// IHarmonicity
public double GetDistance(Rational r)
{
double d = 0.0;
int[] pows = r.GetPrimePowers();
for (int i = 0; i < pows.Length; ++i)
{
int e = pows[i];
int p = Utils.GetPrime(i);
d += e * e * Math.Pow(p, _exp);
}
return(d);
}
public override double GetDistance(Rational r)
{
double d = 0.0;
int[] pows = r.GetPrimePowers();
for (int i = 0; i < pows.Length; ++i)
{
int e = pows[i];
if (e != 0)
{
int p = Utils.GetPrime(i);
d += Math.Abs(e) * 2.0 * (p - 1) * (p - 1) / p;
}
}
return(d);
}
public int[] FindCoordinates(Rational vector)
{
int len = vector.GetInvolvedPowerCount();
if (len > height)
{
return(null);
}
//if (width < basisSize + len) throw new Exception("");
int[] pows = vector.GetPrimePowers();
int[] v = new int[height];
Array.Copy(pows, 0, v, 0, len);
//
int[] result = new int[basisSize];
for (int row = 0; row < height; ++row)
{
//
int col = leadCols[row];
int lead = col == -1 ? 0 : m[col, ro[row]];
//
int b = 0;
for (int i = 0; i < height; ++i)
{
b += v[i] * m[basisSize + i, ro[row]];
}
//
if (lead == 0)
{
if (b != 0)
{
return(null);
}
}
else
{
if (b % lead != 0)
{
return(null); // non-integer coordinate
}
result[col] = b / lead;
}
}
return(result);
}
public override double GetDistance(Rational r)
{
double d = 1.0;
int[] pows = r.GetPrimePowers();
for (int i = 0; i < pows.Length; ++i)
{
int e = pows[i];
if (e != 0)
{
int p = Utils.GetPrime(i);
d +=
(double)Math.Abs(e)
// * Math.Exp(-e * 0.0001) // make a bit non-commutative to fix the order (avoiding blinking on count increase) - seems needed only if use "overage" in GridDrawer.GenerateItems
// / (p-1); -- backward..
* (p - 1);
}
}
return(d);
}
public RationalX[] FindRationalCoordinates(Rational vector)
{
//!!! seems fails if vector == 1/1
int len = vector.GetInvolvedPowerCount();
if (len > height)
{
return(null);
}
//if (width < basisSize + len) throw new Exception("");
int[] pows = vector.GetPrimePowers();
int[] v = new int[height];
Array.Copy(pows, 0, v, 0, len);
//
RationalX[] result = new RationalX[basisSize];
for (int row = 0; row < height; ++row)
{
//
int col = leadCols[row];
int lead = col == -1 ? 0 : m[col, ro[row]];
//
int b = 0;
for (int i = 0; i < height; ++i)
{
b += v[i] * m[basisSize + i, ro[row]];
}
//
if (lead == 0)
{
if (b != 0)
{
return(null); // no solution
}
}
else
{
result[col] = new RationalX(b, lead);
}
}
return(result);
}
public static int[] FindCoordinates(Rational[] basis, Rational vector, int vectorLength)
{
int basisSize = basis.Length;
// get prime powers
int[][] b = new int[basisSize][];
for (int i = 0; i < basisSize; ++i)
{
b[i] = basis[i].GetPrimePowers();
}
int[] v = vector.GetPrimePowers();
//
Matrix matrix = new Matrix(b, v, vectorLength);
int[] coordinates = matrix.FindCoordinates();
#if DEBUG
// check result
if (coordinates != null)
{
Rational r = Rational.One;
for (int i = 0; i < coordinates.Length; ++i)
{
r *= basis[i].Power(coordinates[i]);
}
if (!r.Equals(vector))
{
throw new Exception(
String.Format("FindCoordinates failed: {0} != {1}", r, vector)
);
}
}
#endif
return(coordinates);
}