使用Math.NET C#计算导数

我正在寻找一个简单的函数,它将接受一个double值数组并返回数学导数.

Math.NET似乎有这样的功能,但它要求以下语法:

double FirstDerivative(Func f, double x)

我不确定为什么我需要指定一个函数.我只想要一个可以传递数据的预先存在的函数.

获取数据点并创建Math.NET Numerics Cubic Spline对象.然后使用该.Differentiate()方法获得所需的每个点的斜率.

例

请尝试以下代码:

static class Program
{
    const int column_width = 12;
    /// 

    /// The main entry point for the application.
    /// 
    [STAThread]
    static void Main(string[] args)
    {
        var xvec = new DenseVector(new double[] { 0.0, 1.0, 2.0, 3.0, 4.0 });
        var yvec = new DenseVector(new double[] { 3.0, 2.7, 2.3, 1.6, 0.2 });
        Debug.WriteLine("Input Data Table");
        Debug.WriteLine($"{"x",column_width} {"y",column_width}");
        for(int i = 0; i < xvec.Count; i++)
        {
            Debug.WriteLine($"{xvec[i],column_width:G5} {yvec[i],column_width:G5}");
        }
        Debug.WriteLine(" ");
        var cs = CubicSpline.InterpolateNatural(xvec, yvec);

        var x = new DenseVector(15);
        var y = new DenseVector(x.Count);
        var dydx = new DenseVector(x.Count);
        Debug.WriteLine("Interpoaltion Results Table");
        Debug.WriteLine($"{"x",column_width} {"y",column_width} {"dy/dx",column_width}");
        for(int i = 0; i < x.Count; i++)
        {
            x[i] = (4.0*i)/(x.Count-1);
            y[i] = cs.Interpolate(x[i]);
            dydx[i] = cs.Differentiate(x[i]);
            Debug.WriteLine($"{x[i],column_width:G5} {y[i],column_width:G5} {dydx[i],column_width:G5}");
        }


    }
}

看看调试输出:

Input Data Table
           x            y
           0            3
           1          2.7
           2          2.3
           3          1.6
           4          0.2

Interpoaltion Results Table
           x            y        dy/dx
           0            3     -0.28214
     0.28571        2.919     -0.28652
     0.57143       2.8354     -0.29964
     0.85714       2.7469      -0.3215
      1.1429       2.6509     -0.35168
      1.4286       2.5454     -0.38754
      1.7143        2.429     -0.42864
           2          2.3       -0.475
      2.2857        2.154     -0.55809
      2.5714       1.9746      -0.7094
      2.8571       1.7422     -0.92894
      3.1429       1.4382      -1.1979
      3.4286       1.0646      -1.4034
      3.7143      0.64404      -1.5267
           4          0.2      -1.5679