double ConvolutionIntegral(const VecTypeA& a, const VecTypeB& b) const
{
double distance = sqrt(metric::SquaredEuclideanDistance::Evaluate(a, b));
if (distance >= 2.0 * bandwidth)
{
return 0.0;
}
double volumeSquared = pow(Normalizer(a.n_rows), 2.0);
switch(a.n_rows)
{
case 1:
return 1.0 / volumeSquared * (2.0 * bandwidth - distance);
break;
case 2:
return 1.0 / volumeSquared *
(2.0 * bandwidth * bandwidth * acos(distance/(2.0 * bandwidth)) -
distance / 4.0 * sqrt(4.0*bandwidth*bandwidth-distance*distance));
break;
default:
Log::Fatal << "The spherical kernel does not support convolution\
integrals above dimension two, yet..." << std::endl;
return -1.0;
break;
}
}
double EpanechnikovKernel::ConvolutionIntegral(const VecType& a,
const VecType& b)
{
double distance = sqrt(metric::SquaredEuclideanDistance::Evaluate(a, b));
if (distance >= 2.0 * bandwidth)
return 0.0;
double volumeSquared = std::pow(Normalizer(a.n_rows), 2.0);
switch (a.n_rows)
{
case 1:
return 1.0 / volumeSquared *
(16.0 / 15.0 * bandwidth - 4.0 * distance * distance /
(3.0 * bandwidth) + 2.0 * distance * distance * distance /
(3.0 * bandwidth * bandwidth) -
std::pow(distance, 5.0) / (30.0 * std::pow(bandwidth, 4.0)));
break;
case 2:
return 1.0 / volumeSquared *
((2.0 / 3.0 * bandwidth * bandwidth - distance * distance) *
asin(sqrt(1.0 - std::pow(distance / (2.0 * bandwidth), 2.0))) +
sqrt(4.0 * bandwidth * bandwidth - distance * distance) *
(distance / 6.0 + 2.0 / 9.0 * distance *
std::pow(distance / bandwidth, 2.0) - distance / 72.0 *
std::pow(distance / bandwidth, 4.0)));
break;
default:
Log::Fatal << "EpanechnikovKernel::ConvolutionIntegral(): dimension "
<< a.n_rows << " not supported.";
return -1.0; // This line will not execute.
break;
}
}
double ConvolutionIntegral(const VecType& a, const VecType& b)
{
return Evaluate(sqrt(metric::SquaredEuclideanDistance::Evaluate(a, b) / 2.0)) /
(Normalizer(a.n_rows) * pow(2.0, (double) a.n_rows / 2.0));
}
