private static void Test3_FindCoordinates()
{
Rational r0 = new Rational(25, 24); // 25/24 |-3 -1 2> Chroma, Chromatic semitone
Rational r1 = new Rational(81, 80); // 81/80 |-4 4 -1> Syntonic comma
Rational r2 = new Rational(128, 125); // 128/125 |7 0 -3> Enharmonic diesis, Lesser diesis
Rational r3 = new Rational(2048, 2025); // 2048/2025 |11 -4 -2> Diaschisma (128/125 / 81/80)
Rational r4 = new Rational(531441, 524288); // 531441/524288 |-19 12 > Pif (81/80 * 32805/32768)
Rational[] rs = new[] {
//new Rational(2, 1),
//new Rational(3, 2),
r1,
r2,
//new Rational(36, 25),
//new Rational(9, 8),
//new Rational(2, 1),
Rational.Prime(0), // 2
Rational.Prime(1), // 3
Rational.Prime(2), // 5
Rational.Prime(3), // 7
};
var matrix = new Matrix(rs, vectorLength: 3);
matrix.Trace("----------------------------------------- start:");
matrix.MakeEchelon();
matrix.ReduceRows();
var r =
//new Rational(81, 80)
//r2
//new Rational(10, 9)
new Rational(9, 8)
;
var coords = matrix
//.FindCoordinates(r);
.FindFloatCoordinates(r);
Debug.WriteLine(r.FormatFraction() + " =");
if (coords != null)
{
for (int i = 0; i < coords.Length; ++i)
{
Debug.WriteLine("{0,8}: {1,5}", rs[i].FormatFraction(), coords[i]);
}
}
}
/*
* 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();
*
* //
* int[] coordinates = FindCoordinates(b, v, vectorLength);
*
#if DEBUG
* // check result
* if (coordinates != null) {
* Rational r = Rational.One;
* for (int i = 0; i < coordinates.Length; ++i) {
* r *= basis[i].Pow(coordinates[i]);
* }
* if (!r.Equals(vector)) throw new Exception(
* String.Format("FindCoordinates failed: {0} != {1}", r, vector)
* );
* }
#endif
*
* return coordinates;
* }
*/
#region Tests
#if DEBUG
private static void CheckVector(Rational[] basis, Rational vector, int vectorLength, bool addStandard = false)
{
// add standard basis
int basisSize = basis.Length;
if (addStandard)
{
Array.Resize(ref basis, basisSize + vectorLength);
for (int i = 0; i < vectorLength; ++i)
{
basis[basisSize + i] = Rational.Prime(i);
}
}
//
for (int i = 0; i < basis.Length; ++i)
{
Debug.WriteLine(String.Format("Basis {0}. {1,-15} {2}", i, basis[i].FormatFraction(), basis[i].FormatMonzo()));
}
Debug.WriteLine(String.Format("Vector {0,-15} {1}", vector.FormatFraction(), vector.FormatMonzo()));
//
int[] coords = FindCoordinates(basis, vector, vectorLength);
if (coords == null)
{
Debug.WriteLine("Invalid Basis or Out of basis subspace");
}
else
{
Debug.WriteLine("Coordinates: " + Powers.ToString(coords, "()"));
//
Debug.WriteLine(vector.FormatFraction() + " = ");
for (int i = 0; i < basisSize; ++i)
{
int e = Powers.SafeAt(coords, i);
Debug.Print(" * ({0})^{1}", basis[i].FormatFraction(), e);
}
if (addStandard)
{
Rational r = new Rational(coords.Skip(basisSize).ToArray());
Debug.Print(" * {0} {1} {2}", r.FormatFraction(), r.FormatMonzo(), r.FormatNarrowPowers());
}
}
}
public static Rational MakeNarrow(int narrowIndex, int basePrimeIndex)
{
Rational r = Rational.Prime(narrowIndex); // just prime: 2/1, 3/1, 5/1, 7/1, ..
return(MakeNarrow(r, basePrimeIndex));
}
