public static IList <double> QuadraticDRootsPoMax(double a, double b, double c, double epsilon = Epsilon)
{
// If a is 0 the polynomial is linear.
if (a is 0d)
{
return(LinearRootsTests.LinearRoots(b, c, epsilon));
}
var d = a - (2d * b) + c;
if (d != 0)
{
// The 4 is missing?
var m1 = -Sqrt((b * b) - (a * c));
var m2 = -a + b;
var v1 = -(m1 + m2) / d;
var v2 = -(-m1 + m2) / d;
return(new List <double> {
v1, v2
});
}
else if (b != c && d == 0d)
{
return(new List <double> {
((2d * b) - c) / (2d * (b - c))
});
}
return(new List <double>());
}
public static IList <double> QuadraticEquation(double a, double b, double c, double epsilon = Epsilon)
{
// If a is 0 the polynomial is linear.
if (a is 0d)
{
return(LinearRootsTests.LinearRoots(b, c, epsilon));
}
return(new List <double> {
(-b - Sqrt((b * b) - (4d * a * c))) / (2d * a),
(-b + Sqrt((b * b) - (4d * a * c))) / (2d * a),
});
}
public static IList <double> QuadraticRootsKevinLinDev(double a, double b, double c, double epsilon = Epsilon)
{
// If a is 0 the polynomial is linear.
if (a is 0d)
{
return(LinearRootsTests.LinearRoots(b, c, epsilon));
}
var b_ = b / a;
var c_ = c / a;
// Polynomial discriminant.
var discriminant = (b_ * b_) - (4d * c_);
if (Abs(discriminant) <= epsilon)
{
discriminant = 0d;
}
// ToDo: May need to switch from a hash set to a list for scan-beams.
var results = new HashSet <double>();
if (discriminant > 0d)
{
// Complex or duplicate roots.
var e = Sqrt(discriminant);
results.Add(OneHalf * (-b_ + e));
results.Add(OneHalf * (-b_ - e));
}
else if (discriminant == 0)
{
// There should actually be two roots with same value, but we will only return one.
results.Add(OneHalf * -b_);
}
else if (discriminant < 0d)
{
// Complex or duplicate roots.
var e = -Sqrt(-discriminant);
results.Add(OneHalf * (-b_ + e));
results.Add(OneHalf * (-b_ - e));
}
return(results.ToList());
}