using System;

using System.Collections.Generic;

using System.Globalization;

using System.IO;

using System.Reflection;

using System.Threading;

using System.Threading.Tasks;

using System.Xml.Serialization;

using OxyPlot;

using OxyPlot.Annotations;

using OxyPlot.Axes;

using OxyPlot.Series;

[Examples("Misc")]

public static class MiscExamples

{

[Example("Numeric ODE solvers (y'=y)")]

public static PlotModel NumericOdeSolvers1()

{

return NumericOdeSolvers("Numeric ODE solvers", "y'=y, y(0)=1", 0, 1, Math.Exp, (t, y) => y);

}

[Example("Numeric ODE solvers (y'=x)")]

public static PlotModel NumericOdeSolvers2()

{

return NumericOdeSolvers("Numeric ODE solvers", "y'=x, y(0)=0", 0, 0, t => 0.5 * t * t, (t, y) => t);

}

[Example("Numeric ODE solvers (y'=cos(x))")]

public static PlotModel NumericOdeSolvers3()

{

return NumericOdeSolvers("Numeric ODE solvers", "y'=cos(x), y(0)=0", 0, 0, Math.Sin, (t, y) => Math.Cos(t));

}

public static PlotModel NumericOdeSolvers(

string title,

string subtitle,

double t0,

double y0,

Func<double, double> exact,

Func<double, double, double> f)

{

var model = new PlotModel

{

Title = title,

Subtitle = subtitle,

LegendPosition = LegendPosition.BottomCenter,

LegendPlacement = LegendPlacement.Outside,

LegendOrientation = LegendOrientation.Horizontal

};

model.Series.Add(new FunctionSeries(exact, 0, 4, 100) { Title = "Exact solution", StrokeThickness = 5 });

var eulerSeries = new LineSeries

{

Title = "Euler, h=0.25",

MarkerType = MarkerType.Circle,

MarkerFill = OxyColors.Black,

};

eulerSeries.Points.AddRange(Euler(f, t0, y0, 4, 0.25));

model.Series.Add(eulerSeries);

//model.Series.Add(new LineSeries("Euler, h=1")

// {

// MarkerType = MarkerType.Circle,

// MarkerFill = OxyColors.Black,

// Points = Euler(f, t0, y0, 4, 1)

// });

var heunSeries = new LineSeries

{

Title = "Heun, h=0.25",

MarkerType = MarkerType.Circle,

MarkerFill = OxyColors.Black,

};

heunSeries.Points.AddRange(Heun(f, t0, y0, 4, 0.25));

model.Series.Add(heunSeries);

var midpointSeries = new LineSeries

{

Title = "Midpoint, h=0.25",

MarkerType = MarkerType.Circle,

MarkerFill = OxyColors.Black,

};

midpointSeries.Points.AddRange(Midpoint(f, t0, y0, 4, 0.25));

model.Series.Add(midpointSeries);

var rkSeries = new LineSeries

{

Title = "RK4, h=0.25",

MarkerType = MarkerType.Circle,

MarkerFill = OxyColors.Black,

};

rkSeries.Points.AddRange(RungeKutta4(f, t0, y0, 4, 0.25));

model.Series.Add(rkSeries);

//model.Series.Add(new LineSeries("RK4, h=1")

//{

// MarkerType = MarkerType.Circle,

// MarkerFill = OxyColors.Black,

// Points = RungeKutta4(f, t0, y0, 4, 1)

//});

model.Axes.Add(new LinearAxis { Position = AxisPosition.Left });

return model;

}

private static List<DataPoint> Euler(

Func<double, double, double> f, double t0, double y0, double t1, double h)

{

var points = new List<DataPoint>();

double y = y0;

for (double t = t0; t < t1 + h / 2; t += h)

{

points.Add(new DataPoint(t, y));

y += h * f(t, y);

}

return points;

}

private static IList<DataPoint> Heun(Func<double, double, double> f, double t0, double y0, double t1, double h)

{

var points = new List<DataPoint>();

double y = y0;

for (double t = t0; t < t1 + h / 2; t += h)

{

points.Add(new DataPoint(t, y));

double ytilde = y + h * f(t, y);

y = y + h / 2 * (f(t, y) + f(t + h, ytilde));

}

return points;

}

private static List<DataPoint> Midpoint(

Func<double, double, double> f, double t0, double y0, double t1, double h)

{

var points = new List<DataPoint>();

double y = y0;

for (double t = t0; t < t1 + h / 2; t += h)

{

points.Add(new DataPoint(t, y));

y += h * f(t + h / 2, y + h / 2 * f(t, y));

}

return points;

}

private static List<DataPoint> RungeKutta4(

Func<double, double, double> f, double t0, double y0, double t1, double h)

{

var points = new List<DataPoint>();

double y = y0;

for (double t = t0; t < t1 + h / 2; t += h)

{

points.Add(new DataPoint(t, y));

double k1 = h * f(t, y);

double k2 = h * f(t + h / 2, y + k1 / 2);

double k3 = h * f(t + h / 2, y + k2 / 2);

double k4 = h * f(t + h, y + k3);

y += (k1 + 2 * k2 + 2 * k3 + k4) / 6;

}

return points;

}

[Example("MatrixSeries (chemical process simulation problem)")]

public static PlotModel MatrixSeriesWest0479()

{

// http://www.cise.ufl.edu/research/sparse/matrices/HB/west0479

var model = new PlotModel();

double[,] matrix = null;

using (var reader = new StreamReader(typeof(MiscExamples).GetTypeInfo().Assembly.GetManifestResourceStream("ExampleLibrary.Resources.west0479.mtx")))

{

while (!reader.EndOfStream)

{

var line = reader.ReadLine();

if (line.StartsWith("%"))

{

continue;

}

var v = line.Split(' ');

if (matrix == null)

{

int m = int.Parse(v[0]);

int n = int.Parse(v[1]);

matrix = new double[m, n];

continue;

}

int i = int.Parse(v[0]) - 1;

int j = int.Parse(v[1]) - 1;

matrix[i, j] = double.Parse(v[2], CultureInfo.InvariantCulture);

}

}

// Reverse the vertical axis

model.Axes.Add(new LinearAxis { Position = AxisPosition.Left, StartPosition = 1, EndPosition = 0 });

model.Axes.Add(new LinearAxis { Position = AxisPosition.Bottom });

model.Series.Add(new MatrixSeries { Matrix = matrix, ShowDiagonal = true });

return model;

}

[Example("Train schedule")]

public static PlotModel TrainSchedule()

{

//// http://www.edwardtufte.com/tufte/books_vdqi

//// http://marlenacompton.com/?p=103

//// http://mbostock.github.com/protovis/ex/caltrain.html

//// http://en.wikipedia.org/wiki/%C3%89tienne-Jules_Marey

//// http://mbostock.github.com/protovis/ex/marey-train-schedule.jpg

//// http://c82.net/posts.php?id=66

var model = new PlotModel

{

Title = "Train schedule",

Subtitle = "Bergensbanen (Oslo-Bergen, Norway)",

IsLegendVisible = false,

PlotAreaBorderThickness = new OxyThickness(0),

PlotMargins = new OxyThickness(60, 4, 60, 40)

};

model.Axes.Add(

new LinearAxis

{

Position = AxisPosition.Left,

Minimum = -20,

Maximum = 540,

Title = "Distance from Oslo S",

IsAxisVisible = true,

StringFormat = "0"

});

model.Axes.Add(

new TimeSpanAxis

{

Position = AxisPosition.Bottom,

Minimum = 0,

Maximum = TimeSpanAxis.ToDouble(TimeSpan.FromHours(24)),

StringFormat = "hh",

Title = "Time",

MajorStep = TimeSpanAxis.ToDouble(TimeSpan.FromHours(1)),

MinorStep = TimeSpanAxis.ToDouble(TimeSpan.FromMinutes(10)),

TickStyle = TickStyle.None,

MajorGridlineStyle = LineStyle.Solid,

MajorGridlineColor = OxyColors.LightGray,

MinorGridlineStyle = LineStyle.Solid,

MinorGridlineColor = OxyColor.FromArgb(255, 240, 240, 240)

});

// Read the train schedule from a .csv resource

using (var reader = new StreamReader(GetResourceStream("Bergensbanen.csv")))

{

string header = reader.ReadLine();

var headerFields = header.Split(';');

int lines = headerFields.Length - 3;

var stations = new LineSeries()

{

StrokeThickness = 0,

MarkerType = MarkerType.Circle,

MarkerFill = OxyColor.FromAColor(200, OxyColors.Black),

MarkerSize = 4,

};

// Add the line series for each train line

var series = new LineSeries[lines];

for (int i = 0; i < series.Length; i++)

{

series[i] = new LineSeries

{

Title = headerFields[3 + i],

Color =

OxyColor.FromAColor(

180, OxyColors.Black),

StrokeThickness = 2,

TrackerFormatString =

"Train {0}\nTime: {2}\nDistance from Oslo S: {4:0.0} km",

};

model.Series.Add(series[i]);

}

// Parse the train schedule

while (!reader.EndOfStream)

{

var line = reader.ReadLine();

// skip comments

if (line == null || line.StartsWith("//"))

{

continue;

}

var fields = line.Split(';');

double x = double.Parse(fields[1], CultureInfo.InvariantCulture);

if (!string.IsNullOrEmpty(fields[0]))

{

// Add a horizontal annotation line for the station

model.Annotations.Add(

new LineAnnotation

{

Type = LineAnnotationType.Horizontal,

Y = x,

Layer = AnnotationLayer.BelowSeries,

LineStyle = LineStyle.Solid,

Color = OxyColors.LightGray,

Text = fields[0] + " ",

TextVerticalAlignment = VerticalAlignment.Middle,

TextLinePosition = 1,

TextMargin = 0,

TextPadding = 4,

ClipText = false,

TextHorizontalAlignment = HorizontalAlignment.Left

});

}

for (int i = 0; i < series.Length; i++)

{

if (string.IsNullOrEmpty(fields[i + 3]))

{

continue;

}

// Convert time from hhmm to a time span

int hhmm = int.Parse(fields[i + 3]);

var span = new TimeSpan(0, hhmm / 100, (hhmm % 100), 0);

double t = TimeSpanAxis.ToDouble(span);

// Add the point to the line

series[i].Points.Add(new DataPoint(t, x));

// Add the point for the station

stations.Points.Add(new DataPoint(t, x));

}

}

// add points and NaN (to make a line break) when passing midnight

double tmidnight = TimeSpanAxis.ToDouble(TimeSpan.FromHours(24));

foreach (LineSeries s in model.Series)

{

for (int i = 0; i + 1 < s.Points.Count; i++)

{

if (Math.Abs(s.Points[i].X - s.Points[i + 1].X) > tmidnight / 2)

{

double x0 = s.Points[i].X;

if (x0 > tmidnight / 2)

{

x0 -= tmidnight;

}

double x1 = s.Points[i + 1].X;

if (x1 > tmidnight / 2)

{

x1 -= tmidnight;

}

double y = s.Points[i].Y + (s.Points[i + 1].Y - s.Points[i].Y) / (x1 - x0) * (0 - x0);

s.Points.Insert(i + 1, new DataPoint(x0 < x1 ? 0 : tmidnight, y));

s.Points.Insert(i + 1, new DataPoint(double.NaN, y));

s.Points.Insert(i + 1, new DataPoint(x0 < x1 ? tmidnight : 0, y));

i += 3;

}

}

}

model.Series.Add(stations);

}

return model;

}

/* [Example("World population")]

[Example("La Linea (AreaSeries)")]

public static PlotModel LaLineaAreaSeries()

{

// http://en.wikipedia.org/wiki/La_Linea_(TV_series)

var model = new PlotModel

{

Title = "La Linea",

PlotType = PlotType.Cartesian,

Background = OxyColor.FromRgb(84, 98, 207)

};

model.Axes.Add(new LinearAxis { Position = AxisPosition.Left, Minimum = -500, Maximum = 1000 });

var series1 = new AreaSeries { Fill = OxyColors.White, StrokeThickness = 0 };

series1.Points.Append(GetLineaPoints());

model.Series.Add(series1);

return model;

}

[Example("La Linea (LineSeries)")]

public static PlotModel LaLinea()

{

// http://en.wikipedia.org/wiki/La_Linea_(TV_series)

var model = new PlotModel

{

Title = "La Linea",

PlotType = PlotType.Cartesian,

Background = OxyColor.FromRgb(84, 98, 207)

};

model.Axes.Add(new LinearAxis { Position = AxisPosition.Left, Minimum = -500, Maximum = 1000 });

var series1 = new LineSeries { Color = OxyColors.White, StrokeThickness = 1.5 };

series1.Points.Append(GetLineaPoints());

model.Series.Add(series1);

return model;

}

/// <summary>

/// Appends the specified target.

/// </summary>

/// <typeparam name="T"></typeparam>

/// <param name="target">The target.</param>

/// <param name="source">The source.</param>

public static void Append<T>(this IList<T> target, IEnumerable<T> source)

{

foreach (var item in source)

{

target.Add(item);

}

}

private static IEnumerable<DataPoint> GetLineaPoints()

{

var points = new List<DataPoint>();

// The original image was vectorized by http://www.autotracer.org/

// Then inkscape was used to convert from svg to xaml http://inkscape.org/

// The xaml geometry was imported by Geometry.Parse and converted to a polyline

// by Geometry.GetFlattenedPathGeometry();

// The resulting points were output to the following code:

points.Add(new DataPoint(589.3649979, 16.10595703));

points.Add(new DataPoint(437.9979935, 16.10595703));

points.Add(new DataPoint(400.4249954, 16.10595703));

points.Add(new DataPoint(399.1255264, 16.05047607));

points.Add(new DataPoint(397.463356, 15.92333984));

points.Add(new DataPoint(393.5852432, 15.69073486));

points.Add(new DataPoint(389.8589859, 15.88067627));

points.Add(new DataPoint(388.3866653, 16.28186035));

points.Add(new DataPoint(387.3529739, 16.96594238));

points.Add(new DataPoint(386.8373489, 18.53930664));

points.Add(new DataPoint(387.2163773, 20.51794434));

points.Add(new DataPoint(387.9814529, 22.51843262));

points.Add(new DataPoint(388.6240005, 24.15698242));

points.Add(new DataPoint(395.958992, 45.09094238));

points.Add(new DataPoint(399.2686234, 54.89562988));

points.Add(new DataPoint(402.1330338, 64.90338135));

points.Add(new DataPoint(404.5822525, 75.06884766));

points.Add(new DataPoint(406.6462479, 85.34680176));

points.Add(new DataPoint(409.7385635, 106.0593262));

points.Add(new DataPoint(411.6500015, 126.6789551));

points.Add(new DataPoint(412.0961685, 137.0930786));

points.Add(new DataPoint(412.0253677, 147.4713135));

points.Add(new DataPoint(411.4655228, 157.8103638));

points.Add(new DataPoint(410.4446182, 168.1069336));

points.Add(new DataPoint(408.9906387, 178.3577881));

points.Add(new DataPoint(407.1315689, 188.5595703));

points.Add(new DataPoint(404.8953629, 198.7091064));

points.Add(new DataPoint(402.3099747, 208.8029785));

points.Add(new DataPoint(392.9860001, 237.2509766));

points.Add(new DataPoint(392.1175613, 240.0527954));

points.Add(new DataPoint(391.2060013, 243.0959473));

points.Add(new DataPoint(390.5509415, 246.1691284));

points.Add(new DataPoint(390.4520035, 249.0609741));

points.Add(new DataPoint(391.406044, 252.6694336));

points.Add(new DataPoint(393.1980057, 256.0982056));

points.Add(new DataPoint(395.3566971, 259.3631287));

points.Add(new DataPoint(397.4109879, 262.47995));

points.Add(new DataPoint(411.7649918, 287.7079468));

points.Add(new DataPoint(426.5997696, 312.9102173));

points.Add(new DataPoint(441.8913651, 337.8200684));

points.Add(new DataPoint(457.3402786, 362.6333923));

points.Add(new DataPoint(472.6469803, 387.5459595));

points.Add(new DataPoint(478.0007401, 395.7557983));

points.Add(new DataPoint(483.6958694, 403.8400879));

points.Add(new DataPoint(489.2894974, 411.9628296));

points.Add(new DataPoint(494.3389969, 420.2879639));

points.Add(new DataPoint(494.9800491, 421.8480225));

points.Add(new DataPoint(495.4455032, 423.6903687));

points.Add(new DataPoint(496.1577225, 427.7724609));

points.Add(new DataPoint(497.0915604, 431.6355591));

points.Add(new DataPoint(497.8341141, 433.2041321));

points.Add(new DataPoint(498.8629837, 434.3809509));

points.Add(new DataPoint(500.0935135, 434.9877625));

points.Add(new DataPoint(501.7391434, 435.3059082));

points.Add(new DataPoint(505.7623367, 435.3148193));

points.Add(new DataPoint(509.9061356, 434.8848267));

points.Add(new DataPoint(511.7024612, 434.6542969));

points.Add(new DataPoint(513.1439896, 434.4929504));

points.Add(new DataPoint(520.0768509, 434.1251831));

points.Add(new DataPoint(527.3961258, 434.1952209));

points.Add(new DataPoint(534.6892776, 434.728363));

points.Add(new DataPoint(541.544014, 435.7499695));

points.Add(new DataPoint(544.2357864, 436.3025513));

points.Add(new DataPoint(547.021492, 437.0792236));

points.Add(new DataPoint(549.6099319, 438.2590027));

points.Add(new DataPoint(551.7099686, 440.0209656));

points.Add(new DataPoint(552.7028275, 441.4446106));

points.Add(new DataPoint(553.2691116, 442.791626));

points.Add(new DataPoint(553.4498978, 444.0619202));

points.Add(new DataPoint(553.2864456, 445.2554626));

points.Add(new DataPoint(552.0910721, 447.4119873));

points.Add(new DataPoint(550.0122147, 449.2607117));

points.Add(new DataPoint(547.3790359, 450.8010864));

points.Add(new DataPoint(544.5206985, 452.0325928));

points.Add(new DataPoint(541.766304, 452.9547119));

points.Add(new DataPoint(539.445015, 453.5669556));

points.Add(new DataPoint(539.445015, 454.6409607));

points.Add(new DataPoint(542.6554031, 455.4246521));

points.Add(new DataPoint(546.0063553, 455.8735962));

points.Add(new DataPoint(549.2799149, 456.4869385));

points.Add(new DataPoint(552.2580032, 457.7639465));

points.Add(new DataPoint(554.3335648, 459.5966797));

points.Add(new DataPoint(555.6600418, 461.8208313));

points.Add(new DataPoint(556.278389, 464.282959));

points.Add(new DataPoint(556.2294998, 466.8295898));

points.Add(new DataPoint(555.55439, 469.307251));

points.Add(new DataPoint(554.2939529, 471.5625));

points.Add(new DataPoint(552.4892044, 473.4418945));

points.Add(new DataPoint(550.1809769, 474.7919617));

points.Add(new DataPoint(547.1414261, 475.8059387));

points.Add(new DataPoint(543.8482132, 476.5288391));

points.Add(new DataPoint(537.2979813, 477.0559692));

points.Add(new DataPoint(535.5239944, 476.8666077));

points.Add(new DataPoint(533.5114822, 476.5535889));

points.Add(new DataPoint(531.5334549, 476.4162598));

points.Add(new DataPoint(529.8629837, 476.7539673));

points.Add(new DataPoint(529.0471268, 477.3421631));

points.Add(new DataPoint(528.5394363, 478.1289673));

points.Add(new DataPoint(528.1448441, 480.0927124));

points.Add(new DataPoint(528.071846, 482.2338257));

points.Add(new DataPoint(527.7129593, 484.1409607));

points.Add(new DataPoint(526.901741, 485.4877014));

points.Add(new DataPoint(525.8139114, 486.4950867));

points.Add(new DataPoint(523.0528641, 487.6643372));

points.Add(new DataPoint(519.9188919, 487.9933777));

points.Add(new DataPoint(516.9010086, 487.8269653));

points.Add(new DataPoint(511.7325516, 486.9451599));

points.Add(new DataPoint(506.4563065, 485.4539185));

points.Add(new DataPoint(501.155159, 483.4500427));

points.Add(new DataPoint(495.912117, 481.0302124));

points.Add(new DataPoint(485.9321365, 475.3295898));

points.Add(new DataPoint(481.3610916, 472.2423096));

points.Add(new DataPoint(477.1800003, 469.125946));

points.Add(new DataPoint(465.3709793, 459.3179626));

points.Add(new DataPoint(464.3509598, 458.3116455));

points.Add(new DataPoint(463.1867142, 457.1624451));

points.Add(new DataPoint(461.9141312, 456.2180176));

points.Add(new DataPoint(460.5689774, 455.8259583));

points.Add(new DataPoint(459.6923904, 456.0762939));

points.Add(new DataPoint(458.8656693, 456.7503662));

points.Add(new DataPoint(457.3631058, 458.907959));

points.Add(new DataPoint(456.063179, 461.3753052));

points.Add(new DataPoint(455.4898758, 462.436554));

points.Add(new DataPoint(454.9679642, 463.2289734));

points.Add(new DataPoint(453.0795364, 465.3183289));

points.Add(new DataPoint(450.8528519, 467.2734985));

points.Add(new DataPoint(448.3575516, 468.9848328));

points.Add(new DataPoint(445.6630936, 470.3425903));

points.Add(new DataPoint(442.83918, 471.2370605));

points.Add(new DataPoint(439.9552689, 471.5585938));

points.Add(new DataPoint(437.0810318, 471.1974487));

points.Add(new DataPoint(434.2859879, 470.0439453));

points.Add(new DataPoint(432.4744034, 468.6621399));

points.Add(new DataPoint(431.3244705, 467.0726013));

points.Add(new DataPoint(430.7551956, 465.3302612));

points.Add(new DataPoint(430.6856155, 463.4900818));

points.Add(new DataPoint(431.0347672, 461.6070251));

points.Add(new DataPoint(431.7216873, 459.7360229));

points.Add(new DataPoint(433.7849808, 456.2499695));

points.Add(new DataPoint(438.1093216, 450.118988));

points.Add(new DataPoint(441.4749832, 444.3893433));

points.Add(new DataPoint(444.0351639, 438.28302));

points.Add(new DataPoint(445.0610428, 434.845459));

points.Add(new DataPoint(445.9430008, 431.0219727));

points.Add(new DataPoint(446.6270218, 428.7687378));

points.Add(new DataPoint(447.4476395, 426.4767151));

points.Add(new DataPoint(447.9032059, 424.1760559));

points.Add(new DataPoint(447.492012, 421.8969727));

points.Add(new DataPoint(445.6156082, 418.2295837));

points.Add(new DataPoint(443.3608475, 414.6139832));

points.Add(new DataPoint(438.1008682, 407.5364685));

points.Add(new DataPoint(432.48069, 400.6614685));

points.Add(new DataPoint(427.2689896, 393.9859619));

points.Add(new DataPoint(389.1699905, 339.2359619));

points.Add(new DataPoint(374.5550003, 318.3009644));

points.Add(new DataPoint(372.5515823, 314.8404541));

points.Add(new DataPoint(370.2787552, 310.9485779));

points.Add(new DataPoint(367.7467728, 307.2946777));

points.Add(new DataPoint(366.3868484, 305.7660828));

points.Add(new DataPoint(364.9659805, 304.5479736));

points.Add(new DataPoint(363.9477615, 304.0406799));

points.Add(new DataPoint(363.082222, 304.0159912));

points.Add(new DataPoint(361.6236038, 304.9024658));

points.Add(new DataPoint(360.2191849, 306.1834412));

points.Add(new DataPoint(359.4213638, 306.651886));

points.Add(new DataPoint(358.4979935, 306.8349609));

points.Add(new DataPoint(356.6694107, 306.4464722));

points.Add(new DataPoint(354.9371109, 305.5308228));

points.Add(new DataPoint(353.2544937, 304.4515076));

points.Add(new DataPoint(351.5749893, 303.5719604));

points.Add(new DataPoint(343.4895706, 301.1234131));

points.Add(new DataPoint(335.0169449, 299.8048401));

points.Add(new DataPoint(326.3076553, 299.5128174));