using Imsl.Chart2D;
using System;
using System.Drawing;
using Imsl.Stat;

public class SampleHistogram : FrameChart {

    public SampleHistogram() {
        int nSamples = 1000;
        int nBins = 20;

        // Setup the bins
        double[] bins = new double[nBins];
        double dx = 6.0/nBins;
        double[] x = new double[nBins];
        for (int k = 0; k < x.Length; k++) {
            x[k] = -3.0 + (k+0.5)*dx;
        }

        Imsl.Stat.Random r = new Imsl.Stat.Random(123457);
        for (int k = 0; k < nSamples; k++) {
            double t = r.NextNormal();
            int j = (int)Math.Round((t+3.0-0.5*dx)/dx);
            if (j >= 0 && j < nBins)  bins[j]++;
        }

        // Scale the bins
        for (int k = 0; k < nBins; k++) {
            bins[k] /= nSamples*dx;
        }

        // create the chart
        Chart chart = this.Chart;
        AxisXY axis = new AxisXY(chart);

        chart.ChartTitle.SetTitle("Normal Distribution");
        chart.Legend.IsVisible = true;
        chart.Legend.SetViewport(0.7, 1.0, 0.2, 0.3);
        chart.Legend.FillOutlineType = Chart.FILL_TYPE_NONE;

        Bar bar = new Bar(axis, x, bins);
        bar.BarType = Bar.BAR_TYPE_VERTICAL;
        bar.FillColor = Color.LightGreen;
        bar.BarWidth = 0.5*dx;
        bar.SetTitle("Random Samples");

        // plot the expected curve
        Data data = new Data(axis, new NormalDist(), -3, 3.0);
        data.LineColor = Color.Blue;
        data.SetTitle("Exact Curve");
        data.LineWidth = 2.0;
    }

    public static void Main(string[] argv) {
        System.Windows.Forms.Application.Run(new SampleHistogram());
    }
}

class NormalDist : ChartFunction {
    public double F(double x) {
        return Math.Exp(-0.5*x*x)/Math.Sqrt(2.0*Math.PI);
    }
}