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Piecewise Curves QuickStart Sample (VB.NET)
Extreme Optimization QuickStart Samples
Piecewise Curves QuickStart Sample (VB.NET)
Illustrates working with piecewise constant and piecewise linear curves using classes from the
Extreme.Mathematics.Curves namespace in Visual Basic.
C# code Back
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' The piecewise curve classes reside in the
' Extreme.Mathematics.Curves namespace.
Imports Extreme.Mathematics.Curves
Imports Extreme.Mathematics.LinearAlgebra
Namespace Extreme.Mathematics.QuickStart.VB
' Illustrates the use of the PiecewiseConstantCurve and
' PiecewiseLinearCurve classes.
Module NumericalDifferentiation
Sub Main()
' A piecewise curve is a curve that has a different definition
' on subintervals of its domain.
'
' This QuickStart Sample illustrates constant and linear piecewise
' curves, which - as the name suggest - are constant or linear
' on each interval.
'
' For an example of cubic splines, see the CubicSplines QuickStart
' Sample.
'
'
' Piecewise constants
'
' All piecewise curves inherit from the PiecewiseCurve class.
' Piecewise constant curves are implemented by the
' PiecewiseConstantCurve class. It has three constructors.
' The first constructor takes two double arrays as parameters.
' These contain the x and y values of the data points:
Dim xValues As Double() = {1, 2, 3, 4, 5, 6}
Dim yValues As Double() = {1, 3, 4, 3, 4, 2}
Dim constant1 As PiecewiseConstantCurve =
New PiecewiseConstantCurve(xValues, yValues)
' The second constructor takes two Vector objects, containing the
' x and y-values of the data points:
Dim xVector As GeneralVector = New GeneralVector(xValues)
Dim yVector As GeneralVector = New GeneralVector(yValues)
Dim constant2 As PiecewiseConstantCurve =
New PiecewiseConstantCurve(xVector, yVector)
' The third constructor only takes one parameter: an array of
' Point structures that represent the data point.
Dim dataPoints As Point() = New Point() _
{New Point(1, 1), New Point(2, 3), New Point(3, 4), _
New Point(4, 3), New Point(5, 4), New Point(6, 2)}
Dim constant3 As PiecewiseConstantCurve =
New PiecewiseConstantCurve(dataPoints)
'
' Curve Parameters
'
' The shape of any curve is determined by a set of parameters.
' These parameters can be retrieved and set through the
' Parameters collection. The number of parameters for a curve
' is given by this collection's Count property.
'
' Piecewise constant curves have 2n parameters, where n is
' the number of data points. The first n parameters are the
' x-values. The next n parameters are the y-values.
Console.WriteLine("Parameters.Count = {0}", _
constant1.Parameters.Count)
' Parameters can easily be retrieved:
Console.WriteLine("Parameters(0) = {0}", constant1.Parameters(0))
' Parameters can also be set:
constant1.Parameters(0) = 1
'
' Curve Methods
'
' The ValueAt method returns the y value of the
' curve at the specified x value:
Console.WriteLine("ValueAt(2.4) = {0}", constant1.ValueAt(2.4))
' The SlopeAt method returns the slope of the curve
' a the specified x value:
Console.WriteLine("SlopeAt(2.4) = {0}", constant1.SlopeAt(2.4))
' The slope at the data points is Double.NaN if the value
' of the constant is different on either side of the data point:
Console.WriteLine("SlopeAt(2) = {0}", constant1.SlopeAt(2))
' Piecewise constant curves do not have a defined derivative.
' The GetDerivative method returns a GeneralCurve:
Dim derivative As Curve = constant1.GetDerivative()
Console.WriteLine("Type of derivative: {0}", _
derivative.GetType().ToString())
Console.WriteLine("derivative(2.4) = {0}", derivative.ValueAt(2.4))
' You can get a Line that is the tangent to a curve
' at a specified x value using the TangentAt method:
Dim tangent As Line = constant1.TangentAt(2.4)
Console.WriteLine("Slope of tangent line at 2.4 = {0}", tangent.Slope)
' The integral of a piecewise constant curve can be calculated
' exactly.
Console.WriteLine("Integral of constant1 between 1.4 and 4.6 = {0}", _
constant1.Integral(1.4, 4.6))
'
' Piecewise linear curves
'
' Piecewise linear curves are used for linear interpolation
' between data points. They are implemented by the
' PiecewiseLinearCurve class. It has three constructors,
' similar to the constructors for the PiecewiseLinearCurve
' class..These constructors create the linear interpolating
' curve between the data points.
' The first constructor takes two double arrays as parameters.
' These contain the x and y values of the data points:
Dim xValues2 As Double() = {1, 2, 3, 4, 5, 6}
Dim yValues2 As Double() = {1, 3, 4, 3, 4, 2}
Dim line1 As PiecewiseLinearCurve =
New PiecewiseLinearCurve(xValues2, yValues2)
' The second constructor takes two Vector objects, containing the
' x and y-values of the data points:
Dim xVector2 As GeneralVector = New GeneralVector(xValues2)
Dim yVector2 As GeneralVector = New GeneralVector(yValues2)
Dim line2 As PiecewiseLinearCurve =
New PiecewiseLinearCurve(xVector2, yVector2)
' The third constructor only takes one parameter: an array of
' Point structures that represent the data point.
Dim dataPoints2 As Point() = New Point() _
{New Point(1, 1), New Point(2, 3), New Point(3, 4), _
New Point(4, 3), New Point(5, 4), New Point(6, 2)}
Dim line3 As PiecewiseLinearCurve =
New PiecewiseLinearCurve(dataPoints)
'
' Curve Parameters
'
' Piecewise linear curves have 2n parameters, where n is
' the number of data points. The first n parameters are the
' x-values. The next n parameters are the y-values.
Console.WriteLine("Parameters.Count = {0}", _
line1.Parameters.Count)
' Parameters can easily be retrieved:
Console.WriteLine("Parameters(0) = {0}", _
line1.Parameters(0))
' Parameters can also be set:
line1.Parameters(0) = 1
'
' Curve Methods
'
' The ValueAt method returns the y value of the
' curve at the specified x value:
Console.WriteLine("ValueAt(2.4) = {0}", line1.ValueAt(2.4))
' The SlopeAt method returns the slope of the curve
' a the specified x value:
Console.WriteLine("SlopeAt(2.4) = {0}", line1.SlopeAt(2.4))
' The slope at the data points is Double.NaN if the slope
' of the line is different on either side of the data point:
Console.WriteLine("SlopeAt(2) = {0}", line1.SlopeAt(2))
' Piecewise line curves do not have a defined derivative.
' The GetDerivative method returns a GeneralCurve:
derivative = line1.GetDerivative()
Console.WriteLine("Type of derivative: {0}", _
derivative.GetType().ToString())
Console.WriteLine("derivative(2.4) = {0}", derivative.ValueAt(2.4))
' You can get a Line that is the tangent to a curve
' at a specified x value using the TangentAt method:
tangent = line1.TangentAt(2.4)
Console.WriteLine("Slope of tangent line at 2.4 = {0}", tangent.Slope)
' The integral of a piecewise constant curve can be calculated
' exactly.
Console.WriteLine("Integral of line1 between 1.4 and 4.6 = {0}", _
line1.Integral(1.4, 4.6))
Console.Write("Press Enter key to exit...")
Console.ReadLine()
End Sub
End Module
End Namespace
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