LinearAlgebra.java

  1. package org.drip.sample.matrix;

  3. import org.drip.numerical.common.*;
  4. import org.drip.numerical.linearalgebra.*;
  5. import org.drip.service.env.EnvManager;

  7. /*

  9.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  10.  */

  12. /*!
  13.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  14.  * Copyright (C) 2018 Lakshmi Krishnamurthy
  15.  * Copyright (C) 2017 Lakshmi Krishnamurthy
  16.  * Copyright (C) 2016 Lakshmi Krishnamurthy
  17.  * Copyright (C) 2015 Lakshmi Krishnamurthy
  18.  * Copyright (C) 2014 Lakshmi Krishnamurthy
  19.  * Copyright (C) 2013 Lakshmi Krishnamurthy
  20.  * 
  21.  *  This file is part of DROP, an open-source library targeting risk, transaction costs, exposure, margin
  22.  *      calculations, valuation adjustment, and portfolio construction within and across fixed income,
  23.  *      credit, commodity, equity, FX, and structured products.
  24.  *  
  25.  *      https://lakshmidrip.github.io/DROP/
  26.  *  
  27.  *  DROP is composed of three modules:
  28.  *  
  29.  *  - DROP Analytics Core - https://lakshmidrip.github.io/DROP-Analytics-Core/
  30.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  31.  *  - DROP Numerical Core - https://lakshmidrip.github.io/DROP-Numerical-Core/
  32.  * 
  33.  *  DROP Analytics Core implements libraries for the following:
  34.  *  - Fixed Income Analytics
  35.  *  - Asset Backed Analytics
  36.  *  - XVA Analytics
  37.  *  - Exposure and Margin Analytics
  38.  * 
  39.  *  DROP Portfolio Core implements libraries for the following:
  40.  *  - Asset Allocation Analytics
  41.  *  - Transaction Cost Analytics
  42.  * 
  43.  *  DROP Numerical Core implements libraries for the following:
  44.  *  - Statistical Learning
  45.  *  - Numerical Optimizer
  46.  *  - Spline Builder
  47.  *  - Algorithm Support
  48.  * 
  49.  *  Documentation for DROP is Spread Over:
  50.  * 
  51.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  52.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  53.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  54.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  55.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  56.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  57.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  58.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  59.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  60.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  61.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  62.  * 
  63.  *  Licensed under the Apache License, Version 2.0 (the "License");
  64.  *      you may not use this file except in compliance with the License.
  65.  *   
  66.  *  You may obtain a copy of the License at
  67.  *      http://www.apache.org/licenses/LICENSE-2.0
  68.  *  
  69.  *  Unless required by applicable law or agreed to in writing, software
  70.  *      distributed under the License is distributed on an "AS IS" BASIS,
  71.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  72.  *  
  73.  *  See the License for the specific language governing permissions and
  74.  *      limitations under the License.
  75.  */

  77. /**
  78.  * <i>LinearAlgebra</i> implements Samples for Linear Algebra and Matrix Manipulations. It demonstrates the
  79.  * following:
  80.  *  
  81.  * <br><br>
  82.  *  <ul>
  83.  *      <li>
  84.  *          Compute the inverse of a matrix, and multiply with the original to recover the unit matrix
  85.  *      </li>
  86.  *      <li>
  87.  *          Solves system of linear equations using one the exposed techniques
  88.  *      </li>
  89.  *  </ul>
  90.  *  
  91.  * <br><br>
  92.  *  <ul>
  93.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalCore.md">Numerical Core Module</a></li>
  94.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalSupportLibrary.md">Numerical Support Library</a></li>
  95.  *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/README.md">Sample</a></li>
  96.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/matrix/README.md">Linear Algebra and Matrix Utilities</a></li>
  97.  *  </ul>
  98.  * <br><br>
  99.  *
  100.  * @author Lakshmi Krishnamurthy
  101.  */

  103. public class LinearAlgebra {

  105.     /*
  106.      * Sample illustrating the Invocation of Base Matrix Inversion and Product Computation Verification.
  107.      * 
  108.      *  WARNING: Insufficient Error Checking, so use caution
  109.      */

  111.     private static final void InverseVerifyDump (
  112.         final String strLabel,
  113.         final double[][] aadblA)
  114.     {
  115.         double[][] aadblAInv = Matrix.InvertUsingGaussianElimination (aadblA);

  117.         System.out.println ("--- TESTS FOR " + strLabel + "---");

  119.         System.out.println ("---------------------------------");

  121.         NumberUtil.Print2DArrayTriplet (
  122.             "\tSOURCE" + strLabel,
  123.             "INVERSE" + strLabel,
  124.             "PRODUCT" + strLabel,
  125.             aadblA,
  126.             aadblAInv,
  127.             Matrix.Product (
  128.                 aadblA,
  129.                 aadblAInv
  130.             ),
  131.             false
  132.         );

  134.         System.out.println ("---------------------------------\n\n");
  135.     }

  137.     /*
  138.      * Sample illustrating the Invocation of Base Matrix Manipulation Functionality
  139.      * 
  140.      *  WARNING: Insufficient Error Checking, so use caution
  141.      */

  143.     public static final void MatrixManipulation()
  144.     {
  145.         InverseVerifyDump ("#A", new double[][] {
  146.             {1, 2, 3},
  147.             {4, 5, 6},
  148.             {7, 8, 9.01}
  149.         });

  151.         InverseVerifyDump ("#B", new double[][] {
  152.             { 0.1667,  0.0000,  0.0000,  0.0000},
  153.             { 0.0000,  0.0000,  0.0000,  0.1667},
  154.             {-0.6667,  0.5000,  0.0000,  0.0000},
  155.             { 2.6667, -3.0000,  1.0000,  0.0000}
  156.         });

  158.         InverseVerifyDump ("#C", new double[][] {
  159.             { 1.0000,  0.0000,  0.0000,  0.0000},
  160.             { 1.0000,  1.0000,  1.0000,  1.0000},
  161.             { 0.0000,  1.0000,  0.0000,  0.0000},
  162.             { 0.0000,  0.0000,  2.0000,  0.0000}
  163.         });

  165.         InverseVerifyDump ("#D", new double[][] {
  166.             { 0.0000,  1.0000},
  167.             { 1.0000,  2.0000}
  168.         });

  170.         InverseVerifyDump ("#E", new double[][] {
  171.             { 0.0000,  1.0000},
  172.             { 1.0000,  0.0000}
  173.         });

  175.         InverseVerifyDump ("#F", new double[][] {
  176.             { 1.0000,  0.0000,  0.0000,  0.0000},
  177.             { 1.0000,  1.0000,  1.0000,  1.0000},
  178.             {-1.0000,  1.0000,  0.0000,  0.0000},
  179.             { 1.0000,  2.0000,  3.0000,  4.0000}
  180.         });

  182.         InverseVerifyDump ("#G", new double[][] {
  183.             { 0.0000,  1.0000,  0.0000,  0.0000},
  184.             { 0.0000,  0.0000,  2.0000,  0.0000},
  185.             { 0.0434,  0.0188, 16.0083, 24.0037},
  186.             { 0.0188,  0.0083, 24.0037, 48.0017}
  187.         });
  188.     }

  190.     /*
  191.      * Sample illustrating the Invocation of Linear System Solver Functionality
  192.      * 
  193.      *  WARNING: Insufficient Error Checking, so use caution
  194.      */

  196.     public static final void LinearSystemSolver()
  197.     {
  198.         double[][] aadblA = new double[][] {
  199.             {1.000, 0.500, 0.333,  0.000,  0.000, 0.000},
  200.             {0.000, 0.000, 0.000,  1.000,  0.500, 0.333},
  201.             {1.000, 1.000, 1.000, -1.000,  0.000, 0.000},
  202.             {0.000, 0.500, 2.000,  0.000, -0.500, 0.000},
  203.             {0.000, 1.000, 0.000,  0.000,  0.000, 0.000},
  204.             {0.000, 0.000, 0.000,  0.000,  1.000, 0.000},
  205.         };
  206.         double[] adblB = new double[] {0.02, 0.026, 0., 0., 0., 0.};

  208.         org.drip.numerical.common.NumberUtil.Print2DArray (
  209.             "\tCOEFF",
  210.             aadblA,
  211.             false
  212.         );

  214.         /*
  215.          * Solve the Linear System using Gaussian Elimination
  216.          */

  218.         LinearizationOutput lssGaussianElimination = LinearSystemSolver.SolveUsingGaussianElimination (
  219.             aadblA,
  220.             adblB
  221.         );

  223.         for (int i = 0; i < lssGaussianElimination.getTransformedRHS().length; ++i)
  224.             System.out.println ("GaussianElimination[" + i + "] = " + FormatUtil.FormatDouble
  225.                 (lssGaussianElimination.getTransformedRHS()[i], 0, 6, 1.));

  227.         for (int i = 0; i < 6; ++i) {
  228.             double dblRHS = 0.;

  230.             for (int j = 0; j < 6; ++j)
  231.                 dblRHS += aadblA[i][j] * lssGaussianElimination.getTransformedRHS()[j];

  233.             System.out.println ("RHS[" + i + "]: " + dblRHS);
  234.         }

  236.         /*
  237.          * Solve the Linear System using the Gauss-Seidel method
  238.          */

  240.         /* LinearSystemSolution lssGaussSeidel = LinearSystemSolver.SolveUsingGaussSeidel (aadblA, adblB);

  242.         for (int i = 0; i < lssGaussSeidel.getSolution().length; ++i)
  243.             System.out.println ("GaussSeidel[" + i + "] = " + FormatUtil.FormatDouble (lssGaussSeidel.getSolution()[i], 0, 2, 1.)); */
  244.     }

  246.     public static final void main (
  247.         final String[] astrArgs)
  248.     {
  249.         EnvManager.InitEnv ("");

  251.         MatrixManipulation();

  253.         LinearSystemSolver();

  255.         EnvManager.TerminateEnv();
  256.     }
  257. }
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