LinearAlgebra.java
package org.drip.sample.matrix;
import org.drip.numerical.common.*;
import org.drip.numerical.linearalgebra.*;
import org.drip.service.env.EnvManager;
/*
* -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*/
/*!
* 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
* Copyright (C) 2014 Lakshmi Krishnamurthy
* Copyright (C) 2013 Lakshmi Krishnamurthy
*
* This file is part of DROP, an open-source library targeting risk, transaction costs, exposure, margin
* calculations, valuation adjustment, and portfolio construction within and across fixed income,
* credit, commodity, equity, FX, and structured products.
*
* https://lakshmidrip.github.io/DROP/
*
* DROP is composed of three modules:
*
* - DROP Analytics Core - https://lakshmidrip.github.io/DROP-Analytics-Core/
* - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
* - DROP Numerical Core - https://lakshmidrip.github.io/DROP-Numerical-Core/
*
* DROP Analytics Core implements libraries for the following:
* - Fixed Income Analytics
* - Asset Backed Analytics
* - XVA Analytics
* - Exposure and Margin Analytics
*
* DROP Portfolio Core implements libraries for the following:
* - Asset Allocation Analytics
* - Transaction Cost Analytics
*
* DROP Numerical Core implements libraries for the following:
* - Statistical Learning
* - Numerical Optimizer
* - Spline Builder
* - Algorithm Support
*
* 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>LinearAlgebra</i> implements Samples for Linear Algebra and Matrix Manipulations. It demonstrates the
* following:
*
* <br><br>
* <ul>
* <li>
* Compute the inverse of a matrix, and multiply with the original to recover the unit matrix
* </li>
* <li>
* Solves system of linear equations using one the exposed techniques
* </li>
* </ul>
*
* <br><br>
* <ul>
* <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalCore.md">Numerical Core Module</a></li>
* <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalSupportLibrary.md">Numerical Support Library</a></li>
* <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/README.md">Sample</a></li>
* <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>
* </ul>
* <br><br>
*
* @author Lakshmi Krishnamurthy
*/
public class LinearAlgebra {
/*
* Sample illustrating the Invocation of Base Matrix Inversion and Product Computation Verification.
*
* WARNING: Insufficient Error Checking, so use caution
*/
private static final void InverseVerifyDump (
final String strLabel,
final double[][] aadblA)
{
double[][] aadblAInv = Matrix.InvertUsingGaussianElimination (aadblA);
System.out.println ("--- TESTS FOR " + strLabel + "---");
System.out.println ("---------------------------------");
NumberUtil.Print2DArrayTriplet (
"\tSOURCE" + strLabel,
"INVERSE" + strLabel,
"PRODUCT" + strLabel,
aadblA,
aadblAInv,
Matrix.Product (
aadblA,
aadblAInv
),
false
);
System.out.println ("---------------------------------\n\n");
}
/*
* Sample illustrating the Invocation of Base Matrix Manipulation Functionality
*
* WARNING: Insufficient Error Checking, so use caution
*/
public static final void MatrixManipulation()
{
InverseVerifyDump ("#A", new double[][] {
{1, 2, 3},
{4, 5, 6},
{7, 8, 9.01}
});
InverseVerifyDump ("#B", new double[][] {
{ 0.1667, 0.0000, 0.0000, 0.0000},
{ 0.0000, 0.0000, 0.0000, 0.1667},
{-0.6667, 0.5000, 0.0000, 0.0000},
{ 2.6667, -3.0000, 1.0000, 0.0000}
});
InverseVerifyDump ("#C", new double[][] {
{ 1.0000, 0.0000, 0.0000, 0.0000},
{ 1.0000, 1.0000, 1.0000, 1.0000},
{ 0.0000, 1.0000, 0.0000, 0.0000},
{ 0.0000, 0.0000, 2.0000, 0.0000}
});
InverseVerifyDump ("#D", new double[][] {
{ 0.0000, 1.0000},
{ 1.0000, 2.0000}
});
InverseVerifyDump ("#E", new double[][] {
{ 0.0000, 1.0000},
{ 1.0000, 0.0000}
});
InverseVerifyDump ("#F", new double[][] {
{ 1.0000, 0.0000, 0.0000, 0.0000},
{ 1.0000, 1.0000, 1.0000, 1.0000},
{-1.0000, 1.0000, 0.0000, 0.0000},
{ 1.0000, 2.0000, 3.0000, 4.0000}
});
InverseVerifyDump ("#G", new double[][] {
{ 0.0000, 1.0000, 0.0000, 0.0000},
{ 0.0000, 0.0000, 2.0000, 0.0000},
{ 0.0434, 0.0188, 16.0083, 24.0037},
{ 0.0188, 0.0083, 24.0037, 48.0017}
});
}
/*
* Sample illustrating the Invocation of Linear System Solver Functionality
*
* WARNING: Insufficient Error Checking, so use caution
*/
public static final void LinearSystemSolver()
{
double[][] aadblA = new double[][] {
{1.000, 0.500, 0.333, 0.000, 0.000, 0.000},
{0.000, 0.000, 0.000, 1.000, 0.500, 0.333},
{1.000, 1.000, 1.000, -1.000, 0.000, 0.000},
{0.000, 0.500, 2.000, 0.000, -0.500, 0.000},
{0.000, 1.000, 0.000, 0.000, 0.000, 0.000},
{0.000, 0.000, 0.000, 0.000, 1.000, 0.000},
};
double[] adblB = new double[] {0.02, 0.026, 0., 0., 0., 0.};
org.drip.numerical.common.NumberUtil.Print2DArray (
"\tCOEFF",
aadblA,
false
);
/*
* Solve the Linear System using Gaussian Elimination
*/
LinearizationOutput lssGaussianElimination = LinearSystemSolver.SolveUsingGaussianElimination (
aadblA,
adblB
);
for (int i = 0; i < lssGaussianElimination.getTransformedRHS().length; ++i)
System.out.println ("GaussianElimination[" + i + "] = " + FormatUtil.FormatDouble
(lssGaussianElimination.getTransformedRHS()[i], 0, 6, 1.));
for (int i = 0; i < 6; ++i) {
double dblRHS = 0.;
for (int j = 0; j < 6; ++j)
dblRHS += aadblA[i][j] * lssGaussianElimination.getTransformedRHS()[j];
System.out.println ("RHS[" + i + "]: " + dblRHS);
}
/*
* Solve the Linear System using the Gauss-Seidel method
*/
/* LinearSystemSolution lssGaussSeidel = LinearSystemSolver.SolveUsingGaussSeidel (aadblA, adblB);
for (int i = 0; i < lssGaussSeidel.getSolution().length; ++i)
System.out.println ("GaussSeidel[" + i + "] = " + FormatUtil.FormatDouble (lssGaussSeidel.getSolution()[i], 0, 2, 1.)); */
}
public static final void main (
final String[] astrArgs)
{
EnvManager.InitEnv ("");
MatrixManipulation();
LinearSystemSolver();
EnvManager.TerminateEnv();
}
}