public static double[] Solve(double c, double d)
{
if (d < 0)
{
return(Solve(c, -d).Reverse().Select(x => - x).ToArray());
}
// 3重解の場合 (c = d = 0) を含む
if (d == 0)
{
return c >= 0 ? new[] { 0D }
}
: new[] { -Sqrt(-c), 0D, Sqrt(-c) };
// この式では誤差が大きくなることがあります。
var det3 = -4 * c * c * c - 27 * d * d;
// 重解の場合
if (det3.EqualsNearly(0, 8))
{
return new[] { -2 * Sqrt(-c / 3), Sqrt(-c / 3) }
}
;
// 負の実数解
var x1 = SolveNegative();
if (det3 < 0)
{
return new[] { x1 }
}
;
// f(x) = (x - x_1) (x^2 + x_1 x + x_1^2 + c)
var sqrt_det2 = Sqrt(-3 * x1 * x1 - 4 * c);
return(new[] { x1, (-x1 - sqrt_det2) / 2, (-x1 + sqrt_det2) / 2 });
double SolveNegative()
{
var f = CubicEquation1.CreateFunction(c, d);
var f1 = CubicEquation1.CreateDerivative(c);
var x0 = -1D;
while (f(x0) > 0)
{
x0 *= 2;
}
return(NewtonMethod.Solve(f, f1, x0));
}
}
}
}
public static double[] Solve(double c, double d)
{
if (d < 0)
{
return(Solve(c, -d).Reverse().Select(x => - x).ToArray());
}
// 自明解
if (d == 0 && c >= 0)
{
return new[] { 0D }
}
;
// 負の実数解
var x1 = SolveNegative();
// f(x) = (x - x_1) (x^2 + x_1 x + x_1^2 + c)
var det = -3 * x1 * x1 - 4 * c;
if (det < 0)
{
return new[] { x1 }
}
;
if (det == 0)
{
return new[] { x1, -x1 / 2 }
}
;
return(new[] { x1, (-x1 - Sqrt(det)) / 2, (-x1 + Sqrt(det)) / 2 });
double SolveNegative()
{
var f = CubicEquation1.CreateFunction(c, d);
var f1 = CubicEquation1.CreateDerivative(c);
var x0 = -1D;
while (f(x0) > 0)
{
x0 *= 2;
}
return(NewtonMethod.Solve(f, f1, x0));
}
}
}
}
public void Solve_2()
{
void Test(double c, double d)
{
var actual = target2(c, d);
var det = -4 * c * c * c - 27 * d * d;
Assert.AreEqual(c == 0 & d == 0 || det < 0 ? 1 : det == 0 ? 2 : 3, actual.Length);
var f = CubicEquation1.CreateFunction(c, d);
foreach (var x in actual)
{
Assert2.AreNearlyEqual(0, f(x));
}
}
for (int c = -100; c <= 100; c++)
{
for (int d = 0; d <= 100; d++)
{
Test(c, d);
}
}
for (int c1 = 1; c1 <= 20; c1++)
{
for (double c2 = -20; c2 <= 20; c2++)
{
for (int d1 = 1; d1 <= 20; d1++)
{
for (double d2 = -20; d2 <= 20; d2++)
{
Test(c2 / c1, d2 / d1);
}
}
}
}
}
public void Solve_1()
{
void Test(double a, double b, double c, double d)
{
var actual = target1(a, b, c, d);
var f = CubicEquation1.CreateFunction(a, b, c, d);
foreach (var x in actual)
{
Assert2.AreNearlyEqual(0, f(x), -9);
}
}
// A case with error for the determinant.
Test(20, 8, 0, 0);
Test(6, 47, 0, 0);
Test(5, 33, 0, 0);
Test(2, 49, 0, 0);
Test(5, 50, -6, 5);
for (int a = -15; a <= 15; a++)
{
if (a != 0)
{
for (int b = -15; b <= 15; b++)
{
for (int c = -15; c <= 15; c++)
{
for (int d = -15; d <= 15; d++)
{
Test(a, b, c, d);
}
}
}
}
}
}