From 7cd119d2b0a94d52e9b1c59ba737edee1173725e Mon Sep 17 00:00:00 2001
From: Neil Lawrence <lawrennd@gmail.com>
Date: Thu, 22 Aug 2013 14:03:35 +0200
Subject: [PATCH] Added missing poly.py file.

---
 GPy/kern/parts/poly.py | 131 +++++++++++++++++++++++++++++++++++++++++
 1 file changed, 131 insertions(+)
 create mode 100644 GPy/kern/parts/poly.py

diff --git a/GPy/kern/parts/poly.py b/GPy/kern/parts/poly.py
new file mode 100644
index 00000000..b1c2c09b
--- /dev/null
+++ b/GPy/kern/parts/poly.py
@@ -0,0 +1,131 @@
+# Copyright (c) 2013, GPy authors (see AUTHORS.txt).
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+from kernpart import Kernpart
+import numpy as np
+four_over_tau = 2./np.pi
+
+class POLY(Kernpart):
+    """
+    polynomial kernel parameter initialisation.  Included for completeness, but generally not recommended, is the polynomial kernel,
+    .. math::
+    
+    k(x, y) = \sigma^2*(\sigma_w^2 x'y+\sigma_b^b)^d
+
+    The kernel parameters are \sigma^2 (variance), \sigma^2_w
+    (weight_variance), \sigma^2_b (bias_variance) and d
+    (degree). Only gradients of the first three are provided for
+    kernel optimisation, it is assumed that polynomial degree would
+    be set by hand.
+
+    The kernel is not recommended as it is badly behaved when the
+    \sigma^2_w*x'*y + \sigma^2_b has a magnitude greater than one. For completeness
+    there is an automatic relevance determination version of this
+    kernel provided.
+
+    :param input_dim: the number of input dimensions
+    :type input_dim: int 
+    :param variance: the variance :math:`\sigma^2`
+    :type variance: float
+    :param weight_variance: the vector of the variances of the prior over input weights in the neural network :math:`\sigma^2_w`
+    :type weight_variance: array or list of the appropriate size (or float if there is only one weight variance parameter)
+    :param bias_variance: the variance of the prior over bias parameters :math:`\sigma^2_b`
+    :param degree: the degree of the polynomial.
+    :type degree: int
+    :param ARD: Auto Relevance Determination. If equal to "False", the kernel is isotropic (ie. one weight variance parameter \sigma^2_w), otherwise there is one weight variance parameter per dimension.
+    :type ARD: Boolean
+    :rtype: Kernpart object
+
+    """
+
+    def __init__(self, input_dim, variance=1., weight_variance=None, bias_variance=1., degree=2, ARD=False):
+        ARD = False
+        self.input_dim = input_dim
+        self.ARD = ARD
+        if not ARD:
+            self.num_params=3
+            if weight_variance is not None:
+                weight_variance = np.asarray(weight_variance)
+                assert weight_variance.size == 1, "Only one weight variance needed for non-ARD kernel"
+            else:
+                weight_variance = 1.*np.ones(1)
+        else:
+            self.num_params = self.input_dim + 2
+            if weight_variance is not None:
+                weight_variance = np.asarray(weight_variance)
+                assert weight_variance.size == self.input_dim, "bad number of weight variances"
+            else:
+                weight_variance = np.ones(self.input_dim)
+        self.degree=degree
+        self.name='poly_deg' + str(self.degree)
+        self._set_params(np.hstack((variance, weight_variance.flatten(), bias_variance)))
+
+    def _get_params(self):
+        return np.hstack((self.variance, self.weight_variance.flatten(), self.bias_variance))
+
+    def _set_params(self, x):
+        assert x.size == (self.num_params)
+        self.variance = x[0]
+        self.weight_variance = x[1:-1]
+        self.weight_std = np.sqrt(self.weight_variance)
+        self.bias_variance = x[-1]
+
+    def _get_param_names(self):
+        if self.num_params == 3:
+            return ['variance', 'weight_variance', 'bias_variance']
+        else:
+            return ['variance'] + ['weight_variance_%i' % i for i in range(self.lengthscale.size)] + ['bias_variance']
+
+    def K(self, X, X2, target):
+        """Return covariance between X and X2."""
+        self._K_computations(X, X2)
+        target += self.variance*self._K_dvar
+
+    def Kdiag(self, X, target):
+        """Compute the diagonal of the covariance matrix for X."""
+        self._K_diag_computations(X)
+        target+= self.variance*self._K_diag_dvar
+
+    def dK_dtheta(self, dL_dK, X, X2, target):
+        """Derivative of the covariance with respect to the parameters."""
+        self._K_computations(X, X2)
+        base = self.variance*self.degree*self._K_poly_arg**(self.degree-1)
+        base_cov_grad = base*dL_dK
+
+
+            
+        target[0] += np.sum(self._K_dvar*dL_dK)
+        target[1] += (self._K_inner_prod*base_cov_grad).sum()
+        target[2] += base_cov_grad.sum()
+
+
+    def dK_dX(self, dL_dK, X, X2, target):
+        """Derivative of the covariance matrix with respect to X"""
+        pass
+            
+    def _dK_dX_point(self, dL_dK, X, X2, target, i):
+        """Gradient with respect to one point of X"""
+        pass
+    
+    
+    def _K_computations(self, X, X2):
+        if self.ARD:
+            pass
+        else:
+            if X2 is None:
+                self._K_inner_prod = np.dot(X,X.T)
+            else:
+                self._K_inner_prod = np.dot(X,X2.T)
+            self._K_poly_arg = self._K_inner_prod*self.weight_variance + self.bias_variance
+        self._K_dvar = self._K_poly_arg**self.degree
+
+    def _K_diag_computations(self, X):
+        if self.ARD:
+            pass
+        else:
+            self._K_diag_poly_arg = (X*X).sum(1)*self.weight_variance + self.bias_variance
+        self._K_diag_dvar = self._K_diag_poly_arg**self.degree
+
+  
+
+