public PowerViewModel(double[] xdata, double[] ydata, Tuple <double, double> xlimit, Tuple <double, double> ylimit)
{
DirectRegressionMethod method = DirectRegressionMethod.QR;
Tuple <double, double> p = Fit.Power(xdata, ydata, method);
double a = p.Item1;
double b = p.Item2;
if (!Double.IsNaN(a) && !Double.IsNaN(b))
{
this.FunctionModel = new PlotModel {
Title = "Power regresion [ f(x) = " + a + " x ^ " + b + " ]"
};
Func <double, double> powerFunction = (x) => a *Math.Pow(x, b);
FunctionModel.Series.Add(new FunctionSeries(powerFunction, xlimit.Item1, xlimit.Item2, 0.0001));
// view limits
FunctionModel.Axes.Add(new LinearAxis {
Position = AxisPosition.Bottom, Minimum = xlimit.Item1, Maximum = xlimit.Item2
});
FunctionModel.Axes.Add(new LinearAxis {
Position = AxisPosition.Left, Minimum = ylimit.Item1, Maximum = ylimit.Item2
});
}
else
{
displayed = false;
}
}
/// <summary>
/// Least-Squares fitting the points (x, y) to a power
/// y : x -> a * x^b.
/// </summary>
public static IModelledFunction PowerFunc(double[] xArray, double[] yArray)
{
Tuple <double, double> parameters = Fit.Power(xArray, yArray);
double a = parameters.Item1;
double b = parameters.Item2;
Func <double, double> function = t => a *System.Math.Pow(t, b);
return(new PowerFunction(function, parameters));
}
public List <DataPoint> CalculatePoints(List <DataPoint> points)
{
var pointsLine = new List <DataPoint>();
Tuple <double, double> p = Fit.Power(points.Select(x => x.X).ToArray(), points.Select(x => x.Y).ToArray());
double a = p.Item1;
double b = p.Item2;
foreach (var item in points)
{
var y = a * Math.Pow(item.X, b);
pointsLine.Add(new DataPoint(item.X, y));
}
return(pointsLine);
}
/// https://numerics.mathdotnet.com/Regression.html#Linearizing-non-linear-models-by-transformation
/// https://github.com/mathnet/mathnet-numerics/blob/master/src/Numerics/Fit.cs
/// https://discuss.mathdotnet.com/t/exponential-fit/131/2
/// https://discuss.mathdotnet.com/t/curve-fitting-power/605
/// Power function: y = a * (x ^ b)
private void ApplyPowerFunctionFitting()
{
double[] x = Points.Select(p => p.X).ToArray();
double[] y = Points.Select(p => p.Y).ToArray();
Tuple <double, double> p = Fit.Power(x, y); // a=1.017, r=0.687
A = p.Item1;
B = p.Item2;
Func <double, double> f = Fit.LinearCombinationFunc(
Points.Select(p => p.X).ToArray(),
Points.Select(p => p.Y).ToArray(),
x => p.Item1 * Math.Pow(x, p.Item2));
List <DataPoint> fittedPoints = new List <DataPoint>();
foreach (var item in Points)
{
fittedPoints.Add(new DataPoint(item.X, f(item.X)));
}
FittedPoints = fittedPoints;
}
public FitData CalcFit(List <DataPoint> points)
{
FitData result = new FitData("Power function");
var xdata = points.Select(x => x.X).ToArray();
var ydata = points.Select(x => x.Y).ToArray();
Tuple <double, double> p = Fit.Power(xdata, ydata);
result.A = p.Item1;
result.B = p.Item2;
result.Points = DataPoints(points).ToList();
return(result);
//local function for return list of regresion Points[need to C# 8]
IEnumerable <DataPoint> DataPoints(List <DataPoint> points)
{
foreach (var point in points)
{
yield return(new DataPoint(point.X, result.A * Math.Exp(result.B * point.X)));
}
}
}
public void FitsToPowerSameAsExcelTrendLine()
{
// X Y
// 1 0.2
// 2 0.3
// 4 1.3
// 6 4.2
// -> y = 0.1454*x^1.7044
var x = new[] { 1.0, 2.0, 4.0, 6.0 };
var y = new[] { 0.2, 0.3, 1.3, 4.2 };
var resp = Fit.Power(x, y);
Assert.AreEqual(0.1454, resp.Item1, 1e-3);
Assert.AreEqual(1.7044, resp.Item2, 1e-3);
var resf = Fit.PowerFunc(x, y);
foreach (var z in Enumerable.Range(-3, 10))
{
Assert.AreEqual(0.1454 * Math.Pow(z, 1.7044), resf(z), 1e-2);
}
}