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;
}
}