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Diffstat (limited to 'src/main/java/org/apache/commons/math3/analysis/function/Gaussian.java')
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diff --git a/src/main/java/org/apache/commons/math3/analysis/function/Gaussian.java b/src/main/java/org/apache/commons/math3/analysis/function/Gaussian.java new file mode 100644 index 0000000..8c64c8b --- /dev/null +++ b/src/main/java/org/apache/commons/math3/analysis/function/Gaussian.java @@ -0,0 +1,259 @@ +/* + * 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.NotStrictlyPositiveException; +import org.apache.commons.math3.exception.NullArgumentException; +import org.apache.commons.math3.exception.DimensionMismatchException; +import org.apache.commons.math3.util.FastMath; +import org.apache.commons.math3.util.Precision; + +/** + * <a href="http://en.wikipedia.org/wiki/Gaussian_function"> + * Gaussian</a> function. + * + * @since 3.0 + */ +public class Gaussian implements UnivariateDifferentiableFunction, DifferentiableUnivariateFunction { + /** Mean. */ + private final double mean; + /** Inverse of the standard deviation. */ + private final double is; + /** Inverse of twice the square of the standard deviation. */ + private final double i2s2; + /** Normalization factor. */ + private final double norm; + + /** + * Gaussian with given normalization factor, mean and standard deviation. + * + * @param norm Normalization factor. + * @param mean Mean. + * @param sigma Standard deviation. + * @throws NotStrictlyPositiveException if {@code sigma <= 0}. + */ + public Gaussian(double norm, + double mean, + double sigma) + throws NotStrictlyPositiveException { + if (sigma <= 0) { + throw new NotStrictlyPositiveException(sigma); + } + + this.norm = norm; + this.mean = mean; + this.is = 1 / sigma; + this.i2s2 = 0.5 * is * is; + } + + /** + * Normalized gaussian with given mean and standard deviation. + * + * @param mean Mean. + * @param sigma Standard deviation. + * @throws NotStrictlyPositiveException if {@code sigma <= 0}. + */ + public Gaussian(double mean, + double sigma) + throws NotStrictlyPositiveException { + this(1 / (sigma * FastMath.sqrt(2 * Math.PI)), mean, sigma); + } + + /** + * Normalized gaussian with zero mean and unit standard deviation. + */ + public Gaussian() { + this(0, 1); + } + + /** {@inheritDoc} */ + public double value(double x) { + return value(x - mean, norm, i2s2); + } + + /** {@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 Gaussian, ordered as follows: + * <ul> + * <li>Norm</li> + * <li>Mean</li> + * <li>Standard deviation</li> + * </ul> + */ + public static class Parametric implements ParametricUnivariateFunction { + /** + * Computes the value of the Gaussian at {@code x}. + * + * @param x Value for which the function must be computed. + * @param param Values of norm, mean and standard deviation. + * @return the value of the function. + * @throws NullArgumentException if {@code param} is {@code null}. + * @throws DimensionMismatchException if the size of {@code param} is + * not 3. + * @throws NotStrictlyPositiveException if {@code param[2]} is negative. + */ + public double value(double x, double ... param) + throws NullArgumentException, + DimensionMismatchException, + NotStrictlyPositiveException { + validateParameters(param); + + final double diff = x - param[1]; + final double i2s2 = 1 / (2 * param[2] * param[2]); + return Gaussian.value(diff, param[0], i2s2); + } + + /** + * 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> (norm, mean and standard deviation). + * + * @param x Value at which the gradient must be computed. + * @param param Values of norm, mean and standard deviation. + * @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 3. + * @throws NotStrictlyPositiveException if {@code param[2]} is negative. + */ + public double[] gradient(double x, double ... param) + throws NullArgumentException, + DimensionMismatchException, + NotStrictlyPositiveException { + validateParameters(param); + + final double norm = param[0]; + final double diff = x - param[1]; + final double sigma = param[2]; + final double i2s2 = 1 / (2 * sigma * sigma); + + final double n = Gaussian.value(diff, 1, i2s2); + final double m = norm * n * 2 * i2s2 * diff; + final double s = m * diff / sigma; + + return new double[] { n, m, s }; + } + + /** + * 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 of norm, mean and standard deviation. + * @throws NullArgumentException if {@code param} is {@code null}. + * @throws DimensionMismatchException if the size of {@code param} is + * not 3. + * @throws NotStrictlyPositiveException if {@code param[2]} is negative. + */ + private void validateParameters(double[] param) + throws NullArgumentException, + DimensionMismatchException, + NotStrictlyPositiveException { + if (param == null) { + throw new NullArgumentException(); + } + if (param.length != 3) { + throw new DimensionMismatchException(param.length, 3); + } + if (param[2] <= 0) { + throw new NotStrictlyPositiveException(param[2]); + } + } + } + + /** + * @param xMinusMean {@code x - mean}. + * @param norm Normalization factor. + * @param i2s2 Inverse of twice the square of the standard deviation. + * @return the value of the Gaussian at {@code x}. + */ + private static double value(double xMinusMean, + double norm, + double i2s2) { + return norm * FastMath.exp(-xMinusMean * xMinusMean * i2s2); + } + + /** {@inheritDoc} + * @since 3.1 + */ + public DerivativeStructure value(final DerivativeStructure t) + throws DimensionMismatchException { + + final double u = is * (t.getValue() - mean); + double[] f = new double[t.getOrder() + 1]; + + // the nth order derivative of the Gaussian has the form: + // dn(g(x)/dxn = (norm / s^n) P_n(u) exp(-u^2/2) with u=(x-m)/s + // where P_n(u) is a degree n polynomial with same parity as n + // P_0(u) = 1, P_1(u) = -u, P_2(u) = u^2 - 1, P_3(u) = -u^3 + 3 u... + // the general recurrence relation for P_n is: + // P_n(u) = P_(n-1)'(u) - u P_(n-1)(u) + // as per polynomial parity, we can store coefficients of both P_(n-1) and P_n in the same array + final double[] p = new double[f.length]; + p[0] = 1; + final double u2 = u * u; + double coeff = norm * FastMath.exp(-0.5 * u2); + if (coeff <= Precision.SAFE_MIN) { + Arrays.fill(f, 0.0); + } else { + f[0] = coeff; + for (int n = 1; n < f.length; ++n) { + + // update and evaluate polynomial P_n(x) + double v = 0; + p[n] = -p[n - 1]; + for (int k = n; k >= 0; k -= 2) { + v = v * u2 + p[k]; + if (k > 2) { + p[k - 2] = (k - 1) * p[k - 1] - p[k - 3]; + } else if (k == 2) { + p[0] = p[1]; + } + } + if ((n & 0x1) == 1) { + v *= u; + } + + coeff *= is; + f[n] = coeff * v; + + } + } + + return t.compose(f); + + } + +} |