RdContinuousBanach.java
package org.drip.spaces.metric;
/*
* -*- 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>RdContinuousBanach</i> implements the Normed, Bounded/Unbounded Continuous l<sub>p</sub> R<sup>d</sup>
* Spaces. The Reference we've used is:
*
* <br><br>
* <ul>
* <li>
* Carl, B., and I. Stephani (1990): <i>Entropy, Compactness, and the Approximation of Operators</i>
* <b>Cambridge University Press</b> Cambridge UK
* </li>
* </ul>
*
* <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/StatisticalLearningLibrary.md">Statistical Learning Library</a></li>
* <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/spaces/README.md">R<sup>1</sup> and R<sup>d</sup> Vector/Tensor Spaces (Validated and/or Normed), and Function Classes</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/spaces/metric/README.md">Hilbert/Banach Normed Metric Spaces</a></li>
* </ul>
* <br><br>
*
* @author Lakshmi Krishnamurthy
*/
public class RdContinuousBanach extends org.drip.spaces.tensor.RdContinuousVector implements
org.drip.spaces.metric.RdNormed {
private int _iPNorm = -1;
private org.drip.measure.continuous.Rd _distRd = null;
/**
* Construct the Standard l^p R^d Continuous Banach Space Instance
*
* @param iDimension The Space Dimension
* @param distRd The R^d Borel Sigma Measure
* @param iPNorm The p-norm of the Space
*
* @return The Standard l^p R^d Continuous Banach Space Instance
*/
public static final RdContinuousBanach StandardBanach (
final int iDimension,
final org.drip.measure.continuous.Rd distRd,
final int iPNorm)
{
try {
return 0 >= iDimension ? null : new RdContinuousBanach (new
org.drip.spaces.tensor.R1ContinuousVector[iDimension], distRd, iPNorm);
} catch (java.lang.Exception e) {
e.printStackTrace();
}
return null;
}
/**
* Construct the Supremum (i.e., l^Infinity) R^d Continuous Banach Space Instance
*
* @param iDimension The Space Dimension
* @param distRd The R^d Borel Sigma Measure
*
* @return The Supremum (i.e., l^Infinity) R^d Continuous Banach Space Instance
*/
public static final RdContinuousBanach SupremumBanach (
final int iDimension,
final org.drip.measure.continuous.Rd distRd)
{
try {
return 0 >= iDimension ? null : new RdContinuousBanach (new
org.drip.spaces.tensor.R1ContinuousVector[iDimension], distRd, java.lang.Integer.MAX_VALUE);
} catch (java.lang.Exception e) {
e.printStackTrace();
}
return null;
}
/**
* RdContinuousBanach Space Constructor
*
* @param aR1CV Array of R^1 Continuous Vector
* @param distRd The R^d Borel Sigma Measure
* @param iPNorm The p-norm of the Space
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public RdContinuousBanach (
final org.drip.spaces.tensor.R1ContinuousVector[] aR1CV,
final org.drip.measure.continuous.Rd distRd,
final int iPNorm)
throws java.lang.Exception
{
super (aR1CV);
if (0 > (_iPNorm = iPNorm))
throw new java.lang.Exception ("RdContinuousBanach Constructor: Invalid p-norm");
_distRd = distRd;
}
@Override public int pNorm()
{
return _iPNorm;
}
@Override public org.drip.measure.continuous.Rd borelSigmaMeasure()
{
return _distRd;
}
@Override public double sampleSupremumNorm (
final double[] adblX)
throws java.lang.Exception
{
if (!validateInstance (adblX))
throw new java.lang.Exception ("RdContinuousBanach::sampleSupremumNorm => Invalid Inputs");
int iDimension = adblX.length;
double dblNorm = java.lang.Math.abs (adblX[0]);
for (int i = 1; i < iDimension; ++i) {
double dblAbsoluteX = java.lang.Math.abs (adblX[i]);
dblNorm = dblNorm > dblAbsoluteX ? dblNorm : dblAbsoluteX;
}
return dblNorm;
}
@Override public double sampleMetricNorm (
final double[] adblX)
throws java.lang.Exception
{
if (!validateInstance (adblX))
throw new java.lang.Exception ("RdContinuousBanach::sampleMetricNorm => Invalid Inputs");
if (java.lang.Integer.MAX_VALUE == _iPNorm) return sampleSupremumNorm (adblX);
double dblNorm = 0.;
int iDimension = adblX.length;
for (int i = 0; i < iDimension; ++i)
dblNorm += java.lang.Math.pow (java.lang.Math.abs (adblX[i]), _iPNorm);
return java.lang.Math.pow (dblNorm, 1. / _iPNorm);
}
@Override public double[] populationMode()
{
if (null == _distRd) return null;
org.drip.function.definition.RdToR1 funcRdToR1 = new org.drip.function.definition.RdToR1 (null) {
@Override public int dimension()
{
return org.drip.function.definition.RdToR1.DIMENSION_NOT_FIXED;
}
@Override public double evaluate (
final double[] adblX)
throws java.lang.Exception
{
return _distRd.density (adblX);
}
};
org.drip.function.definition.VariateOutputPair vopMode = funcRdToR1.maxima (leftDimensionEdge(),
rightDimensionEdge());
return null == vopMode ? null : vopMode.variates();
}
@Override public double populationSupremumNorm()
throws java.lang.Exception
{
if (null == _distRd)
throw new java.lang.Exception ("RdContinuousBanach::populationSupremumNorm => Invalid Inputs");
return sampleSupremumNorm (populationMode());
}
@Override public double populationMetricNorm()
throws java.lang.Exception
{
if (null == _distRd)
throw new java.lang.Exception ("RdContinuousBanach::populationMetricNorm => Invalid Inputs");
if (java.lang.Integer.MAX_VALUE == _iPNorm) return sampleSupremumNorm (populationMode());
org.drip.function.definition.RdToR1 funcRdToR1 = new org.drip.function.definition.RdToR1 (null) {
@Override public int dimension()
{
return org.drip.function.definition.RdToR1.DIMENSION_NOT_FIXED;
}
@Override public double evaluate (
final double[] adblX)
throws java.lang.Exception
{
double dblNorm = 0.;
int iDimension = adblX.length;
for (int i = 0; i < iDimension; ++i)
dblNorm += java.lang.Math.pow (java.lang.Math.abs (adblX[i]), _iPNorm);
return dblNorm * _distRd.density (adblX);
}
};
return java.lang.Math.pow (funcRdToR1.integrate (leftDimensionEdge(), rightDimensionEdge()), 1. /
_iPNorm);
}
@Override public double borelMeasureSpaceExpectation (
final org.drip.function.definition.RdToR1 funcRdToR1)
throws java.lang.Exception
{
if (null == _distRd || null == funcRdToR1)
throw new java.lang.Exception
("RdContinuousBanach::borelMeasureSpaceExpectation => Invalid Inputs");
org.drip.function.definition.RdToR1 funcDensityRdToR1 = new org.drip.function.definition.RdToR1
(null) {
@Override public int dimension()
{
return org.drip.function.definition.RdToR1.DIMENSION_NOT_FIXED;
}
@Override public double evaluate (
final double[] adblX)
throws java.lang.Exception
{
return funcRdToR1.evaluate (adblX) * _distRd.density (adblX);
}
};
return funcDensityRdToR1.integrate (leftDimensionEdge(), rightDimensionEdge());
}
}