Extreme Optimization >
Mathematics Library for .NET >
QuickStart Samples >
ComplexNumbers QuickStart Sample (VB.NET)
Extreme Optimization Mathematics Library for .NET
ComplexNumbers QuickStart Sample (VB.NET)
Illustrates the use of the DoubleComplex structure for representing complex numbers
in Visual Basic .NET.
C# code Back
to QuickStart Samples
' The DoubleComplex class resides in the Extreme.Mathematics namespace.
Imports Extreme.Mathematics
Namespace Extreme.Mathematics.QuickStart.VB
' Illustrates the use of the DoubleComplex class in the
' Extreme Optimization Mathematics Library for .NET.
' </summary>
Module ComplexNumbers
Sub Main()
'
' DoubleComplex constants:
'
Console.WriteLine("DoubleComplex.Zero = {0}", DoubleComplex.Zero)
Console.WriteLine("DoubleComplex.One = {0}", DoubleComplex.One)
' The imaginary unit is given by DoubleComplex.I:
Console.WriteLine("DoubleComplex.I = {0}", DoubleComplex.I)
Console.WriteLine()
'
' Construct some complex numbers
'
' Real and imaginary parts:
' a = 2 + 4i
Dim a As DoubleComplex = New DoubleComplex(2, 4)
Console.WriteLine("a = {0}", a)
' b = 1 - 3i
Dim b As DoubleComplex = New DoubleComplex(1, -3)
Console.WriteLine("b = {0}", b.ToString())
' From a real number:
' c = -3 + 0i
Dim c As DoubleComplex = New DoubleComplex(-3)
Console.WriteLine("c = {0}", c.ToString())
' Polar form:
' d = 2 (cos(Pi/3) + i sin(Pi/3))
Dim d As DoubleComplex = New DoubleComplex(2, Constants.Pi / 3, True)
' To print this number, use the overloaded ToString
' method and specify the format string for the real
' and imaginary parts:
Console.WriteLine("d = {0}", d.ToString("F4"))
Console.WriteLine()
'
' Parts of complex numbers
'
Console.WriteLine("Parts of a = {0}:", a)
Console.WriteLine("Real part of a = {0}", a.Re)
Console.WriteLine("Imaginary part of a = {0}", a.Im)
Console.WriteLine("Modulus of a = {0}", a.Modulus)
Console.WriteLine("Argument of a = {0}", a.Argument)
Console.WriteLine()
'
' Basic arithmetic:
'
Console.WriteLine("Basic arithmetic:")
Dim e As DoubleComplex
e = DoubleComplex.Negate(a)
Console.WriteLine("-a = {0}", e)
e = DoubleComplex.Add(a, b)
Console.WriteLine("a + b = {0}", e)
e = DoubleComplex.Subtract(a, b)
Console.WriteLine("a - b = {0}", e)
e = DoubleComplex.Multiply(a, b)
Console.WriteLine("a * b = {0}", e)
e = DoubleComplex.Divide(a, b)
Console.WriteLine("a / b = {0}", e)
'BUG e = DoubleComplex.Conjugate(a)
e = a.Conjugate
Console.WriteLine("Conjugate(a) = {0}", e)
Console.WriteLine()
'
' Functions of complex numbers
'
' Most of these have corresponding Shared methods
' in the System.Math class, but are extended to complex
' arguments.
Console.WriteLine("Functions of complex numbers:")
' Exponentials and logarithms
Console.WriteLine("Exponentials and logarithms:")
e = DoubleComplex.Exp(a)
Console.WriteLine("Exp(a) = {0}", e.ToString("F4"))
e = DoubleComplex.Log(a)
Console.WriteLine("Log(a) = {0}", e.ToString("F4"))
e = DoubleComplex.Log10(a)
Console.WriteLine("Log10(a) = {0}", e.ToString("F4"))
' You can get a point on the unit circle by calling
' the ExpI method:
e = DoubleComplex.ExpI(2 * Extreme.Mathematics.Constants.Pi / 3)
Console.WriteLine("ExpI(2*Pi/3) = {0}", e.ToString("F4"))
' The RootOfUnity method also returns points on the
' unit circle. The above is equivalent to the second
' root of z^6 = 1:
e = DoubleComplex.RootOfUnity(6, 2)
Console.WriteLine("RootOfUnity(6, 2) = {0}", e.ToString("F4"))
' The Pow method is overloaded for integer, double,
' and complex argument:
e = DoubleComplex.Pow(a, 3)
Console.WriteLine("Pow(a,3) = {0}", e.ToString("F4"))
e = DoubleComplex.Pow(a, 1.5)
Console.WriteLine("Pow(a,1.5) = {0}", e.ToString("F4"))
e = DoubleComplex.Pow(a, b)
Console.WriteLine("Pow(a,b) = {0}", e.ToString("F4"))
' Square root
e = DoubleComplex.Sqrt(a)
Console.WriteLine("Sqrt(a) = {0}", e.ToString("F4"))
' The Sqrt method is overloaded. Here's the square
' root of a negative double:
e = DoubleComplex.Sqrt(-4)
Console.WriteLine("Sqrt(-4) = {0}", e.ToString("F4"))
Console.WriteLine()
'
' Trigonometric functions:
'
Console.WriteLine("Trigonometric function:")
e = DoubleComplex.Sin(a)
Console.WriteLine("Sin(a) = {0}", e.ToString("F4"))
e = DoubleComplex.Cos(a)
Console.WriteLine("Cos(a) = {0}", e.ToString("F4"))
e = DoubleComplex.Tan(a)
Console.WriteLine("Tan(a) = {0}", e.ToString("F4"))
' GetInverse Trigonometric functions:
e = DoubleComplex.Asin(a)
Console.WriteLine("Asin(a) = {0}", e.ToString("F4"))
e = DoubleComplex.Acos(a)
Console.WriteLine("Acos(a) = {0}", e.ToString("F4"))
e = DoubleComplex.Atan(a)
Console.WriteLine("Atan(a) = {0}", e.ToString("F4"))
' Asin and Acos have overloads with real argument
' not restricted to [-1,1]:
e = DoubleComplex.Asin(2)
Console.WriteLine("Asin(2) = {0}", e.ToString("F4"))
e = DoubleComplex.Acos(2)
Console.WriteLine("Acos(2) = {0}", e.ToString("F4"))
Console.WriteLine()
'
' Hyperbolic and inverse hyperbolic functions:
'
Console.WriteLine("Hyperbolic function:")
e = DoubleComplex.Sinh(a)
Console.WriteLine("Sinh(a) = {0}", e.ToString("F4"))
e = DoubleComplex.Cosh(a)
Console.WriteLine("Cosh(a) = {0}", e.ToString("F4"))
e = DoubleComplex.Tanh(a)
Console.WriteLine("Tanh(a) = {0}", e.ToString("F4"))
e = DoubleComplex.Asinh(a)
Console.WriteLine("Asinh(a) = {0}", e.ToString("F4"))
e = DoubleComplex.Acosh(a)
Console.WriteLine("Acosh(a) = {0}", e.ToString("F4"))
e = DoubleComplex.Atanh(a)
Console.WriteLine("Atanh(a) = {0}", e.ToString("F4"))
Console.WriteLine()
Console.Write("Press Enter key to exit...")
Console.ReadLine()
End Sub
End Module
End Namespace
Copyright 2004-2008,
Extreme Optimization. All rights reserved.
Extreme Optimization, Complexity made simple, M#, and M
Sharp are trademarks of ExoAnalytics Inc.
Microsoft, Visual C#, Visual Basic, Visual Studio, Visual
Studio.NET, and the Visual Studio Logo are registered trademarks of Microsoft Corporation