LetchfordLodiCut.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>LetchfordLodiCut</i> implements the Letchford-Lodi 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 LetchfordLodiCut
extends org.drip.linearprogram.cuttingplane.ChvatalGomoryCut
{
private static final java.util.Set<java.lang.Integer> Partition (
final double[] coefficientFractionArray)
{
java.util.Set<java.lang.Integer> partitionSet = new java.util.TreeSet<java.lang.Integer>();
int coefficientCount = coefficientFractionArray.length;
double a0Fraction = coefficientFractionArray[0];
for (int coefficientIndex = 1;
coefficientIndex < coefficientCount;
++coefficientIndex)
{
if (a0Fraction >= coefficientFractionArray[coefficientIndex])
{
partitionSet.add (
coefficientIndex
);
}
}
return partitionSet;
}
private static final java.util.Set<java.lang.Integer> Partition (
final double[] coefficientFractionArray,
final int k,
final int p)
{
java.util.Set<java.lang.Integer> partitionSet = new java.util.TreeSet<java.lang.Integer>();
int coefficientCount = coefficientFractionArray.length;
double oneMinusA0FractionOverK = (1. - coefficientFractionArray[0]) / k;
double upperBound = coefficientFractionArray[0] + oneMinusA0FractionOverK * p;
double lowerBound = coefficientFractionArray[0] + oneMinusA0FractionOverK * (p - 1);
for (int coefficientIndex = 1;
coefficientIndex < coefficientCount;
++coefficientIndex)
{
if (lowerBound < coefficientFractionArray[coefficientIndex] &&
upperBound >= coefficientFractionArray[coefficientIndex])
{
partitionSet.add (
coefficientIndex
);
}
}
return partitionSet;
}
/**
* LetchfordLodiCut 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 LetchfordLodiCut (
final int[][] aGrid,
final int[] bArray,
final double[] lambdaArray)
throws java.lang.Exception
{
super (
aGrid,
bArray,
lambdaArray
);
}
/**
* Generate the Partition Map
*
* @return The Partition Map
*/
public org.drip.linearprogram.cuttingplane.LetchfordLodiPartitionMap partitionMap()
{
double[] unadjustedCoefficientArray = unadjustedCoefficientArray();
if (null == unadjustedCoefficientArray)
{
return null;
}
int coefficientCount = unadjustedCoefficientArray.length;
double[] coefficientFractionArray = new double[coefficientCount];
if (0 == coefficientCount)
{
return null;
}
java.util.TreeMap<java.lang.Integer, java.util.Set<java.lang.Integer>> partitionMap =
new java.util.TreeMap<java.lang.Integer, java.util.Set<java.lang.Integer>>();
try
{
for (int coefficientIndex = 0;
coefficientIndex < coefficientCount;
++coefficientIndex)
{
coefficientFractionArray[coefficientIndex] =
org.drip.numerical.common.NumberUtil.Fractional (
unadjustedCoefficientArray[0]
);
}
partitionMap.put (
0,
Partition (
unadjustedCoefficientArray
)
);
int k = org.drip.numerical.common.NumberUtil.ReciprocalIntegerFloor (
coefficientFractionArray[0]
);
for (int p = 1;
p <= k;
++p)
{
partitionMap.put (
p,
Partition (
unadjustedCoefficientArray,
k,
p
)
);
}
return new org.drip.linearprogram.cuttingplane.LetchfordLodiPartitionMap (
k,
unadjustedCoefficientArray,
partitionMap
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
@Override public double[] adjustedCoefficientArray()
{
org.drip.linearprogram.cuttingplane.LetchfordLodiPartitionMap letchfordLodiPartitionMap =
partitionMap();
if (null == letchfordLodiPartitionMap)
{
return null;
}
java.util.TreeMap<java.lang.Integer, java.util.Set<java.lang.Integer>> partitionMap =
letchfordLodiPartitionMap.partitionMap();
double[] unadjustedCoefficientArray = letchfordLodiPartitionMap.unadjustedCoefficientArray();
int k = letchfordLodiPartitionMap.k();
int coefficientCount = unadjustedCoefficientArray.length;
double[] adjustedCoefficientArray = new double[coefficientCount];
for (int coefficientIndex = 0;
coefficientIndex < coefficientCount;
++coefficientIndex)
{
adjustedCoefficientArray[coefficientIndex] = 0.;
}
try
{
for (int p = 0;
p <= k;
++p)
{
for (int listEntry : partitionMap.get (
p
))
{
adjustedCoefficientArray[listEntry] += p +
(k + 1) * ((int) unadjustedCoefficientArray[listEntry]);
}
}
}
catch (java.lang.Exception e)
{
e.printStackTrace();
return null;
}
adjustedCoefficientArray[0] = (k + 1) * ((int) unadjustedCoefficientArray[0]);
return adjustedCoefficientArray;
}
}