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samba_models.py
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samba_models.py
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###########################################################
# Models from the SAndbox for Mixing using Bayesian
# Analysis (SAMBA) package
# Author : Alexandra Semposki
# Original models : M. Honda, JHEP 12, 019 (2014).
# ##########################################################
# imports
import numpy as np
from scipy import special, integrate
import math as math
import sys
sys.path.append('../../Taweret')
from Taweret.core.base_model import BaseModel
from Taweret.utils.utils import normal_log_likelihood_elementwise as log_likelihood_elementwise_utils
__all__ = ['Loworder', 'Highorder', 'TrueModel', 'Data']
class Loworder(BaseModel):
def __init__(self, order, error_model='informative'):
"""
The SAMBA loworder series expansion function.
This model has been previously calibrated.
Parameters
----------
order : int
Truncation order of expansion
error_model : str
Error calculation method. Either 'informative' or
'uninformative'
Raises
------
TypeError
If the order is not an integer
"""
if isinstance(order, int):
self.order = order
else:
raise TypeError(f"order has to be an integer number: {order}")
self.error_model = error_model
self.prior = None
def evaluate(self, input_values : np.array) -> np.array:
"""
Evaluate the mean and standard deviation for
given input values to the function
Parameters
----------
input_values : numpy 1darray
coupling strength (g) values
Returns:
--------
mean : numpy 1darray
The mean of the model
np.sqrt(var) : numpy 1darray
The truncation error of the model
"""
self.x = input_values
# model function
output = []
low_c = np.empty([int(self.order)+1])
low_terms = np.empty([int(self.order) + 1])
#if g is an array, execute here
try:
value = np.empty([len(self.x)])
#loop over array in g
for i in range(len(self.x)):
#loop over orders
for k in range(int(self.order)+1):
if k % 2 == 0:
low_c[k] = np.sqrt(2.0) * special.gamma(k + 0.5) * (-4.0)**(k//2) / (math.factorial(k//2))
else:
low_c[k] = 0
low_terms[k] = low_c[k] * self.x[i]**(k)
value[i] = np.sum(low_terms)
output.append(value)
data = np.array(output, dtype = np.float64)
#if g is a single value, execute here
except:
value = 0.0
for k in range(int(self.order)+1):
if k % 2 == 0:
low_c[k] = np.sqrt(2.0) * special.gamma(k + 0.5) * (-4.0)**(k//2) / (math.factorial(k//2))
else:
low_c[k] = 0
low_terms[k] = low_c[k] * self.x**(k)
value = np.sum(low_terms)
data = value
# rename for clarity
mean = data
# uncertainties function
# even order
if self.order % 2 == 0:
#find coefficients
c = np.empty([int(self.order + 2)])
#model 1 for even orders
if self.error_model == 'uninformative':
for k in range(int(self.order + 2)):
if k % 2 == 0:
c[k] = np.sqrt(2.0) * special.gamma(k + 0.5) * (-4.0)**(k//2) / (math.factorial(k) * math.factorial(k//2))
else:
c[k] = 0.0
#rms value
cbar = np.sqrt(np.sum((np.asarray(c))**2.0) / (self.order//2 + 1))
#variance
var1 = (cbar)**2.0 * (math.factorial(self.order + 2))**2.0 * self.x**(2.0*(self.order + 2))
#model 2 for even orders
elif self.error_model == 'informative':
for k in range(int(self.order + 2)):
if k % 2 == 0:
#skip first coefficient
if k == 0:
c[k] = 0.0
else:
c[k] = np.sqrt(2.0) * special.gamma(k + 0.5) * (-4.0)**(k//2) / (math.factorial(k//2) \
* math.factorial(k//2 - 1) * 4.0**(k))
else:
c[k] = 0.0
#rms value
cbar = np.sqrt(np.sum((np.asarray(c))**2.0) / (self.order//2 + 1))
#variance
var1 = (cbar)**2.0 * (math.factorial(self.order//2))**2.0 * (4.0 * self.x)**(2.0*(self.order + 2))
#odd order
else:
#find coefficients
c = np.empty([int(self.order + 1)])
#model 1 for odd orders
if self.error_model == 'uninformative':
for k in range(int(self.order + 1)):
if k % 2 == 0:
c[k] = np.sqrt(2.0) * special.gamma(k + 0.5) * (-4.0)**(k//2) / (math.factorial(k) * math.factorial(k//2))
else:
c[k] = 0.0
#rms value
cbar = np.sqrt(np.sum((np.asarray(c))**2.0) / (self.order//2 + 1))
#variance
var1 = (cbar)**2.0 * (math.factorial(self.order + 1))**2.0 * self.x**(2.0*(self.order + 1))
#model 2 for odd orders
elif self.error_model == 'informative':
for k in range(int(self.order + 1)):
if k % 2 == 0:
#skip first coefficient
if k == 0:
c[k] = 0.0
else:
c[k] = np.sqrt(2.0) * special.gamma(k + 0.5) * (-4.0)**(k//2) / (math.factorial(k//2) \
* math.factorial(k//2 - 1) * 4.0**(k))
else:
c[k] = 0.0
#rms value
cbar = np.sqrt(np.sum((np.asarray(c))**2.0) / (self.order//2 + 1))
#variance
var1 = (cbar)**2.0 * (math.factorial((self.order-1)//2))**2.0 * (4.0 * self.x)**(2.0*(self.order + 1))
# rename for clarity
var = var1
return mean, np.sqrt(var)
def log_likelihood_elementwise(self):
'''
Obtain the log likelihood for this model.
Not needed for this model.
'''
return None
def set_prior(self):
'''
Set the prior on model parameters.
Not needed for this model.
'''
return None
class Highorder(BaseModel):
def __init__(self, order, error_model='informative'):
"""
The SAMBA highorder series expansion function.
Parameters
----------
order : int
Truncation order of expansion
error_model : str
Error calculation method. Either 'informative' or 'uninformative'
Raises
------
TypeError
If the order is not an integer
"""
if isinstance(order, int):
self.order = order
else:
raise TypeError(f"order has to be an integer number: {order}")
self.error_model = error_model
self.prior = None
def evaluate(self, input_values : np.array) -> np.array:
"""
Evaluate the mean and standard deviation for given
input values
Parameters
----------
input_values : numpy 1darray
coupling strength (g) values
Returns:
--------
mean : numpy 1darray
The mean of the model
np.sqrt(var) : numpy 1darray
The truncation error of the model
"""
order = self.order
self.x = input_values
# mean function
output = []
high_c = np.empty([int(order) + 1])
high_terms = np.empty([int(order) + 1])
#if g is an array, execute here
try:
value = np.empty([len(self.x)])
#loop over array in g
for i in range(len(self.x)):
#loop over orders
for k in range(int(order)+1):
high_c[k] = special.gamma(k/2.0 + 0.25) * (-0.5)**k / (2.0 * math.factorial(k))
high_terms[k] = (high_c[k] * self.x[i]**(-k)) / np.sqrt(self.x[i])
#sum the terms for each value of g
value[i] = np.sum(high_terms)
output.append(value)
data = np.array(output, dtype = np.float64)
#if g is a single value, execute here
except:
value = 0.0
#loop over orders
for k in range(int(order)+1):
high_c[k] = special.gamma(k/2.0 + 0.25) * (-0.5)**k / (2.0 * math.factorial(k))
high_terms[k] = (high_c[k] * self.x**(-k)) / np.sqrt(self.x)
#sum the terms for each value of g
value = np.sum(high_terms)
data = value
# rename for clarity
mean = data
# uncertainties function
#find coefficients
d = np.zeros([int(self.order) + 1])
#model 1
if self.error_model == 'uninformative':
for k in range(int(self.order) + 1):
d[k] = special.gamma(k/2.0 + 0.25) * (-0.5)**k * (math.factorial(k)) / (2.0 * math.factorial(k))
#rms value (ignore first two coefficients in this model)
dbar = np.sqrt(np.sum((np.asarray(d)[2:])**2.0) / (self.order-1))
#variance
var2 = (dbar)**2.0 * (self.x)**(-1.0) * (math.factorial(self.order + 1))**(-2.0) \
* self.x**(-2.0*self.order - 2)
#model 2
elif self.error_model == 'informative':
for k in range(int(self.order) + 1):
d[k] = special.gamma(k/2.0 + 0.25) * special.gamma(k/2.0 + 1.0) * 4.0**(k) \
* (-0.5)**k / (2.0 * math.factorial(k))
#rms value
dbar = np.sqrt(np.sum((np.asarray(d))**2.0) / (self.order + 1))
#variance
var2 = (dbar)**2.0 * self.x**(-1.0) * (special.gamma((self.order + 3)/2.0))**(-2.0) \
* (4.0 * self.x)**(-2.0*self.order - 2.0)
# rename for clarity
var = var2
return mean, np.sqrt(var)
def log_likelihood_elementwise(self):
'''
Obtain the log likelihood for the model.
Not needed for this model.
'''
return None
def set_prior(self):
'''
Set the prior on the model parameters.
Not needed for this model.
'''
return None
class TrueModel(BaseModel):
def evaluate(self, input_values : np.array) -> np.array:
"""
Evaluate the mean of the true model for given input values.
Parameters:
----------
input_values : numpy 1darray
coupling strength (g) values
Returns:
--------
mean : numpy 1darray
The true model evaluated at each point of the
given input space
np.sqrt(var) : numpy 1darray
The standard deviation of the true model. This
will obviously be an array of zeros.
"""
self.x = input_values
# true model
def function(x,g):
return np.exp(-(x**2.0)/2.0 - (g**2.0 * x**4.0))
#initialization
self.model = np.zeros([len(self.x)])
#perform the integral for each g
for i in range(len(self.x)):
self.model[i], self.err = integrate.quad(function, -np.inf, np.inf, args=(self.x[i],))
mean = self.model
var = np.zeros(shape=mean.shape)
return mean, np.sqrt(var)
def log_likelihood_elementwise(self):
'''
Obtain the log likelihood for the model.
Not needed for this model.
'''
return None
def set_prior(self):
'''
Set the prior on any model parameters.
Not needed for this model.
'''
return None
class Data(BaseModel): # --> check that this model is set up correctly
def evaluate(self, input_values : np.array, error = 0.01) -> np.array:
"""
Evaluate the data and error for given input values
Parameters:
----------
input_values : numpy 1darray
coupling strength (g) values for data generation
error : float
defines the relative error as a fraction between (0,1)
Returns:
--------
data : numpy 1darray
The array of data points
sigma : numpy 1darray
The errors on each data point
"""
# call class for true model
truemodel = TrueModel()
# data generation input values
x_data = input_values
# adding data using the add_data function from SAMBA
if error is None:
raise ValueError('Please enter a error in decimal form for the data set generation.')
elif error < 0.0 or error > 1.0:
raise ValueError('Error must be between 0.0 and 1.0.')
#generate fake data
data = truemodel.evaluate(x_data)
rand = np.random.RandomState()
var = error*rand.randn(len(x_data))
data = data*(1 + var)
#calculate standard deviation
sigma = error*data
return data, sigma
def log_likelihood_elementwise(self):
'''
Obtain the log likelihood for the model.
Not needed for this model.
'''
return None
def set_prior(self):
'''
Set the prior on any model parameters.
Not needed for this model.
'''
return None