# Source code for openquake.hazardlib.pmf

```# The Hazard Library
# Copyright (C) 2012-2023 GEM Foundation
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU Affero General Public License as
# published by the Free Software Foundation, either version 3 of the
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU Affero General Public License for more details.
#
# You should have received a copy of the GNU Affero General Public License
# along with this program.  If not, see <http://www.gnu.org/licenses/>.
"""
Module :mod:`openquake.hazardlib.pmf` implements :class:`PMF`.
"""
import numpy as np

PRECISION = 1E-7  # precision used when comparing sum(probs) to 1

[docs]class PMF(object):
"""
Probability mass function is a function that gives the probability
that a discrete random variable is exactly equal to some value.

:param data:
The PMF data in a form of list of tuples. Each tuple must contain
two items with the first item being the probability of the implied
random variable to take value of the second item.

There must be at least one tuple in the list. All probabilities
must sum up to 1 within the given precision.

The type of values (second items in tuples) is not strictly defined,
those can be objects of any (mixed or homogeneous) type.

:param epsilon:
the tolerance for the sum of the probabilities (default %e)

:raises ValueError:
If probabilities do not sum up to 1 or there is zero or negative
probability.
""" % PRECISION

def __init__(self, data, epsilon=PRECISION):
probs, values = list(zip(*data))
if any(prob < 0 for prob in probs):
raise ValueError('a probability in %s is not positive'
% list(probs))
if abs(float(sum(probs)) - 1.0) > epsilon:
raise ValueError('probabilities %s do not sum up to 1.0'
% list(probs))
self.data = list(zip(map(float, probs), values))

[docs]    def sample(self, number_samples):
"""
Produces a list of samples from the probability mass function.

:param int data:
Number of samples
:returns:
Samples from PMF as a list
"""
return [pair[1] for pair in self.sample_pairs(number_samples)]

[docs]    def sample_pairs(self, number_samples):
"""
Produces a list of samples from the probability mass function.

:param int data:
Number of samples
:returns:
Samples from PMF as a list of pairs
"""
probs = np.cumsum([val[0] for val in self.data])
sampler = np.random.uniform(0., 1., number_samples)
return [self.data[ival] for ival in np.searchsorted(probs, sampler)]

[docs]    def reduce(self, bin=0):
"""
Reduce the original PMF to a single bin distribution.

:param bin: the bin to keep (default the first)
"""
self.data = [(1, self.data[bin][1])]
```