DP44/DataPRO/ExocortexDSP/ComplexMath.cs

/*
 * BSD Licence:
 * Copyright (c) 2001, 2002 Ben Houston [ ben@exocortex.org ]
 * Exocortex Technologies [ www.exocortex.org ]
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without 
 * modification, are permitted provided that the following conditions are met:
 *
 * 1. Redistributions of source code must retain the above copyright notice, 
 * this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright 
 * notice, this list of conditions and the following disclaimer in the 
 * documentation and/or other materials provided with the distribution.
 * 3. Neither the name of the <ORGANIZATION> nor the names of its contributors
 * may be used to endorse or promote products derived from this software
 * without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
 * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE FOR
 * ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
 * SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
 * CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 
 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH
 * DAMAGE.
 */

using System;
using System.Diagnostics;


namespace Exocortex.DSP
{

    // Comments? Questions? Bugs? Tell Ben Houston at ben@exocortex.org
    // Version: May 4, 2002

    /// <summary>
    /// <p>Various mathematical functions for complex numbers.</p>
    /// </summary>
    public class ComplexMath
    {

        //---------------------------------------------------------------------------------------------------

        private ComplexMath()
        {
        }

        //---------------------------------------------------------------------------------------------------

        /// <summary>
        /// Swap two complex numbers
        /// </summary>
        /// <param name="a"></param>
        /// <param name="b"></param>
        static public void Swap(ref Complex a, ref Complex b)
        {
            Complex temp = a;
            a = b;
            b = temp;
        }

        /// <summary>
        /// Swap two complex numbers
        /// </summary>
        /// <param name="a"></param>
        /// <param name="b"></param>
        static public void Swap(ref ComplexF a, ref ComplexF b)
        {
            ComplexF temp = a;
            a = b;
            b = temp;
        }

        //---------------------------------------------------------------------------------------------------

        static private double _halfOfRoot2 = 0.5 * Math.Sqrt(2);

        /// <summary>
        /// Calculate the square root of a complex number
        /// </summary>
        /// <param name="c"></param>
        /// <returns></returns>
        static public ComplexF Sqrt(ComplexF c)
        {
            double x = c.Re;
            double y = c.Im;

            double modulus = Math.Sqrt(x * x + y * y);
            int sign = (y < 0) ? -1 : 1;

            c.Re = (float)(_halfOfRoot2 * Math.Sqrt(modulus + x));
            c.Im = (float)(_halfOfRoot2 * sign * Math.Sqrt(modulus - x));

            return c;
        }

        /// <summary>
        /// Calculate the square root of a complex number
        /// </summary>
        /// <param name="c"></param>
        /// <returns></returns>
        static public Complex Sqrt(Complex c)
        {
            double x = c.Re;
            double y = c.Im;

            double modulus = Math.Sqrt(x * x + y * y);
            int sign = (y < 0) ? -1 : 1;

            c.Re = _halfOfRoot2 * Math.Sqrt(modulus + x);
            c.Im = _halfOfRoot2 * sign * Math.Sqrt(modulus - x);

            return c;
        }

        //---------------------------------------------------------------------------------------------------

        /// <summary>
        /// Calculate the power of a complex number
        /// </summary>
        /// <param name="c"></param>
        /// <param name="exponent"></param>
        /// <returns></returns>
        static public ComplexF Pow(ComplexF c, double exponent)
        {
            double x = c.Re;
            double y = c.Im;

            double modulus = Math.Pow(x * x + y * y, exponent * 0.5);
            double argument = Math.Atan2(y, x) * exponent;

            c.Re = (float)(modulus * System.Math.Cos(argument));
            c.Im = (float)(modulus * System.Math.Sin(argument));

            return c;
        }

        /// <summary>
        /// Calculate the power of a complex number
        /// </summary>
        /// <param name="c"></param>
        /// <param name="exponent"></param>
        /// <returns></returns>
        static public Complex Pow(Complex c, double exponent)
        {
            double x = c.Re;
            double y = c.Im;

            double modulus = Math.Pow(x * x + y * y, exponent * 0.5);
            double argument = Math.Atan2(y, x) * exponent;

            c.Re = modulus * System.Math.Cos(argument);
            c.Im = modulus * System.Math.Sin(argument);

            return c;
        }

        //---------------------------------------------------------------------------------------------------

    }
}