/*
* 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.Runtime.InteropServices;
namespace DuplicateTracks.Fingerprinting.MathUtils
{
// Comments? Questions? Bugs? Tell Ben Houston at ben@exocortex.org
// Version: May 4, 2002
/// <summary>
/// <p>A double-precision complex number representation.</p>
/// </summary>
[StructLayout(LayoutKind.Sequential)]
public struct Complex : IComparable, ICloneable
{
//-----------------------------------------------------------------------------------
//-----------------------------------------------------------------------------------
/// <summary>
/// The real component of the complex number
/// </summary>
public double Re;
/// <summary>
/// The imaginary component of the complex number
/// </summary>
public double Im;
//-----------------------------------------------------------------------------------
//-----------------------------------------------------------------------------------
/// <summary>
/// Create a complex number from a real and an imaginary component
/// </summary>
/// <param name = "real"></param>
/// <param name = "imaginary"></param>
public Complex(double real, double imaginary)
{
Re = real;
Im = imaginary;
}
/// <summary>
/// Create a complex number based on an existing complex number
/// </summary>
/// <param name = "c"></param>
public Complex(Complex c)
{
Re = c.Re;
Im = c.Im;
}
/// <summary>
/// Create a complex number from a real and an imaginary component
/// </summary>
/// <param name = "real"></param>
/// <param name = "imaginary"></param>
/// <returns></returns>
public static Complex FromRealImaginary(double real, double imaginary)
{
Complex c;
c.Re = real;
c.Im = imaginary;
return c;
}
/// <summary>
/// Create a complex number from a modulus (length) and an argument (radian)
/// </summary>
/// <param name = "modulus"></param>
/// <param name = "argument"></param>
/// <returns></returns>
public static Complex FromModulusArgument(double modulus, double argument)
{
Complex c;
c.Re = (modulus*Math.Cos(argument));
c.Im = (modulus*Math.Sin(argument));
return c;
}
//-----------------------------------------------------------------------------------
//-----------------------------------------------------------------------------------
object ICloneable.Clone()
{
return new Complex(this);
}
/// <summary>
/// Clone the complex number
/// </summary>
/// <returns></returns>
public Complex Clone()
{
return new Complex(this);
}
//-----------------------------------------------------------------------------------
//-----------------------------------------------------------------------------------
/// <summary>
/// The modulus (length) of the complex number
/// </summary>
/// <returns></returns>
public double GetModulus()
{
double x = Re;
double y = Im;
return Math.Sqrt(x*x + y*y);
}
/// <summary>
/// The squared modulus (length^2) of the complex number
/// </summary>
/// <returns></returns>
public double GetModulusSquared()
{
double x = Re;
double y = Im;
return x*x + y*y;
}
/// <summary>
/// The argument (radians) of the complex number
/// </summary>
/// <returns></returns>
public double GetArgument()
{
return Math.Atan2(Im, Re);
}
//-----------------------------------------------------------------------------------
/// <summary>
/// Get the conjugate of the complex number
/// </summary>
/// <returns></returns>
public Complex GetConjugate()
{
return FromRealImaginary(Re, -Im);
}
//-----------------------------------------------------------------------------------
/// <summary>
/// Scale the complex number to 1.
/// </summary>
public void Normalize()
{
double modulus = GetModulus();
if (modulus == 0)
{
throw new DivideByZeroException("Can not normalize a complex number that is zero.");
}
Re = (Re/modulus);
Im = (Im/modulus);
}
//-----------------------------------------------------------------------------------
//-----------------------------------------------------------------------------------
/// <summary>
/// Convert to a from double precision complex number to a single precison complex number
/// </summary>
/// <param name = "cF"></param>
/// <returns></returns>
public static explicit operator Complex(ComplexF cF)
{
Complex c;
c.Re = cF.Re;
c.Im = cF.Im;
return c;
}
/// <summary>
/// Convert from a single precision real number to a complex number
/// </summary>
/// <param name = "d"></param>
/// <returns></returns>
public static explicit operator Complex(double d)
{
Complex c;
c.Re = d;
c.Im = 0;
return c;
}
/// <summary>
/// Convert from a single precision complex to a real number
/// </summary>
/// <param name = "c"></param>
/// <returns></returns>
public static explicit operator double(Complex c)
{
return c.Re;
}
//-----------------------------------------------------------------------------------
//-----------------------------------------------------------------------------------
/// <summary>
/// Are these two complex numbers equivalent?
/// </summary>
/// <param name = "a"></param>
/// <param name = "b"></param>
/// <returns></returns>
public static bool operator ==(Complex a, Complex b)
{
return (a.Re == b.Re) && (a.Im == b.Im);
}
/// <summary>
/// Are these two complex numbers different?
/// </summary>
/// <param name = "a"></param>
/// <param name = "b"></param>
/// <returns></returns>
public static bool operator !=(Complex a, Complex b)
{
return (a.Re != b.Re) || (a.Im != b.Im);
}
/// <summary>
/// Get the hash code of the complex number
/// </summary>
/// <returns></returns>
public override int GetHashCode()
{
return (Re.GetHashCode() ^ Im.GetHashCode());
}
/// <summary>
/// Is this complex number equivalent to another object?
/// </summary>
/// <param name = "o"></param>
/// <returns></returns>
public override bool Equals(object o)
{
if (o is Complex)
{
Complex c = (Complex) o;
return (this == c);
}
return false;
}
//-----------------------------------------------------------------------------------
//-----------------------------------------------------------------------------------
/// <summary>
/// Compare to other complex numbers or real numbers
/// </summary>
/// <param name = "o"></param>
/// <returns></returns>
public int CompareTo(object o)
{
if (o == null)
{
return 1; // null sorts before current
}
if (o is Complex)
{
return GetModulus().CompareTo(((Complex) o).GetModulus());
}
if (o is double)
{
return GetModulus().CompareTo((double) o);
}
if (o is ComplexF)
{
return GetModulus().CompareTo(((ComplexF) o).GetModulus());
}
if (o is float)
{
return GetModulus().CompareTo((float) o);
}
throw new ArgumentException();
}
//-----------------------------------------------------------------------------------
//-----------------------------------------------------------------------------------
/// <summary>
/// This operator doesn't do much. :-)
/// </summary>
/// <param name = "a"></param>
/// <returns></returns>
public static Complex operator +(Complex a)
{
return a;
}
/// <summary>
/// Negate the complex number
/// </summary>
/// <param name = "a"></param>
/// <returns></returns>
public static Complex operator -(Complex a)
{
a.Re = -a.Re;
a.Im = -a.Im;
return a;
}
/// <summary>
/// Add a complex number to a real
/// </summary>
/// <param name = "a"></param>
/// <param name = "f"></param>
/// <returns></returns>
public static Complex operator +(Complex a, double f)
{
a.Re = (a.Re + f);
return a;
}
/// <summary>
/// Add a real to a complex number
/// </summary>
/// <param name = "f"></param>
/// <param name = "a"></param>
/// <returns></returns>
public static Complex operator +(double f, Complex a)
{
a.Re = (a.Re + f);
return a;
}
/// <summary>
/// Add to complex numbers
/// </summary>
/// <param name = "a"></param>
/// <param name = "b"></param>
/// <returns></returns>
public static Complex operator +(Complex a, Complex b)
{
a.Re = a.Re + b.Re;
a.Im = a.Im + b.Im;
return a;
}
/// <summary>
/// Subtract a real from a complex number
/// </summary>
/// <param name = "a"></param>
/// <param name = "f"></param>
/// <returns></returns>
public static Complex operator -(Complex a, double f)
{
a.Re = (a.Re - f);
return a;
}
/// <summary>
/// Subtract a complex number from a real
/// </summary>
/// <param name = "f"></param>
/// <param name = "a"></param>
/// <returns></returns>
public static Complex operator -(double f, Complex a)
{
a.Re = (float) (f - a.Re);
a.Im = (float) (0 - a.Im);
return a;
}
/// <summary>
/// Subtract two complex numbers
/// </summary>
/// <param name = "a"></param>
/// <param name = "b"></param>
/// <returns></returns>
public static Complex operator -(Complex a, Complex 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 Complex operator *(Complex a, double 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 Complex operator *(double f, Complex 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 Complex operator *(Complex a, Complex b)
{
// (x + yi)(u + vi) = (xu – yv) + (xv + yu)i.
double x = a.Re, y = a.Im;
double u = b.Re, v = b.Im;
a.Re = (x*u - y*v);
a.Im = (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 Complex operator /(Complex a, double 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 Complex operator /(Complex a, Complex 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 = ((x*u + y*v)/denom);
a.Im = ((y*u - x*v)/denom);
return a;
}
/// <summary>
/// Parse a complex representation in this fashion: "( %f, %f )"
/// </summary>
/// <param name = "s"></param>
/// <returns></returns>
public static Complex Parse(string s)
{
throw new NotImplementedException("Complex Complex.Parse( string s ) is not implemented.");
}
/// <summary>
/// Get the string representation
/// </summary>
/// <returns></returns>
public override string ToString()
{
return String.Format("( {0}, {1}i )", Re, 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>
public static bool IsEqual(Complex a, Complex b, double tolerance)
{
return
(Math.Abs(a.Re - b.Re) < tolerance) &&
(Math.Abs(a.Im - b.Im) < tolerance);
}
//----------------------------------------------------------------------------------
//----------------------------------------------------------------------------------
/// <summary>
/// Represents zero
/// </summary>
public static Complex Zero
{
get { return new Complex(0, 0); }
}
/// <summary>
/// Represents the result of sqrt( -1 )
/// </summary>
public static Complex I
{
get { return new Complex(0, 1); }
}
/// <summary>
/// Represents the largest possible value of Complex.
/// </summary>
public static Complex MaxValue
{
get { return new Complex(double.MaxValue, double.MaxValue); }
}
/// <summary>
/// Represents the smallest possible value of Complex.
/// </summary>
public static Complex MinValue
{
get { return new Complex(double.MinValue, double.MinValue); }
}
//----------------------------------------------------------------------------------
//----------------------------------------------------------------------------------
}
}
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