//龙贝格表格
public void Romberg(double a, double b, FuncOfOneVar F)
{
double[,] TCSR = new double[20, 6];
for (int i = 0; i < 5; i++)
{
TCSR[i, 0] = Math.Pow(2, i);
if (TiXing(a, b, (int)TCSR[i, 0], out double y, F))
{
TCSR[i, 1] = y;
}
if (i > 0)
{
TCSR[i, 2] = (4 * TCSR[i, 1] - TCSR[i - 1, 1]) / 3;
if (i > 1)
{
TCSR[i, 3] = (16 * TCSR[i, 2] - TCSR[i - 1, 2]) / 15;
if (i > 2)
{
TCSR[i, 4] = (64 * TCSR[i, 3] - TCSR[i - 1, 3]) / 63;
}
}
}
}
for (int i = 0; i < 5; i++)
{
Console.WriteLine($"i: {i}\tn: {TCSR[i, 0]}\t" +
$"T: {TCSR[i, 1]}\tS: {TCSR[i, 2]}\t" +
$"C: {TCSR[i, 3]}\tR: {TCSR[i, 4]}");
}
}
//二分法计算
public void Bs(double a, double b, double ep, FuncOfOneVar function)
{
//
int num = 2;
//二分循环
while (b - a >= ep)
{
num *= 2;
double x = (b + a) / 2.0;
if (function(x, out double y1) && function(a, out double y2) && y1 * y2 > 0)
{
a = x;
}
else
{
b = x;
}
}
//生成计算误差
//生成计算结果
//生成输出字符串
Console.WriteLine($"\t计算误差： {(b - a) / num}\t计算结果: {(b + a) / 2.0}");
}
public Function(FuncOfOneVar _Function, double _min, bool _minAllow, double _max, bool _maxAllow)//构造函数2
{
function = _Function;
valueMin = _min;
minAllow = _minAllow;
valueMax = _max;
maxAllow = _maxAllow;
}
public Function(FuncOfOneVar mainFunction, double min, double max)//构造函数2
{
function = mainFunction;
valueMin = min;
minAllow = false;
valueMax = max;
maxAllow = false;
}
//逐次分半加速
public void QuBanTiXing(double a, double b, double ep, FuncOfOneVar F)
{
n = 1;
double Tn, T2n;
Tn = 0;
while (true)
{
this.TiXing(a, b, n, out T2n, F);
Console.WriteLine("n: {" + n + "}\tT2n: {" + T2n + "+}\t|T2n-Tn|: {" + Math.Abs(T2n - Tn) / 3 + "}");
if (Math.Abs((T2n - Tn) / 3) > ep)
{
Tn = T2n;
n = n * 2;
}
else
{
break;
}
}
}
private bool TiXing(double a, double b, int n, out double res, FuncOfOneVar F)
{
h = (b - a) / n;
double sum = 0;
F(a, out double fa);
F(b, out double fb);
for (int i = 1; i < n; i++)
{
if (F(a + i * h, out double s))
{
sum += s;
}
else
{
Console.WriteLine($"错误：梯形公式计算错误");
res = 0;
return(false);
}
}
res = h / 2 * (fa + fb + sum * 2);
return(true);
}
//构造函数
public Function(FuncOfOneVar mainFunction)//构造函数1
{
valueMin = double.MinValue;
valueMax = double.MaxValue;
function = mainFunction;
}
