# Path: pygp/kernels/_base.py
# class Kernel(Parameterized):
#     """
#     The base Kernel interface.
#     """
#     def __call__(self, x1, x2):
#         return self.get(x1[None], x2[None])[0]
# 
#     @abstractmethod
#     def get(self, X1, X2=None):
#         """
#         Evaluate the kernel.
# 
#         Returns the matrix of covariances between points in `X1` and `X2`. If
#         `X2` is not given this will return the pairwise covariances between
#         points in `X1`.
#         """
#         raise NotImplementedError
# 
#     @abstractmethod
#     def dget(self, X):
#         """Evaluate the self covariances."""
#         raise NotImplementedError
# 
#     @abstractmethod
#     def grad(self, X1, X2=None):
#         """
#         Evaluate the gradient of the kernel.
# 
#         Returns an iterator over the gradients of the covariances between
#         points in `X1` and `X2`. If `X2` is not given this will iterate over
#         the the gradients of the pairwise covariances.
#         """
#         raise NotImplementedError
# 
#     @abstractmethod
#     def dgrad(self, X):
#         """Evaluate the gradients of the self covariances."""
#         raise NotImplementedError
# 
#     @abstractmethod
#     def transform(self, X):
#         """Format the inputs X as arrays."""
#         raise NotImplementedError
# 
# Path: pygp/kernels/_combo.py
# class SumKernel(ComboKernel):
#     """Kernel representing a sum of other kernels."""
# 
#     def get(self, X1, X2=None):
#         fiterable = (p.get(X1, X2) for p in self._parts)
#         return sum(fiterable)
# 
#     def dget(self, X):
#         fiterable = (p.dget(X) for p in self._parts)
#         return sum(fiterable)
# 
#     def grad(self, X1, X2=None):
#         giterable = (p.grad(X1, X2) for p in self._parts)
#         return it.chain.from_iterable(giterable)
# 
#     def dgrad(self, X):
#         giterable = (p.dgrad(X) for p in self._parts)
#         return it.chain.from_iterable(giterable)
# 
# Path: pygp/kernels/_combo.py
# class ProductKernel(ComboKernel):
#     """Kernel representing a product of other kernels."""
# 
#     def get(self, X1, X2=None):
#         fiterable = (p.get(X1, X2) for p in self._parts)
#         return product(fiterable)
# 
#     def dget(self, X):
#         fiterable = (p.dget(X) for p in self._parts)
#         return product(fiterable)
# 
#     def grad(self, X1, X2=None):
#         fiterable = (p.get(X1, X2) for p in self._parts)
#         giterable = (p.grad(X1, X2) for p in self._parts)
#         for Mi, grads in zip(product_but(fiterable), giterable):
#             for dM in grads:
#                 yield Mi*dM
# 
#     def dgrad(self, X):
#         fiterable = (p.dget(X) for p in self._parts)
#         giterable = (p.dgrad(X) for p in self._parts)
#         for Mi, grads in zip(product_but(fiterable), giterable):
#             for dM in grads:
#                 yield Mi*dM
# 
# Path: pygp/kernels/_combo.py
# def combine(cls, *parts):
#     """
#     Given a list of kernels return another list of kernels where objects of
#     type cls have been "combined". This applies to ComboKernel objects which
#     represent associative operations.
#     """
#     combined = []
#     for part in parts:
#         combined += part._parts if isinstance(part, cls) else [part]
#     return combined
# 
# Path: pygp/kernels/_combo.py
# def product_but(fiterable):
#     """
#     Given an iterator over function evaluations return an array such that
#     `M[i]` is the product of every evaluation except for the ith one.
#     """
#     A = list(fiterable)
# 
#     # allocate memory for M and fill everything but the last element with
#     # the product of A[i+1:]. Note that we're using the cumprod in place.
#     M = np.empty_like(A)
#     np.cumprod(A[:0:-1], axis=0, out=M[:-1][::-1])
# 
#     # use an explicit loop to iteratively set M[-1] equal to the product of
#     # A[:-1]. While doing this we can multiply M[i] by A[:i].
#     M[-1] = A[0]
#     for i in xrange(1, len(A)-1):
#         M[i] *= M[-1]
#         M[-1] *= A[i]
# 
#     return M


import numpy as np
from abc import abstractmethod
from ._base import Kernel
from ._combo import SumKernel as SumKernel_
from ._combo import ProductKernel as ProductKernel_
from ._combo import combine
from ._combo import product_but
"""
Base class for real-valued kernels.
"""

# future imports
from __future__ import division
from __future__ import absolute_import
from __future__ import print_function

# global imports

# local imports

# import the generic sum/product kernels and change their names. We'll call the
# real-valued versions SumKernel and ProductKernel as well since they really
# shouldn't be used outside of this module anyway.

# exported symbols
__all__ = ['RealKernel']


class RealKernel(Kernel):
    """Kernel whose inputs are real-valued vectors."""

    def __add__(self, other):
        return SumKernel(*combine(SumKernel, self, other))

    def __mul__(self, other):

# Path: pygp/kernels/_base.py
# class Kernel(Parameterized):
#     """
#     The base Kernel interface.
#     """
#     def __call__(self, x1, x2):
#         return self.get(x1[None], x2[None])[0]
# 
#     @abstractmethod
#     def get(self, X1, X2=None):
#         """
#         Evaluate the kernel.
# 
#         Returns the matrix of covariances between points in `X1` and `X2`. If
#         `X2` is not given this will return the pairwise covariances between
#         points in `X1`.
#         """
#         raise NotImplementedError
# 
#     @abstractmethod
#     def dget(self, X):
#         """Evaluate the self covariances."""
#         raise NotImplementedError
# 
#     @abstractmethod
#     def grad(self, X1, X2=None):
#         """
#         Evaluate the gradient of the kernel.
# 
#         Returns an iterator over the gradients of the covariances between
#         points in `X1` and `X2`. If `X2` is not given this will iterate over
#         the the gradients of the pairwise covariances.
#         """
#         raise NotImplementedError
# 
#     @abstractmethod
#     def dgrad(self, X):
#         """Evaluate the gradients of the self covariances."""
#         raise NotImplementedError
# 
#     @abstractmethod
#     def transform(self, X):
#         """Format the inputs X as arrays."""
#         raise NotImplementedError
# 
# Path: pygp/kernels/_combo.py
# class SumKernel(ComboKernel):
#     """Kernel representing a sum of other kernels."""
# 
#     def get(self, X1, X2=None):
#         fiterable = (p.get(X1, X2) for p in self._parts)
#         return sum(fiterable)
# 
#     def dget(self, X):
#         fiterable = (p.dget(X) for p in self._parts)
#         return sum(fiterable)
# 
#     def grad(self, X1, X2=None):
#         giterable = (p.grad(X1, X2) for p in self._parts)
#         return it.chain.from_iterable(giterable)
# 
#     def dgrad(self, X):
#         giterable = (p.dgrad(X) for p in self._parts)
#         return it.chain.from_iterable(giterable)
# 
# Path: pygp/kernels/_combo.py
# class ProductKernel(ComboKernel):
#     """Kernel representing a product of other kernels."""
# 
#     def get(self, X1, X2=None):
#         fiterable = (p.get(X1, X2) for p in self._parts)
#         return product(fiterable)
# 
#     def dget(self, X):
#         fiterable = (p.dget(X) for p in self._parts)
#         return product(fiterable)
# 
#     def grad(self, X1, X2=None):
#         fiterable = (p.get(X1, X2) for p in self._parts)
#         giterable = (p.grad(X1, X2) for p in self._parts)
#         for Mi, grads in zip(product_but(fiterable), giterable):
#             for dM in grads:
#                 yield Mi*dM
# 
#     def dgrad(self, X):
#         fiterable = (p.dget(X) for p in self._parts)
#         giterable = (p.dgrad(X) for p in self._parts)
#         for Mi, grads in zip(product_but(fiterable), giterable):
#             for dM in grads:
#                 yield Mi*dM
# 
# Path: pygp/kernels/_combo.py
# def combine(cls, *parts):
#     """
#     Given a list of kernels return another list of kernels where objects of
#     type cls have been "combined". This applies to ComboKernel objects which
#     represent associative operations.
#     """
#     combined = []
#     for part in parts:
#         combined += part._parts if isinstance(part, cls) else [part]
#     return combined
# 
# Path: pygp/kernels/_combo.py
# def product_but(fiterable):
#     """
#     Given an iterator over function evaluations return an array such that
#     `M[i]` is the product of every evaluation except for the ith one.
#     """
#     A = list(fiterable)
# 
#     # allocate memory for M and fill everything but the last element with
#     # the product of A[i+1:]. Note that we're using the cumprod in place.
#     M = np.empty_like(A)
#     np.cumprod(A[:0:-1], axis=0, out=M[:-1][::-1])
# 
#     # use an explicit loop to iteratively set M[-1] equal to the product of
#     # A[:-1]. While doing this we can multiply M[i] by A[:i].
#     M[-1] = A[0]
#     for i in xrange(1, len(A)-1):
#         M[i] *= M[-1]
#         M[-1] *= A[i]
# 
#     return M


# Path: pygp/kernels/_real.py
import numpy as np
from abc import abstractmethod
from ._base import Kernel
from ._combo import SumKernel as SumKernel_
from ._combo import ProductKernel as ProductKernel_
from ._combo import combine
from ._combo import product_but

"""
Base class for real-valued kernels.
"""

# future imports
from __future__ import division
from __future__ import absolute_import
from __future__ import print_function

# global imports

# local imports

# import the generic sum/product kernels and change their names. We'll call the
# real-valued versions SumKernel and ProductKernel as well since they really
# shouldn't be used outside of this module anyway.

# exported symbols
__all__ = ['RealKernel']


class RealKernel(Kernel):
    """Kernel whose inputs are real-valued vectors."""

    def __add__(self, other):
        return SumKernel(*combine(SumKernel, self, other))

    def __mul__(self, other):

        return ProductKernel(*combine(ProductKernel, self, other))