# Copyright (c) 2012-2015 The GPy authors (see AUTHORS.txt)

import numpy as np
import scipy
from ..util.univariate_Gaussian import std_norm_cdf, std_norm_pdf
import scipy as sp
from ..util.misc import safe_exp, safe_square, safe_cube, safe_quad, safe_three_times

[docs]class GPTransformation(object):
"""
Link function class for doing non-Gaussian likelihoods approximation

:param Y: observed output (Nx1 numpy.darray)

.. note:: Y values allowed depend on the likelihood_function used

"""
def __init__(self):
pass

[docs]    def transf(self,f):
"""
Gaussian process tranformation function, latent space -> output space
"""
raise NotImplementedError

[docs]    def dtransf_df(self,f):
"""
derivative of transf(f) w.r.t. f
"""
raise NotImplementedError

[docs]    def d2transf_df2(self,f):
"""
second derivative of transf(f) w.r.t. f
"""
raise NotImplementedError

[docs]    def d3transf_df3(self,f):
"""
third derivative of transf(f) w.r.t. f
"""
raise NotImplementedError

[docs]    def to_dict(self):
raise NotImplementedError

def _save_to_input_dict(self):
return {}

[docs]    @staticmethod
def from_dict(input_dict):
"""
Instantiate an object of a derived class using the information
in input_dict (built by the to_dict method of the derived class).
More specifically, after reading the derived class from input_dict,
it calls the method _build_from_input_dict of the derived class.
Note: This method should not be overrided in the derived class. In case
it is needed, please override _build_from_input_dict instate.

:param dict input_dict: Dictionary with all the information needed to
instantiate the object.
"""

import copy
input_dict = copy.deepcopy(input_dict)
import GPy

@staticmethod

[docs]class Identity(GPTransformation):
"""
.. math::

g(f) = f

"""
[docs]    def transf(self,f):
return f

[docs]    def dtransf_df(self,f):
return np.ones_like(f)

[docs]    def d2transf_df2(self,f):
return np.zeros_like(f)

[docs]    def d3transf_df3(self,f):
return np.zeros_like(f)

[docs]    def to_dict(self):
"""
Convert the object into a json serializable dictionary.

Note: It uses the private method _save_to_input_dict of the parent.

:return dict: json serializable dictionary containing the needed information to instantiate the object
"""

input_dict = super(Identity, self)._save_to_input_dict()
return input_dict

[docs]class Probit(GPTransformation):
"""
.. math::

g(f) = \\Phi^{-1} (mu)

"""
[docs]    def transf(self,f):
return std_norm_cdf(f)

[docs]    def dtransf_df(self,f):
return std_norm_pdf(f)

[docs]    def d2transf_df2(self,f):
return -f * std_norm_pdf(f)

[docs]    def d3transf_df3(self,f):
return (safe_square(f)-1.)*std_norm_pdf(f)

[docs]    def to_dict(self):
"""
Convert the object into a json serializable dictionary.

Note: It uses the private method _save_to_input_dict of the parent.

:return dict: json serializable dictionary containing the needed information to instantiate the object
"""

input_dict = super(Probit, self)._save_to_input_dict()
return input_dict

[docs]class ScaledProbit(Probit):
"""
.. math::
g(f) = \\Phi^{-1} (nu*mu)
"""
def __init__(self, nu=1.):
self.nu = float(nu)

[docs]    def transf(self,f):
return std_norm_cdf(f*self.nu)

[docs]    def dtransf_df(self,f):
return std_norm_pdf(f*self.nu)*self.nu

[docs]    def d2transf_df2(self,f):
return -(f*self.nu) * std_norm_pdf(f*self.nu)*(self.nu**2)

[docs]    def d3transf_df3(self,f):
return (safe_square(f*self.nu)-1.)*std_norm_pdf(f*self.nu)*(self.nu**3)

[docs]    def to_dict(self):
"""
Convert the object into a json serializable dictionary.

Note: It uses the private method _save_to_input_dict of the parent.

:return dict: json serializable dictionary containing the needed information to instantiate the object
"""

input_dict = super(ScaledProbit, self)._save_to_input_dict()
return input_dict

[docs]class Cloglog(GPTransformation):
"""
.. math::

p(f) = 1 - e^{-e^f}

or

f = \log (-\log(1-p))

"""
[docs]    def transf(self,f):
ef = safe_exp(f)
return 1-np.exp(-ef)

[docs]    def dtransf_df(self,f):
ef = safe_exp(f)
return np.exp(f-ef)

[docs]    def d2transf_df2(self,f):
ef = safe_exp(f)
return -np.exp(f-ef)*(ef-1.)

[docs]    def d3transf_df3(self,f):
ef = safe_exp(f)
ef2 = safe_square(ef)
three_times_ef = safe_three_times(ef)
r_val = np.exp(f-ef)*(1.-three_times_ef + ef2)
return r_val

[docs]class Log(GPTransformation):
"""
.. math::

g(f) = \\log(\\mu)

"""
[docs]    def transf(self,f):
return safe_exp(f)

[docs]    def dtransf_df(self,f):
return safe_exp(f)

[docs]    def d2transf_df2(self,f):
return safe_exp(f)

[docs]    def d3transf_df3(self,f):
return safe_exp(f)

[docs]class Log_ex_1(GPTransformation):
"""
.. math::

g(f) = \\log(\\exp(\\mu) - 1)

"""
[docs]    def transf(self,f):
return scipy.special.log1p(safe_exp(f))

[docs]    def dtransf_df(self,f):
ef = safe_exp(f)
return ef/(1.+ef)

[docs]    def d2transf_df2(self,f):
ef = safe_exp(f)
aux = ef/(1.+ef)
return aux*(1.-aux)

[docs]    def d3transf_df3(self,f):
ef = safe_exp(f)
aux = ef/(1.+ef)
daux_df = aux*(1.-aux)
return daux_df - (2.*aux*daux_df)

[docs]class Reciprocal(GPTransformation):
[docs]    def transf(self,f):
return 1./f

[docs]    def dtransf_df(self, f):
f2 = safe_square(f)
return -1./f2

[docs]    def d2transf_df2(self, f):
f3 = safe_cube(f)
return 2./f3

[docs]    def d3transf_df3(self,f):
return -6./f4

[docs]class Heaviside(GPTransformation):
"""

.. math::

g(f) = I_{x \\geq 0}

"""
[docs]    def transf(self,f):
#transformation goes here
return np.where(f>0, 1, 0)

[docs]    def dtransf_df(self,f):
raise NotImplementedError("This function is not differentiable!")

[docs]    def d2transf_df2(self,f):
raise NotImplementedError("This function is not differentiable!")