public static double?Limit(MonoFunctionHandler f, double precision, LimVariable point) //返回一个一元函数在某点的左右极限值
{
if (f == null)
{
throw new ArgumentNullException("Function Null");
}
double res = 0;
precision = Math.Abs(precision);
try
{
switch (point.Sign)
{
case LimSign.Negative:
res = f(point.Value - precision);
break;
case LimSign.Positive:
res = f(point.Value + precision);
break;
}
}
catch (Exception) //极限不存在或其他错误
{
//MessageBox
return(null);
}
return(res);
}
public static double?Derivative(MonoFunctionHandler f, LimVariable x, double precision = 1E-3) //返回一个一元函数在某点的左右导数值；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");
}
double res = 0;
precision = Math.Abs(precision);
try
{
switch (x.Sign)
{
case LimSign.Negative:
res = (-25 * f(x.Value) + 48 * f(x.Value - precision) - 36 * f(x.Value - 2 * precision) + 16 * f(x.Value - 3 * precision) - 3 * f(x.Value - 4 * precision)) / (12 * -precision); //五点公式
break;
case LimSign.Positive:
res = (-25 * f(x.Value) + 48 * f(x.Value + precision) - 36 * f(x.Value + 2 * precision) + 16 * f(x.Value + 3 * precision) - 3 * f(x.Value + 4 * precision)) / (12 * precision);
break;
}
}
catch (Exception) //导数不存在或其他错误
{
//MessageBox
return(null);
}
return(res);
}
public static double?Integrate(MonoFunctionHandler f, double lower, double upper, double precision = 1E-12) //返回一个一元函数在(lower,upper)区间上的定积分
{
//采用Romberg积分算法
if (lower > upper)
{
return(-Integrate(f, upper, lower, precision));
}
if (lower == upper)
{
return(0);
}
double fa, fb;
try
{
fa = f(lower);
}
catch
{
fa = Limit(f, 1E-15, new LimVariable(lower, LimSign.Positive)).Value;
}
try
{
fb = f(upper);
}
catch
{
fb = Limit(f, 1E-15, new LimVariable(upper, LimSign.Negative)).Value;
}
precision = Math.Abs(precision);
double h = upper - lower;
int k = 1;
double delta = 0;
double[][] arrRbg = new double[2][];
arrRbg[0] = new double[] { (fa + fb) * h / 2 };
try
{
do
{
arrRbg[1] = new double[arrRbg[0].Length + 1];
h /= 2;
k++;
for (UInt64 i = 1; i <= (UInt64)Math.Pow(2, k - 2); i++)
{
arrRbg[1][0] += f(lower + (2 * i - 1) * h);
}
arrRbg[1][0] = (arrRbg[0][0] + 2 * h * arrRbg[1][0]) / 2;
for (int i = 1; i < arrRbg[0].Length + 1; i++)
{
arrRbg[1][i] = arrRbg[1][i - 1] + (arrRbg[1][i - 1] - arrRbg[0][i - 1]) / (Math.Pow(4, i) - 1);
}
delta = arrRbg[1][arrRbg[0].Length] - arrRbg[0][arrRbg[0].Length - 1];
arrRbg[0] = arrRbg[1];
} while (Math.Abs(delta) >= precision);
return(arrRbg[0][arrRbg[0].Length - 1]);
}
catch
{
return(null);
}
}