R1Combinatorial.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>R1Combinatorial</i> implements the Normed, 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 R1Combinatorial extends org.drip.spaces.tensor.R1CombinatorialVector implements
  106.     org.drip.spaces.metric.R1Normed {
  107.     private int _iPNorm = -1;
  108.     private org.drip.measure.continuous.R1Univariate _distR1 = null;

  110.     /**
  111.      * Construct the Standard l^p R^1 Combinatorial Space Instance
  112.      * 
  113.      * @param lsElementSpace The List Space of Elements
  114.      * @param distR1 The R^1 Borel Sigma Measure
  115.      * @param iPNorm The p-norm of the Space
  116.      * 
  117.      * @return The Standard l^p R^1 Combinatorial Space Instance
  118.      */

  120.     public static final R1Combinatorial Standard (
  121.         final java.util.List<java.lang.Double> lsElementSpace,
  122.         final org.drip.measure.continuous.R1Univariate distR1,
  123.         final int iPNorm)
  124.     {
  125.         try {
  126.             return new R1Combinatorial (lsElementSpace, distR1, iPNorm);
  127.         } catch (java.lang.Exception e) {
  128.             e.printStackTrace();
  129.         }

  131.         return null;
  132.     }

  134.     /**
  135.      * Construct the Supremum (i.e., l^Infinity) R^1 Combinatorial Space Instance
  136.      * 
  137.      * @param lsElementSpace The List Space of Elements
  138.      * @param distR1 The R^1 Borel Sigma Measure
  139.      * 
  140.      * @return The Supremum (i.e., l^Infinity) R^1 Combinatorial Space Instance
  141.      */

  143.     public static final R1Combinatorial Supremum (
  144.         final java.util.List<java.lang.Double> lsElementSpace,
  145.         final org.drip.measure.continuous.R1Univariate distR1)
  146.     {
  147.         try {
  148.             return new R1Combinatorial (lsElementSpace, distR1, java.lang.Integer.MAX_VALUE);
  149.         } catch (java.lang.Exception e) {
  150.             e.printStackTrace();
  151.         }

  153.         return null;
  154.     }

  156.     /**
  157.      * R1Combinatorial Space Constructor
  158.      * 
  159.      * @param lsElementSpace The List Space of Elements
  160.      * @param distR1 The R^1 Borel Sigma Measure
  161.      * @param iPNorm The p-norm of the Space
  162.      * 
  163.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  164.      */

  166.     public R1Combinatorial (
  167.         final java.util.List<java.lang.Double> lsElementSpace,
  168.         final org.drip.measure.continuous.R1Univariate distR1,
  169.         final int iPNorm)
  170.         throws java.lang.Exception
  171.     {
  172.         super (lsElementSpace);

  174.         if (0 > (_iPNorm = iPNorm))
  175.             throw new java.lang.Exception ("R1Combinatorial Constructor: Invalid p-norm");

  177.         _distR1 = distR1;
  178.     }

  180.     @Override public int pNorm()
  181.     {
  182.         return _iPNorm;
  183.     }

  185.     @Override public org.drip.measure.continuous.R1Univariate borelSigmaMeasure()
  186.     {
  187.         return _distR1;
  188.     }

  190.     @Override public double sampleMetricNorm (
  191.         final double dblX)
  192.         throws java.lang.Exception
  193.     {
  194.         if (!validateInstance (dblX))
  195.             throw new java.lang.Exception ("R1Combinatorial::sampleMetricNorm => Invalid Inputs");

  197.         return java.lang.Math.abs (dblX);
  198.     }

  200.     @Override public double populationMode()
  201.         throws java.lang.Exception
  202.     {
  203.         if (null == _distR1)
  204.             throw new java.lang.Exception ("R1Combinatorial::populationMode => Invalid Inputs");

  206.         double dblMode = java.lang.Double.NaN;
  207.         double dblModeProbability = java.lang.Double.NaN;

  209.         for (double dblElement : elementSpace()) {
  210.             if (!org.drip.numerical.common.NumberUtil.IsValid (dblMode))
  211.                 dblModeProbability = _distR1.density (dblMode = dblElement);
  212.             else {
  213.                 double dblElementProbability = _distR1.density (dblElement);

  215.                 if (dblElementProbability > dblModeProbability) {
  216.                     dblMode = dblElement;
  217.                     dblModeProbability = dblElementProbability;
  218.                 }
  219.             }
  220.         }

  222.         return dblMode;
  223.     }

  225.     @Override public double populationMetricNorm()
  226.         throws java.lang.Exception
  227.     {
  228.         if (null == _distR1)
  229.             throw new java.lang.Exception ("R1Combinatorial::populationMetricNorm => Invalid Inputs");

  231.         double dblNorm = 0.;
  232.         double dblNormalizer = 0.;

  234.         for (double dblElement : elementSpace()) {
  235.             double dblElementProbability = _distR1.density (dblElement);

  237.             dblNormalizer += dblElementProbability;

  239.             dblNorm += sampleMetricNorm (dblElement) * dblElementProbability;
  240.         }

  242.         return dblNorm / dblNormalizer;
  243.     }

  245.     @Override public double borelMeasureSpaceExpectation (
  246.         final org.drip.function.definition.R1ToR1 funcR1ToR1)
  247.         throws java.lang.Exception
  248.     {
  249.         if (null == funcR1ToR1 || null == _distR1)
  250.             throw new java.lang.Exception
  251.                 ("R1Combinatorial::borelMeasureSpaceExpectation => Invalid Inputs");

  253.         double dblNormalizer = 0.;
  254.         double dblBorelMeasureSpaceExpectation = 0.;

  256.         for (double dblElement : elementSpace()) {
  257.             double dblElementProbability = _distR1.density (dblElement);

  259.             dblNormalizer += dblElementProbability;

  261.             dblBorelMeasureSpaceExpectation += funcR1ToR1.evaluate (dblElement) * dblElementProbability;
  262.         }

  264.         return dblBorelMeasureSpaceExpectation / dblNormalizer;
  265.     }
  266. }
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