/* XXL: The eXtensible and fleXible Library for data processing
Copyright (C) 2000-2011 Prof. Dr. Bernhard Seeger
Head of the Database Research Group
Department of Mathematics and Computer Science
University of Marburg
Germany
This library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 3 of the License, or (at your option) any later version.
This library 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
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with this library; If not, see <http://www.gnu.org/licenses/>.
http://code.google.com/p/xxl/
*/
package xxl.core.math.statistics.nonparametric.kernels;
import xxl.core.math.Statistics;
import xxl.core.math.functions.Differentiable;
import xxl.core.math.functions.Integrable;
import xxl.core.math.functions.RealFunction;
/**
* This class models the <tt>CosineArch kernel function</tt>. Thus, it extends
* {@link xxl.core.math.statistics.nonparametric.kernels.KernelFunction KernelFunction}.
* Since the primitive as well as the first derivative are known, this class also
* implements {@link xxl.core.math.functions.Integrable Integrable} and
* {@link xxl.core.math.functions.Differentiable Differentiable}.
*
* @see xxl.core.math.statistics.nonparametric.kernels.KernelFunction
* @see xxl.core.math.statistics.nonparametric.kernels.Kernels
* @see xxl.core.math.statistics.nonparametric.kernels.KernelFunctionND
* @see xxl.core.math.statistics.nonparametric.kernels.KernelBandwidths
*/
public class CosineArchKernel extends KernelFunction implements Integrable, Differentiable {
/**
* Constructs a new CosineArchKernel and initializes the parameters.
*
*/
public CosineArchKernel() {
AVG = 0.0;
VAR = 1.0 - (8.0 / (Math.PI * Math.PI)); // 1 - ( 8 / pi^2)
R = Math.PI * Math.PI / 16.0; // pi^2 / 16
}
/**
* Evaluates the CosineArch kernel at x.
*
* @param x point to evaluate
* @return value of the CosineArch kernel at x
*/
public double eval(double x) {
return Statistics.cosineArch(x);
}
/** Returns the primitive of the <tt>CosineArch</tt> kernel function
* as {@link xxl.core.math.functions.RealFunction real-valued function}
*
* @return primitive of the <tt>CosineArch</tt> kernel function
*/
public RealFunction primitive() {
return new RealFunction() {
public double eval(double x) {
return Statistics.cosineArchPrimitive(x);
}
};
}
/** Returns the first derivative of the <tt>CosineArch</tt> kernel function
* as {@link xxl.core.math.functions.RealFunction real-valued function}
*
* @return first derivative of the <tt>CosineArch</tt> kernel function
*/
public RealFunction derivative() {
return new RealFunction() {
public double eval(double x) {
return Statistics.cosineArchDerivative(x);
}
};
}
}