SphericalFirstEstimator.java

package org.drip.specialfunction.bessel;

/*
 * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
 */

/*!
 * Copyright (C) 2020 Lakshmi Krishnamurthy
 * Copyright (C) 2019 Lakshmi Krishnamurthy
 * 
 *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
 *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
 *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
 *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
 *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
 *      and computational support.
 *  
 *      https://lakshmidrip.github.io/DROP/
 *  
 *  DROP is composed of three modules:
 *  
 *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
 *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
 *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
 * 
 *  DROP Product Core implements libraries for the following:
 *  - Fixed Income Analytics
 *  - Loan Analytics
 *  - Transaction Cost Analytics
 * 
 *  DROP Portfolio Core implements libraries for the following:
 *  - Asset Allocation Analytics
 *  - Asset Liability Management Analytics
 *  - Capital Estimation Analytics
 *  - Exposure Analytics
 *  - Margin Analytics
 *  - XVA Analytics
 * 
 *  DROP Computational Core implements libraries for the following:
 *  - Algorithm Support
 *  - Computation Support
 *  - Function Analysis
 *  - Model Validation
 *  - Numerical Analysis
 *  - Numerical Optimizer
 *  - Spline Builder
 *  - Statistical Learning
 * 
 *  Documentation for DROP is Spread Over:
 * 
 *  - Main                     => https://lakshmidrip.github.io/DROP/
 *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
 *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
 *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
 *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
 *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
 *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
 *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
 *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
 *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
 *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
 * 
 *  Licensed 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.
 */

/**
 * <i>SphericalFirstEstimator</i> implements the Integral Estimator for the Spherical Bessel Function of the
 * First Kind. The References are:
 * 
 * <br><br>
 *  <ul>
 *      <li>
 *          Abramowitz, M., and I. A. Stegun (2007): <i>Handbook of Mathematics Functions</i> <b>Dover Book
 *              on Mathematics</b>
 *      </li>
 *      <li>
 *          Arfken, G. B., and H. J. Weber (2005): <i>Mathematical Methods for Physicists 6<sup>th</sup>
 *              Edition</i> <b>Harcourt</b> San Diego
 *      </li>
 *      <li>
 *          Temme N. M. (1996): <i>Special Functions: An Introduction to the Classical Functions of
 *              Mathematical Physics 2<sup>nd</sup> Edition</i> <b>Wiley</b> New York
 *      </li>
 *      <li>
 *          Watson, G. N. (1995): <i>A Treatise on the Theory of Bessel Functions</i> <b>Cambridge University
 *              Press</b>
 *      </li>
 *      <li>
 *          Wikipedia (2019): Bessel Function https://en.wikipedia.org/wiki/Bessel_function
 *      </li>
 *  </ul>
 *
 *  <br><br>
 *  <ul>
 *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
 *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/FunctionAnalysisLibrary.md">Function Analysis Library</a></li>
 *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/specialfunction/README.md">Special Function Implementation Analysis</a></li>
 *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/specialfunction/bessel/README.md">Ordered Bessel Function Variant Estimators</a></li>
 *  </ul>
 *
 * @author Lakshmi Krishnamurthy
 */

public class SphericalFirstEstimator extends
    org.drip.specialfunction.definition.SphericalBesselFirstKindEstimator
{
    private org.drip.specialfunction.definition.BesselFirstKindEstimator _besselFirstKindEstimator = null;

    /**
     * Retrieve the Order 0 Spherical Bessel First Kind Estimator
     * 
     * @return The Order 0 Spherical Bessel First Kind Estimator
     */

    public static final org.drip.specialfunction.definition.SphericalBesselFirstKindEstimator OrderZero()
    {
        return new org.drip.specialfunction.definition.SphericalBesselFirstKindEstimator()
        {
            @Override public double smallJ (
                final double alpha,
                final double z)
                throws java.lang.Exception
            {
                if (0. != alpha ||
                    !org.drip.numerical.common.NumberUtil.IsValid (z))
                {
                    throw new java.lang.Exception
                        ("SphericalFirstEstimator::OrderZero::smallJ => Invalid Inputs");
                }

                return 0. == z ? 1. : java.lang.Math.sin (z) / z;
            }
        };
    }

    /**
     * Retrieve the Order +1 Spherical Bessel First Kind Estimator
     * 
     * @return The Order +1 Spherical Bessel First Kind Estimator
     */

    public static final org.drip.specialfunction.definition.SphericalBesselFirstKindEstimator OrderPlusOne()
    {
        return new org.drip.specialfunction.definition.SphericalBesselFirstKindEstimator()
        {
            @Override public double smallJ (
                final double alpha,
                final double z)
                throws java.lang.Exception
            {
                if (1. != alpha ||
                    !org.drip.numerical.common.NumberUtil.IsValid (z))
                {
                    throw new java.lang.Exception
                        ("SphericalFirstEstimator::OrderPlusOne::smallJ => Invalid Inputs");
                }

                return java.lang.Math.sin (z) / (z * z) - java.lang.Math.cos (z) / z;
            }
        };
    }

    /**
     * Retrieve the Order -1 Spherical Bessel First Kind Estimator
     * 
     * @return The Order -1 Spherical Bessel First Kind Estimator
     */

    public static final org.drip.specialfunction.definition.SphericalBesselFirstKindEstimator OrderMinusOne()
    {
        return new org.drip.specialfunction.definition.SphericalBesselFirstKindEstimator()
        {
            @Override public double smallJ (
                final double alpha,
                final double z)
                throws java.lang.Exception
            {
                if (-1. != alpha ||
                    !org.drip.numerical.common.NumberUtil.IsValid (z))
                {
                    throw new java.lang.Exception
                        ("SphericalFirstEstimator::OrderMinusOne::smallJ => Invalid Inputs");
                }

                return java.lang.Math.cos (z) / z;
            }
        };
    }

    /**
     * Retrieve the Order +2 Spherical Bessel First Kind Estimator
     * 
     * @return The Order +2 Spherical Bessel First Kind Estimator
     */

    public static final org.drip.specialfunction.definition.SphericalBesselFirstKindEstimator OrderPlusTwo()
    {
        return new org.drip.specialfunction.definition.SphericalBesselFirstKindEstimator()
        {
            @Override public double smallJ (
                final double alpha,
                final double z)
                throws java.lang.Exception
            {
                if (2. != alpha ||
                    !org.drip.numerical.common.NumberUtil.IsValid (z))
                {
                    throw new java.lang.Exception
                        ("SphericalFirstEstimator::OrderPlusTwo::smallJ => Invalid Inputs");
                }

                double oneOverZ = 1. / z;
                double oneOverZ2 = oneOverZ * oneOverZ;

                return (3. * oneOverZ2 - 1.) * java.lang.Math.sin (z) * oneOverZ -
                    3. * java.lang.Math.cos (z) * oneOverZ2;
            }
        };
    }

    /**
     * Retrieve the Order -2 Spherical Bessel First Kind Estimator
     * 
     * @return The Order -2 Spherical Bessel First Kind Estimator
     */

    public static final org.drip.specialfunction.definition.SphericalBesselFirstKindEstimator OrderMinusTwo()
    {
        return new org.drip.specialfunction.definition.SphericalBesselFirstKindEstimator()
        {
            @Override public double smallJ (
                final double alpha,
                final double z)
                throws java.lang.Exception
            {
                if (-2. != alpha ||
                    !org.drip.numerical.common.NumberUtil.IsValid (z))
                {
                    throw new java.lang.Exception
                        ("SphericalFirstEstimator::OrderMinusTwo::smallJ => Invalid Inputs");
                }

                double oneOverZ = 1. / z;

                return -1. * java.lang.Math.cos (z) * oneOverZ * oneOverZ -
                    java.lang.Math.sin (z) * oneOverZ;
            }
        };
    }

    /**
     * Retrieve the Order +3 Spherical Bessel First Kind Estimator
     * 
     * @return The Order +3 Spherical Bessel First Kind Estimator
     */

    public static final org.drip.specialfunction.definition.SphericalBesselFirstKindEstimator
        OrderPlusThree()
    {
        return new org.drip.specialfunction.definition.SphericalBesselFirstKindEstimator()
        {
            @Override public double smallJ (
                final double alpha,
                final double z)
                throws java.lang.Exception
            {
                if (3. != alpha ||
                    !org.drip.numerical.common.NumberUtil.IsValid (z))
                {
                    throw new java.lang.Exception
                        ("SphericalFirstEstimator::OrderPlusThree::smallJ => Invalid Inputs");
                }

                double oneOverZ = 1. / z;
                double oneOverZ2 = oneOverZ * oneOverZ;

                return (15. * oneOverZ2 * oneOverZ - 6. * oneOverZ) * java.lang.Math.sin (z) * oneOverZ -
                    (15. * oneOverZ2 - 1.) * java.lang.Math.cos (z) * oneOverZ;
            }
        };
    }

    /**
     * Retrieve the Order -3 Spherical Bessel First Kind Estimator
     * 
     * @return The Order -3 Spherical Bessel First Kind Estimator
     */

    public static final org.drip.specialfunction.definition.SphericalBesselFirstKindEstimator
        OrderMinusThree()
    {
        return new org.drip.specialfunction.definition.SphericalBesselFirstKindEstimator()
        {
            @Override public double smallJ (
                final double alpha,
                final double z)
                throws java.lang.Exception
            {
                if (-3. != alpha ||
                    !org.drip.numerical.common.NumberUtil.IsValid (z))
                {
                    throw new java.lang.Exception
                        ("SphericalFirstEstimator::OrderMinusThree::smallJ => Invalid Inputs");
                }

                double oneOverZ = 1. / z;
                double oneOverZ2 = oneOverZ * oneOverZ;

                return (1. - 3. * oneOverZ2) * java.lang.Math.cos (z) * oneOverZ -
                    3. * java.lang.Math.sin (z) * oneOverZ2;
            }
        };
    }

    /**
     * Retrieve the Order -4 Spherical Bessel First Kind Estimator
     * 
     * @return The Order -4 Spherical Bessel First Kind Estimator
     */

    public static final org.drip.specialfunction.definition.SphericalBesselFirstKindEstimator
        OrderMinusFour()
    {
        return new org.drip.specialfunction.definition.SphericalBesselFirstKindEstimator()
        {
            @Override public double smallJ (
                final double alpha,
                final double z)
                throws java.lang.Exception
            {
                if (-4. != alpha ||
                    !org.drip.numerical.common.NumberUtil.IsValid (z))
                {
                    throw new java.lang.Exception
                        ("SphericalFirstEstimator::OrderOrderMinusFour::smallJ => Invalid Inputs");
                }

                double oneOverZ = 1. / z;
                double oneOverZ2 = oneOverZ * oneOverZ;

                return (6. * oneOverZ - 15. * oneOverZ2 * oneOverZ) * java.lang.Math.cos (z) * oneOverZ -
                    (15. * oneOverZ2 - 1.) * java.lang.Math.sin (z) * oneOverZ;
            }
        };
    }

    /**
     * SphericalFirstEstimator Constructor
     * 
     * @param besselFirstKindEstimator Bessel Function First Kind Estimator
     * 
     * @throws java.lang.Exception Thrown if Inputs are Invalid
     */

    public SphericalFirstEstimator (
        final org.drip.specialfunction.definition.BesselFirstKindEstimator besselFirstKindEstimator)
        throws java.lang.Exception
    {
        if (null == (_besselFirstKindEstimator = besselFirstKindEstimator))
        {
            throw new java.lang.Exception ("SphericalFirstEstimator Constructor => Invalid Inputs");
        }
    }

    @Override public double smallJ (
        final double alpha,
        final double z)
        throws java.lang.Exception
    {
        return java.lang.Math.sqrt (0.5 * java.lang.Math.PI / z) * _besselFirstKindEstimator.bigJ (
            alpha + 0.5,
            z
        );
    }

    /**
     * Retrieve the Bessel Function First Kind Estimator
     * 
     * @return Bessel Function First Kind Estimator
     */

    public org.drip.specialfunction.definition.BesselFirstKindEstimator besselFirstKindEstimator()
    {
        return _besselFirstKindEstimator;
    }
}