public static double[] Solve(double c, double d)
{
if (d < 0)
{
return(Solve(c, -d).Reverse().Select(x => - x).ToArray());
}
// 最小の実数解
var x1 = d == 0 && c >= 0 ? 0 : 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 }
}
;
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_2()
{
Test(0, 2);
Test(0, -100);
Test(3, 0);
Test(1, 1);
Test(10, -10);
Test(-7, 0);
Test(-10, 127);
Test(-1, -10);
Test(-100, 90);
Test(-15, -4);
Test(-1.5, Math.Sqrt(2) / 2);
Test(-6 * Math.Pow(2, 1 / 3.0), -8);
void Test(double c, double d)
{
var actual = target2(c, d);
var det = (-4 * c * c * c - 27 * d * d).RoundAlmost();
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));
}
}
}
public void Solve_2_1()
{
Test(new[] { 0.0 }, 0, 0);
Test(new[] { -1.0 }, 0, 1);
Test(new[] { 2.0 }, 0, -8);
Test(new[] { 0.0 }, 1, 0);
Test(new[] { -2.0 }, 2, 12);
Test(new[] { 1.0 }, 1, -2);
Test(new[] { -3.0, 0.0, 3.0 }, -9, 0);
Test(new[] { -3.0 }, -5, 12);
Test(new[] { 5.0 }, -7, -90);
Test(new[] { -4.0, 2.0 }, -12, 16);
Test(new[] { -1.5, 3.0 }, -6.75, -6.75);
Test(new[] { -3.0, 1.0, 2.0 }, -7, 6);
Test(new[] { -7.0, -5.0, 12.0 }, -109, -420);
void Test(double[] expected, double c, double d)
{
var actual = target2(c, d);
CollectionAssert.AreEqual(expected, actual);
var f = CubicEquation1.CreateFunction(c, d);
foreach (var x in actual)
{
Assert2.AreNearlyEqual(0, f(x));
}
}
}
public void Solve_1_2()
{
Test(3, 3, 3);
Test(1, 0, 1);
Test(1, -1, 0);
Test(3, -2, -6);
void Test(double b, double c, double d)
{
var actual = target1(b, c, d);
var f = CubicEquation1.CreateFunction(1, b, c, d);
foreach (var x in actual)
{
Assert2.AreNearlyEqual(0, f(x));
}
}
}
public void Solve_1_1()
{
Test(new[] { 0.0 }, 1, 1, 0);
Test(new[] { -2.0 }, 3, 4, 4);
Test(new[] { -2.0 }, 1, -1, 2);
Test(new[] { -3.0, 1.0 }, 1, -5, 3);
void Test(double[] expected, double b, double c, double d)
{
var actual = target1(b, c, d);
actual = Array.ConvertAll(actual, x => x.RoundAlmost());
CollectionAssert.AreEqual(expected, actual);
var f = CubicEquation1.CreateFunction(1, b, c, d);
foreach (var x in actual)
{
Assert2.AreNearlyEqual(0, f(x));
}
}
}