# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2012-2020 GEM Foundation
#
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# 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.
#
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# GNU Affero General Public License for more details.
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"""
:mod:`openquake.hazardlib.calc.disagg` contains
:func:`disaggregation` as well as several aggregation functions for
extracting a specific PMF from the result of :func:`disaggregation`.
"""
import warnings
import operator
import collections
from functools import partial
import numpy
import scipy.stats
from openquake.hazardlib import contexts
from openquake.baselib.general import AccumDict, groupby, pprod
from openquake.hazardlib.calc import filters
from openquake.hazardlib.geo.utils import get_longitudinal_extent
from openquake.hazardlib.geo.utils import (angular_distance, KM_TO_DEGREES,
cross_idl)
from openquake.hazardlib.site import SiteCollection
from openquake.hazardlib.gsim.base import (
ContextMaker, to_distribution_values)
BIN_NAMES = 'mag', 'dist', 'lon', 'lat', 'eps', 'trt'
BinData = collections.namedtuple('BinData', 'dists, lons, lats, pnes')
[docs]def assert_same_shape(arrays):
"""
Raises an AssertionError if the shapes are not consistent
"""
shape = arrays[0].shape
for arr in arrays[1:]:
assert arr.shape == shape, (arr.shape, shape)
[docs]def get_edges_shapedic(oq, sitecol, mags_by_trt):
"""
:returns: (mag dist lon lat eps trt) edges and shape dictionary
"""
tl = oq.truncation_level
if oq.rlz_index is None:
Z = oq.num_rlzs_disagg or 1
else:
Z = len(oq.rlz_index)
eps_edges = numpy.linspace(-tl, tl, oq.num_epsilon_bins + 1)
# build mag_edges
mags = set()
trts = []
for trt, _mags in mags_by_trt.items():
mags.update(float(mag) for mag in _mags)
trts.append(trt)
mags = sorted(mags)
mag_edges = oq.mag_bin_width * numpy.arange(
int(numpy.floor(min(mags) / oq.mag_bin_width)),
int(numpy.ceil(max(mags) / oq.mag_bin_width) + 1))
# build dist_edges
maxdist = max(oq.maximum_distance(trt) for trt in trts)
dist_edges = oq.distance_bin_width * numpy.arange(
0, int(numpy.ceil(maxdist / oq.distance_bin_width) + 1))
# build eps_edges
eps_edges = numpy.linspace(-tl, tl, oq.num_epsilon_bins + 1)
# build lon_edges, lat_edges per sid
lon_edges, lat_edges = {}, {} # by sid
for site in sitecol:
loc = site.location
lon_edges[site.id], lat_edges[site.id] = lon_lat_bins(
loc.x, loc.y, maxdist, oq.coordinate_bin_width)
# sanity check: the shapes of the lon lat edges are consistent
assert_same_shape(list(lon_edges.values()))
assert_same_shape(list(lat_edges.values()))
bin_edges = [mag_edges, dist_edges, lon_edges, lat_edges, eps_edges]
edges = [mag_edges, dist_edges, lon_edges[0], lat_edges[0], eps_edges]
shape = [len(edge) - 1 for edge in edges] + [len(trts)]
shapedic = dict(zip(BIN_NAMES, shape))
shapedic['N'] = len(sitecol)
shapedic['M'] = len(oq.imtls)
shapedic['P'] = len(oq.poes_disagg or (None,))
shapedic['Z'] = Z
return bin_edges + [trts], shapedic
def _eps3(truncation_level, n_epsilons):
# NB: instantiating truncnorm is slow and calls the infamous "doccer"
tn = scipy.stats.truncnorm(-truncation_level, truncation_level)
eps = numpy.linspace(-truncation_level, truncation_level, n_epsilons + 1)
eps_bands = tn.cdf(eps[1:]) - tn.cdf(eps[:-1])
return tn, eps, eps_bands
DEBUG = AccumDict(accum=[]) # sid -> pnes.mean(), useful for debugging
# this is inside an inner loop
[docs]def disaggregate(ctxs, g_by_z, iml2dict, eps3, sid=0, bin_edges=()):
"""
:param ctxs: a list of U fat RuptureContexts
:param imts: a list of Intensity Measure Type objects
:param g_by_z: an array of gsim indices
:param imt: an Intensity Measure Type
:param iml2dict: a dictionary of arrays imt -> (P, Z)
:param eps3: a triplet (truncnorm, epsilons, eps_bands)
"""
# disaggregate (separate) PoE in different contributions
U, E, M = len(ctxs), len(eps3[2]), len(iml2dict)
iml2 = next(iter(iml2dict.values()))
P, Z = iml2.shape
dists = numpy.zeros(U)
lons = numpy.zeros(U)
lats = numpy.zeros(U)
# switch to logarithmic intensities
iml3 = numpy.zeros((M, P, Z))
for m, (imt, iml2) in enumerate(iml2dict.items()):
# 0 values are converted into -inf
iml3[m] = to_distribution_values(iml2, imt)
truncnorm, epsilons, eps_bands = eps3
cum_bands = numpy.array([eps_bands[e:].sum() for e in range(E)] + [0])
G = ctxs[0].mean_std.shape[-1]
mean_std = numpy.zeros((2, U, M, G), numpy.float32)
for u, ctx in enumerate(ctxs):
if not hasattr(ctx, 'idx'): # assume single site
idx = 0
else:
idx = ctx.idx[sid]
dists[u] = ctx.rrup[idx] # distance to the site
lons[u] = ctx.clon[idx] # closest point of the rupture lon
lats[u] = ctx.clat[idx] # closest point of the rupture lat
mean_std[:, u] = ctx.mean_std[:, idx] # (2, N, M, G) => (2, M, G)
poes = numpy.zeros((U, E, M, P, Z))
pnes = numpy.ones((U, E, M, P, Z))
for (m, p, z), iml in numpy.ndenumerate(iml3):
if iml == -numpy.inf: # zero hazard
continue
# discard the z contributions coming from wrong realizations: see
# the test disagg/case_2
try:
g = g_by_z[z]
except KeyError:
continue
lvls = (iml - mean_std[0, :, m, g]) / mean_std[1, :, m, g]
idxs = numpy.searchsorted(epsilons, lvls)
poes[:, :, m, p, z] = _disagg_eps(
truncnorm.sf(lvls), idxs, eps_bands, cum_bands)
for u, ctx in enumerate(ctxs):
pnes[u] *= ctx.get_probability_no_exceedance(poes[u]) # this is slow
bindata = BinData(dists, lons, lats, pnes)
DEBUG[idx].append(pnes.mean())
if not bin_edges:
return bindata
return _build_disagg_matrix(bindata, bin_edges)
[docs]def set_mean_std(ctxs, imts, gsims):
for u, ctx in enumerate(ctxs):
ctx.mean_std = ctx.get_mean_std(imts, gsims) # (2, N, M, G)
def _disagg_eps(survival, bins, eps_bands, cum_bands):
# disaggregate PoE of `iml` in different contributions,
# each coming from ``epsilons`` distribution bins
res = numpy.zeros((len(bins), len(eps_bands)))
for e, eps_band in enumerate(eps_bands):
res[bins <= e, e] = eps_band # left bins
inside = bins == e + 1 # inside bins
res[inside, e] = survival[inside] - cum_bands[bins[inside]]
return res # shape (U, E)
# used in calculators/disaggregation
[docs]def lon_lat_bins(lon, lat, size_km, coord_bin_width):
"""
Define lon, lat bin edges for disaggregation histograms.
:param lon: longitude of the site
:param lat: latitude of the site
:param size_km: total size of the bins in km
:param coord_bin_width: bin width in degrees
:returns: two arrays lon bins, lat bins
"""
nbins = numpy.ceil(size_km * KM_TO_DEGREES / coord_bin_width)
delta_lon = min(angular_distance(size_km, lat), 180)
delta_lat = min(size_km * KM_TO_DEGREES, 90)
EPS = .001 # avoid discarding the last edgebdata.pnes.shape
lon_bins = lon + numpy.arange(-delta_lon, delta_lon + EPS,
delta_lon / nbins)
lat_bins = lat + numpy.arange(-delta_lat, delta_lat + EPS,
delta_lat / nbins)
if cross_idl(*lon_bins):
lon_bins %= 360
return lon_bins, lat_bins
# this is fast
def _build_disagg_matrix(bdata, bins):
"""
:param bdata: a dictionary of probabilities of no exceedence
:param bins: bin edges
:returns:
a 7D-matrix of shape (#distbins, #lonbins, #latbins, #epsbins, M, P, Z)
"""
dist_bins, lon_bins, lat_bins, eps_bins = bins
dim1, dim2, dim3, dim4 = shape = [len(b) - 1 for b in bins]
# find bin indexes of rupture attributes; bins are assumed closed
# on the lower bound, and open on the upper bound, that is [ )
# longitude values need an ad-hoc method to take into account
# the 'international date line' issue
# the 'minus 1' is needed because the digitize method returns the
# index of the upper bound of the bin
dists_idx = numpy.digitize(bdata.dists, dist_bins) - 1
lons_idx = _digitize_lons(bdata.lons, lon_bins)
lats_idx = numpy.digitize(bdata.lats, lat_bins) - 1
# because of the way numpy.digitize works, values equal to the last bin
# edge are associated to an index equal to len(bins) which is not a
# valid index for the disaggregation matrix. Such values are assumed
# to fall in the last bin
dists_idx[dists_idx == dim1] = dim1 - 1
lons_idx[lons_idx == dim2] = dim2 - 1
lats_idx[lats_idx == dim3] = dim3 - 1
U, E, M, P, Z = bdata.pnes.shape
mat7D = numpy.ones(shape + [M, P, Z])
for i_dist, i_lon, i_lat, pne in zip(
dists_idx, lons_idx, lats_idx, bdata.pnes):
mat7D[i_dist, i_lon, i_lat] *= pne # shape E, M, P, Z
return 1. - mat7D
def _digitize_lons(lons, lon_bins):
"""
Return indices of the bins to which each value in lons belongs.
Takes into account the case in which longitude values cross the
international date line.
:parameter lons:
An instance of `numpy.ndarray`.
:parameter lons_bins:
An instance of `numpy.ndarray`.
"""
if cross_idl(lon_bins[0], lon_bins[-1]):
idx = numpy.zeros_like(lons, dtype=numpy.int)
for i_lon in range(len(lon_bins) - 1):
extents = get_longitudinal_extent(lons, lon_bins[i_lon + 1])
lon_idx = extents > 0
if i_lon != 0:
extents = get_longitudinal_extent(lon_bins[i_lon], lons)
lon_idx &= extents >= 0
idx[lon_idx] = i_lon
return numpy.array(idx)
else:
return numpy.digitize(lons, lon_bins) - 1
def _magbin_groups(rups, mag_bins):
# returns lists of ruptures, one list per each magnitude bin
groups = [[] for _ in mag_bins[1:]]
for rup in rups:
magi = numpy.searchsorted(mag_bins, rup.mag) - 1
groups[magi].append(rup)
return groups
# this is used in the hazardlib tests, not in the engine
[docs]def disaggregation(
sources, site, imt, iml, gsim_by_trt, truncation_level,
n_epsilons, mag_bin_width, dist_bin_width, coord_bin_width,
source_filter=filters.nofilter, **kwargs):
"""
Compute "Disaggregation" matrix representing conditional probability of an
intensity mesaure type ``imt`` exceeding, at least once, an intensity
measure level ``iml`` at a geographical location ``site``, given rupture
scenarios classified in terms of:
- rupture magnitude
- Joyner-Boore distance from rupture surface to site
- longitude and latitude of the surface projection of a rupture's point
closest to ``site``
- epsilon: number of standard deviations by which an intensity measure
level deviates from the median value predicted by a GSIM, given the
rupture parameters
- rupture tectonic region type
In other words, the disaggregation matrix allows to compute the probability
of each scenario with the specified properties (e.g., magnitude, or the
magnitude and distance) to cause one or more exceedences of a given hazard
level.
For more detailed information about the disaggregation, see for instance
"Disaggregation of Seismic Hazard", Paolo Bazzurro, C. Allin Cornell,
Bulletin of the Seismological Society of America, Vol. 89, pp. 501-520,
April 1999.
:param sources:
Seismic source model, as for
:mod:`PSHA <openquake.hazardlib.calc.hazard_curve>` calculator it
should be an iterator of seismic sources.
:param site:
:class:`~openquake.hazardlib.site.Site` of interest to calculate
disaggregation matrix for.
:param imt:
Instance of :mod:`intensity measure type <openquake.hazardlib.imt>`
class.
:param iml:
Intensity measure level. A float value in units of ``imt``.
:param gsim_by_trt:
Tectonic region type to GSIM objects mapping.
:param truncation_level:
Float, number of standard deviations for truncation of the intensity
distribution.
:param n_epsilons:
Integer number of epsilon histogram bins in the result matrix.
:param mag_bin_width:
Magnitude discretization step, width of one magnitude histogram bin.
:param dist_bin_width:
Distance histogram discretization step, in km.
:param coord_bin_width:
Longitude and latitude histograms discretization step,
in decimal degrees.
:param source_filter:
Optional source-site filter function. See
:mod:`openquake.hazardlib.calc.filters`.
:returns:
A tuple of two items. First is itself a tuple of bin edges information
for (in specified order) magnitude, distance, longitude, latitude,
epsilon and tectonic region types.
Second item is 6d-array representing the full disaggregation matrix.
Dimensions are in the same order as bin edges in the first item
of the result tuple. The matrix can be used directly by pmf-extractor
functions.
"""
trts = sorted(set(src.tectonic_region_type for src in sources))
trt_num = dict((trt, i) for i, trt in enumerate(trts))
rlzs_by_gsim = {gsim_by_trt[trt]: [0] for trt in trts}
by_trt = groupby(sources, operator.attrgetter('tectonic_region_type'))
bdata = {} # by trt, magi
sitecol = SiteCollection([site])
iml2 = numpy.array([[iml]])
eps3 = _eps3(truncation_level, n_epsilons)
rups = AccumDict(accum=[])
cmaker = {} # trt -> cmaker
for trt, srcs in by_trt.items():
contexts.RuptureContext.temporal_occurrence_model = (
srcs[0].temporal_occurrence_model)
cmaker[trt] = ContextMaker(
trt, rlzs_by_gsim,
{'truncation_level': truncation_level,
'maximum_distance': source_filter.integration_distance,
'imtls': {str(imt): [iml]}})
rups[trt].extend(cmaker[trt].from_srcs(srcs, sitecol))
min_mag = min(r.mag for rs in rups.values() for r in rs)
max_mag = max(r.mag for rs in rups.values() for r in rs)
mag_bins = mag_bin_width * numpy.arange(
int(numpy.floor(min_mag / mag_bin_width)),
int(numpy.ceil(max_mag / mag_bin_width) + 1))
for trt in cmaker:
gsim = gsim_by_trt[trt]
for magi, ctxs in enumerate(_magbin_groups(rups[trt], mag_bins)):
set_mean_std(ctxs, [imt], [gsim])
bdata[trt, magi] = disaggregate(ctxs, [0], {imt: iml2}, eps3)
if sum(len(bd.dists) for bd in bdata.values()) == 0:
warnings.warn(
'No ruptures have contributed to the hazard at site %s'
% site, RuntimeWarning)
return None, None
min_dist = min(bd.dists.min() for bd in bdata.values())
max_dist = max(bd.dists.max() for bd in bdata.values())
dist_bins = dist_bin_width * numpy.arange(
int(numpy.floor(min_dist / dist_bin_width)),
int(numpy.ceil(max_dist / dist_bin_width) + 1))
lon_bins, lat_bins = lon_lat_bins(site.location.x, site.location.y,
max_dist, coord_bin_width)
eps_bins = numpy.linspace(-truncation_level, truncation_level,
n_epsilons + 1)
bin_edges = (mag_bins, dist_bins, lon_bins, lat_bins, eps_bins)
matrix = numpy.zeros((len(mag_bins) - 1, len(dist_bins) - 1,
len(lon_bins) - 1, len(lat_bins) - 1,
len(eps_bins) - 1, len(trts))) # 6D
for trt, magi in bdata:
mat7 = _build_disagg_matrix(bdata[trt, magi], bin_edges[1:])
matrix[magi, ..., trt_num[trt]] = mat7[..., 0, 0, 0]
return bin_edges + (trts,), matrix
MAG, DIS, LON, LAT, EPS = 0, 1, 2, 3, 4
mag_pmf = partial(pprod, axis=(DIS, LON, LAT, EPS))
dist_pmf = partial(pprod, axis=(MAG, LON, LAT, EPS))
mag_dist_pmf = partial(pprod, axis=(LON, LAT, EPS))
mag_dist_eps_pmf = partial(pprod, axis=(LON, LAT))
lon_lat_pmf = partial(pprod, axis=(DIS, MAG, EPS))
mag_lon_lat_pmf = partial(pprod, axis=(DIS, EPS))
trt_pmf = partial(pprod, axis=(1, 2, 3, 4, 5))
# applied on matrix TRT MAG DIS LON LAT EPS
[docs]def lon_lat_trt_pmf(matrices):
"""
Fold full disaggregation matrices to lon / lat / TRT PMF.
:param matrices:
a matrix with T submatrices
:returns:
4d array. First dimension represents longitude histogram bins,
second one latitude histogram bins, third one trt histogram bins,
last dimension is the z index, associatd to the realization.
"""
res = numpy.array([lon_lat_pmf(mat) for mat in matrices])
return res.transpose(1, 2, 0, 3)
# this dictionary is useful to extract a fixed set of
# submatrices from the full disaggregation matrix
pmf_map = dict([
('Mag', mag_pmf),
('Dist', dist_pmf),
('TRT', trt_pmf),
('Mag_Dist', mag_dist_pmf),
('Mag_Dist_Eps', mag_dist_eps_pmf),
('Lon_Lat', lon_lat_pmf),
('Mag_Lon_Lat', mag_lon_lat_pmf),
('Lon_Lat_TRT', lon_lat_trt_pmf),
])