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;
}
private static void SwitchRows(ref Sign[,] matrix, int row1, int row2)
{
for (int i = 0; i < matrix.GetLength(1); i++)
{
Sign temp = matrix[row1, i];
matrix[row1, i] = matrix[row2, i];
matrix[row2, i] = temp;
}
}
private static void SwitchColumns(ref Sign[,] matrix, int col1, int col2)
{
for (int i = 0; i < matrix.GetLength(0); i++)
{
Sign temp = matrix[i, col1];
matrix[i, col1] = matrix[i, col2];
matrix[i, col2] = temp;
}
}
private static int[] GetSignFrequencyVector(Sign[] row, Sign[] distinct)
{
int[] frequency = new int[distinct.Length];
for (int i = 0; i < frequency.Length; i++)
{
int count = 0;
foreach (Sign s in row)
if (s.Equals(distinct[i]))
count++;
frequency[i] = count;
}
return frequency;
}
//Procedure 3.3
public static void GetSignMatrixAndCanonicalForm(Graph graph, ref Sign[,] matrix, ref Sign[,] canonical)
{
matrix = GetSignMatrix(graph);
canonical = GetCanonicalForm(matrix);
}
public static Sign[,] GetSignMatrix(Graph graph)
{
Sign[,] signMatrix = new Sign[graph.Vertices.Count, graph.Vertices.Count];
foreach (Vertice v1 in graph.Vertices)
{
foreach (Vertice v2 in graph.Vertices)
{
Sign sign = new Sign();
int i = graph.Vertices.IndexOf(v1);
int j = graph.Vertices.IndexOf(v2);
Graph collaterial = GetCollaterialGraph(graph, new Edge(v1.index, v2.index));
List<List<Vertice>> collPaths = GetDijkstraShortestPaths(collaterial, v1);
sign.binarySign = GetCollaterialSign(graph, new Edge(v1.index, v2.index));
if (collPaths[j] != null && collPaths[j].Count != 0)
{
sign.collDistance = collPaths[j].Count - 1;
}
Graph pair = GetPairGraph(graph, v1, v2);
sign.pairNumEdges = pair.Edges.Count;
sign.pairNumVertices = pair.Vertices.Count;
signMatrix[i, j] = sign;
}
}
return signMatrix;
}
public static int[,] GetFrequencyMatrix(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);
int[] row;
//Calculate frequency vectors
//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);
}
int[,] frequencyVectorsMatrix = new int[matrix.GetLength(0), distinctSignsArray.Length];
int columnIndex = 0;
foreach (int[] row2 in frequencyVectors)
{
for (int i = 0; i < row2.Length; i++)
{
frequencyVectorsMatrix[columnIndex, i] = row2[i];
}
}
return frequencyVectorsMatrix;
}
