前言

上一篇文章跟大家分享了用NumSharp实现简单的线性回归，但是没有进行可视化，可能对拟合的过程没有直观的感受，因此今天跟大家介绍一下使用C#基于Scottplot进行可视化，当然Python的代码，我也会同步进行可视化。

Python代码进行可视化

Python代码用matplotlib做了可视化，我就不具体介绍了。

修改之后的python代码如下：

#The optimal values of m and b can be actually calculated with way less effort than doing a linear regression. 
#this is just to demonstrate gradient descent

import numpy as np
import matplotlib.pyplot as plt
from matplotlib.animation import FuncAnimation


# y = mx + b
# m is slope, b is y-intercept
def compute_error_for_line_given_points(b, m, points):
    totalError = 0
    for i in range(0, len(points)):
        x = points[i, 0]
        y = points[i, 1]
        totalError += (y - (m * x + b)) ** 2
    return totalError / float(len(points))

def step_gradient(b_current, m_current, points, learningRate):
    b_gradient = 0
    m_gradient = 0
    N = float(len(points))
    for i in range(0, len(points)):
        x = points[i, 0]
        y = points[i, 1]
        b_gradient += -(2/N) * (y - ((m_current * x) + b_current))
        m_gradient += -(2/N) * x * (y - ((m_current * x) + b_current))
    new_b = b_current - (learningRate * b_gradient)
    new_m = m_current - (learningRate * m_gradient)
    return [new_b, new_m]

def gradient_descent_runner(points, starting_b, starting_m, learning_rate, num_iterations):
    b = starting_b
    m = starting_m
    args_data = []
    for i in range(num_iterations):
        b, m = step_gradient(b, m, np.array(points), learning_rate)
        args_data.append((b,m))
    return args_data

if __name__ == '__main__':
     points = np.genfromtxt("data.csv", delimiter=",")
     learning_rate = 0.0001
     initial_b = 0 # initial y-intercept guess
     initial_m = 0 # initial slope guess
     num_iterations = 10
     print ("Starting gradient descent at b = {0}, m = {1}, error = {2}".format(initial_b, initial_m, compute_error_for_line_given_points(initial_b, initial_m, points)))
     print ("Running...")
     args_data = gradient_descent_runner(points, initial_b, initial_m, learning_rate, num_iterations)
     
     b = args_data[-1][0]
     m = args_data[-1][1]

     print ("After {0} iterations b = {1}, m = {2}, error = {3}".format(num_iterations, b, m, compute_error_for_line_given_points(b, m, points)))
    
     data = np.array(points).reshape(100,2)
     x1 = data[:,0]
     y1 = data[:,1]
     
     x2 = np.linspace(20, 80, 100)
     y2 = initial_m * x2 + initial_b

     data2 = np.array(args_data)
     b_every = data2[:,0]
     m_every = data2[:,1]

     # 创建图形和轴
     fig, ax = plt.subplots()
     line1, = ax.plot(x1, y1, 'ro')
     line2, = ax.plot(x2,y2)

     # 添加标签和标题
     plt.xlabel('x')
     plt.ylabel('y')
     plt.title('Graph of y = mx + b')

     # 添加网格
     plt.grid(True)

    # 定义更新函数
     def update(frame):
        line2.set_ydata(m_every[frame] * x2 + b_every[frame])
        ax.set_title(f'{frame} Graph of y = {m_every[frame]:.2f}x + {b_every[frame]:.2f}')
    
# 创建动画
animation = FuncAnimation(fig, update, frames=len(data2), interval=500)

# 显示动画
plt.show()

实现的效果如下所示：

C#代码进行可视化

这是本文重点介绍的内容，本文的C#代码通过Scottplot进行可视化。

Scottplot简介

ScottPlot 是一个免费的开源绘图库，用于 .NET，可以轻松以交互方式显示大型数据集。

控制台程序可视化

首先我先介绍一下在控制台程序中进行可视化。

首先添加Scottplot包：

将上篇文章中的C#代码修改如下：

using NumSharp;

namespace LinearRegressionDemo
{
    internal class Program
    {    
        static void Main(string[] args)
        {   
            //创建double类型的列表
            List<double> Array = new List<double>();
            List<double> ArgsList = new List<double>();

            // 指定CSV文件的路径
            string filePath = "你的data.csv路径";

            // 调用ReadCsv方法读取CSV文件数据
            Array = ReadCsv(filePath);

            var array = np.array(Array).reshape(100,2);

            double learning_rate = 0.0001;
            double initial_b = 0;
            double initial_m = 0;
            double num_iterations = 10;

            Console.WriteLine($"Starting gradient descent at b = {initial_b}, m = {initial_m}, error = {compute_error_for_line_given_points(initial_b, initial_m, array)}");
            Console.WriteLine("Running...");
            ArgsList = gradient_descent_runner(array, initial_b, initial_m, learning_rate, num_iterations);
            double b = ArgsList[ArgsList.Count - 2];
            double m = ArgsList[ArgsList.Count - 1];
            Console.WriteLine($"After {num_iterations} iterations b = {b}, m = {m}, error = {compute_error_for_line_given_points(b, m, array)}");
            Console.ReadLine();

            var x1 = array[$":", 0];
            var y1 = array[$":", 1];
            var y2 = m * x1 + b;

            ScottPlot.Plot myPlot = new(400, 300);
            myPlot.AddScatterPoints(x1.ToArray<double>(), y1.ToArray<double>(), markerSize: 5);
            myPlot.AddScatter(x1.ToArray<double>(), y2.ToArray<double>(), markerSize: 0);
            myPlot.Title($"y = {m:0.00}x + {b:0.00}");

            myPlot.SaveFig("图片.png");
       
        }

        static List<double> ReadCsv(string filePath)
        {
            List<double> array = new List<double>();
            try
            {
                // 使用File.ReadAllLines读取CSV文件的所有行
                string[] lines = File.ReadAllLines(filePath);             

                // 遍历每一行数据
                foreach (string line in lines)
                {
                    // 使用逗号分隔符拆分每一行的数据
                    string[] values = line.Split(',');

                    // 打印每一行的数据
                    foreach (string value in values)
                    {
                        array.Add(Convert.ToDouble(value));
                    }                  
                }
            }
            catch (Exception ex)
            {
                Console.WriteLine("发生错误: " + ex.Message);
            }
            return array;
        }

        public static double compute_error_for_line_given_points(double b,double m,NDArray array)
        {
            double totalError = 0;
            for(int i = 0;i < array.shape[0];i++)
            {
                double x = array[i, 0];
                double y = array[i, 1];
                totalError += Math.Pow((y - (m*x+b)),2);
            }
            return totalError / array.shape[0];
        }

        public static double[] step_gradient(double b_current,double m_current,NDArray array,double learningRate)
        {
            double[] args = new double[2];
            double b_gradient = 0;
            double m_gradient = 0;
            double N = array.shape[0];

            for (int i = 0; i < array.shape[0]; i++)
            {
                double x = array[i, 0];
                double y = array[i, 1];
                b_gradient += -(2 / N) * (y - ((m_current * x) + b_current));
                m_gradient += -(2 / N) * x * (y - ((m_current * x) + b_current));
            }

            double new_b = b_current - (learningRate * b_gradient);
            double new_m = m_current - (learningRate * m_gradient);
            args[0] = new_b;
            args[1] = new_m;

            return args;
        }

        public static List<double> gradient_descent_runner(NDArray array, double starting_b, double starting_m, double learningRate,double num_iterations)
        {
            double[] args = new double[2];
            List<double> argsList = new List<double>();
            args[0] = starting_b;
            args[1] = starting_m;

            for(int i = 0 ; i < num_iterations; i++) 
            {
                args = step_gradient(args[0], args[1], array, learningRate);
                argsList.AddRange(args);
            }

            return argsList;
        }


    }
}

然后得到的图片如下所示：

在以上代码中需要注意的地方：

  var x1 = array[$":", 0];
  var y1 = array[$":", 1];

是在使用NumSharp中的切片，x1表示所有行的第一列，y1表示所有行的第二列。

当然我们不满足于只是保存图片，在控制台应用程序中，再添加一个 ScottPlot.WinForms包：

右键控制台项目选择属性，将目标OS改为Windows：

将上述代码中的

  myPlot.SaveFig("图片.png");

修改为：

 var viewer = new ScottPlot.FormsPlotViewer(myPlot);
 viewer.ShowDialog();

再次运行结果如下：

winform进行可视化

我也想像Python代码中那样画动图，因此做了个winform程序进行演示。

首先创建一个winform，添加ScottPlot.WinForms包，然后从工具箱中添加FormsPlot这个控件：

有两种方法实现，第一种方法用了定时器：

using NumSharp;
namespace WinFormDemo
{
    public partial class Form1 : Form
    {
        System.Windows.Forms.Timer updateTimer = new System.Windows.Forms.Timer();
        int num_iterations;
        int count = 0;
        NDArray? x1, y1, b_each, m_each;
        public Form1()
        {
            InitializeComponent();
        }

        private void button1_Click(object sender, EventArgs e)
        {
            StartLinearRegression();
        }

        public void StartLinearRegression()
        {
            //创建double类型的列表
            List<double> Array = new List<double>();
            List<double> ArgsList = new List<double>();

            // 指定CSV文件的路径
            string filePath = "你的data.csv路径";

            // 调用ReadCsv方法读取CSV文件数据
            Array = ReadCsv(filePath);

            var array = np.array(Array).reshape(100, 2);

            double learning_rate = 0.0001;
            double initial_b = 0;
            double initial_m = 0;
            num_iterations = 10;

            ArgsList = gradient_descent_runner(array, initial_b, initial_m, learning_rate, num_iterations);

            x1 = array[$":", 0];
            y1 = array[$":", 1];

            var argsArr = np.array(ArgsList).reshape(num_iterations, 2);
            b_each = argsArr[$":", 0];
            m_each = argsArr[$":", 1];

            double b = b_each[-1];
            double m = m_each[-1];
            var y2 = m * x1 + b;

            formsPlot1.Plot.AddScatterPoints(x1.ToArray<double>(), y1.ToArray<double>(), markerSize: 5);
            //formsPlot1.Plot.AddScatter(x1.ToArray<double>(), y2.ToArray<double>(), markerSize: 0);
            formsPlot1.Render();


        }

        static List<double> ReadCsv(string filePath)
        {
            List<double> array = new List<double>();
            try
            {
                // 使用File.ReadAllLines读取CSV文件的所有行
                string[] lines = File.ReadAllLines(filePath);

                // 遍历每一行数据
                foreach (string line in lines)
                {
                    // 使用逗号分隔符拆分每一行的数据
                    string[] values = line.Split(',');

                    // 打印每一行的数据
                    foreach (string value in values)
                    {
                        array.Add(Convert.ToDouble(value));
                    }
                }
            }
            catch (Exception ex)
            {
                Console.WriteLine("发生错误: " + ex.Message);
            }
            return array;
        }

        public static double compute_error_for_line_given_points(double b, double m, NDArray array)
        {
            double totalError = 0;
            for (int i = 0; i < array.shape[0]; i++)
            {
                double x = array[i, 0];
                double y = array[i, 1];
                totalError += Math.Pow((y - (m * x + b)), 2);
            }
            return totalError / array.shape[0];
        }

        public static double[] step_gradient(double b_current, double m_current, NDArray array, double learningRate)
        {
            double[] args = new double[2];
            double b_gradient = 0;
            double m_gradient = 0;
            double N = array.shape[0];

            for (int i = 0; i < array.shape[0]; i++)
            {
                double x = array[i, 0];
                double y = array[i, 1];
                b_gradient += -(2 / N) * (y - ((m_current * x) + b_current));
                m_gradient += -(2 / N) * x * (y - ((m_current * x) + b_current));
            }

            double new_b = b_current - (learningRate * b_gradient);
            double new_m = m_current - (learningRate * m_gradient);
            args[0] = new_b;
            args[1] = new_m;

            return args;
        }

        public static List<double> gradient_descent_runner(NDArray array, double starting_b, double starting_m, double learningRate, double num_iterations)
        {
            double[] args = new double[2];
            List<double> argsList = new List<double>();
            args[0] = starting_b;
            args[1] = starting_m;

            for (int i = 0; i < num_iterations; i++)
            {
                args = step_gradient(args[0], args[1], array, learningRate);
                argsList.AddRange(args);
            }

            return argsList;
        }

        private void button2_Click(object sender, EventArgs e)
        {
            // 初始化定时器
            updateTimer.Interval = 1000; // 设置定时器触发间隔（毫秒）
            updateTimer.Tick += UpdateTimer_Tick;
            updateTimer.Start();
        }

        private void UpdateTimer_Tick(object? sender, EventArgs e)
        {
            if (count >= num_iterations)
            {
                updateTimer.Stop();
            }
            else
            {
                UpdatePlot(count);
            }

            count++;
        }

        public void UpdatePlot(int count)
        {

            double b = b_each?[count];
            double m = m_each?[count];

            var y2 = m * x1 + b;

            formsPlot1.Plot.Clear();
            formsPlot1.Plot.AddScatterPoints(x1?.ToArray<double>(), y1?.ToArray<double>(), markerSize: 5);
            formsPlot1.Plot.AddScatter(x1?.ToArray<double>(), y2.ToArray<double>(), markerSize: 0);
            formsPlot1.Plot.Title($"第{count + 1}次迭代：y = {m:0.00}x + {b:0.00}");
            formsPlot1.Render();
        }

        private void button3_Click(object sender, EventArgs e)
        {
            updateTimer.Stop();
        }

        private void Form1_Load(object sender, EventArgs e)
        {

        }
    }
}

简单介绍一下思路，首先创建List<double> argsList用来保存每次迭代生成的参数b、m，然后用

           var argsArr = np.array(ArgsList).reshape(num_iterations, 2);  

将argsList通过np.array()方法转化为NDArray，然后再调用reshape方法，转化成行数等于迭代次数，列数为2，即每一行对应一组参数值b、m。

            b_each = argsArr[$":", 0];
            m_each = argsArr[$":", 1];

argsArr[$":", 0]表示每一行中第一列的值，也就是每一个b，argsArr[$":", 1]表示每一行中第二列的值。

            double b = b_each[-1];
            double m = m_each[-1];

b_each[-1]用了NumSharp的功能表示b_each最后一个元素。

实现效果如下所示：

另一种方法可以通过异步实现：

using NumSharp;

namespace WinFormDemo
{
    public partial class Form2 : Form
    {      
        int num_iterations;
        NDArray? x1, y1, b_each, m_each;
        public Form2()
        {
            InitializeComponent();
        }

        private void button1_Click(object sender, EventArgs e)
        {
            StartLinearRegression();
        }

        public void StartLinearRegression()
        {
            //创建double类型的列表
            List<double> Array = new List<double>();
            List<double> ArgsList = new List<double>();

            // 指定CSV文件的路径
            string filePath = "你的data.csv路径";

            // 调用ReadCsv方法读取CSV文件数据
            Array = ReadCsv(filePath);

            var array = np.array(Array).reshape(100, 2);

            double learning_rate = 0.0001;
            double initial_b = 0;
            double initial_m = 0;
            num_iterations = 10;

            ArgsList = gradient_descent_runner(array, initial_b, initial_m, learning_rate, num_iterations);

            x1 = array[$":", 0];
            y1 = array[$":", 1];

            var argsArr = np.array(ArgsList).reshape(num_iterations, 2);
            b_each = argsArr[$":", 0];
            m_each = argsArr[$":", 1];

            double b = b_each[-1];
            double m = m_each[-1];
            var y2 = m * x1 + b;

            formsPlot1.Plot.AddScatterPoints(x1.ToArray<double>(), y1.ToArray<double>(), markerSize: 5);      
            formsPlot1.Render();
        }

        static List<double> ReadCsv(string filePath)
        {
            List<double> array = new List<double>();
            try
            {
                // 使用File.ReadAllLines读取CSV文件的所有行
                string[] lines = File.ReadAllLines(filePath);

                // 遍历每一行数据
                foreach (string line in lines)
                {
                    // 使用逗号分隔符拆分每一行的数据
                    string[] values = line.Split(',');

                    // 打印每一行的数据
                    foreach (string value in values)
                    {
                        array.Add(Convert.ToDouble(value));
                    }
                }
            }
            catch (Exception ex)
            {
                Console.WriteLine("发生错误: " + ex.Message);
            }
            return array;
        }

        public static double compute_error_for_line_given_points(double b, double m, NDArray array)
        {
            double totalError = 0;
            for (int i = 0; i < array.shape[0]; i++)
            {
                double x = array[i, 0];
                double y = array[i, 1];
                totalError += Math.Pow((y - (m * x + b)), 2);
            }
            return totalError / array.shape[0];
        }

        public static double[] step_gradient(double b_current, double m_current, NDArray array, double learningRate)
        {
            double[] args = new double[2];
            double b_gradient = 0;
            double m_gradient = 0;
            double N = array.shape[0];

            for (int i = 0; i < array.shape[0]; i++)
            {
                double x = array[i, 0];
                double y = array[i, 1];
                b_gradient += -(2 / N) * (y - ((m_current * x) + b_current));
                m_gradient += -(2 / N) * x * (y - ((m_current * x) + b_current));
            }

            double new_b = b_current - (learningRate * b_gradient);
            double new_m = m_current - (learningRate * m_gradient);
            args[0] = new_b;
            args[1] = new_m;

            return args;
        }

        public static List<double> gradient_descent_runner(NDArray array, double starting_b, double starting_m, double learningRate, double num_iterations)
        {
            double[] args = new double[2];
            List<double> argsList = new List<double>();
            args[0] = starting_b;
            args[1] = starting_m;

            for (int i = 0; i < num_iterations; i++)
            {
                args = step_gradient(args[0], args[1], array, learningRate);
                argsList.AddRange(args);
            }

            return argsList;
        }

        private void Form2_Load(object sender, EventArgs e)
        {

        }

        public async Task UpdateGraph()
        {
            for (int i = 0; i < num_iterations; i++)
            {
                double b = b_each?[i];
                double m = m_each?[i];
                var y2 = m * x1 + b;

                formsPlot1.Plot.Clear();
                formsPlot1.Plot.AddScatterPoints(x1?.ToArray<double>(), y1?.ToArray<double>(), markerSize: 5);
                formsPlot1.Plot.AddScatter(x1?.ToArray<double>(), y2.ToArray<double>(), markerSize: 0);
                formsPlot1.Plot.Title($"第{i + 1}次迭代：y = {m:0.00}x + {b:0.00}");
                formsPlot1.Render();
           
                await Task.Delay(1000);
            }


        }

        private async void button2_Click(object sender, EventArgs e)
        {
            await UpdateGraph();
        }
    }
}

点击更新按钮开始执行异步任务：

 private async void button2_Click(object sender, EventArgs e)
        {
            await UpdateGraph();
        }

 public async Task UpdateGraph()
        {
            for (int i = 0; i < num_iterations; i++)
            {
                double b = b_each?[i];
                double m = m_each?[i];
                var y2 = m * x1 + b;

                formsPlot1.Plot.Clear();
                formsPlot1.Plot.AddScatterPoints(x1?.ToArray<double>(), y1?.ToArray<double>(), markerSize: 5);
                formsPlot1.Plot.AddScatter(x1?.ToArray<double>(), y2.ToArray<double>(), markerSize: 0);
                formsPlot1.Plot.Title($"第{i + 1}次迭代：y = {m:0.00}x + {b:0.00}");
                formsPlot1.Render();
           
                await Task.Delay(1000);
            }

实现效果如下：

总结

本文以一个控制台应用与一个winform程序为例向大家介绍了C#如何基于ScottPlot进行数据可视化，并介绍了实现动态绘图的两种方式，一种是使用定时器，另一种是使用异步操作，希望对你有所帮助。