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package de.lmu.ifi.dbs.elki.math.statistics.kernelfunctions;
/*
This file is part of ELKI:
Environment for Developing KDD-Applications Supported by Index-Structures
Copyright (C) 2015
Ludwig-Maximilians-Universität München
Lehr- und Forschungseinheit für Datenbanksysteme
ELKI Development Team
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU Affero General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Affero General Public License for more details.
You should have received a copy of the GNU Affero General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
import de.lmu.ifi.dbs.elki.math.MathUtil;
import de.lmu.ifi.dbs.elki.utilities.optionhandling.AbstractParameterizer;
/**
* Cosine kernel density estimator.
*
* @author Erich Schubert
* @since 0.6.0
*/
public final class CosineKernelDensityFunction implements KernelDensityFunction {
/**
* Static instance.
*/
public static final CosineKernelDensityFunction KERNEL = new CosineKernelDensityFunction();
/**
* Canonical bandwidth.
*
* Computed as (R / STDDEV^4)^(1/5)
*
* This is approximately: 1.7662654022050532
*/
public static final double CANONICAL_BANDWIDTH = Math.pow(MathUtil.PISQUARE / (16. * (1. - 8. / MathUtil.PISQUARE) * (1. - 8. / MathUtil.PISQUARE)), .2);
/**
* Standard deviation.
*/
private static final double STDDEV = Math.sqrt(1. - 8. / MathUtil.PISQUARE);
/**
* R constant.
*/
private static final double R = Math.PI * Math.PI / 16.;
/**
* Private, empty constructor. Use the static instance!
*/
private CosineKernelDensityFunction() {
// Nothing to do.
}
@Override
public double density(double delta) {
return (delta < 1.) ? MathUtil.QUARTERPI * Math.cos(MathUtil.HALFPI * delta) : 0.;
}
@Override
public double canonicalBandwidth() {
return CANONICAL_BANDWIDTH;
}
@Override
public double standardDeviation() {
return STDDEV;
}
@Override
public double getR() {
return R;
}
/**
* Parameterization stub.
*
* @author Erich Schubert
*
* @apiviz.exclude
*/
public static class Parameterizer extends AbstractParameterizer {
@Override
protected CosineKernelDensityFunction makeInstance() {
return KERNEL;
}
}
}
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