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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.
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package org.apache.commons.math3.analysis.function;

import org.apache.commons.math3.analysis.DifferentiableUnivariateFunction;
import org.apache.commons.math3.analysis.FunctionUtils;
import org.apache.commons.math3.analysis.ParametricUnivariateFunction;
import org.apache.commons.math3.analysis.UnivariateFunction;
import org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
import org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.NullArgumentException;
import org.apache.commons.math3.util.FastMath;


 simple harmonic oscillator function.
Since:
3.0/**
 * <a href="http://en.wikipedia.org/wiki/Harmonic_oscillator">
 *  simple harmonic oscillator</a> function.
 *
 * @since 3.0
 */
public class HarmonicOscillator implements UnivariateDifferentiableFunction, DifferentiableUnivariateFunction {
    
Amplitude. /** Amplitude. */
    private final double amplitude;
    
Angular frequency. /** Angular frequency. */
    private final double omega;
    
Phase. /** Phase. */
    private final double phase;

    
Harmonic oscillator function.
Params:
amplitude – Amplitude.
omega – Angular frequency.
phase – 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} /** {@inheritDoc} */
    public double value(double x) {
        return value(omega * x + phase, amplitude);
    }

    
{@inheritDoc}
Deprecated:
as of 3.1, replaced by value(DerivativeStructure)/** {@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 harmonic oscillator function, ordered as follows:

 
Amplitude
 
Angular frequency
 
Phase

/**
     * 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 x. 
Params:
x – Value for which the function must be computed.
param – Values of norm, mean and standard deviation.
Throws:
NullArgumentException – if param is null.
DimensionMismatchException – if the size of param is not 3.
Returns:
the value of the function./**
         * 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.
         */
        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 x. The components of the gradient vector are the partial derivatives of the function with respect to each of the parameters (amplitude, angular frequency and phase).
Params:
x – Value at which the gradient must be computed.
param – Values of amplitude, angular frequency and phase.
Throws:
NullArgumentException – if param is null.
DimensionMismatchException – if the size of param is not 3.
Returns:
the gradient vector at x./**
         * 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.
         */
        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 * FastMath.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 value(double, double[]) and gradient(double, double[]) methods. 
Params:
param – Values of norm, mean and standard deviation.
Throws:
NullArgumentException – if param is null.
DimensionMismatchException – if the size of param is not 3./**
         * 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);
            }
        }
    }

    
Params:
xTimesOmegaPlusPhase – omega * x + phase.
amplitude – Amplitude.
Returns:
the value of the harmonic oscillator function at x./**
     * @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 * FastMath.cos(xTimesOmegaPlusPhase);
    }

    
{@inheritDoc}
Since:
3.1/** {@inheritDoc}
     * @since 3.1
     */
    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 * FastMath.cos(alpha);
        if (f.length > 1) {
            f[1] = -amplitude * omega * FastMath.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);

    }

}