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80 lines
2.6 KiB
Python
80 lines
2.6 KiB
Python
# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
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# Licensed under the BSD 3-clause license (see LICENSE.txt)
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from kernpart import kernpart
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import numpy as np
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class rational_quadratic(kernpart):
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"""
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rational quadratic kernel
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.. math::
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k(r) = \sigma^2 \\bigg( 1 + \\frac{r^2}{2 \ell^2} \\bigg)^{- \\alpha} \ \ \ \ \ \\text{ where } r^2 = (x-y)^2
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:param D: the number of input dimensions
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:type D: int (D=1 is the only value currently supported)
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:param variance: the variance :math:`\sigma^2`
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:type variance: float
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:param lengthscale: the lengthscale :math:`\ell`
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:type lengthscale: float
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:param power: the power :math:`\\alpha`
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:type power: float
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:rtype: kernpart object
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"""
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def __init__(self,D,variance=1.,lengthscale=1.,power=1.):
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assert D == 1, "For this kernel we assume D=1"
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self.D = D
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self.Nparam = 3
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self.name = 'rat_quad'
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self.variance = variance
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self.lengthscale = lengthscale
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self.power = power
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def _get_params(self):
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return np.hstack((self.variance,self.lengthscale,self.power))
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def _set_params(self,x):
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self.variance = x[0]
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self.lengthscale = x[1]
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self.power = x[2]
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def _get_param_names(self):
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return ['variance','lengthscale','power']
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def K(self,X,X2,target):
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if X2 is None: X2 = X
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dist2 = np.square((X-X2.T)/self.lengthscale)
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target += self.variance*(1 + dist2/2.)**(-self.power)
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def Kdiag(self,X,target):
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target += self.variance
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def dK_dtheta(self,dL_dK,X,X2,target):
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if X2 is None: X2 = X
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dist2 = np.square((X-X2.T)/self.lengthscale)
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dvar = (1 + dist2/2.)**(-self.power)
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dl = self.power * self.variance * dist2 * self.lengthscale**(-3) * (1 + dist2/2./self.power)**(-self.power-1)
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dp = - self.variance * np.log(1 + dist2/2.) * (1 + dist2/2.)**(-self.power)
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target[0] += np.sum(dvar*dL_dK)
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target[1] += np.sum(dl*dL_dK)
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target[2] += np.sum(dp*dL_dK)
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def dKdiag_dtheta(self,dL_dKdiag,X,target):
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target[0] += np.sum(dL_dKdiag)
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# here self.lengthscale and self.power have no influence on Kdiag so target[1:] are unchanged
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def dK_dX(self,dL_dK,X,X2,target):
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"""derivative of the covariance matrix with respect to X."""
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if X2 is None: X2 = X
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dist2 = np.square((X-X2.T)/self.lengthscale)
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dX = -self.variance*self.power * (X-X2.T)/self.lengthscale**2 * (1 + dist2/2./self.lengthscale)**(-self.power-1)
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target += np.sum(dL_dK*dX,1)[:,np.newaxis]
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def dKdiag_dX(self,dL_dKdiag,X,target):
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pass
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