private void SubdivideSegment(float from, float to, int level)
{
//Profiler.BeginSample( "Approximation" );
var coefficients = CalculateChebyshefCoefficients(maxDegree, from, to);
var error = 0f;
for (var i = desiredDegree; i < maxDegree; ++i)
{
error += Mathf.Abs(coefficients[i]);
}
if (error < maxError || level > maxLevel)
{
//Profiler.BeginSample( "Compose" );
var approximation = new ChebyshevApproximation();
approximation.CopyCoefficients(f, from, to, desiredDegree, coefficients, 0, desiredDegree);
//Profiler.EndSample();
//Profiler.BeginSample( "Insertion" );
approximations.Add(approximation);
//Profiler.EndSample();
}
else
{
var mid = (from + to) * 0.5f;
SubdivideSegment(from, mid, level + 1);
SubdivideSegment(mid, to, level + 1);
}
//Profiler.EndSample();
}
private void DrawChebyshevTable()
{
float[] xValues = new float[]
{
-3.2f, -2.1f, 0.4f, 0.7f, 2.0f, 2.5f, 2.777f
};
float[] yValues = new float[]
{
10.0f, -2.0f, 0, -7.0f, 7.0f, 0, 0
};
float a = xValues[0];
float b = xValues[xValues.Length - 1];
var coefs = ChebyshevApproximation.Approximate(xValues, yValues, 0);
coefs = ChebyshevApproximation.Approximate(xValues, yValues, 1);
MnkK1Plotter.ItemsSource = GeneratePoints(coefs, a, b);
coefs = ChebyshevApproximation.Approximate(xValues, yValues, 2);
MnkK2Plotter.ItemsSource = GeneratePoints(coefs, a, b);
coefs = ChebyshevApproximation.Approximate(xValues, yValues, 3);
MnkK3Plotter.ItemsSource = GeneratePoints(coefs, a, b);
coefs = ChebyshevApproximation.Approximate(xValues, yValues, 4);
MnkK4Plotter.ItemsSource = GeneratePoints(coefs, a, b);
coefs = ChebyshevApproximation.Approximate(xValues, yValues, 5);
MnkK5Plotter.ItemsSource = GeneratePoints(coefs, a, b);
coefs = ChebyshevApproximation.Approximate(xValues, yValues, 6);
MnkK6Plotter.ItemsSource = GeneratePoints(coefs, a, b);
}
private void DrawChebyshevFunc()
{
var coefs = ChebyshevApproximation.Approximate(a, b, 1, ApproximatedFunction);
MnkK1Plotter.ItemsSource = GeneratePoints(coefs, a, b);
coefs = ChebyshevApproximation.Approximate(a, b, 2, ApproximatedFunction);
MnkK2Plotter.ItemsSource = GeneratePoints(coefs, a, b);
coefs = ChebyshevApproximation.Approximate(a, b, 3, ApproximatedFunction);
MnkK3Plotter.ItemsSource = GeneratePoints(coefs, a, b);
coefs = ChebyshevApproximation.Approximate(a, b, 4, ApproximatedFunction);
MnkK4Plotter.ItemsSource = GeneratePoints(coefs, a, b);
coefs = ChebyshevApproximation.Approximate(a, b, 5, ApproximatedFunction);
MnkK5Plotter.ItemsSource = GeneratePoints(coefs, a, b);
coefs = ChebyshevApproximation.Approximate(a, b, 6, ApproximatedFunction);
MnkK6Plotter.ItemsSource = GeneratePoints(coefs, a, b);
coefs = ChebyshevApproximation.Approximate(a, b, 7, ApproximatedFunction);
MnkK7Plotter.ItemsSource = GeneratePoints(coefs, a, b);
coefs = ChebyshevApproximation.Approximate(a, b, 8, ApproximatedFunction);
MnkK8Plotter.ItemsSource = GeneratePoints(coefs, a, b);
coefs = ChebyshevApproximation.Approximate(a, b, 9, ApproximatedFunction);
MnkK9Plotter.ItemsSource = GeneratePoints(coefs, a, b);
}
private static float[] GenerateX(float a, float b, float step)
{
int pointCount = ChebyshevApproximation.CalculateRank(a, b, step);
var result = new float[pointCount];
for (int i = 0; i < pointCount; i++)
{
result[i] = a + i * step;
}
return(result);
}
private List <Point> GeneratePoints(float[] coefficients, float a, float b)
{
var points = new List <Point>();
for (float i = a; i <= b; i += 0.001f)
{
float x = ChebyshevApproximation.Squish(i, a, b);
float y = ChebyshevApproximation.Evaluate(coefficients, x);
points.Add(new Point(i, y));
}
return(points);
}
public void ApproximateTableValues()
{
float[] xValues = new float[]
{
-3.2f, -2.1f, 0.4f, 0.7f, 2.0f, 2.5f, 2.777f
};
float[] yValues = new float[]
{
10.0f, -2.0f, 0, -7.0f, 7.0f, 0, 0
};
var polynom = ChebyshevApproximation.Approximate(xValues, yValues, xValues.Length - 1);
Assert.That(polynom.Length == xValues.Length);
}
private void DrawBasePoints(FittingFunction fittingFunction)
{
var points = new List <Point>();
var xValues = ChebyshevApproximation.GenerateX(a, b, step);
for (int i = 0; i < xValues.Length; i++)
{
points.Add(new Point(xValues[i], fittingFunction(xValues[i])));
}
RealDataPlotFor1.ItemsSource = RealDataPlotFor2.ItemsSource = RealDataPlotFor3.ItemsSource
= RealDataPlotFor4.ItemsSource = RealDataPlotFor5.ItemsSource = RealDataPlotFor6.ItemsSource
= RealDataPlotFor7.ItemsSource = RealDataPlotFor8.ItemsSource = RealDataPlotFor9.ItemsSource
= points;
}
public void Approximate()
{
float a = -2.0f;
float b = 2.0f;
float step = 0.5f;
int rank = ChebyshevApproximation.CalculateRank(a, b, step);
var polynom = ChebyshevApproximation.Approximate(a, b, rank, myFunc);
List <float> results = new List <float>();
var xApprox = GenerateX(a, b, 0.0001f);
for (float i = a; i <= b; i += 0.0001f)
{
float x = ChebyshevApproximation.Squish(i, a, b);
results.Add(ChebyshevApproximation.Evaluate(polynom, x));
}
Assert.That(polynom.Length == rank + 1);
}
public void CompareTableAndFunc()
{
float a = -2.0f;
float b = 2.0f;
float step = 0.5f;
int rank = ChebyshevApproximation.CalculateRank(a, b, step);
var xValues = GenerateX(a, b, step);
var yValues = new float[rank];
for (int i = 0; i < rank; i++)
{
yValues[i] = (float)myFunc(xValues[i]);
}
var expectedCoefficients = new Matrix(ChebyshevApproximation.Approximate(a, b, rank - 1, myFunc));
var actualCoefficients = new Matrix(ChebyshevApproximation.Approximate(xValues, yValues, xValues.Length - 1));
Assert.That(actualCoefficients.NearEquals(expectedCoefficients, (float)Math.PI + 0.2f), $"Expected: {expectedCoefficients.ToString()}, actual {actualCoefficients.ToString()}");
}
private void DemoTable_Chebyshev_Click(object sender, RoutedEventArgs e)
{
CleanDataSources();
float[] xValues = new float[]
{
0, 3.3f, 6.6f, 9.9f
};
float[] yValues = new float[]
{
2.1f, 5.9f, 2.4f, 3.4f
};
var coefs = ChebyshevApproximation.Approximate(
xValues,
yValues,
1
);
MnkK1Plotter.ItemsSource = GeneratePoints(coefs, xValues[0], xValues[xValues.Length - 1]);
coefs = ChebyshevApproximation.Approximate(
xValues,
yValues,
2
);
MnkK2Plotter.ItemsSource = GeneratePoints(coefs, xValues[0], xValues[xValues.Length - 1]);
coefs = ChebyshevApproximation.Approximate(
xValues,
yValues,
3
);
MnkK3Plotter.ItemsSource = GeneratePoints(coefs, xValues[0], xValues[xValues.Length - 1]);
DrawBasePoints(xValues, yValues);
}
private void DrawMSE_Func()
{
var rank = ChebyshevApproximation.CalculateRank(a, b, step);
var xValues = new Libs.Matrix(ChebyshevApproximation.GenerateX(a, b, step));
var yValues = new Libs.Matrix(new float[rank, 1]);
for (int j = 0; j < yValues.Height; j++)
{
yValues[j, 0] = (float)ApproximatedFunction(xValues[0, j]);
}
var coefs = MeanSquaredErrorApproximation.Approximate(xValues, yValues, 1);
MnkK1Plotter.ItemsSource = GeneratePoints(coefs);
coefs = MeanSquaredErrorApproximation.Approximate(xValues, yValues, 2);
MnkK2Plotter.ItemsSource = GeneratePoints(coefs);
coefs = MeanSquaredErrorApproximation.Approximate(xValues, yValues, 3);
MnkK3Plotter.ItemsSource = GeneratePoints(coefs);
coefs = MeanSquaredErrorApproximation.Approximate(xValues, yValues, 4);
MnkK4Plotter.ItemsSource = GeneratePoints(coefs);
coefs = MeanSquaredErrorApproximation.Approximate(xValues, yValues, 5);
MnkK5Plotter.ItemsSource = GeneratePoints(coefs);
coefs = MeanSquaredErrorApproximation.Approximate(xValues, yValues, 6);
MnkK6Plotter.ItemsSource = GeneratePoints(coefs);
coefs = MeanSquaredErrorApproximation.Approximate(xValues, yValues, 7);
MnkK7Plotter.ItemsSource = GeneratePoints(coefs);
coefs = MeanSquaredErrorApproximation.Approximate(xValues, yValues, 8);
MnkK8Plotter.ItemsSource = GeneratePoints(coefs);
coefs = MeanSquaredErrorApproximation.Approximate(xValues, yValues, 9);
MnkK9Plotter.ItemsSource = GeneratePoints(coefs);
}
private void SubdivideSegment( float from, float to, int level )
{
//Profiler.BeginSample( "Approximation" );
var coefficients = CalculateChebyshefCoefficients( maxDegree, from, to );
var error = 0f;
for ( var i = desiredDegree; i < maxDegree; ++i ) {
error += Mathf.Abs( coefficients[i] );
}
if ( error < maxError || level > maxLevel ) {
//Profiler.BeginSample( "Compose" );
var approximation = new ChebyshevApproximation();
approximation.CopyCoefficients( f, from, to, desiredDegree, coefficients, 0, desiredDegree );
//Profiler.EndSample();
//Profiler.BeginSample( "Insertion" );
approximations.Add( approximation );
//Profiler.EndSample();
} else {
var mid = ( from + to ) * 0.5f;
SubdivideSegment( from, mid, level + 1 );
SubdivideSegment( mid, to, level + 1 );
}
//Profiler.EndSample();
}
