LinearDistribution.java
/*
* Java Genetic Algorithm Library (@__identifier__@).
* Copyright (c) @__year__@ Franz Wilhelmstötter
*
* Licensed 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.
*
* Author:
* Franz Wilhelmstötter (franz.wilhelmstoetter@gmx.at)
*/
package org.jenetics.stat;
import static java.lang.String.format;
import static java.util.Objects.requireNonNull;
import static org.jenetics.internal.util.object.eq;
import java.io.Serializable;
import java.util.Locale;
import org.jscience.mathematics.number.Float64;
import org.jenetics.internal.util.HashBuilder;
import org.jenetics.util.Function;
import org.jenetics.util.Range;
/**
* <p>This distribution has the following cdf.</p>
* <p><img src="doc-files/LinearDistribution.png" /></p>
* <p>
* The only restriction is that the integral of the cdf must be one.
* </p>
* <p>
* <img src="doc-files/linear-precondition.gif"
* alt="\int_{x_1}^{x_2}\left(
* \\underset{k} {\\underbrace {\frac{y_2-y_1}{x_2-x_1}}} \cdot x +
* \\underset{d}{\\underbrace {y_1-\frac{y_2-y_1}{x_2-x_1}\cdot x_1}}
* \right)\mathrm{d}x = 1"
* />
* </p>
*
* Solving this integral leads to
* <p>
* <img src="doc-files/linear-precondition-y2.gif"
* alt="y_2 = -\frac{(x_2-x_1)\cdot y_1 - 2}{x_2-x_1}"
* />
* </p>
*
* for fixed values for <i>x<sub>1</sub></i>, <i>x<sub>2</sub></i> and
* <i>y<sub>1</sub></i>.
* <p>
* If the value of <i>y<sub>2</sub></i> < 0, the value of <i>x<sub>2</sub></i>
* is decreased so that the resulting triangle (<i>x<sub>1</sub></i>,0),
* (<i>x<sub>1</sub></i>,<i>y<sub>1</sub></i>), (<i>x<sub>2</sub></i>,0) has
* an area of <i>one</i>.
* </p>
*
* @author <a href="mailto:franz.wilhelmstoetter@gmx.at">Franz Wilhelmstötter</a>
* @since 1.0
* @version 1.0 — <em>$Date: 2014-03-01 $</em>
*/
public class LinearDistribution<
N extends Number & Comparable<? super N>
>
implements Distribution<N>
{
/**
* <p>
* <img
* src="doc-files/linear-pdf.gif"
* alt="f(x) = \left(
* \frac{y_2-y_1}{x_2-x_1} \cdot x +
* y_1-\frac{y_2-y_1}{x_2-x_1}\cdot x_1
* \right)"
* />
* </p>
*
* @author <a href="mailto:franz.wilhelmstoetter@gmx.at">Franz Wilhelmstötter</a>
* @since 1.0
* @version 1.0 — <em>$Date: 2014-03-01 $</em>
*/
static final class PDF<N extends Number & Comparable<? super N>>
implements
Function<N, Float64>,
Serializable
{
private static final long serialVersionUID = 1L;
private final double _min;
private final double _max;
private final double _k;
private final double _d;
public PDF(
final double x1, final double y1,
final double x2, final double y2
) {
_min = x1;
_max = x2;
_k = (y2 - y1)/(x2 - x1);
_d = y1 - _k*x1;
}
@Override
public Float64 apply(final N value) {
final double x = value.doubleValue();
Float64 result = Float64.ZERO;
if (x >= _min && x <= _max) {
result = Float64.valueOf(_k*x + _d);
}
return result;
}
@Override
public String toString() {
return format(Locale.ENGLISH, "p(x) = %f·x + %f", _k, _d);
}
}
/**
* <p>
* <img
* src="doc-files/linear-cdf.gif"
* alt="f(x)=-\frac{(x^2-2x_2x)y_1 - (x^2 - 2x_1x)y_2}
* {2(x_2 - x_1)}"
* />
* </p>
*
* @author <a href="mailto:franz.wilhelmstoetter@gmx.at">Franz Wilhelmstötter</a>
* @since 1.0
* @version 1.0 — <em>$Date: 2014-03-01 $</em>
*/
static final class CDF<N extends Number & Comparable<? super N>>
implements
Function<N, Float64>,
Serializable
{
private static final long serialVersionUID = 1L;
private final double _x1;
private final double _x2;
private final double _k;
private final double _d;
public CDF(
final double x1, final double y1,
final double x2, final double y2
) {
_x1 = x1;
_x2 = x2;
_k = (y2 - y1)/(x2 - x1);
_d = y1 - _k*x1;
}
@Override
public Float64 apply(final N value) {
final double x = value.doubleValue();
Float64 result = null;
if (x < _x1) {
result = Float64.ZERO;
} else if (x > _x2) {
result = Float64.ONE;
} else {
// result = Float64.valueOf(
// -((x*x - 2*x*_x2)*_y1 - (x*x - 2*x*_x1)*_y2)/
// (2*(_x2 - _x1))
// );
result = Float64.valueOf( _k*x*x/2.0 + _d*x);
}
return result;
}
@Override
public String toString() {
return format(Locale.ENGLISH, "P(x) = %f·x² - %f·x", _k/2.0, _d);
}
}
private final Range<N> _domain;
private final Function<N, Float64> _cdf;
private final Function<N, Float64> _pdf;
private final double _x1;
private final double _x2;
private final double _y1;
private final double _y2;
public LinearDistribution(final Range<N> domain, final double y1) {
_domain = requireNonNull(domain);
_y1 = Math.max(y1, 0.0);
_x1 = domain.getMin().doubleValue();
_y2 = Math.max(y2(_x1, domain.getMax().doubleValue(), y1), 0.0);
if (_y2 == 0) {
_x2 = 2.0/_y1 + _x1;
} else {
_x2 = domain.getMax().doubleValue();
}
_cdf = new CDF<>(_x1, _y1, _x2, _y2);
_pdf = new PDF<>(_x1, _y1, _x2, _y2);
}
private static double y2(final double x1, final double x2, final double y1) {
return -((x2 - x1)*y1 - 2)/(x2 - x1);
}
@Override
public Range<N> getDomain() {
return _domain;
}
/**
* Return a new CDF object.
*
* <p>
* <img
* src="doc-files/linear-cdf.gif"
* alt="f(x)=-\frac{(x^2-2x_2x)y_1 - (x^2 - 2x_1x)y_2}
* {2(x_2 - x_1)}"
* />
* </p>
*
*/
@Override
public Function<N, Float64> getCDF() {
return _cdf;
}
/**
* Return a new PDF object.
*
* <p>
* <img
* src="doc-files/linear-pdf.gif"
* alt="f(x) = \left(
* \frac{y_2-y_1}{x_2-x_1} \cdot x +
* y_1-\frac{y_2-y_1}{x_2-x_1}\cdot x_1
* \right)"
* />
* </p>
*
*/
@Override
public Function<N, Float64> getPDF() {
return _pdf;
}
@Override
public int hashCode() {
return HashBuilder.of(getClass()).
and(_domain).
and(_x1).and(_x2).
and(_y1).and(_y2).value();
}
@Override
public boolean equals(final Object obj) {
if (obj == this) {
return true;
}
if (obj == null || getClass() != obj.getClass()) {
return false;
}
final LinearDistribution<?> dist = (LinearDistribution<?>)obj;
return eq(_domain, dist._domain) &&
eq(_x1, dist._x1) && eq(_x2, dist._x2) &&
eq(_y1, dist._y1) && eq(_y2, dist._y2);
}
@Override
public String toString() {
return format(
"LinearDistribution[(%f, %f), (%f, %f)]",
_x1, _y1, _x2, _y2
) ;
}
}