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# -*- mode: python; coding: utf-8 -*-
#
# Weitan LI
# Created: 2016-06-26
# Updated: 2016-06-26
#
import numpy as np
import lmfit
class FittingModel:
"""
Base/Meta class for model fitting, with data and parameters scaling.
"""
name = ""
params = lmfit.Parameters()
# optimization method
fit_method = "lbfgsb"
# whether the 'ydata' and 'yerr' to be scaled in order to reduce
# the dynamical range for a more stable fitting
scale = False
scale_factor = 1.0
def __init__(self, fit_method="lbfgsb", params=None, scale=True):
self.fit_method = fit_method
if params is not None:
self.load_params(params)
self.scale = scale
@staticmethod
def model(x, params):
pass
def f(self, x):
return self.model(x, self.params) * self.scale_factor
def load_data(self, xdata, ydata=None, xerr=None, yerr=None,
update_params=False):
if xdata.ndim == 2 and xdata.shape[1] == 4:
# 4-column data
self.xdata = xdata[:, 0].copy()
self.xerr = xdata[:, 1].copy()
self.ydata = xdata[:, 2].copy()
self.yerr = xdata[:, 3].copy()
else:
self.xdata = np.array(xdata)
self.ydata = np.array(ydata)
self.xerr = np.array(xerr)
self.yerr = np.array(yerr)
self.scale_data(update_params=update_params)
def scale_data(self, update_params=False):
"""
Scale the ydata and yerr to reduce their dynamical ranges,
for a more stable model fitting.
"""
if self.scale:
y_min = np.min(self.ydata)
y_max = np.max(self.ydata)
self.scale_factor = np.exp(np.log(y_min*y_max) / 2)
self.ydata /= self.scale_factor
self.yerr /= self.scale_factor
if update_params:
self.scale_params()
def scale_params(self):
"""
Scale the paramters' min/max values accordingly.
"""
pass
def f_residual(self, params):
if self.yerr is None:
return self.model(self.xdata, params) - self.ydata
else:
return (self.model(self.xdata, params) - self.ydata) / self.yerr
def fit(self, method=None):
if method is None:
method = self.fit_method
self.fitter = lmfit.Minimizer(self.f_residual, self.params)
self.fitted = self.fitter.minimize(method=method)
self.load_params(self.fitted.params)
def get_param(self, name=None):
"""
Return the requested 'Parameter' object or the whole
'Parameters' object of no name supplied.
"""
try:
return self.params[name]
except KeyError:
return self.params
def set_param(self, name, *args, **kwargs):
"""
Set the properties of the specified parameter.
"""
param = self.params[name]
param.set(*args, **kwargs)
def dump_params(self, serialize=True):
"""
Dump the current values/settings for all model parameters,
and these dumped results can be later loaded by 'load_params()'.
"""
if serialize:
return self.params.dumps()
else:
return self.params.copy()
def load_params(self, params):
"""
Load the provided parameters values/settings.
"""
if isinstance(params, lmfit.parameter.Parameters):
self.params = params.copy()
else:
p = lmfit.parameter.Parameters()
p.loads(params)
self.params = p
class ABModel(FittingModel):
"""
AB model is a modified beta model, which can roughly fit both
centrally peaked and cored models, e.g., central excess emission.
This model is used here to constrain the deprojected 3D gas density
profile, in order to require it is smooth enough.
References:
[1] Pratt & Arnaud, 2002, A&A, 394, 375; eq.(2)
[2] Croston et al. 2006, A&A, 459, 1007-1019; eq.(10)
"""
name = "AB model"
# model parameters
params = lmfit.Parameters()
params.add_many( # (name, value, vary, min, max, expr)
("A", 1.0e-9, True, 0.0, 1.0e-5, None),
("alpha", 0.7, True, 0.1, 1.1, None),
("rc", 30.0, True, 1.0, 1.0e4, None),
("beta", 0.7, True, 0.3, 1.1, None))
def scale_params(self):
A_min = 1.0
A_max = np.max(self.ydata)
self.set_param("A", value=(A_min+A_max)*0.5,
min=A_min, max=A_max)
@staticmethod
def model(x, params):
parvals = params.valuesdict()
A = parvals["A"]
alpha = parvals["alpha"]
rc = parvals["rc"]
beta = parvals["beta"]
return (A * np.power(x/rc, -alpha) *
np.power((1 + (x/rc)**2), -1.5*beta + 0.5*alpha))
class PLCModel(FittingModel):
"""
PLC model consists of a powerlaw and an constant, that is used
to fit/approximate the outer SBP.
Therefore, the fitted constant is used to subtract the uniform
background from the SBP, and the fitted powerlaw index is used
to extrapolate the SBP in order to mitigate the deprojection
errors due to FoV limit.
NOTE:
I think the uniform background (i.e., by fitting the whole or
core-excluded SBP) should be subtracted from the SBP first, then
adopt this PLCModel to fit the outer part of SBP, with the 'bkg'
parameter fixed at zero.
"""
name = "PLC model"
# model parameters
params = lmfit.Parameters()
params.add_many( # (name, value, vary, min, max, expr)
("A", 1.0e-9, True, 0.0, 1.0e-5, None),
("rmin", 30.0, False, 1.0, 1.0e4, None),
("alpha", 1.6, True, 0.4, 2.8, None),
("bkg", 0.0, False, 0.0, 1.0e-5, None))
def load_data(self, xdata, ydata=None, xerr=None, yerr=None,
update_params=False):
super().load_data(xdata=xdata, ydata=ydata, xerr=xerr, yerr=yerr,
update_params=update_params)
self.set_param("rmin", value=np.min(xdata), vary=False)
def scale_params(self):
ymin = np.min(self.ydata)
ymax = np.max(self.ydata)
self.set_param("A", value=ymax, min=ymax/10.0, max=ymax*10.0)
self.set_param("bkg", value=ymin, min=0.0, max=ymin)
@staticmethod
def model(x, params):
parvals = params.valuesdict()
A = parvals["A"]
rmin = parvals["rmin"]
alpha = parvals["alpha"]
bkg = parvals["bkg"]
return A * np.power(x/rmin, -alpha) + bkg
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