ILPConstraint.java
package org.drip.linearprogram.canonical;
/*
* -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*/
/*!
* Copyright (C) 2020 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>ILPConstraint</i> holds the Constraint Matrix LHS and Constraint Array RHS for an Integer Linear
* 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>.
* The References are:
*
* <br><br>
* <ul>
* <li>
* Burdet, C. A., and E. L. Johnson (1977): A Sub-additive Approach to Solve Linear Integer Programs
* <i>Annals of Discrete Mathematics</i> <b>1</b> 117-143
* </li>
* <li>
* Chvatal, V. (1973): Edmonds Polytopes in a Hierarchy of Combinatorial Problems <i>Discrete
* Mathematics</i> <b>4 (4)</b> 305-337
* </li>
* <li>
* Gomory, R. E. (1958): Outline of an Algorithm for Integer Solutions to Linear Programs
* <i>Bulletin of the American Mathematical Society</i> <b>64 (5)</b> 275-278
* </li>
* <li>
* Kelley, J. E. (1960): The Cutting Plane Method for Solving Convex Problems <i>Journal for the
* Society of the Industrial and Applied Mathematics</i> <b>8 (4)</b> 703-712
* </li>
* <li>
* Letchford, A. N. and A. Lodi (2002): Strengthening Chvatal-Gomory Cuts and Gomory Fractional Cuts
* <i>Operations Research Letters</i> <b>30 (2)</b> 74-82
* </li>
* </ul>
*
* <br><br>
* <ul>
* <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/PortfolioCore.md">Portfolio Core Module</a></li>
* <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/AssetAllocationAnalyticsLibrary.md">Asset Allocation Analytics</a></li>
* <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>
* <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>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class ILPConstraint
{
private int[] _bArray = null;
private int[][] _aGrid = null;
/**
* ILPConstraint Constructor
*
* @param aGrid "A" Constraint Grid
* @param bArray "b" Constraint Array
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public ILPConstraint (
final int[][] aGrid,
final int[] bArray)
throws java.lang.Exception
{
if (null == (_aGrid = aGrid) ||
null == (_bArray = bArray)
)
{
throw new java.lang.Exception (
"ILPConstraint Constructor => Invalid Inputs"
);
}
int dimension = -1;
int constraintCount = _bArray.length;
if (0 == constraintCount ||
_aGrid.length != constraintCount)
{
throw new java.lang.Exception (
"ILPConstraint Constructor => Invalid Inputs"
);
}
for (int constraintIndex = 0;
constraintIndex < constraintCount;
++constraintIndex)
{
if (null == _aGrid[constraintIndex])
{
throw new java.lang.Exception (
"ILPConstraint Constructor => Invalid Inputs"
);
}
if (-1 == dimension)
{
if (0 == (dimension = _aGrid[constraintIndex].length))
{
throw new java.lang.Exception (
"ILPConstraint Constructor => Invalid Inputs"
);
}
}
else
{
if (dimension != _aGrid[constraintIndex].length)
{
throw new java.lang.Exception (
"ILPConstraint Constructor => Invalid Inputs"
);
}
}
}
}
/**
* Retrieve "A" Grid
*
* @return A Grid
*/
public int[][] aGrid()
{
return _aGrid;
}
/**
* Retrieve "b" Array
*
* @return b Array
*/
public int[] bArray()
{
return _bArray;
}
/**
* Retrieve the Constraint Count
*
* @return Constraint Count
*/
public int constraintCount()
{
return _bArray.length;
}
/**
* Retrieve the Variate Dimension
*
* @return Variate Dimension
*/
public int dimension()
{
return _aGrid[0].length;
}
/**
* Validate the Variate Input
*
* @param variateArray The Input Variate Array
*
* @return TRUE - The Input Variate successfully Validated
*/
public boolean validate (
final int[] variateArray)
{
if (null == variateArray)
{
return false;
}
int dimension = _aGrid[0].length;
if (dimension != variateArray.length)
{
return false;
}
for (int dimensionIndex = 0;
dimensionIndex < dimension;
++dimensionIndex)
{
if (0 >= variateArray[dimensionIndex])
{
return false;
}
}
return true;
}
/**
* Verify if the Variate Array satisfies the Constraint
*
* @param variateArray The Input Variate Array
*
* @return TRUE - The Variate Array satisfies the Constraint
*
* @throws java.lang.Exception Thrown if the Verification cannot be done
*/
public boolean verify (
final int[] variateArray)
throws java.lang.Exception
{
if (!validate (
variateArray
))
{
throw new java.lang.Exception (
"ILPConstraint::verify => Variate Array not Valid"
);
}
int dimension = _aGrid[0].length;
int constraintCount = _bArray.length;
for (int constraintIndex = 0;
constraintIndex < constraintCount;
++constraintIndex)
{
int constraintLHS = 0;
for (int dimensionIndex = 0;
dimensionIndex < dimension;
++dimensionIndex)
{
constraintLHS += _aGrid[constraintIndex][dimensionIndex] * variateArray[dimensionIndex];
}
if (constraintLHS > _bArray[constraintIndex])
{
return false;
}
}
return true;
}
/**
* Generate a Chvatal-Gomory Cut
*
* @param lambdaArray The Lambda Array
*
* @return The Chvatal-Gomory Cut
*/
public org.drip.linearprogram.cuttingplane.ChvatalGomoryCut chvatalGomoryCut (
final double[] lambdaArray)
{
try
{
return new org.drip.linearprogram.cuttingplane.ChvatalGomoryCut (
_aGrid,
_bArray,
lambdaArray
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Generate a Strengthened Chvatal-Gomory Cut
*
* @param lambdaArray The Lambda Array
* @param t Strengthening Integer
*
* @return The Chvatal-Gomory Cut
*/
public org.drip.linearprogram.cuttingplane.StrengthenedChvatalGomoryCut strengthenedChvatalGomoryCut (
final double[] lambdaArray,
final int t)
{
if (null == lambdaArray)
{
return null;
}
double lambdaB = 0.;
int constraintCount = _bArray.length;
if (lambdaArray.length != constraintCount)
{
return null;
}
for (int constraintIndex = 0;
constraintIndex < constraintCount;
++constraintIndex)
{
lambdaB = lambdaB + lambdaArray[constraintIndex] * _bArray[constraintIndex];
}
try
{
double fractionalLambdaB = org.drip.numerical.common.NumberUtil.Fractional (
lambdaB
);
if (0.5 >= fractionalLambdaB)
{
return null;
}
double tFractionalLambdaB = org.drip.numerical.common.NumberUtil.Fractional (
t * fractionalLambdaB
);
return 0.5 <= tFractionalLambdaB && tFractionalLambdaB < 1. ? null :
new org.drip.linearprogram.cuttingplane.StrengthenedChvatalGomoryCut (
_aGrid,
_bArray,
lambdaArray,
t
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Generate a Burdet-Johnson Cut
*
* @param lambdaArray The Lambda Array
*
* @return The Burdet-Johnson Cut
*/
public org.drip.linearprogram.cuttingplane.BurdetJohnsonCut burdetJohnsonCut (
final double[] lambdaArray)
{
try
{
return new org.drip.linearprogram.cuttingplane.BurdetJohnsonCut (
_aGrid,
_bArray,
lambdaArray
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Generate a Strengthened Burdet-Johnson Cut
*
* @param lambdaArray The Lambda Array
* @param r1ToR1Increasing R<sup>1</sup> To R<sup>1</sup> Increasing Function
*
* @return The Strengthened Burdet-Johnson Cut
*/
public org.drip.linearprogram.cuttingplane.StrengthenedBurdetJohnsonCut strengthenedBurdetJohnsonCut (
final double[] lambdaArray,
final org.drip.function.definition.R1ToR1 r1ToR1Increasing)
{
try
{
return new org.drip.linearprogram.cuttingplane.StrengthenedBurdetJohnsonCut (
_aGrid,
_bArray,
lambdaArray,
r1ToR1Increasing
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
}