BellmanFordScheme.java

package org.drip.spaces.graph;

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

/*!
 * Copyright (C) 2020 Lakshmi Krishnamurthy
 * Copyright (C) 2019 Lakshmi Krishnamurthy
 * Copyright (C) 2018 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>BellmanFordScheme</i> implements the Bellman Ford Algorithm for finding the Shortest Path between a
 * Pair of Vertexes in a Graph. The References are:
 *
 * <br><br>
 *  <ul>
 *      <li>
 *          Wikipedia (2018a): Graph (Abstract Data Type)
 *              https://en.wikipedia.org/wiki/Graph_(abstract_data_type)
 *      </li>
 *      <li>
 *          Wikipedia (2018b): Graph Theory https://en.wikipedia.org/wiki/Graph_theory
 *      </li>
 *      <li>
 *          Wikipedia (2018c): Graph (Discrete Mathematics)
 *              https://en.wikipedia.org/wiki/Graph_(discrete_mathematics)
 *      </li>
 *      <li>
 *          Wikipedia (2018d): Dijkstra's Algorithm https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm
 *      </li>
 *      <li>
 *          Wikipedia (2018e): Bellman-Ford Algorithm
 *              https://en.wikipedia.org/wiki/Bellman%E2%80%93Ford_algorithm
 *      </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/StatisticalLearningLibrary.md">Statistical Learning Library</a></li>
 *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/spaces/README.md">R<sup>1</sup> and R<sup>d</sup> Vector/Tensor Spaces (Validated and/or Normed), and Function Classes</a></li>
 *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/spaces/graph/README.md">Graph Representation and Traversal Algorithms</a></li>
 *  </ul>
 * <br><br>
 *
 * @author Lakshmi Krishnamurthy
 */

public class BellmanFordScheme
{
    private org.drip.spaces.graph.Topography _topography = null;

    private void visitEdge (
        final org.drip.spaces.graph.Edge edge,
        final org.drip.spaces.graph.ShortestPathFirstWengert spfWengert)
    {
        java.lang.String leftVertex = edge.source();

        org.drip.spaces.graph.ShortestPathTree vertexPeripheryMap = spfWengert.vertexPeripheryMap();

        org.drip.spaces.graph.ShortestPathVertex vertexPeripheryLeft = vertexPeripheryMap.shortestPathVertex
            (leftVertex);

        org.drip.spaces.graph.ShortestPathVertex vertexPeripheryRight = vertexPeripheryMap.shortestPathVertex
            (edge.destination());

        double sourceToRightThroughLeft = vertexPeripheryLeft.weightFromSource() + edge.weight();

        if (sourceToRightThroughLeft < vertexPeripheryRight.weightFromSource())
        {
            vertexPeripheryRight.setWeightFromSource (sourceToRightThroughLeft);

            vertexPeripheryRight.setPreceeding (leftVertex);
        }
    }

    /**
     * BellmanFordScheme Constructor
     * 
     * @param topography The Topography Map
     * 
     * @throws java.lang.Exception Thrown if the Inputs are Invalid
     */

    public BellmanFordScheme (
        final org.drip.spaces.graph.Topography topography)
        throws java.lang.Exception
    {
        if (null == (_topography = topography))
        {
            throw new java.lang.Exception ("BellmanFordScheme Constructor => Invalid Inputs");
        }
    }

    /**
     * Retrieve the Topography Map
     * 
     * @return The Topography Map
     */

    public org.drip.spaces.graph.Topography topography()
    {
        return _topography;
    }

    /**
     * Initialize the Bellman Ford Scheme
     * 
     * @param source The Source Vertex
     * 
     * @return The Initial Bellman Ford Wengert
     */

    public org.drip.spaces.graph.ShortestPathFirstWengert setup (
        final java.lang.String source)
    {
        return org.drip.spaces.graph.ShortestPathFirstWengert.BellmanFord (
            _topography,
            source
        );
    }

    /**
     * Run the Bellman Ford SPF Algorithm
     * 
     * @param source The Source Vertex
     * 
     * @return The Bellman Ford Wengert
     */

    public org.drip.spaces.graph.ShortestPathFirstWengert spf (
        final java.lang.String source)
    {
        org.drip.spaces.graph.ShortestPathFirstWengert spfWengert = setup (source);

        if (null == spfWengert)
        {
            return null;
        }

        int vertexCount = _topography.vertexNameSet().size();

        for (int vertexIndex = 0; vertexIndex < vertexCount; ++vertexIndex)
        {
            java.util.Map<java.lang.String, org.drip.spaces.graph.Edge> edgeMap =
                _topography.topographyEdgeMap().edgeMap();

            for (java.util.Map.Entry<java.lang.String, org.drip.spaces.graph.Edge> edgeEntry :
                edgeMap.entrySet())
            {
                visitEdge (
                    edgeEntry.getValue(),
                    spfWengert
                );
            }
        }

        return spfWengert;
    }
}