/// <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);
}
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>
/// Return multiplication of two polynoms using nonrecursive FFT
/// </summary>
/// <param name="p">First polynom</param>
/// <param name="q">Second polynom</param>
/// <returns>p * q</returns>
public static Polynom operator *(Polynom p, Polynom q)
{
p = p.Clone();
q = q.Clone();
p.Trim();
q.Trim();
//set rank of mul
int count = p.Count + q.Count - 1;
if (p.Count == 0 || q.Count == 0)
{
throw new ArgumentException("Polynom must have at least one member.");
}
// So FFT returns polynom with bigger rank
while (p.Count < count)
{
p.Add(0);
p = p.ComplementWithNulls();
}
while (q.Count < count)
{
q.Add(0);
q = q.ComplementWithNulls();
}
// Nonrecursive FFT
Polynom p_vals = FFT.NonrecursiveFFT(p);
Polynom q_vals = FFT.NonrecursiveFFT(q);
Polynom r_vals = new Polynom(count).ComplementWithNulls();
count = r_vals.Count;
for (int i = 0; i < count; i++)
{
Complex a = p_vals[i];
Complex b = q_vals[i];
r_vals[i] = a * b;
}
Polynom ret = FFT.NonrecursiveFFT(r_vals, true) / count;
ret.Trim();
return(ret);
}
