRYE25uAqNZATeIk0qwvG4+\nh1ZXIuVc9o6l6U1kqAmarKyvwFBnZxPnw1TO5svPjrL7RJ7FDX5Wtgb4jRuqWFDnI2SqBAxl1h3q\nEjGjb54Q4teEEJPAz4DvCSEmhBC/+84O7bT+TSFEAM8VXRdCXCulTALPAJuBz5XPn+v6XxdCbBFC\nbBkbG7tgf3+4axItVoXVNwhOPaUTOygO7kLxR8ls/XeEEUYp+1YCqJEg0VvXYCcOIKXrGZNsfxjw\nynwU3Y+bm5puX0rPvs3JjKFXdxK5/j8ifBHPmfwscNIj4LoUDj+P0bCU6E2/R3jNp/F13oTV+xJu\nfuq01wszjJtPIEsFsOeh+OYgNJXMa7uZ+PenKRw6jlYRRlopfO3XgRC4VubN8dkWTmYU4YvilvIU\n+l7F13mL577eXossWaxvip98b1lcE+He+Q2sa6qcJbMZ4KEtCRI5hx/9hza+/Zk5/D931HHj/Aj1\nUYOwT50ls7eBC377hBC/jDcri0spO6SU86SUld4p8bl3eoBlA5Xfx5Pgvh9oB+4RQiySUk4BLwI5\noPlcbUgpvyqlXCWlXFVdXX3BPqXjgKohizaoOm4hiRppwMlOIItZcEuokRBONk9p+BjZLc+jVYYR\nPgNpZbAn+tDrFiMLKaSVQfFHT1n+OUjHws1OEF7/eczmFQjd9EjpHMs+oagIM4RQTfI9z5B549sU\nR3ooHN6EVjXPE1w8OXbXmVbBdUt58vt+Qnb7I0w98SNKw6Mo/mZKg2OgqSihGnJ7H0cN16IE3gyH\nStvyXNqFQK9dRPyBB3HSfYSu66Y0egS9fi7KbMrFJePupVFsR/K73z9B34Q1q2d2GTGTx2mblPIv\n33qwfOwdVdkTXpboJ/BKo74OLAY2AfuBLwghrgdG8NQ7llyuftVQFDeVQK+rRK9JY7asxp7o87Lx\nG718MTdvofhN3HwGWbKwJ0cx6irR6tJoFS2URvbh5BKokQbcYg4nl8AtpLAnjqCYYYIrPjItzlga\nOYBihs4rqCiEQPFHPbISCm5mDKN2oZfUKhQvDucLY4/34iT6CS5/kOyWf0PoPpRglZfh74uQ2/EI\nTiqIai7GSQzgJIcQqnnaklU6JcyWNRgtq1HMPIUDx4jduR4tIpCFHLs3nvPZMYsZoDFm8P8/0MSa\nOQE+8rU+/va5kQtfNIsZYcaJtZdw7m2jLCm0E29W9jyeAfHHpZSfE0I4QAvwReAg3nL4suB76yq5\n90c78S1cytTjr2A2bSB87X/ALaRQyoXgasDEmcqg1QRBUSmNDOBbsIDkU697RrqL7sQ6vgMnPYTR\n2O05f7uOp0Kr6gj9KOgqFOZSHNxdLlmakX+kJ48tHZzU0PQ1ii+MPXmM8IbPo/gi2FMnQNW9GWKZ\nOGV+CjVcR27XDwhf81kvFqecnrQrpcTNJ8EI4qT24Otswb90HkIInKyG8AVY8LVNqLFqnrhlDvPi\nQY4ksmwdmiJbclheF2VJTXR26XkBmJrC/Svi6IrCN16d5NPrqojOVga8bVxUYu1FnrtciAMLgL1S\nyq8LIU6mTb+Ot9R0gHw5pnZZsLQmgtB0hGqjVUZx8wmUYBVuZtRTxajpRKj15HbsouLDNwIHcfNp\nhFrEN78V68hWFP9cgkvvQzol3HwCrbqELBaxpw7jpLL457eS292Lb24jTvIEWsWlz3q0yjYKh18g\ndM2vohjezqK0C2etsVTMEGqkjkLfqyj+GK6VQkp3epanBCpQCkmEa+NKOU1m0nZwJvNo0TaUVh9u\napzbH9mCLFkI048aqUCoGs7WE7jFAkbzPA7e1TJbDXAODE4V+dorExwetfjchkpm+f/y4FISa09C\nACu5QGLtpUAI0Q0slVJ+W0r5pBBiU1lHDeCkUNjtQJ+U8vF3oH+E6UPaJbAd0FUKh56jNHoQrbKN\nzOZv4e/aiN5YTaGnHy1eC9LFOrIXX8cS9OoYuT1HsE70oBg6el0cNRxDmFF881vR6yoRqoI1MIK0\nLc+OTrz5UchyOVNxaA9GwxKczPg5iUFKSW7vj7160ME9ngWc5vMSeMXZn/hOahjp2p5sUKIfOzGA\nFq3HSY/i5iYJLL4bO9lD5AMrwHbIbD9Ifu8RtLinfWZPpPAvmkNg1fWgCJyxKaxjI0iriF7bgtkW\nwerby7yH0xx8oGs2yP0WvHw4w1eeG+WOxRH+6PZaFtT7CRizjHY5MNMl57nyzd4pAas5wB8LIQwp\n5dellHkhhF7OZ/t52Xz4T4Ab3qH+kVYBpIKdSKPG8hQHd3uzKLuAGm0gv+8Jgqs+SWH8CJGbu7An\nhvnBL63gl364Ff+i1VTcfa3XjuuWzULOZgungHQRqlHO8SoXeBdSFFNDBLo2kj/4HGqo+pyCj0II\n9Jr5FIf2oEYayvLcifMKRKrhmrIlnEFoxYM46RGc7DhG6zWY7Rr5HfsJLOtEq4wy+cNNaBVh9Jpu\nnPQIQjMxmhZiTx4i8f3nEbqGWyjia2+kNKLhTB0j80aW6O1rsIcO0vnQLvY+sPgMbbj3M57rSdNS\naXD/igqWt1y9psjvRbzdxNptZzt+KSiTVxGmlWtfAv7ZM9OQXz8lOXcRnhvUTVLKvZer/1ORtEq4\nhQx2soheX4l1eCtm61rcjKdwpBgBRHwOduIYuAVwFWQhx8KqcJmkJIXDx8lu68GZyoDwUjuM5hqM\nxmoUn4l0XZx0Fi1iokbqcK3MtMuT0P2YDUvQKloIdn+I1KavoNfMP6cpilBU1GAVOEWk82aFwsmy\nJimlR3CugxKpo3h8G+FrPodaPUJuaw/S9tQ8ZHYENVxHdON6tHiUqcdexGyto9CbobD/X1CjDV4c\n0RchsOwB1OAUSBctVok9OoksjaNEFxFsT5J84jWiG9fjjPex4Buv8vi9S1lSc9GeOr+Q+OKN1Xxv\ne4LfengAx5V01ftZ0uhnaaOfrgYfrXFjdufzEnFRibUXc+5iUE7N+CMhRD3wLPBs2TH9N4B/PElq\n5Zc/DfzscibSvhXHU3kU04/MFlAjQezEAEoxf5plnFtIQaIf34L52KkSbrHAom9vRo1Wkd8/iHX4\nOMJoAG3IIxMZRWga+T1HcC2Pm/1dbcisD3PuBnK7fgCujVbVTmlwF+bcdWS3P0Jp4gh63aJzLh8v\nBCmlR7xO0ZPXNvyE1/4qxlyL3LZeYndfixL0yrGEoU3PFgqHjyNdSXFAUjjwNGq57lPoftzsBM7k\nEfTqDgBKE0fI7fwhaqiawsFnCa39DMHVC0n++FVCH1iOEa/l7u9t5d/v7mZ98wWr5X7hEQtofG5D\nNR9fHac/UeLohEX/RJHNR7McnSiStVwW1JksbvDT3eRnaZOfjhof+qxa7QVxxdXjhBAq8CngK8CN\neIXsfcCIlHK4vLz8shBiIfCvUsrdb6e/PYkCrX//LFq0kmc2dpy1PCdXckDRkLZEKIqnuipOj3EI\nzYebnUQNBZDZAlqsCntiBLWijULPdiBMfscj6HWLEKpO4fCLFA45GI3L0KvaUUI1yKz3BdUr5xBc\n9mGKQ3vAsQks2kh2+8OYczeAol5SgfppY1V1/F13oVe1eYH/8HHSm3ow2xpIvbANXBejsRr/knbU\nkDery+8/ilCbyB/8KWowPj3bO2mCLEtvWs6Vhvai+CMo/ihKsJJC70soxm1o8UVkXtqJ0VhNoHsp\nH/vxTnZ85lpivgu7ub8f4DdUFtSqLKj1fEqLjqRoS8azNv0TFv2TJb6/fYovPzvKeNpmXo3J0iY/\ntywIc31nGP+siu0ZuOKEVnZL3w7EpZTfLZdXfRJ4rWw8PCKE+Ce8xNq/e9sdKhpGQxeSHB/499cx\n5yzg4J2Np70kZZUQqgpCxU3bqKEa3GIW9VR9f+mCooAqkK6Lr6MbOiD59GYUs47crh+hxpo9TTCn\n5KnLFnO4uQTZ7Y+AEARXfmx6mamGa/HHmhFCkO95BqNxGW565O2TmRAoRtBzgtrwBdxCmsLBA945\nU0cptnu7mCSY/P4LxO5Yh15TgT2awGzt8qoZKtun23NLeZypE/gX3Tl9TK9dSGm8F5RJFCOEkx4m\nW8xgNK1Ar12Lk9qNdWQctaKGVU8c5fAvd76te/pFhBACUxOYGoR9KnMrvfCC40pKjiSRczgyXqB3\nrMj/eHqE33roOJ/dUMkf3D6rYHIqrhaKrwc2lmdrXwZOmgt3CSEq8BJn10sp+99uR9JxSb+4B86F\nwQAAIABJREFUm+yrfRjNiykeO8Sm/jfLoRxX8msv9qPGPF1+KSVG03KkXZhWjp22YKtdiD2eRI28\nOcsrDU/g5JJolW2nLVGFEF4ahWujxpowGpdR6PFS55ToCQp9L2EntyJdB3uyHyc1/HZvdRqKP4ri\ni1Ia3ovQdNBUL0HY6UBaaUrjR5CZRvSKBSSf3ox0XISpI20LLdaMMENIx8bJT+Ekh/AvvB2jJUdx\n9HWk8LwCAovv8QxQpo6hBOJoFS3k9z5BcWALijmf3O5etMp6nKnxy3Zf7weoisCnK9RHdTa0h/nU\nNZX8+b0N3Lk4wtdeHudEonjhRt5HuFoI7XHg78vO6Qpvzhw/AHRJKVNSysvyP8HNFHHSFr4FraSe\n3obRsoBPP7kXx/VS6hY82uupU5hxctsO4qYq0Gvmo1W0YCeOIQEneQJcB726AyeRwmiIY/Xtx81n\nAS8A/1a3plMhhKA0dgjp2Ejpktt1mPgDH0RaJdzcpGeWch6dMuk6uPkk7jlqP89+jU1p7BCKEcTf\nfhNqqJrS6EGyO39AaWQ/2R2PoIZrUAImpaFxfJ0tIPrxd92FLCQpTfSCdAks/SXMtiC5XYcJX78c\noSgUhzej+EKEVjyIf/4tuFYGe+oESqgKq3+zF3vTVCQ6bi6N7b7VV3oW54PtSHpGCvxo5xR//uQw\nn/xmPwdGCvzJxjois8m4p+GKLTlPdUwv/1soLzGLQogXhRCfwNvNXHs5+5V2ASczQvLpYYKrVmL1\njqOEfDx1ZISV9TGKg/34Fqxm6rFXCa7twh6MI10H/8I7MJqW4ySHMJtXgmpQmthH+KaVWMcO4EyO\neJpoNXGcpI519FXPlVyc+cxwizkv32vph3BSI2jxCFoshFBVLy4XrjnrdeARk5MeQTEjHrFGG2ek\nPCtU3VPHPQWliSMYjd242QlKoz1I10UN+nALRYLLO5n6yasIvQ/f/A8S0AM4+QSudYzSuI/Yndfg\n5hIElrditjWQfnEHWm0BrW4xyvEdyGIOaRc8wUvXRlolhOqNY1Yb7fyYytnsHy6wb8j76R2zqA5r\ndNSYLKr38YXrKulq8FMR0GZt7d6Cd53QhBDLgISUsv9UUgMvnlb+9TrgD4HrpZQ9Z2vn0gegIFQT\nZ2oAe0wFMUZo3Ry+uD3BnxVKaLFKin0jGA1VlAbCZHc+hD12CKNpBYGujajhOqS9H3t8isita5CF\nUWSpyEufvp7r/u01fB0dZLcc9ExLinmvzOmUonO3mMNJDhJYfBdavIXi4GtEblxx8v693cjz+GOq\n0QZAEOz+EPlDz3vXvdVY+GyQLkI9/eM2G5eR2fJvSMfC13YdICkOTRBavxQERG+/hsKBfgq9R7DH\nc2hVMYJLFqD4S+R7NqPFqigO9qEEQsTuXkfyyc0YLZLAyo9SGtyFUDT0ui7U6BBGUzUyO4UanfXe\nPBWOK+mfKLJ3qMC+4Tz7hgpkCi7t1SYdNSb3LYuyujVIc1wnaKiETGU2peM8uBIztPuA+4UQd5U9\nCk4jtTK+AzwipRx4Jwbg7dRFvQx9t4RQVFzX5Y93JVBjVRQOHwO7Dntql7e0rOuiNLIfZ+56T1W2\nlCP+kQ9SGuqjNDLAX9+yhPFcES1ahTBLqNEQWrwTq/cExeM7UKP1aFXzcFJDqMEqlEAcvWY+TnYc\nNejDaPQUQISuIl0DaWXhHKRWPL6dQNfd3usV7bS8s7fCe1u9pF5ZKqC+pbxKjdQRuf63kK5Tdkk/\niNFci3TzZLe+7BmfRCsJb2gvy48ncRJHcbMqz310Le0VIUqOy8IfHKTQu4PIbatJPb0VYSZQo41e\nORWHyB9MENt4DdahrXz/vmVnHev7BSeVabcey7H7RJ79wxYxv0JHjUlnrY8HVlSwtMlH1K/hNxR8\n2tmTsmdxdlwJQvsLvCD/3wohvngqqQkh7gXukFJ+4Z0cgFvMeXpfRhDFLOEWsii6iSsLSMdGaCpu\n0UEYQdxCClH0lmqKEQB1BKO6GaEqKOEYarSS/7xlBGnlcXNpVKea6M2rSD2/DTUWItjwK8h8gkLf\nK+jVnTjJE9iJY7hzrkE69nQOGIDi9yEJ4WTHUIKVZ3yRpW15xBRrAqA00eeZB/tPT1h1S3ncXKJc\n/qQgNB/SthC+MLndj6FVz8OoW1TuVEOvTZDfswM1Hia0oQurZyvfvnsFnZUhNvWP84c7J5B2CSUQ\n5tu3LWBdY3y6nElXFQ7fv4COH+pYh3cQuXU5pcEk1tFBcFz06hqCa+ZT7N+LVlXPyvp3VKDlqoTj\nSvYM5nm+J83rfTn8hmBJo5+b54f5ozvqaK82CRgKfn129vV28a4TWrkm80dCCBP4n0KI35ZSnrTK\ne7SsrvGOQagaTvIE/q6NSOsEvuWLKI0d4MWPrWPPWIrffnUAY049hf1H0aqXYVoZnPQw/kUbkdKl\neHSY0DpPqUiLVoJrYI9PoVb70aojCNVTr4jeuobCwQHSr+3GqF+NUVjiqWNoJnrNAooj+9FrFuBk\n3gzsy5K3mSBUw0vGfYs+mjCCGI3diLIgo5Menk5uPeX9xc1OYM7dgNHY7VUP2BZ24jiFvpeRxdy0\nhLde04lb2EPxuCB0w3LUAFg9WzGaO7i+1dvl/UhXEx/parrg+3rol9rp/ImfQs9W1GCEwJIaUFSc\nVILCgWMYjXM5eO/cC7bziwTHlTy1L8Uj2xLoqmB9W5C/ub+RZc1+wj5ttn7zHcCViKEJ6eHh8gzk\nS0KIbwLbpZRDZQPjd65/zUdg+QPgDKHXVYOcQquopjUWoDpo4D6zH3NeG4UDAlnah1bVjtGwFDef\noDS+neCqBZ4OWsEi9ewW7IkUel0lTiqLWygSuXkVRr2XDe/rbKY0MonwjSGLcykcfgHFH0M6RXzV\n8xCagTuRR5ZsCgcHcBJptEoV6drwFilut5jDSQ0R3uBNXotDu71yqLfeoOsgizn0hiUooQGEoeFM\n1iF0EyEUz6ilci72ZD9a5VxKQxNU/spGiv37sUYn+d93LeXaS8zmP3hnA5liDS8PTPBb2yaRrstf\nrazh+tZF7ztn9MGpIn/x9AhCwG/cUM3ti8JUh3WMWbOTdxRXYoZ2qs/nw0KIBXgJs+vejf6F5iC0\nCXxLOhBKCic1yc5PXQNAQNf46q2L+PWf7Sb8gWVYvaMUDvZQyhbQqqKE1y3GnOsZnSR/9gZaPILi\nXwJOCS1u4GbHST71OvEP34Qa8iNLRfxL20n8cBNmw1oC3R+mOLgTLVKPXjMfAL02ztjXH0evr0Kr\n6ia/7wnM5lVI600zK+nauLlJ/Atum97RtMd7vQJzX+T0G5QOwgjgZsZwJocRfhPFn0KLdyLUV7AT\n/TBuE1z1cfSGKVy7BmdqFDeTZN9n1hPQ395XImRo3N5ey+H296+PZLrg8IePDnLT/DBfvKmapths\nbea7hSsxQ6sCVCnlSZnO7wL/IqUcfVf69+kEllRiT/aiRirZ/al1hM0334Zb22sxehysnm2o8Rqi\nH1yC8AU8ZVorj2vlcdIWTiqLGuymcPgFrL5XUaMNhFZ+DN+8ZvL7jxJYOofctk34OpcR6O6g0LMd\nLbqY4JJ7Tx+P0YWvcxFuforc7h+h6D4vbndSsltKpFNCq5qHVjkH18qgmCGc9BhaxZlLQenYCN2P\nVpVDCTYR6Gpj8vvP4180SnDVJ3AyI55lnlDJbt1K+KaVlAYP87WbOt42mc3CW2b+9yeH6W7y8we3\n1VIVPr+b1iwuL97Vb7AQogm4FXjy5DEp5f53cwwAvzfPz4amlSyuiZz1/ME7GxjPVbLu6UFKowNI\nq4Dw+ZG2jSxZuHk/Rn0lslTAOvoaeu0CZMmiOLwPLdYIyjBuvgo0HatvH+bcRSiBTjKvbcOoXY7i\ni+AWcxSPbcHJjOJkxpDFLOaca87QPlP8UexEErNlNcWhLQCYDWsBeVZ5TTVS62X1JzPotXGErhG7\ncz1TP30NxTiB3lSDmzmBdXSI4OpFCDw1kBvnXNhr4f0GIWAiO3MHxuOJIt96PYGmCn5/lsyuCN41\nQhNCNOKJMr5wuX00LwaLIxqfX3Hh4HRVwOTQfXOBN1/7xmCCB36yFzXegZ3MokU9vX63kMbNTeCf\nfzNGq4s96cPNpNCrGnj0xkY2fm8L5rylBJa041oTyEKY7LaHUIKVuMUsSqACEanHzU6cRmZqrAmr\n7zWCKx6kNLGHyE0rKRwcQKuZQq+a5xm52EXKaiS4hSTu+GFCKz9OaeQA4RuWku/ZjlBVYhvXYo9n\nKI1MolXHCKyYj5M4Tml4mFc+vnZWhPEsCBgKq1rP7y2aL7o8fzDNj3en2DGQ41fXV/Ir6ypn5bSv\nEN4VQhNCtAAfxCOzw+9Gn+8EVtbHkKUiWoUfN5PD1ScJrfok9sQR1JCXX5bbvZnwDcuxJw7xb7ct\noKs6wl99YD7/eesAaqQK++gQuDmczBhKII5a9ig4FZ5ibZzCkVcILn8QJ3uI4KoFmC11KAEfySde\nxWy/jtyexzzPgEAcNzsOqkGg+8M4haMEVy6gNHwUoSgoviD5/ZsRmoEWjyJLkxQOHEGL1/LGp9ZR\n/T4L2M8UivAKxd+KQskjscd2Jnm+J83y5gD3dEf5x481z5oCX2G844QmhNDwajJfuRrILFuy+dau\nY7RE/KxvvjgfSUUI9Ia5FI/1EL5xJaln3sDX1ogarsFoccjt2YyvvRHFLOFIydpGLyt+XVMc5/kD\nmG1tlF7fg96woFwwHsbNjIOigvCEIWUpj7Qt3EKS0MqP4eR7Mdsa0Wv95PdvRatuILCsg9yeffjn\n34qUDtLKoug+9GZB4cBR/Ivb0ao0SiOT7Pr0OiKmju3O5cB4hr1jKSr9BqsblxE1Z5dEM4XjSp7v\nSfPoziTPHEjRVe/n3u4o/+2eBipDs7HHqwXv+CchpbSFEN85RXH2baGcv/YhPEWOnaeUS80IfXnJ\nn+5P4+YGcfO70Gua2H3vPPz6zJ6se+9qZf63RpGFESo+dD3WoRM46UHshJ/wB1agGEWKR3v4yf2r\nppdxjWE/ij+EEAXUUAC9ZozQigfJH3oBJzuOdIrIUgGhaCihKszW1SjRRuyJvfi756HFoXjsIH95\nXTu/92IPel0zoeu6ye84hDOaQLouMuhHK9YRvXUVTnaU0sgILz24ikiZtDRFYXFN5Jxxw1mcHVJK\nHtqS4O+eHyPqV7l/ZYw/3lhHzWx87KqEOCWL4qpHmcyuA8aATuBxKWXh/FedDrNtqaz5wjfQ4lGM\nudXYw324hRw7PrF6xjOWbNFm6SN7cNJTaPFalFAUt5DFSYyB6/Lj+5bSVX06cTzVO8Lnn+3BaO0m\n+cRrmK11uPmGMwrLpZQowWMUeo4RvnEFsjiGm0vzxoMrqAqYDKbzbHhkB0iJ3jAHrbIOELiZKUpD\n/djJCfTqRrbe3U7UN/ufbqYQQmyVUq469diqVavk7X/8GJuPZvlv9zawuvXq1/8/2328n/BeI7RG\noEpKubPsDKUDw8DgWepBzwqjsVtWffph1FgW6+gQoeuXoYgUbrHAkU+umNE4pJSkizYDqTz3vTSK\nm88gTD/fXFt1WlnQW9H+0B7cfBaztYvcnj4KPccwW+sQzJ9+jZMexckfoeKe67CnhrEnhtjz8VUE\njTcn044r+e6+4/zBc3vRm9qR+Sz2xDBaVQM/v2/++y6J9XLgXISWv/tb/PALbXTWntsE+mrC+53Q\n3hOL//LMTAVcoE0I8Td45sNpvHv4lhDim+faPRVC/Drw6wBqpIHC4RcxW1Zh1K0g89J2oneuwz2+\nm92jyfMaeewZTXHvs0dxpsaRjgOKglZRzY9va2dhVfiC93HoI110fu8A1pGdhK5Zh29eE4lHX8LX\n1jn95BdGADdRRDoubi7Nn6yoP43MABY+NYzVdxC9rhWjsR2EQI1WUjzey9rHD7P/wwtnjX4vE75w\nfRUf/ec+/vKXm7hpwYU/41lcWVz1M7SygcrvAfOBF4BNeOT2O3hJuX3AFLBYSvnihdrTKufK8I2/\niyyk8HXchG9hBU4yg9nqQxg+Dt3XdtbrOh7vpzTQi97YhhqtBEcBDZypUYonjmDOWcjBOxsueD9S\nStq+/ipm2yKyb/SiRsM4yQZKQ3tAul7JUvg4TjJLYHEtTiZJ70eXTF8//8lhrKP7MTvLReC9J5BF\nG72xGv+CZoonehCKyuGPdV/1y6OrCeeaoW3ZsoVXejP8X48c54aOEP/1rnpCV/FO5vt9hnZVP8aF\np3L4CbzSqK8Dy4B55WTcHwBvlAvbo8CF2cRrFdUfQ/giFIf2YA+HsMcSXhwsmz7rFc8cGaU02Ie5\nYBVW7xSTD28i8ehLTD70PMX+LP4Fqyj2H2DrUGIm9+RJeSsa1tFhnMkqrCMvYx19HWtgK4VDz+NO\n1VHsH0YJRXFSk9PXJgslL1F33jIym/ZS2N+PLNUgtFZk3iLxw5fQqttxcxme7B05zyhmcTHY0B7i\n2d/pwHbhtq8cZu9g/sIXzeKK4KomtHJcbCfe8vIF4A3g4+XTIeBBIcQNwAbgZzNv10XxRVCDlchS\nHiXg96oBjDNjT7br8rmf7cdsW0z6uR1I28FsXofZdC1m0zXYyQyZ1w5gtC7gwz+ZYdGD44BQkLYN\nqoGdGABVQyiaZzmn6p4vPRqy9Kbe2aMHh1AjlRQHEl6uWmQ5spDCHu9FWi0EVs4n8/IujOZ5/ObL\nx2b6dsxiBgj7VP7m/ib+0wdr+OQ3jpK1LmpzfRbvEq5qQisjDlwLmFLKbwKvl49vB44BvXg+nRMz\naUyoulfY7ZQw267FtQcw5zXipBL83fIzk1x3jCQRqoqTcpBFG+l2YB17g9TL/0BxeC+KsYjSaAJJ\nAGkVOJ668NNbCYSR+TRaRQQ3n8DXtgEnPYqdPIGv7VqklUYYBtLOowRC09f9v7smUCuqsQ4PIEQT\npeF95A88TWn8MLk9j2KPVGFPpkAP4WSSWPasdv/lxj3d3ndkMHlZspBmcZlxVW4KlHcwl0opvy2l\nfFIIsamsowbexgDAHcAxKeXxi2pbMwmt+zWQLm5uL2rIj9FcSWFvL9c2V53x+o++PoEaq6Z4bBiz\no4nikRMUj29HCcQpHHoerXIu5twGSsdHUSIVbB1K0BQ5t4Q2gBqrwp4Yxr+kndyuQ+gVy4ne+H8D\nEoSCk95BYEkbTmoSNfKmZLUsFRGGiZuz0OI+nNQQWlUbbm4SOzlUlgfyeUbGQpAr2ZjnMWuZxcVh\nLF3itx8+TndTgHnVszvJVyOu1hnaHOCPhRCfBU8UUghxMqnq52Xz4T8Fjlxsw0JzKA68gZPpwdfR\nQuSDa5DFPNJ1WPHTfg5NZji5UeJKiZvLoJh+rw7GlQjdRDolZDHryfeohifMqKvgOpjahQPG225v\n8nLYanyYc+qxTryGGh/ByU5gT21HCQfxL52HMznKQxtqpq9TQxHc9BR6XSV6fRqzdQ12YgB76jj+\nBbd6SrXZAqpfQagasdk8tMuGZw+kuPUrh1nR7Odrn2iZ3XC5SnHVzNCEEIaUsgjTyrUvAf9cLrz+\n+imVBovw3KBuklLuvdh+lICPql/diKK/+Z9djVbhX7SK0ugJbvnuFoSme5JBmSmEpv+f9s48Ou7q\nyvOfW/WrUlVpXy3b8iLvxkjewdhgIOAkQFhNaELi0EmngSzdDaeT02cmZyY5vUwnPZwQ+iQTIPRk\n6SzTECYEwpIGNxhsGOMVvK+SbWzJ1r6UVOvvzh/vp7QwGDAqlUrS+/yj0q+W76tf1e/Wu/fddy/B\naXMJ1uQR3bwbp3w54QuuJdV6hNDcjyP+IPHGJiKLZhM7cJSLJ9V/4BgK8xyeuHEha5/cQf6S1YRm\nTia6dT/png58kRDBadXeWAu4fdMZDt9qylb/dEUVn3t+L6ELF9D17OsEKuspXHmXedF0gnR0N5H6\nmaRam3BKq+xFlyEeebWVH29s5YefmcLKmQUf/ATLiJETBs1LzfimiEwE1gPrvY7pXwEeGjBq3sP/\nHRMza/ooWppK0Ld1PeH6VfgiBSQam4gdPYX2x3GqSsmbsxSRBJpM4JsyC1wH8QUITqmif3cYN7EX\np3gagcrZuP2dpDp3EJ4/Hbe/DX9hCaXhD+fiLakuMQsDiRjp7iiJplacoloQH/07DxLb20DRxxYT\nO7CVjcfLuXRqBatqyvDlRdC+0xResYTeTW8hvX58oTxSbV2EF9SSN6uK2KGdbLnz0o9yeixnoar8\nw3PNvPLXc5hWbt33XGfEDZrXLf3zwIPAlZiN7A3AaVVt9tzL74nIfOBnqrprKHrzi4O0OwHw+el5\naTvJ1k58gcmIU46me+l88hWCNVXguiTebkEcH24iRXBiBQWr6okdOEb8yC7SvX045cWE62fjlAdI\nNOzjpTs+fAvR3S3d4PORTijdG3YQnLAYySs0ezoDk5HAUXpe3UXBRfNYt/4wDV+oQETY9uk6lvxq\nKxLso+SGFbjRFJpM4ZTlk2pvInZoJ7+6fhFV+TbGkwlEhMtm5fM/nmvm/lsnv2f1DUvuMOIGTVXT\nIrIDKFPVx0RkOrAOeN1rPHxaRB4GHsXkow2J7ngSf1EZyaYOUu1dBMqXmU5MbQ1IsI68yZNJ97YA\nPvKmzDQdk9w0/tJmOp/ZRNnaKym4eAGu6+J2tZE88zaJ4908tXYptSXvrJ3lqvLaiTb+9I023Gg3\nEsjjHxaWcXVtJTe/ehqntJL4/mOE500j3eXQ89ojuH1t5E1fQWjWFaRaNqGEcfuinO6NMaEgRGk4\nyP47V3Dh7xuJH9oJXk5bsimJU1rJ6+tWMqnw/RclLOfHj9dN49tPN3HV9w/xTzdP5oq5dsdArpIT\nOwW89nUzMbM0Ab6qqg+KSD1wAkgDQVVtHapWXu0FOu2HL9K3/QRufymaitO360mckimke89QuPJu\nxGd+hRMn3yR+/A2cslpCcz6G6kEC5cWE62rpe3Oj6QJeVcOb10x+V/nq5t4Ylzz+JqRT+Eur8BeW\nGPeyq41UVxukUoTrV9K9fifim0qq9Yip9y8+kmcOUnT5vUjgGIGJFSDtPHBRNTfOfXfu8MmefvqS\naWaU5NsijUPg/XYKDPDywR6+8cRJ7l5dwZdWvXtFPBewOwVyg6eB/+WVAvLxnzPHK4AFqtqdCWMG\ngCq+vBDp3n4kECHVcZxA5RwQH268F9drTpKOttF/4AXECZNqbyTZvBeNlpE42YIm4mgqxU+unsMz\nq8oJn7WyebyrjxW/3IxTUoG/ci6xg510Pb+D3jeOoekSwnUrCV94Mf78QnyREJrsx19SQ6rjBJqM\n4wuXIIEQmkojjh+nrIp7XznK3pZ3d0ifXBhmdlmBNWZZ4Io5hfzqi9N54MWstL+wfARGzOUc3DHd\n+xvzXMyEiLwiIp/DrGZ++MDUh8HvI93dQaCqBF+kF5FF9G75OW6sm+DkRfhC3ub0gYKLbtJsVRKf\nl72vSChCoHoqX9zQiBvrA9fFFylAnADqpkn3dJI3dTapdpfoli1ElsyF1BQ00UfswDESJ05TtOYi\nAEKza+j9f3sIVCwjf/FtpKOtBCpmISKk+2Jo2sVfXgOuy7W/2UpgUi2Hxll/y1xiw6FeFtVYlz5X\nGYmuT4uADlU9NtiogYmneTcvA/4rsFpVD2RSf0ZBgP7WU4QW1NP51EYCVQspvPQraDqBLxA2OWaA\nP1JKpO4G4ie2E6iYRWDCfOAA/lITnHfKppBKF+AvDuArDkEyhqaSiN9P3vT5pLvj9G5+jeDE5SQa\nosRPbCJQXotTuZhUxzbiR08RmjmZ4NRqgsdPkzi1FV9oGsHqBYjXYDhcN4vo5j30vr6L0NyphOuW\nET/yJnOe9nPw+qmZPC2WD0Es6fLA+jP89p73LmBgGXlGYoZ2E/BpEfmUqjacbdQ8fg08rqonMi2e\nH3CI54Vxu06Z1IcNO/CXFuIvjJBo6cTtMZ3MgzVV+Aonk7/kdkgnkHAjicYOIsvn0/Xvm0mcaiUw\noQyNJ0i1deMvzkeCATSVRpMp3L4YgfILEJ+fni3/SnDyIvr2PUe+cxPin0S84RR5MyaRamsmsngG\nwSkT6N/TQKxhL+F50yA1i+TxYoITV+Im+9HECbqe20LxJ5cSO7CN09EqJuSPjhpdY4VowiWeUkoi\ndqUzVxkJg/ZdYCfwzyLyl4ONmrc4cI2q3jOcA9h+Wz2Lf7kVyYtRuvZSUm1R3GiM0LxpOBXFgNC/\n+yixg/tJvB1FHD95tRMpvWk13S9twxfOI2/KpWg6ia/QwV8IGo+ibgoJ+ZGIHykPI36HdNSE/ty+\ndvyRctJ97TjFk9FEknR3O/GjexCfD39RGcWfWE66N07n0xvJq5lFOtpO7Oir+PMryKtdiVO2n/jh\n0zilVTx7qJkvLJo+nKfJchbl+Q5fXl3BXb84zuN3zSDgt3HLXCPriwKq2q+qTwK/AH4gIjMGxdJ+\nB3xnuMdQEgqy704TlI/t20qq/RBoC8mTu+jb9hJ9OzfglKYpXlNPxec/QfmfXkvRlUtx40lSrV2g\ns4kf20z3hgfpfukB4o2bkVARGu8l8fYOUm2NpvEJ4IuUE5xUR/LMfvA7BCdeiK+gg8CkClJnThKs\nmcWeP1sNPh/xYwdwo/34C01Z7ujOx/GFCkmeOUDixDY0PoF4YxP+4jL+fk/ncJ8my3tw31VVhAM+\nHt2YmTUqS2YZiRiaqOHfvK053xGRnwI7VLVJVRuzMY6Q4+fQzbNwdSb7W3to608wvSRCTWGYxq4+\nPv5SM8mmRtK9XSBCXu0FpLsVp6oU3DSxwxsIVM4GVZItB4k3vo4EwgSqFxBvfB23v5PQzMsQEcJz\n1xCaczUAzoQW+ra3ULp8Dv373mDzDXPIDzo8ffV0rv3tTnzhatQ1Hrgm+0h1nPAaE0cRn2NWPn1+\nUzHXknVEYP7EEA2tiQ9+sCXrZN2g6aDEN8+ozcMkzF6S7bGAaU13wVkNTWpL8jl080y6Tu6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+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x7fcd4294d190>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "nsamples: 186\n",
+ "noise_logz: -27681.688\n",
+ "logz: -2143.922 +/- 0.252\n",
+ "log_bayes_factor: 25537.767 +/- 0.252\n",
+ "\n",
+ "CPU times: user 11.9 s, sys: 1.1 s, total: 13 s\n",
+ "Wall time: 13.1 s\n"
+ ]
+ }
+ ],
+ "source": [
+ "%%time \n",
+ "result = peyote.sampler.run_sampler(\n",
+ " likelihood, priors=priors, sampler='pymultinest', label='pymultinest',\n",
+ " npoints=200, verbose=False, resume=False)\n",
+ "fig = result.plot_corner(save=False)\n",
+ "plt.show()\n",
+ "print(result)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# dynesty"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "09:49 WARNING : No default prior found for unspecified variable waveform_approximant.\n",
+ "09:49 WARNING : This variable will NOT be sampled.\n",
+ "09:49 INFO : Search parameters:\n",
+ "09:49 INFO : ra ~ Uniform(support=6.28318530718, minimum=0, name=ra, maximum=6.28318530718, _Prior__latex_label=$\\mathrm{RA}$)\n",
+ "09:49 INFO : dec ~ Uniform(support=3.14159265359, minimum=-1.57079632679, name=dec, maximum=1.57079632679, _Prior__latex_label=$\\mathrm{DEC}$)\n",
+ "09:49 INFO : psi = 2.659\n",
+ "09:49 INFO : a_2 = 0\n",
+ "09:49 INFO : a_1 = 0\n",
+ "09:49 INFO : geocent_time = 1126259642.41\n",
+ "09:49 INFO : reference_frequency = 50.0\n",
+ "09:49 INFO : phi_jl = 0\n",
+ "09:49 INFO : phase = 1.3\n",
+ "09:49 INFO : mass_2 = 29.0\n",
+ "09:49 INFO : mass_1 = 36.0\n",
+ "09:49 INFO : phi_12 = 0\n",
+ "09:49 INFO : luminosity_distance = 100.0\n",
+ "09:49 INFO : tilt_2 = 0\n",
+ "09:49 INFO : iota = 0.4\n",
+ "09:49 INFO : tilt_1 = 0\n",
+ "09:49 INFO : Using sampler Dynesty with kwargs {'dlogz': 0.1, 'verbose': False, 'bound': 'multi', 'sample': 'rwalk', 'walks': 1, 'npoints': 200, 'update_interval': 100}\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Writing priors to outdir/prior.txt\n"
+ ]
+ },
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "iter: 996 | bound: 4 | nc: 1 | ncall: 9243 | eff(%): 10.776 | loglstar: -inf < 12037.340 < inf | logz: 12027.149 +/- 0.202 | dlogz: 13550.032 > 0.100 /home/user1/anaconda2/lib/python2.7/site-packages/dynesty/sampling.py:218: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.\n",
+ " warnings.warn(\"Random walk proposals appear to be \"\n",
+ "iter: 3994+250 | bound: 147 | nc: 1 | ncall: 24445 | eff(%): 17.361 | loglstar: -inf < 25551.669 < inf | logz: 25538.075 +/- 0.224 | dlogz: 0.000 > 0.100 09:51 INFO : Renaming existing file outdir/nestle_result.h5 to outdir/nestle_result.h5.old\n",
+ "09:51 INFO : Saving result to outdir/nestle_result.h5\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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WA5dSPiGE2DvRNk0HFv2ullhnK56Vl6E43cS62vjsH/fy5K1rUiZdbvj9CbT8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\n3wH0AAAAAElFTkSuQmCC\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x7fcd255b8150>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "nsamples: 4244\n",
+ "noise_logz: -27681.688\n",
+ "logz: -2143.614 +/- 0.224\n",
+ "log_bayes_factor: 25538.075 +/- 0.224\n",
+ "\n",
+ "CPU times: user 1min 14s, sys: 12.4 s, total: 1min 26s\n",
+ "Wall time: 1min 10s\n"
+ ]
+ }
+ ],
+ "source": [
+ "%%time \n",
+ "result = peyote.sampler.run_sampler(\n",
+ " likelihood, priors=priors, sampler='dynesty', label='nestle',\n",
+ " bound='multi', sample='rwalk', npoints=200, walks=1, verbose=False,\n",
+ " update_interval=100)\n",
+ "fig = result.plot_corner(save=False)\n",
+ "plt.show()\n",
+ "print(result)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# ptemcee"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "09:51 WARNING : No default prior found for unspecified variable waveform_approximant.\n",
+ "09:51 WARNING : This variable will NOT be sampled.\n",
+ "09:51 INFO : Search parameters:\n",
+ "09:51 INFO : ra ~ Uniform(support=6.28318530718, minimum=0, name=ra, maximum=6.28318530718, _Prior__latex_label=$\\mathrm{RA}$)\n",
+ "09:51 INFO : dec ~ Uniform(support=3.14159265359, minimum=-1.57079632679, name=dec, maximum=1.57079632679, _Prior__latex_label=$\\mathrm{DEC}$)\n",
+ "09:51 INFO : psi = 2.659\n",
+ "09:51 INFO : a_2 = 0\n",
+ "09:51 INFO : a_1 = 0\n",
+ "09:51 INFO : geocent_time = 1126259642.41\n",
+ "09:51 INFO : reference_frequency = 50.0\n",
+ "09:51 INFO : phi_jl = 0\n",
+ "09:51 INFO : phase = 1.3\n",
+ "09:51 INFO : mass_2 = 29.0\n",
+ "09:51 INFO : mass_1 = 36.0\n",
+ "09:51 INFO : phi_12 = 0\n",
+ "09:51 INFO : luminosity_distance = 100.0\n",
+ "09:51 INFO : tilt_2 = 0\n",
+ "09:51 INFO : iota = 0.4\n",
+ "09:51 INFO : tilt_1 = 0\n",
+ "09:51 INFO : Using sampler Ptemcee with kwargs {'tqdm': 'tqdm_notebook', 'nwalkers': 100, 'nburn': 100, 'ntemps': 2, 'nsteps': 200}\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Writing priors to outdir/prior.txt\n"
+ ]
+ },
+ {
+ "data": {
+ "application/vnd.jupyter.widget-view+json": {
+ "model_id": "29f59ef596b043efb2b87b14c4701569",
+ "version_major": 2,
+ "version_minor": 0
+ },
+ "text/plain": [
+ "A Jupyter Widget"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "/home/user1/anaconda2/lib/python2.7/site-packages/peyote/sampler.py:148: RuntimeWarning: divide by zero encountered in log\n",
+ " zip(self.__search_parameter_keys, theta)])\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n"
+ ]
+ },
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "09:52 INFO : Saving walkers plot to filename\n",
+ "09:52 INFO : Max autocorr time = 59.0675487444\n",
+ "09:52 INFO : Tswap frac = [0.02425 0.02425]\n",
+ "09:52 INFO : Renaming existing file outdir/ptemcee_result.h5 to outdir/ptemcee_result.h5.old\n",
+ "09:52 INFO : Saving result to outdir/ptemcee_result.h5\n",
+ "09:52 WARNING : Parameter $\\mathrm{RA}$ in chain Chain 0 is not constrained\n",
+ "09:52 WARNING : Parameter $\\mathrm{DEC}$ in chain Chain 0 is not constrained\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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mKJfLYwEQxl2+x+Phs88+48GDB7z33nsHmtD9fl+63rxeL5FIhHa7LV/P5XKYTCYqlQrR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\ngZJIJBLJWCINlEQikUjGkv8PKwkGCydkJ54AAAAASUVORK5CYII=\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x7fcd2483c810>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "image/png": 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lcqqVZ+/dcqkfwaRYNA5l+Y762o9zzKeKjwwT3P0S3up69nzimml3fryTl453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\nmI1xCAuzMQ5hYTbGISzMxjiEhdkYh/j/qpH6AGvD2XkAAAAASUVORK5CYII=\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x7fcd24806250>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "nsamples: 10000\n",
+ "noise_logz: -27681.688\n",
+ "logz: nan +/- nan\n",
+ "log_bayes_factor: nan +/- nan\n",
+ "\n",
+ "CPU times: user 1min 29s, sys: 1.12 s, total: 1min 30s\n",
+ "Wall time: 1min 29s\n"
+ ]
+ }
+ ],
+ "source": [
+ "%%time \n",
+ "result = peyote.sampler.run_sampler(\n",
+ " likelihood, priors=priors, sampler='ptemcee', label='ptemcee',\n",
+ " nwalkers=100, nsteps=200, nburn=100, ntemps=2,\n",
+ " tqdm='tqdm_notebook')\n",
+ "fig = result.plot_corner(save=False)\n",
+ "plt.show()\n",
+ "print(result)"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.14"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/tutorials/GW150914.py b/tutorials/GW150914.py
index 7aa29d29210e8d7cf2f279a9f03cc0e679eb0562..bdfdbc1851eaf2c55f2fe3cb9de86c3913733fe1 100644
--- a/tutorials/GW150914.py
+++ b/tutorials/GW150914.py
@@ -1,8 +1,12 @@
-from __future__ import division
-import matplotlib
-matplotlib.use('AGG')
+#!/bin/python
+"""
+Tutorial to demonstrate running parameter estimation on GW150914 using open data.
+
+This example estimates all 15 parameters of the binary black hole system using commonly used prior distributions.
+This will take a few hours to run.
+"""
+from __future__ import division, print_function
import peyote
-import numpy as np
peyote.utils.setup_logger()
@@ -10,41 +14,28 @@ outdir = 'outdir'
label = 'GW150914'
time_of_event = 1126259462.422
-H1, sampling_frequency, time_duration = peyote.detector.get_inteferometer('H1', time_of_event, version=1)
-L1, sampling_frequency, time_duration = peyote.detector.get_inteferometer('L1', time_of_event, version=1)
-IFOs = [H1, L1]
-
-maximum_posterior_estimates = dict(
- a_1=0, a_2=0, tilt_1=0, tilt_2=0, phi_1=0, phi_2=0,
- luminosity_distance=410., iota=2.97305, phase=1.145,
- waveform_approximant='IMRPhenomPv2', reference_frequency=50., ra=1.375,
- dec=-1.2108, geocent_time=time_of_event, psi=2.659, mass_1=36, mass_2=29)
+H1, sampling_frequency, time_duration = peyote.detector.get_inteferometer('H1', time_of_event, version=1, outdir=outdir)
+L1, _, _ = peyote.detector.get_inteferometer('L1', time_of_event, version=1, outdir=outdir)
+interferometers = [H1, L1]
# Define the prior
-prior = peyote.prior.parse_floats_to_fixed_priors(maximum_posterior_estimates)
-prior['ra'] = peyote.prior.create_default_prior(name='ra')
-prior['dec'] = peyote.prior.create_default_prior(name='dec')
-prior['psi'] = peyote.prior.Uniform(0, np.pi/2, 'psi')
-prior['phase'] = peyote.prior.Uniform(0, np.pi/2, 'phase')
-prior['iota'] = peyote.prior.create_default_prior(name='iota')
-prior['mass_1'] = peyote.prior.Uniform(10, 80, 'mass_1')
-prior['mass_2'] = peyote.prior.Uniform(10, 80, 'mass_2')
-prior['geocent_time'] = peyote.prior.Uniform(
- time_of_event-0.1, time_of_event+0.1, name='geocent_time')
-prior['luminosity_distance'] = peyote.prior.create_default_prior(
- name='luminosity_distance')
-
-# Create the waveformgenerator
-waveformgenerator = peyote.waveform_generator.WaveformGenerator(
- peyote.source.lal_binary_black_hole, sampling_frequency,
- time_duration, parameters=prior)
+prior = dict()
+prior['mass_1'] = peyote.prior.Uniform(30, 50, 'mass_1')
+prior['mass_2'] = peyote.prior.Uniform(20, 40, 'mass_2')
+prior['geocent_time'] = peyote.prior.Uniform(time_of_event-0.1, time_of_event+0.1, name='geocent_time')
+prior['luminosity_distance'] = peyote.prior.PowerLaw(alpha=2, minimum=100, maximum=1000)
+
+# Create the waveform generator
+waveform_generator = peyote.waveform_generator.WaveformGenerator(
+ peyote.source.lal_binary_black_hole, sampling_frequency, time_duration,
+ parameters={'waveform_approximant': 'IMRPhenomPv2', 'reference_frequency': 50})
# Define a likelihood
-likelihood = peyote.likelihood.Likelihood(IFOs, waveformgenerator)
+likelihood = peyote.likelihood.Likelihood(interferometers, waveform_generator)
# Run the sampler
-result = peyote.sampler.run_sampler(
- likelihood, prior, label='GW150914', sampler='pymultinest',
- npoints=1024, resume=False, outdir=outdir, use_ratio=True)
-truth = [maximum_posterior_estimates[x] for x in result.search_parameter_keys]
-result.plot_corner(truth=truth)
+result = peyote.sampler.run_sampler(likelihood, prior, sampler='dynesty', outdir=outdir, label='label')
+result.plot_corner()
+result.plot_walks()
+result.plot_distributions()
+print(result)
diff --git a/tutorials/Injection.py b/tutorials/Injection.py
index 080bdace58d11f0630e17d77a95a8b117b547cd0..1060f0467c0c1d53bfbd0d19a3d686feff3cb522 100644
--- a/tutorials/Injection.py
+++ b/tutorials/Injection.py
@@ -1,44 +1,62 @@
"""
Tutorial to show signal injection using new features of detector.py
"""
-from __future__ import print_function, division
-
-import corner
-
+from __future__ import division, print_function
+import numpy as np
import peyote
-
-time_duration = 1.
-sampling_frequency = 4096.
-
-source = peyote.source.BinaryBlackHole('BBH', sampling_frequency, time_duration, mass_1=36., mass_2=29., spin11=0,
- spin12=0, spin13=0, spin21=0, spin22=0,
- spin23=0, luminosity_distance=5000., iota=0., phase=0.,
- waveform_approximant='IMRPhenomPv2', reference_frequency=50., ra=0, dec=1,
- geocent_time=0, psi=1)
-
-IFO_1 = peyote.detector.H1
-IFO_2 = peyote.detector.L1
-IFO_3 = peyote.detector.V1
-IFOs = [IFO_1, IFO_2, IFO_3]
-for IFO in IFOs:
- IFO.set_data(from_power_spectral_density=True, sampling_frequency=sampling_frequency, duration=time_duration)
- IFO.inject_signal(source)
-
-
-likelihood = peyote.likelihood.Likelihood(source=source, interferometers=IFOs)
-
-print(likelihood.noise_log_likelihood())
-print(likelihood.log_likelihood())
-print(likelihood.log_likelihood_ratio())
-
-prior = source.copy()
-prior.mass_1 = peyote.parameter.PriorFactory('mass_1', prior=peyote.prior.Uniform(lower=35, upper=37),
- latex_label='$m_1$')
-prior.mass_2 = peyote.parameter.PriorFactory('mass_2', prior=peyote.prior.Uniform(lower=28, upper=30),
- latex_label='$m_2$')
-
-# result = peyote.sampler.run_sampler(likelihood, prior, sampler='dynesty', npoints=100, print_progress=True)
-
-# truths = [source.__dict__[x] for x in result.search_parameter_keys]
-# fig = corner.corner(result.samples, labels=result.labels, truths=truths)
-# fig.savefig('Injection Test')
+import logging
+
+
+def main():
+
+ peyote.utils.setup_logger()
+
+ outdir = 'outdir'
+ label = 'injection'
+
+ # Create the waveform generator
+ waveform_generator = peyote.waveform_generator.WaveformGenerator(
+ peyote.source.lal_binary_black_hole, sampling_frequency=2048, time_duration=4,
+ parameters={'reference_frequency': 50.0, 'waveform_approximant': 'IMRPhenomPv2'})
+
+ # Define the prior
+ # Merger time is some time in 2018, shame LIGO will never see it...
+ time_of_event = np.random.uniform(1198800018, 1230336018)
+ prior = dict()
+ prior['luminosity_distance'] = peyote.prior.PowerLaw(alpha=2, minimum=100, maximum=5000, name='luminosity_distance')
+ prior['geocent_time'] = peyote.prior.Uniform(time_of_event-0.01, time_of_event+0.01, name='geocent_time')
+ prior['mass_1'] = peyote.prior.Gaussian(mu=40, sigma=5, name='mass_1')
+ prior['mass_2'] = peyote.prior.Gaussian(mu=40, sigma=5, name='mass_2')
+ peyote.prior.fill_priors(prior, waveform_generator)
+
+ # Create signal injection
+ injection_parameters = {name: prior[name].sample() for name in prior}
+ if injection_parameters['mass_1'] < injection_parameters['mass_2']:
+ injection_parameters['mass_1'], injection_parameters['mass_2'] =\
+ injection_parameters['mass_2'], injection_parameters['mass_1']
+ logging.info("Injection parameters:\n{}".format("\n".join(["{}: {}".format(key, injection_parameters[key])
+ for key in injection_parameters])))
+ for parameter in injection_parameters:
+ waveform_generator.parameters[parameter] = injection_parameters[parameter]
+ injection_polarizations = waveform_generator.frequency_domain_strain()
+
+ # Create interferometers and inject signal
+ interferometers = [peyote.detector.get_inteferometer_with_fake_noise_and_injection(
+ name, injection_polarizations=injection_polarizations, injection_parameters=injection_parameters,
+ sampling_frequency=2048, time_duration=4, outdir=outdir) for name in ['H1', 'L1', 'V1']]
+
+ # Define a likelihood
+ likelihood = peyote.likelihood.MarginalizedLikelihood(interferometers, waveform_generator, prior=prior,
+ distance_marginalization=True, phase_marginalization=True)
+
+ # Run the sampler
+ result = peyote.sampler.run_sampler(
+ likelihood, prior, label=label, sampler='dynesty', npoints=500, resume=False, outdir=outdir, use_ratio=True,
+ injection_parameters=injection_parameters)
+ truth = [injection_parameters[parameter] for parameter in result.search_parameter_keys]
+ result.plot_corner(truth=truth)
+ print(result)
+
+
+if __name__ == "__main__":
+ main()
diff --git a/tutorials/custom_source_tutorial.py b/tutorials/custom_source_tutorial.py
index 982c550f49141139c73d35207a822093d309d9dd..e879acac222c353647d47f76c2753f29d7c7cf6b 100644
--- a/tutorials/custom_source_tutorial.py
+++ b/tutorials/custom_source_tutorial.py
@@ -81,9 +81,9 @@ IFOs = generate_and_plot_data(wg, injection_parameters)
likelihood = peyote.likelihood.Likelihood(IFOs, wg)
-sampling_parameters['amplitude'] = peyote.prior.Uniform(lower=0.9 * 1e-21, upper=1.1 * 1e-21)
-sampling_parameters['sigma'] = peyote.prior.Uniform(lower=0, upper=10)
-sampling_parameters['mu'] = peyote.prior.Uniform(lower=50, upper=200)
+sampling_parameters['amplitude'] = peyote.prior.Uniform(minimum=0.9 * 1e-21, maximum=1.1 * 1e-21)
+sampling_parameters['sigma'] = peyote.prior.Uniform(minimum=0, maximum=10)
+sampling_parameters['mu'] = peyote.prior.Uniform(minimum=50, maximum=200)
result = peyote.sampler.run_sampler(likelihood, priors=sampling_parameters, verbose=True)
diff --git a/tutorials/make_standard_data.py b/tutorials/make_standard_data.py
index eeee0ebdcea91f25e7f28d0bc064b7edc89aa812..2945055a0fb1b4c443091ad3c6ad91fe23029e34 100644
--- a/tutorials/make_standard_data.py
+++ b/tutorials/make_standard_data.py
@@ -19,8 +19,8 @@ simulation_parameters = dict(
a_2=0,
tilt_1=0,
tilt_2=0,
- phi_1=0,
- phi_2=0,
+ phi_12=0,
+ phi_jl=0,
luminosity_distance=100.,
iota=0.4,
phase=1.3,
diff --git a/tutorials/standard_data.txt b/tutorials/standard_data.txt
index a3487b11402c1b49b1665897d619f98ca0ec8f36..f8dc4388f21f877670cf48a765ad947f41ae6963 100644
--- a/tutorials/standard_data.txt
+++ b/tutorials/standard_data.txt
@@ -19,610 +19,610 @@
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