# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2012-2019 GEM Foundation
#
# OpenQuake 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 License, or
# (at your option) any later version.
#
# OpenQuake 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 OpenQuake. If not, see <http://www.gnu.org/licenses/>.
"""
This module includes the scientific API of the oq-risklib
"""
import abc
import copy
import bisect
import warnings
import itertools
import collections
from functools import lru_cache
import numpy
from numpy.testing import assert_equal
from scipy import interpolate, stats, random
from openquake.baselib.general import CallableDict, cached_property
from openquake.hazardlib.stats import compute_stats2
F64 = numpy.float64
F32 = numpy.float32
U32 = numpy.uint32
[docs]def pairwise(iterable):
"s -> (s0,s1), (s1,s2), (s2, s3), ..."
a, b = itertools.tee(iterable)
# b ahead one step; if b is empty do not raise StopIteration
next(b, None)
return zip(a, b) # if a is empty will return an empty iter
[docs]def fine_graining(points, steps):
"""
:param points: a list of floats
:param int steps: expansion steps (>= 2)
>>> fine_graining([0, 1], steps=0)
[0, 1]
>>> fine_graining([0, 1], steps=1)
[0, 1]
>>> fine_graining([0, 1], steps=2)
array([0. , 0.5, 1. ])
>>> fine_graining([0, 1], steps=3)
array([0. , 0.33333333, 0.66666667, 1. ])
>>> fine_graining([0, 0.5, 0.7, 1], steps=2)
array([0. , 0.25, 0.5 , 0.6 , 0.7 , 0.85, 1. ])
N points become S * (N - 1) + 1 points with S > 0
"""
if steps < 2:
return points
ls = numpy.concatenate([numpy.linspace(x, y, num=steps + 1)[:-1]
for x, y in pairwise(points)])
return numpy.concatenate([ls, [points[-1]]])
#
# Input models
#
[docs]class VulnerabilityFunction(object):
dtype = numpy.dtype([('iml', F64), ('loss_ratio', F64), ('cov', F64)])
seed = None # to be overridden
def __init__(self, vf_id, imt, imls, mean_loss_ratios, covs=None,
distribution="LN"):
"""
A wrapper around a probabilistic distribution function
(currently, the Log-normal ("LN") and Beta ("BT")
distributions are supported amongst the continuous probability
distributions. For specifying a discrete probability
distribution refer to the class VulnerabilityFunctionWithPMF.
It is meant to be pickeable to allow distributed computation.
The only important method is `.__call__`, which applies
the vulnerability function to a given set of ground motion
fields and epsilons and return a loss matrix with N x R
elements.
:param str vf_id: Vulnerability Function ID
:param str imt: Intensity Measure Type as a string
:param list imls: Intensity Measure Levels for the
vulnerability function. All values must be >= 0.0, values
must be arranged in ascending order with no duplicates
:param list mean_loss_ratios: Mean Loss ratio values, equal in
length to imls, where value >= 0.
:param list covs: Coefficients of Variation. Equal in length
to mean loss ratios. All values must be >= 0.0.
:param str distribution_name: The probabilistic distribution
related to this function.
"""
self.id = vf_id
self.imt = imt
self._check_vulnerability_data(
imls, mean_loss_ratios, covs, distribution)
self.imls = numpy.array(imls)
self.mean_loss_ratios = numpy.array(mean_loss_ratios)
if covs is not None:
self.covs = numpy.array(covs)
else:
self.covs = numpy.zeros(self.imls.shape)
for lr, cov in zip(self.mean_loss_ratios, self.covs):
if lr == 0.0 and cov > 0.0:
msg = ("It is not valid to define a loss ratio = 0.0 with a "
"corresponding coeff. of variation > 0.0")
raise ValueError(msg)
if distribution == 'BT':
if lr > 1:
raise ValueError('The meanLRs must be <= 1, got %s' % lr)
elif cov ** 2 > 1 / lr - 1:
# see https://github.com/gem/oq-engine/issues/4841
raise ValueError(
'The coefficient of variation %s > %s is too large '
'in %s' % (cov, numpy.sqrt(1 / lr - 1), self))
self.distribution_name = distribution
[docs] def init(self):
# called by CompositeRiskModel and by __setstate__
self.stddevs = self.covs * self.mean_loss_ratios
self._mlr_i1d = interpolate.interp1d(self.imls, self.mean_loss_ratios)
self._covs_i1d = interpolate.interp1d(self.imls, self.covs)
self.set_distribution(None)
[docs] def set_distribution(self, epsilons=None):
if (self.covs > 0).any():
self.distribution = DISTRIBUTIONS[self.distribution_name]()
else:
self.distribution = DegenerateDistribution()
self.distribution.epsilons = (numpy.array(epsilons)
if epsilons is not None else None)
assert self.seed is not None, self
numpy.random.seed(self.seed) # set by CompositeRiskModel.init
[docs] def interpolate(self, gmvs):
"""
:param gmvs:
array of intensity measure levels
:returns:
(interpolated loss ratios, interpolated covs, indices > min)
"""
# gmvs are clipped to max(iml)
gmvs_curve = numpy.piecewise(
gmvs, [gmvs > self.imls[-1]], [self.imls[-1], lambda x: x])
idxs = gmvs_curve >= self.imls[0] # indices over the minimum
gmvs_curve = gmvs_curve[idxs]
return self._mlr_i1d(gmvs_curve), self._cov_for(gmvs_curve), idxs
[docs] def sample(self, means, covs, idxs, epsilons=None):
"""
Sample the epsilons and apply the corrections to the means.
This method is called only if there are nonzero covs.
:param means:
array of E' loss ratios
:param covs:
array of E' floats
:param idxs:
array of E booleans with E >= E'
:param epsilons:
array of E floats (or None)
:returns:
array of E' loss ratios
"""
if self.distribution_name == 'LN' and epsilons is None:
return means
self.set_distribution(epsilons)
res = self.distribution.sample(means, covs, means * covs, idxs)
return res
# this is used in the tests, not in the engine code base
def __call__(self, gmvs, epsilons):
"""
A small wrapper around .interpolate and .apply_to
"""
means, covs, idxs = self.interpolate(gmvs)
# for gmvs < min(iml) we return a loss of 0 (default)
ratios = numpy.zeros(len(gmvs))
ratios[idxs] = self.sample(means, covs, idxs, epsilons)
return ratios
[docs] def strictly_increasing(self):
"""
:returns:
a new vulnerability function that is strictly increasing.
It is built by removing piece of the function where the mean
loss ratio is constant.
"""
imls, mlrs, covs = [], [], []
previous_mlr = None
for i, mlr in enumerate(self.mean_loss_ratios):
if previous_mlr == mlr:
continue
else:
mlrs.append(mlr)
imls.append(self.imls[i])
covs.append(self.covs[i])
previous_mlr = mlr
return self.__class__(
self.id, self.imt, imls, mlrs, covs, self.distribution_name)
[docs] def mean_loss_ratios_with_steps(self, steps):
"""
Split the mean loss ratios, producing a new set of loss ratios. The new
set of loss ratios always includes 0.0 and 1.0
:param int steps:
the number of steps we make to go from one loss
ratio to the next. For example, if we have [0.5, 0.7]::
steps = 1 produces [0.0, 0.5, 0.7, 1]
steps = 2 produces [0.0, 0.25, 0.5, 0.6, 0.7, 0.85, 1]
steps = 3 produces [0.0, 0.17, 0.33, 0.5, 0.57, 0.63,
0.7, 0.8, 0.9, 1]
"""
loss_ratios = self.mean_loss_ratios
if min(loss_ratios) > 0.0:
# prepend with a zero
loss_ratios = numpy.concatenate([[0.0], loss_ratios])
if max(loss_ratios) < 1.0:
# append a 1.0
loss_ratios = numpy.concatenate([loss_ratios, [1.0]])
return fine_graining(loss_ratios, steps)
def _cov_for(self, imls):
"""
Clip `imls` to the range associated with the support of the
vulnerability function and returns the corresponding
covariance values by linear interpolation. For instance
if the range is [0.005, 0.0269] and the imls are
[0.0049, 0.006, 0.027], the clipped imls are
[0.005, 0.006, 0.0269].
"""
return self._covs_i1d(
numpy.piecewise(
imls,
[imls > self.imls[-1], imls < self.imls[0]],
[self.imls[-1], self.imls[0], lambda x: x]))
def __getstate__(self):
return (self.id, self.imt, self.imls, self.mean_loss_ratios,
self.covs, self.distribution_name, self.seed)
def __setstate__(self, state):
self.id = state[0]
self.imt = state[1]
self.imls = state[2]
self.mean_loss_ratios = state[3]
self.covs = state[4]
self.distribution_name = state[5]
self.seed = state[6]
self.init()
def _check_vulnerability_data(self, imls, loss_ratios, covs, distribution):
assert_equal(imls, sorted(set(imls)))
assert all(x >= 0.0 for x in imls)
assert covs is None or len(covs) == len(imls)
assert len(loss_ratios) == len(imls)
assert all(x >= 0.0 for x in loss_ratios)
assert covs is None or all(x >= 0.0 for x in covs)
assert distribution in ["LN", "BT"]
[docs] @lru_cache(100)
def loss_ratio_exceedance_matrix(self, loss_ratios):
"""
Compute the LREM (Loss Ratio Exceedance Matrix).
"""
# LREM has number of rows equal to the number of loss ratios
# and number of columns equal to the number of imls
lrem = numpy.empty((len(loss_ratios), len(self.imls)))
for row, loss_ratio in enumerate(loss_ratios):
for col, (mean_loss_ratio, stddev) in enumerate(
zip(self.mean_loss_ratios, self.stddevs)):
lrem[row, col] = self.distribution.survival(
loss_ratio, mean_loss_ratio, stddev)
return lrem
[docs] @lru_cache(100)
def mean_imls(self):
"""
Compute the mean IMLs (Intensity Measure Level)
for the given vulnerability function.
:param vulnerability_function: the vulnerability function where
the IMLs (Intensity Measure Level) are taken from.
:type vuln_function:
:py:class:`openquake.risklib.vulnerability_function.\
VulnerabilityFunction`
"""
return numpy.array(
[max(0, self.imls[0] - (self.imls[1] - self.imls[0]) / 2.)] +
[numpy.mean(pair) for pair in pairwise(self.imls)] +
[self.imls[-1] + (self.imls[-1] - self.imls[-2]) / 2.])
def __toh5__(self):
"""
:returns: a pair (array, attrs) suitable for storage in HDF5 format
"""
array = numpy.zeros(len(self.imls), self.dtype)
array['iml'] = self.imls
array['loss_ratio'] = self.mean_loss_ratios
array['cov'] = self.covs
return array, {'id': self.id, 'imt': self.imt,
'distribution_name': self.distribution_name}
def __fromh5__(self, array, attrs):
vars(self).update(attrs)
self.imls = array['iml']
self.mean_loss_ratios = array['loss_ratio']
self.covs = array['cov']
def __repr__(self):
return '<VulnerabilityFunction(%s, %s)>' % (self.id, self.imt)
[docs]class VulnerabilityFunctionWithPMF(VulnerabilityFunction):
"""
Vulnerability function with an explicit distribution of probabilities
:param str vf_id: vulnerability function ID
:param str imt: Intensity Measure Type
:param imls: intensity measure levels (L)
:param ratios: an array of mean ratios (M)
:param probs: a matrix of probabilities of shape (M, L)
"""
seed = None
def __init__(self, vf_id, imt, imls, loss_ratios, probs):
self.id = vf_id
self.imt = imt
self._check_vulnerability_data(imls, loss_ratios, probs)
self.imls = imls
self.loss_ratios = loss_ratios
self.probs = probs
self.distribution_name = "PM"
# to be set in .init(), called also by __setstate__
(self._probs_i1d, self.distribution) = None, None
self.init()
ls = [('iml', F32)] + [('prob-%s' % lr, F32) for lr in loss_ratios]
self.dtype = numpy.dtype(ls)
[docs] def init(self):
# the seed is reset in CompositeRiskModel.__init__
self._probs_i1d = interpolate.interp1d(self.imls, self.probs)
self.set_distribution(None)
[docs] def set_distribution(self, epsilons=None):
self.distribution = DISTRIBUTIONS[self.distribution_name]()
self.distribution.epsilons = epsilons
self.distribution.seed = self.seed # needed only for PM
def __getstate__(self):
return (self.id, self.imt, self.imls, self.loss_ratios,
self.probs, self.distribution_name, self.seed)
def __setstate__(self, state):
self.id = state[0]
self.imt = state[1]
self.imls = state[2]
self.loss_ratios = state[3]
self.probs = state[4]
self.distribution_name = state[5]
self.seed = state[6]
self.init()
def _check_vulnerability_data(self, imls, loss_ratios, probs):
assert all(x >= 0.0 for x in imls)
assert all(x >= 0.0 for x in loss_ratios)
assert all([1.0 >= x >= 0.0 for x in y] for y in probs)
assert probs.shape[0] == len(loss_ratios)
assert probs.shape[1] == len(imls)
# MN: in the test gmvs_curve is of shape (5,), self.probs of shape (7, 8)
# self.imls of shape (8,) and the returned means have shape (7, 5)
[docs] def interpolate(self, gmvs):
"""
:param gmvs:
array of intensity measure levels
:returns:
(interpolated probabilities, zeros, indices > min)
"""
# gmvs are clipped to max(iml)
gmvs_curve = numpy.piecewise(
gmvs, [gmvs > self.imls[-1]], [self.imls[-1], lambda x: x])
idxs = gmvs_curve >= self.imls[0] # indices over the minimum
gmvs_curve = gmvs_curve[idxs]
return self._probs_i1d(gmvs_curve), numpy.zeros_like(gmvs_curve), idxs
[docs] def sample(self, probs, _covs, idxs, epsilons):
"""
Sample the .loss_ratios with the given probabilities.
:param probs:
array of E' floats
:param _covs:
ignored, it is there only for API consistency
:param idxs:
array of E booleans with E >= E'
:param epsilons:
array of E floats
:returns:
array of E' probabilities
"""
self.set_distribution(epsilons)
return self.distribution.sample(self.loss_ratios, probs)
[docs] @lru_cache(100)
def loss_ratio_exceedance_matrix(self, loss_ratios):
"""
Compute the LREM (Loss Ratio Exceedance Matrix).
Required for the Classical Risk and BCR Calculators.
Currently left unimplemented as the PMF format is used only for the
Scenario and Event Based Risk Calculators.
:param int steps:
Number of steps between loss ratios.
"""
# TODO: to be implemented if the classical risk calculator
# needs to support the pmf vulnerability format
def __toh5__(self):
"""
:returns: a pair (array, attrs) suitable for storage in HDF5 format
"""
array = numpy.zeros(len(self.imls), self.dtype)
array['iml'] = self.imls
for i, lr in enumerate(self.loss_ratios):
array['prob-%s' % lr] = self.probs[i]
return array, {'id': self.id, 'imt': self.imt,
'distribution_name': self.distribution_name}
def __fromh5__(self, array, attrs):
lrs = [n.split('-')[1] for n in array.dtype.names if '-' in n]
self.loss_ratios = map(float, lrs)
self.imls = array['iml']
self.probs = array
vars(self).update(attrs)
def __repr__(self):
return '<VulnerabilityFunctionWithPMF(%s, %s)>' % (self.id, self.imt)
# this is meant to be instantiated by riskmodels.get_risk_models
[docs]class VulnerabilityModel(dict):
"""
Container for a set of vulnerability functions. You can access each
function given the IMT and taxonomy with the square bracket notation.
:param str id: ID of the model
:param str assetCategory: asset category (i.e. buildings, population)
:param str lossCategory: loss type (i.e. structural, contents, ...)
All such attributes are None for a vulnerability model coming from a
NRML 0.4 file.
"""
def __init__(self, id=None, assetCategory=None, lossCategory=None):
self.id = id
self.assetCategory = assetCategory
self.lossCategory = lossCategory
def __repr__(self):
return '<%s %s %s>' % (
self.__class__.__name__, self.lossCategory, sorted(self))
# ############################## fragility ############################### #
[docs]class FragilityFunctionContinuous(object):
# FIXME (lp). Should be re-factored with LogNormalDistribution
def __init__(self, limit_state, mean, stddev):
self.limit_state = limit_state
self.mean = mean
self.stddev = stddev
def __call__(self, imls):
"""
Compute the Probability of Exceedance (PoE) for the given
Intensity Measure Levels (IMLs).
"""
variance = self.stddev ** 2.0
sigma = numpy.sqrt(numpy.log(
(variance / self.mean ** 2.0) + 1.0))
mu = self.mean ** 2.0 / numpy.sqrt(
variance + self.mean ** 2.0)
return stats.lognorm.cdf(imls, sigma, scale=mu)
def __getstate__(self):
return dict(limit_state=self.limit_state,
mean=self.mean, stddev=self.stddev)
def __repr__(self):
return '<%s(%s, %s, %s)>' % (
self.__class__.__name__, self.limit_state, self.mean, self.stddev)
[docs]class FragilityFunctionDiscrete(object):
def __init__(self, limit_state, imls, poes, no_damage_limit=None):
self.limit_state = limit_state
self.imls = imls
self.poes = poes
if len(imls) != len(poes):
raise ValueError('%s: %d levels but %d poes' % (
limit_state, len(imls), len(poes)))
self._interp = None
self.no_damage_limit = no_damage_limit
@property
def interp(self):
if self._interp is not None:
return self._interp
self._interp = interpolate.interp1d(self.imls, self.poes,
bounds_error=False)
return self._interp
def __call__(self, imls):
"""
Compute the Probability of Exceedance (PoE) for the given
Intensity Measure Levels (IMLs).
"""
highest_iml = self.imls[-1]
imls = numpy.array(imls)
if imls.sum() == 0.0:
return numpy.zeros_like(imls)
imls[imls > highest_iml] = highest_iml
result = self.interp(imls)
if self.no_damage_limit:
result[imls < self.no_damage_limit] = 0
return result
# so that the curve is pickeable
def __getstate__(self):
return dict(limit_state=self.limit_state,
poes=self.poes, imls=self.imls, _interp=None,
no_damage_limit=self.no_damage_limit)
def __eq__(self, other):
return (self.poes == other.poes and self.imls == other.imls and
self.no_damage_limit == other.no_damage_limit)
def __ne__(self, other):
return not self == other
def __repr__(self):
return '<%s(%s, %s, %s)>' % (
self.__class__.__name__, self.limit_state, self.imls, self.poes)
[docs]class FragilityFunctionList(list):
"""
A list of fragility functions with common attributes; there is a
function for each limit state.
"""
# NB: the list is populated after instantiation by .append calls
def __init__(self, array, **attrs):
self.array = array
vars(self).update(attrs)
[docs] def mean_loss_ratios_with_steps(self, steps):
"""For compatibility with vulnerability functions"""
return fine_graining(self.imls, steps)
[docs] def build(self, limit_states, discretization, steps_per_interval):
"""
:param limit_states: a sequence of limit states
:param discretization: continouos fragility discretization parameter
:param steps_per_interval: steps_per_interval parameter
:returns: a populated FragilityFunctionList instance
"""
new = copy.copy(self)
add_zero = (self.format == 'discrete' and
self.nodamage and self.nodamage <= self.imls[0])
new.imls = build_imls(new, discretization)
if steps_per_interval > 1:
new.interp_imls = build_imls( # passed to classical_damage
new, discretization, steps_per_interval)
for i, ls in enumerate(limit_states):
data = self.array[i]
if self.format == 'discrete':
if add_zero:
new.append(FragilityFunctionDiscrete(
ls, [self.nodamage] + self.imls,
numpy.concatenate([[0.], data]),
self.nodamage))
else:
new.append(FragilityFunctionDiscrete(
ls, self.imls, data, self.nodamage))
else: # continuous
new.append(FragilityFunctionContinuous(
ls, data['mean'], data['stddev']))
return new
def __toh5__(self):
return self.array, {k: v for k, v in vars(self).items()
if k != 'array' and v is not None}
def __fromh5__(self, array, attrs):
self.array = array
vars(self).update(attrs)
def __repr__(self):
kvs = ['%s=%s' % item for item in vars(self).items()]
return '<FragilityFunctionList %s>' % ', '.join(kvs)
[docs]class ConsequenceFunction(object):
def __init__(self, id, dist, params):
self.id = id
self.dist = dist
self.params = numpy.array(params)
def __toh5__(self):
return self.params, dict(id=self.id, dist=self.dist)
def __fromh5__(self, params, attrs):
self.params = params
vars(self).update(attrs)
[docs]class ConsequenceModel(dict):
"""
Dictionary of consequence functions. You can access each
function given its name with the square bracket notation.
:param str id: ID of the model
:param str assetCategory: asset category (i.e. buildings, population)
:param str lossCategory: loss type (i.e. structural, contents, ...)
:param str description: description of the model
:param limitStates: a list of limit state strings
"""
def __init__(self, id, assetCategory, lossCategory, description,
limitStates):
self.id = id
self.assetCategory = assetCategory
self.lossCategory = lossCategory
self.description = description
self.limitStates = limitStates
def __repr__(self):
return '<%s %s %s %s>' % (
self.__class__.__name__, self.lossCategory,
', '.join(self.limitStates), ' '.join(sorted(self)))
[docs]def build_imls(ff, continuous_fragility_discretization,
steps_per_interval=0):
"""
Build intensity measure levels from a fragility function. If the function
is continuous, they are produced simply as a linear space between minIML
and maxIML. If the function is discrete, they are generated with a
complex logic depending on the noDamageLimit and the parameter
steps per interval.
:param ff: a fragility function object
:param continuous_fragility_discretization: .ini file parameter
:param steps_per_interval: .ini file parameter
:returns: generated imls
"""
if ff.format == 'discrete':
imls = ff.imls
if ff.nodamage and ff.nodamage < imls[0]:
imls = [ff.nodamage] + imls
if steps_per_interval > 1:
gen_imls = fine_graining(imls, steps_per_interval)
else:
gen_imls = imls
else: # continuous
gen_imls = numpy.linspace(ff.minIML, ff.maxIML,
continuous_fragility_discretization)
return gen_imls
# this is meant to be instantiated by riskmodels.get_fragility_model
[docs]class FragilityModel(dict):
"""
Container for a set of fragility functions. You can access each
function given the IMT and taxonomy with the square bracket notation.
:param str id: ID of the model
:param str assetCategory: asset category (i.e. buildings, population)
:param str lossCategory: loss type (i.e. structural, contents, ...)
:param str description: description of the model
:param limitStates: a list of limit state strings
"""
def __init__(self, id, assetCategory, lossCategory, description,
limitStates):
self.id = id
self.assetCategory = assetCategory
self.lossCategory = lossCategory
self.description = description
self.limitStates = limitStates
def __repr__(self):
return '<%s %s %s %s>' % (
self.__class__.__name__, self.lossCategory,
self.limitStates, sorted(self))
[docs] def build(self, continuous_fragility_discretization, steps_per_interval):
"""
Return a new FragilityModel instance, in which the values have been
replaced with FragilityFunctionList instances.
:param continuous_fragility_discretization:
configuration parameter
:param steps_per_interval:
configuration parameter
"""
newfm = copy.copy(self)
for key, ffl in self.items():
newfm[key] = ffl.build(self.limitStates,
continuous_fragility_discretization,
steps_per_interval)
return newfm
#
# Distribution & Sampling
#
DISTRIBUTIONS = CallableDict()
[docs]class Distribution(metaclass=abc.ABCMeta):
"""
A Distribution class models continuous probability distribution of
random variables used to sample losses of a set of assets. It is
usually registered with a name (e.g. LN, BT, PM) by using
:class:`openquake.baselib.general.CallableDict`
"""
[docs] @abc.abstractmethod
def sample(self, means, covs, stddevs, idxs):
"""
:returns: sample a set of losses
:param means: an array of mean losses
:param covs: an array of covariances
:param stddevs: an array of stddevs
"""
raise NotImplementedError
[docs] @abc.abstractmethod
def survival(self, loss_ratio, mean, stddev):
"""
Return the survival function of the distribution with `mean`
and `stddev` applied to `loss_ratio`
"""
raise NotImplementedError
[docs]class DegenerateDistribution(Distribution):
"""
The degenerate distribution. E.g. a distribution with a delta
corresponding to the mean.
"""
[docs] def sample(self, means, _covs, _stddev, _idxs):
return means
[docs] def survival(self, loss_ratio, mean, _stddev):
return numpy.piecewise(
loss_ratio, [loss_ratio > mean or not mean], [0, 1])
[docs]def make_epsilons(matrix, seed, correlation):
"""
Given a matrix N * R returns a matrix of the same shape N * R
obtained by applying the multivariate_normal distribution to
N points and R samples, by starting from the given seed and
correlation.
"""
if seed is not None:
numpy.random.seed(seed)
asset_count = len(matrix)
samples = len(matrix[0])
if not correlation: # avoid building the covariance matrix
return numpy.random.normal(size=(samples, asset_count)).transpose()
means_vector = numpy.zeros(asset_count)
covariance_matrix = (
numpy.ones((asset_count, asset_count)) * correlation +
numpy.diag(numpy.ones(asset_count)) * (1 - correlation))
return numpy.random.multivariate_normal(
means_vector, covariance_matrix, samples).transpose()
[docs]@DISTRIBUTIONS.add('LN')
class LogNormalDistribution(Distribution):
"""
Model a distribution of a random variable whoose logarithm are
normally distributed.
:attr epsilons: An array of random numbers generated with
:func:`numpy.random.multivariate_normal` with size E
"""
def __init__(self, epsilons=None):
self.epsilons = epsilons
[docs] def sample(self, means, covs, _stddevs, idxs):
if self.epsilons is None:
raise ValueError("A LogNormalDistribution must be initialized "
"before you can use it")
eps = self.epsilons[idxs]
sigma = numpy.sqrt(numpy.log(covs ** 2.0 + 1.0))
probs = means / numpy.sqrt(1 + covs ** 2) * numpy.exp(eps * sigma)
return probs
[docs] def survival(self, loss_ratio, mean, stddev):
# scipy does not handle correctly the limit case stddev = 0.
# In that case, when `mean` > 0 the survival function
# approaches to a step function, otherwise (`mean` == 0) we
# returns 0
if stddev == 0:
return numpy.piecewise(
loss_ratio, [loss_ratio > mean or not mean], [0, 1])
variance = stddev ** 2.0
sigma = numpy.sqrt(numpy.log((variance / mean ** 2.0) + 1.0))
mu = mean ** 2.0 / numpy.sqrt(variance + mean ** 2.0)
return stats.lognorm.sf(loss_ratio, sigma, scale=mu)
[docs]@DISTRIBUTIONS.add('BT')
class BetaDistribution(Distribution):
[docs] def sample(self, means, _covs, stddevs, _idxs=None):
alpha = self._alpha(means, stddevs)
beta = self._beta(means, stddevs)
res = numpy.random.beta(alpha, beta, size=None)
return res
[docs] def survival(self, loss_ratio, mean, stddev):
return stats.beta.sf(loss_ratio,
self._alpha(mean, stddev),
self._beta(mean, stddev))
@staticmethod
def _alpha(mean, stddev):
return ((1 - mean) / stddev ** 2 - 1 / mean) * mean ** 2
@staticmethod
def _beta(mean, stddev):
return ((1 - mean) / stddev ** 2 - 1 / mean) * (mean - mean ** 2)
[docs]@DISTRIBUTIONS.add('PM')
class DiscreteDistribution(Distribution):
seed = None # to be set
[docs] def sample(self, loss_ratios, probs):
ret = []
r = numpy.arange(len(loss_ratios))
for i in range(probs.shape[1]):
random.seed(self.seed + i)
# the seed is set inside the loop to avoid block-size dependency
pmf = stats.rv_discrete(name='pmf', values=(r, probs[:, i])).rvs()
ret.append(loss_ratios[pmf])
return ret
[docs] def survival(self, loss_ratios, probs):
"""
Required for the Classical Risk and BCR Calculators.
Currently left unimplemented as the PMF format is used only for the
Scenario and Event Based Risk Calculators.
:param int steps: number of steps between loss ratios.
"""
# TODO: to be implemented if the classical risk calculator
# needs to support the pmf vulnerability format
return
#
# Event Based
#
CurveParams = collections.namedtuple(
'CurveParams',
['index', 'loss_type', 'curve_resolution', 'ratios', 'user_provided'])
#
# Scenario Damage
#
[docs]def scenario_damage(fragility_functions, gmvs):
"""
:param fragility_functions: a list of D - 1 fragility functions
:param gmvs: an array of E ground motion values
:returns: an array of (D, E) damage fractions
"""
lst = [numpy.ones_like(gmvs)]
for f, ff in enumerate(fragility_functions): # D - 1 functions
lst.append(ff(gmvs))
lst.append(numpy.zeros_like(gmvs))
# convert a (D + 1, E) array into a (D, E) array
arr = pairwise_diff(numpy.array(lst))
arr[arr < 1E-7] = 0 # sanity check
return arr
#
# Classical Damage
#
[docs]def annual_frequency_of_exceedence(poe, t_haz):
"""
:param poe: array of probabilities of exceedence
:param t_haz: hazard investigation time
:returns: array of frequencies (with +inf values where poe=1)
"""
with warnings.catch_warnings():
warnings.simplefilter("ignore")
# avoid RuntimeWarning: divide by zero encountered in log
return - numpy.log(1. - poe) / t_haz
[docs]def classical_damage(
fragility_functions, hazard_imls, hazard_poes,
investigation_time, risk_investigation_time):
"""
:param fragility_functions:
a list of fragility functions for each damage state
:param hazard_imls:
Intensity Measure Levels
:param hazard_poes:
hazard curve
:param investigation_time:
hazard investigation time
:param risk_investigation_time:
risk investigation time
:returns:
an array of M probabilities of occurrence where M is the numbers
of damage states.
"""
spi = fragility_functions.steps_per_interval
if spi and spi > 1: # interpolate
imls = numpy.array(fragility_functions.interp_imls)
min_val, max_val = hazard_imls[0], hazard_imls[-1]
assert min_val > 0, hazard_imls # sanity check
numpy.putmask(imls, imls < min_val, min_val)
numpy.putmask(imls, imls > max_val, max_val)
poes = interpolate.interp1d(hazard_imls, hazard_poes)(imls)
else:
imls = hazard_imls
poes = numpy.array(hazard_poes)
afe = annual_frequency_of_exceedence(poes, investigation_time)
annual_frequency_of_occurrence = pairwise_diff(
pairwise_mean([afe[0]] + list(afe) + [afe[-1]]))
poes_per_damage_state = []
for ff in fragility_functions:
frequency_of_exceedence_per_damage_state = numpy.dot(
annual_frequency_of_occurrence, list(map(ff, imls)))
poe_per_damage_state = 1. - numpy.exp(
- frequency_of_exceedence_per_damage_state *
risk_investigation_time)
poes_per_damage_state.append(poe_per_damage_state)
poos = pairwise_diff([1] + poes_per_damage_state + [0])
return poos
#
# Classical
#
[docs]def classical(vulnerability_function, hazard_imls, hazard_poes, loss_ratios):
"""
:param vulnerability_function:
an instance of
:py:class:`openquake.risklib.scientific.VulnerabilityFunction`
representing the vulnerability function used to compute the curve.
:param hazard_imls:
the hazard intensity measure type and levels
:type hazard_poes:
the hazard curve
:param loss_ratios:
a tuple of C loss ratios
:returns:
an array of shape (2, C)
"""
assert len(hazard_imls) == len(hazard_poes), (
len(hazard_imls), len(hazard_poes))
vf = vulnerability_function
imls = vf.mean_imls()
lrem = vf.loss_ratio_exceedance_matrix(loss_ratios)
# saturate imls to hazard imls
min_val, max_val = hazard_imls[0], hazard_imls[-1]
numpy.putmask(imls, imls < min_val, min_val)
numpy.putmask(imls, imls > max_val, max_val)
# interpolate the hazard curve
poes = interpolate.interp1d(hazard_imls, hazard_poes)(imls)
# compute the poos
pos = pairwise_diff(poes)
lrem_po = numpy.empty(lrem.shape)
for idx, po in enumerate(pos):
lrem_po[:, idx] = lrem[:, idx] * po # column * po
return numpy.array([loss_ratios, lrem_po.sum(axis=1)])
[docs]def conditional_loss_ratio(loss_ratios, poes, probability):
"""
Return the loss ratio corresponding to the given PoE (Probability
of Exceendance). We can have four cases:
1. If `probability` is in `poes` it takes the bigger
corresponding loss_ratios.
2. If it is in `(poe1, poe2)` where both `poe1` and `poe2` are
in `poes`, then we perform a linear interpolation on the
corresponding losses
3. if the given probability is smaller than the
lowest PoE defined, it returns the max loss ratio .
4. if the given probability is greater than the highest PoE
defined it returns zero.
:param loss_ratios: an iterable over non-decreasing loss ratio
values (float)
:param poes: an iterable over non-increasing probability of
exceedance values (float)
:param float probability: the probability value used to
interpolate the loss curve
"""
assert len(loss_ratios) >= 3, loss_ratios
rpoes = poes[::-1]
if probability > poes[0]: # max poes
return 0.0
elif probability < poes[-1]: # min PoE
return loss_ratios[-1]
if probability in poes:
return max([loss
for i, loss in enumerate(loss_ratios)
if probability == poes[i]])
else:
interval_index = bisect.bisect_right(rpoes, probability)
if interval_index == len(poes): # poes are all nan
return float('nan')
elif interval_index == 1: # boundary case
x1, x2 = poes[-2:]
y1, y2 = loss_ratios[-2:]
else:
x1, x2 = poes[-interval_index-1:-interval_index + 1]
y1, y2 = loss_ratios[-interval_index-1:-interval_index + 1]
return (y2 - y1) / (x2 - x1) * (probability - x1) + y1
#
# Insured Losses
#
[docs]def insured_losses(losses, deductible, insured_limit):
"""
:param losses: an array of ground-up loss ratios
:param float deductible: the deductible limit in fraction form
:param float insured_limit: the insured limit in fraction form
Compute insured losses for the given asset and losses, from the point
of view of the insurance company. For instance:
>>> insured_losses(numpy.array([3, 20, 101]), 5, 100)
array([ 0, 15, 95])
- if the loss is 3 (< 5) the company does not pay anything
- if the loss is 20 the company pays 20 - 5 = 15
- if the loss is 101 the company pays 100 - 5 = 95
"""
return numpy.piecewise(
losses,
[losses < deductible, losses > insured_limit],
[0, insured_limit - deductible, lambda x: x - deductible])
[docs]def insured_loss_curve(curve, deductible, insured_limit):
"""
Compute an insured loss ratio curve given a loss ratio curve
:param curve: an array 2 x R (where R is the curve resolution)
:param float deductible: the deductible limit in fraction form
:param float insured_limit: the insured limit in fraction form
>>> losses = numpy.array([3, 20, 101])
>>> poes = numpy.array([0.9, 0.5, 0.1])
>>> insured_loss_curve(numpy.array([losses, poes]), 5, 100)
array([[ 3. , 20. ],
[ 0.85294118, 0.5 ]])
"""
losses, poes = curve[:, curve[0] <= insured_limit]
limit_poe = interpolate.interp1d(
*curve, bounds_error=False, fill_value=1)(deductible)
return numpy.array([
losses,
numpy.piecewise(poes, [poes > limit_poe], [limit_poe, lambda x: x])])
#
# Benefit Cost Ratio Analysis
#
[docs]def bcr(eal_original, eal_retrofitted, interest_rate,
asset_life_expectancy, asset_value, retrofitting_cost):
"""
Compute the Benefit-Cost Ratio.
BCR = (EALo - EALr)(1-exp(-r*t))/(r*C)
Where:
* BCR -- Benefit cost ratio
* EALo -- Expected annual loss for original asset
* EALr -- Expected annual loss for retrofitted asset
* r -- Interest rate
* t -- Life expectancy of the asset
* C -- Retrofitting cost
"""
return ((eal_original - eal_retrofitted) * asset_value *
(1 - numpy.exp(- interest_rate * asset_life_expectancy)) /
(interest_rate * retrofitting_cost))
# ####################### statistics #################################### #
[docs]def pairwise_mean(values):
"Averages between a value and the next value in a sequence"
return numpy.array([numpy.mean(pair) for pair in pairwise(values)])
[docs]def pairwise_diff(values):
"Differences between a value and the next value in a sequence"
return numpy.array([x - y for x, y in pairwise(values)])
[docs]def mean_std(fractions):
"""
Given an N x M matrix, returns mean and std computed on the rows,
i.e. two M-dimensional vectors.
"""
n = fractions.shape[0]
if n == 1: # avoid warnings when computing the stddev
return fractions[0], numpy.ones_like(fractions[0]) * numpy.nan
return numpy.mean(fractions, axis=0), numpy.std(fractions, axis=0, ddof=1)
[docs]def loss_maps(curves, conditional_loss_poes):
"""
:param curves: an array of loss curves
:param conditional_loss_poes: a list of conditional loss poes
:returns: a composite array of loss maps with the same shape
"""
loss_maps_dt = numpy.dtype([('poe-%s' % poe, F32)
for poe in conditional_loss_poes])
loss_maps = numpy.zeros(curves.shape, loss_maps_dt)
for idx, curve in numpy.ndenumerate(curves):
for poe in conditional_loss_poes:
loss_maps['poe-%s' % poe][idx] = conditional_loss_ratio(
curve['losses'], curve['poes'], poe)
return loss_maps
[docs]def broadcast(func, composite_array, *args):
"""
Broadcast an array function over a composite array
"""
dic = {}
dtypes = []
for name in composite_array.dtype.names:
dic[name] = func(composite_array[name], *args)
dtypes.append((name, dic[name].dtype))
res = numpy.zeros(dic[name].shape, numpy.dtype(dtypes))
for name in dic:
res[name] = dic[name]
return res
# TODO: remove this from openquake.risklib.qa_tests.bcr_test
[docs]def average_loss(lc):
"""
Given a loss curve array with `poe` and `loss` fields,
computes the average loss on a period of time.
:note: As the loss curve is supposed to be piecewise linear as it
is a result of a linear interpolation, we compute an exact
integral by using the trapeizodal rule with the width given by the
loss bin width.
"""
losses, poes = (lc['loss'], lc['poe']) if lc.dtype.names else lc
[docs] return -pairwise_diff(losses) @ pairwise_mean(poes)
def normalize_curves_eb(curves):
"""
A more sophisticated version of normalize_curves, used in the event
based calculator.
:param curves: a list of pairs (losses, poes)
:returns: first losses, all_poes
"""
# we assume non-decreasing losses, so losses[-1] is the maximum loss
non_zero_curves = [(losses, poes)
for losses, poes in curves if losses[-1] > 0]
if not non_zero_curves: # no damage. all zero curves
return curves[0][0], numpy.array([poes for _losses, poes in curves])
else: # standard case
max_losses = [losses[-1] for losses, _poes in non_zero_curves]
reference_curve = non_zero_curves[numpy.argmax(max_losses)]
loss_ratios = reference_curve[0]
curves_poes = [interpolate.interp1d(
losses, poes, bounds_error=False, fill_value=0)(loss_ratios)
for losses, poes in curves]
# fix degenerated case with flat curve
for cp in curves_poes:
if numpy.isnan(cp[0]):
cp[0] = 0
return loss_ratios, numpy.array(curves_poes)
[docs]def build_loss_curve_dt(curve_resolution, insured_losses=False):
"""
:param curve_resolution:
dictionary loss_type -> curve_resolution
:param insured_losses:
configuration parameter
:returns:
loss_curve_dt
"""
lc_list = []
for lt in sorted(curve_resolution):
C = curve_resolution[lt]
pairs = [('losses', (F32, C)), ('poes', (F32, C))]
lc_dt = numpy.dtype(pairs)
lc_list.append((str(lt), lc_dt))
if insured_losses:
for lt in sorted(curve_resolution):
C = curve_resolution[lt]
pairs = [('losses', (F32, C)), ('poes', (F32, C))]
lc_dt = numpy.dtype(pairs)
lc_list.append((str(lt) + '_ins', lc_dt))
loss_curve_dt = numpy.dtype(lc_list) if lc_list else None
return loss_curve_dt
[docs]def return_periods(eff_time, num_losses):
"""
:param eff_time: ses_per_logic_tree_path * investigation_time
:param num_losses: used to determine the minimum period
:returns: an array of 32 bit periods
Here are a few examples:
>>> return_periods(1, 1)
Traceback (most recent call last):
...
AssertionError: eff_time too small: 1
>>> return_periods(2, 2)
array([1, 2], dtype=uint32)
>>> return_periods(2, 10)
array([1, 2], dtype=uint32)
>>> return_periods(100, 2)
array([ 50, 100], dtype=uint32)
>>> return_periods(1000, 1000)
array([ 1, 2, 5, 10, 20, 50, 100, 200, 500, 1000],
dtype=uint32)
"""
assert eff_time >= 2, 'eff_time too small: %s' % eff_time
assert num_losses >= 2, 'num_losses too small: %s' % num_losses
min_time = eff_time / num_losses
period = 1
periods = []
loop = True
while loop:
for val in [1, 2, 5]:
time = period * val
if time >= min_time:
if time > eff_time:
loop = False
break
periods.append(time)
period *= 10
return U32(periods)
[docs]def losses_by_period(losses, return_periods, num_events=None, eff_time=None):
"""
:param losses: array of simulated losses
:param return_periods: return periods of interest
:param num_events: the number of events (>= to the number of losses)
:param eff_time: investigation_time * ses_per_logic_tree_path
:returns: interpolated losses for the return periods, possibly with NaN
NB: the return periods must be ordered integers >= 1. The interpolated
losses are defined inside the interval min_time < time < eff_time
where min_time = eff_time /num_events. Outside the interval they
have NaN values. Here is an example:
>>> losses = [3, 2, 3.5, 4, 3, 23, 11, 2, 1, 4, 5, 7, 8, 9, 13]
>>> losses_by_period(losses, [1, 2, 5, 10, 20, 50, 100], 20)
array([ nan, nan, 0. , 3.5, 8. , 13. , 23. ])
If num_events is not passed, it is inferred from the number of losses;
if eff_time is not passed, it is inferred from the longest return period.
"""
if len(losses) == 0: # zero-curve
return numpy.zeros(len(return_periods))
if num_events is None:
num_events = len(losses)
elif num_events < len(losses):
raise ValueError(
'There are not enough events (%d) to compute the loss curve '
'from %d losses' % (num_events, len(losses)))
if eff_time is None:
eff_time = return_periods[-1]
losses = numpy.sort(losses)
num_zeros = num_events - len(losses)
if num_zeros:
losses = numpy.concatenate(
[numpy.zeros(num_zeros, losses.dtype), losses])
periods = eff_time / numpy.arange(num_events, 0., -1)
rperiods = [rp if periods[0] <= rp <= periods[-1] else numpy.nan
for rp in return_periods]
curve = numpy.interp(numpy.log(rperiods), numpy.log(periods), losses)
return curve
[docs]class LossCurvesMapsBuilder(object):
"""
Build losses curves and maps for all loss types at the same time.
:param conditional_loss_poes: a list of PoEs, possibly empty
:param return_periods: ordered array of return periods
:param loss_dt: composite dtype for the loss types
:param weights: weights of the realizations
:param num_events: number of events for each realization
:param eff_time: ses_per_logic_tree_path * hazard investigation time
"""
def __init__(self, conditional_loss_poes, return_periods, loss_dt,
weights, num_events, eff_time, risk_investigation_time):
self.conditional_loss_poes = conditional_loss_poes
self.return_periods = return_periods
self.loss_dt = loss_dt
self.weights = weights
self.num_events = num_events
self.eff_time = eff_time
self.poes = 1. - numpy.exp(- risk_investigation_time / return_periods)
[docs] def pair(self, array, stats):
"""
:return (array, array_stats) if stats, else (array, None)
"""
if len(self.weights) > 1 and stats:
statnames, statfuncs = zip(*stats)
array_stats = compute_stats2(array, statfuncs, self.weights)
else:
array_stats = None
return array, array_stats
# used in event_based_risk postproc
[docs] def build(self, losses_by_event, stats=()):
"""
:param losses_by_event:
the aggregate loss table with shape R -> (E, L)
:param stats:
list of pairs [(statname, statfunc), ...]
:returns:
two arrays with shape (P, R, L) and (P, S, L)
"""
P, R = len(self.return_periods), len(self.weights)
L = len(self.loss_dt.names)
array = numpy.zeros((P, R, L), F32)
for r in losses_by_event:
num_events = self.num_events[r]
losses = losses_by_event[r]
for l, lt in enumerate(self.loss_dt.names):
ls = losses[:, l].flatten() # flatten only in ucerf
# NB: do not use squeeze or the gmf_ebrisk tests will break
lbp = losses_by_period(
ls, self.return_periods, num_events, self.eff_time)
array[:, r, l] = lbp
return self.pair(array, stats)
[docs] def build_pair(self, losses, stats):
"""
:param losses: a list of lists with R elements
:returns: two arrays of shape (P, R) and (P, S) respectively
"""
P, R = len(self.return_periods), len(self.weights)
assert len(losses) == R, len(losses)
array = numpy.zeros((P, R), F32)
for r, ls in enumerate(losses):
ne = self.num_events.get(r, 0)
if ne:
array[:, r] = losses_by_period(
ls, self.return_periods, ne, self.eff_time)
return self.pair(array, stats)
# used in event_based_risk
[docs] def build_curve(self, asset_value, loss_ratios, rlzi):
return asset_value * losses_by_period(
loss_ratios, self.return_periods,
self.num_events[rlzi], self.eff_time)
# used in event_based_risk
[docs] def build_maps(self, losses, clp, stats=()):
"""
:param losses: an array of shape (A, R, P)
:param clp: a list of C conditional loss poes
:param stats: list of pairs [(statname, statfunc), ...]
:returns: an array of loss_maps of shape (A, R, C, LI)
"""
shp = losses.shape[:2] + (len(clp), len(losses.dtype)) # (A, R, C, LI)
array = numpy.zeros(shp, F32)
for lti, lt in enumerate(losses.dtype.names):
for a, losses_ in enumerate(losses[lt]):
for r, ls in enumerate(losses_):
for c, poe in enumerate(clp):
clratio = conditional_loss_ratio(ls, self.poes, poe)
array[a, r, c, lti] = clratio
return self.pair(array, stats)
# used in ebrisk
[docs] def build_loss_maps(self, losses, clp, stats=()):
"""
:param losses: an array of shape R, E
:param clp: a list of C conditional loss poes
:param stats: list of pairs [(statname, statfunc), ...]
:returns: two arrays of shape (C, R) and (C, S)
"""
array = numpy.zeros((len(clp), len(losses)), F32)
for r, ls in enumerate(losses):
if len(ls) < 2:
continue
for c, poe in enumerate(clp):
array[c, r] = conditional_loss_ratio(ls, self.poes, poe)
return self.pair(array, stats)
# used in ebrisk
[docs] def build_curves_maps(self, loss_arrays, rlzi):
if len(loss_arrays) == 0:
return (), ()
shp = loss_arrays[0].shape # (L, T...)
P = len(self.return_periods)
curves = numpy.zeros((P,) + shp, F32)
C = len(self.conditional_loss_poes)
maps = numpy.zeros((C,) + shp, F32)
num_events = self.num_events[rlzi]
acc = collections.defaultdict(list)
for loss_array in loss_arrays:
for idx, loss in numpy.ndenumerate(loss_array):
acc[idx].append(loss)
for idx, losses in acc.items():
curves[(slice(None),) + idx] = lbp = losses_by_period(
losses, self.return_periods, num_events, self.eff_time)
for p, poe in enumerate(self.conditional_loss_poes):
maps[(p,) + idx] = conditional_loss_ratio(
lbp, self.poes, poe)
return curves, maps
[docs]class LossesByAsset(object):
"""
A class to compute losses by asset.
:param assetcol: an AssetCollection instance
:param policy_name: the name of the policy field (can be empty)
:param policy_dict: dict loss_type -> array(deduct, limit) (can be empty)
"""
def __init__(self, assetcol, loss_names, policy_name='', policy_dict={}):
self.A = len(assetcol)
self.policy_name = policy_name
self.policy_dict = policy_dict
self.loss_names = loss_names
[docs] def compute(self, asset, losses_by_lt):
"""
:param asset: an asset record
:param losses_by_lt: a dictionary loss_type -> losses (of size E)
:yields: pairs (loss_idx, losses)
"""
idx = 0
for lt, losses in losses_by_lt.items():
yield idx, losses
idx += 1
if lt in self.policy_dict:
val = asset['value-' + lt]
ded, lim = self.policy_dict[lt][asset[self.policy_name]]
ins_losses = insured_losses(losses, ded * val, lim * val)
yield idx, ins_losses
idx += 1
@cached_property
def losses_by_A(self):
"""
:returns: an array of shape (A, L)
"""
return numpy.zeros((self.A, len(self.loss_names)), F32)