Square.java
package org.drip.function.matrix;
/*
* -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*/
/*!
* Copyright (C) 2019 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>Square</i> implements a Square Matrix. The References are:
*
* <br><br>
* <ul>
* <li>
* Claerbout, J. F. (1985): <i>Fundamentals of Geo-physical Data Processing</i> <b>Blackwell
* Scientific</b>
* </li>
* <li>
* Horn, R. A., and C. R. Johnson (1991): <i>Topics in Matrix Analysis</i> <b>Cambridge University
* Press</b>
* </li>
* <li>
* Schwerdtfeger, A. (1938): <i>Les Fonctions de Matrices: Les Fonctions Univalentes I</i>
* <b>Hermann</b> Paris, France
* </li>
* <li>
* Sylvester, J. J. (1883): On the Equation to the Secular Inequalities in the Planetary Theory
* <i>The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science</i> <b>16
* (100)</b> 267-269
* </li>
* <li>
* Wikipedia (2019): Sylvester Formula https://en.wikipedia.org/wiki/Sylvester%27s_formula
* </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 Square
{
public double[][] _grid = null;
/**
* Square Constructor
*
* @param grid Grid of Elements
*
* @throws java.lang.Exception Throwjn if the Inputs are Invalid
*/
public Square (
final double[][] grid)
throws java.lang.Exception
{
if (null == (_grid = grid))
{
throw new java.lang.Exception (
"Square Constructor => Invalid Inputs"
);
}
int dimension = _grid.length;
if (0 == dimension)
{
throw new java.lang.Exception (
"Square Constructor => Invalid Inputs"
);
}
for (int dimensionIndex = 0;
dimensionIndex < dimension;
++dimensionIndex)
{
if (null == _grid[dimensionIndex] ||
dimension != _grid[dimensionIndex].length ||
!org.drip.numerical.common.NumberUtil.IsValid (
_grid[dimensionIndex]
)
)
{
throw new java.lang.Exception (
"Square Constructor => Invalid Inputs"
);
}
}
}
/**
* Retrieve the Grid of Elements
*
* @return Grid of Elements
*/
public double[][] grid()
{
return _grid;
}
/**
* Retrieve the Dimension of the Square Matrix
*
* @return Dimension of the Square Matrix
*/
public int dimension()
{
return _grid.length;
}
/**
* Retrieve the Eigen-Components of the Square Matrix
*
* @return The Eigen-Components of the Square Matrix
*/
public org.drip.numerical.eigen.EigenOutput eigenize()
{
try
{
return new org.drip.numerical.eigen.QREigenComponentExtractor (
100,
1.e-06
).eigenize (
_grid
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Generate the Frobenius Covariance
*
* @return The Frobenius Covariance
*/
public org.drip.function.matrix.FrobeniusCovariance frobeniusCovariance()
{
org.drip.function.matrix.FrobeniusCovariance frobeniusCovariance =
new org.drip.function.matrix.FrobeniusCovariance();
org.drip.numerical.eigen.EigenOutput eigenOutput = eigenize();
if (null == eigenOutput)
{
return null;
}
double[] eigenValueArray = eigenOutput.eigenValueArray();
int dimension = _grid.length;
double[][][] eigenShadowArray = new double[dimension][dimension][dimension];
for (int eigenIndex = 0;
eigenIndex < dimension;
++eigenIndex)
{
for (int dimensionIndexI = 0;
dimensionIndexI < dimension;
++dimensionIndexI)
{
for (int dimensionIndexJ = 0;
dimensionIndexJ < dimension;
++dimensionIndexJ)
{
eigenShadowArray[eigenIndex][dimensionIndexI][dimensionIndexJ] =
_grid[dimensionIndexI][dimensionIndexJ] - (
dimensionIndexI == dimensionIndexJ ? eigenValueArray[eigenIndex] : 0.
);
}
}
}
for (int componentIndex = 0;
componentIndex < dimension;
++componentIndex)
{
double[][] frobeniusComponentMatrix = null;
double componentEigenValue = eigenValueArray[componentIndex];
for (int eigenIndex = 0;
eigenIndex < dimension;
++eigenIndex)
{
if (eigenIndex == componentIndex)
{
continue;
}
if (null == frobeniusComponentMatrix)
{
frobeniusComponentMatrix = org.drip.numerical.linearalgebra.Matrix.Scale2D (
eigenShadowArray[eigenIndex],
1. / (componentEigenValue - eigenValueArray[eigenIndex])
);
}
else
{
frobeniusComponentMatrix = org.drip.numerical.linearalgebra.Matrix.Scale2D (
org.drip.numerical.linearalgebra.Matrix.Product (
frobeniusComponentMatrix,
eigenShadowArray[eigenIndex]
),
1. / (componentEigenValue - eigenValueArray[eigenIndex])
);
}
}
try
{
if (!frobeniusCovariance.addComponent (
componentEigenValue,
new org.drip.function.matrix.Square (
frobeniusComponentMatrix
)
))
{
return null;
}
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
}
return frobeniusCovariance;
}
/**
* Compute the Value of the Matrix using the specified Function
*
* @param r1ToR1Function The R<sup>1</sup> To R<sup>1</sup> Function
*
* @return The Function Matrix Value
*/
public double[][] evaluate (
final org.drip.function.definition.R1ToR1 r1ToR1Function)
{
if (null == r1ToR1Function)
{
return null;
}
int dimension = _grid.length;
double[][] matrixFunction = null;
org.drip.function.matrix.FrobeniusCovariance frobeniusCovariance = frobeniusCovariance();
if (null == frobeniusCovariance)
{
return null;
}
for (java.util.Map.Entry<java.lang.Double, org.drip.function.matrix.Square> componentMapEntry :
frobeniusCovariance.componentMap().entrySet())
{
double[][] frobeniusComponentFunctionProjection = null;
try
{
frobeniusComponentFunctionProjection = org.drip.numerical.linearalgebra.Matrix.Scale2D (
componentMapEntry.getValue().grid(),
r1ToR1Function.evaluate (
componentMapEntry.getKey()
)
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
return null;
}
if (null == frobeniusComponentFunctionProjection)
{
return null;
}
if (null == matrixFunction)
{
matrixFunction = frobeniusComponentFunctionProjection;
}
else
{
for (int dimensionIndexI = 0;
dimensionIndexI < dimension;
++dimensionIndexI)
{
for (int dimensionIndexJ = 0;
dimensionIndexJ < dimension;
++dimensionIndexJ)
{
matrixFunction[dimensionIndexI][dimensionIndexJ] =
matrixFunction[dimensionIndexI][dimensionIndexJ] +
frobeniusComponentFunctionProjection[dimensionIndexI][dimensionIndexJ];
}
}
}
}
return matrixFunction;
}
/**
* Compute the Determinant
*
* @return The Determinant
*/
public double determinant()
{
org.drip.numerical.eigen.EigenOutput eigenOutput = eigenize();
if (null == eigenOutput)
{
return 0.;
}
double[] eigenValueArray = eigenOutput.eigenValueArray();
double determinant = 1.;
int dimension = _grid.length;
for (int eigenIndex = 0;
eigenIndex < dimension;
++eigenIndex)
{
determinant = determinant * eigenValueArray[eigenIndex];
}
return determinant;
}
}