Source code for infpy.gp.periodic_kernel

#
# Copyright John Reid 2006, 2012
#


from kernel import *
from real_kernel import *
import numpy, math


class FixedPeriod1DKernel( RealKernel ):
    """See 4.31 in `Gaussian Processes for Machine Learning`__ by Rasmussen and Williams. 

    __ http://www.amazon.co.uk/Gaussian-Processes-Learning-Adaptive-Computation/dp/026218253X/

    .. math::
        
        k(x_1, x_2) = e^\\frac{-2 \sin^2( \\pi (x_1 - x_2) )}{p^2}

    Could be generalised to more than one dimension or for parameterisable periods
    """
    def __init__(
            self,
            fixed_period,
            length = 1.0,
            prior = infpy.LogNormalDistribution()
    ):
        self.period = fixed_period
        RealKernel.__init__(
            self,
            numpy.asarray( [ length ] ),
            [ prior ],
            0
        )

    def d( self, x1, x2 ):
        return math.pi * (x1[0] - x2[0]) / self.period

    def __str__( self ):
        return """PeriodicKernel( period = %f )""" % self.period

    def __call__( self, x1, x2, identical = False ):
        (x1, x2) = self._check_args( x1, x2 )
        return math.exp(
                - 2.0
                * math.sin( self.d(x1, x2) ) ** 2
                / self.params[0] ** 2
        )

    class Derivative( object ):
        def __init__( self, k, i ):
            self.k = k
            assert 0 == i
        def __call__( self, x1, x2, identical = False ):
            (x1, x2) = self.k._check_args( x1, x2 )
            d = self.k.d(x1, x2)
            return (
                    4.0 * math.sin( d ) ** 2
                    * math.exp(
                            - 2.0
                            * math.sin( d ) ** 2
                            / self.k.params[0] ** 2
                    )
                    / self.k.params[0] ** 3
            )