# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (c) 2016-2023 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 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/>.
import math
import copy
import warnings
import numpy
import pandas
from openquake.baselib.general import cached_property
from openquake.baselib.performance import numba, compile
from openquake.hazardlib.tom import get_pnes
U16 = numpy.uint16
U32 = numpy.uint32
F32 = numpy.float32
F64 = numpy.float64
BYTES_PER_FLOAT = 8
TWO24 = 2 ** 24
rates_dt = {'gid': U16, 'sid': U32, 'lid': U16, 'rate': F32}
if numba:
@compile("void(float64[:, :], float64[:], uint32[:])")
def combine_probs(array, other, rlzs):
for li in range(len(array)):
for ri in rlzs:
if other[li] != 0.:
array[li, ri] = (
1. - (1. - array[li, ri]) * (1. - other[li]))
else:
[docs] def combine_probs(array, other, rlzs):
for r in rlzs:
array[:, r] = (1. - (1. - array[:, r]) * (1. - other))
[docs]def get_mean_curve(dstore, imt, site_id=0):
"""
Extract the mean hazard curve from the datastore for the first site.
"""
if 'hcurves-stats' in dstore: # shape (N, S, M, L1)
arr = dstore.sel('hcurves-stats', stat='mean', imt=imt)
else: # there is only 1 realization
arr = dstore.sel('hcurves-rlzs', rlz_id=0, imt=imt)
return arr[site_id, 0, 0]
[docs]def get_poe_from_mean_curve(dstore, imt, iml, site_id=0):
"""
Extract the poe corresponding to the given iml by looking at the mean
curve for the given imt. `iml` can also be an array.
"""
imls = dstore['oqparam'].imtls[imt]
mean_curve = get_mean_curve(dstore, imt, site_id)
return numpy.interp(imls, mean_curve)[iml]
[docs]class ProbabilityCurve(object):
"""
This class is a small wrapper over an array of PoEs associated to
a set of intensity measure types and levels. It provides a few operators,
including the complement operator `~`
~p = 1 - p
and the inclusive or operator `|`
p = p1 | p2 = ~(~p1 * ~p2)
Such operators are implemented efficiently at the numpy level, by
dispatching on the underlying array.
Here is an example of use:
>>> poe = ProbabilityCurve(numpy.array([0.1, 0.2, 0.3, 0, 0]))
>>> ~(poe | poe) * .5
<ProbabilityCurve
[0.405 0.32 0.245 0.5 0.5 ]>
"""
def __init__(self, array):
self.array = array
def __or__(self, other):
if other == 0:
return self
else:
return self.__class__(1. - (1. - self.array) * (1. - other.array))
__ror__ = __or__
def __iadd__(self, other):
# this is used when composing mutually exclusive probabilities
self.array += other.array
return self
def __add__(self, other):
# this is used when composing mutually exclusive probabilities
self.array += other.array
return self.__class__(self.array)
def __mul__(self, other):
if isinstance(other, self.__class__):
return self.__class__(self.array * other.array)
elif other == 1:
return self
else:
return self.__class__(self.array * other)
__rmul__ = __mul__
def __pow__(self, n):
return self.__class__(self.array ** n)
def __invert__(self):
return self.__class__(1. - self.array)
def __bool__(self):
return bool(self.array.any())
def __repr__(self):
return '<ProbabilityCurve\n%s>' % self.array
# used when exporting to HDF5
[docs] def convert(self, imtls, idx=0):
"""
Convert a probability curve into a record of dtype `imtls.dt`.
:param imtls: DictArray instance
:param idx: extract the data corresponding to the given inner index
"""
curve = numpy.zeros(1, imtls.dt)
for imt in imtls:
curve[imt] = self.array[imtls(imt), idx]
return curve[0]
# ######################### hazard maps ################################### #
# cutoff value for the poe
EPSILON = 1E-30
[docs]def compute_hazard_maps(curves, imls, poes):
"""
Given a set of hazard curve poes, interpolate hazard maps at the specified
``poes``.
:param curves:
Array of floats of shape N x L. Each row represents a curve, where the
values in the row are the PoEs (Probabilities of Exceedance)
corresponding to the ``imls``.
Each curve corresponds to a geographical location.
:param imls:
Intensity Measure Levels associated with these hazard ``curves``. Type
should be an array-like of floats.
:param poes:
Value(s) on which to interpolate a hazard map from the input
``curves``.
:returns:
An array of shape N x P, where N is the number of curves and P the
number of poes.
"""
P = len(poes)
N, L = curves.shape # number of levels
if L != len(imls):
raise ValueError('The curves have %d levels, %d were passed' %
(L, len(imls)))
log_poes = numpy.log(poes)
hmap = numpy.zeros((N, P))
with warnings.catch_warnings():
warnings.simplefilter("ignore")
# avoid RuntimeWarning: divide by zero for zero levels
imls = numpy.log(numpy.array(imls[::-1]))
for n, curve in enumerate(curves):
# the hazard curve, having replaced the too small poes with EPSILON
log_curve = numpy.log([max(poe, EPSILON) for poe in curve[::-1]])
for p, log_poe in enumerate(log_poes):
if log_poe > log_curve[-1]:
# special case when the interpolation poe is bigger than the
# maximum, i.e the iml must be smaller than the minimum;
# extrapolate the iml to zero as per
# https://bugs.launchpad.net/oq-engine/+bug/1292093;
# then the hmap goes automatically to zero
pass
else:
# exp-log interpolation, to reduce numerical errors
# see https://bugs.launchpad.net/oq-engine/+bug/1252770
hmap[n, p] = numpy.exp(numpy.interp(log_poe, log_curve, imls))
return hmap
[docs]def compute_hmaps(curvesNML, imtls, poes):
"""
:param curvesNML: an array of shape (N, M, L1)
:param imlts: a DictArray with M keys
:param poes: a sequence of P poes
:returns: array of shape (N, M, P) with the hazard maps
"""
N = len(curvesNML)
M = len(imtls)
P = len(poes)
assert M == len(imtls)
iml3 = numpy.zeros((N, M, P))
for m, imls in enumerate(imtls.values()):
curves = curvesNML[:, m]
iml3[:, m] = compute_hazard_maps(curves, imls, poes)
return iml3
[docs]def get_lvl(hcurve, imls, poe):
"""
:param hcurve: a hazard curve, i.e. array of L1 PoEs
:param imls: L1 intensity measure levels
:returns: index of the intensity measure level associated to the poe
>>> imls = numpy.array([.1, .2, .3, .4])
>>> hcurve = numpy.array([1., .99, .90, .8])
>>> get_lvl(hcurve, imls, 1)
0
>>> get_lvl(hcurve, imls, .99)
1
>>> get_lvl(hcurve, imls, .91)
2
>>> get_lvl(hcurve, imls, .8)
3
"""
[[iml]] = compute_hazard_maps(hcurve.reshape(1, -1), imls, [poe])
iml -= 1E-10 # small buffer
return numpy.searchsorted(imls, iml)
############################## probability maps ###############################
# numbified below
[docs]def update_pmap_i(arr, poes, inv, rates, probs_occur, idxs, itime):
levels = range(arr.shape[1])
for i, rate, probs, idx in zip(inv, rates, probs_occur, idxs):
if itime == 0: # FatedTOM
arr[idx] *= 1. - poes[i]
elif len(probs) == 0 and numba is not None:
# looping is faster than building arrays
for lvl in levels:
arr[idx, lvl] *= math.exp(-rate * poes[i, lvl] * itime)
else:
arr[idx] *= get_pnes(rate, probs, poes[i], itime) # shape L
# numbified below
[docs]def update_pmap_m(arr, poes, inv, rates, probs_occur, weights, idxs, itime):
for i, rate, probs, w, idx in zip(inv, rates, probs_occur, weights, idxs):
pne = get_pnes(rate, probs, poes[i], itime) # shape L
arr[idx] += (1. - pne) * w
if numba:
t = numba.types
sig = t.void(t.float64[:, :], # pmap
t.float64[:, :], # poes
t.uint32[:], # invs
t.float64[:], # rates
t.float64[:, :], # probs_occur
t.uint32[:], # sids
t.float64) # itime
update_pmap_i = compile(sig)(update_pmap_i)
sig = t.void(t.float64[:, :], # pmap
t.float64[:, :], # poes
t.uint32[:], # invs
t.float64[:], # rates
t.float64[:, :], # probs_occur
t.float64[:], # weights
t.uint32[:], # sids
t.float64) # itime
update_pmap_m = compile(sig)(update_pmap_m)
[docs]def fix_probs_occur(probs_occur):
"""
Try to convert object arrays into regular arrays
"""
if probs_occur.dtype.name == 'object':
n = len(probs_occur)
p = len(probs_occur[0])
po = numpy.zeros((n, p))
for p, probs in enumerate(probs_occur):
po[p] = probs_occur[p]
return po
return probs_occur
[docs]class ProbabilityMap(object):
"""
Thin wrapper over a 3D-array of probabilities.
"""
def __init__(self, sids, shape_y, shape_z):
self.sids = sids
self.shape = (len(sids), shape_y, shape_z)
@cached_property
def sidx(self):
"""
:returns: an array of length N site_id -> index
"""
idxs = numpy.zeros(self.sids.max() + 1, numpy.uint32)
for idx, sid in enumerate(self.sids):
idxs[sid] = idx
return idxs
[docs] def new(self, array):
new = copy.copy(self)
new.array = array
return new
[docs] def split(self):
"""
:yields: G ProbabilityMaps of shape (N, L, 1)
"""
N, L, G = self.array.shape
for g in range(G):
yield self.__class__(self.sids, L, 1).new(self.array[:, :, [g]])
[docs] def fill(self, value):
"""
:param value: a scalar probability
Fill the ProbabilityMap underlying array with the given scalar
and build the .sidx array
"""
assert 0 <= value <= 1, value
self.array = numpy.empty(self.shape)
self.array.fill(value)
return self
[docs] def reshape(self, N, M, P):
"""
:returns: a new Pmap associated to a reshaped array
"""
return self.new(self.array.reshape(N, M, P))
# used in calc/disagg_test.py
[docs] def expand(self, full_lt, trt_rlzs):
"""
Convert a ProbabilityMap with shape (N, L, Gt) into a ProbabilityMap
with shape (N, L, R): works only for rates
"""
N, L, Gt = self.array.shape
assert Gt == len(trt_rlzs), (Gt, len(trt_rlzs))
R = full_lt.get_num_paths()
out = ProbabilityMap(range(N), L, R).fill(0.)
for g, trs in enumerate(trt_rlzs):
for sid in range(N):
for rlz in trs % TWO24:
out.array[sid, :, rlz] += self.array[sid, :, g]
# NB: for probabilities use
# combine_probs(out.array[sid], self.array[sid, :, g], rlzs)
return out
# used in calc_hazard_curves
[docs] def convert(self, imtls, nsites, idx=0):
"""
Convert a probability map into a composite array of length `nsites`
and dtype `imtls.dt`.
:param imtls:
DictArray instance
:param nsites:
the total number of sites
:param idx:
index on the z-axis (default 0)
"""
curves = numpy.zeros(nsites, imtls.dt)
for imt in curves.dtype.names:
curves[imt][self.sids] = self.array[:, imtls(imt), idx]
return curves
[docs] def to_rates(self, slc=slice(None)):
"""
Assuming self contains an array of probabilities of no exceedance,
returns an array of rates of shape (N, L, G).
"""
pnes = self.array[:, slc]
# Physically, an extremely small intensity measure level can have an
# extremely large probability of exceedence,however that probability
# cannot be exactly 1 unless the level is exactly 0. Numerically,
# the PoE can be 1 and this give issues when calculating the damage:
# there is a log(0) in scientific.annual_frequency_of_exceedence.
# Here we solve the issue by replacing the unphysical probabilities
# 1 with .9999999999999999 (the float64 closest to 1).
pnes[pnes == 0.] = 1.11E-16
return -numpy.log(pnes)
[docs] def interp4D(self, imtls, poes):
"""
:param imtls: a dictionary imt->imls with M items
:param poes: a list of P PoEs
:returns: an array of shape (N, M, P, Z)
"""
poes3 = self.array
N, L, Z = poes3.shape
M = len(imtls)
P = len(poes)
L1 = len(imtls[next(iter(imtls))])
hmap4 = numpy.zeros((N, M, P, Z))
for m, imt in enumerate(imtls):
slc = slice(m*L1, m*L1 + L1)
for z in range(Z):
hmap4[:, m, :, z] = compute_hazard_maps(
poes3[:, slc, z], imtls[imt], poes)
return hmap4
# dangerous since it changes the shape by removing sites
[docs] def remove_zeros(self):
ok = self.array.sum(axis=(1, 2)) > 0
if ok.sum() == 0: # avoid empty array
ok = slice(0, 1)
new = self.__class__(self.sids[ok], self.shape[1], self.shape[2])
new.array = self.array[ok]
return new
# used in classical_risk from CSV
[docs] def to_dframe(self):
"""
:returns: a DataFrame with fields sid, gid, lid, poe
"""
dic = dict(sid=[], gid=[], lid=[], rate=[])
for sid, arr in zip(self.sids, self.array):
for (lid, gid), rate in numpy.ndenumerate(arr):
dic['sid'].append(sid)
dic['gid'].append(gid)
dic['lid'].append(lid)
dic['rate'].append(rate)
for key, dt in rates_dt.items():
dic[key] = dt(dic[key])
return pandas.DataFrame(dic)
[docs] def multiply_pnes(self, other, g, i):
"""
Multiply by the probabilities of no exceedence
"""
# assume other.sids are a subset of self.sids
self.array[self.sidx[other.sids], :, g] *= other.array[:, :, i]
[docs] def update(self, poes, invs, ctxt, itime, mutex_weight):
"""
Update probabilities
"""
rates = ctxt.occurrence_rate
probs_occur = fix_probs_occur(ctxt.probs_occur)
idxs = self.sidx[ctxt.sids]
for i in range(self.shape[-1]): # G indices
if len(mutex_weight) == 0: # indep
update_pmap_i(self.array[:, :, i], poes[:, :, i], invs, rates,
probs_occur, idxs, itime)
else: # mutex
weights = [mutex_weight[src_id, rup_id]
for src_id, rup_id in zip(ctxt.src_id, ctxt.rup_id)]
update_pmap_m(self.array[:, :, i], poes[:, :, i],
invs, rates, probs_occur,
numpy.array(weights), idxs, itime)
def __invert__(self):
return self.new(1. - self.array)
def __pow__(self, n):
return self.new(self.array ** n)
def __repr__(self):
return '<ProbabilityMap(%d, %d, %d)>' % self.shape
