| /* |
| * 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.math4.legacy.analysis.function; |
| |
| import org.apache.commons.math4.legacy.analysis.ParametricUnivariateFunction; |
| import org.apache.commons.math4.legacy.analysis.differentiation.DerivativeStructure; |
| import org.apache.commons.math4.legacy.analysis.differentiation.UnivariateDifferentiableFunction; |
| import org.apache.commons.math4.legacy.exception.DimensionMismatchException; |
| import org.apache.commons.math4.legacy.exception.NotStrictlyPositiveException; |
| import org.apache.commons.math4.legacy.exception.NullArgumentException; |
| import org.apache.commons.math4.legacy.core.jdkmath.AccurateMath; |
| |
| /** |
| * <a href="http://en.wikipedia.org/wiki/Generalised_logistic_function"> |
| * Generalised logistic</a> function. |
| * |
| * @since 3.0 |
| */ |
| 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; |
| |
| /** |
| * @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} */ |
| @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 { |
| /** |
| * 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}. |
| */ |
| @Override |
| 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 |
| * <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 DimensionMismatchException if the size of {@code param} is |
| * not 6. |
| * @throws NotStrictlyPositiveException if {@code param[5] <= 0}. |
| */ |
| @Override |
| 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 = AccurateMath.exp(b * mMinusX); |
| final double qExp = q * exp; |
| final double qExp1 = qExp + 1; |
| final double factor1 = (param[0] - param[4]) * oneOverN / AccurateMath.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 * AccurateMath.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) / AccurateMath.pow(1 + q * AccurateMath.exp(b * mMinusX), oneOverN); |
| } |
| |
| /** {@inheritDoc} |
| * @since 3.1 |
| */ |
| @Override |
| 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); |
| } |
| |
| } |
