CartesianComplexNumber.java

  1. package org.drip.function.definition;

  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.  * Copyright (C) 2014 Lakshmi Krishnamurthy
  15.  * 
  16.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  17.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  18.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  19.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  20.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  21.  *      and computational support.
  22.  *  
  23.  *      https://lakshmidrip.github.io/DROP/
  24.  *  
  25.  *  DROP is composed of three modules:
  26.  *  
  27.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  28.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  29.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  30.  * 
  31.  *  DROP Product Core implements libraries for the following:
  32.  *  - Fixed Income Analytics
  33.  *  - Loan Analytics
  34.  *  - Transaction Cost Analytics
  35.  * 
  36.  *  DROP Portfolio Core implements libraries for the following:
  37.  *  - Asset Allocation Analytics
  38.  *  - Asset Liability Management Analytics
  39.  *  - Capital Estimation Analytics
  40.  *  - Exposure Analytics
  41.  *  - Margin Analytics
  42.  *  - XVA Analytics
  43.  * 
  44.  *  DROP Computational Core implements libraries for the following:
  45.  *  - Algorithm Support
  46.  *  - Computation Support
  47.  *  - Function Analysis
  48.  *  - Model Validation
  49.  *  - Numerical Analysis
  50.  *  - Numerical Optimizer
  51.  *  - Spline Builder
  52.  *  - Statistical Learning
  53.  * 
  54.  *  Documentation for DROP is Spread Over:
  55.  * 
  56.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  57.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  58.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  59.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  60.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  61.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  62.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  63.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  64.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  65.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  66.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  67.  * 
  68.  *  Licensed under the Apache License, Version 2.0 (the "License");
  69.  *      you may not use this file except in compliance with the License.
  70.  *   
  71.  *  You may obtain a copy of the License at
  72.  *      http://www.apache.org/licenses/LICENSE-2.0
  73.  *  
  74.  *  Unless required by applicable law or agreed to in writing, software
  75.  *      distributed under the License is distributed on an "AS IS" BASIS,
  76.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  77.  *  
  78.  *  See the License for the specific language governing permissions and
  79.  *      limitations under the License.
  80.  */

  82. /**
  83.  * <i>CartesianComplexNumber</i> implements the functionality for dealing with the Cartesian Form of Complex
  84.  * Numbers.
  85.  * 
  86.  * <br><br>
  87.  *  <ul>
  88.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  89.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalAnalysisLibrary.md">Numerical Analysis Library</a></li>
  90.  *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/function/README.md">R<sup>d</sup> To R<sup>d</sup> Function Analysis</a></li>
  91.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/function/definition/README.md">Function Implementation Ancillary Support Objects</a></li>
  92.  *  </ul>
  93.  * <br><br>
  94.  * 
  95.  * @author Lakshmi Krishnamurthy
  96.  */

  98. public class CartesianComplexNumber
  99. {
  100.     private double _real = java.lang.Double.NaN;
  101.     private double _imaginary = java.lang.Double.NaN;

  103.     /**
  104.      * Add the 2 Complex Numbers
  105.      * 
  106.      * @param complexNumber1 The First Complex Number
  107.      * @param complexNumber2 The Second Complex Number
  108.      * 
  109.      * @return The Complex Number instance that is a sum of the two
  110.      */

  112.     public static final CartesianComplexNumber Add (
  113.         final CartesianComplexNumber complexNumber1,
  114.         final CartesianComplexNumber complexNumber2)
  115.     {
  116.         if (null == complexNumber1 || null == complexNumber2)
  117.         {
  118.             return null;
  119.         }

  121.         try
  122.         {
  123.             return new CartesianComplexNumber (
  124.                 complexNumber1.real() + complexNumber2.real(),
  125.                 complexNumber1.imaginary() + complexNumber2.imaginary()
  126.             );
  127.         }
  128.         catch (java.lang.Exception e)
  129.         {
  130.             e.printStackTrace();
  131.         }

  133.         return null;
  134.     }

  136.     /**
  137.      * Scale the Complex Number with the factor
  138.      * 
  139.      * @param complexNumber The Complex Number
  140.      * @param scale The Scaling Factor
  141.      * 
  142.      * @return The Scaled Complex Number
  143.      */

  145.     public static final CartesianComplexNumber Scale (
  146.         final CartesianComplexNumber complexNumber,
  147.         final double scale)
  148.     {
  149.         if (null == complexNumber || !org.drip.numerical.common.NumberUtil.IsValid (scale))
  150.         {
  151.             return null;
  152.         }

  154.         try
  155.         {
  156.             return new CartesianComplexNumber (
  157.                 scale * complexNumber.real(),
  158.                 scale * complexNumber.imaginary()
  159.             );
  160.         }
  161.         catch (java.lang.Exception e)
  162.         {
  163.             e.printStackTrace();
  164.         }

  166.         return null;
  167.     }

  169.     /**
  170.      * Subtract the Second Complex Number from the First
  171.      * 
  172.      * @param complexNumber1 The First Complex Number
  173.      * @param complexNumber2 The Second Complex Number
  174.      * 
  175.      * @return The "Difference" Complex Number
  176.      */

  178.     public static final CartesianComplexNumber Subtract (
  179.         final CartesianComplexNumber complexNumber1,
  180.         final CartesianComplexNumber complexNumber2)
  181.     {
  182.         if (null == complexNumber1 || null == complexNumber2)
  183.         {
  184.             return null;
  185.         }

  187.         try {
  188.             return new CartesianComplexNumber (
  189.                 complexNumber1.real() - complexNumber2.real(),
  190.                 complexNumber1.imaginary() - complexNumber2.imaginary()
  191.             );
  192.         }
  193.         catch (java.lang.Exception e)
  194.         {
  195.             e.printStackTrace();
  196.         }

  198.         return null;
  199.     }

  201.     /**
  202.      * Multiply the 2 Complex Numbers
  203.      * 
  204.      * @param complexNumber1 The First Complex Number
  205.      * @param complexNumber2 The Second Complex Number
  206.      * 
  207.      * @return The Complex Number instance that is a product of the two
  208.      */

  210.     public static final CartesianComplexNumber Multiply (
  211.         final CartesianComplexNumber complexNumber1,
  212.         final CartesianComplexNumber complexNumber2)
  213.     {
  214.         if (null == complexNumber1 || null == complexNumber2)
  215.         {
  216.             return null;
  217.         }

  219.         double real1 = complexNumber1.real();

  221.         double real2 = complexNumber2.real();

  223.         double imaginary1 = complexNumber1.imaginary();

  225.         double imaginary2 = complexNumber2.imaginary();

  227.         try
  228.         {
  229.             return new CartesianComplexNumber (
  230.                 real1 * real2 - imaginary1 * imaginary2,
  231.                 real1 * imaginary2 + real2 * imaginary1
  232.             );
  233.         }
  234.         catch (java.lang.Exception e)
  235.         {
  236.             e.printStackTrace();
  237.         }

  239.         return null;
  240.     }

  242.     /**
  243.      * Divide the Numerator Complex Number by the Denominator Complex Number
  244.      * 
  245.      * @param numerator The Numerator Complex Number
  246.      * @param denominator The Denominator Complex Number
  247.      * 
  248.      * @return The "Divided" Complex Number
  249.      */

  251.     public static final CartesianComplexNumber Divide (
  252.         final CartesianComplexNumber numerator,
  253.         final CartesianComplexNumber denominator)
  254.     {
  255.         if (null == numerator || null == denominator)
  256.         {
  257.             return null;
  258.         }

  260.         double numeratorReal = numerator.real();

  262.         double denominatorReal = denominator.real();

  264.         double numeratorImaginary = numerator.imaginary();

  266.         double denominatorImaginary = denominator.imaginary();

  268.         if (0. == denominatorReal && 0. == denominatorImaginary)
  269.         {
  270.             return null;
  271.         }

  273.         double inverseDenominatorModulus = 1. / denominator.modulus();

  275.         try
  276.         {
  277.             return new CartesianComplexNumber (
  278.                 (numeratorReal * denominatorReal + numeratorImaginary * denominatorImaginary) *
  279.                     inverseDenominatorModulus,
  280.                 (denominatorReal * numeratorImaginary - numeratorReal * denominatorImaginary) *
  281.                     inverseDenominatorModulus
  282.             );
  283.         }
  284.         catch (java.lang.Exception e)
  285.         {
  286.             e.printStackTrace();
  287.         }

  289.         return null;
  290.     }

  292.     /**
  293.      * Square the Complex Number
  294.      * 
  295.      * @param complexNumber The Complex Number
  296.      * 
  297.      * @return The Squared Complex Number Instance
  298.      */

  300.     public static final CartesianComplexNumber Square (
  301.         final CartesianComplexNumber complexNumber)
  302.     {
  303.         if (null == complexNumber)
  304.         {
  305.             return null;
  306.         }

  308.         double modulus = complexNumber.modulus();

  310.         if (0. == modulus)
  311.         {
  312.             try
  313.             {
  314.                 return new CartesianComplexNumber (
  315.                     0.,
  316.                     0.
  317.                 );
  318.             }
  319.             catch (java.lang.Exception e)
  320.             {
  321.                 e.printStackTrace();
  322.             }

  324.             return null;
  325.         }

  327.         double argument = 2. * complexNumber.argument();

  329.         try
  330.         {
  331.             return new CartesianComplexNumber (
  332.                 modulus * java.lang.Math.cos (argument),
  333.                 modulus * java.lang.Math.sin (argument)
  334.             );
  335.         }
  336.         catch (java.lang.Exception e)
  337.         {
  338.             e.printStackTrace();
  339.         }

  341.         return null;
  342.     }

  344.     /**
  345.      * Compute the Square Root of the Complex Number
  346.      * 
  347.      * @param complexNumber The Complex Number
  348.      * 
  349.      * @return The Square Root Complex Number Instance
  350.      */

  352.     public static final CartesianComplexNumber SquareRoot (
  353.         final CartesianComplexNumber complexNumber)
  354.     {
  355.         if (null == complexNumber)
  356.         {
  357.             return null;
  358.         }

  360.         double modulus = java.lang.Math.sqrt (complexNumber.modulus());

  362.         if (0. == modulus)
  363.         {
  364.             try
  365.             {
  366.                 return new CartesianComplexNumber (
  367.                     0.,
  368.                     0.
  369.                 );
  370.             }
  371.             catch (java.lang.Exception e)
  372.             {
  373.                 e.printStackTrace();
  374.             }

  376.             return null;
  377.         }

  379.         double argument = 0.5 * complexNumber.argument();

  381.         try
  382.         {
  383.             return new CartesianComplexNumber (
  384.                 modulus * java.lang.Math.cos (argument),
  385.                 modulus * java.lang.Math.sin (argument)
  386.             );
  387.         }
  388.         catch (java.lang.Exception e)
  389.         {
  390.             e.printStackTrace();
  391.         }

  393.         return null;
  394.     }

  396.     /**
  397.      * Exponentiate the Complex Number
  398.      * 
  399.      * @param complexNumber The Complex Number
  400.      * 
  401.      * @return The Exponentiated Complex Number Instance
  402.      */

  404.     public static final CartesianComplexNumber Exponentiate (
  405.         final CartesianComplexNumber complexNumber)
  406.     {
  407.         if (null == complexNumber)
  408.         {
  409.             return null;
  410.         }

  412.         double argument = complexNumber.imaginary();

  414.         double modulus = java.lang.Math.exp (complexNumber.real());

  416.         try
  417.         {
  418.             return new CartesianComplexNumber (
  419.                 modulus * java.lang.Math.cos (argument),
  420.                 modulus * java.lang.Math.sin (argument)
  421.             );
  422.         }
  423.         catch (java.lang.Exception e)
  424.         {
  425.             e.printStackTrace();
  426.         }

  428.         return null;
  429.     }

  431.     /**
  432.      * Compute Logarithm of the Complex Number
  433.      * 
  434.      * @param complexNumber The Complex Number
  435.      * 
  436.      * @return The Complex Number Logarithm Instance
  437.      */

  439.     public static final CartesianComplexNumber Logarithm (
  440.         final CartesianComplexNumber complexNumber)
  441.     {
  442.         if (null == complexNumber)
  443.         {
  444.             return null;
  445.         }

  447.         double modulus = complexNumber.modulus();

  449.         if (0. == modulus)
  450.         {
  451.             return null;
  452.         }

  454.         try
  455.         {
  456.             return new CartesianComplexNumber (
  457.                 0.5 * java.lang.Math.log (modulus),
  458.                 complexNumber.argument()
  459.             );
  460.         }
  461.         catch (java.lang.Exception e)
  462.         {
  463.             e.printStackTrace();
  464.         }

  466.         return null;
  467.     }

  469.     /**
  470.      * Construct the Complex Number from its Polar Representation
  471.      * 
  472.      * @param r r
  473.      * @param theta theta
  474.      * 
  475.      * @return Complex Number from its Polar Representation
  476.      */

  478.     public static final CartesianComplexNumber FromPolar (
  479.         final double r,
  480.         final double theta)
  481.     {
  482.         try
  483.         {
  484.             return !org.drip.numerical.common.NumberUtil.IsValid (r) ||
  485.                 !org.drip.numerical.common.NumberUtil.IsValid (theta) ? null :
  486.                 new CartesianComplexNumber (
  487.                     r * java.lang.Math.cos (theta),
  488.                     r * java.lang.Math.sin (theta)
  489.                 );
  490.         }
  491.         catch (java.lang.Exception e)
  492.         {
  493.             e.printStackTrace();
  494.         }

  496.         return null;
  497.     }

  499.     /**
  500.      * CartesianComplexNumber constructor
  501.      * 
  502.      * @param real Real Part
  503.      * @param imaginary Imaginary Part
  504.      * 
  505.      * @throws java.lang.Exception Thrown if the Inputs are invalid
  506.      */

  508.     public CartesianComplexNumber (
  509.         final double real,
  510.         final double imaginary)
  511.         throws java.lang.Exception
  512.     {
  513.         if (!org.drip.numerical.common.NumberUtil.IsValid (_real = real) ||
  514.             !org.drip.numerical.common.NumberUtil.IsValid (_imaginary = imaginary))
  515.         {
  516.             throw new java.lang.Exception ("CartesianComplexNumber Constructor => Invalid Inputs");
  517.         }
  518.     }

  520.     /**
  521.      * Retrieve the Real Part
  522.      * 
  523.      * @return The Real Part
  524.      */

  526.     public double real()
  527.     {
  528.         return _real;
  529.     }

  531.     /**
  532.      * Retrieve the Imaginary Part
  533.      * 
  534.      * @return The Imaginary Part
  535.      */

  537.     public double imaginary()
  538.     {
  539.         return _imaginary;
  540.     }

  542.     /**
  543.      * Retrieve the Modulus
  544.      * 
  545.      * @return The Modulus
  546.      */

  548.     public double modulus()
  549.     {
  550.         return _real * _real + _imaginary * _imaginary;
  551.     }

  553.     /**
  554.      * Retrieve the Absolute Value
  555.      * 
  556.      * @return The Absolute Value
  557.      */

  559.     public double abs()
  560.     {
  561.         return java.lang.Math.sqrt (modulus());
  562.     }

  564.     /**
  565.      * Retrieve the Argument
  566.      * 
  567.      * @return The Argument
  568.      */

  570.     public double argument()
  571.     {
  572.         return 0. == _real && 0. == _imaginary ? 0. : java.lang.Math.atan (_imaginary / _real);
  573.     }

  575.     /**
  576.      * Display the Real/Imaginary Contents
  577.      * 
  578.      * @return The Real/Imaginary Contents
  579.      */

  581.     public java.lang.String display()
  582.     {
  583.         return "\t[" + _real + ", " + _imaginary + "]";
  584.     }
  585. }
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