org.apache.commons.math3.analysis.function.Sinc Maven / Gradle / Ivy
Go to download
Show more of this group Show more artifacts with this name
Show all versions of commons-math3 Show documentation
Show all versions of commons-math3 Show documentation
The Apache Commons Math project is a library of lightweight, self-contained mathematics and statistics components addressing the most common practical problems not immediately available in the Java programming language or commons-lang.
/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.commons.math3.analysis.function;
import org.apache.commons.math3.analysis.UnivariateFunction;
import org.apache.commons.math3.analysis.DifferentiableUnivariateFunction;
import org.apache.commons.math3.util.FastMath;
/**
* Sinc function,
* defined by
*
* sinc(x) = 1 if x = 0,
* sin(x) / x otherwise.
*
*
* @version $Id$
* @since 3.0
*/
public class Sinc implements DifferentiableUnivariateFunction {
/**
* Value below which the result of the computation will not change
* anymore due to the finite precision of the "double" representation
* of real numbers.
*/
private static final double SHORTCUT = 1e-9;
/** For normalized sinc function. */
private final boolean normalized;
/**
* The sinc function, {@code sin(x) / x}.
*/
public Sinc() {
this(false);
}
/**
* Instantiates the sinc function.
*
* @param normalized If {@code true}, the function is
* sin(πx) / πx, otherwise {@code sin(x) / x}.
*/
public Sinc(boolean normalized) {
this.normalized = normalized;
}
/** {@inheritDoc} */
public double value(double x) {
if (normalized) {
final double piTimesX = Math.PI * x;
return sinc(piTimesX);
} else {
return sinc(x);
}
}
/** {@inheritDoc} */
public UnivariateFunction derivative() {
if (normalized) {
return new UnivariateFunction() {
/** {@inheritDoc} */
public double value(double x) {
final double piTimesX = Math.PI * x;
return sincDerivative(piTimesX);
}
};
} else {
return new UnivariateFunction() {
/** {@inheritDoc} */
public double value(double x) {
return sincDerivative(x);
}
};
}
}
/**
* @param x Argument.
* @return {@code sin(x) / x}.
*/
private static double sinc(double x) {
// The direct assignment to 1 for values below 1e-9 is an efficiency
// optimization on the ground that the result of the full computation
// is indistinguishable from 1 due to the limited accuracy of the
// floating point representation.
return FastMath.abs(x) < SHORTCUT ? 1 :
FastMath.sin(x) / x;
}
/**
* @param x Argument.
* @return {@code (cos(x) - sin(x) / x) / x}.
*/
private static double sincDerivative(double x) {
// The direct assignment to 0 for values below 1e-9 is an efficiency
// optimization on the ground that the result of the full computation
// is indistinguishable from 1 due to the limited accuracy of the
// floating point representation.
return FastMath.abs(x) < SHORTCUT ? 0 :
(FastMath.cos(x) - FastMath.sin(x) / x) / x;
}
}