| /* |
| * 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.NullArgumentException; |
| import org.apache.commons.math4.core.jdkmath.JdkMath; |
| |
| /** |
| * <a href="http://en.wikipedia.org/wiki/Harmonic_oscillator"> |
| * simple harmonic oscillator</a> function. |
| * |
| * @since 3.0 |
| */ |
| public class HarmonicOscillator implements UnivariateDifferentiableFunction { |
| /** Amplitude. */ |
| private final double amplitude; |
| /** Angular frequency. */ |
| private final double omega; |
| /** Phase. */ |
| private final double phase; |
| |
| /** |
| * Harmonic oscillator function. |
| * |
| * @param amplitude Amplitude. |
| * @param omega Angular frequency. |
| * @param phase Phase. |
| */ |
| public HarmonicOscillator(double amplitude, |
| double omega, |
| double phase) { |
| this.amplitude = amplitude; |
| this.omega = omega; |
| this.phase = phase; |
| } |
| |
| /** {@inheritDoc} */ |
| @Override |
| public double value(double x) { |
| return value(omega * x + phase, amplitude); |
| } |
| |
| /** |
| * Parametric function where the input array contains the parameters of |
| * the harmonic oscillator function. Ordered as follows: |
| * <ul> |
| * <li>Amplitude</li> |
| * <li>Angular frequency</li> |
| * <li>Phase</li> |
| * </ul> |
| */ |
| public static class Parametric implements ParametricUnivariateFunction { |
| /** |
| * Computes the value of the harmonic oscillator 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. |
| */ |
| @Override |
| public double value(double x, double ... param) |
| throws NullArgumentException, |
| DimensionMismatchException { |
| validateParameters(param); |
| return HarmonicOscillator.value(x * param[1] + param[2], param[0]); |
| } |
| |
| /** |
| * 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> (amplitude, angular frequency and phase). |
| * |
| * @param x Value at which the gradient must be computed. |
| * @param param Values of amplitude, angular frequency and phase. |
| * @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. |
| */ |
| @Override |
| public double[] gradient(double x, double ... param) |
| throws NullArgumentException, |
| DimensionMismatchException { |
| validateParameters(param); |
| |
| final double amplitude = param[0]; |
| final double omega = param[1]; |
| final double phase = param[2]; |
| |
| final double xTimesOmegaPlusPhase = omega * x + phase; |
| final double a = HarmonicOscillator.value(xTimesOmegaPlusPhase, 1); |
| final double p = -amplitude * JdkMath.sin(xTimesOmegaPlusPhase); |
| final double w = p * x; |
| |
| return new double[] { a, w, p }; |
| } |
| |
| /** |
| * 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. |
| */ |
| private void validateParameters(double[] param) |
| throws NullArgumentException, |
| DimensionMismatchException { |
| if (param == null) { |
| throw new NullArgumentException(); |
| } |
| if (param.length != 3) { |
| throw new DimensionMismatchException(param.length, 3); |
| } |
| } |
| } |
| |
| /** |
| * @param xTimesOmegaPlusPhase {@code omega * x + phase}. |
| * @param amplitude Amplitude. |
| * @return the value of the harmonic oscillator function at {@code x}. |
| */ |
| private static double value(double xTimesOmegaPlusPhase, |
| double amplitude) { |
| return amplitude * JdkMath.cos(xTimesOmegaPlusPhase); |
| } |
| |
| /** {@inheritDoc} |
| * @since 3.1 |
| */ |
| @Override |
| public DerivativeStructure value(final DerivativeStructure t) |
| throws DimensionMismatchException { |
| final double x = t.getValue(); |
| double[] f = new double[t.getOrder() + 1]; |
| |
| final double alpha = omega * x + phase; |
| f[0] = amplitude * JdkMath.cos(alpha); |
| if (f.length > 1) { |
| f[1] = -amplitude * omega * JdkMath.sin(alpha); |
| final double mo2 = - omega * omega; |
| for (int i = 2; i < f.length; ++i) { |
| f[i] = mo2 * f[i - 2]; |
| } |
| } |
| |
| return t.compose(f); |
| |
| } |
| |
| } |