LetchfordLodiCut.java

  1. package org.drip.linearprogram.cuttingplane;

  3. /*
  4.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  5.  */

  7. /*!
  8.  * Copyright (C) 2020 Lakshmi Krishnamurthy
  9.  * 
  10.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  11.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  12.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  13.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  14.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  15.  *      and computational support.
  16.  *  
  17.  *      https://lakshmidrip.github.io/DROP/
  18.  *  
  19.  *  DROP is composed of three modules:
  20.  *  
  21.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  22.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  23.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  24.  * 
  25.  *  DROP Product Core implements libraries for the following:
  26.  *  - Fixed Income Analytics
  27.  *  - Loan Analytics
  28.  *  - Transaction Cost Analytics
  29.  * 
  30.  *  DROP Portfolio Core implements libraries for the following:
  31.  *  - Asset Allocation Analytics
  32.  *  - Asset Liability Management Analytics
  33.  *  - Capital Estimation Analytics
  34.  *  - Exposure Analytics
  35.  *  - Margin Analytics
  36.  *  - XVA Analytics
  37.  * 
  38.  *  DROP Computational Core implements libraries for the following:
  39.  *  - Algorithm Support
  40.  *  - Computation Support
  41.  *  - Function Analysis
  42.  *  - Model Validation
  43.  *  - Numerical Analysis
  44.  *  - Numerical Optimizer
  45.  *  - Spline Builder
  46.  *  - Statistical Learning
  47.  * 
  48.  *  Documentation for DROP is Spread Over:
  49.  * 
  50.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  51.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  52.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  53.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  54.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  55.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  56.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  57.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  58.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  59.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  60.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  61.  * 
  62.  *  Licensed under the Apache License, Version 2.0 (the "License");
  63.  *      you may not use this file except in compliance with the License.
  64.  *   
  65.  *  You may obtain a copy of the License at
  66.  *      http://www.apache.org/licenses/LICENSE-2.0
  67.  *  
  68.  *  Unless required by applicable law or agreed to in writing, software
  69.  *      distributed under the License is distributed on an "AS IS" BASIS,
  70.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  71.  *  
  72.  *  See the License for the specific language governing permissions and
  73.  *      limitations under the License.
  74.  */

  76. /**
  77.  * <i>LetchfordLodiCut</i> implements the Letchford-Lodi Cut. The References are:
  78.  * 
  79.  * <br><br>
  80.  *  <ul>
  81.  *      <li>
  82.  *          Burdet, C. A., and E. L. Johnson (1977): A Sub-additive Approach to Solve Linear Integer Programs
  83.  *              <i>Annals of Discrete Mathematics</i> <b>1</b> 117-143
  84.  *      </li>
  85.  *      <li>
  86.  *          Chvatal, V. (1973): Edmonds Polytopes in a Hierarchy of Combinatorial Problems <i>Discrete
  87.  *              Mathematics</i> <b>4 (4)</b> 305-337
  88.  *      </li>
  89.  *      <li>
  90.  *          Gomory, R. E. (1958): Outline of an Algorithm for Integer Solutions to Linear Programs
  91.  *              <i>Bulletin of the American Mathematical Society</i> <b>64 (5)</b> 275-278
  92.  *      </li>
  93.  *      <li>
  94.  *          Kelley, J. E. (1960): The Cutting Plane Method for Solving Convex Problems <i>Journal for the
  95.  *              Society of the Industrial and Applied Mathematics</i> <b>8 (4)</b> 703-712
  96.  *      </li>
  97.  *      <li>
  98.  *          Letchford, A. N. and A. Lodi (2002): Strengthening Chvatal-Gomory Cuts and Gomory Fractional Cuts
  99.  *              <i>Operations Research Letters</i> <b>30 (2)</b> 74-82
  100.  *      </li>
  101.  *  </ul>
  102.  *
  103.  *  <br><br>
  104.  *  <ul>
  105.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/PortfolioCore.md">Portfolio Core Module</a></li>
  106.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/AssetAllocationAnalyticsLibrary.md">Asset Allocation Analytics</a></li>
  107.  *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/linearprogram/README.md">Linear Programming Solution Suite</a></li>
  108.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/linearprogram/cuttingplane/README.md">Polyhedral Cutting Plane Generation Schemes</a></li>
  109.  *  </ul>
  110.  *
  111.  * @author Lakshmi Krishnamurthy
  112.  */

  114. public class LetchfordLodiCut
  115.     extends org.drip.linearprogram.cuttingplane.ChvatalGomoryCut
  116. {

  118.     private static final java.util.Set<java.lang.Integer> Partition (
  119.         final double[] coefficientFractionArray)
  120.     {
  121.         java.util.Set<java.lang.Integer> partitionSet = new java.util.TreeSet<java.lang.Integer>();

  123.         int coefficientCount = coefficientFractionArray.length;
  124.         double a0Fraction = coefficientFractionArray[0];

  126.         for (int coefficientIndex = 1;
  127.             coefficientIndex < coefficientCount;
  128.             ++coefficientIndex)
  129.         {
  130.             if (a0Fraction >= coefficientFractionArray[coefficientIndex])
  131.             {
  132.                 partitionSet.add (
  133.                     coefficientIndex
  134.                 );
  135.             }
  136.         }

  138.         return partitionSet;
  139.     }

  141.     private static final java.util.Set<java.lang.Integer> Partition (
  142.         final double[] coefficientFractionArray,
  143.         final int k,
  144.         final int p)
  145.     {
  146.         java.util.Set<java.lang.Integer> partitionSet = new java.util.TreeSet<java.lang.Integer>();

  148.         int coefficientCount = coefficientFractionArray.length;
  149.         double oneMinusA0FractionOverK = (1. - coefficientFractionArray[0]) / k;
  150.         double upperBound = coefficientFractionArray[0] + oneMinusA0FractionOverK * p;
  151.         double lowerBound = coefficientFractionArray[0] + oneMinusA0FractionOverK * (p - 1);

  153.         for (int coefficientIndex = 1;
  154.             coefficientIndex < coefficientCount;
  155.             ++coefficientIndex)
  156.         {
  157.             if (lowerBound < coefficientFractionArray[coefficientIndex] &&
  158.                 upperBound >= coefficientFractionArray[coefficientIndex])
  159.             {
  160.                 partitionSet.add (
  161.                     coefficientIndex
  162.                 );
  163.             }
  164.         }

  166.         return partitionSet;
  167.     }

  169.     /**
  170.      * LetchfordLodiCut Constructor
  171.      * 
  172.      * @param aGrid "A" Constraint Grid
  173.      * @param bArray "b" Constraint Array
  174.      * @param lambdaArray The Lambda Array
  175.      * 
  176.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  177.      */

  179.     public LetchfordLodiCut (
  180.         final int[][] aGrid,
  181.         final int[] bArray,
  182.         final double[] lambdaArray)
  183.         throws java.lang.Exception
  184.     {
  185.         super (
  186.             aGrid,
  187.             bArray,
  188.             lambdaArray
  189.         );
  190.     }

  192.     /**
  193.      * Generate the Partition Map
  194.      * 
  195.      * @return The Partition Map
  196.      */

  198.     public org.drip.linearprogram.cuttingplane.LetchfordLodiPartitionMap partitionMap()
  199.     {
  200.         double[] unadjustedCoefficientArray = unadjustedCoefficientArray();

  202.         if (null == unadjustedCoefficientArray)
  203.         {
  204.             return null;
  205.         }

  207.         int coefficientCount = unadjustedCoefficientArray.length;
  208.         double[] coefficientFractionArray = new double[coefficientCount];

  210.         if (0 == coefficientCount)
  211.         {
  212.             return null;
  213.         }

  215.         java.util.TreeMap<java.lang.Integer, java.util.Set<java.lang.Integer>> partitionMap =
  216.             new java.util.TreeMap<java.lang.Integer, java.util.Set<java.lang.Integer>>();

  218.         try
  219.         {
  220.             for (int coefficientIndex = 0;
  221.                 coefficientIndex < coefficientCount;
  222.                 ++coefficientIndex)
  223.             {
  224.                 coefficientFractionArray[coefficientIndex] =
  225.                     org.drip.numerical.common.NumberUtil.Fractional (
  226.                         unadjustedCoefficientArray[0]
  227.                     );
  228.             }

  230.             partitionMap.put (
  231.                 0,
  232.                 Partition (
  233.                     unadjustedCoefficientArray
  234.                 )
  235.             );

  237.             int k = org.drip.numerical.common.NumberUtil.ReciprocalIntegerFloor (
  238.                 coefficientFractionArray[0]
  239.             );

  241.             for (int p = 1;
  242.                 p <= k;
  243.                 ++p)
  244.             {
  245.                 partitionMap.put (
  246.                     p,
  247.                     Partition (
  248.                         unadjustedCoefficientArray,
  249.                         k,
  250.                         p
  251.                     )
  252.                 );
  253.             }

  255.             return new org.drip.linearprogram.cuttingplane.LetchfordLodiPartitionMap (
  256.                 k,
  257.                 unadjustedCoefficientArray,
  258.                 partitionMap
  259.             );
  260.         }
  261.         catch (java.lang.Exception e)
  262.         {
  263.             e.printStackTrace();
  264.         }

  266.         return null;
  267.     }

  269.     @Override public double[] adjustedCoefficientArray()
  270.     {
  271.         org.drip.linearprogram.cuttingplane.LetchfordLodiPartitionMap letchfordLodiPartitionMap =
  272.             partitionMap();

  274.         if (null == letchfordLodiPartitionMap)
  275.         {
  276.             return null;
  277.         }

  279.         java.util.TreeMap<java.lang.Integer, java.util.Set<java.lang.Integer>> partitionMap =
  280.             letchfordLodiPartitionMap.partitionMap();

  282.         double[] unadjustedCoefficientArray = letchfordLodiPartitionMap.unadjustedCoefficientArray();

  284.         int k = letchfordLodiPartitionMap.k();

  286.         int coefficientCount = unadjustedCoefficientArray.length;
  287.         double[] adjustedCoefficientArray = new double[coefficientCount];

  289.         for (int coefficientIndex = 0;
  290.             coefficientIndex < coefficientCount;
  291.             ++coefficientIndex)
  292.         {
  293.             adjustedCoefficientArray[coefficientIndex] = 0.;
  294.         }

  296.         try
  297.         {
  298.             for (int p = 0;
  299.                 p <= k;
  300.                 ++p)
  301.             {
  302.                 for (int listEntry : partitionMap.get (
  303.                     p
  304.                 ))
  305.                 {
  306.                     adjustedCoefficientArray[listEntry] += p +
  307.                         (k + 1) * ((int) unadjustedCoefficientArray[listEntry]);
  308.                 }
  309.             }
  310.         }
  311.         catch (java.lang.Exception e)
  312.         {
  313.             e.printStackTrace();

  315.             return null;
  316.         }

  318.         adjustedCoefficientArray[0] = (k + 1) * ((int) unadjustedCoefficientArray[0]);
  319.         return adjustedCoefficientArray;
  320.     }
  321. }
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