public static double?PartialDerivative(FunctionHandler f, LimSign xSign, uint index = 1, double precision = 1E-3, params double[] points) //返回一个多元函数在某点的指定趋向方向的偏导数值；index指示要求偏微分的自变量序号，从1开始；precision过大会引入较大误差，precision过小会导致数值结果不稳定
{
if (f == null)
{
throw new ArgumentNullException("Function Null");
}
if ((points == null) || (points.Length == 0))
{
throw new ArgumentNullException("Variable Null");
}
double res = 0;
if (index-- == 0)
{
index = 0;
}
precision = Math.Abs(precision);
try
{
if (xSign == LimSign.Negative)
{
precision = -precision;
}
double[][] fi = new double[5][];
for (int i = 0; i < 5; i++)
{
fi[i] = (double[])points.Clone();
fi[i][index] += i * precision;
}
res = (-25 * f(fi[0]) + 48 * f(fi[1]) - 36 * f(fi[2]) + 16 * f(fi[3]) - 3 * f(fi[4])) / (12 * precision); //五点公式
}
catch (Exception) //导数不存在或其他错误
{
//MessageBox
return(null);
}
return(res);
}
public LimVariable(double _p, LimSign _s)
{
this.Value = _p;
this.Sign = _s;
}
