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+/*
+ * 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;
+using System.Runtime.InteropServices;
+
+
+namespace Exocortex.DSP
+{
+
+    // 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)
+        {
+            this.Re = real;
+            this.Im = imaginary;
+        }
+
+        /// <summary>
+        /// Create a complex number based on an existing complex number
+        /// </summary>
+        /// <param name="c"></param>
+        public Complex(Complex c)
+        {
+            this.Re = c.Re;
+            this.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>
+        static public 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>
+        static public Complex FromModulusArgument(double modulus, double argument)
+        {
+            Complex c;
+            c.Re = modulus * System.Math.Cos(argument);
+            c.Im = modulus * System.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 = this.Re;
+            double y = this.Im;
+            return (double)Math.Sqrt(x * x + y * y);
+        }
+
+        /// <summary>
+        /// The squared modulus (length^2) of the complex number
+        /// </summary>
+        /// <returns></returns>
+        public double GetModulusSquared()
+        {
+            double x = this.Re;
+            double y = this.Im;
+            return (double)x * x + y * y;
+        }
+
+        /// <summary>
+        /// The argument (radians) of the complex number
+        /// </summary>
+        /// <returns></returns>
+        public double GetArgument()
+        {
+            return (double)Math.Atan2(this.Im, this.Re);
+        }
+
+        //-----------------------------------------------------------------------------------
+
+        /// <summary>
+        /// Get the conjugate of the complex number
+        /// </summary>
+        /// <returns></returns>
+        public Complex GetConjugate()
+        {
+            return FromRealImaginary(this.Re, -this.Im);
+        }
+
+        //-----------------------------------------------------------------------------------
+
+        /// <summary>
+        /// Scale the complex number to 1.
+        /// </summary>
+        public void Normalize()
+        {
+            double modulus = this.GetModulus();
+            if (modulus == 0)
+            {
+                throw new DivideByZeroException("Can not normalize a complex number that is zero.");
+            }
+            this.Re = this.Re / modulus;
+            this.Im = this.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 (this.Re.GetHashCode() ^ this.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 this.GetModulus().CompareTo(((Complex)o).GetModulus());
+            }
+            if (o is double)
+            {
+                return this.GetModulus().CompareTo((double)o);
+            }
+            if (o is ComplexF)
+            {
+                return this.GetModulus().CompareTo(((ComplexF)o).GetModulus());
+            }
+            if (o is float)
+            {
+                return this.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>
+        static public 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 )", 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(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>
+        static public Complex Zero
+        {
+            get { return new Complex(0, 0); }
+        }
+
+        /// <summary>
+        /// Represents the result of sqrt( -1 )
+        /// </summary>
+        static public Complex I
+        {
+            get { return new Complex(0, 1); }
+        }
+
+        /// <summary>
+        /// Represents the largest possible value of Complex.
+        /// </summary>
+        static public Complex MaxValue
+        {
+            get { return new Complex(double.MaxValue, double.MaxValue); }
+        }
+
+        /// <summary>
+        /// Represents the smallest possible value of Complex.
+        /// </summary>
+        static public Complex MinValue
+        {
+            get { return new Complex(double.MinValue, double.MinValue); }
+        }
+
+
+        //----------------------------------------------------------------------------------
+        //----------------------------------------------------------------------------------
+    }
+
+}