Source code for openquake.hazardlib.gsim.base

# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
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#
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"""
Module :mod:`openquake.hazardlib.gsim.base` defines base classes for
different kinds of :class:`ground shaking intensity models
<GroundShakingIntensityModel>`.
"""
import abc
import math
import warnings
import functools
import numpy
from scipy.special import ndtr

from openquake.baselib.general import DeprecationWarning
from openquake.hazardlib import imt as imt_module
from openquake.hazardlib import const
from openquake.hazardlib.contexts import KNOWN_DISTANCES
from openquake.hazardlib.contexts import *  # for backward compatibility


ADMITTED_STR_PARAMETERS = ['DEFINED_FOR_TECTONIC_REGION_TYPE',
                           'DEFINED_FOR_INTENSITY_MEASURE_COMPONENT']
ADMITTED_FLOAT_PARAMETERS = ['DEFINED_FOR_REFERENCE_VELOCITY']
ADMITTED_TABLE_PARAMETERS = ['COEFFS_STRESS', 'COEFFS_HARD_ROCK',
                             'COEFFS_SITE_RESPONSE']
ADMITTED_SET_PARAMETERS = ['DEFINED_FOR_INTENSITY_MEASURE_TYPES',
                           'DEFINED_FOR_STANDARD_DEVIATION_TYPES',
                           'REQUIRES_DISTANCES',
                           'REQUIRES_SITES_PARAMETERS',
                           'REQUIRES_RUPTURE_PARAMETERS']

registry = {}  # GSIM name -> GSIM class
gsim_aliases = {}  # populated for instance in nbcc2015_AA13.py


[docs]class NotVerifiedWarning(UserWarning): """ Raised when a non verified GSIM is instantiated """
[docs]class ExperimentalWarning(UserWarning): """ Raised for GMPEs that are intended for experimental use or maybe subject to changes in future version. """
[docs]class AdaptedWarning(UserWarning): """ Raised for GMPEs that are intended for experimental use or maybe subject to changes in future version. """
[docs]def gsim_imt_dt(sorted_gsims, sorted_imts): """ Build a numpy dtype as a nested record with keys 'idx' and nested (gsim, imt). :param sorted_gsims: a list of GSIM instances, sorted lexicographically :param sorted_imts: a list of intensity measure type strings """ dtlist = [(imt, numpy.float32) for imt in sorted_imts] imt_dt = numpy.dtype(dtlist) return numpy.dtype([(str(gsim), imt_dt) for gsim in sorted_gsims])
[docs]def get_mean_std(sctx, rctx, dctx, imts, gsims): """ :returns: an array of shape (2, N, M, G) with means and stddevs """ N = len(sctx.sids) M = len(imts) G = len(gsims) arr = numpy.zeros((2, N, M, G)) num_tables = CoeffsTable.num_instances for g, gsim in enumerate(gsims): d = dctx.roundup(gsim.minimum_distance) for m, imt in enumerate(imts): mean, [std] = gsim.get_mean_and_stddevs(sctx, rctx, d, imt, [const.StdDev.TOTAL]) arr[0, :, m, g] = mean arr[1, :, m, g] = std if CoeffsTable.num_instances > num_tables: raise RuntimeError('Instantiating CoeffsTable inside ' '%s.get_mean_and_stddevs' % gsim.__class__.__name__) return arr
[docs]def get_poes(mean_std, loglevels, truncation_level, gsims=()): """ Calculate and return probabilities of exceedance (PoEs) of one or more intensity measure levels (IMLs) of one intensity measure type (IMT) for one or more pairs "site -- rupture". :param mean_std: An array of shape (2, N, M, G) with mean and standard deviation for the current intensity measure type :param loglevels: A DictArray imt -> logs of intensity measure levels :param truncation_level: Can be ``None``, which means that the distribution of intensity is treated as Gaussian distribution with possible values ranging from minus infinity to plus infinity. When set to zero, the mean intensity is treated as an exact value (standard deviation is not even computed for that case) and resulting array contains 0 in places where IMT is strictly lower than the mean value of intensity and 1.0 where IMT is equal or greater. When truncation level is positive number, the intensity distribution is processed as symmetric truncated Gaussian with range borders being ``mean - truncation_level * stddev`` and ``mean + truncation_level * stddev``. That is, the truncation level expresses how far the range borders are from the mean value and is defined in units of sigmas. The resulting PoEs for that mode are values of complementary cumulative distribution function of that truncated Gaussian applied to IMLs. :returns: array of PoEs of shape (N, L, G) :raises ValueError: If truncation level is not ``None`` and neither non-negative float number, and if ``imts`` dictionary contain wrong or unsupported IMTs (see :attr:`DEFINED_FOR_INTENSITY_MEASURE_TYPES`). """ if truncation_level is not None and truncation_level < 0: raise ValueError('truncation level must be zero, positive number ' 'or None') if len(gsims): assert mean_std.shape[-1] == len(gsims) tl = truncation_level if any(hasattr(gsim, 'weights_signs') for gsim in gsims): # implement average get_poes for the nshmp_2014 model shp = list(mean_std[0].shape) # (N, M, G) shp[1] = len(loglevels.array) # L arr = numpy.zeros(shp) for g, gsim in enumerate(gsims): if hasattr(gsim, 'weights_signs'): outs = [] weights, signs = zip(*gsim.weights_signs) for s in signs: ms = numpy.array(mean_std[:, :, :, g]) # make a copy for m in range(len(loglevels)): ms[0, :, m] += s * gsim.adjustment outs.append(_get_poes(ms, loglevels, tl, squeeze=1)) arr[:, :, g] = numpy.average(outs, weights=weights, axis=0) else: ms = mean_std[:, :, :, g] arr[:, :, g] = _get_poes(ms, loglevels, tl, squeeze=1) return arr elif any("mixture_model" in gsim.kwargs for gsim in gsims): shp = list(mean_std[0].shape) # (N, M, G) shp[1] = len(loglevels.array) # L arr = numpy.zeros(shp) for g, gsim in enumerate(gsims): if "mixture_model" in gsim.kwargs: for fact, wgt in zip( gsim.kwargs["mixture_model"]["factors"], gsim.kwargs["mixture_model"]["weights"]): mean_stdi = numpy.array(mean_std[:, :, :, g]) # make a copy mean_stdi[1] *= fact arr[:, :, g] += (wgt * _get_poes(mean_stdi, loglevels, tl, squeeze=1)) else: ms = mean_std[:, :, :, g] arr[:, :, g] = _get_poes(ms, loglevels, tl, squeeze=1) return arr else: # regular case return _get_poes(mean_std, loglevels, truncation_level)
# this is the critical function for the performance of the classical calculator # it is dominated by memory allocations (i.e. _truncnorm_sf is ultra-fast) # the only way to speedup is to reduce the maximum_distance, then the array # will become shorted in the N dimension (number of affected sites) def _get_poes(mean_std, loglevels, truncation_level, squeeze=False): mean, stddev = mean_std # shape (N, M, G) each N, L, G = len(mean), len(loglevels.array), mean.shape[-1] out = numpy.zeros((N, L) if squeeze else (N, L, G)) lvl = 0 for m, imt in enumerate(loglevels): for iml in loglevels[imt]: if truncation_level == 0: # just compare imls to mean out[:, lvl] = iml <= mean[:, m] else: out[:, lvl] = (iml - mean[:, m]) / stddev[:, m] lvl += 1 return _truncnorm_sf(truncation_level, out)
[docs]class MetaGSIM(abc.ABCMeta): """ A metaclass converting set class attributes into frozensets, to avoid mutability bugs without having to change already written GSIMs. Moreover it performs some checks against typos. """ def __new__(meta, name, bases, dic): for k, v in dic.items(): if isinstance(v, set): dic[k] = frozenset(v) if k == 'REQUIRES_DISTANCES': missing = v - KNOWN_DISTANCES if missing: raise ValueError('Unknown distance %s in %s' % (missing, name)) return super().__new__(meta, name, bases, dic)
[docs]@functools.total_ordering class GroundShakingIntensityModel(metaclass=MetaGSIM): """ Base class for all the ground shaking intensity models. A Ground Shaking Intensity Model (GSIM) defines a set of equations for computing mean and standard deviation of a Normal distribution representing the variability of an intensity measure (or of its logarithm) at a site given an earthquake rupture. This class is not intended to be subclassed directly, instead the actual GSIMs should subclass :class:`GMPE` Subclasses of both must implement :meth:`get_mean_and_stddevs` and all the class attributes with names starting from ``DEFINED_FOR`` and ``REQUIRES``. """ #: Reference to a #: :class:`tectonic region type <openquake.hazardlib.const.TRT>` this GSIM #: is defined for. One GSIM can implement only one tectonic region type. DEFINED_FOR_TECTONIC_REGION_TYPE = abc.abstractproperty() #: Set of :mod:`intensity measure types <openquake.hazardlib.imt>` #: this GSIM can #: calculate. A set should contain classes from module #: :mod:`openquake.hazardlib.imt`. DEFINED_FOR_INTENSITY_MEASURE_TYPES = abc.abstractproperty() #: Reference to a :class:`intensity measure component type #: <openquake.hazardlib.const.IMC>` this GSIM can calculate mean #: and standard #: deviation for. DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = abc.abstractproperty() #: Set of #: :class:`standard deviation types <openquake.hazardlib.const.StdDev>` #: this GSIM can calculate. DEFINED_FOR_STANDARD_DEVIATION_TYPES = abc.abstractproperty() #: Set of site parameters names this GSIM needs. The set should include #: strings that match names of the attributes of a :class:`site #: <openquake.hazardlib.site.Site>` object. #: Those attributes are then available in the #: :class:`SitesContext` object with the same names. REQUIRES_SITES_PARAMETERS = abc.abstractproperty() #: Set of rupture parameters (excluding distance information) required #: by GSIM. Supported parameters are: #: #: ``mag`` #: Magnitude of the rupture. #: ``dip`` #: Rupture's surface dip angle in decimal degrees. #: ``rake`` #: Angle describing the slip propagation on the rupture surface, #: in decimal degrees. See :mod:`~openquake.hazardlib.geo.nodalplane` #: for more detailed description of dip and rake. #: ``ztor`` #: Depth of rupture's top edge in km. See #: :meth:`~openquake.hazardlib.geo.surface.base.BaseSurface.get_top_edge_depth`. #: #: These parameters are available from the :class:`RuptureContext` object #: attributes with same names. REQUIRES_RUPTURE_PARAMETERS = abc.abstractproperty() #: Set of types of distance measures between rupture and sites. Possible #: values are: #: #: ``rrup`` #: Closest distance to rupture surface. See #: :meth:`~openquake.hazardlib.geo.surface.base.BaseSurface.get_min_distance`. #: ``rjb`` #: Distance to rupture's surface projection. See #: :meth:`~openquake.hazardlib.geo.surface.base.BaseSurface.get_joyner_boore_distance`. #: ``rx`` #: Perpendicular distance to rupture top edge projection. #: See :meth:`~openquake.hazardlib.geo.surface.base.BaseSurface.get_rx_distance`. #: ``ry0`` #: Horizontal distance off the end of the rupture measured parallel to # strike. See: #: See :meth:`~openquake.hazardlib.geo.surface.base.BaseSurface.get_ry0_distance`. #: ``rcdpp`` #: Direct point parameter for directivity effect centered on the site- and earthquake-specific # average DPP used. See: #: See :meth:`~openquake.hazardlib.source.rupture.ParametricProbabilisticRupture.get_dppvalue`. #: ``rvolc`` #: Source to site distance passing through surface projection of volcanic zone #: #: All the distances are available from the :class:`DistancesContext` #: object attributes with same names. Values are in kilometers. REQUIRES_DISTANCES = abc.abstractproperty() _toml = '' # set by valid.gsim minimum_distance = 0 # set by valid.gsim superseded_by = None non_verified = False experimental = False adapted = False get_poes = staticmethod(get_poes) @classmethod def __init_subclass__(cls): stddevtypes = cls.DEFINED_FOR_STANDARD_DEVIATION_TYPES if not isinstance(stddevtypes, abc.abstractproperty): # concrete class if const.StdDev.TOTAL not in stddevtypes: raise ValueError('%s.DEFINED_FOR_STANDARD_DEVIATION_TYPES is ' 'not defined for const.StdDev.TOTAL' % cls.__name__) registry[cls.__name__] = cls def __init__(self, **kwargs): self.kwargs = kwargs cls = self.__class__ if cls.superseded_by: msg = '%s is deprecated - use %s instead' % ( cls.__name__, cls.superseded_by.__name__) warnings.warn(msg, DeprecationWarning) if cls.non_verified: msg = ('%s is not independently verified - the user is liable ' 'for their application') % cls.__name__ warnings.warn(msg, NotVerifiedWarning) if cls.experimental: msg = ('%s is experimental and may change in future versions - ' 'the user is liable for their application') % cls.__name__ warnings.warn(msg, ExperimentalWarning) if cls.adapted: msg = ('%s is not intended for general use and the behaviour ' 'may not be as expected - ' 'the user is liable for their application') % cls.__name__ warnings.warn(msg, AdaptedWarning)
[docs] @abc.abstractmethod def get_mean_and_stddevs(self, sites, rup, dists, imt, stddev_types): """ Calculate and return mean value of intensity distribution and it's standard deviation. Method must be implemented by subclasses. :param sites: Instance of :class:`openquake.hazardlib.site.SiteCollection` with parameters of sites collection assigned to respective values as numpy arrays. Only those attributes that are listed in class' :attr:`REQUIRES_SITES_PARAMETERS` set are available. :param rup: Instance of :class:`openquake.hazardlib.source.rupture.BaseRupture` with parameters of a rupture assigned to respective values. Only those attributes that are listed in class' :attr:`REQUIRES_RUPTURE_PARAMETERS` set are available. :param dists: Instance of :class:`DistancesContext` with values of distance measures between the rupture and each site of the collection assigned to respective values as numpy arrays. Only those attributes that are listed in class' :attr:`REQUIRES_DISTANCES` set are available. :param imt: An instance (not a class) of intensity measure type. See :mod:`openquake.hazardlib.imt`. :param stddev_types: List of standard deviation types, constants from :class:`openquake.hazardlib.const.StdDev`. Method result value should include standard deviation values for each of types in this list. :returns: Method should return a tuple of two items. First item should be a numpy array of floats -- mean values of respective component of a chosen intensity measure type, and the second should be a list of numpy arrays of standard deviation values for the same single component of the same single intensity measure type, one array for each type in ``stddev_types`` parameter, preserving the order. Combining interface to mean and standard deviation values in a single method allows to avoid redoing the same intermediate calculations if there are some shared between stddev and mean formulae without resorting to keeping any sort of internal state (and effectively making GSIM not reenterable). However it is advised to split calculation of mean and stddev values and make ``get_mean_and_stddevs()`` just combine both (and possibly compute interim steps). """
def _check_imt(self, imt): """ Make sure that ``imt`` is valid and is supported by this GSIM. """ names = set(f.__name__ for f in self.DEFINED_FOR_INTENSITY_MEASURE_TYPES) if imt.name not in names: raise ValueError('imt %s is not supported by %s' % (imt.name, type(self).__name__)) def __lt__(self, other): """ The GSIMs are ordered according to string representation """ return str(self) < str(other) def __eq__(self, other): """ The GSIMs are equal if their string representations are equal """ return str(self) == str(other) def __hash__(self): """ We use the __str__ representation as hash: it means that we can use equivalently GSIM instances or strings as dictionary keys. """ return hash(str(self)) def __repr__(self): """ String representation for GSIM instances in TOML format. """ if self._toml: return self._toml return '[%s]' % self.__class__.__name__
def _truncnorm_sf(truncation_level, values): """ Survival function for truncated normal distribution. Assumes zero mean, standard deviation equal to one and symmetric truncation. :param truncation_level: Positive float number representing the truncation on both sides around the mean, in units of sigma, or None, for non-truncation :param values: Numpy array of values as input to a survival function for the given distribution. :returns: Numpy array of survival function results in a range between 0 and 1. >>> from scipy.stats import truncnorm >>> truncnorm(-3, 3).sf(0.12345) == _truncnorm_sf(3, 0.12345) True >>> from scipy.stats import norm >>> norm.sf(0.12345) == _truncnorm_sf(None, 0.12345) True """ if truncation_level == 0: return values if truncation_level is None: return ndtr(- values) # notation from http://en.wikipedia.org/wiki/Truncated_normal_distribution. # given that mu = 0 and sigma = 1, we have alpha = a and beta = b. # "CDF" in comments refers to cumulative distribution function # of non-truncated distribution with that mu and sigma values. # assume symmetric truncation, that is ``a = - truncation_level`` # and ``b = + truncation_level``. # calculate CDF of b phi_b = ndtr(truncation_level) # calculate Z as ``Z = CDF(b) - CDF(a)``, here we assume that # ``CDF(a) == CDF(- truncation_level) == 1 - CDF(b)`` z = phi_b * 2 - 1 # calculate the result of survival function of ``values``, # and restrict it to the interval where probability is defined -- # 0..1. here we use some transformations of the original formula # that is ``SF(x) = 1 - (CDF(x) - CDF(a)) / Z`` in order to minimize # number of arithmetic operations and function calls: # ``SF(x) = (Z - CDF(x) + CDF(a)) / Z``, # ``SF(x) = (CDF(b) - CDF(a) - CDF(x) + CDF(a)) / Z``, # ``SF(x) = (CDF(b) - CDF(x)) / Z``. return ((phi_b - ndtr(values)) / z).clip(0.0, 1.0)
[docs]def to_distribution_values(vals, imt): """ :returns: the logarithm of the values unless the IMT is MMI """ if str(imt) == 'MMI': return vals with warnings.catch_warnings(): warnings.simplefilter("ignore") return numpy.log(vals)
[docs]class GMPE(GroundShakingIntensityModel): """ Ground-Motion Prediction Equation is a subclass of generic :class:`GroundShakingIntensityModel` with a distinct feature that the intensity values are log-normally distributed. Method :meth:`~GroundShakingIntensityModel.get_mean_and_stddevs` of actual GMPE implementations is supposed to return the mean value as a natural logarithm of intensity. """
[docs] def open(self, fname_or_file): """ :param fname_or_file: filename or filelike object :returns: the file object """ if hasattr(fname_or_file, 'read'): return fname_or_file return open(fname_or_file, 'rb')
[docs] def set_parameters(self): """ Combines the parameters of the GMPE provided at the construction level with the ones originally assigned to the backbone modified GMPE. """ for key in (ADMITTED_STR_PARAMETERS + ADMITTED_FLOAT_PARAMETERS + ADMITTED_SET_PARAMETERS): try: val = getattr(self.gmpe, key) except AttributeError: pass else: setattr(self, key, val)
[docs]class CoeffsTable(object): r""" Instances of :class:`CoeffsTable` encapsulate tables of coefficients corresponding to different IMTs. Tables are defined in a space-separated tabular form in a simple string literal (heading and trailing whitespace does not matter). The first column in the table must be named "IMT" (or "imt") and thus should represent IMTs: >>> CoeffsTable(table='''imf z ... pga 1''') Traceback (most recent call last): ... ValueError: first column in a table must be IMT Names of other columns are used as coefficients dicts keys. The values in the first column should correspond to real intensity measure types, see :mod:`openquake.hazardlib.imt`: >>> CoeffsTable(table='''imt z ... pgx 2''') Traceback (most recent call last): ... ValueError: unknown IMT 'PGX' Note that :class:`CoeffsTable` only accepts keyword argumets: >>> CoeffsTable() Traceback (most recent call last): ... TypeError: CoeffsTable requires "table" kwarg >>> CoeffsTable(table='', foo=1) Traceback (most recent call last): ... TypeError: CoeffsTable got unexpected kwargs: {'foo': 1} If there are :class:`~openquake.hazardlib.imt.SA` IMTs in the table, they are not referenced by name, because they require parametrization: >>> CoeffsTable(table='''imt x ... sa 15''') Traceback (most recent call last): ... ValueError: specify period as float value to declare SA IMT >>> CoeffsTable(table='''imt x ... 0.1 20''') Traceback (most recent call last): ... TypeError: attribute "sa_damping" is required for tables defining SA So proper table defining SA looks like this: >>> ct = CoeffsTable(sa_damping=5, table=''' ... imt a b c d ... pga 1 2.4 -5 0.01 ... pgd 7.6 12 0 44.1 ... 0.1 10 20 30 40 ... 1.0 1 2 3 4 ... 10 2 4 6 8 ... ''') Table objects could be indexed by IMT objects (this returns a dictionary of coefficients): >>> from openquake.hazardlib import imt >>> ct[imt.PGA()] == dict(a=1, b=2.4, c=-5, d=0.01) True >>> ct[imt.PGD()] == dict(a=7.6, b=12, c=0, d=44.1) True >>> ct[imt.SA(damping=5, period=0.1)] == dict(a=10, b=20, c=30, d=40) True >>> ct[imt.PGV()] Traceback (most recent call last): ... KeyError: PGV >>> ct[imt.SA(1.0, 4)] Traceback (most recent call last): ... KeyError: SA(1.0, 4) Table of coefficients for spectral acceleration could be indexed by instances of :class:`openquake.hazardlib.imt.SA` with period value that is not specified in the table. The coefficients then get interpolated between the ones for closest higher and closest lower period. That scaling of coefficients works in a logarithmic scale of periods and only within the same damping: >>> '%.5f' % ct[imt.SA(period=0.2, damping=5)]['a'] '7.29073' >>> '%.5f' % ct[imt.SA(period=0.9, damping=5)]['c'] '4.23545' >>> '%.5f' % ct[imt.SA(period=5, damping=5)]['c'] '5.09691' >>> ct[imt.SA(period=0.9, damping=15)] Traceback (most recent call last): ... KeyError: SA(0.9, 15) Extrapolation is not possible: >>> ct[imt.SA(period=0.01, damping=5)] Traceback (most recent call last): ... KeyError: SA(0.01) It is also possible to instantiate a table from a tuple of dictionaries, corresponding to the SA coefficients and non-SA coefficients: >>> coeffs = {imt.SA(0.1): {"a": 1.0, "b": 2.0}, ... imt.SA(1.0): {"a": 3.0, "b": 4.0}, ... imt.PGA(): {"a": 0.1, "b": 1.0}, ... imt.PGV(): {"a": 0.5, "b": 10.0}} >>> ct = CoeffsTable(sa_damping=5, table=coeffs) """ num_instances = 0 def __init__(self, **kwargs): if 'table' not in kwargs: raise TypeError('CoeffsTable requires "table" kwarg') self._coeffs = {} # cache table = kwargs.pop('table') self.sa_coeffs = {} self.non_sa_coeffs = {} sa_damping = kwargs.pop('sa_damping', None) if kwargs: raise TypeError('CoeffsTable got unexpected kwargs: %r' % kwargs) if isinstance(table, str): self._setup_table_from_str(table, sa_damping) elif isinstance(table, dict): for imt in table: if imt.name == 'SA': self.sa_coeffs[imt] = table[imt] else: self.non_sa_coeffs[imt] = table[imt] else: raise TypeError("CoeffsTable cannot be constructed with inputs " "of the form '%s'" % table.__class__.__name__) self.__class__.num_instances += 1 def _setup_table_from_str(self, table, sa_damping): """ Builds the input tables from a string definition """ table = table.strip().splitlines() header = table.pop(0).split() if not header[0].upper() == "IMT": raise ValueError('first column in a table must be IMT') coeff_names = header[1:] for row in table: row = row.split() imt_name = row[0].upper() if imt_name == 'SA': raise ValueError('specify period as float value ' 'to declare SA IMT') imt_coeffs = dict(zip(coeff_names, map(float, row[1:]))) try: sa_period = float(imt_name) except Exception: if imt_name not in imt_module.registry: raise ValueError('unknown IMT %r' % imt_name) imt = imt_module.registry[imt_name]() self.non_sa_coeffs[imt] = imt_coeffs else: if sa_damping is None: raise TypeError('attribute "sa_damping" is required ' 'for tables defining SA') imt = imt_module.SA(sa_period, sa_damping) self.sa_coeffs[imt] = imt_coeffs def __getitem__(self, imt): """ Return a dictionary of coefficients corresponding to ``imt`` from this table (if there is a line for requested IMT in it), or the dictionary of interpolated coefficients, if ``imt`` is of type :class:`~openquake.hazardlib.imt.SA` and interpolation is possible. :raises KeyError: If ``imt`` is not available in the table and no interpolation can be done. """ try: return self._coeffs[imt] except KeyError: pass if imt.name != 'SA': self._coeffs[imt] = c = self.non_sa_coeffs[imt] return c try: self._coeffs[imt] = c = self.sa_coeffs[imt] return c except KeyError: pass max_below = min_above = None for unscaled_imt in list(self.sa_coeffs): if unscaled_imt.damping != imt.damping: continue if unscaled_imt.period > imt.period: if min_above is None or unscaled_imt.period < min_above.period: min_above = unscaled_imt elif unscaled_imt.period < imt.period: if max_below is None or unscaled_imt.period > max_below.period: max_below = unscaled_imt if max_below is None or min_above is None: raise KeyError(imt) # ratio tends to 1 when target period tends to a minimum # known period above and to 0 if target period is close # to maximum period below. ratio = ((math.log(imt.period) - math.log(max_below.period)) / (math.log(min_above.period) - math.log(max_below.period))) max_below = self.sa_coeffs[max_below] min_above = self.sa_coeffs[min_above] self._coeffs[imt] = c = { co: (min_above[co] - max_below[co]) * ratio + max_below[co] for co in max_below} return c