ChvatalGomoryCut.java
package org.drip.linearprogram.cuttingplane;
/*
* -*- 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>ChvatalGomoryCut</i> implements the Chvatal-Gomory Cut. 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/cuttingplane/README.md">Polyhedral Cutting Plane Generation Schemes</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class ChvatalGomoryCut
extends org.drip.linearprogram.canonical.ILPConstraint
{
private double[] _lambdaArray = null;
/**
* ChvatalGomoryCut Constructor
*
* @param aGrid "A" Constraint Grid
* @param bArray "b" Constraint Array
* @param lambdaArray The Lambda Array
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public ChvatalGomoryCut (
final int[][] aGrid,
final int[] bArray,
final double[] lambdaArray)
throws java.lang.Exception
{
super (
aGrid,
bArray
);
if (null == (_lambdaArray = lambdaArray))
{
throw new java.lang.Exception (
"ChvatalGomoryCut Constructor => Invalid Inputs"
);
}
int constraintCount = constraintCount();
if (_lambdaArray.length != constraintCount)
{
throw new java.lang.Exception (
"ChvatalGomoryCut Constructor => Invalid Inputs"
);
}
for (int constraintIndex = 0;
constraintIndex < constraintCount;
++constraintIndex)
{
if (!org.drip.numerical.common.NumberUtil.IsValid (
_lambdaArray[constraintIndex]
) || 0. > _lambdaArray[constraintIndex]
)
{
throw new java.lang.Exception (
"ChvatalGomoryCut Constructor => Invalid Inputs"
);
}
}
}
/**
* Retrieve the Lambda Array
*
* @return The Lambda Array
*/
public double[] lambdaArray()
{
return _lambdaArray;
}
/**
* Generate the Unadjusted Coefficient Array
*
* @return The Unadjusted Coefficient Array
*/
public double[] unadjustedCoefficientArray()
{
int[] bArray = bArray();
int[][] aGrid = aGrid();
int dimension = aGrid.length;
int constraintCount = bArray.length;
double[] unadjustedCoefficientArray = new double[dimension + 1];
for (int dimensionIndex = 0;
dimensionIndex <= dimension;
++dimensionIndex)
{
unadjustedCoefficientArray[dimensionIndex] = 0.;
}
for (int constraintIndex = 0;
constraintIndex < constraintCount;
++constraintIndex)
{
for (int dimensionIndex = 0;
dimensionIndex < dimension;
++dimensionIndex)
{
unadjustedCoefficientArray[dimensionIndex + 1] += _lambdaArray[constraintIndex] *
aGrid[constraintIndex][dimensionIndex];
}
unadjustedCoefficientArray[0] = unadjustedCoefficientArray[0] +
_lambdaArray[constraintIndex] * bArray[constraintIndex];
}
return unadjustedCoefficientArray;
}
/**
* Generate the Adjusted Coefficient Array
*
* @return The Adjusted Coefficient Array
*/
public double[] adjustedCoefficientArray()
{
double[] unadjustedCoefficientArray = unadjustedCoefficientArray();
if (null == unadjustedCoefficientArray)
{
return null;
}
int coefficientCount = unadjustedCoefficientArray.length;
double[] adjustedCoefficientArray = new double[coefficientCount];
for (int coefficientIndex = 0;
coefficientIndex < coefficientCount;
++coefficientIndex)
{
adjustedCoefficientArray[coefficientIndex] = (int) unadjustedCoefficientArray[coefficientIndex];
}
return adjustedCoefficientArray;
}
/**
* Verify if the Variate Array satisfies the Constraint
*
* @param variateArray The Input Variate Array
*
* @return TRUE - The Variate Array satisfies the Constraint
*/
public boolean verify (
final int[] variateArray)
throws java.lang.Exception
{
if (!super.verify (
variateArray
))
{
return false;
}
double[] adjustedCoefficientArray = adjustedCoefficientArray();
if (null == adjustedCoefficientArray)
{
return false;
}
double lhs = 0.;
int coefficientCount = adjustedCoefficientArray.length;
for (int coefficientIndex = 1;
coefficientIndex < coefficientCount;
++coefficientIndex)
{
lhs += variateArray[coefficientIndex] * adjustedCoefficientArray[coefficientIndex];
}
return lhs <= adjustedCoefficientArray[0];
}
}