10 #ifndef MLPACK_CORE_KERNELS_SPHERICAL_KERNEL_HPP 11 #define MLPACK_CORE_KERNELS_SPHERICAL_KERNEL_HPP 30 bandwidthSquared(
std::pow(bandwidth, 2.0))
42 template<
typename VecTypeA,
typename VecTypeB>
43 double Evaluate(
const VecTypeA& a,
const VecTypeB& b)
const 60 template<
typename VecTypeA,
typename VecTypeB>
64 if (distance >= 2.0 * bandwidth)
68 double volumeSquared = pow(
Normalizer(a.n_rows), 2.0);
73 return 1.0 / volumeSquared * (2.0 * bandwidth - distance);
75 return 1.0 / volumeSquared *
76 (2.0 * bandwidth * bandwidth * acos(distance/(2.0 * bandwidth)) -
77 distance / 4.0 * sqrt(4.0*bandwidth*bandwidth-distance*distance));
79 Log::Fatal <<
"The spherical kernel does not support convolution\ 80 integrals above dimension two, yet..." << std::endl;
86 return pow(bandwidth, (
double) dimension) * pow(
M_PI, dimension / 2.0) /
87 std::tgamma(dimension / 2.0 + 1.0);
97 return (t <= bandwidth) ? 1.0 : 0.0;
101 return t == bandwidth ? arma::datum::nan : 0.0;
105 template<
typename Archive>
108 ar(CEREAL_NVP(bandwidth));
109 ar(CEREAL_NVP(bandwidthSquared));
114 double bandwidthSquared;
123 static const bool IsNormalized =
true;
125 static const bool UsesSquaredDistance =
false;
double Evaluate(const double t) const
Evaluate the kernel when only a distance is given, not two points.
void serialize(Archive &ar, const uint32_t)
Serialize the object.
This is a template class that can provide information about various kernels.
Linear algebra utility functions, generally performed on matrices or vectors.
double Evaluate(const VecTypeA &a, const VecTypeB &b) const
Evaluate the spherical kernel with the given two vectors.
The core includes that mlpack expects; standard C++ includes and Armadillo.
static VecTypeA::elem_type Evaluate(const VecTypeA &a, const VecTypeB &b)
Computes the distance between two points.
static MLPACK_EXPORT util::PrefixedOutStream Fatal
Prints fatal messages prefixed with [FATAL], then terminates the program.
SphericalKernel(const double bandwidth=1.0)
Construct the SphericalKernel with the given bandwidth.
double ConvolutionIntegral(const VecTypeA &a, const VecTypeB &b) const
Obtains the convolution integral [integral K(||x-a||)K(||b-x||)dx] for the two vectors.
The spherical kernel, which is 1 when the distance between the two argument points is less than or eq...
double Normalizer(size_t dimension) const
double Gradient(double t)