RdContinuousBanach.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>RdContinuousBanach</i> implements the Normed, Bounded/Unbounded Continuous 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 RdContinuousBanach extends org.drip.spaces.tensor.RdContinuousVector implements
  106.     org.drip.spaces.metric.RdNormed {
  107.     private int _iPNorm = -1;
  108.     private org.drip.measure.continuous.Rd _distRd = null;

  110.     /**
  111.      * Construct the Standard l^p R^d Continuous Banach Space Instance
  112.      * 
  113.      * @param iDimension The Space Dimension
  114.      * @param distRd The R^d Borel Sigma Measure
  115.      * @param iPNorm The p-norm of the Space
  116.      * 
  117.      * @return The Standard l^p R^d Continuous Banach Space Instance
  118.      */

  120.     public static final RdContinuousBanach StandardBanach (
  121.         final int iDimension,
  122.         final org.drip.measure.continuous.Rd distRd,
  123.         final int iPNorm)
  124.     {
  125.         try {
  126.             return 0 >= iDimension ? null : new RdContinuousBanach (new
  127.                 org.drip.spaces.tensor.R1ContinuousVector[iDimension], distRd, iPNorm);
  128.         } catch (java.lang.Exception e) {
  129.             e.printStackTrace();
  130.         }

  132.         return null;
  133.     }

  135.     /**
  136.      * Construct the Supremum (i.e., l^Infinity) R^d Continuous Banach Space Instance
  137.      * 
  138.      * @param iDimension The Space Dimension
  139.      * @param distRd The R^d Borel Sigma Measure
  140.      * 
  141.      * @return The Supremum (i.e., l^Infinity) R^d Continuous Banach Space Instance
  142.      */

  144.     public static final RdContinuousBanach SupremumBanach (
  145.         final int iDimension,
  146.         final org.drip.measure.continuous.Rd distRd)
  147.     {
  148.         try {
  149.             return 0 >= iDimension ? null : new RdContinuousBanach (new
  150.                 org.drip.spaces.tensor.R1ContinuousVector[iDimension], distRd, java.lang.Integer.MAX_VALUE);
  151.         } catch (java.lang.Exception e) {
  152.             e.printStackTrace();
  153.         }

  155.         return null;
  156.     }

  158.     /**
  159.      * RdContinuousBanach Space Constructor
  160.      * 
  161.      * @param aR1CV Array of R^1 Continuous Vector
  162.      * @param distRd The R^d Borel Sigma Measure
  163.      * @param iPNorm The p-norm of the Space
  164.      * 
  165.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  166.      */

  168.     public RdContinuousBanach (
  169.         final org.drip.spaces.tensor.R1ContinuousVector[] aR1CV,
  170.         final org.drip.measure.continuous.Rd distRd,
  171.         final int iPNorm)
  172.         throws java.lang.Exception
  173.     {
  174.         super (aR1CV);

  176.         if (0 > (_iPNorm = iPNorm))
  177.             throw new java.lang.Exception ("RdContinuousBanach Constructor: Invalid p-norm");

  179.         _distRd = distRd;
  180.     }

  182.     @Override public int pNorm()
  183.     {
  184.         return _iPNorm;
  185.     }

  187.     @Override public org.drip.measure.continuous.Rd borelSigmaMeasure()
  188.     {
  189.         return _distRd;
  190.     }

  192.     @Override public double sampleSupremumNorm (
  193.         final double[] adblX)
  194.         throws java.lang.Exception
  195.     {
  196.         if (!validateInstance (adblX))
  197.             throw new java.lang.Exception ("RdContinuousBanach::sampleSupremumNorm => Invalid Inputs");

  199.         int iDimension = adblX.length;

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

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

  206.             dblNorm = dblNorm > dblAbsoluteX ? dblNorm : dblAbsoluteX;
  207.         }

  209.         return dblNorm;
  210.     }

  212.     @Override public double sampleMetricNorm (
  213.         final double[] adblX)
  214.         throws java.lang.Exception
  215.     {
  216.         if (!validateInstance (adblX))
  217.             throw new java.lang.Exception ("RdContinuousBanach::sampleMetricNorm => Invalid Inputs");

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

  221.         double dblNorm = 0.;
  222.         int iDimension = adblX.length;

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

  227.         return java.lang.Math.pow (dblNorm, 1. / _iPNorm);
  228.     }

  230.     @Override public double[] populationMode()
  231.     {
  232.         if (null == _distRd) return null;

  234.         org.drip.function.definition.RdToR1 funcRdToR1 = new org.drip.function.definition.RdToR1 (null) {
  235.             @Override public int dimension()
  236.             {
  237.                 return org.drip.function.definition.RdToR1.DIMENSION_NOT_FIXED;
  238.             }

  240.             @Override public double evaluate (
  241.                 final double[] adblX)
  242.                 throws java.lang.Exception
  243.             {
  244.                 return _distRd.density (adblX);
  245.             }
  246.         };

  248.         org.drip.function.definition.VariateOutputPair vopMode = funcRdToR1.maxima (leftDimensionEdge(),
  249.             rightDimensionEdge());

  251.         return null == vopMode ? null : vopMode.variates();
  252.     }

  254.     @Override public double populationSupremumNorm()
  255.         throws java.lang.Exception
  256.     {
  257.         if (null == _distRd)
  258.             throw new java.lang.Exception ("RdContinuousBanach::populationSupremumNorm => Invalid Inputs");

  260.         return sampleSupremumNorm (populationMode());
  261.     }

  263.     @Override public double populationMetricNorm()
  264.         throws java.lang.Exception
  265.     {
  266.         if (null == _distRd)
  267.             throw new java.lang.Exception ("RdContinuousBanach::populationMetricNorm => Invalid Inputs");

  269.         if (java.lang.Integer.MAX_VALUE == _iPNorm) return sampleSupremumNorm (populationMode());

  271.         org.drip.function.definition.RdToR1 funcRdToR1 = new org.drip.function.definition.RdToR1 (null) {
  272.             @Override public int dimension()
  273.             {
  274.                 return org.drip.function.definition.RdToR1.DIMENSION_NOT_FIXED;
  275.             }

  277.             @Override public double evaluate (
  278.                 final double[] adblX)
  279.                 throws java.lang.Exception
  280.             {
  281.                 double dblNorm = 0.;
  282.                 int iDimension = adblX.length;

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

  287.                 return dblNorm * _distRd.density (adblX);
  288.             }
  289.         };

  291.         return java.lang.Math.pow (funcRdToR1.integrate (leftDimensionEdge(), rightDimensionEdge()), 1. /
  292.             _iPNorm);
  293.     }

  295.     @Override public double borelMeasureSpaceExpectation (
  296.         final org.drip.function.definition.RdToR1 funcRdToR1)
  297.         throws java.lang.Exception
  298.     {
  299.         if (null == _distRd || null == funcRdToR1)
  300.             throw new java.lang.Exception
  301.                 ("RdContinuousBanach::borelMeasureSpaceExpectation => Invalid Inputs");

  303.         org.drip.function.definition.RdToR1 funcDensityRdToR1 = new org.drip.function.definition.RdToR1
  304.             (null) {
  305.             @Override public int dimension()
  306.             {
  307.                 return org.drip.function.definition.RdToR1.DIMENSION_NOT_FIXED;
  308.             }

  310.             @Override public double evaluate (
  311.                 final double[] adblX)
  312.                 throws java.lang.Exception
  313.             {
  314.                 return funcRdToR1.evaluate (adblX) * _distRd.density (adblX);
  315.             }
  316.         };

  318.         return funcDensityRdToR1.integrate (leftDimensionEdge(), rightDimensionEdge());
  319.     }
  320. }
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