174 lines
3.4 KiB
C++
174 lines
3.4 KiB
C++
// Copyright 2007 Georgia Institute of Technology. All rights reserved.
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// ABSOLUTELY NOT FOR DISTRIBUTION
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/**
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* @file kernel.h
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*
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* Common statistical kernels.
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*/
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#ifndef MATH_KERNEL_H
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#define MATH_KERNEL_H
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#include "base/common.h"
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#include "math/geometry.h"
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#include "math/math.h"
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#include <math.h>
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/* More to come soon - Gaussian, Epanechnakov, etc. */
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/**
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* Standard multivariate Gaussian kernel.
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*
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*/
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struct GaussianKernel {
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private:
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double inv_bandwidth_2sq_;
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OT_DEF(GaussianKernel) {
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OT_MY_OBJECT(inv_bandwidth_2sq_);
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}
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public:
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static const bool HAS_CUTOFF = false;
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public:
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GaussianKernel() {}
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~GaussianKernel() {}
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/**
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* Initializes to a specific bandwidth.
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*
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* @param bandwidth_in the standard deviation sigma
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*/
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void Init(double bandwidth_in) {
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inv_bandwidth_2sq_ = 1.0 / (2.0 * bandwidth_in * bandwidth_in);
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}
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void Copy(const GaussianKernel& other) {
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inv_bandwidth_2sq_ = other.inv_bandwidth_2sq_;
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}
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/**
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* Evaluates an unnormalized density, given the distance between
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* the kernel's mean and a query point.
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*/
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double EvalUnnorm(double dist) const {
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return EvalUnnormOnSq(dist * dist);
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}
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/**
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* Evaluates an unnormalized density, given the square of the
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* distance.
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*/
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double EvalUnnormOnSq(double sqdist) const {
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double d = exp(-sqdist * inv_bandwidth_2sq_);
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return d;
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}
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/**
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* Gets the maximum unnormalized value.
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*/
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double MaxUnnormValue() {
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return 1;
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}
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/**
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* Divide by this constant when you're done.
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*/
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double CalcNormConstant(index_t dims) const {
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return pow((math::PI/inv_bandwidth_2sq_), dims/2.0);
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}
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};
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/**
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* Multivariate Epanechnikov kernel.
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*
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* To use, first get an unnormalized density, and divide by the
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* normalizeation factor.
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*/
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struct EpanKernel {
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private:
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double inv_bandwidth_sq_;
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double bandwidth_sq_;
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OT_DEF(EpanKernel) {
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OT_MY_OBJECT(inv_bandwidth_sq_);
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OT_MY_OBJECT(bandwidth_sq_);
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}
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public:
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static const bool HAS_CUTOFF = true;
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public:
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EpanKernel() {}
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~EpanKernel() {}
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/**
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* Initializes to a specific bandwidth.
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*/
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void Init(double bandwidth_in) {
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bandwidth_sq_ = (bandwidth_in * bandwidth_in);
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inv_bandwidth_sq_ = 1.0 / bandwidth_sq_;
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}
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void Copy(const EpanKernel& other) {
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bandwidth_sq_ = other.bandwidth_sq_;
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inv_bandwidth_sq_ = other.inv_bandwidth_sq_;
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}
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/**
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* Evaluates an unnormalized density, given the distance between
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* the kernel's mean and a query point.
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*/
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double EvalUnnorm(double dist) const {
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return EvalUnnormOnSq(dist * dist);
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}
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/**
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* Evaluates an unnormalized density, given the square of the
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* distance.
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*/
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double EvalUnnormOnSq(double sqdist) const {
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// TODO: Try the fabs non-branching version.
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if (sqdist < bandwidth_sq_) {
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return 1 - sqdist * inv_bandwidth_sq_;
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} else {
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return 0;
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}
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}
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/**
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* Gets the maximum unnormalized value.
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*/
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double MaxUnnormValue() {
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return 1.0;
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}
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/**
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* Divide by this constant when you're done.
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*/
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double CalcNormConstant(index_t dims) const {
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return 2.0 * math::SphereVolume(sqrt(bandwidth_sq_), dims)
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/ (dims + 2.0);
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}
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/**
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* Gets the squared bandwidth.
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*/
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double bandwidth_sq() const {
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return bandwidth_sq_;
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}
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/**
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* Gets the reciproccal of the squared bandwidth.
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*/
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double inv_bandwidth_sq() const {
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return inv_bandwidth_sq_;
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}
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};
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#endif
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