def get_confidence_bounds(self, confidence_level=0.68, cache=False ):
"""
Computes the marginal 1D confidence bounds on the Fisher parameters
:param confidence_level: (optional) C.L. of the bounds. Default 68%.
:type confidence_level: :class:`float` in [0,1]
:param cache: (optional) wether to use cached results or compute everything again
:type cache: bool
"""
# check input:
if confidence_level<0.0 or confidence_level>1.0:
raise ValueError('Invalid confidence level. Legal input is between 0 and 1.')
# invert the Fisher matrix:
if cache:
fisher_matrix_inv_temp = self.fisher_matrix_inv
else:
fisher_matrix_inv_temp = self.inverse_fisher_matrix()
# compute the coefficient that correspond to the desired confidence level:
coefficient = fu.confidence_coefficient( confidence_level )
# compute the result:
return coefficient*np.sqrt( np.diagonal( fisher_matrix_inv_temp ) )
def get_confidence_bounds(self, confidence_level=0.68, cache=False ):
"""
Computes the marginal 1D confidence bounds on the Fisher parameters
:param confidence_level: (optional) C.L. of the bounds. Default 68%.
:type confidence_level: :class:`float` in [0,1]
:param cache: (optional) wether to use cached results or compute everything again
:type cache: bool
"""
# check input:
if confidence_level<0.0 or confidence_level>1.0:
raise ValueError('Invalid confidence level. Legal input is between 0 and 1.')
# invert the Fisher matrix:
if cache:
fisher_matrix_inv_temp = self.fisher_matrix_inv
else:
fisher_matrix_inv_temp = self.inverse_fisher_matrix()
# compute the coefficient that correspond to the desired confidence level:
coefficient = fu.confidence_coefficient( confidence_level )
# compute the result:
return coefficient*np.sqrt( np.diagonal( fisher_matrix_inv_temp ) )
def compute_ellipse(self, params1=None, params2=None, confidence_level=0.68, names=None, num_points=100):
"""
Function that computes the (2D) ellipses for a given parameters combination.
Returns a dictionary with all the meaningul information about the ellipses.
:param params1: name of the first parameter or list of names of parameters.
:type params1: a :class:`string` or a :class:`list` of :class:`string`
:param params2: name of the second parameter or list of names of parameters.
:type params3: a :class:`string` or a :class:`list` of :class:`string`
:param confidence_level: (optional) Confidence Level of the bounds. Default 68%.
:type confidence_level: :class:`float`
:param names: names of the Fisher matrices.
:type names: a :class:`string` or a :class:`list` of :class:`string`
:param num_points: number of (x,y) points.
:type num_points: :class:`int`
:returns: a dictionary mapping name and parameters to a tuple of: [x, y, [fiducial_x, fiducial_y, coeff_a, coeff_b, theta_0]]
:rtype: :class:`dict`
"""
# process names:
if names==None:
names_temp = self.fisher_name_list
else:
names_temp = [ i for i in fu.make_list(names) if i in self.fisher_name_list ]
# process parameters:
total_paramnames_list = self.get_parameter_list(names_temp)
if params1==None:
params_temp_1 = total_paramnames_list
else:
params_temp_1 = [ i for i in fu.make_list(params1) if i in total_paramnames_list ]
if params2==None:
params_temp_2 = total_paramnames_list
else:
params_temp_2 = [ i for i in fu.make_list(params2) if i in total_paramnames_list ]
# get the fishers:
fisher_temp_list = self.get_fisher_matrix(names_temp)
# compute the confidence coefficient:
confidence_coefficient = fu.confidence_coefficient( confidence_level )
# get the distributions:
gaussian_distro = {}
for par1 in params_temp_1:
dict_names_1 = {}
for par2 in params_temp_2:
dict_names_2 = {}
for mat,name in zip(fisher_temp_list,names_temp):
# get the index of the parameter:
try:
index_1 = mat.get_param_index(par1)
index_2 = mat.get_param_index(par2)
except:
dict_names_2[name] = [np.array([0.0]), np.array([0.0]), [0.0, 0.0, 0.0, 0.0, 0.0]]
continue
# get sigmas:
sigma_x = mat.get_fisher_inverse()[index_1,index_1]
sigma_y = mat.get_fisher_inverse()[index_2,index_2]
sigma_xy = mat.get_fisher_inverse()[index_1,index_2]
# get fiducial:
fiducial_x = mat.get_fiducial(par1)
fiducial_y = mat.get_fiducial(par2)
# compute the ellipse coefficients:
coeff_a = confidence_coefficient*math.sqrt((sigma_x + sigma_y)/2.0 + math.sqrt( (sigma_x - sigma_y)**2/4.0 + sigma_xy**2 ))
coeff_b = confidence_coefficient*math.sqrt((sigma_x + sigma_y)/2.0 - math.sqrt( (sigma_x - sigma_y)**2/4.0 + sigma_xy**2 ))
theta_0 = math.atan2( (2.0*sigma_xy), (sigma_x - sigma_y) )/2.0
# generate the ellipses
angles = np.linspace( 0, 2.0*math.pi, num_points )
x_points = np.array( [+coeff_a*math.cos(theta)*math.cos(theta_0)
-coeff_b*math.sin(theta)*math.sin(theta_0) + fiducial_x for theta in angles ] )
y_points = np.array( [+coeff_a*math.cos(theta)*math.sin(theta_0)
+coeff_b*math.sin(theta)*math.cos(theta_0) + fiducial_y for theta in angles ] )
# save the result:
dict_names_2[name] = [x_points, y_points, [fiducial_x, fiducial_y, coeff_a, coeff_b, theta_0]]
dict_names_1[par2] = dict_names_2
gaussian_distro[par1] = dict_names_1
return gaussian_distro
# -----------------------------------------------------------------------------------
# ***************************************************************************************
def compute_gaussian( self, params=None, confidence_level=0.68, names=None, num_points=100, normalized=False, nice_bounds=True ):
"""
Function that computes the (1D) gaussian distribution of a given parameter.
Returns a dictionary with all the meaningul information about the gaussian.
:param params: name of the parameter or list of names of parameters.
:type params: a :class:`string` or a :class:`list` of :class:`string`
:param confidence_level: (optional) Confidence Level of the bounds. Default 68%.
:type confidence_level: :class:`float`
:param names: names of the Fisher matrices.
:type names: a :class:`string` or a :class:`list` of :class:`string`
:param num_points: number of (x,y) points.
:type num_points: :class:`int`
:param normalized: wether the distribution is normalized or not.
:type normalized: :class:`bool`
:param nice_bounds: wether the x range is properly rounded to be nice or not.
:type nice_bounds: :class:`bool`
:returns: a dictionary mapping name and parameter to a tuple of: [x, y, [fiducial,sigma]]
:rtype: :class:`dict`
"""
# process names:
if names==None:
names_temp = self.fisher_name_list
else:
names_temp = [ i for i in fu.make_list(names) if i in self.fisher_name_list ]
# process parameters:
total_paramnames_list = self.get_parameter_list(names_temp)
if params==None:
params_temp = total_paramnames_list
else:
params_temp = [ i for i in fu.make_list(params) if i in total_paramnames_list ]
# get the fishers:
fisher_temp_list = self.get_fisher_matrix(names_temp)
# compute the confidence coefficient:
confidence_coefficient = fu.confidence_coefficient( confidence_level )
# get the plot ranges:
plot_ranges = self.compute_plot_range( params=params_temp, confidence_level=confidence_level, names=names_temp, nice=nice_bounds )
# get the distributions:
gaussian_distro = {}
for par1 in params_temp:
dict_names = {}
for mat,name in zip(fisher_temp_list,names_temp):
# get the index of the parameter:
try:
index = mat.get_param_index(par1)
except:
dict_names[name] = [np.array([0.0]), np.array([0.0]), [0.0,0.0]]
continue
# get sigma and fiducial:
sigma = math.sqrt( mat.get_fisher_inverse()[index,index] )
fiducial = mat.get_fiducial(par1)
# get optimal x:
if nice_bounds:
lower_bound = plot_ranges[par1][0]
upper_bound = plot_ranges[par1][1]
else:
lower_bound = fiducial -confidence_coefficient*sigma
upper_bound = fiducial +confidence_coefficient*sigma
x_points = np.linspace( lower_bound, upper_bound, num_points )
# get y:
if normalized:
y_points = np.array([ np.exp( -( x-fiducial )**2/(2.0*sigma**2) )/( sigma*np.sqrt(2.0*math.pi) ) for x in x_points ])
else:
y_points = np.array([ np.exp( -( x-fiducial )**2/(2.0*sigma**2) ) for x in x_points ])
dict_names[name] = [x_points, y_points, [fiducial,sigma]]
gaussian_distro[par1] = dict_names
return gaussian_distro
def compute_plot_range(self, params=None, confidence_level=0.68, names=None, nice=True ):
"""
Function that computes a meaningfull plot range for the plots involving the specified parameters
and the specified Fisher names.
:param params: name of the parameter or list of names of parameters.
:type params: a :class:`string` or a :class:`list` of :class:`string`
:param confidence_level: (optional) Confidence Level of the bounds. Default 68%.
:type confidence_level: :class:`float`
:param names: names of the Fisher matrices.
:type names: a :class:`string` or a :class:`list` of :class:`string`
:param nice: wether the number is properly rounded to be nice.
:type nice: :class:`bool`
:returns: a dictionary of name and bounds
:rtype: :class:`dict`
"""
# process names:
if names==None:
names_temp = self.fisher_name_list
else:
names_temp = [ i for i in fu.make_list(names) if i in self.fisher_name_list ]
# process parameters:
total_paramnames_list = self.get_parameter_list(names_temp)
if params==None:
params_temp = total_paramnames_list
else:
params_temp = [ i for i in fu.make_list(params) if i in total_paramnames_list ]
# get the fishers:
fisher_temp_list = self.get_fisher_matrix(names_temp)
# compute the confidence coefficient:
confidence_coefficient = fu.confidence_coefficient( confidence_level )
# get the ranges:
range = []
for i in params_temp:
lower_bound = []
upper_bound = []
for j in fisher_temp_list:
# get the index of the parameter:
try:
index = j.get_param_index(i)
except:
continue
# get sigma and fiducial:
sigma = j.get_fisher_inverse()[index,index]
sigma = math.sqrt( sigma )
fiducial = j.get_fiducial(i)
# apply a coefficient to safeguard:
if not nice:
sigma = confidence_coefficient*sigma
# store the values:
if nice:
lower_bound.append(fu.significant_digits( (fiducial-confidence_coefficient*sigma, sigma), mode=2 ) )
upper_bound.append(fu.significant_digits( (fiducial+confidence_coefficient*sigma, sigma), mode=0 ) )
else:
lower_bound.append(fiducial-sigma)
upper_bound.append(fiducial+sigma)
# decide what to use:
upper_bound = np.array(upper_bound)
lower_bound = np.array(lower_bound)
range.append([ float(str(np.amin(lower_bound))), float(str(np.amax(upper_bound))) ])
dict = {}
for i,j in zip(params_temp,xrange(len(params_temp))):
dict[i] = range[j]
return dict
def compute_ellipse(self,
params1=None,
params2=None,
confidence_level=0.68,
names=None,
num_points=100):
"""
Function that computes the (2D) ellipses for a given parameters combination.
Returns a dictionary with all the meaningul information about the ellipses.
:param params1: name of the first parameter or list of names of parameters.
:type params1: a :class:`string` or a :class:`list` of :class:`string`
:param params2: name of the second parameter or list of names of parameters.
:type params3: a :class:`string` or a :class:`list` of :class:`string`
:param confidence_level: (optional) Confidence Level of the bounds. Default 68%.
:type confidence_level: :class:`float`
:param names: names of the Fisher matrices.
:type names: a :class:`string` or a :class:`list` of :class:`string`
:param num_points: number of (x,y) points.
:type num_points: :class:`int`
:returns: a dictionary mapping name and parameters to a tuple of: [x, y, [fiducial_x, fiducial_y, coeff_a, coeff_b, theta_0]]
:rtype: :class:`dict`
"""
# process names:
if names == None:
names_temp = self.fisher_name_list
else:
names_temp = [
i for i in fu.make_list(names) if i in self.fisher_name_list
]
# process parameters:
total_paramnames_list = self.get_parameter_list(names_temp)
if params1 == None:
params_temp_1 = total_paramnames_list
else:
params_temp_1 = [
i for i in fu.make_list(params1) if i in total_paramnames_list
]
if params2 == None:
params_temp_2 = total_paramnames_list
else:
params_temp_2 = [
i for i in fu.make_list(params2) if i in total_paramnames_list
]
# get the fishers:
fisher_temp_list = self.get_fisher_matrix(names_temp)
# compute the confidence coefficient:
confidence_coefficient = fu.confidence_coefficient(confidence_level)
# get the distributions:
gaussian_distro = {}
for par1 in params_temp_1:
dict_names_1 = {}
for par2 in params_temp_2:
dict_names_2 = {}
for mat, name in zip(fisher_temp_list, names_temp):
# get the index of the parameter:
try:
index_1 = mat.get_param_index(par1)
index_2 = mat.get_param_index(par2)
except:
dict_names_2[name] = [
np.array([0.0]),
np.array([0.0]), [0.0, 0.0, 0.0, 0.0, 0.0]
]
continue
# get sigmas:
sigma_x = mat.get_fisher_inverse()[index_1, index_1]
sigma_y = mat.get_fisher_inverse()[index_2, index_2]
sigma_xy = mat.get_fisher_inverse()[index_1, index_2]
# get fiducial:
fiducial_x = mat.get_fiducial(par1)
fiducial_y = mat.get_fiducial(par2)
# compute the ellipse coefficients:
coeff_a = confidence_coefficient * math.sqrt(
(sigma_x + sigma_y) / 2.0 +
math.sqrt((sigma_x - sigma_y)**2 / 4.0 + sigma_xy**2))
coeff_b = confidence_coefficient * math.sqrt(
(sigma_x + sigma_y) / 2.0 -
math.sqrt((sigma_x - sigma_y)**2 / 4.0 + sigma_xy**2))
theta_0 = math.atan2((2.0 * sigma_xy),
(sigma_x - sigma_y)) / 2.0
# generate the ellipses
angles = np.linspace(0, 2.0 * math.pi, num_points)
x_points = np.array([
+coeff_a * math.cos(theta) * math.cos(theta_0) -
coeff_b * math.sin(theta) * math.sin(theta_0) +
fiducial_x for theta in angles
])
y_points = np.array([
+coeff_a * math.cos(theta) * math.sin(theta_0) +
coeff_b * math.sin(theta) * math.cos(theta_0) +
fiducial_y for theta in angles
])
# save the result:
dict_names_2[name] = [
x_points, y_points,
[fiducial_x, fiducial_y, coeff_a, coeff_b, theta_0]
]
dict_names_1[par2] = dict_names_2
gaussian_distro[par1] = dict_names_1
return gaussian_distro
# -----------------------------------------------------------------------------------
# ***************************************************************************************
def compute_gaussian(self,
params=None,
confidence_level=0.68,
names=None,
num_points=100,
normalized=False,
nice_bounds=True):
"""
Function that computes the (1D) gaussian distribution of a given parameter.
Returns a dictionary with all the meaningul information about the gaussian.
:param params: name of the parameter or list of names of parameters.
:type params: a :class:`string` or a :class:`list` of :class:`string`
:param confidence_level: (optional) Confidence Level of the bounds. Default 68%.
:type confidence_level: :class:`float`
:param names: names of the Fisher matrices.
:type names: a :class:`string` or a :class:`list` of :class:`string`
:param num_points: number of (x,y) points.
:type num_points: :class:`int`
:param normalized: wether the distribution is normalized or not.
:type normalized: :class:`bool`
:param nice_bounds: wether the x range is properly rounded to be nice or not.
:type nice_bounds: :class:`bool`
:returns: a dictionary mapping name and parameter to a tuple of: [x, y, [fiducial,sigma]]
:rtype: :class:`dict`
"""
# process names:
if names == None:
names_temp = self.fisher_name_list
else:
names_temp = [
i for i in fu.make_list(names) if i in self.fisher_name_list
]
# process parameters:
total_paramnames_list = self.get_parameter_list(names_temp)
if params == None:
params_temp = total_paramnames_list
else:
params_temp = [
i for i in fu.make_list(params) if i in total_paramnames_list
]
# get the fishers:
fisher_temp_list = self.get_fisher_matrix(names_temp)
# compute the confidence coefficient:
confidence_coefficient = fu.confidence_coefficient(confidence_level)
# get the plot ranges:
plot_ranges = self.compute_plot_range(
params=params_temp,
confidence_level=confidence_level,
names=names_temp,
nice=nice_bounds)
# get the distributions:
gaussian_distro = {}
for par1 in params_temp:
dict_names = {}
for mat, name in zip(fisher_temp_list, names_temp):
# get the index of the parameter:
try:
index = mat.get_param_index(par1)
except:
dict_names[name] = [
np.array([0.0]),
np.array([0.0]), [0.0, 0.0]
]
continue
# get sigma and fiducial:
sigma = math.sqrt(mat.get_fisher_inverse()[index, index])
fiducial = mat.get_fiducial(par1)
# get optimal x:
if nice_bounds:
lower_bound = plot_ranges[par1][0]
upper_bound = plot_ranges[par1][1]
else:
lower_bound = fiducial - confidence_coefficient * sigma
upper_bound = fiducial + confidence_coefficient * sigma
x_points = np.linspace(lower_bound, upper_bound, num_points)
# get y:
if normalized:
y_points = np.array([
np.exp(-(x - fiducial)**2 / (2.0 * sigma**2)) /
(sigma * np.sqrt(2.0 * math.pi)) for x in x_points
])
else:
y_points = np.array([
np.exp(-(x - fiducial)**2 / (2.0 * sigma**2))
for x in x_points
])
dict_names[name] = [x_points, y_points, [fiducial, sigma]]
gaussian_distro[par1] = dict_names
return gaussian_distro
def compute_plot_range(self,
params=None,
confidence_level=0.68,
names=None,
nice=True):
"""
Function that computes a meaningfull plot range for the plots involving the specified parameters
and the specified Fisher names.
:param params: name of the parameter or list of names of parameters.
:type params: a :class:`string` or a :class:`list` of :class:`string`
:param confidence_level: (optional) Confidence Level of the bounds. Default 68%.
:type confidence_level: :class:`float`
:param names: names of the Fisher matrices.
:type names: a :class:`string` or a :class:`list` of :class:`string`
:param nice: wether the number is properly rounded to be nice.
:type nice: :class:`bool`
:returns: a dictionary of name and bounds
:rtype: :class:`dict`
"""
# process names:
if names == None:
names_temp = self.fisher_name_list
else:
names_temp = [
i for i in fu.make_list(names) if i in self.fisher_name_list
]
# process parameters:
total_paramnames_list = self.get_parameter_list(names_temp)
if params == None:
params_temp = total_paramnames_list
else:
params_temp = [
i for i in fu.make_list(params) if i in total_paramnames_list
]
# get the fishers:
fisher_temp_list = self.get_fisher_matrix(names_temp)
# compute the confidence coefficient:
confidence_coefficient = fu.confidence_coefficient(confidence_level)
# get the ranges:
range = []
for i in params_temp:
lower_bound = []
upper_bound = []
for j in fisher_temp_list:
# get the index of the parameter:
try:
index = j.get_param_index(i)
except:
continue
# get sigma and fiducial:
sigma = j.get_fisher_inverse()[index, index]
sigma = math.sqrt(sigma)
fiducial = j.get_fiducial(i)
# apply a coefficient to safeguard:
if not nice:
sigma = confidence_coefficient * sigma
# store the values:
if nice:
lower_bound.append(
fu.significant_digits(
(fiducial - confidence_coefficient * sigma, sigma),
mode=2))
upper_bound.append(
fu.significant_digits(
(fiducial + confidence_coefficient * sigma, sigma),
mode=0))
else:
lower_bound.append(fiducial - sigma)
upper_bound.append(fiducial + sigma)
# decide what to use:
upper_bound = np.array(upper_bound)
lower_bound = np.array(lower_bound)
range.append([
float(str(np.amin(lower_bound))),
float(str(np.amax(upper_bound)))
])
dict = {}
for i, j in zip(params_temp, xrange(len(params_temp))):
dict[i] = range[j]
return dict