/// <summary>
/// 提供正态分布的数据和图片
/// </summary>
public class StandardDistribution
{ /// <summary>
/// 样本数据
/// </summary>
public List<double> Xs { get; private set; } public StandardDistribution(List<double> Xs)
{
this.Xs = Xs; Average = Xs.Average();
Variance = GetVariance(Xs); if (Variance == 0) throw new Exception("方差为0");//此时不需要统计 因为每个样本数据都相同，可以在界面做相应提示 StandardVariance = Math.Sqrt(Variance);
} /// <summary>
/// 方差/标准方差的平方
/// </summary>
public double Variance { get; private set; } /// <summary>
/// 标准方差
/// </summary>
public double StandardVariance { get; private set; } /// <summary>
/// 算数平均值/数学期望
/// </summary>
public double Average { get; private set; } /// <summary>
/// 1/ (2π的平方根)的值
/// </summary>
public static double InverseSqrt2PI = 1 / Math.Sqrt(2 * Math.PI); /// <summary>
/// 获取指定X值的Y值 计算正太分布的公式
/// </summary>
/// <param name="x"></param>
/// <returns></returns>
public double GetGaussianDistributionY(double x)
{
double PowOfE = -(Math.Pow(Math.Abs(x - Average), 2) / (2 * Variance)); double result = (StandardDistribution.InverseSqrt2PI / StandardVariance) * Math.Pow(Math.E, PowOfE); return result;
} /// <summary>
/// 获取正太分布的坐标<x,y>
/// </summary>
/// <returns></returns>
public List<Tuple<double, double>> GetGaussianDistributionYs()
{
List<Tuple<double, double>> XYs = new List<Tuple<double, double>>(); Tuple<double, double> xy = null; foreach (double x in Xs)
{
xy = new Tuple<double, double>(x, GetGaussianDistributionY(x));
XYs.Add(xy);
} return XYs;
} /// <summary>
/// 获取整型列表的方差
/// </summary>
/// <param name="src">要计算方差的数据列表</param>
/// <returns></returns>
public static double GetVariance(List<double> src)
{
double average = src.Average();
double SumOfSquares = 0;
src.ForEach(x => { SumOfSquares += Math.Pow(x - average, 2); });
return SumOfSquares / src.Count;//方差
} /// <summary>
/// 获取整型列表的方差
/// </summary>
/// <param name="src">要计算方差的数据列表</param>
/// <returns></returns>
public static float GetVariance(List<float> src)
{
float average = src.Average();
double SumOfSquares = 0;
src.ForEach(x => { SumOfSquares += Math.Pow(x - average, 2); });
return (float)SumOfSquares / src.Count;//方差
} /// <summary>
/// 画学生成绩的正态分布
/// </summary>
/// <param name="Width"></param>
/// <param name="Height"></param>
/// <param name="Scores">分数，Y值</param>
/// <param name="familyName"></param>
/// <returns></returns>
public Bitmap GetGaussianDistributionGraph(int Width, int Height,int TotalScore, string familyName = "宋体")
{
//横轴 分数；纵轴 正态分布的值 Bitmap bitmap = new Bitmap(Width, Height); Graphics gdi = Graphics.FromImage(bitmap); gdi.Clear(Color.White);
gdi.SmoothingMode = SmoothingMode.HighQuality;
gdi.TextRenderingHint = TextRenderingHint.ClearTypeGridFit;
gdi.PixelOffsetMode = PixelOffsetMode.HighQuality; List<Tuple<double, double>> Scores = GetGaussianDistributionYs().OrderBy(x => x.Item1).ToList();//排序 方便后面点与点之间的连线 保证 分数低的 在左边 float YHeight = 0.8F * Height;// 相对左下角 YHeight*0.9F 将表示 maxY
float XWidth = 0.9F * Width;//相对左下角 XWidth*0.9F 将表示 maxX float marginX = (Width - XWidth) / 2F;//x轴相对左右图片边缘的像素
float marginY = (Height - YHeight) / 2F;//y轴相对上下图片边缘的像素 PointF leftTop = new PointF(marginX, marginY); PointF leftBottom = new PointF(marginX, marginY + YHeight);//坐标轴的左下角 PointF rightBottom = new PointF(marginX + XWidth, marginY + YHeight);//坐标轴的右下角 gdi.DrawLine(Pens.Gray, leftBottom, rightBottom);//x轴
gdi.DrawLine(Pens.Gray, leftBottom, leftTop);//Y轴 //两个箭头 四条线 6个坐标 另需4个坐标 PointF YArrowLeft = new PointF(leftTop.X - 5, leftTop.Y + 5);
PointF YArrowRight = new PointF(leftTop.X + 5, leftTop.Y + 5);
PointF XArrowTop = new PointF(rightBottom.X - 5, rightBottom.Y - 5);
PointF XArrowBottom = new PointF(rightBottom.X - 5, rightBottom.Y + 5); gdi.DrawLine(Pens.Gray, leftTop, YArrowLeft);
gdi.DrawLine(Pens.Gray, leftTop, YArrowRight);
gdi.DrawLine(Pens.Gray, rightBottom, XArrowTop);
gdi.DrawLine(Pens.Gray, rightBottom, XArrowBottom); float unitX = 0.0F;//X轴转换比率
float unitY = 0.0F;//Y轴转换比率 List<PointF> pointFs = ConvertToPointF(Scores, XWidth * 0.9F, YHeight * 0.9F, leftTop, out unitX, out unitY);//将分数和概率 转换成 坐标 gdi.DrawCurve(Pens.Black, pointFs.ToArray(), 0.0F);//基数样条 //平均分 与 Y轴平行 PointF avg_top = new PointF(leftTop.X + (float)Average * unitX, leftTop.Y);
PointF avg_bottom = new PointF(leftTop.X + (float)Average * unitX, leftBottom.Y);
gdi.DrawLine(Pens.Black, avg_top, avg_bottom);
gdi.DrawString(string.Format("{0}", ((float)Average ).ToString("F2")), new Font("宋体", 11), Brushes.Black, avg_bottom.X, avg_bottom.Y-25); //将期望和方差写在横轴下方中间 PointF variance_pf = new PointF(leftBottom.X+(XWidth/2)-120, avg_bottom.Y + 25);
gdi.DrawString(string.Format("期望：{0}；方差：{1}", ((float)Average).ToString("F2"), Variance.ToString("F2")), new Font("宋体", 11), Brushes.Black, variance_pf.X, variance_pf.Y); //将最小分数 和 最大分数 分成9段 标记在坐标轴横轴上 double minX = Scores.Min(x => x.Item1);
double maxX = Scores.Max(x => x.Item1); double perSegment = TotalScore/10;// (maxX - minX) / 9F;//每一段表示的分数 List<double> segs = new List<double>();//每一个分段分界线横轴的值 segs.Add(leftBottom.X + (float)minX * unitX); for (int i = 1; i < 11; i++)
{
segs.Add(leftBottom.X + (float)minX * unitX + perSegment * i * unitX);
}
for (int i = 0; i < 11; i++)
{
gdi.DrawPie(Pens.Black, (float)segs[i] - 1, leftBottom.Y - 1, 2, 2, 0, 360); gdi.DrawString(string.Format("{0}", ((minX + perSegment * (i))).ToString("F0")), new Font("宋体", 11), Brushes.Black, (float)segs[i] - 15, leftBottom.Y + 5);
} return bitmap;
} /// <summary>
/// 将数据转换为坐标
/// </summary>
/// <param name="Scores"></param>
/// <param name="X">最长利用横轴</param>
/// <param name="Y">最长利用纵轴 </param>
/// <param name="leftTop">左上角原点</param>
/// <returns></returns>
private static List<PointF> ConvertToPointF(List<Tuple<double, double>> Scores, float X, float Y, PointF leftTop, out float unitX, out float unitY)
{
double maxY = Scores.Max(x => x.Item2);
double maxX = Scores.Max(x => x.Item1); List<PointF> result = new List<PointF>(); float paddingY = Y * 0.01F;
float paddingX = X * 0.01F; unitY = (float)((Y - paddingY) / maxY);//单位纵轴表示出来需要的高度 计算出来的纵坐标需要 leftTop.Y+(Y-item2*unitY)+paddingY
unitX = (float)((X - paddingX) / maxX);//单位横轴表示出来需要的宽度 计算出来的横坐标需要 leftTop.X+item1*unitX PointF pf = new PointF();
foreach (Tuple<double, double> item in Scores)
{
pf = new PointF(leftTop.X + (float)item.Item1 * unitX, leftTop.Y + (Y - (float)item.Item2 * unitY) + paddingY);
result.Add(pf);
} return result;
} }
调用：
StandardDistribution mathX = new StandardDistribution(scores);
Bitmap bitmap = mathX.GetGaussianDistributionGraph(800, 480, totalScore);
bitmap.Save("tt.jpg", System.Drawing.Imaging.ImageFormat.Jpeg);
测试数据生成的正态分布图：