Piecewise Curves in C# QuickStart Sample

Illustrates working with piecewise constant and piecewise linear curves using classes from the Numerics.NET.Curves namespace in C#.

This sample is also available in: Visual Basic, F#, IronPython.

Overview

This QuickStart sample demonstrates how to work with piecewise constant and piecewise linear curves in Numerics.NET. These curves are useful for interpolating discrete data points where the function behavior between points is either constant or linear.

The sample covers:

Creating piecewise constant curves using different constructor overloads
Creating piecewise linear curves using different constructor overloads
Accessing and modifying curve parameters
Evaluating curves at specific points using ValueAt()
Computing slopes and derivatives
Finding tangent lines at points
Computing definite integrals

The code demonstrates practical usage of the PiecewiseConstantCurve and PiecewiseLinearCurve classes from the Numerics.NET.Curves namespace. It shows how to construct curves from arrays of x,y coordinates or Point objects, access curve parameters, evaluate curve values and derivatives, and compute integrals.

This sample is particularly useful for developers working with discrete data that requires interpolation, such as in signal processing, data analysis, or scientific computing applications where data points need to be connected using either constant or linear segments.

The code

using System;

using Numerics.NET;
// The piecewise curve classes reside in the
// Numerics.NET.Curves namespace.
using Numerics.NET.Curves;

// Illustrates the use of the PiecewiseConstantCurve and
// PiecewiseLinearCurve classes.

// The license is verified at runtime. We're using
// a 30 day trial key here. For more information, see
//     https://numerics.net/trial-key
Numerics.NET.License.Verify("your-trial-key-here");

// 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:
double[] xValues = {1, 2, 3, 4, 5, 6};
double[] yValues = {1, 3, 4, 3, 4, 2};
var constant1 = new PiecewiseConstantCurve(xValues, yValues);

// The second constructor takes two vectors, containing the
// x and y-values of the data points:
var xVector = Vector.Create(xValues);
var yVector = Vector.Create(yValues);
var constant2 = new PiecewiseConstantCurve(xVector, yVector);

// The third constructor only takes one parameter: an array of
// Point structures that represent the data point.
var dataPoints = 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)};
var constant3 = 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("constant1.Parameters.Count = {0}",
    constant1.Parameters.Count);
// Parameters can easily be retrieved:
Console.WriteLine("constant1.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($"constant1.ValueAt(2.4) = {constant1.ValueAt(2.4)}");

// The SlopeAt method returns the slope of the curve
// a the specified x value:
Console.WriteLine($"constant1.SlopeAt(2.4) = {constant1.SlopeAt(2.4)}");
// The slope at the data points is Double.NaN if the value of the constant
// is different on either side of the data point:
Console.WriteLine($"constant1.SlopeAt(2) = {constant1.SlopeAt(2)}");

// Piecewise constant curves do not have a defined derivative.
// The GetDerivative method returns a GeneralCurve:
Curve derivative = constant1.GetDerivative();
Console.WriteLine($"Type of derivative: {derivative.GetType().ToString()}");
Console.WriteLine($"derivative(2.4) = {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:
Polynomial tangent = constant1.TangentAt(2.4);
Console.WriteLine("Slope of tangent line at 2.4 = {0}",
    tangent.Parameters[1]);

// 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:
double[] xValues2 = {1, 2, 3, 4, 5, 6};
double[] yValues2 = {1, 3, 4, 3, 4, 2};
var line1 = new PiecewiseLinearCurve(xValues2, yValues2);

// The second constructor takes two vectors, containing the
// x and y-values of the data points:
var xVector2 = Vector.Create(xValues2);
var yVector2 = Vector.Create(yValues2);
var line2 = new PiecewiseLinearCurve(xVector2, yVector2);

// The third constructor only takes one parameter: an array of
// Point structures that represent the data point.
Point[] dataPoints2 = 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)};
PiecewiseLinearCurve line3 = 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("line1.Parameters.Count = {0}",
    line1.Parameters.Count);
// Parameters can easily be retrieved:
Console.WriteLine("line1.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($"line1.ValueAt(2.4) = {line1.ValueAt(2.4)}");

// The SlopeAt method returns the slope of the curve
// a the specified x value:
Console.WriteLine($"line1.SlopeAt(2.4) = {line1.SlopeAt(2.4)}");
// The slope at the data points is Double.NaN if the slope of the line
// is different on either side of the data point:
Console.WriteLine($"line1.SlopeAt(2) = {line1.SlopeAt(2)}");

// Piecewise line curves do not have a defined derivative.
// The GetDerivative method returns a GeneralCurve:
derivative = line1.GetDerivative();
Console.WriteLine($"Type of derivative: {derivative.GetType().ToString()}");
Console.WriteLine($"derivative(2.4) = {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.Parameters[1]);

// The integral of a piecewise line 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();