/// <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：
