# Path: pygp/utils/models.py
# class Parameterized(object):
#     """
#     Interface for objects that are parameterized by some set of
#     hyperparameters.
#     """
#     __metaclass__ = ABCMeta
# 
#     @abstractmethod
#     def _params(self):
#         """
#         Define the set of parameters for the model. This should return a list
#         of tuples of the form `(name, size, islog)`. If only a 2-tuple is given
#         then islog will be assumed to be `True`.
#         """
#         raise NotImplementedError
# 
#     @abstractmethod
#     def get_hyper(self):
#         """Return a vector of model hyperparameters."""
#         raise NotImplementedError
# 
#     @abstractmethod
#     def set_hyper(self, hyper):
#         """Set the model hyperparameters to the given vector."""
#         raise NotImplementedError
# 
#     def copy(self, hyper=None):
#         """
#         Copy the model. If `hyper` is given use this vector to immediately set
#         the copied model's hyperparameters.
#         """
#         model = copy.deepcopy(self)
#         if hyper is not None:
#             model.set_hyper(hyper)
#         return model
# 
# Path: pygp/inference/_fourier.py
# class FourierSample(object):
#     """
#     Approximate sample from a Gaussian process, approximated using random
#     Fourier features.
#     """
#     def __init__(self, N, likelihood, kernel, mean, X, y, rng=None):
#         # if given a seed or an instantiated RandomState make sure that we use
#         # it here, but also within the sample_spectrum code.
#         rng = rstate(rng)
# 
#         if not isinstance(likelihood, Gaussian):
#             raise ValueError('Fourier samples only defined for Gaussian'
#                              'likelihoods')
# 
#         # this randomizes the feature.
#         W, alpha = kernel.sample_spectrum(N, rng)
# 
#         self._W = W
#         self._b = rng.rand(N) * 2 * np.pi
#         self._a = np.sqrt(2 * alpha / N)
#         self._mean = mean
#         self._theta = None
# 
#         if X is not None:
#             # evaluate the features
#             Z = np.dot(X, self._W.T) + self._b
#             Phi = np.cos(Z) * self._a
# 
#             # get the components for regression
#             A = np.dot(Phi.T, Phi) + likelihood.s2 * np.eye(Phi.shape[1])
#             R = sla.cholesky(A)
#             r = y - mean
#             p = np.sqrt(likelihood.s2) * rng.randn(N)
# 
#             # FIXME: we can do a smarter update here when the number of points
#             # is less than the number of features.
# 
#             self._theta = sla.cho_solve((R, False), np.dot(Phi.T, r))
#             self._theta += sla.solve_triangular(R, p)
# 
#         else:
#             self._theta = rng.randn(N)
# 
#     def get(self, X, grad=False):
#         """
#         Evaluate the function at a collection of points.
#         """
#         X = np.array(X, ndmin=2, copy=False)
#         Z = np.dot(X, self._W.T) + self._b
# 
#         # evaluate the sample
#         F = np.dot(self._a * np.cos(Z), self._theta) + self._mean
# 
#         if not grad:
#             return F
# 
#         # evaluate the gradient
#         dPhi = (-self._a * np.sin(Z))[:, :, None] * self._W[None]
#         G = np.einsum('ijk,j', dPhi, self._theta)
# 
#         return F, G
# 
#     def __call__(self, x, grad=False):
#         if grad:
#             F, G = self.get(x, True)
#             return F[0], G[0]
#         else:
#             return self.get(x)[0]


import numpy as np
import scipy.linalg as sla
from mwhutils.abc import abstractmethod, abstractclassmethod
from mwhutils.random import rstate
from ..utils.models import Parameterized
from ._fourier import FourierSample
        # if a seed or instantiated RandomState is given use that, otherwise
        # use the global object.
        rng = rstate(rng)

        # add a tiny amount to the diagonal to make the cholesky of Sigma
        # stable and then add this correlated noise onto mu to get the sample.
        mu, Sigma = self._full_posterior(X)
        Sigma += 1e-10 * np.eye(n)
        f = mu[None] + np.dot(rng.normal(size=(m, n)), sla.cholesky(Sigma))

        if not latent:
            f = self._likelihood.sample(f.ravel(), rng).reshape(m, n)

        return f.ravel() if flatten else f

    def posterior(self, X, grad=False):
        """
        Return the marginal posterior. This should return the mean and variance
        of the given points, and if `grad == True` should return their
        derivatives with respect to the input location as well (i.e. a
        4-tuple).
        """
        return self._marg_posterior(self._kernel.transform(X), grad)

    def sample_fourier(self, N, rng=None):
        """
        Approximately sample a function from the GP using a fourier-basis
        expansion with N bases. See the documentation on `FourierSample` for
        details on the returned function object.
        """

# Path: pygp/utils/models.py
# class Parameterized(object):
#     """
#     Interface for objects that are parameterized by some set of
#     hyperparameters.
#     """
#     __metaclass__ = ABCMeta
# 
#     @abstractmethod
#     def _params(self):
#         """
#         Define the set of parameters for the model. This should return a list
#         of tuples of the form `(name, size, islog)`. If only a 2-tuple is given
#         then islog will be assumed to be `True`.
#         """
#         raise NotImplementedError
# 
#     @abstractmethod
#     def get_hyper(self):
#         """Return a vector of model hyperparameters."""
#         raise NotImplementedError
# 
#     @abstractmethod
#     def set_hyper(self, hyper):
#         """Set the model hyperparameters to the given vector."""
#         raise NotImplementedError
# 
#     def copy(self, hyper=None):
#         """
#         Copy the model. If `hyper` is given use this vector to immediately set
#         the copied model's hyperparameters.
#         """
#         model = copy.deepcopy(self)
#         if hyper is not None:
#             model.set_hyper(hyper)
#         return model
# 
# Path: pygp/inference/_fourier.py
# class FourierSample(object):
#     """
#     Approximate sample from a Gaussian process, approximated using random
#     Fourier features.
#     """
#     def __init__(self, N, likelihood, kernel, mean, X, y, rng=None):
#         # if given a seed or an instantiated RandomState make sure that we use
#         # it here, but also within the sample_spectrum code.
#         rng = rstate(rng)
# 
#         if not isinstance(likelihood, Gaussian):
#             raise ValueError('Fourier samples only defined for Gaussian'
#                              'likelihoods')
# 
#         # this randomizes the feature.
#         W, alpha = kernel.sample_spectrum(N, rng)
# 
#         self._W = W
#         self._b = rng.rand(N) * 2 * np.pi
#         self._a = np.sqrt(2 * alpha / N)
#         self._mean = mean
#         self._theta = None
# 
#         if X is not None:
#             # evaluate the features
#             Z = np.dot(X, self._W.T) + self._b
#             Phi = np.cos(Z) * self._a
# 
#             # get the components for regression
#             A = np.dot(Phi.T, Phi) + likelihood.s2 * np.eye(Phi.shape[1])
#             R = sla.cholesky(A)
#             r = y - mean
#             p = np.sqrt(likelihood.s2) * rng.randn(N)
# 
#             # FIXME: we can do a smarter update here when the number of points
#             # is less than the number of features.
# 
#             self._theta = sla.cho_solve((R, False), np.dot(Phi.T, r))
#             self._theta += sla.solve_triangular(R, p)
# 
#         else:
#             self._theta = rng.randn(N)
# 
#     def get(self, X, grad=False):
#         """
#         Evaluate the function at a collection of points.
#         """
#         X = np.array(X, ndmin=2, copy=False)
#         Z = np.dot(X, self._W.T) + self._b
# 
#         # evaluate the sample
#         F = np.dot(self._a * np.cos(Z), self._theta) + self._mean
# 
#         if not grad:
#             return F
# 
#         # evaluate the gradient
#         dPhi = (-self._a * np.sin(Z))[:, :, None] * self._W[None]
#         G = np.einsum('ijk,j', dPhi, self._theta)
# 
#         return F, G
# 
#     def __call__(self, x, grad=False):
#         if grad:
#             F, G = self.get(x, True)
#             return F[0], G[0]
#         else:
#             return self.get(x)[0]


# Path: pygp/inference/_base.py
import numpy as np
import scipy.linalg as sla
from mwhutils.abc import abstractmethod, abstractclassmethod
from mwhutils.random import rstate
from ..utils.models import Parameterized
from ._fourier import FourierSample

        # if a seed or instantiated RandomState is given use that, otherwise
        # use the global object.
        rng = rstate(rng)

        # add a tiny amount to the diagonal to make the cholesky of Sigma
        # stable and then add this correlated noise onto mu to get the sample.
        mu, Sigma = self._full_posterior(X)
        Sigma += 1e-10 * np.eye(n)
        f = mu[None] + np.dot(rng.normal(size=(m, n)), sla.cholesky(Sigma))

        if not latent:
            f = self._likelihood.sample(f.ravel(), rng).reshape(m, n)

        return f.ravel() if flatten else f

    def posterior(self, X, grad=False):
        """
        Return the marginal posterior. This should return the mean and variance
        of the given points, and if `grad == True` should return their
        derivatives with respect to the input location as well (i.e. a
        4-tuple).
        """
        return self._marg_posterior(self._kernel.transform(X), grad)

    def sample_fourier(self, N, rng=None):
        """
        Approximately sample a function from the GP using a fourier-basis
        expansion with N bases. See the documentation on `FourierSample` for
        details on the returned function object.
        """

        return FourierSample(N,