/// <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);
}
/// <summary>
/// Multiple a and b by convolution
/// </summary>
/// <param name="a"></param>
/// <param name="b"></param>
/// <returns></returns>
public static Polynom MulByConvolution(Polynom a, Polynom b)
{
Polynom ret = new Polynom();
for (int i = 0; i < a.Count + b.Count - 1; i++) //i index of ret
{
Complex c = 0;
for (int ii = 0; ii <= i; ii++)
{
if (ii >= a.Count)
{
continue;
}
if ((i - ii) >= b.Count)
{
continue;
}
c += a[ii] * b[i - ii];
}
ret.Add(c);
}
ret.Trim();
return(ret);
}
static void TestWithRandomPolynoms(int polynomALength, int polynomBLength, double maxValue)
{
Random rnd = new Random();
Polynom a = new Polynom();
for (int i = 0; i < polynomALength; i++)
{
a.Add(new Complex(rnd.NextDouble() * maxValue, rnd.NextDouble() * maxValue));
}
Polynom b = new Polynom();
for (int i = 0; i < polynomBLength; i++)
{
b.Add(new Complex(rnd.NextDouble() * maxValue, rnd.NextDouble() * maxValue));
}
Polynom ret1 = a * b;
Polynom ret2 = Polynom.MulByConvolution(a, b);
if (Polynom.AreAlmostEquival(ret1, ret2, output: false)) // output:true to see what members are not equal
{
Console.WriteLine("Equival");
}
else
{
Console.WriteLine("Nonequival");
}
}
/// <summary>
/// Complements polynom with nulls so rank would be pow of 2
/// </summary>
/// <returns>New polynom</returns>
public Polynom ComplementWithNulls()
{
Polynom ret = this.Clone();
int l = (int)Math.Ceiling(Math.Log(ret.Count, 2));
while (ret.Count < Math.Pow(2, l))
{
ret.Add(0);
}
return(ret);
}
