PowerIterationComponentExtractor.java

  1. package org.drip.numerical.eigen;

  3. /*
  4.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  5.  */

  7. /*!
  8.  * Copyright (C) 2020 Lakshmi Krishnamurthy
  9.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  10.  * Copyright (C) 2018 Lakshmi Krishnamurthy
  11.  * Copyright (C) 2017 Lakshmi Krishnamurthy
  12.  * Copyright (C) 2016 Lakshmi Krishnamurthy
  13.  * Copyright (C) 2015 Lakshmi Krishnamurthy
  14.  * 
  15.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  16.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  17.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  18.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  19.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  20.  *      and computational support.
  21.  *  
  22.  *      https://lakshmidrip.github.io/DROP/
  23.  *  
  24.  *  DROP is composed of three modules:
  25.  *  
  26.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  27.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  28.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  29.  * 
  30.  *  DROP Product Core implements libraries for the following:
  31.  *  - Fixed Income Analytics
  32.  *  - Loan Analytics
  33.  *  - Transaction Cost Analytics
  34.  * 
  35.  *  DROP Portfolio Core implements libraries for the following:
  36.  *  - Asset Allocation Analytics
  37.  *  - Asset Liability Management Analytics
  38.  *  - Capital Estimation Analytics
  39.  *  - Exposure Analytics
  40.  *  - Margin Analytics
  41.  *  - XVA Analytics
  42.  * 
  43.  *  DROP Computational Core implements libraries for the following:
  44.  *  - Algorithm Support
  45.  *  - Computation Support
  46.  *  - Function Analysis
  47.  *  - Model Validation
  48.  *  - Numerical Analysis
  49.  *  - Numerical Optimizer
  50.  *  - Spline Builder
  51.  *  - Statistical Learning
  52.  * 
  53.  *  Documentation for DROP is Spread Over:
  54.  * 
  55.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  56.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  57.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  58.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  59.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  60.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  61.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  62.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  63.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  64.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  65.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  66.  * 
  67.  *  Licensed under the Apache License, Version 2.0 (the "License");
  68.  *      you may not use this file except in compliance with the License.
  69.  *   
  70.  *  You may obtain a copy of the License at
  71.  *      http://www.apache.org/licenses/LICENSE-2.0
  72.  *  
  73.  *  Unless required by applicable law or agreed to in writing, software
  74.  *      distributed under the License is distributed on an "AS IS" BASIS,
  75.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  76.  *  
  77.  *  See the License for the specific language governing permissions and
  78.  *      limitations under the License.
  79.  */

  81. /**
  82.  * <i>PowerIterationComponentExtractor</i> extracts the Linear System Components using the Power Iteration
  83.  * Method.
  84.  * 
  85.  * <br><br>
  86.  *  <ul>
  87.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  88.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalAnalysisLibrary.md">Numerical Analysis Library</a></li>
  89.  *      <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>
  90.  *      <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>
  91.  *  </ul>
  92.  * <br><br>
  93.  *
  94.  * @author Lakshmi Krishnamurthy
  95.  */

  97. public class PowerIterationComponentExtractor
  98.     implements org.drip.numerical.eigen.ComponentExtractor
  99. {
  100.     private int _maxIterations = -1;
  101.     private boolean _isToleranceAbsolute = false;
  102.     private double _tolerance = java.lang.Double.NaN;

  104.     /**
  105.      * PowerIterationComponentExtractor Constructor
  106.      * 
  107.      * @param maxIterations Maximum Number of Iterations
  108.      * @param tolerance Tolerance
  109.      * @param isToleranceAbsolute Is Tolerance Absolute
  110.      * 
  111.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  112.      */

  114.     public PowerIterationComponentExtractor (
  115.         final int maxIterations,
  116.         final double tolerance,
  117.         final boolean isToleranceAbsolute)
  118.         throws java.lang.Exception
  119.     {
  120.         if (0 >= (_maxIterations = maxIterations) ||
  121.             !org.drip.numerical.common.NumberUtil.IsValid (
  122.                 _tolerance = tolerance
  123.             ) || 0. == _tolerance
  124.         )
  125.         {
  126.             throw new java.lang.Exception (
  127.                 "PowerIterationComponentExtractor ctr: Invalid Inputs!"
  128.             );
  129.         }

  131.         _isToleranceAbsolute = isToleranceAbsolute;
  132.     }

  134.     /**
  135.      * Retrieve the Maximum Number of Iterations
  136.      * 
  137.      * @return The Maximum Number of Iterations
  138.      */

  140.     public int maxIterations()
  141.     {
  142.         return _maxIterations;
  143.     }

  145.     /**
  146.      * Retrieve the Tolerance Level
  147.      * 
  148.      * @return The Tolerance Level
  149.      */

  151.     public double tolerance()
  152.     {
  153.         return _tolerance;
  154.     }

  156.     /**
  157.      * Indicate if the specified Tolerance is Absolute
  158.      * 
  159.      * @return TRUE - The specified Tolerance is Absolute
  160.      */

  162.     public boolean isToleranceAbsolute()
  163.     {
  164.         return _isToleranceAbsolute;
  165.     }

  167.     @Override public org.drip.numerical.eigen.EigenComponent principalComponent (
  168.         final double[][] a)
  169.     {
  170.         if (null == a)
  171.         {
  172.             return null;
  173.         }

  175.         int iterationIndex = 0;
  176.         int componentCount = a.length;
  177.         double eigenValue = componentCount;
  178.         double[] eigenVector = new double[componentCount];
  179.         double[] eigenVectorArray = new double[componentCount];

  181.         if (0 == componentCount || null == a[0] || componentCount != a[0].length)
  182.         {
  183.             return null;
  184.         }

  186.         for (int componentIndex = 0;
  187.             componentIndex < componentCount;
  188.             ++componentIndex)
  189.         {
  190.             eigenVector[componentIndex] = 1.;
  191.         }

  193.         eigenVector = org.drip.numerical.linearalgebra.Matrix.Normalize (
  194.             eigenVector
  195.         );

  197.         double oldEigenValue = eigenValue;
  198.         double absoluteTolerance = _isToleranceAbsolute ? _tolerance : eigenValue * _tolerance;
  199.         absoluteTolerance = absoluteTolerance > _tolerance ? absoluteTolerance : _tolerance;

  201.         while (iterationIndex < _maxIterations)
  202.         {
  203.             for (int componentIndexI = 0;
  204.                 componentIndexI < componentCount;
  205.                 ++componentIndexI)
  206.             {
  207.                 eigenVectorArray[componentIndexI] = 0.;

  209.                 for (int componentIndexJ = 0;
  210.                     componentIndexJ < componentCount;
  211.                     ++componentIndexJ)
  212.                 {
  213.                     eigenVectorArray[componentIndexI] +=
  214.                         a[componentIndexI][componentIndexJ] * eigenVector[componentIndexJ];
  215.                 }
  216.             }

  218.             eigenVectorArray = org.drip.numerical.linearalgebra.Matrix.Normalize (
  219.                 eigenVectorArray
  220.             );

  222.             try {
  223.                 eigenValue = org.drip.numerical.linearalgebra.Matrix.RayleighQuotient (
  224.                     a,
  225.                     eigenVectorArray
  226.                 );
  227.             }
  228.             catch (java.lang.Exception e)
  229.             {
  230.                 e.printStackTrace();

  232.                 return null;
  233.             }

  235.             if (absoluteTolerance > java.lang.Math.abs (
  236.                 eigenValue - oldEigenValue
  237.             ))
  238.             {
  239.                 break;
  240.             }

  242.             eigenVector = eigenVectorArray;
  243.             oldEigenValue = eigenValue;
  244.             ++iterationIndex;
  245.         }

  247.         if (iterationIndex >= _maxIterations)
  248.         {
  249.             return null;
  250.         }

  252.         try
  253.         {
  254.             return new org.drip.numerical.eigen.EigenComponent (
  255.                 eigenVectorArray,
  256.                 eigenValue
  257.             );
  258.         }
  259.         catch (java.lang.Exception e)
  260.         {
  261.             e.printStackTrace();
  262.         }

  264.         return null;
  265.     }

  267.     @Override public org.drip.numerical.eigen.EigenOutput eigenize (
  268.         final double[][] a)
  269.     {
  270.         return null;
  271.     }
  272. }
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