__author__ = "Andrea Tramacere"
from .model_parameters import ModelParameterArray, ModelParameter
from .base_model import Model
from .spectral_shapes import SED
from numpy import log10,power,sqrt,shape,zeros
import numpy as np
from numpy import polyfit,polyval,polyder
__all__=['find_max_cubic','LogCubic','LogLinear','LogLogModel','LogParabolaEp','LogParabolaPL','PolyParameter']
[docs]
class PolyParameter(ModelParameter):
"""
This class is a subclass of the :class:`.ModelParameter` class,
extending the base class to loglog polynomial parameters.
"""
def __init__(self,polymodel,**keywords):
"""Create a new `PolyParameter` instance.
Parameters
----------
polymodel : object
Parameter controlling polymodel.
**keywords : dict
Parameter controlling keywords.
"""
self.polymodel=polymodel
self.allowed_par_types=['curvature','peak freq','peak flux','third-degree','spectral-slope','flux-const','turn-over freq']
super(PolyParameter,self).__init__( **keywords)
if 'val' in keywords.keys():
val=keywords['val']
self.assign_val(self.name,val)
[docs]
def set(self,**keywords):
"""Set.
Parameters
----------
**keywords : dict
Parameter controlling keywords.
"""
super(PolyParameter,self).set(**keywords )
"""
sets a parameter value checking for physical boundaries
"""
if 'val' in keywords.keys():
self.assign_val(self.name,keywords['val'])
[docs]
def assign_val(self,name,val):
"""Assign val.
Parameters
----------
name : object
Name identifier.
val : object
Value to assign.
"""
setattr(self.polymodel,name,val)
[docs]
class LogLogModel(Model):
"""Base class for spectral models defined in log-log frequency space.
Notes
-----
Subclasses implement ``log_func``; this base class converts it to linear
``nuFnu`` values through :meth:`lin_func`.
"""
def __init__(self,nu_size=100, **keywords):
"""Create a new `LogLogModel` instance.
Parameters
----------
nu_size : int, optional
Frequency/energy control value for nu size.
**keywords : dict
Parameter controlling keywords.
"""
super(LogLogModel,self).__init__(**keywords)
self.model_type='LogLogModel'
[docs]
def lin_func(self,nu):
"""Lin func.
Parameters
----------
nu : object
Frequency values in Hz.
Returns
-------
object
Computed result.
"""
nu_log=np.log10(nu)
return np.power(10.0,self.log_func(nu_log))
[docs]
class LogLinear(LogLogModel):
"""
Class to handle log-linear model
"""
def __init__(self,nu_size=100,**keywords):
"""Create a new `LogLinear` instance.
Parameters
----------
nu_size : int, optional
Number of points for frequency grids.
**keywords : dict
Additional keyword arguments.
"""
super(LogLinear,self).__init__( **keywords)
self.name='LogLinear'
self.SED = SED(name=self.model_type)
self.parameters = ModelParameterArray()
self.alpha=-1.0
self.parameters.add_par(PolyParameter(self,name='alpha',par_type='spectral-slope',val=-1.0,val_min=-10.,val_max=10.,units=''))
self.K=-10
self.parameters.add_par(PolyParameter(self,name='K',par_type='flux-const',val=-10.0,val_min=None,val_max=None,units='erg cm^-2 s^-1',log=True))
[docs]
def log_func(self,log_nu):
#x_log=log_nu
#print(x_log)
#print self.Ep,self.Sp,self.b,self.c,x_log
"""Log func.
Parameters
----------
log_nu : object
Frequency/energy control value for log nu.
Returns
-------
object
Computed result.
"""
return self.K + self.alpha*(log_nu)
[docs]
class LogParabolaEp(LogLogModel):
"""
Class to handle log-parabolic model
"""
def __init__(self,nu_size=100, **keywords):
"""Create a new `LogParabolaEp` instance.
Parameters
----------
nu_size : int, optional
Number of points for frequency grids.
**keywords : dict
Additional keyword arguments.
"""
super(LogParabolaEp,self).__init__( **keywords)
self.name='LogParabolaEp'
self.SED = SED(name=self.model_type)
self.parameters = ModelParameterArray()
self.b=-1.0
self.parameters.add_par(PolyParameter(self,name='b',par_type='curvature',val=-1.0,val_min=-10.,val_max=10.,units=''))
self.Ep=14.0
self.parameters.add_par(PolyParameter(self,name='Ep',par_type='peak freq',val=14.0,val_min=0.,val_max=30.,units='Hz',log=True))
self.Sp=-10
self.parameters.add_par(PolyParameter(self,name='Sp',par_type='peak flux',val=-10.0,val_min=-30.,val_max=0.,units='erg cm^-2 s^-1',log=True))
[docs]
def log_func(self,log_nu):
"""Log func.
Parameters
----------
log_nu : object
Frequency/energy control value for log nu.
Returns
-------
object
Computed result.
"""
x_log=log_nu-self.Ep
return self.Sp + self.b*(x_log*x_log)
[docs]
class LogParabolaPL(LogLogModel):
"""
Class to handle a log-par + pl model
"""
def __init__(self,nu_size=100,**keywords):
"""Create a new `LogParabolaPL` instance.
Parameters
----------
nu_size : int, optional
Number of points for frequency grids.
**keywords : dict
Additional keyword arguments.
"""
super(LogParabolaPL,self).__init__( **keywords)
self.name='LogParabolaPL'
self.SED = SED(name=self.model_type)
self.parameters = ModelParameterArray()
self.b=-1.0
self.parameters.add_par(PolyParameter(self,name='b',par_type='curvature',val=-1.0,val_min=-10.,val_max=10.,units=''))
self.E0=14.0
self.parameters.add_par(PolyParameter(self,name='E0',par_type='turn-over freq',val=14.0,val_min=0.,val_max=30.,units='Hz',log=True))
self.alpha=0.5
self.parameters.add_par(PolyParameter(self,name='alpha',par_type='spectral-slope',val=0.5,val_min=-10.,val_max=10.,units=''))
self.K=-10
self.parameters.add_par(PolyParameter(self,name='K',par_type='flux-const',val=-10.0,val_min=-30.,val_max=0.,units='erg cm^-2 s^-1',log=True))
[docs]
def log_func(self,log_nu):
#TODO fix this to numpy array function
"""Log func.
Parameters
----------
log_nu : object
Frequency/energy control value for log nu.
Returns
-------
object
Computed result.
"""
if shape(log_nu)==():
return self.composite_func(log_nu)
else:
y_log=zeros(log_nu.size)
for i in range(log_nu.size):
y_log[i]=self.composite_func(log_nu[i])
return y_log
[docs]
def composite_func(self,log_nu):
"""Composite func.
Parameters
----------
log_nu : object
Frequency/energy control value for log nu.
Returns
-------
object
Computed result.
"""
x_log=log_nu-self.E0
if log_nu >= self.E0:
return self.K + x_log*(self.alpha + self.b*x_log)
else:
return self.K + x_log*self.alpha
[docs]
class LogCubic(LogLogModel):
"""
Class to handle log-cubic model
"""
def __init__(self,nu_size=100, **keywords):
"""Create a new `LogCubic` instance.
Parameters
----------
nu_size : int, optional
Number of points for frequency grids.
**keywords : dict
Additional keyword arguments.
"""
super(LogCubic,self).__init__( **keywords)
self.name='LogCubic'
self.SED = SED(name=self.model_type)
self.parameters = ModelParameterArray()
self.b=-1.0
self.parameters.add_par(PolyParameter(self,name='b',par_type='curvature',val=-1.0,val_min=-10.,val_max=10.,units=''))
self.c=0.0
self.parameters.add_par(PolyParameter(self,name='c',par_type='third-degree',val=-1.0,val_min=-10.,val_max=10.,units=''))
self.Ep=14.0
self.parameters.add_par(PolyParameter(self,name='Ep',par_type='peak freq',val=14.0,val_min=0.,val_max=30.,units='Hz',log=True))
self.Sp=-10
self.parameters.add_par(PolyParameter(self,name='Sp',par_type='peak flux',val=-10.0,val_min=-30.,val_max=0.,units='erg cm^-2 s^-1',log=True))
[docs]
def log_func(self,log_nu):
"""Log func.
Parameters
----------
log_nu : object
Frequency/energy control value for log nu.
Returns
-------
object
Computed result.
"""
x_log=log_nu-self.Ep
#print self.Ep,self.Sp,self.b,self.c,x_log
return self.Sp + self.b*(x_log*x_log)+ self.c*(x_log*x_log*x_log)
[docs]
def find_max_cubic(x_log,y_log,x_range=None):
"""Find max cubic.
Parameters
----------
x_log : object
Parameter controlling x log.
y_log : object
Parameter controlling y log.
x_range : object, optional
Range for x.
Returns
-------
object
Computed result.
"""
if x_range is not None:
msk = x_log >x_range[0]
msk*= x_log <x_range[1]
x_log=x_log[msk]
y_log=y_log[msk]
p=polyfit(x_log,y_log,3)
der=polyder(p,1)
delta=der[1]*der[1] -(4*der[0]*der[2])
if delta>=0:
#print p,der
root1=(-der[1]+sqrt(delta))/(2*der[0])
root2=(-der[1]-sqrt(delta))/(2*der[0])
#print root1,root2
if der[0]>0:
xp=min(root1,root2)
else:
xp=max(root1,root2)
return xp
else:
print("!!! no maxima found for cubic fit")
return None
