/// <summary>
/// 実係数n次多項式p(x)の定積分 ∫_a^b{p(x)dx}を求める。
/// </summary>
/// <param name="p">実係数n次多項式p(x)。</param>
/// <param name="a">区間a。</param>
/// <param name="b">区間b。</param>
/// <returns>∫_a^b{p(x)dx}</returns>
public double Calc(RealPolynomial p, double a, double b)
{
// xの積分区間 [a b]
// ξの積分区間 [-1 +1]
double flipInterval = 1;
if (b < a)
{
// swap a and b
double t = a;
a = b;
b = t;
flipInterval = -1;
}
int np = NumberOfEvalPoints(p);
var ξwList = GetξwList(np);
// 定積分結果値r。
double r = 0;
for (int k = 0; k < np; ++k)
{
var ξ = ξwList[k].ξ;
var w = ξwList[k].w;
double x = ((a + b) + ξ * (b - a)) / 2.0;
// 地点xでpを評価：p(x)を求める。
double px = p.Evaluate(x);
r += w * px;
}
// 積分変数をx→ξに置き換えたことによるスケーリング。
r *= (b - a) / 2.0;
r *= flipInterval;
return(r);
}
/// <summary>
/// Find one real root of specified real poly
/// </summary>
/// <param name="coeffs">poly coeffs. coef[0]: constant, coef[1] 1st degree coeff</param>
/// <param name="initialX">initial estimate of the root position</param>
/// <returns>p</returns>
public static double FindRoot(RealPolynomial rpoly, double initialX, double kEpsilon, int loopCount)
{
var deriv = rpoly.Derivative();
double prev = initialX;
double x = initialX;
for (int i = 0; i < loopCount; ++i)
{
double f = rpoly.Evaluate(x);
double fPrime = deriv.Evaluate(x);
x = x - f / fPrime;
if (Math.Abs(prev - x) < kEpsilon)
{
break;
}
prev = x;
}
return(x);
}