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# -*- coding: utf-8 -*- |
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# vim:fileencoding=utf-8 |
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# |
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# Copyright (c) 2017-2018 Stefan Bender |
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# |
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# This module is part of sciapy. |
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# sciapy is free software: you can redistribute it or modify |
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# it under the terms of the GNU General Public License as published |
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# by the Free Software Foundation, version 2. |
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# See accompanying LICENSE file or http://www.gnu.org/licenses/gpl-2.0.html. |
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"""SCIAMACHY regression models (celerite version) |
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Model classes for SCIAMACHY data regression fits using the |
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:mod:`celerite` [#]_ modeling protocol. |
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.. [#] https://celerite.readthedocs.io |
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""" |
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from __future__ import absolute_import, division, print_function |
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import numpy as np |
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from scipy.interpolate import interp1d |
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from celerite.modeling import Model, ModelSet, ConstantModel |
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__all__ = ["ConstantModel", |
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"HarmonicModelCosineSine", "HarmonicModelAmpPhase", |
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"ProxyModel", "CeleriteModelSet"] |
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View Code Duplication |
class HarmonicModelCosineSine(Model): |
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"""Model for harmonic terms |
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Models harmonic terms using a cosine and sine part. |
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The total amplitude and phase can be inferred from that. |
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Parameters |
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---------- |
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freq : float |
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The frequency in years^-1 |
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cos : float |
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The amplitude of the cosine part |
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sin : float |
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The amplitude of the sine part |
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""" |
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parameter_names = ("freq", "cos", "sin") |
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def get_value(self, t): |
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return (self.cos * np.cos(self.freq * 2 * np.pi * t) + |
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self.sin * np.sin(self.freq * 2 * np.pi * t)) |
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def get_amplitude(self): |
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return np.sqrt(self.cos**2 + self.sin**2) |
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def get_phase(self): |
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return np.arctan2(self.sin, self.cos) |
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def compute_gradient(self, t): |
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dcos = np.cos(self.freq * 2 * np.pi * t) |
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dsin = np.sin(self.freq * 2 * np.pi * t) |
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df = 2 * np.pi * t * (self.sin * dcos - self.cos * dsin) |
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return np.array([df, dcos, dsin]) |
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View Code Duplication |
class HarmonicModelAmpPhase(Model): |
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"""Model for harmonic terms |
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Models harmonic terms using a cosine and sine part. |
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The total amplitude and phase can be inferred from that. |
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Parameters |
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---------- |
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freq : float |
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The frequency in years^-1 |
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amp : float |
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The amplitude of the harmonic term |
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phase : float |
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The phase of the harmonic part |
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""" |
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parameter_names = ("freq", "amp", "phase") |
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def get_value(self, t): |
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return self.amp * np.cos(self.freq * 2 * np.pi * t + self.phase) |
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def get_amplitude(self): |
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return self.amp |
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def get_phase(self): |
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return self.phase |
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def compute_gradient(self, t): |
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damp = np.cos(self.freq * 2 * np.pi * t + self.phase) |
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dphi = -self.amp * np.sin(self.freq * 2 * np.pi * t + self.phase) |
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df = 2 * np.pi * t * dphi |
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return np.array([df, damp, dphi]) |
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View Code Duplication |
class ProxyModel(Model): |
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"""Model for proxy terms |
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Models proxy terms with a finite and (semi-)annually varying life time. |
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Parameters |
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---------- |
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proxy_times : (N,) array_like |
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The data times of the proxy values |
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proxy_vals : (N,) array_like |
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The proxy values at `proxy_times` |
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amp : float |
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The amplitude of the proxy term |
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lag : float |
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The lag of the proxy value in years. |
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tau0 : float |
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The base life time of the proxy |
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taucos1 : float |
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The amplitude of the cosine part of the annual life time variation. |
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tausin1 : float |
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The amplitude of the sine part of the annual life time variation. |
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taucos2 : float |
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The amplitude of the cosine part of the semi-annual life time variation. |
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tausin2 : float |
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The amplitude of the sine part of the semi-annual life time variation. |
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ltscan : float |
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The number of days to sum the previous proxy values. If it is |
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negative, the value will be set to three times the maximal lifetime. |
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No lifetime adjustemets are calculated when set to zero. |
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center : bool, optional |
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Centers the proxy values by subtracting the overall mean. The mean is |
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calculated from the whole `proxy_vals` array and is stored in the |
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`mean` attribute. |
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Default: False |
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sza_intp : scipy.interpolate.interp1d() instance, optional |
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When not `None`, cos(sza) and sin(sza) are used instead |
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of the time to model the annual variation of the lifetime. |
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Semi-annual variations are not used in that case. |
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Default: None |
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fit_phase : bool, optional |
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Fit the phase shift directly instead of using sine and cosine |
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terms for the (semi-)annual lifetime variations. If True, the fitted |
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cosine parameter is the amplitude and the sine parameter the phase. |
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Default: False (= fit sine and cosine terms) |
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lifetime_prior : str, optional |
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The prior probability density for each coefficient of the lifetime. |
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Possible types are "flat" or `None` for a flat prior, "exp" for an |
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exponential density ~ :math:`\\text{exp}(-|\\tau| / \\text{metric})`, |
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and "normal" for a normal distribution |
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~ :math:`\\text{exp}(-\\tau^2 / (2 * \\text{metric}^2))`. |
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Default: None (= flat prior). |
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lifetime_metric : float, optional |
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The metric (scale) of the lifetime priors in days, see `prior`. |
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Default 1. |
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days_per_time_unit : float, optional |
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The number of days per time unit, used to normalize the lifetime |
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units. Use 365.25 if the times are in fractional years, or 1 if |
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they are in days. |
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Default: 365.25 |
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""" |
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parameter_names = ("amp", "lag", "tau0", |
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"taucos1", "tausin1", "taucos2", "tausin2", |
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"ltscan") |
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def __init__(self, proxy_times, proxy_vals, |
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center=False, |
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sza_intp=None, fit_phase=False, |
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lifetime_prior=None, lifetime_metric=1., |
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days_per_time_unit=365.25, |
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*args, **kwargs): |
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self.mean = 0. |
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if center: |
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self.mean = np.nanmean(proxy_vals) |
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self.intp = interp1d(proxy_times, proxy_vals - self.mean, |
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bounds_error=False) |
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self.sza_intp = sza_intp |
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self.fit_phase = fit_phase |
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self.days_per_time_unit = days_per_time_unit |
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self.omega = 2 * np.pi * days_per_time_unit / 365.25 |
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self.lifetime_prior = lifetime_prior |
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self.lifetime_metric = lifetime_metric |
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super(ProxyModel, self).__init__(*args, **kwargs) |
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def get_value(self, t): |
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proxy_val = self.intp(t - self.lag) |
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if self.ltscan == 0: |
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# no lifetime, nothing else to do |
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return self.amp * proxy_val |
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# annual variation of the proxy lifetime |
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if self.sza_intp is not None: |
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# using the solar zenith angle |
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tau_cs = (self.taucos1 * np.cos(np.radians(self.sza_intp(t))) |
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+ self.tausin1 * np.sin(np.radians(self.sza_intp(t)))) |
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elif self.fit_phase: |
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# using time (cos) and phase (sin) |
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tau_cs = (self.taucos1 * np.cos(1 * self.omega * t + self.tausin1) |
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+ self.taucos2 * np.cos(2 * self.omega * t + self.tausin2)) |
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else: |
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# using time |
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tau_cs = (self.taucos1 * np.cos(1 * self.omega * t) |
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+ self.tausin1 * np.sin(1 * self.omega * t) |
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+ self.taucos2 * np.cos(2 * self.omega * t) |
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+ self.tausin2 * np.sin(2 * self.omega * t)) |
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tau_cs[tau_cs < 0] = 0. # clip to zero |
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tau = self.tau0 + tau_cs |
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if self.ltscan > 0: |
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_ltscn = int(np.floor(self.ltscan)) |
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else: |
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# infer the scan time from the maximal lifetime |
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_ltscn = 3 * int(np.ceil(self.tau0 + |
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np.sqrt(self.taucos1**2 + self.tausin1**2))) |
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if np.all(tau > 0): |
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bs = np.arange(1, _ltscn + 1, 1.)[None, :] |
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taufacs = np.exp(-bs / tau[:, None]) |
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proxy_val += np.sum( |
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self.intp(t[:, None] - self.lag - |
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bs / self.days_per_time_unit) * taufacs, |
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axis=1) |
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return self.amp * proxy_val |
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def compute_gradient(self, t): |
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proxy_val = self.intp(t - self.lag) |
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proxy_val_grad0 = self.intp(t - self.lag) |
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# annual variation of the proxy lifetime |
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if self.sza_intp is not None: |
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# using the solar zenith angle |
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dtau_cos1 = np.cos(np.radians(self.sza_intp(t))) |
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dtau_sin1 = np.sin(np.radians(self.sza_intp(t))) |
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dtau_cos2 = np.zeros_like(t) |
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dtau_sin2 = np.zeros_like(t) |
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tau_cs = self.taucos1 * dtau_cos1 + self.tausin1 * dtau_sin1 |
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elif self.fit_phase: |
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# using time (cos) and phase (sin) |
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dtau_cos1 = np.cos(1 * self.omega * t + self.tausin1) |
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dtau_sin1 = -self.taucos1 * np.sin(1 * self.omega * t + self.tausin1) |
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dtau_cos2 = np.cos(2 * self.omega * t + self.tausin2) |
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dtau_sin2 = -self.taucos2 * np.sin(2 * self.omega * t + self.tausin2) |
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tau_cs = self.taucos1 * dtau_cos1 + self.taucos2 * dtau_cos2 |
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else: |
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# using time |
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dtau_cos1 = np.cos(1 * self.omega * t) |
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dtau_sin1 = np.sin(1 * self.omega * t) |
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dtau_cos2 = np.cos(2 * self.omega * t) |
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dtau_sin2 = np.sin(2 * self.omega * t) |
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tau_cs = (self.taucos1 * dtau_cos1 + self.tausin1 * dtau_sin1 + |
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self.taucos2 * dtau_cos2 + self.tausin2 * dtau_sin2) |
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tau_cs[tau_cs < 0] = 0. # clip to zero |
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tau = self.tau0 + tau_cs |
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if self.ltscan > 0: |
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_ltscn = int(np.floor(self.ltscan)) |
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else: |
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# infer the scan time from the maximal lifetime |
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_ltscn = 3 * int(np.ceil(self.tau0 + |
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np.sqrt(self.taucos1**2 + self.tausin1**2))) |
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if np.all(tau > 0): |
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bs = np.arange(1, _ltscn + 1, 1.)[None, :] |
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taufacs = np.exp(-bs / tau[:, None]) |
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proxy_ts = self.intp(t[:, None] - self.lag - |
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bs / self.days_per_time_unit) * taufacs |
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proxy_val += np.sum(proxy_ts, axis=1) |
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proxy_val_grad0 += np.sum(proxy_ts * bs / tau[:, None]**2, axis=1) |
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return np.array([proxy_val, |
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# set the gradient wrt lag to zero for now |
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np.zeros_like(t), |
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self.amp * proxy_val_grad0, |
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self.amp * proxy_val_grad0 * dtau_cos1, |
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self.amp * proxy_val_grad0 * dtau_sin1, |
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self.amp * proxy_val_grad0 * dtau_cos2, |
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self.amp * proxy_val_grad0 * dtau_sin2, |
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# set the gradient wrt lifetime scan to zero for now |
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np.zeros_like(t)]) |
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def _log_prior_normal(self): |
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l_prior = super(ProxyModel, self).log_prior() |
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if not np.isfinite(l_prior): |
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return -np.inf |
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for n, p in self.get_parameter_dict().items(): |
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if n.startswith("tau"): |
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# Gaussian prior for the lifetimes |
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l_prior -= 0.5 * (p / self.lifetime_metric)**2 |
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return l_prior |
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def _log_prior_exp(self): |
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l_prior = super(ProxyModel, self).log_prior() |
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if not np.isfinite(l_prior): |
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return -np.inf |
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for n, p in self.get_parameter_dict().items(): |
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283
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if n.startswith("tau"): |
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284
|
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# exponential prior for the lifetimes |
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285
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l_prior -= np.abs(p / self.lifetime_metric) |
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286
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return l_prior |
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287
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288
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1 |
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def log_prior(self): |
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289
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_priors = {"exp": self._log_prior_exp, |
|
290
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"normal": self._log_prior_normal} |
|
291
|
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if self.lifetime_prior is None or self.lifetime_prior == "flat": |
|
292
|
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return super(ProxyModel, self).log_prior() |
|
293
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return _priors[self.lifetime_prior]() |
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294
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295
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296
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1 |
View Code Duplication |
class CeleriteModelSet(ModelSet): |
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|
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297
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|
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298
|
1 |
|
def get_value(self, t): |
|
299
|
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v = np.zeros_like(t) |
|
300
|
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for m in self.models.values(): |
|
301
|
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v += m.get_value(t) |
|
302
|
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return v |
|
303
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|
|
304
|
1 |
|
def compute_gradient(self, t): |
|
305
|
|
|
grad = [] |
|
306
|
|
|
for m in self.models.values(): |
|
307
|
|
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grad.extend(list(m.compute_gradient(t))) |
|
308
|
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return np.array(grad) |
|
309
|
|
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|
|
310
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311
|
1 |
View Code Duplication |
def _setup_proxy_model_with_bounds(times, values, |
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|
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|
|
312
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max_amp=1e10, max_days=100, |
|
313
|
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**kwargs): |
|
314
|
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|
# extract setup from `kwargs` |
|
315
|
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center = kwargs.get("center", False) |
|
316
|
|
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fit_phase = kwargs.get("fit_phase", False) |
|
317
|
|
|
lag = kwargs.get("lag", 0.) |
|
318
|
|
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lt_metric = kwargs.get("lifetime_metric", 1) |
|
319
|
|
|
lt_prior = kwargs.get("lifetime_prior", "exp") |
|
320
|
|
|
lt_scan = kwargs.get("lifetime_scan", 60) |
|
321
|
|
|
positive = kwargs.get("positive", False) |
|
322
|
|
|
sza_intp = kwargs.get("sza_intp", None) |
|
323
|
|
|
time_format = kwargs.get("time_format", "jyear") |
|
324
|
|
|
|
|
325
|
|
|
return ProxyModel(times, values, |
|
326
|
|
|
center=center, |
|
327
|
|
|
sza_intp=sza_intp, |
|
328
|
|
|
fit_phase=fit_phase, |
|
329
|
|
|
lifetime_prior=lt_prior, |
|
330
|
|
|
lifetime_metric=lt_metric, |
|
331
|
|
|
days_per_time_unit=1 if time_format.endswith("d") else 365.25, |
|
332
|
|
|
amp=0., |
|
333
|
|
|
lag=lag, |
|
334
|
|
|
tau0=0, |
|
335
|
|
|
taucos1=0, tausin1=0, |
|
336
|
|
|
taucos2=0, tausin2=0, |
|
337
|
|
|
ltscan=lt_scan, |
|
338
|
|
|
bounds=dict([ |
|
339
|
|
|
("amp", [0, max_amp] if positive else [-max_amp, max_amp]), |
|
340
|
|
|
("lag", [0, max_days]), |
|
341
|
|
|
("tau0", [0, max_days]), |
|
342
|
|
|
("taucos1", [0, max_days] if fit_phase else [-max_days, max_days]), |
|
343
|
|
|
("tausin1", [-np.pi, np.pi] if fit_phase else [-max_days, max_days]), |
|
344
|
|
|
# semi-annual cycles for the life time |
|
345
|
|
|
("taucos2", [0, max_days] if fit_phase else [-max_days, max_days]), |
|
346
|
|
|
("tausin2", [-np.pi, np.pi] if fit_phase else [-max_days, max_days]), |
|
347
|
|
|
("ltscan", [0, 200])]) |
|
348
|
|
|
) |
|
349
|
|
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|