//!!! standard basis added here
public Matrix(Rational[] basis, int vectorLength = -1, int vectorCount = -1, bool makeDiagonal = false)
{
//
if (basis == null)
{
throw new ArgumentException();
}
if (vectorCount == -1)
{
vectorCount = basis.Length; // other vectors may be invalid
}
if (vectorLength == -1)
{
vectorLength = GetMaxLength(basis, vectorCount);
}
//
basisSize = vectorCount;
width = basisSize + vectorLength; // we add standard basis here
height = vectorLength;
//
m = new int[width, height];
for (int j = 0; j < basisSize; ++j)
{
//!!! fail: C# can't copy memory from 1d to 2d - we might use 1d array for matrix!
int[] pows = basis[j].GetPrimePowers();
//Array.Copy(basis[i], 0, m, i * height, vectorLength);
for (int i = 0; i < vectorLength; ++i)
{
m[j, i] = Powers.SafeAt(pows, i);
}
}
// add standard basis
for (int j = 0; j < vectorLength; ++j)
{
m[basisSize + j, j] = 1;
}
Init();
if (makeDiagonal)
{
MakeEchelon();
ReduceRows();
}
}
/*
* 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 int[] leadCols; // column -> row
//
public Matrix(int[][] basis, int[] vector, int vectorLength)
{
basisSize = basis.Length;
width = basisSize + 1;
height = vectorLength;
//
m = new int[width, height];
for (int j = 0; j < basisSize; ++j)
{
//!!! fail: C# can't copy memory from 1d to 2d - we might use 1d array for matrix!
//Array.Copy(basis[i], 0, m, i * height, vectorLength);
for (int i = 0; i < vectorLength; ++i)
{
m[j, i] = Powers.SafeAt(basis[j], i);
}
}
//Array.Copy(vector, 0, m, basisSize * height, vectorLength);
for (int i = 0; i < vectorLength; ++i)
{
m[basisSize, i] = Powers.SafeAt(vector, i);
}
Init();
}