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/*
 * 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); } }




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