/Utilities/Math/Complex.cs

using System;

using System.Diagnostics;

using System.IO;

using System.Runtime.InteropServices;

using Delta.Utilities.Helpers;

using NUnit.Framework;



namespace Delta.Utilities.Math

{

	/// <summary>

	/// Complex number with real and imaginary parts as floats. Rarely used,

	/// but can be useful for complex mathematical problems.

	/// </summary>

	[StructLayout(LayoutKind.Explicit)]

	[DebuggerDisplay("Complex(Real={Real}, Imaginary={Imaginary})")]

	public struct Complex : ISaveLoadBinary, IEquatable<Complex>

	{

		#region Constants

		/// <summary>

		/// Represents the size in bytes of each Complex (2 * 4 = 8 bytes).

		/// </summary>

		public const int DataSize = 2 * 4;



		/// <summary>

		/// Returns a Complex with all values filled to zero

		/// </summary>

		public static readonly Complex Zero =

			new Complex(0, 0);

		#endregion



		#region FromSqrt (Static)

		/// <summary>

		/// From sqrt

		/// </summary>

		public static Complex FromSqrt(float setR)

		{

			return new Complex(

				setR >= 0.0f

					? MathHelper.Sqrt(setR)

					: 0.0f,

				setR < 0.0f

					? MathHelper.Sqrt(-setR)

					: 0.0f);

		}

		#endregion



		#region Real (Public)

		/// <summary>

		/// Real

		/// </summary>

		[FieldOffset(0)]

		public float Real;

		#endregion



		#region Imaginary (Public)

		/// <summary>

		/// Imaginary

		/// </summary>

		[FieldOffset(4)]

		public float Imaginary;

		#endregion



		#region LengthSquared (Public)

		/// <summary>

		/// Length squared

		/// </summary>

		public float LengthSquared

		{

			get

			{

				return Real * Real + Imaginary * Imaginary;

			}

		}

		#endregion



		#region Length (Public)

		/// <summary>

		/// Length

		/// </summary>

		public float Length

		{

			get

			{

				return MathHelper.Sqrt(Real * Real + Imaginary * Imaginary);

			}

		}

		#endregion



		#region Argument (Public)

		/// <summary>

		/// Argument

		/// </summary>

		public float Argument

		{

			get

			{

				return MathHelper.Atan(Imaginary, Real);

			}

		}

		#endregion



		#region Constructors

		/// <summary>

		/// Create complex

		/// </summary>

		public Complex(float setR, float setI)

		{

			Real = setR;

			Imaginary = setI;

		}



		/// <summary>

		/// Create complex from phasor values.

		/// </summary>

		public Complex(float setModulus, float setArgument, bool phasorDummy)

		{

			Real = setModulus * MathHelper.Cos(setArgument);

			Imaginary = setModulus * MathHelper.Sin(setArgument);

		}

		#endregion



		#region IEquatable<Complex> Members

		/// <summary>

		/// Equals

		/// </summary>

		/// <param name="other">Other</param>

		/// <returns>Value indicating the equality of two vectors</returns>

		public bool Equals(Complex other)

		{

			return Real == other.Real &&

			       Imaginary == other.Imaginary;

		}

		#endregion



		#region ISaveLoadBinary Members

		/// <summary>

		/// Load real and imaginary part of this complex number from a stream.

		/// </summary>

		public void Load(BinaryReader reader)

		{

			Real = reader.ReadSingle();

			Imaginary = reader.ReadSingle();

		}



		/// <summary>

		/// Save real and imaginary part of this complex number to a stream.

		/// </summary>

		public void Save(BinaryWriter writer)

		{

			writer.Write(Real);

			writer.Write(Imaginary);

		}

		#endregion



		#region op_UnaryNegation (Operator)

		/// <summary>

		/// Op unary negation

		/// </summary>

		public static Complex operator -(Complex value1)

		{

			return new Complex(-value1.Real, -value1.Imaginary);

		}

		#endregion



		#region op_UnaryPlus (Operator)

		/// <summary>

		/// Op unary plus

		/// </summary>

		public static Complex operator +(Complex value1)

		{

			return new Complex(+value1.Real, +value1.Imaginary);

		}

		#endregion



		#region op_Addition (Operator)

		/// <summary>

		/// Op addition

		/// </summary>

		public static Complex operator +(Complex value1, Complex value2)

		{

			return new Complex(value1.Real + value2.Real,

				value1.Imaginary + value2.Imaginary);

		}

		#endregion



		#region op_Subtraction (Operator)

		/// <summary>

		/// Op subtraction

		/// </summary>

		public static Complex operator -(Complex value1, Complex value2)

		{

			return new Complex(value1.Real - value2.Real,

				value1.Imaginary - value2.Imaginary);

		}

		#endregion



		#region op_Multiply (Operator)

		/// <summary>

		/// Op multiply

		/// </summary>

		public static Complex operator *(Complex value1, Complex value2)

		{

			return

				new Complex(value1.Real * value2.Real - value1.Imaginary * value2.Imaginary,

					value1.Real * value2.Imaginary + value2.Real * value1.Imaginary);

		}



		/// <summary>

		/// Op multiply

		/// </summary>

		public static Complex operator *(Complex value1, float scalar)

		{

			return new Complex(value1.Real * scalar, value1.Imaginary * scalar);

		}



		/// <summary>

		/// Op multiply

		/// </summary>

		public static Complex operator *(float scalar, Complex value1)

		{

			return new Complex(value1.Real * scalar, value1.Imaginary * scalar);

		}

		#endregion



		#region op_Division (Operator)

		/// <summary>

		/// Op division

		/// </summary>

		public static Complex operator /(Complex value1, Complex value2)

		{

			float invertedSquared = 1.0f / value2.LengthSquared;

			return new Complex(

				(value1.Real * value2.Real + value1.Imaginary * value2.Imaginary) *

				invertedSquared,

				(value1.Imaginary * value2.Real - value1.Real * value2.Imaginary) *

				invertedSquared);

		}



		/// <summary>

		/// Op division

		/// </summary>

		public static Complex operator /(Complex value1, float scalar)

		{

			float Is = 1.0f / scalar;

			return new Complex(value1.Real * Is, value1.Imaginary * Is);

		}

		#endregion



		#region op_Equality (Operator)

		/// <summary>

		/// Check for equality

		/// </summary>

		/// <param name="value1">Value 1</param>

		/// <param name="value2">Value 2</param>

		/// <returns>True if the values are equal, false otherwise</returns>

		public static bool operator ==(Complex value1, Complex value2)

		{

			return value1.Real == value2.Real &&

			       value1.Imaginary == value2.Imaginary;

		}

		#endregion



		#region op_Inequality (Operator)

		/// <summary>

		/// Check for inequality

		/// </summary>

		/// <param name="value1">Value 1</param>

		/// <param name="value2">Value 2</param>

		/// <returns>Bool</returns>	

		public static bool operator !=(Complex value1, Complex value2)

		{

			return value1.Real != value2.Real ||

			       value1.Imaginary != value2.Imaginary;

		}

		#endregion



		#region Min (Public)

		/// <summary>

		/// Minimum

		/// </summary>

		public float Min()

		{

			return MathHelper.Min(Real, Imaginary);

		}



		/// <summary>

		/// Minimum

		/// </summary>

		public void Min(Complex other)

		{

			Real = MathHelper.Min(Real, other.Real);

			Imaginary = MathHelper.Min(Imaginary, other.Imaginary);

		}

		#endregion



		#region Max (Public)

		/// <summary>

		/// Maximum

		/// </summary>

		public float Max()

		{

			return MathHelper.Max(Real, Imaginary);

		}



		/// <summary>

		/// Maximum

		/// </summary>

		public void Max(Complex other)

		{

			Real = MathHelper.Max(Real, other.Real);

			Imaginary = MathHelper.Max(Imaginary, other.Imaginary);

		}

		#endregion



		#region Sum (Public)

		/// <summary>

		/// Sum

		/// </summary>

		public float Sum()

		{

			return Real + Imaginary;

		}

		#endregion



		#region Product (Public)

		/// <summary>

		/// Product

		/// </summary>

		public float Product()

		{

			return Real * Imaginary;

		}

		#endregion



		#region Conjugate (Public)

		/// <summary>

		/// Conjugate

		/// </summary>

		public Complex Conjugate()

		{

			return new Complex(Real, -Imaginary);

		}

		#endregion



		#region Sqrt (Public)

		/// <summary>

		/// Sqrt

		/// </summary>

		public Complex Sqrt()

		{

			return new Complex(MathHelper.Pow(LengthSquared, 0.25f),

				0.5f * Argument, true);

		}

		#endregion



		#region ToString (Public)

		/// <summary>

		/// To string

		/// </summary>

		public override string ToString()

		{

			return Real.ToString() + " + i * " + Imaginary.ToString();

		}

		#endregion



		#region GetHashCode (Public)

		/// <summary>

		/// Get hash code

		/// </summary>

		public override int GetHashCode()

		{

			return Real.GetHashCode() ^ (Imaginary.GetHashCode() * 7);

		}

		#endregion



		#region Equals (Public)

		/// <summary>

		/// Equals

		/// </summary>

		public override bool Equals(object obj)

		{

			if (obj is Complex)

			{

				return Equals((Complex)obj);

			}

			return base.Equals(obj);

		}

		#endregion



		/// <summary>

		/// Tests

		/// </summary>

		internal class ComplexTests

		{

			#region TestCreate

			/// <summary>

			/// Test Constructors

			/// </summary>

			[Test]

			public void TestCreate()

			{

				// Create complex

				Complex complex = new Complex(1.0f, 5.0f);



				// Make sure the values are correct

				Assert.NearlyEqual(complex.Real, 1.0f);

				Assert.NearlyEqual(complex.Imaginary, 5.0f);

			}

			#endregion



			#region Equality

			/// <summary>

			/// Equality

			/// </summary>

			[Test]

			public void Equality()

			{

				Complex c1 = new Complex(1.0f, 2.0f);

				Complex c2 = new Complex(1.0f, 2.0f);

				Complex c3 = new Complex(1.5f, 2.0f);



				Assert.True(c1 == c2);

				Assert.False(c1 == c3);

			}

			#endregion



			#region Inequality

			/// <summary>

			/// Inequality

			/// </summary>

			[Test]

			public void Inequality()

			{

				Complex c1 = new Complex(1.0f, 2.0f);

				Complex c2 = new Complex(1.0f, 2.0f);

				Complex c3 = new Complex(1.5f, 2.0f);



				Assert.False(c1 != c2);

				Assert.True(c1 != c3);

			}

			#endregion



			#region ScalarDivison

			/// <summary>

			/// Scalar divison

			/// </summary>

			[Test]

			public void ScalarDivison()

			{

				Complex c1 = new Complex(6.0f, 20.0f);

				float scalar = 2.0f;

				Complex result = c1 / scalar;



				Assert.NearlyEqual(result.Real, 3.0f);

				Assert.NearlyEqual(result.Imaginary, 10.0f);

			}

			#endregion



			#region ComplexDivision

			/// <summary>

			/// Complex division

			/// </summary>

			[Test]

			public void ComplexDivision()

			{

				float r1 = 12.0f;

				float i1 = 20.0f;

				float r2 = 2.0f;

				float i2 = 4.0f;



				Complex c1 = new Complex(r1, i1);

				Complex c2 = new Complex(r2, i2);

				Complex result = c1 / c2;



				// Source: http://de.wikipedia.org/wiki/Komplexe_Zahl#Division

				float rResult = ((r1 * r2) + (i1 * i2)) / ((r2 * r2) + (i2 * i2));

				float iResult = ((i1 * r2) - (r1 * i2)) / ((r2 * r2) + (i2 * i2));



				Assert.NearlyEqual(result.Real, rResult);

				Assert.NearlyEqual(result.Imaginary, iResult);

			}

			#endregion



			#region ScalarMultiply

			/// <summary>

			/// Scalar multiplyScalar

			/// </summary>

			[Test]

			public void ScalarMultiply()

			{

				Complex c1 = new Complex(6.0f, 20.0f);

				float scalar = 2.0f;

				Complex result = c1 * scalar;

				// Test reverse too

				Complex result2 = scalar * c1;



				Assert.NearlyEqual(result.Real, 12.0f);

				Assert.NearlyEqual(result.Imaginary, 40.0f);



				Assert.NearlyEqual(result2.Real, 12.0f);

				Assert.NearlyEqual(result2.Imaginary, 40.0f);

			}

			#endregion



			#region ComplexMultiply

			/// <summary>

			/// Complex multiply

			/// </summary>

			[Test]

			public void ComplexMultiply()

			{

				float r1 = 1.0f;

				float i1 = 2.0f;

				float r2 = 4.0f;

				float i2 = 8.0f;



				Complex c1 = new Complex(r1, i1);

				Complex c2 = new Complex(r2, i2);

				Complex result = c1 * c2;



				// Source: http://de.wikipedia.org/wiki/Komplexe_Zahl#Multiplikation

				float rResult = (r1 * r2) - (i1 * i2);

				float iResult = (r1 * i2) + (i1 * r2);



				Assert.NearlyEqual(result.Real, rResult);

				Assert.NearlyEqual(result.Imaginary, iResult);

			}

			#endregion



			#region ComplexSubtract

			/// <summary>

			/// Complex subtract

			/// </summary>

			[Test]

			public void ComplexSubtract()

			{

				float r1 = 10.0f;

				float i1 = 20.0f;

				float r2 = 5.0f;

				float i2 = 7.0f;



				Complex c1 = new Complex(r1, i1);

				Complex c2 = new Complex(r2, i2);

				Complex result = c1 - c2;



				// Source: http://de.wikipedia.org/wiki/Komplexe_Zahl#Subtraktion

				float rResult = r1 - r2;

				float iResult = i1 - i2;



				Assert.NearlyEqual(result.Real, rResult);

				Assert.NearlyEqual(result.Imaginary, iResult);

			}

			#endregion



			#region ComplexAddition

			/// <summary>

			/// Complex addition

			/// </summary>

			[Test]

			public void ComplexAddition()

			{

				float r1 = 10.0f;

				float i1 = 20.0f;

				float r2 = 5.0f;

				float i2 = 7.0f;



				Complex c1 = new Complex(r1, i1);

				Complex c2 = new Complex(r2, i2);

				Complex result = c1 + c2;



				// Source: http://de.wikipedia.org/wiki/Komplexe_Zahl#Addition

				float rResult = r1 + r2;

				float iResult = i1 + i2;



				Assert.NearlyEqual(result.Real, rResult);

				Assert.NearlyEqual(result.Imaginary, iResult);

			}

			#endregion



			#region DataSize

			/// <summary>

			/// Data size

			/// </summary>

			[Test]

			public void DataSize()

			{

				int calculatedDatasize = sizeof(float) + sizeof(float);

				Assert.Equal(calculatedDatasize, Complex.DataSize);

			}

			#endregion



			#region ComplexMin

			/// <summary>

			/// Complex minimum

			/// </summary>

			[Test]

			public void ComplexMin()

			{

				float r1 = 1.0f;

				float i1 = 5.0f;

				float r2 = 2.0f;

				float i2 = 3.0f;



				Complex c1 = new Complex(r1, i1);

				Complex c2 = new Complex(r2, i2);

				c1.Min(c2);



				Assert.NearlyEqual(c1.Real, r1);

				Assert.NearlyEqual(c1.Imaginary, i2);

			}

			#endregion



			#region ComplexMax

			/// <summary>

			/// Complex maximum

			/// </summary>

			[Test]

			public void ComplexMax()

			{

				float r1 = 1.0f;

				float i1 = 5.0f;

				float r2 = 2.0f;

				float i2 = 3.0f;



				Complex c1 = new Complex(r1, i1);

				Complex c2 = new Complex(r2, i2);

				c1.Max(c2);



				Assert.NearlyEqual(c1.Real, r2);

				Assert.NearlyEqual(c1.Imaginary, i1);

			}

			#endregion



			#region Sum

			/// <summary>

			/// Complex sum

			/// </summary>

			[Test]

			public void Sum()

			{

				float r1 = 1.0f;

				float i1 = 5.0f;

				Complex c1 = new Complex(r1, i1);



				Assert.NearlyEqual(c1.Sum(), r1 + i1);

			}

			#endregion



			#region Product

			/// <summary>

			/// Product

			/// </summary>

			[Test]

			public void Product()

			{

				float r1 = 2.0f;

				float i1 = 5.0f;

				Complex c1 = new Complex(r1, i1);



				Assert.NearlyEqual(c1.Product(), r1 * i1);

			}

			#endregion



			#region LengthSquared

			/// <summary>

			/// Length squared

			/// </summary>

			[Test]

			public void LengthSquared()

			{

				float r1 = 2.0f;

				float i1 = 5.0f;

				Complex c1 = new Complex(r1, i1);



				Assert.NearlyEqual(c1.LengthSquared, (r1 * r1) + (i1 * i1));

			}

			#endregion



			#region Length

			/// <summary>

			/// Length

			/// </summary>

			[Test]

			public void Length()

			{

				float r1 = 2.0f;

				float i1 = 5.0f;

				Complex c1 = new Complex(r1, i1);



				Assert.NearlyEqual(c1.Length,

					MathHelper.Sqrt((r1 * r1) + (i1 * i1)));

			}

			#endregion



			#region FromSqrt

			/// <summary>

			/// From sqrt

			/// </summary>

			[Test]

			public void FromSqrt()

			{

				float square = 4.0f;

				Complex c1 = Complex.FromSqrt(square);

				Complex c2 = Complex.FromSqrt(-square);



				Assert.Equal(c1, new Complex(MathHelper.Sqrt(square), 0.0f));

				Assert.Equal(c2, new Complex(0.0f, MathHelper.Sqrt(square)));

			}

			#endregion



			#region Argument

			/// <summary>

			/// Argument

			/// </summary>

			[Test]

			public void Argument()

			{

				float r1 = 2.0f;

				float i1 = 5.0f;

				float result = (new Complex(r1, i1)).Argument;



				Assert.NearlyEqual(result, MathHelper.Atan(i1, r1));

			}

			#endregion



			#region Conjugate

			/// <summary>

			/// Conjugate

			/// </summary>

			[Test]

			public void Conjugate()

			{

				float r1 = 2.0f;

				float i1 = 5.0f;

				Complex c1 = new Complex(r1, i1).Conjugate();



				Assert.NearlyEqual(c1.Real, r1);

				Assert.NearlyEqual(c1.Imaginary, -i1);

			}

			#endregion



			#region Sqrt

			/// <summary>

			/// Sqrt

			/// </summary>

			[Test]

			public void Sqrt()

			{

				float r1 = 2.0f;

				float i1 = 5.0f;

				Complex c1 = new Complex(r1, i1).Sqrt();

				float modulus = (float)System.Math.Pow((r1 * r1) + (i1 * i1), 0.25f);

				float argument = 0.5f * MathHelper.Atan(i1, r1);



				Assert.NearlyEqual(c1.Real, modulus * MathHelper.Cos(argument));

				Assert.NearlyEqual(c1.Imaginary, modulus * MathHelper.Sin(argument));

			}

			#endregion



			#region ToString

			/// <summary>

			/// To string

			/// </summary>

			[Test]

			public new void ToString()

			{

				Assert.Equal("5 + i * 2", new Complex(5.0f, 2.0f).ToString());

			}

			#endregion

		}

	}

}