RiemannSphereSpanner.java

package org.drip.specialfunction.group;

/*
 * -*- 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>RiemannSphereSpanner</i> determines the Conformality and Tile Scheme of the Schwarz Singular Triangle
 * Maps over the Riemann Sphere. The References are:
 * 
 * <br><br>
 *  <ul>
 *      <li>
 *          Gessel, I., and D. Stanton (1982): Strange Evaluations of Hyper-geometric Series <i>SIAM Journal
 *              on Mathematical Analysis</i> <b>13 (2)</b> 295-308
 *      </li>
 *      <li>
 *          Koepf, W (1995): Algorithms for m-fold Hyper-geometric Summation <i>Journal of Symbolic
 *              Computation</i> <b>20 (4)</b> 399-417
 *      </li>
 *      <li>
 *          Lavoie, J. L., F. Grondin, and A. K. Rathie (1996): Generalization of Whipple’s Theorem on the
 *              Sum of a (_2^3)F(a,b;c;z) <i>Journal of Computational and Applied Mathematics</i> <b>72</b>
 *              293-300
 *      </li>
 *      <li>
 *          National Institute of Standards and Technology (2019): Hyper-geometric Function
 *              https://dlmf.nist.gov/15
 *      </li>
 *      <li>
 *          Wikipedia (2019): Hyper-geometric Function https://en.wikipedia.org/wiki/Hypergeometric_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/group/README.md">Special Function Singularity Solution Group</a></li>
 *  </ul>
 *
 * @author Lakshmi Krishnamurthy
 */

public class RiemannSphereSpanner
{

    /**
     * Schwarz Triangle Tiles Nothing
     */

    public static final int SCHWARZ_TRIANGLE_TILES_NOTHING = 0;

    /**
     * Schwarz Triangle Tiles the Riemann Sphere
     */

    public static final int SCHWARZ_TRIANGLE_TILES_RIEMANN_SPHERE = 1;

    /**
     * Schwarz Triangle Tiles the Complex Plane
     */

    public static final int SCHWARZ_TRIANGLE_TILES_COMPLEX_PLANE = 2;

    /**
     * Schwarz Triangle Tiles the Upper Half Plane
     */

    public static final int SCHWARZ_TRIANGLE_TILES_UPPER_HALF_PLANE = 3;

    private org.drip.specialfunction.group.SchwarzTriangleMap[] _schwarzTriangleMapArray = null;

    /**
     * RiemannSphereSpanner Constructor
     * 
     * @param schwarzTriangleMapArray The Schwarz Triangle Map Array
     * 
     * @throws java.lang.Exception Thrown if the Inputs are Invalid
     */

    public RiemannSphereSpanner (
        final org.drip.specialfunction.group.SchwarzTriangleMap[] schwarzTriangleMapArray)
        throws java.lang.Exception
    {
        if (null == (_schwarzTriangleMapArray = schwarzTriangleMapArray))
        {
            throw new java.lang.Exception ("RiemannSphereSpanner Constructor => Invalid Inputs");
        }

        int singularityCount = _schwarzTriangleMapArray.length;

        if (0 == singularityCount)
        {
            throw new java.lang.Exception ("RiemannSphereSpanner Constructor => Invalid Inputs");
        }

        for (int singularityIndex = 0; singularityIndex < singularityCount; ++singularityIndex)
        {
            if (null == _schwarzTriangleMapArray[singularityCount])
            {
                throw new java.lang.Exception ("RiemannSphereSpanner Constructor => Invalid Inputs");
            }
        }
    }

    /**
     * Retrieve the Schwarz Triangle Map Array
     * 
     * @return The Schwarz Triangle Map Array
     */

    public org.drip.specialfunction.group.SchwarzTriangleMap[] schwarzTriangleMapArray()
    {
        return _schwarzTriangleMapArray;
    }

    /**
     * Indicate if the Spanner is Conformal
     * 
     * @return TRUE - The Spanner is Conformal
     */

    public boolean isConformal()
    {
        for (org.drip.specialfunction.group.SchwarzTriangleMap schwarzTriangleMap : _schwarzTriangleMapArray)
        {
            if (!schwarzTriangleMap.isConformal())
            {
                return false;
            }
        }

        return true;
    }

    /**
     * Indicate how the Schwarz Triangle Tiles the Riemann Sphere
     * 
     * @return Indicator of how the Schwarz Triangle Tiles the Riemann Sphere
     * 
     * @throws java.lang.Exception Thrown if the Inputs are Invalid
     */

    public int tileIndicator()
        throws java.lang.Exception
    {
        double connectionCoefficientCumulative = 0.;
        int singularityCount = _schwarzTriangleMapArray.length;

        for (int singularityIndex = 0; singularityIndex < singularityCount; ++singularityIndex)
        {
            double connectionCoefficient =
                _schwarzTriangleMapArray[singularityIndex].connectionCoefficient();

            if (!org.drip.numerical.common.NumberUtil.IsInteger (1. / connectionCoefficient))
            {
                return SCHWARZ_TRIANGLE_TILES_NOTHING;
            }

            connectionCoefficientCumulative = connectionCoefficientCumulative + connectionCoefficient;
        }

        if (0. == connectionCoefficientCumulative)
        {
            return SCHWARZ_TRIANGLE_TILES_COMPLEX_PLANE;
        }

        return 0. > connectionCoefficientCumulative ? SCHWARZ_TRIANGLE_TILES_UPPER_HALF_PLANE :
            SCHWARZ_TRIANGLE_TILES_COMPLEX_PLANE;
    }
}