ILPConstraint.java

  1. package org.drip.linearprogram.canonical;

  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>ILPConstraint</i> holds the Constraint Matrix LHS and Constraint Array RHS for an Integer Linear
  78.  *  Program Ax lte B, where A is Z<sup>m x n</sup>, B is Z<sup>m</sup>, and x is Z<sub>+</sub><sup>n</sup>.
  79.  *  The References are:
  80.  * 
  81.  * <br><br>
  82.  *  <ul>
  83.  *      <li>
  84.  *          Burdet, C. A., and E. L. Johnson (1977): A Sub-additive Approach to Solve Linear Integer Programs
  85.  *              <i>Annals of Discrete Mathematics</i> <b>1</b> 117-143
  86.  *      </li>
  87.  *      <li>
  88.  *          Chvatal, V. (1973): Edmonds Polytopes in a Hierarchy of Combinatorial Problems <i>Discrete
  89.  *              Mathematics</i> <b>4 (4)</b> 305-337
  90.  *      </li>
  91.  *      <li>
  92.  *          Gomory, R. E. (1958): Outline of an Algorithm for Integer Solutions to Linear Programs
  93.  *              <i>Bulletin of the American Mathematical Society</i> <b>64 (5)</b> 275-278
  94.  *      </li>
  95.  *      <li>
  96.  *          Kelley, J. E. (1960): The Cutting Plane Method for Solving Convex Problems <i>Journal for the
  97.  *              Society of the Industrial and Applied Mathematics</i> <b>8 (4)</b> 703-712
  98.  *      </li>
  99.  *      <li>
  100.  *          Letchford, A. N. and A. Lodi (2002): Strengthening Chvatal-Gomory Cuts and Gomory Fractional Cuts
  101.  *              <i>Operations Research Letters</i> <b>30 (2)</b> 74-82
  102.  *      </li>
  103.  *  </ul>
  104.  *
  105.  *  <br><br>
  106.  *  <ul>
  107.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/PortfolioCore.md">Portfolio Core Module</a></li>
  108.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/AssetAllocationAnalyticsLibrary.md">Asset Allocation Analytics</a></li>
  109.  *      <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>
  110.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/linearprogram/canonical/README.md">Linear Programming Framework Canonical Elements</a></li>
  111.  *  </ul>
  112.  *
  113.  * @author Lakshmi Krishnamurthy
  114.  */

  116. public class ILPConstraint
  117. {
  118.     private int[] _bArray = null;
  119.     private int[][] _aGrid = null;

  121.     /**
  122.      * ILPConstraint Constructor
  123.      * 
  124.      * @param aGrid "A" Constraint Grid
  125.      * @param bArray "b" Constraint Array
  126.      * 
  127.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  128.      */

  130.     public ILPConstraint (
  131.         final int[][] aGrid,
  132.         final int[] bArray)
  133.         throws java.lang.Exception
  134.     {
  135.         if (null == (_aGrid = aGrid) ||
  136.             null == (_bArray = bArray)
  137.         )
  138.         {
  139.             throw new java.lang.Exception (
  140.                 "ILPConstraint Constructor => Invalid Inputs"
  141.             );
  142.         }

  144.         int dimension = -1;
  145.         int constraintCount = _bArray.length;

  147.         if (0 == constraintCount ||
  148.             _aGrid.length != constraintCount)
  149.         {
  150.             throw new java.lang.Exception (
  151.                 "ILPConstraint Constructor => Invalid Inputs"
  152.             );
  153.         }

  155.         for (int constraintIndex = 0;
  156.             constraintIndex < constraintCount;
  157.             ++constraintIndex)
  158.         {
  159.             if (null == _aGrid[constraintIndex])
  160.             {
  161.                 throw new java.lang.Exception (
  162.                     "ILPConstraint Constructor => Invalid Inputs"
  163.                 );
  164.             }

  166.             if (-1 == dimension)
  167.             {
  168.                 if (0 == (dimension = _aGrid[constraintIndex].length))
  169.                 {
  170.                     throw new java.lang.Exception (
  171.                         "ILPConstraint Constructor => Invalid Inputs"
  172.                     );
  173.                 }
  174.             }
  175.             else
  176.             {
  177.                 if (dimension != _aGrid[constraintIndex].length)
  178.                 {
  179.                     throw new java.lang.Exception (
  180.                         "ILPConstraint Constructor => Invalid Inputs"
  181.                     );
  182.                 }
  183.             }
  184.         }
  185.     }

  187.     /**
  188.      * Retrieve "A" Grid
  189.      * 
  190.      * @return A Grid
  191.      */

  193.     public int[][] aGrid()
  194.     {
  195.         return _aGrid;
  196.     }

  198.     /**
  199.      * Retrieve "b" Array
  200.      * 
  201.      * @return b Array
  202.      */

  204.     public int[] bArray()
  205.     {
  206.         return _bArray;
  207.     }

  209.     /**
  210.      * Retrieve the Constraint Count
  211.      * 
  212.      * @return Constraint Count
  213.      */

  215.     public int constraintCount()
  216.     {
  217.         return _bArray.length;
  218.     }

  220.     /**
  221.      * Retrieve the Variate Dimension
  222.      * 
  223.      * @return Variate Dimension
  224.      */

  226.     public int dimension()
  227.     {
  228.         return _aGrid[0].length;
  229.     }

  231.     /**
  232.      * Validate the Variate Input
  233.      * 
  234.      * @param variateArray The Input Variate Array
  235.      * 
  236.      * @return TRUE - The Input Variate successfully Validated
  237.      */

  239.     public boolean validate (
  240.         final int[] variateArray)
  241.     {
  242.         if (null == variateArray)
  243.         {
  244.             return false;
  245.         }

  247.         int dimension = _aGrid[0].length;

  249.         if (dimension != variateArray.length)
  250.         {
  251.             return false;
  252.         }

  254.         for (int dimensionIndex = 0;
  255.             dimensionIndex < dimension;
  256.             ++dimensionIndex)
  257.         {
  258.             if (0 >= variateArray[dimensionIndex])
  259.             {
  260.                 return false;
  261.             }
  262.         }

  264.         return true;
  265.     }

  267.     /**
  268.      * Verify if the Variate Array satisfies the Constraint
  269.      * 
  270.      * @param variateArray The Input Variate Array
  271.      * 
  272.      * @return TRUE - The Variate Array satisfies the Constraint
  273.      * 
  274.      * @throws java.lang.Exception Thrown if the Verification cannot be done
  275.      */

  277.     public boolean verify (
  278.         final int[] variateArray)
  279.         throws java.lang.Exception
  280.     {
  281.         if (!validate (
  282.             variateArray
  283.         ))
  284.         {
  285.             throw new java.lang.Exception (
  286.                 "ILPConstraint::verify => Variate Array not Valid"
  287.             );
  288.         }

  290.         int dimension = _aGrid[0].length;
  291.         int constraintCount = _bArray.length;

  293.         for (int constraintIndex = 0;
  294.             constraintIndex < constraintCount;
  295.             ++constraintIndex)
  296.         {
  297.             int constraintLHS = 0;

  299.             for (int dimensionIndex = 0;
  300.                 dimensionIndex < dimension;
  301.                 ++dimensionIndex)
  302.             {
  303.                 constraintLHS += _aGrid[constraintIndex][dimensionIndex] * variateArray[dimensionIndex];
  304.             }

  306.             if (constraintLHS > _bArray[constraintIndex])
  307.             {
  308.                 return false;
  309.             }
  310.         }

  312.         return true;
  313.     }

  315.     /**
  316.      * Generate a Chvatal-Gomory Cut
  317.      * 
  318.      * @param lambdaArray The Lambda Array
  319.      * 
  320.      * @return The Chvatal-Gomory Cut
  321.      */

  323.     public org.drip.linearprogram.cuttingplane.ChvatalGomoryCut chvatalGomoryCut (
  324.         final double[] lambdaArray)
  325.     {
  326.         try
  327.         {
  328.             return new org.drip.linearprogram.cuttingplane.ChvatalGomoryCut (
  329.                 _aGrid,
  330.                 _bArray,
  331.                 lambdaArray
  332.             );
  333.         }
  334.         catch (java.lang.Exception e)
  335.         {
  336.             e.printStackTrace();
  337.         }

  339.         return null;
  340.     }

  342.     /**
  343.      * Generate a Strengthened Chvatal-Gomory Cut
  344.      * 
  345.      * @param lambdaArray The Lambda Array
  346.      * @param t Strengthening Integer
  347.      * 
  348.      * @return The Chvatal-Gomory Cut
  349.      */

  351.     public org.drip.linearprogram.cuttingplane.StrengthenedChvatalGomoryCut strengthenedChvatalGomoryCut (
  352.         final double[] lambdaArray,
  353.         final int t)
  354.     {
  355.         if (null == lambdaArray)
  356.         {
  357.             return null;
  358.         }

  360.         double lambdaB = 0.;
  361.         int constraintCount = _bArray.length;

  363.         if (lambdaArray.length != constraintCount)
  364.         {
  365.             return null;
  366.         }

  368.         for (int constraintIndex = 0;
  369.             constraintIndex < constraintCount;
  370.             ++constraintIndex)
  371.         {
  372.             lambdaB = lambdaB + lambdaArray[constraintIndex] * _bArray[constraintIndex];
  373.         }

  375.         try
  376.         {
  377.             double fractionalLambdaB = org.drip.numerical.common.NumberUtil.Fractional (
  378.                 lambdaB
  379.             );

  381.             if (0.5 >= fractionalLambdaB)
  382.             {
  383.                 return null;
  384.             }

  386.             double tFractionalLambdaB = org.drip.numerical.common.NumberUtil.Fractional (
  387.                 t * fractionalLambdaB
  388.             );

  390.             return 0.5 <= tFractionalLambdaB && tFractionalLambdaB < 1. ? null :
  391.                 new org.drip.linearprogram.cuttingplane.StrengthenedChvatalGomoryCut (
  392.                     _aGrid,
  393.                     _bArray,
  394.                     lambdaArray,
  395.                     t
  396.                 );
  397.         }
  398.         catch (java.lang.Exception e)
  399.         {
  400.             e.printStackTrace();
  401.         }

  403.         return null;
  404.     }

  406.     /**
  407.      * Generate a Burdet-Johnson Cut
  408.      * 
  409.      * @param lambdaArray The Lambda Array
  410.      * 
  411.      * @return The Burdet-Johnson Cut
  412.      */

  414.     public org.drip.linearprogram.cuttingplane.BurdetJohnsonCut burdetJohnsonCut (
  415.         final double[] lambdaArray)
  416.     {
  417.         try
  418.         {
  419.             return new org.drip.linearprogram.cuttingplane.BurdetJohnsonCut (
  420.                 _aGrid,
  421.                 _bArray,
  422.                 lambdaArray
  423.             );
  424.         }
  425.         catch (java.lang.Exception e)
  426.         {
  427.             e.printStackTrace();
  428.         }

  430.         return null;
  431.     }

  433.     /**
  434.      * Generate a Strengthened Burdet-Johnson Cut
  435.      * 
  436.      * @param lambdaArray The Lambda Array
  437.      * @param r1ToR1Increasing R<sup>1</sup> To R<sup>1</sup> Increasing Function
  438.      * 
  439.      * @return The Strengthened Burdet-Johnson Cut
  440.      */

  442.     public org.drip.linearprogram.cuttingplane.StrengthenedBurdetJohnsonCut strengthenedBurdetJohnsonCut (
  443.         final double[] lambdaArray,
  444.         final org.drip.function.definition.R1ToR1 r1ToR1Increasing)
  445.     {
  446.         try
  447.         {
  448.             return new org.drip.linearprogram.cuttingplane.StrengthenedBurdetJohnsonCut (
  449.                 _aGrid,
  450.                 _bArray,
  451.                 lambdaArray,
  452.                 r1ToR1Increasing
  453.             );
  454.         }
  455.         catch (java.lang.Exception e)
  456.         {
  457.             e.printStackTrace();
  458.         }

  460.         return null;
  461.     }
  462. }
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