Vector Operations in Visual Basic QuickStart Sample

Illustrates how to perform operations on Vector objects, including construction, element access, arithmetic operations in Visual Basic.

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Option Infer On

' The Vector class resides in the Extreme.Mathematics.LinearAlgebra namespace.
Imports Extreme.Mathematics.LinearAlgebra
' The delegate classes reside in the Extreme.Mathematics 
' namespace.
Imports Extreme.Mathematics

    ' Illustrates operations on Vector objects from the
    ' Extreme.Mathematics.LinearAlgebra namespace of Extreme Numerics.NET.
    Module VectorOperations

        Sub Main()
        ' The license is verified at runtime. We're using
        ' a demo license here. For more information, see
        ' https://numerics.net/trial-key
        Extreme.License.Verify("Demo license")

        ' For details on the basic workings of Vector 
        ' objects, including constructing, copying and
        ' cloning vectors, see the BasicVectors QuickStart
        ' Sample.
        '
        ' Let's create some vectors to work with.
        Dim v1 = Vector.Create(New Double() {1, 2, 3, 4, 5})
        Dim v2 = Vector.Create(New Double() {1, -2, 3, -4, 5})
        Dim v3 = Vector.Create(New Double() {3, 2, 1, 0, -1})
        ' This one will hold results.
        Dim v As Vector(Of Double)

        '
        ' Vector Arithmetic
        '
        ' The Vector class defines static methods for
        ' addition and subtraction:
        Console.WriteLine("v1 = {0:F4}", v1)
        Console.WriteLine("v2 = {0:F4}", v2)
        Console.WriteLine("Basic arithmetic:")
        v = Vector.Negate(v1)
        Console.WriteLine("-v1 = {0:F4}", v)
        v = Vector.Add(v1, v2)
        Console.WriteLine("v1 + v2 = {0:F4}", v)
        v = Vector.Subtract(v1, v2)
        Console.WriteLine("v1 - v2 = {0:F4}", v)
        ' Vectors can only be multiplied or divided by
        ' a real number. For dot products, see the
        ' DotProduct method.
        v = Vector.Multiply(5, v1)
        Console.WriteLine("5 * v1 = {0:F4}", v)

        ' You can also apply these methods to Vector objects.
        ' In this case, they change the first operand.
        Console.WriteLine("v3 = {0:F4}", v3)
        v3.AddInPlace(v1)
        ' Note that this is different from the += operator!
        ' The += operator creates a new Vector object, 
        ' whereas the Add method above does not.
        Console.WriteLine("v3+v1 -> v3 = {0:F4}", v3)
        ' This method is overloaded so you can directly
        ' add a scaled vector:
        v3.AddScaledInPlace(-2, v1)
        Console.WriteLine("v3-2v1 -> v3 = {0:F4}", v3)
        Console.WriteLine()

        '
        ' Norms, dot products, etc.
        '
        Console.WriteLine("Norms, dot products, etc.")
        ' The dot product is calculated in one of two ways:
        ' Using the static DotProduct method:
        Dim a As Double = Vector.DotProduct(v1, v2)
        ' Or using the DotProduct method on one of the two
        ' vectors:
        Dim b As Double = v1.DotProduct(v2)
        Console.WriteLine("DotProduct(v1, v2) = {0} = {0:F4}",
                a, b)
        ' The Norm method returns the standard two norm 
        ' of a Vector:
        a = v1.Norm()
        Console.WriteLine("|v1| = {0}", a)
        ' .the Norm method is overloaded to allow other norms,
        ' including the one-norm:
        a = v1.Norm(1)
        Console.WriteLine("one norm(v1) = {0}", a)
        ' ...the positive infinity norm, which returns the
        ' absolute value of the largest component:
        a = v1.Norm(Double.PositiveInfinity)
        Console.WriteLine("+inf norm(v1) = {0}", a)
        ' ...the negative infinity norm, which returns the
        ' absolute value of the smallest component:
        a = v1.Norm(Double.NegativeInfinity)
        Console.WriteLine("-inf norm(v1) = {0}", a)
        ' ...and even the zero norm, which simply returns
        ' the number of components of the vector:
        a = v1.Norm(0)
        Console.WriteLine("zero-norm(v1) = {0}", a)
        ' You can get the square of the two norm with the
        ' NormSquared method.
        a = v1.NormSquared()
        Console.WriteLine("|v1|^2 = {0}", a)
        Console.WriteLine()

        '
        ' Largest and smallest elements
        '
        ' The Vector class defines methods to find the
        ' largest or smallest element or its index.
        Console.WriteLine("v2 = {0:F4}", v2)
        ' The Max method returns the largest element:
        Console.WriteLine("Max(v2) = {0}", v2.Max())
        ' The AbsoluteMax method returns the element with
        ' the largest absolute value.
        Console.WriteLine("Absolute max(v2) = {0}",
                v2.AbsoluteMax())
        ' The Min method returns the smallest element:
        Console.WriteLine("Min(v2) = {0}", v2.Min())
        ' The AbsoluteMin method returns the element with
        ' the smallest absolute value.
        Console.WriteLine("Absolute min(v2) = {0}",
                v2.AbsoluteMin())
        ' Each of these methods has an equivalent method
        ' that returns the zero-based index of the element 
        ' instead of its value, for example:
        Console.WriteLine("Index of Min(v2) = {0}",
                v2.MinIndex())

        ' Finally, the Map method lets you apply
        ' an arbitrary function to each element of the
        ' vector:
        v3.Map(AddressOf Math.Exp)
        Console.WriteLine("Exp(v3) = {0:F4}", v3)
        ' There is also a static method that returns a 
        ' new Vector object:
        v = Vector.Map(AddressOf Math.Exp, v3)

        Console.Write("Press Enteruner key to exit...")
        Console.ReadLine()
    End Sub

End Module