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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.FunctionUtils;
import org.apache.commons.math3.analysis.UnivariateFunction;
import org.apache.commons.math3.analysis.DifferentiableUnivariateFunction;
import org.apache.commons.math3.analysis.ParametricUnivariateFunction;
import org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
import org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;
import org.apache.commons.math3.exception.NotStrictlyPositiveException;
import org.apache.commons.math3.exception.NullArgumentException;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.util.FastMath;
/**
*
* Generalised logistic function.
*
* @since 3.0
*/
public class Logistic implements UnivariateDifferentiableFunction, DifferentiableUnivariateFunction {
/** 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;
/**
* @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 NotStrictlyPositiveException if {@code n <= 0}.
*/
public Logistic(double k,
double m,
double b,
double q,
double a,
double n)
throws NotStrictlyPositiveException {
if (n <= 0) {
throw new NotStrictlyPositiveException(n);
}
this.k = k;
this.m = m;
this.b = b;
this.q = q;
this.a = a;
oneOverN = 1 / n;
}
/** {@inheritDoc} */
public double value(double x) {
return value(m - x, k, b, q, a, oneOverN);
}
/** {@inheritDoc}
* @deprecated as of 3.1, replaced by {@link #value(DerivativeStructure)}
*/
@Deprecated
public UnivariateFunction derivative() {
return FunctionUtils.toDifferentiableUnivariateFunction(this).derivative();
}
/**
* 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:
*
* - k
* - m
* - b
* - q
* - a
* - n
*
*/
public static class Parametric implements ParametricUnivariateFunction {
/**
* 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 DimensionMismatchException if the size of {@code param} is
* not 6.
* @throws NotStrictlyPositiveException if {@code param[5] <= 0}.
*/
public double value(double x, double ... param)
throws NullArgumentException,
DimensionMismatchException,
NotStrictlyPositiveException {
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
* parameters.
*
* @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 DimensionMismatchException if the size of {@code param} is
* not 6.
* @throws NotStrictlyPositiveException if {@code param[5] <= 0}.
*/
public double[] gradient(double x, double ... param)
throws NullArgumentException,
DimensionMismatchException,
NotStrictlyPositiveException {
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 DimensionMismatchException if the size of {@code param} is
* not 6.
* @throws NotStrictlyPositiveException if {@code param[5] <= 0}.
*/
private void validateParameters(double[] param)
throws NullArgumentException,
DimensionMismatchException,
NotStrictlyPositiveException {
if (param == null) {
throw new NullArgumentException();
}
if (param.length != 6) {
throw new DimensionMismatchException(param.length, 6);
}
if (param[5] <= 0) {
throw new NotStrictlyPositiveException(param[5]);
}
}
}
/**
* @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}
* @since 3.1
*/
public DerivativeStructure value(final DerivativeStructure t) {
return t.negate().add(m).multiply(b).exp().multiply(q).add(1).pow(oneOverN).reciprocal().multiply(k - a).add(a);
}
}