public static Sign[,] GetCanonicalForm(Sign[,] matrix)
{
List<Sign> distinctSigns = new List<Sign>();
foreach (Sign s in matrix)
if (!distinctSigns.Contains(s))
distinctSigns.Add(s);
//Get sorted array of distinct signs
Sign[] distinctSignsArray = distinctSigns.ToArray();
SortLexicoGraphic(distinctSignsArray);
//Calculate frequency vectors
int[][] frequencyVectors = new int[matrix.GetLength(0)][];
for(int i = 0; i < matrix.GetLength(0); i++)
{
Sign[] currentRow = new Sign[matrix.GetLength(0)];
for(int j = 0; j < currentRow.Length; j++)
currentRow[j] = matrix[i, j];
frequencyVectors[i] = GetSignFrequencyVector(currentRow, distinctSignsArray);
}
string[] frequencyVectorStrings = new string[frequencyVectors.Length];
string[] frequencyVectorBackup = new string[frequencyVectors.Length]; //for comparison
for (int i = 0; i < frequencyVectors.Length; i++)
frequencyVectorStrings[i] = GetFrequencyVectorString(frequencyVectors[i]);
Sign[,] canonical = (Sign[,])matrix.Clone();
SortLexicoGraphic(frequencyVectorStrings);
for (int i = 0; i < frequencyVectorStrings.Length; i++ )
{
//column j=>i; row j=>i
int j = frequencyVectorBackup.ToList().IndexOf(frequencyVectorStrings[i]);
frequencyVectorBackup[j] = null;
SwitchRows(ref canonical, j, i);
SwitchColumns(ref canonical, j, i);
}
return canonical;
}
