/// <summary>
/// Demonstrates linear reression in two dimensions.
/// </summary>
void LinearRegression()
{
// Set up example description
nRichDescription.Text = "A linear regression model is computed from the sample data containing random normal noise. \n\nA point is then predicted from the model with a 95% confidence interval - meaning the predicted point is expected to lie within the confidence interval 95% of the time.";
// First read in the independent (or predictor) values. This is a matrix
// with one column and a row for each amounts measurement.
DoubleVector raw_data = new DoubleVector(25, 0, 1);
DoubleMatrix measurements = new DoubleMatrix(raw_data);
// Next, read in the responses
// Build a linear polynomial and add noise for interest
RandomNumberGenerator rand = new RandGenNormal(0, noiselevel_);
Polynomial poly = new Polynomial(new DoubleVector("0, 1"));
DoubleVector responses = poly.Evaluate(raw_data) + new DoubleVector(raw_data.Length, rand); ;
// Construct a linear regression. If we want our regression to calculate a
// y-intercept we must send in true for the "addIntercept" parameter (the
// third paramameter in the constructor).
LinearRegression regression = new LinearRegression(measurements, responses, true);
DoubleVector residues = regression.Residuals;
// Use the linear regression class to make a prediction according to the model
DoubleVector xvalues = new DoubleVector("30"); // Use the model to predict the observation at 30.
Interval pi = regression.PredictionInterval(xvalues, 0.95);
// Build some data points along the regression line for display
DoubleMatrix abcissae = new DoubleMatrix(new DoubleVector(raw_data));
DoubleVector predicted_ys = regression.PredictedObservations(abcissae);
// Build the chart
SetupChartLayout("Linear Regression");
NChart chart = nChartControl1.Charts[0];
SetupChartAxes(chart);
// Set up the line series
NLineSeries line = new NLineSeries();
chart.Series.Add(line);
// tell the series to regard the X values
line.UseXValues = true;
// no data labels
line.DataLabelStyle.Visible = false;
// Set the line color
line.BorderStyle = new NStrokeStyle(2.0f, Color.Tomato);
// name data set
line.Name = "Linear Regression";
// Add the the Linear Regression line data to the line series
line.XValues.AddRange(abcissae.DataBlock.Data);
line.Values.AddRange(predicted_ys.DataBlock.Data);
// Draw the raw data points
NPointSeries point = new NPointSeries();
chart.Series.Add(point);
point.UseXValues = true;
point.DataLabelStyle.Visible = false;
// Set the point appearance properties
point.FillStyle = new NColorFillStyle(Color.SkyBlue);
point.BorderStyle = new NStrokeStyle(1.0f,Color.DarkGray);
point.PointShape = PointShape.Cross;
point.Size = new NLength(6.0f);
// Points must fit in the chart area
point.InflateMargins = true;
// Name point set
point.Name = "Observations";
// set the point data
point.Values.AddRange(responses.DataBlock.Data);
point.XValues.AddRange(measurements.DataBlock.Data);
double m = (pi.Min + pi.Max) / 2.0;
// Display the predicted value with an error bar series
NErrorBarSeries predicted_points = new NErrorBarSeries();
chart.Series.Add(predicted_points);
predicted_points.Name = "Predicted Point";
predicted_points.UseXValues = true;
predicted_points.InflateMargins = true;
predicted_points.FillStyle = new NColorFillStyle(Color.Crimson);
predicted_points.BorderStyle = new NStrokeStyle(1.0f, Color.DarkGray);
predicted_points.DataLabelStyle.Visible = false;
predicted_points.MarkerStyle.Visible = true;
predicted_points.MarkerStyle.FillStyle = new NColorFillStyle(Color.Crimson);
predicted_points.MarkerStyle.BorderStyle = new NStrokeStyle(1.0f, Color.DarkGray);
predicted_points.MarkerStyle.PointShape = PointShape.Bar;
predicted_points.MarkerStyle.Width = new NLength(5);
predicted_points.MarkerStyle.Height = new NLength(5);
predicted_points.SizeY = new NLength(5);
// Fill the data for the predicted point
predicted_points.XValues.AddRange(xvalues.DataBlock.Data);
predicted_points.Values.Add(m);
predicted_points.UpperErrorsY.Add(pi.Max - m);
predicted_points.LowerErrorsY.Add(m - pi.Min);
// Create a label to display the predicted value
NLabel label = new NLabel();
label.BoundsMode = BoundsMode.None;
label.ContentAlignment = ContentAlignment.BottomLeft;
label.Location = new NPointL(
new NLength(87, NRelativeUnit.ParentPercentage),
new NLength(3, NRelativeUnit.ParentPercentage));
label.TextStyle.TextFormat = TextFormat.XML;
label.TextStyle.FontStyle = new NFontStyle("Arial", 9);
label.TextStyle.StringFormatStyle.HorzAlign = Nevron.HorzAlign.Right;
label.TextStyle.BackplaneStyle.Visible = true;
label.TextStyle.BackplaneStyle.FillStyle = new NGradientFillStyle(GradientStyle.Horizontal, GradientVariant.Variant1, Color.FromArgb(130, 255, 255, 255), Color.FromArgb(130, 233, 233, 255));
label.TextStyle.BackplaneStyle.Shape = BackplaneShape.SmoothEdgeRectangle;
label.TextStyle.BackplaneStyle.StandardFrameStyle.InnerBorderColor = Color.White;
label.Text = "<font color = 'crimson'>" + m.ToString("0.###") + "</font> - predicted value with 95% confidence interval";
chart.ChildPanels.Add(label);
nChartControl1.Refresh();
}
/// <summary>
/// Demonstrates polynomial least squares curve fitting
/// </summary>
void CurveFitting()
{
// Set up example description
nRichDescription.Text = "A 4th degree polynomial is fitted to the noisy sampled data. \n\nFitting a polynomial of any degree is accomplished in one line of code specifing the polynomial degree, and arrays of the x and y values. ";
// Build the data sets using some random normal noise
DoubleVector x = new DoubleVector("[0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5]");
DoubleVector y = new DoubleVector("[0 0.112462916018285 0.222702589210478 0.328626759459127 0.428392355046668 0.520499877813047 0.603856090847926 0.677801193837419 0.742100964707661 0.796908212422832 0.842700792949715 0.880205069574082 0.910313978229635 0.934007944940652 0.952285119762649 0.966105146475311 0.976348383344644 0.983790458590775 0.989090501635731 0.992790429235257 0.995322265018953 0.997020533343667 0.998137153702018 0.998856823402643 0.999311486103355 0.999593047982555]");
RandomNumberGenerator rand = new RandGenNormal(0.0, noiselevel_);
y = y + 0.025 * (new DoubleVector(y.Length, rand));
// Build the least squares polynomial fit and make readable display label
int polynomialdeg = 4;
PolynomialLeastSquares pls = new PolynomialLeastSquares(polynomialdeg, x, y);
// Build fitted polynomial
DoubleVector xs = new DoubleVector(100, 0, 0.025);
DoubleVector ys = pls.FittedPolynomial.Evaluate(xs);
// Build the chart
SetupChartLayout("Curve Fitting");
NChart chart = nChartControl1.Charts[0];
SetupChartAxes(chart);
// Draw the raw data points
NPointSeries point = new NPointSeries();
chart.Series.Add(point);
point.UseXValues = true;
point.DataLabelStyle.Visible = false;
// set some appearance properties
point.FillStyle = new NColorFillStyle(Color.SkyBlue);
point.BorderStyle = new NStrokeStyle(1.0f, Color.DarkGray);
point.PointShape = PointShape.Star;
point.Size = new NLength(6.0f);
// Points must fit in the chart area
point.InflateMargins = true;
// Name points data set
point.Name = "Observations";
// Add data points from the NMath DoubleVectors to the point series
point.Values.AddRange(y.DataBlock.Data);
point.XValues.AddRange(x.DataBlock.Data);
// Build polynomial line series and style it
NLineSeries polyline = new NLineSeries();
chart.Series.Add(polyline);
polyline.UseXValues = true;
polyline.DataLabelStyle.Visible = false;
polyline.BorderStyle = new NStrokeStyle(2.0f, Color.Tomato);
// Name polynomial fit
polyline.Name = polynomialdeg.ToString() + "th Degree Polynomial";
// Load the polynomial data into the line series
polyline.XValues.AddRange(xs.DataBlock.Data);
polyline.Values.AddRange(ys.DataBlock.Data);
// Create a label to display the polynomial
NLabel label = new NLabel();
label.BoundsMode = BoundsMode.None;
label.ContentAlignment = ContentAlignment.MiddleLeft;
label.Location = new NPointL(
new NLength(92, NRelativeUnit.ParentPercentage),
new NLength(70, NRelativeUnit.ParentPercentage));
label.TextStyle.TextFormat = TextFormat.XML;
label.TextStyle.FontStyle = new NFontStyle("Arial", 9);
label.TextStyle.StringFormatStyle.HorzAlign = Nevron.HorzAlign.Center;
label.TextStyle.BackplaneStyle.Visible = true;
label.TextStyle.BackplaneStyle.FillStyle = new NGradientFillStyle(GradientStyle.Horizontal, GradientVariant.Variant1, Color.FromArgb(180, 255, 255, 255), Color.FromArgb(180, 233, 233, 255));
label.TextStyle.BackplaneStyle.Shape = BackplaneShape.Rectangle;
label.TextStyle.BackplaneStyle.StandardFrameStyle.InnerBorderColor = Color.FromArgb(200, 200, 255);
label.Text = "Equation for fitted polynomial:<br /><font size='10' color = 'tomato'><b>";
label.Text += FormatPolymonial(pls.FittedPolynomial.Coeff.ToArray());
label.Text += "</b></font>";
chart.ChildPanels.Add(label);
nChartControl1.Refresh();
}
/// <summary>
/// Demonstrates the use of Savitzky-Golay smoothing filter.
/// </summary>
void DataSmoothing()
{
// Set up example description
nRichDescription.Text = "Smoothing discrete data with random normal noise using a 5th degree Savitzky-Golay filter. \n\nWhen using the Savitzky-Golay filter class, both the degree of the fitting polynomial and the filter width can be easily controlled. Good defaults are available.";
// Create an interesting noisy sampled signal to smooth.
DoubleVector xs = new DoubleVector(50, 0, Math.PI / 25);
RandomNumberGenerator rand = new RandGenNormal(0.0, noiselevel_);
DoubleVector raw_data = 10.0 * NMathFunctions.Tanh(NMathFunctions.Sin(xs)) + 0.2 * new DoubleVector(xs.Length, rand);
// Create the filter and smooth the data
MovingWindowFilter filter = new MovingWindowFilter(10, 10, MovingWindowFilter.SavitzkyGolayCoefficients(10, 10, 5));
DoubleVector smoothed_data = filter.Filter(raw_data, MovingWindowFilter.BoundaryOption.PadWithZeros);
SetupChartLayout("Data Smoothing");
NChart chart = nChartControl1.Charts[0];
SetupChartAxes(chart);
// Create a point series to display the raw data
NPointSeries point = new NPointSeries();
chart.Series.Add(point);
// Tell the series to regard the X values
point.UseXValues = true;
// Points must fit in the chart area
point.InflateMargins = true;
// No data labels
point.DataLabelStyle.Visible = false;
// Set up the data look and feel
point.FillStyle = new NColorFillStyle(Color.SkyBlue);
point.BorderStyle = new NStrokeStyle(1.0f, Color.DarkGray);
point.PointShape = PointShape.Ellipse;
point.Size = new NLength(4.0f);
// Name points
point.Name = "Observations";
// Load data into points collection
point.XValues.AddRange(xs.DataBlock.Data);
point.Values.AddRange(raw_data.DataBlock.Data);
// Create a line series to display the smoothed data
NLineSeries smoothline = new NLineSeries();
chart.Series.Add(smoothline);
smoothline.UseXValues = true;
smoothline.DataLabelStyle.Visible = false;
smoothline.BorderStyle = new NStrokeStyle(2.0f, Color.Tomato);
// Name smooth line
smoothline.Name = "Savitzky-Golay Smoothed Data";
// Load the smoothed data into the line series
smoothline.XValues.AddRange(xs.DataBlock.Data);
smoothline.Values.AddRange(smoothed_data.DataBlock.Data);
nChartControl1.Refresh();
}