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/// <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 StandardDistributionList<double> Xs) { this.Xs = Xs; Average = Xs.Average); Variance = GetVarianceXs); 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.SqrtVariance); } /// <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.Sqrt2 * 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 GetGaussianDistributionYdouble x) { double PowOfE = -Math.PowMath.Absx - Average), 2) / 2 * Variance)); double result = StandardDistribution.InverseSqrt2PI / StandardVariance) * Math.PowMath.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, GetGaussianDistributionYx)); XYs.Addxy); } 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 GetVarianceList<double> src) { double average = src.Average); double SumOfSquares = 0; src.ForEachx => { SumOfSquares += Math.Powx - 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 GetVarianceList<float> src) { float average = src.Average); double SumOfSquares = 0; src.ForEachx => { SumOfSquares += Math.Powx - 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 GetGaussianDistributionGraphint Width, int Height,int TotalScore, string familyName = "宋体") { //横轴 分数;纵轴 正态分布的值 Bitmap bitmap = new BitmapWidth, Height); Graphics gdi = Graphics.FromImagebitmap); gdi.ClearColor.White); gdi.SmoothingMode = SmoothingMode.HighQuality; gdi.TextRenderingHint = TextRenderingHint.ClearTypeGridFit; gdi.PixelOffsetMode = PixelOffsetMode.HighQuality; List<Tuple<double, double>> Scores = GetGaussianDistributionYs).OrderByx => 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 PointFmarginX, marginY); PointF leftBottom = new PointFmarginX, marginY + YHeight);//坐标轴的左下角 PointF rightBottom = new PointFmarginX + XWidth, marginY + YHeight);//坐标轴的右下角 gdi.DrawLinePens.Gray, leftBottom, rightBottom);//x轴 gdi.DrawLinePens.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 PointFleftTop.X - 5, leftTop.Y + 5); PointF YArrowRight = new PointFleftTop.X + 5, leftTop.Y + 5); PointF XArrowTop = new PointFrightBottom.X - 5, rightBottom.Y - 5); PointF XArrowBottom = new PointFrightBottom.X - 5, rightBottom.Y + 5); gdi.DrawLinePens.Gray, leftTop, YArrowLeft); gdi.DrawLinePens.Gray, leftTop, YArrowRight); gdi.DrawLinePens.Gray, rightBottom, XArrowTop); gdi.DrawLinePens.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 = ConvertToPointFScores, XWidth * 0.9F, YHeight * 0.9F, leftTop, out unitX, out unitY);//将分数和概率 转换成 坐标 gdi.DrawCurvePens.Black, pointFs.ToArray), 0.0F);//基数样条 //平均分 与 Y轴平行 PointF avg_top = new PointFleftTop.X + float)Average * unitX, leftTop.Y); PointF avg_bottom = new PointFleftTop.X + float)Average * unitX, leftBottom.Y); gdi.DrawLinePens.Black, avg_top, avg_bottom); gdi.DrawStringstring.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 PointFleftBottom.X+XWidth/2)-120, avg_bottom.Y + 25); gdi.DrawStringstring.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.Minx => x.Item1); double maxX = Scores.Maxx => 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.AddleftBottom.X + float)minX * unitX); for int i = 1; i < 11; i++) { segs.AddleftBottom.X + float)minX * unitX + perSegment * i * unitX); } for int i = 0; i < 11; i++) { gdi.DrawPiePens.Black, float)segs[i] - 1, leftBottom.Y - 1, 2, 2, 0, 360); gdi.DrawStringstring.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> ConvertToPointFList<Tuple<double, double>> Scores, float X, float Y, PointF leftTop, out float unitX, out float unitY) { double maxY = Scores.Maxx => x.Item2); double maxX = Scores.Maxx => 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 PointFleftTop.X + float)item.Item1 * unitX, leftTop.Y + Y - float)item.Item2 * unitY) + paddingY); result.Addpf); } return result; } }
调用:
StandardDistribution mathX = new StandardDistributionscores); Bitmap bitmap = mathX.GetGaussianDistributionGraph800, 480, totalScore); bitmap.Save"tt.jpg", System.Drawing.Imaging.ImageFormat.Jpeg);
测试数据生成的正态分布图: