571 lines
18 KiB
C#
571 lines
18 KiB
C#
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/*
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* BSD Licence:
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* Copyright (c) 2001, 2002 Ben Houston [ ben@exocortex.org ]
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* Exocortex Technologies [ www.exocortex.org ]
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions are met:
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*
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* 1. Redistributions of source code must retain the above copyright notice,
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* this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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* 3. Neither the name of the <ORGANIZATION> nor the names of its contributors
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* may be used to endorse or promote products derived from this software
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* without specific prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE FOR
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* ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
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* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH
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* DAMAGE.
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*/
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using System;
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using System.Diagnostics;
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using System.Runtime.InteropServices;
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namespace Exocortex.DSP
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{
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// Comments? Questions? Bugs? Tell Ben Houston at ben@exocortex.org
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// Version: May 4, 2002
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/// <summary>
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/// <p>A single-precision complex number representation.</p>
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/// </summary>
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[StructLayout(LayoutKind.Sequential)]
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public struct ComplexF : IComparable, ICloneable
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{
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//-----------------------------------------------------------------------------------
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//-----------------------------------------------------------------------------------
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/// <summary>
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/// The real component of the complex number
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/// </summary>
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public float Re;
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/// <summary>
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/// The imaginary component of the complex number
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/// </summary>
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public float Im;
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//-----------------------------------------------------------------------------------
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//-----------------------------------------------------------------------------------
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/// <summary>
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/// Create a complex number from a real and an imaginary component
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/// </summary>
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/// <param name="real"></param>
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/// <param name="imaginary"></param>
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public ComplexF(float real, float imaginary)
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{
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this.Re = real;
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this.Im = imaginary;
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}
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/// <summary>
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/// Create a complex number based on an existing complex number
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/// </summary>
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/// <param name="c"></param>
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public ComplexF(ComplexF c)
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{
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this.Re = c.Re;
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this.Im = c.Im;
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}
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/// <summary>
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/// Create a complex number from a real and an imaginary component
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/// </summary>
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/// <param name="real"></param>
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/// <param name="imaginary"></param>
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/// <returns></returns>
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static public ComplexF FromRealImaginary(float real, float imaginary)
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{
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ComplexF c;
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c.Re = real;
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c.Im = imaginary;
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return c;
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}
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/// <summary>
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/// Create a complex number from a modulus (length) and an argument (radian)
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/// </summary>
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/// <param name="modulus"></param>
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/// <param name="argument"></param>
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/// <returns></returns>
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static public ComplexF FromModulusArgument(float modulus, float argument)
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{
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ComplexF c;
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c.Re = (float)(modulus * System.Math.Cos(argument));
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c.Im = (float)(modulus * System.Math.Sin(argument));
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return c;
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}
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//-----------------------------------------------------------------------------------
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//-----------------------------------------------------------------------------------
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object ICloneable.Clone()
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{
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return new ComplexF(this);
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}
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/// <summary>
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/// Clone the complex number
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/// </summary>
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/// <returns></returns>
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public ComplexF Clone()
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{
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return new ComplexF(this);
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}
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//-----------------------------------------------------------------------------------
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//-----------------------------------------------------------------------------------
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/// <summary>
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/// The modulus (length) of the complex number
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/// </summary>
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/// <returns></returns>
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public float GetModulus()
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{
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float x = this.Re;
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float y = this.Im;
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return (float)Math.Sqrt(x * x + y * y);
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}
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/// <summary>
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/// The squared modulus (length^2) of the complex number
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/// </summary>
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/// <returns></returns>
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public float GetModulusSquared()
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{
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float x = this.Re;
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float y = this.Im;
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return (float)x * x + y * y;
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}
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/// <summary>
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/// The argument (radians) of the complex number
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/// </summary>
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/// <returns></returns>
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public float GetArgument()
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{
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return (float)Math.Atan2(this.Im, this.Re);
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}
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//-----------------------------------------------------------------------------------
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/// <summary>
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/// Get the conjugate of the complex number
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/// </summary>
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/// <returns></returns>
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public ComplexF GetConjugate()
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{
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return FromRealImaginary(this.Re, -this.Im);
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}
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//-----------------------------------------------------------------------------------
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/// <summary>
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/// Scale the complex number to 1.
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/// </summary>
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public void Normalize()
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{
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double modulus = this.GetModulus();
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if (modulus == 0)
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{
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throw new DivideByZeroException("Can not normalize a complex number that is zero.");
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}
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this.Re = (float)(this.Re / modulus);
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this.Im = (float)(this.Im / modulus);
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}
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//-----------------------------------------------------------------------------------
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//-----------------------------------------------------------------------------------
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/// <summary>
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/// Convert to a from double precision complex number to a single precison complex number
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/// </summary>
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/// <param name="c"></param>
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/// <returns></returns>
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public static explicit operator ComplexF(Complex c)
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{
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ComplexF cF;
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cF.Re = (float)c.Re;
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cF.Im = (float)c.Im;
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return cF;
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}
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/// <summary>
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/// Convert from a single precision real number to a complex number
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/// </summary>
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/// <param name="f"></param>
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/// <returns></returns>
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public static explicit operator ComplexF(float f)
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{
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ComplexF c;
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c.Re = f;
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c.Im = 0;
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return c;
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}
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/// <summary>
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/// Convert from a single precision complex to a real number
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/// </summary>
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/// <param name="c"></param>
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/// <returns></returns>
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public static explicit operator float(ComplexF c)
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{
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return c.Re;
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}
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//-----------------------------------------------------------------------------------
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//-----------------------------------------------------------------------------------
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/// <summary>
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/// Are these two complex numbers equivalent?
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/// </summary>
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/// <param name="a"></param>
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/// <param name="b"></param>
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/// <returns></returns>
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public static bool operator ==(ComplexF a, ComplexF b)
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{
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return (a.Re == b.Re) && (a.Im == b.Im);
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}
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/// <summary>
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/// Are these two complex numbers different?
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/// </summary>
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/// <param name="a"></param>
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/// <param name="b"></param>
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/// <returns></returns>
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public static bool operator !=(ComplexF a, ComplexF b)
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{
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return (a.Re != b.Re) || (a.Im != b.Im);
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}
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/// <summary>
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/// Get the hash code of the complex number
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/// </summary>
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/// <returns></returns>
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public override int GetHashCode()
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{
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return (this.Re.GetHashCode() ^ this.Im.GetHashCode());
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}
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/// <summary>
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/// Is this complex number equivalent to another object?
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/// </summary>
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/// <param name="o"></param>
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/// <returns></returns>
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public override bool Equals(object o)
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{
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if (o is ComplexF)
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{
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ComplexF c = (ComplexF)o;
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return (this == c);
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}
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return false;
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}
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//-----------------------------------------------------------------------------------
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//-----------------------------------------------------------------------------------
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/// <summary>
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/// Compare to other complex numbers or real numbers
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/// </summary>
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/// <param name="o"></param>
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/// <returns></returns>
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public int CompareTo(object o)
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{
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if (o == null)
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{
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return 1; // null sorts before current
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}
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if (o is ComplexF)
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{
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return this.GetModulus().CompareTo(((ComplexF)o).GetModulus());
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}
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if (o is float)
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{
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return this.GetModulus().CompareTo((float)o);
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}
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if (o is Complex)
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{
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return this.GetModulus().CompareTo(((Complex)o).GetModulus());
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}
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if (o is double)
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{
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return this.GetModulus().CompareTo((double)o);
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}
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throw new ArgumentException();
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}
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//-----------------------------------------------------------------------------------
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//-----------------------------------------------------------------------------------
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/// <summary>
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/// This operator doesn't do much. :-)
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/// </summary>
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/// <param name="a"></param>
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/// <returns></returns>
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public static ComplexF operator +(ComplexF a)
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{
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return a;
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}
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/// <summary>
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/// Negate the complex number
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/// </summary>
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/// <param name="a"></param>
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/// <returns></returns>
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public static ComplexF operator -(ComplexF a)
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{
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a.Re = -a.Re;
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a.Im = -a.Im;
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return a;
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}
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/// <summary>
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/// Add a complex number to a real
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/// </summary>
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/// <param name="a"></param>
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/// <param name="f"></param>
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/// <returns></returns>
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public static ComplexF operator +(ComplexF a, float f)
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{
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a.Re = a.Re + f;
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return a;
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}
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/// <summary>
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/// Add a real to a complex number
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/// </summary>
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/// <param name="f"></param>
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/// <param name="a"></param>
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/// <returns></returns>
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public static ComplexF operator +(float f, ComplexF a)
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{
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a.Re = a.Re + f;
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return a;
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}
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/// <summary>
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/// Add to complex numbers
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/// </summary>
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/// <param name="a"></param>
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/// <param name="b"></param>
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/// <returns></returns>
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public static ComplexF operator +(ComplexF a, ComplexF b)
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{
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a.Re = a.Re + b.Re;
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a.Im = a.Im + b.Im;
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return a;
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}
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/// <summary>
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/// Subtract a real from a complex number
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/// </summary>
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/// <param name="a"></param>
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/// <param name="f"></param>
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/// <returns></returns>
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public static ComplexF operator -(ComplexF a, float f)
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{
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a.Re = a.Re - f;
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return a;
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}
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/// <summary>
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/// Subtract a complex number from a real
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/// </summary>
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/// <param name="f"></param>
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/// <param name="a"></param>
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/// <returns></returns>
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public static ComplexF operator -(float f, ComplexF a)
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{
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a.Re = f - a.Re;
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a.Im = 0 - a.Im;
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|||
|
|
return a;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
/// <summary>
|
|||
|
|
/// Subtract two complex numbers
|
|||
|
|
/// </summary>
|
|||
|
|
/// <param name="a"></param>
|
|||
|
|
/// <param name="b"></param>
|
|||
|
|
/// <returns></returns>
|
|||
|
|
public static ComplexF operator -(ComplexF a, ComplexF b)
|
|||
|
|
{
|
|||
|
|
a.Re = a.Re - b.Re;
|
|||
|
|
a.Im = a.Im - b.Im;
|
|||
|
|
return a;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
/// <summary>
|
|||
|
|
/// Multiply a complex number by a real
|
|||
|
|
/// </summary>
|
|||
|
|
/// <param name="a"></param>
|
|||
|
|
/// <param name="f"></param>
|
|||
|
|
/// <returns></returns>
|
|||
|
|
public static ComplexF operator *(ComplexF a, float f)
|
|||
|
|
{
|
|||
|
|
a.Re = a.Re * f;
|
|||
|
|
a.Im = a.Im * f;
|
|||
|
|
return a;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
/// <summary>
|
|||
|
|
/// Multiply a real by a complex number
|
|||
|
|
/// </summary>
|
|||
|
|
/// <param name="f"></param>
|
|||
|
|
/// <param name="a"></param>
|
|||
|
|
/// <returns></returns>
|
|||
|
|
public static ComplexF operator *(float f, ComplexF a)
|
|||
|
|
{
|
|||
|
|
a.Re = a.Re * f;
|
|||
|
|
a.Im = a.Im * f;
|
|||
|
|
return a;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
/// <summary>
|
|||
|
|
/// Multiply two complex numbers together
|
|||
|
|
/// </summary>
|
|||
|
|
/// <param name="a"></param>
|
|||
|
|
/// <param name="b"></param>
|
|||
|
|
/// <returns></returns>
|
|||
|
|
public static ComplexF operator *(ComplexF a, ComplexF b)
|
|||
|
|
{
|
|||
|
|
// (x + yi)(u + vi) = (xu <20> yv) + (xv + yu)i.
|
|||
|
|
double x = a.Re, y = a.Im;
|
|||
|
|
double u = b.Re, v = b.Im;
|
|||
|
|
a.Re = (float)(x * u - y * v);
|
|||
|
|
a.Im = (float)(x * v + y * u);
|
|||
|
|
return a;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
/// <summary>
|
|||
|
|
/// Divide a complex number by a real number
|
|||
|
|
/// </summary>
|
|||
|
|
/// <param name="a"></param>
|
|||
|
|
/// <param name="f"></param>
|
|||
|
|
/// <returns></returns>
|
|||
|
|
public static ComplexF operator /(ComplexF a, float f)
|
|||
|
|
{
|
|||
|
|
if (f == 0)
|
|||
|
|
{
|
|||
|
|
throw new DivideByZeroException();
|
|||
|
|
}
|
|||
|
|
a.Re = a.Re / f;
|
|||
|
|
a.Im = a.Im / f;
|
|||
|
|
return a;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
/// <summary>
|
|||
|
|
/// Divide a complex number by a complex number
|
|||
|
|
/// </summary>
|
|||
|
|
/// <param name="a"></param>
|
|||
|
|
/// <param name="b"></param>
|
|||
|
|
/// <returns></returns>
|
|||
|
|
public static ComplexF operator /(ComplexF a, ComplexF b)
|
|||
|
|
{
|
|||
|
|
double x = a.Re, y = a.Im;
|
|||
|
|
double u = b.Re, v = b.Im;
|
|||
|
|
double denom = u * u + v * v;
|
|||
|
|
|
|||
|
|
if (denom == 0)
|
|||
|
|
{
|
|||
|
|
throw new DivideByZeroException();
|
|||
|
|
}
|
|||
|
|
a.Re = (float)((x * u + y * v) / denom);
|
|||
|
|
a.Im = (float)((y * u - x * v) / denom);
|
|||
|
|
return a;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
/// <summary>
|
|||
|
|
/// Parse a complex representation in this fashion: "( %f, %f )"
|
|||
|
|
/// </summary>
|
|||
|
|
/// <param name="s"></param>
|
|||
|
|
/// <returns></returns>
|
|||
|
|
static public ComplexF Parse(string s)
|
|||
|
|
{
|
|||
|
|
throw new NotImplementedException("ComplexF ComplexF.Parse( string s ) is not implemented.");
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
/// <summary>
|
|||
|
|
/// Get the string representation
|
|||
|
|
/// </summary>
|
|||
|
|
/// <returns></returns>
|
|||
|
|
public override string ToString()
|
|||
|
|
{
|
|||
|
|
return String.Format("( {0}, {1}i )", this.Re, this.Im);
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
//-----------------------------------------------------------------------------------
|
|||
|
|
//-----------------------------------------------------------------------------------
|
|||
|
|
|
|||
|
|
/// <summary>
|
|||
|
|
/// Determine whether two complex numbers are almost (i.e. within the tolerance) equivalent.
|
|||
|
|
/// </summary>
|
|||
|
|
/// <param name="a"></param>
|
|||
|
|
/// <param name="b"></param>
|
|||
|
|
/// <param name="tolerance"></param>
|
|||
|
|
/// <returns></returns>
|
|||
|
|
static public bool IsEqual(ComplexF a, ComplexF b, float tolerance)
|
|||
|
|
{
|
|||
|
|
return
|
|||
|
|
(Math.Abs(a.Re - b.Re) < tolerance) &&
|
|||
|
|
(Math.Abs(a.Im - b.Im) < tolerance);
|
|||
|
|
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
//----------------------------------------------------------------------------------
|
|||
|
|
//----------------------------------------------------------------------------------
|
|||
|
|
|
|||
|
|
/// <summary>
|
|||
|
|
/// Represents zero
|
|||
|
|
/// </summary>
|
|||
|
|
static public ComplexF Zero
|
|||
|
|
{
|
|||
|
|
get { return new ComplexF(0, 0); }
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
/// <summary>
|
|||
|
|
/// Represents the result of sqrt( -1 )
|
|||
|
|
/// </summary>
|
|||
|
|
static public ComplexF I
|
|||
|
|
{
|
|||
|
|
get { return new ComplexF(0, 1); }
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
/// <summary>
|
|||
|
|
/// Represents the largest possible value of ComplexF.
|
|||
|
|
/// </summary>
|
|||
|
|
static public ComplexF MaxValue
|
|||
|
|
{
|
|||
|
|
get { return new ComplexF(float.MaxValue, float.MaxValue); }
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
/// <summary>
|
|||
|
|
/// Represents the smallest possible value of ComplexF.
|
|||
|
|
/// </summary>
|
|||
|
|
static public ComplexF MinValue
|
|||
|
|
{
|
|||
|
|
get { return new ComplexF(float.MinValue, float.MinValue); }
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
|
|||
|
|
//----------------------------------------------------------------------------------
|
|||
|
|
//----------------------------------------------------------------------------------
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
}
|