Logistic.java
/*
* 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
*
* https://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.
*/
/*
* This is not the original file distributed by the Apache Software Foundation
* It has been modified by the Hipparchus project
*/
package org.hipparchus.analysis.function;
import org.hipparchus.analysis.ParametricUnivariateFunction;
import org.hipparchus.analysis.differentiation.Derivative;
import org.hipparchus.analysis.differentiation.UnivariateDifferentiableFunction;
import org.hipparchus.exception.LocalizedCoreFormats;
import org.hipparchus.exception.MathIllegalArgumentException;
import org.hipparchus.exception.NullArgumentException;
import org.hipparchus.util.FastMath;
import org.hipparchus.util.MathUtils;
/**
* <a href="http://en.wikipedia.org/wiki/Generalised_logistic_function">
* Generalised logistic</a> function.
*
*/
public class Logistic implements UnivariateDifferentiableFunction {
/** Lower asymptote. */
private final double a;
/** Upper asymptote. */
private final double k;
/** Growth rate. */
private final double b;
/** Parameter that affects near which asymptote maximum growth occurs. */
private final double oneOverN;
/** Parameter that affects the position of the curve along the ordinate axis. */
private final double q;
/** Abscissa of maximum growth. */
private final double m;
/** Simple constructor.
* @param k If {@code b > 0}, value of the function for x going towards +∞.
* If {@code b < 0}, value of the function for x going towards -∞.
* @param m Abscissa of maximum growth.
* @param b Growth rate.
* @param q Parameter that affects the position of the curve along the
* ordinate axis.
* @param a If {@code b > 0}, value of the function for x going towards -∞.
* If {@code b < 0}, value of the function for x going towards +∞.
* @param n Parameter that affects near which asymptote the maximum
* growth occurs.
* @throws MathIllegalArgumentException if {@code n <= 0}.
*/
public Logistic(double k,
double m,
double b,
double q,
double a,
double n)
throws MathIllegalArgumentException {
if (n <= 0) {
throw new MathIllegalArgumentException(LocalizedCoreFormats.NUMBER_TOO_SMALL_BOUND_EXCLUDED,
n, 0);
}
this.k = k;
this.m = m;
this.b = b;
this.q = q;
this.a = a;
oneOverN = 1 / n;
}
/** {@inheritDoc} */
@Override
public double value(double x) {
return value(m - x, k, b, q, a, oneOverN);
}
/**
* Parametric function where the input array contains the parameters of
* the {@link Logistic#Logistic(double,double,double,double,double,double)
* logistic function}, ordered as follows:
* <ul>
* <li>k</li>
* <li>m</li>
* <li>b</li>
* <li>q</li>
* <li>a</li>
* <li>n</li>
* </ul>
*/
public static class Parametric implements ParametricUnivariateFunction {
/** Empty constructor.
* <p>
* This constructor is not strictly necessary, but it prevents spurious
* javadoc warnings with JDK 18 and later.
* </p>
* @since 3.0
*/
public Parametric() { // NOPMD - unnecessary constructor added intentionally to make javadoc happy
// nothing to do
}
/**
* Computes the value of the sigmoid at {@code x}.
*
* @param x Value for which the function must be computed.
* @param param Values for {@code k}, {@code m}, {@code b}, {@code q},
* {@code a} and {@code n}.
* @return the value of the function.
* @throws NullArgumentException if {@code param} is {@code null}.
* @throws MathIllegalArgumentException if the size of {@code param} is
* not 6.
* @throws MathIllegalArgumentException if {@code param[5] <= 0}.
*/
@Override
public double value(double x, double ... param)
throws MathIllegalArgumentException, NullArgumentException {
validateParameters(param);
return Logistic.value(param[1] - x, param[0],
param[2], param[3],
param[4], 1 / param[5]);
}
/**
* Computes the value of the gradient at {@code x}.
* The components of the gradient vector are the partial
* derivatives of the function with respect to each of the
* <em>parameters</em>.
*
* @param x Value at which the gradient must be computed.
* @param param Values for {@code k}, {@code m}, {@code b}, {@code q},
* {@code a} and {@code n}.
* @return the gradient vector at {@code x}.
* @throws NullArgumentException if {@code param} is {@code null}.
* @throws MathIllegalArgumentException if the size of {@code param} is
* not 6.
* @throws MathIllegalArgumentException if {@code param[5] <= 0}.
*/
@Override
public double[] gradient(double x, double ... param)
throws MathIllegalArgumentException, NullArgumentException {
validateParameters(param);
final double b = param[2];
final double q = param[3];
final double mMinusX = param[1] - x;
final double oneOverN = 1 / param[5];
final double exp = FastMath.exp(b * mMinusX);
final double qExp = q * exp;
final double qExp1 = qExp + 1;
final double factor1 = (param[0] - param[4]) * oneOverN / FastMath.pow(qExp1, oneOverN);
final double factor2 = -factor1 / qExp1;
// Components of the gradient.
final double gk = Logistic.value(mMinusX, 1, b, q, 0, oneOverN);
final double gm = factor2 * b * qExp;
final double gb = factor2 * mMinusX * qExp;
final double gq = factor2 * exp;
final double ga = Logistic.value(mMinusX, 0, b, q, 1, oneOverN);
final double gn = factor1 * FastMath.log(qExp1) * oneOverN;
return new double[] { gk, gm, gb, gq, ga, gn };
}
/**
* Validates parameters to ensure they are appropriate for the evaluation of
* the {@link #value(double,double[])} and {@link #gradient(double,double[])}
* methods.
*
* @param param Values for {@code k}, {@code m}, {@code b}, {@code q},
* {@code a} and {@code n}.
* @throws NullArgumentException if {@code param} is {@code null}.
* @throws MathIllegalArgumentException if the size of {@code param} is
* not 6.
* @throws MathIllegalArgumentException if {@code param[5] <= 0}.
*/
private void validateParameters(double[] param)
throws MathIllegalArgumentException, NullArgumentException {
MathUtils.checkNotNull(param);
MathUtils.checkDimension(param.length, 6);
if (param[5] <= 0) {
throw new MathIllegalArgumentException(LocalizedCoreFormats.NUMBER_TOO_SMALL_BOUND_EXCLUDED,
param[5], 0);
}
}
}
/**
* @param mMinusX {@code m - x}.
* @param k {@code k}.
* @param b {@code b}.
* @param q {@code q}.
* @param a {@code a}.
* @param oneOverN {@code 1 / n}.
* @return the value of the function.
*/
private static double value(double mMinusX,
double k,
double b,
double q,
double a,
double oneOverN) {
return a + (k - a) / FastMath.pow(1 + q * FastMath.exp(b * mMinusX), oneOverN);
}
/** {@inheritDoc}
*/
@Override
public <T extends Derivative<T>> T value(T t) {
return t.negate().add(m).multiply(b).exp().multiply(q).add(1).pow(oneOverN).reciprocal().multiply(k - a).add(a);
}
}