RdCombinatorialBanach.java

  1. package org.drip.spaces.metric;

  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>RdCombinatorialBanach</i> implements the Bounded/Unbounded Combinatorial l<sub>p</sub> R<sup>d</sup>
  83.  * Spaces. The Reference we've used is:
  84.  *
  85.  * <br><br>
  86.  *  <ul>
  87.  *      <li>
  88.  *          Carl, B., and I. Stephani (1990): <i>Entropy, Compactness, and the Approximation of Operators</i>
  89.  *              <b>Cambridge University Press</b> Cambridge UK 
  90.  *      </li>
  91.  *  </ul>
  92.  *
  93.  * <br><br>
  94.  *  <ul>
  95.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  96.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/StatisticalLearningLibrary.md">Statistical Learning Library</a></li>
  97.  *      <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>
  98.  *      <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>
  99.  *  </ul>
  100.  * <br><br>
  101.  *
  102.  * @author Lakshmi Krishnamurthy
  103.  */

  105. public class RdCombinatorialBanach extends org.drip.spaces.tensor.RdCombinatorialVector implements
  106.     org.drip.spaces.metric.RdNormed {
  107.     private int _iPNorm = -1;
  108.     private org.drip.measure.continuous.Rd _distRd = null;

  110.     /**
  111.      * RdCombinatorialBanach Space Constructor
  112.      * 
  113.      * @param aR1CV Array of Combinatorial R^1 Vector Spaces
  114.      * @param distRd The R^d Borel Sigma Measure
  115.      * @param iPNorm The p-norm of the Space
  116.      * 
  117.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  118.      */

  120.     public RdCombinatorialBanach (
  121.         final org.drip.spaces.tensor.R1CombinatorialVector[] aR1CV,
  122.         final org.drip.measure.continuous.Rd distRd,
  123.         final int iPNorm)
  124.         throws java.lang.Exception
  125.     {
  126.         super (aR1CV);

  128.         if (0 > (_iPNorm = iPNorm))
  129.             throw new java.lang.Exception ("RdCombinatorialBanach Constructor: Invalid p-norm");

  131.         _distRd = distRd;
  132.     }

  134.     @Override public int pNorm()
  135.     {
  136.         return _iPNorm;
  137.     }

  139.     @Override public org.drip.measure.continuous.Rd borelSigmaMeasure()
  140.     {
  141.         return _distRd;
  142.     }

  144.     @Override public double sampleSupremumNorm (
  145.         final double[] adblX)
  146.         throws java.lang.Exception
  147.     {
  148.         if (!validateInstance (adblX))
  149.             throw new java.lang.Exception ("RdCombinatorialBanach::sampleSupremumNorm => Invalid Inputs");

  151.         int iDimension = adblX.length;

  153.         double dblNorm = java.lang.Math.abs (adblX[0]);

  155.         for (int i = 1; i < iDimension; ++i) {
  156.             double dblAbsoluteX = java.lang.Math.abs (adblX[i]);

  158.             dblNorm = dblNorm > dblAbsoluteX ? dblNorm : dblAbsoluteX;
  159.         }

  161.         return dblNorm;
  162.     }

  164.     @Override public double sampleMetricNorm (
  165.         final double[] adblX)
  166.         throws java.lang.Exception
  167.     {
  168.         if (!validateInstance (adblX))
  169.             throw new java.lang.Exception ("RdCombinatorialBanach::sampleMetricNorm => Invalid Inputs");

  171.         if (java.lang.Integer.MAX_VALUE == _iPNorm) return sampleSupremumNorm (adblX);

  173.         double dblNorm = 0.;
  174.         int iDimension = adblX.length;

  176.         for (int i = 0; i < iDimension; ++i)
  177.             dblNorm += java.lang.Math.pow (java.lang.Math.abs (adblX[i]), _iPNorm);

  179.         return java.lang.Math.pow (dblNorm, 1. / _iPNorm);
  180.     }

  182.     @Override public double[] populationMode()
  183.     {
  184.         if (null == _distRd) return null;

  186.         org.drip.spaces.iterator.RdSpanningCombinatorialIterator crmi = iterator();

  188.         double[] adblVariate = crmi.cursorVariates();

  190.         int iDimension = adblVariate.length;
  191.         double dblModeProbabilityDensity = 0.;
  192.         double[] adblModeVariate = new double[iDimension];
  193.         double dblProbabilityDensity = java.lang.Double.NaN;

  195.         while (null != adblVariate) {
  196.             try {
  197.                 dblProbabilityDensity = _distRd.density (adblVariate);
  198.             } catch (java.lang.Exception e) {
  199.                 e.printStackTrace();

  201.                 return null;
  202.             }

  204.             if (dblProbabilityDensity > dblModeProbabilityDensity) {
  205.                 for (int i = 0; i < iDimension; ++i)
  206.                     adblModeVariate[i] = adblVariate[i];

  208.                 dblModeProbabilityDensity = dblProbabilityDensity;
  209.             }

  211.             adblVariate = crmi.nextVariates();
  212.         }

  214.         return adblModeVariate;
  215.     }

  217.     @Override public double populationSupremumNorm()
  218.         throws java.lang.Exception
  219.     {
  220.         if (null == _distRd)
  221.             throw new java.lang.Exception
  222.                 ("RdCombinatorialBanach::populationSupremumNorm => Invalid Inputs");

  224.         return sampleSupremumNorm (populationMode());
  225.     }

  227.     @Override public double populationMetricNorm()
  228.         throws java.lang.Exception
  229.     {
  230.         if (java.lang.Integer.MAX_VALUE == _iPNorm) return sampleSupremumNorm (populationMode());

  232.         if (null == _distRd)
  233.             throw new java.lang.Exception
  234.                 ("RdCombinatorialBanach::populationMetricNorm => No Multivariate Distribution");

  236.         org.drip.spaces.iterator.RdSpanningCombinatorialIterator crmi = iterator();

  238.         double[] adblVariate = crmi.cursorVariates();

  240.         double dblNormalizer = 0.;
  241.         double dblPopulationMetricNorm  = 0.;
  242.         int iDimension = adblVariate.length;

  244.         while (null != adblVariate) {
  245.             double dblProbabilityDensity = _distRd.density (adblVariate);

  247.             dblNormalizer += dblProbabilityDensity;

  249.             for (int i = 0; i < iDimension; ++i)
  250.                 dblPopulationMetricNorm += dblProbabilityDensity * java.lang.Math.pow (java.lang.Math.abs
  251.                     (adblVariate[i]), _iPNorm);

  253.             adblVariate = crmi.nextVariates();
  254.         }

  256.         return java.lang.Math.pow (dblPopulationMetricNorm / dblNormalizer, 1. / _iPNorm);
  257.     }

  259.     @Override public double borelMeasureSpaceExpectation (
  260.         final org.drip.function.definition.RdToR1 funcRdToR1)
  261.         throws java.lang.Exception
  262.     {
  263.         if (null == _distRd || null == funcRdToR1)
  264.             throw new java.lang.Exception
  265.                 ("RdCombinatorialBanach::borelMeasureSpaceExpectation => Invalid Inputs");

  267.         org.drip.spaces.iterator.RdSpanningCombinatorialIterator crmi = iterator();

  269.         double[] adblVariate = crmi.cursorVariates();

  271.         double dblBorelMeasureSpaceExpectation = 0.;
  272.         double dblNormalizer = 0.;

  274.         while (null != adblVariate) {
  275.             double dblProbabilityDensity = _distRd.density (adblVariate);

  277.             dblNormalizer += dblProbabilityDensity;

  279.             dblBorelMeasureSpaceExpectation += dblProbabilityDensity * funcRdToR1.evaluate (adblVariate);

  281.             adblVariate = crmi.nextVariates();
  282.         }

  284.         return dblBorelMeasureSpaceExpectation / dblNormalizer;
  285.     }
  286. }
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