public static bool AreAlmostEquival(Polynom p, Polynom q, bool output = false)
{
p = p.Clone();
q = q.Clone();
p.Trim();
q.Trim();
if (p.Count != q.Count)
{
if (output)
{
Console.WriteLine("p.Count: {0},\nq.Count: {1}\n", p.Count, q.Count);
}
return(false);
}
for (int i = 0; i < p.Count; i++)
{
if (!ComplexUtils.IsAlmostEqual(p[i], q[i]))
{
if (output)
{
Console.WriteLine("p[i]: {0},\nq[i]: {1},\ni: {2}\n", p[i], q[i], i);
}
return(false);
}
}
return(true);
}
/// <summary>
/// Make recursive FFT
/// </summary>
/// <param name="a">Polynom. Number of items must be pow of two</param>
/// <param name="omega">Proper sqrt of 1</param>
/// <returns></returns>
public static Polynom RecursiveFFT(Polynom a, Complex omega)
{
if (ComplexUtils.IsAlmostEqual(omega, 1))
{
return(a);
}
Polynom a_s = new Polynom();
Polynom a_l = new Polynom();
for (int i = 0; i < a.Count / 2; i++)
{
a_s.Add(a[2 * i]);
a_l.Add(a[2 * i + 1]);
}
Polynom s = RecursiveFFT(a_s, omega * omega);
Polynom l = RecursiveFFT(a_l, omega * omega);
Complex x = 1;
Polynom ret = new Polynom(a.Count);
for (int i = 0; i < a.Count / 2; i++)
{
ret[i] = s[i] + x * l[i];
ret[i + a.Count / 2] = s[i] - x * l[i];
x *= omega;
}
return(ret);
}
// Remove null members at the end
public void Trim()
{
while (this.Count > 0 && ComplexUtils.IsAlmostEqual(this[this.Count - 1], 0))
{
this.RemoveAt(this.Count - 1);
}
}