PowerIterationComponentExtractor.java
package org.drip.numerical.eigen;
/*
* -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*/
/*!
* Copyright (C) 2020 Lakshmi Krishnamurthy
* Copyright (C) 2019 Lakshmi Krishnamurthy
* Copyright (C) 2018 Lakshmi Krishnamurthy
* Copyright (C) 2017 Lakshmi Krishnamurthy
* Copyright (C) 2016 Lakshmi Krishnamurthy
* Copyright (C) 2015 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>PowerIterationComponentExtractor</i> extracts the Linear System Components using the Power Iteration
* Method.
*
* <br><br>
* <ul>
* <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
* <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalAnalysisLibrary.md">Numerical Analysis Library</a></li>
* <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/numerical">Numerical Quadrature, Differentiation, Eigenization, Linear Algebra, and Utilities</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/numerical/eigen">QR PICE Eigen-Component Extraction Methodologies</a></li>
* </ul>
* <br><br>
*
* @author Lakshmi Krishnamurthy
*/
public class PowerIterationComponentExtractor
implements org.drip.numerical.eigen.ComponentExtractor
{
private int _maxIterations = -1;
private boolean _isToleranceAbsolute = false;
private double _tolerance = java.lang.Double.NaN;
/**
* PowerIterationComponentExtractor Constructor
*
* @param maxIterations Maximum Number of Iterations
* @param tolerance Tolerance
* @param isToleranceAbsolute Is Tolerance Absolute
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public PowerIterationComponentExtractor (
final int maxIterations,
final double tolerance,
final boolean isToleranceAbsolute)
throws java.lang.Exception
{
if (0 >= (_maxIterations = maxIterations) ||
!org.drip.numerical.common.NumberUtil.IsValid (
_tolerance = tolerance
) || 0. == _tolerance
)
{
throw new java.lang.Exception (
"PowerIterationComponentExtractor ctr: Invalid Inputs!"
);
}
_isToleranceAbsolute = isToleranceAbsolute;
}
/**
* Retrieve the Maximum Number of Iterations
*
* @return The Maximum Number of Iterations
*/
public int maxIterations()
{
return _maxIterations;
}
/**
* Retrieve the Tolerance Level
*
* @return The Tolerance Level
*/
public double tolerance()
{
return _tolerance;
}
/**
* Indicate if the specified Tolerance is Absolute
*
* @return TRUE - The specified Tolerance is Absolute
*/
public boolean isToleranceAbsolute()
{
return _isToleranceAbsolute;
}
@Override public org.drip.numerical.eigen.EigenComponent principalComponent (
final double[][] a)
{
if (null == a)
{
return null;
}
int iterationIndex = 0;
int componentCount = a.length;
double eigenValue = componentCount;
double[] eigenVector = new double[componentCount];
double[] eigenVectorArray = new double[componentCount];
if (0 == componentCount || null == a[0] || componentCount != a[0].length)
{
return null;
}
for (int componentIndex = 0;
componentIndex < componentCount;
++componentIndex)
{
eigenVector[componentIndex] = 1.;
}
eigenVector = org.drip.numerical.linearalgebra.Matrix.Normalize (
eigenVector
);
double oldEigenValue = eigenValue;
double absoluteTolerance = _isToleranceAbsolute ? _tolerance : eigenValue * _tolerance;
absoluteTolerance = absoluteTolerance > _tolerance ? absoluteTolerance : _tolerance;
while (iterationIndex < _maxIterations)
{
for (int componentIndexI = 0;
componentIndexI < componentCount;
++componentIndexI)
{
eigenVectorArray[componentIndexI] = 0.;
for (int componentIndexJ = 0;
componentIndexJ < componentCount;
++componentIndexJ)
{
eigenVectorArray[componentIndexI] +=
a[componentIndexI][componentIndexJ] * eigenVector[componentIndexJ];
}
}
eigenVectorArray = org.drip.numerical.linearalgebra.Matrix.Normalize (
eigenVectorArray
);
try {
eigenValue = org.drip.numerical.linearalgebra.Matrix.RayleighQuotient (
a,
eigenVectorArray
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
return null;
}
if (absoluteTolerance > java.lang.Math.abs (
eigenValue - oldEigenValue
))
{
break;
}
eigenVector = eigenVectorArray;
oldEigenValue = eigenValue;
++iterationIndex;
}
if (iterationIndex >= _maxIterations)
{
return null;
}
try
{
return new org.drip.numerical.eigen.EigenComponent (
eigenVectorArray,
eigenValue
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
@Override public org.drip.numerical.eigen.EigenOutput eigenize (
final double[][] a)
{
return null;
}
}