private double CountWaveFunctions(double e)
{
InitSystems(e);
_t = new double[_nodesCount];
_psi = new double[_nodesCount];
_phi = new double[_nodesCount];
var solver = new Solver(_systemForward, -_l, _conditionValuesForward, _h, _nodesCount);
var solutionPsi = solver.Solve();
for (int i = 0; i < _nodesCount; i++)
{
_t[i] = solutionPsi[i][0];
_psi[i] = solutionPsi[i][2];
}
solver = new Solver(_systemBackward, _l, _conditionValuesBackward, -_h, _nodesCount);
var solutionFi = solver.Solve();
for (int i = 0; i < _nodesCount; i++)
{
_phi[i] = solutionFi[_nodesCount - 1 - i][2];
}
Scale(_psi);
NormalizeMath();
NormalizeQuant();
_psiSpline = CubicSpline.InterpolateAkima(_t, _psi);
_phiSpline = CubicSpline.InterpolateAkima(_t, _phi);
return(_psiSpline.Differentiate(_t[_sewNode]) - _phiSpline.Differentiate(_t[_sewNode]));
}
public void FitsAtArbitraryPoints(double t, double x, double maxAbsoluteError)
{
IInterpolation it = CubicSpline.InterpolateAkima(_t, _y);
// TODO: Verify the expected values (that they are really the expected ones)
Assert.AreEqual(x, it.Interpolate(t), maxAbsoluteError, "Interpolation at {0}", t);
}
protected void UpdateInterpolation()
{
int count = _keyFrames.Count;
var xs = new double[count];
var ys = new double[count];
for (int i = 0; i < count; ++i)
{
xs[i] = (double)_keyFrames[i].time;
ys[i] = (double)_keyFrames[i].value;
}
if (count <= 1)
{
_interpolation = StepInterpolation.Interpolate(xs, ys);
}
else if (count <= 2)
{
_interpolation = LinearSpline.Interpolate(xs, ys);
}
else if (count <= 3)
{
_interpolation = MathNet.Numerics.Interpolate.Polynomial(xs, ys);
}
else if (count <= 4)
{
_interpolation = CubicSpline.InterpolateNatural(xs, ys);
}
else
{
_interpolation = CubicSpline.InterpolateAkima(xs, ys);
}
}
public void FitsAtSamplePoints()
{
IInterpolation it = CubicSpline.InterpolateAkima(_t, _y);
for (int i = 0; i < _y.Length; i++)
{
Assert.AreEqual(_y[i], it.Interpolate(_t[i]), "A Exact Point " + i);
}
}
private double CountXSquareQuantAvg()
{
for (var i = 0; i < _nodesCount; i++)
{
_xQuantAvg[i] = _psi[i] * _t[i] * _t[i] * _psi[i];
}
var xQiantAvgSpline = CubicSpline.InterpolateAkima(_t, _xQuantAvg);
return(xQiantAvgSpline.Integrate(-_l, _l));
}
public void SupportsLinearCase(int samples)
{
double[] x, y, xtest, ytest;
LinearInterpolationCase.Build(out x, out y, out xtest, out ytest, samples);
IInterpolation it = CubicSpline.InterpolateAkima(x, y);
for (int i = 0; i < xtest.Length; i++)
{
Assert.AreEqual(ytest[i], it.Interpolate(xtest[i]), 1e-15, "Linear with {0} samples, sample {1}", samples, i);
}
}
public void InterpolateCurveAkima() // generates a smoother version of the random curve
{
List <SensitivityPoint> smoothCurve = new List <SensitivityPoint>();
double[] timestamp = sensCurve.Select(sensCurve => sensCurve.timeStamp).ToArray();
double[] randomsense = sensCurve.Select(sensCurve => sensCurve.sensitivity).ToArray();
CubicSpline spline = CubicSpline.InterpolateAkima(timestamp, randomsense);
for (double timecode = 0; timecode < this.lenght; timecode += timestep)
{
SensitivityPoint sensPoint = new SensitivityPoint(timecode, spline.Interpolate(timecode));
smoothCurve.Add(sensPoint);
}
sensCurve = smoothCurve;
}
private double GetProbalilityDensity(double[] function)
{
var functionSquare = new double[_nodesCount];
for (var i = 0; i < _nodesCount; i++)
{
functionSquare[i] = function[i] * function[i];
}
var functionSquareSpline = CubicSpline.InterpolateAkima(_t, functionSquare);
var x = functionSquareSpline.Integrate(-_l, _l);
return(functionSquareSpline.Integrate(-_l, _l));
}
protected Func <double, double> CreatePolynom(int index)
{
if (points[index].Count == 0)
{
points[index].Add(new DataPoint(currMin, 1));
points[index].Add(new DataPoint(currMax, 1));
}
DataPoint[] currPoints = points[index].ToArray();
double[,] coeffs = new double[currPoints.Length, 2];
List <double> xv = new List <double>();
List <double> yv = new List <double>();
Func <double, double> linear = CreateLinear(index);
for (int i = 0; i < currPoints.Length; i++)
{
xv.Add(currPoints[i].XValue);
yv.Add(currPoints[i].YValues[0]);
coeffs[i, 0] = currPoints[i].XValue;
coeffs[i, 1] = currPoints[i].YValues[0];
}
Random rnd = new Random();
while (xv.Count < 5)
{
int i = rnd.Next(xv.Count - 1);
int j = i + 1;
double x = (xv[i] + xv[j]) / 2;
yv.Insert(j, linear(x));
xv.Insert(j, x);
}
var akima = CubicSpline.InterpolateAkima(xv, yv);
return((x) =>
{
double res = akima.Interpolate(x);
if (res < 0)
{
return 0;
}
if (res > 1)
{
return 1;
}
return res;
});
}
/// <summary>
/// Run example
/// </summary>
/// <seealso cref="http://en.wikipedia.org/wiki/Spline_interpolation">Spline interpolation</seealso>
public void Run()
{
// 1. Generate 10 samples of the function x*x-2*x on interval [0, 10]
Console.WriteLine(@"1. Generate 10 samples of the function x*x-2*x on interval [0, 10]");
double[] points = Generate.LinearSpaced(10, 0, 10);
var values = Generate.Map(points, TargetFunction);
Console.WriteLine();
// 2. Create akima spline interpolation
var method = CubicSpline.InterpolateAkima(points, values);
Console.WriteLine(@"2. Create akima spline interpolation based on arbitrary points");
Console.WriteLine();
// 3. Check if interpolation support integration
Console.WriteLine(@"3. Support integration = {0}", ((IInterpolation)method).SupportsIntegration);
Console.WriteLine();
// 4. Check if interpolation support differentiation
Console.WriteLine(@"4. Support differentiation = {0}", ((IInterpolation)method).SupportsDifferentiation);
Console.WriteLine();
// 5. Differentiate at point 5.2
Console.WriteLine(@"5. Differentiate at point 5.2 = {0}", method.Differentiate(5.2));
Console.WriteLine();
// 6. Integrate at point 5.2
Console.WriteLine(@"6. Integrate at point 5.2 = {0}", method.Integrate(5.2));
Console.WriteLine();
// 7. Interpolate ten random points and compare to function results
Console.WriteLine(@"7. Interpolate ten random points and compare to function results");
var rng = new MersenneTwister(1);
for (var i = 0; i < 10; i++)
{
// Generate random value from [0, 10]
var point = rng.NextDouble() * 10;
Console.WriteLine(@"Interpolate at {0} = {1}. Function({0}) = {2}", point.ToString("N05"), method.Interpolate(point).ToString("N05"), TargetFunction(point).ToString("N05"));
}
Console.WriteLine();
}
/// <summary>
/// Строит функция принадлежности в виде сплайна Акимы.
/// </summary>
/// <param name="points">Список точек для построения сплайна.</param>
protected void InitializeAkima(List <KeyValuePair <double, double> > points)
{
var ordered = points.OrderBy((p) => p.Key).ToList();
var akima = CubicSpline.InterpolateAkima(ordered.Select((p) => p.Key),
ordered.Select((p) => p.Value));
function = (x) =>
{
double res = akima.Interpolate(x[0]);
if (res < 0)
{
return(0);
}
if (res > 1)
{
return(1);
}
return(res);
};
}
private static IReadOnlyCollection <DataPoint> GeneratePointsFromBitmap(Stream stream)
{
const double fmax = 19000.0;
const double fmin = 20.0;
const double dbrange = 16.0;
const double dbmax = 1.0;
const double sampleRate = 48000.0;
const int sampleSize = 16384;
// Create a Bitmap object from an image file.
using var iBitmap = new Bitmap(stream);
//using var oBitmap = new Bitmap(iBitmap.Width, iBitmap.Height);
var first = 0;
//var last = 0;
double min = iBitmap.Height;
double max = 0;
// Get the color of a pixel within myBitmap.
var points = new Collection <KeyValuePair <int, double> >();
for (var x = 0; x < iBitmap.Width; x++)
{
var list = new List <int>();
for (var y = 0; y < iBitmap.Height; y++)
{
var pixelColor = iBitmap.GetPixel(x, y);
if ((pixelColor.R > 200) && (pixelColor.G < 25) && (pixelColor.B < 25))
{
if (first == 0)
{
first = x;
}
//else last = x;
//oBitmap.SetPixel(x, y, Color.FromArgb(255, 0, 0));
list.Add(y);
}
}
if (list.Count > 0)
{
var a = iBitmap.Height - list.Average();
points.Add(new KeyValuePair <int, double>(x, a));
if (a < min)
{
min = a;
}
if (a > max)
{
max = a;
}
}
}
//var size = last - first + 1;
var mag = max - min + 1;
//calculate gain & offset
var scale = dbrange / mag;
var shift = dbmax - max * scale;
//check
//var n_min = min * scale + shift;
//var n_max = max * scale + shift;
//convert bitmap to frequency spectrum
var ex = new List <double>();
var ey = new List <double>();
for (var x = 0; x < points.Count; x++)
{
var df = Math.Log10(fmax / fmin); //over aproximately 3 decades
var f = 20.0 * Math.Pow(10.0, df * x / points.Count); //convert log horizontal image pixels to linear frequency scale in Hz
var y = points[x].Value * scale + shift; //scale and shift vertical image pixels to correct magnitude in dB
ex.Add(f);
ey.Add(Math.Pow(10.0, y / 20.0));
}
//interpolate frequency spectrum to match Audyssey responseData length
var frequency = Enumerable.Range(0, sampleSize).Select(p => p * sampleRate / sampleSize).ToArray();
var spline = CubicSpline.InterpolateAkima(ex, ey);
var frequencyPoints = new List <DataPoint>();
foreach (var f in frequency)
{
if (f < fmin)
{ // exptrapolate
frequencyPoints.Add(new DataPoint(f, double.NegativeInfinity));
}
else
{
frequencyPoints.Add(f > fmax
? new DataPoint(f, double.NegativeInfinity)
: new DataPoint(f, 20 * Math.Log10(spline.Interpolate(f))));
}
}
//oBitmap.Save(Path.ChangeExtension(path, "jpg"), System.Drawing.Imaging.ImageFormat.Jpeg);
return(frequencyPoints);
}
private TradingRecommendation GetTradingRecommendationForCrossOver()
{
int[] Intervals = { 50, 200 };
TradingRecommendation Recommendation = new TradingRecommendation();
List <double[]> MovingAverageObject = new List <double[]>();
List <double> d1 = Statistics.MovingAverage(
GetBusinessDayDataForRange(DateTime.Now, Intervals[0]).
Select(s => Convert.ToDouble(s.Close)).ToArray(), Intervals[0]).ToList();
List <double> d2 = Statistics.MovingAverage(
GetBusinessDayDataForRange(DateTime.Now, Intervals[1]).
Select(s => Convert.ToDouble(s.Close)).ToArray(), Intervals[1]).ToList();
double[] xd = d1.ToArray();
double[] yd = d2.Skip(d2.Count() - d1.Count()).ToArray();
CubicSpline Curvedata = CubicSpline.InterpolateAkima(
d1.Select((s, i2) => new { i2, s })
.Select(t => Convert.ToDouble(t.i2)).ToArray(),
d1);
while (d1.Count() != d2.Count())
{
if (d1.Count() > d2.Count())
{
d2.Insert(0, 0);
}
else
{
d1.Insert(0, 0);
}
}
double[] intersects0 = Polyfit(xd, yd, 0);
List <Tuple <int, double> > Intersects = new List <Tuple <int, double> >();
int i = 0;
foreach (double di in yd)
{
if (di * 0.999 <= intersects0[0] && di * 1.001 >= intersects0[0])
{
Intersects.Add(new Tuple <int, double>(i, di));
}
i++;
}
/*
*
*
* CubicSpline Curvedata = CubicSpline.InterpolateAkima(
* d1.Select((s, i2) => new { i2, s })
* .Select(t => Convert.ToDouble(t.i2)).ToArray(),
* d1);
*
*
* while (d1.Count() != d2.Count())
* {
* if (d1.Count() > d2.Count())
* {
* d2.Insert(0, double.NaN);
* }
* else
* {
* d1.Insert(0, double.NaN);
* }
* }
* List<Tuple<int, double>> Intersects = new List<Tuple<int, double>>();
* int i = 0;
* foreach (double di in d1)
* {
* //need to add a little bit of gliding here as well...
* if (!double.IsNaN(di) && !double.IsNaN(d2[i]) && (di <= d2[i]*0.92 && di >= d2[i] * 1.07))
* {
* Intersects.Add(new Tuple<int, double>(i, di));
* }
* i++;
* }*/
try
{
int Sellmax = (Intersects.Where(x => Curvedata.Differentiate(x.Item2) < 0).Count() > 0) ? Intersects.Where(x => Curvedata.Differentiate(x.Item2) < 0).Last().Item1 : 0;
int Buymax = (Intersects.Where(x => Curvedata.Differentiate(x.Item2) > 0).Count() > 0) ? Intersects.Where(x => Curvedata.Differentiate(x.Item2) > 0).Last().Item1 : 0;
if (Sellmax > Buymax && Sellmax > 0)
{
return(new TradingRecommendation(
Instrument,
ImperaturGlobal.GetMoney(0, Instrument.CurrencyCode),
ImperaturGlobal.GetMoney(Convert.ToDecimal(Intersects.Where(x => x.Item1.Equals(Sellmax)).Last().Item2), Instrument.CurrencyCode),
DateTime.Now,
DateTime.Now,
TradingForecastMethod.Crossover
));
}
if (Buymax > Sellmax && Buymax > 0)
{
return(new TradingRecommendation(
Instrument,
ImperaturGlobal.GetMoney(Convert.ToDecimal(Intersects.Where(x => x.Item1.Equals(Buymax)).Last().Item2), Instrument.CurrencyCode),
ImperaturGlobal.GetMoney(0, Instrument.CurrencyCode),
DateTime.Now,
DateTime.Now,
TradingForecastMethod.Crossover
));
}
}
catch (Exception ex)
{
int gg = 0;
}
return(Recommendation);
}
public void LoadTrajectory(com.robotraconteur.robotics.trajectory.JointTrajectory traj, double speed_ratio)
{
if (traj.joint_names.Count > 0)
{
if (!Enumerable.SequenceEqual(traj.joint_names, joint_names))
{
throw new ArgumentException("Joint names in trajectory must match robot joint names");
}
}
if (traj.waypoints == null)
{
throw new ArgumentException("Waypoint list must not be null");
}
if (traj.waypoints.Count < 5)
{
throw new ArgumentException("Waypoint list must contain five or more waypoints");
}
if (traj.waypoints[0].time_from_start != 0)
{
throw new ArgumentException("Trajectory time_from_start must equal zero for first waypoint");
}
if (traj.interpolation_mode != com.robotraconteur.robotics.trajectory.InterpolationMode.default_ &&
traj.interpolation_mode != com.robotraconteur.robotics.trajectory.InterpolationMode.cubic_spline)
{
throw new ArgumentException($"Only default and cubic_spline interpolation supported for trajectory execution");
}
int n_waypoints = traj.waypoints.Count;
int n_joints = joint_names.Length;
var traj_t = new double[n_waypoints];
List <double[]> traj_j = Enumerable.Range(1, n_joints).Select(i => new double[n_waypoints]).ToList();
double last_t = 0;
for (int i = 0; i < n_waypoints; i++)
{
var w = traj.waypoints[i];
if (w.joint_position.Length != n_joints)
{
throw new ArgumentException($"Waypoint {i} invalid joint array length");
}
if (w.joint_velocity.Length != n_joints && w.joint_velocity.Length != 0)
{
throw new ArgumentException($"Waypoint {i} invalid joint velocity array length");
}
if (w.position_tolerance.Length != n_joints && w.position_tolerance.Length != 0)
{
throw new ArgumentException($"Waypoint {i} invalid tolerance array length");
}
if (w.velocity_tolerance.Length != n_joints && w.velocity_tolerance.Length != 0)
{
throw new ArgumentException($"Waypoint {i} invalid tolerance array length");
}
if (i > 0)
{
if (w.time_from_start / speed_ratio <= last_t)
{
throw new ArgumentException("time_from_start must be increasing");
}
}
for (int j = 0; j < n_joints; j++)
{
if (w.joint_position[j] > joint_max[j] || w.joint_position[j] < joint_min[j])
{
throw new ArgumentException($"Waypoint {i} exceeds joint limits");
}
if (w.joint_velocity.Length > 0)
{
if (Math.Abs(w.joint_velocity[j] * speed_ratio) > joint_vel_max[j])
{
throw new ArgumentException($"Waypoint {i} exceeds joint velocity limits");
}
}
}
if (i > 0)
{
var last_w = traj.waypoints[i - 1];
double dt = w.time_from_start / speed_ratio - last_w.time_from_start / speed_ratio;
for (int j = 0; j < n_joints; j++)
{
double dj = Math.Abs(w.joint_position[j] - last_w.joint_position[j]);
if (dj / dt > joint_vel_max[j])
{
throw new ArgumentException($"Waypoint {i} exceeds joint velocity limits");
}
}
}
traj_t[i] = w.time_from_start / speed_ratio;
for (int j = 0; j < n_joints; j++)
{
traj_j[j][i] = w.joint_position[j];
}
last_t = w.time_from_start / speed_ratio;
}
joint_splines = traj_j.Select(x => CubicSpline.InterpolateAkima(traj_t, x)).ToList();
max_t = last_t;
joint_start = traj.waypoints[0].joint_position;
joint_end = traj.waypoints.Last().joint_position;
waypoint_times = traj_t;
}
public Collection <DataPoint> GeneratePointsFromBitmap(string filename)
{
filename = Path.ChangeExtension(filename, "png");
if (File.Exists(filename))
{
double fmax = 19000.0;
double fmin = 20.0;
double dbrange = 16.0;
double dbmax = 1;
double sampleRate = 48000;
int sampleSize = 16384;
// Create a Bitmap object from an image file.
Bitmap iBitmap = new Bitmap(filename);
Bitmap oBitmap = new Bitmap(iBitmap.Width, iBitmap.Height);
int first = 0;
int last = 0;
int size = 0;
double min = iBitmap.Height;
double max = 0;
double mag = 0;
// Get the color of a pixel within myBitmap.
Collection <KeyValuePair <int, double> > points = new Collection <KeyValuePair <int, double> >();
for (var x = 0; x < iBitmap.Width; x++)
{
List <int> list = new List <int>();
for (var y = 0; y < iBitmap.Height; y++)
{
Color pixelColor = iBitmap.GetPixel(x, y);
if ((pixelColor.R > 200) && (pixelColor.G < 25) && (pixelColor.B < 25))
{
if (first == 0)
{
first = x;
}
else
{
last = x;
}
oBitmap.SetPixel(x, y, Color.FromArgb(255, 0, 0));
list.Add(y);
}
}
if (list.Count > 0)
{
var a = iBitmap.Height - list.Average();
points.Add(new KeyValuePair <int, double>(x, a));
if (a < min)
{
min = a;
}
if (a > max)
{
max = a;
}
}
}
size = last - first + 1;
mag = max - min + 1;
//calculate gain & offset
double scale = dbrange / mag;
double shift = dbmax - max * scale;
//check
double n_min = min * scale + shift;
double n_max = max * scale + shift;
//convert bitmap to frequency spectrum
Collection <double> ex = new Collection <double>();
Collection <double> ey = new Collection <double>();
for (var x = 0; x < points.Count; x++)
{
double df = Math.Log10(fmax / fmin); //over aproximately 3 decades
double f = 20.0 * Math.Pow(10.0, df * x / points.Count); //convert log horizontal image pixels to linear frequency scale in Hz
double y = points[x].Value * scale + shift; //scale and shift vertical image pixels to correct magnitude in dB
ex.Add(f);
ey.Add(Math.Pow(10.0, y / 20.0));
}
//interpolate frequency spectrum to match Audyssey responseData length
double[] frequency = Enumerable.Range(0, sampleSize).Select(p => p * sampleRate / sampleSize).ToArray();
CubicSpline IA = CubicSpline.InterpolateAkima(ex, ey);
Collection <DataPoint> frequency_points = new Collection <DataPoint>();
foreach (var f in frequency)
{
if (f < fmin)
{ // exptrapolate
frequency_points.Add(new DataPoint(f, double.NegativeInfinity));
}
else
{
if (f > fmax)
{ // exptrapolate
frequency_points.Add(new DataPoint(f, double.NegativeInfinity));
}
else
{ //interpolate
frequency_points.Add(new DataPoint(f, 20 * Math.Log10(IA.Interpolate(f))));
}
}
}
oBitmap.Save(Path.ChangeExtension(filename, "jpg"), System.Drawing.Imaging.ImageFormat.Jpeg);
return(frequency_points);
}
else
{
return(null);
}
}
public void FewSamples()
{
Assert.That(() => CubicSpline.InterpolateAkima(new double[0], new double[0]), Throws.ArgumentException);
Assert.That(() => CubicSpline.InterpolateAkima(new double[4], new double[4]), Throws.ArgumentException);
Assert.That(CubicSpline.InterpolateAkima(new[] { 1.0, 2.0, 3.0, 4.0, 5.0 }, new[] { 2.0, 2.0, 2.0, 2.0, 2.0 }).Interpolate(1.0), Is.EqualTo(2.0));
}
public virtual double Interpolate_CubicSpline(double[] x, double[] y, double xValue)
{
return(CubicSpline.InterpolateAkima(x, y).Interpolate(xValue));
}
public override void ExecuteExample()
{
MathDisplay.WriteLine("<b>Linear interpolation between points</b>");
// 1. Generate 20 samples of the function x*x-2*x on interval [0, 10]
MathDisplay.WriteLine(@"1. Generate 20 samples of the function x*x-2*x on interval [0, 10]");
double[] points = Generate.LinearSpaced(20, 0, 10);
var values = Generate.Map <double, double>(points, TargetFunction1);
MathDisplay.WriteLine();
// 2. Create a linear spline interpolation based on arbitrary points
var method = Interpolate.Linear(points, values);
MathDisplay.WriteLine(@"2. Create a linear spline interpolation based on arbitrary points");
MathDisplay.WriteLine();
// 3. Check if interpolation support integration
MathDisplay.WriteLine(@"3. Support integration = {0}", method.SupportsIntegration);
MathDisplay.WriteLine();
// 4. Check if interpolation support differentiation
MathDisplay.WriteLine(@"4. Support differentiation = {0}", method.SupportsDifferentiation);
MathDisplay.WriteLine();
// 5. Differentiate at point 5.2
MathDisplay.WriteLine(@"5. Differentiate at point 5.2 = {0}", method.Differentiate(5.2));
MathDisplay.WriteLine();
// 6. Integrate at point 5.2
MathDisplay.WriteLine(@"6. Integrate at point 5.2 = {0}", method.Integrate(5.2));
MathDisplay.WriteLine();
// 7. Interpolate ten random points and compare to function results
MathDisplay.WriteLine(@"7. Interpolate ten random points and compare to function results");
var rng = new MersenneTwister(1);
for (var i = 0; i < 10; i++)
{
// Generate random value from [0, 10]
var point = rng.NextDouble() * 10;
MathDisplay.WriteLine(
@"Interpolate at {0} = {1}. Function({0}) = {2}",
point.ToString("N05"),
method.Interpolate(point).ToString("N05"),
TargetFunction1(point).ToString("N05"));
}
MathDisplay.WriteLine();
// <seealso cref="http://en.wikipedia.org/wiki/Spline_interpolation">Spline interpolation</seealso>
MathDisplay.WriteLine("<b>Akima spline interpolation</b>");
// 1. Generate 10 samples of the function x*x-2*x on interval [0, 10]
MathDisplay.WriteLine(@"1. Generate 10 samples of the function x*x-2*x on interval [0, 10]");
points = Generate.LinearSpaced(10, 0, 10);
values = Generate.Map <double, double>(points, TargetFunction1);
MathDisplay.WriteLine();
// 2. Create akima spline interpolation
method = CubicSpline.InterpolateAkima(points, values);
MathDisplay.WriteLine(@"2. Create akima spline interpolation based on arbitrary points");
MathDisplay.WriteLine();
// 3. Check if interpolation supports integration
MathDisplay.WriteLine(@"3. Support integration = {0}", ((IInterpolation)method).SupportsIntegration);
MathDisplay.WriteLine();
// 4. Check if interpolation support differentiation
MathDisplay.WriteLine(@"4. Support differentiation = {0}", ((IInterpolation)method).SupportsDifferentiation);
MathDisplay.WriteLine();
// 5. Differentiate at point 5.2
MathDisplay.WriteLine(@"5. Differentiate at point 5.2 = {0}", method.Differentiate(5.2));
MathDisplay.WriteLine();
// 6. Integrate at point 5.2
MathDisplay.WriteLine(@"6. Integrate at point 5.2 = {0}", method.Integrate(5.2));
MathDisplay.WriteLine();
// 7. Interpolate ten random points and compare to function results
MathDisplay.WriteLine(@"7. Interpolate ten random points and compare to function results");
rng = new MersenneTwister(1);
for (var i = 0; i < 10; i++)
{
// Generate random value from [0, 10]
var point = rng.NextDouble() * 10;
MathDisplay.WriteLine(
@"Interpolate at {0} = {1}. Function({0}) = {2}",
point.ToString("N05"),
method.Interpolate(point).ToString("N05"),
TargetFunction1(point).ToString("N05"));
}
MathDisplay.WriteLine();
MathDisplay.WriteLine("<b>Barycentric rational interpolation without poles</b>");
// 1. Generate 10 samples of the function 1/(1+x*x) on interval [-5, 5]
MathDisplay.WriteLine(@"1. Generate 10 samples of the function 1/(1+x*x) on interval [-5, 5]");
points = Generate.LinearSpaced(10, -5, 5);
values = Generate.Map <double, double>(points, TargetFunctionWithoutPolesEx);
MathDisplay.WriteLine();
// 2. Create a floater hormann rational pole-free interpolation based on arbitrary points
// This method is used by default when create an interpolation using Interpolate.Common method
method = Interpolate.RationalWithoutPoles(points, values);
MathDisplay.WriteLine(@"2. Create a floater hormann rational pole-free interpolation based on arbitrary points");
MathDisplay.WriteLine();
// 3. Check if interpolation support integration
MathDisplay.WriteLine(@"3. Support integration = {0}", method.SupportsIntegration);
MathDisplay.WriteLine();
// 4. Check if interpolation support differentiation
MathDisplay.WriteLine(@"4. Support differentiation = {0}", method.SupportsDifferentiation);
MathDisplay.WriteLine();
// 5. Interpolate ten random points and compare to function results
MathDisplay.WriteLine(@"5. Interpolate ten random points and compare to function results");
rng = new MersenneTwister(1);
for (var i = 0; i < 10; i++)
{
// Generate random value from [0, 5]
var point = rng.NextDouble() * 5;
MathDisplay.WriteLine(
@"Interpolate at {0} = {1}. Function({0}) = {2}",
point.ToString("N05"),
method.Interpolate(point).ToString("N05"),
TargetFunctionWithoutPolesEx(point).ToString("N05"));
}
MathDisplay.WriteLine();
MathDisplay.WriteLine("<b>Rational interpolation with poles</b>");
// 1. Generate 20 samples of the function f(x) = x on interval [-5, 5]
MathDisplay.WriteLine(@"1. Generate 20 samples of the function f(x) = x on interval [-5, 5]");
points = Generate.LinearSpaced(20, -5, 5);
values = Generate.Map <double, double>(points, TargetFunctionWithPolesEx);
MathDisplay.WriteLine();
// 2. Create a burlish stoer rational interpolation based on arbitrary points
method = Interpolate.RationalWithPoles(points, values);
MathDisplay.WriteLine(@"2. Create a burlish stoer rational interpolation based on arbitrary points");
MathDisplay.WriteLine();
// 3. Check if interpolation support integration
MathDisplay.WriteLine(@"3. Support integration = {0}", method.SupportsIntegration);
MathDisplay.WriteLine();
// 4. Check if interpolation support differentiation
MathDisplay.WriteLine(@"4. Support differentiation = {0}", method.SupportsDifferentiation);
MathDisplay.WriteLine();
// 5. Interpolate ten random points and compare to function results
MathDisplay.WriteLine(@"5. Interpolate ten random points and compare to function results");
rng = new MersenneTwister(1);
for (var i = 0; i < 10; i++)
{
// Generate random value from [0, 5]
var point = rng.Next(0, 5);
MathDisplay.WriteLine(
@"Interpolate at {0} = {1}. Function({0}) = {2}",
point.ToString("N05"),
method.Interpolate(point).ToString("N05"),
TargetFunctionWithPolesEx(point).ToString("N05"));
}
MathDisplay.WriteLine();
}