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Diffstat (limited to 'src/main/java/org/apache/commons/math3/analysis/function/Sigmoid.java')
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diff --git a/src/main/java/org/apache/commons/math3/analysis/function/Sigmoid.java b/src/main/java/org/apache/commons/math3/analysis/function/Sigmoid.java new file mode 100644 index 0000000..54639f9 --- /dev/null +++ b/src/main/java/org/apache/commons/math3/analysis/function/Sigmoid.java @@ -0,0 +1,218 @@ +/* + * 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 java.util.Arrays; + +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.NullArgumentException; +import org.apache.commons.math3.exception.DimensionMismatchException; +import org.apache.commons.math3.util.FastMath; + +/** + * <a href="http://en.wikipedia.org/wiki/Sigmoid_function"> + * Sigmoid</a> function. + * It is the inverse of the {@link Logit logit} function. + * A more flexible version, the generalised logistic, is implemented + * by the {@link Logistic} class. + * + * @since 3.0 + */ +public class Sigmoid implements UnivariateDifferentiableFunction, DifferentiableUnivariateFunction { + /** Lower asymptote. */ + private final double lo; + /** Higher asymptote. */ + private final double hi; + + /** + * Usual sigmoid function, where the lower asymptote is 0 and the higher + * asymptote is 1. + */ + public Sigmoid() { + this(0, 1); + } + + /** + * Sigmoid function. + * + * @param lo Lower asymptote. + * @param hi Higher asymptote. + */ + public Sigmoid(double lo, + double hi) { + this.lo = lo; + this.hi = hi; + } + + /** {@inheritDoc} + * @deprecated as of 3.1, replaced by {@link #value(DerivativeStructure)} + */ + @Deprecated + public UnivariateFunction derivative() { + return FunctionUtils.toDifferentiableUnivariateFunction(this).derivative(); + } + + /** {@inheritDoc} */ + public double value(double x) { + return value(x, lo, hi); + } + + /** + * Parametric function where the input array contains the parameters of + * the {@link Sigmoid#Sigmoid(double,double) sigmoid function}, ordered + * as follows: + * <ul> + * <li>Lower asymptote</li> + * <li>Higher asymptote</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 of lower asymptote and higher asymptote. + * @return the value of the function. + * @throws NullArgumentException if {@code param} is {@code null}. + * @throws DimensionMismatchException if the size of {@code param} is + * not 2. + */ + public double value(double x, double ... param) + throws NullArgumentException, + DimensionMismatchException { + validateParameters(param); + return Sigmoid.value(x, param[0], param[1]); + } + + /** + * 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> (lower asymptote and higher asymptote). + * + * @param x Value at which the gradient must be computed. + * @param param Values for lower asymptote and higher asymptote. + * @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 2. + */ + public double[] gradient(double x, double ... param) + throws NullArgumentException, + DimensionMismatchException { + validateParameters(param); + + final double invExp1 = 1 / (1 + FastMath.exp(-x)); + + return new double[] { 1 - invExp1, invExp1 }; + } + + /** + * 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 lower and higher asymptotes. + * @throws NullArgumentException if {@code param} is {@code null}. + * @throws DimensionMismatchException if the size of {@code param} is + * not 2. + */ + private void validateParameters(double[] param) + throws NullArgumentException, + DimensionMismatchException { + if (param == null) { + throw new NullArgumentException(); + } + if (param.length != 2) { + throw new DimensionMismatchException(param.length, 2); + } + } + } + + /** + * @param x Value at which to compute the sigmoid. + * @param lo Lower asymptote. + * @param hi Higher asymptote. + * @return the value of the sigmoid function at {@code x}. + */ + private static double value(double x, + double lo, + double hi) { + return lo + (hi - lo) / (1 + FastMath.exp(-x)); + } + + /** {@inheritDoc} + * @since 3.1 + */ + public DerivativeStructure value(final DerivativeStructure t) + throws DimensionMismatchException { + + double[] f = new double[t.getOrder() + 1]; + final double exp = FastMath.exp(-t.getValue()); + if (Double.isInfinite(exp)) { + + // special handling near lower boundary, to avoid NaN + f[0] = lo; + Arrays.fill(f, 1, f.length, 0.0); + + } else { + + // the nth order derivative of sigmoid has the form: + // dn(sigmoid(x)/dxn = P_n(exp(-x)) / (1+exp(-x))^(n+1) + // where P_n(t) is a degree n polynomial with normalized higher term + // P_0(t) = 1, P_1(t) = t, P_2(t) = t^2 - t, P_3(t) = t^3 - 4 t^2 + t... + // the general recurrence relation for P_n is: + // P_n(x) = n t P_(n-1)(t) - t (1 + t) P_(n-1)'(t) + final double[] p = new double[f.length]; + + final double inv = 1 / (1 + exp); + double coeff = hi - lo; + for (int n = 0; n < f.length; ++n) { + + // update and evaluate polynomial P_n(t) + double v = 0; + p[n] = 1; + for (int k = n; k >= 0; --k) { + v = v * exp + p[k]; + if (k > 1) { + p[k - 1] = (n - k + 2) * p[k - 2] - (k - 1) * p[k - 1]; + } else { + p[0] = 0; + } + } + + coeff *= inv; + f[n] = coeff * v; + + } + + // fix function value + f[0] += lo; + + } + + return t.compose(f); + + } + +} |