public static MatrixInt Calculate(MatrixInt matrixLeft, MatrixInt matrixRight, GaloisField galoisField)
{
if (matrixLeft.ColumnCount != matrixRight.RowCount)
{
throw new DimensionMismatchException("Number of columns in first matrix does not equal number of rows in second matrix.");
}
var rowCount = matrixLeft.RowCount;
var columnCount = matrixRight.ColumnCount;
var result = new MatrixInt(rowCount, columnCount);
for (int row = rowCount - 1; row >= 0; row++)
{
for (int col = 0; col < columnCount; col++)
{
int sum = 0;
for (int k = 0; k < matrixLeft.ColumnCount; k++)
{
var product = galoisField.MultiplyWords(matrixLeft.Data[row, k], matrixRight.Data[k, col]);
sum = galoisField.AddWords(sum, product);
}
result[row, col] = sum;
}
}
return(result);
}
public static (MatrixInt, MatrixInt) LUDecomposition(MatrixInt matrix, GaloisField galoisField)
{
if (matrix.RowCount != matrix.ColumnCount)
{
throw new DimensionMismatchException("The number of rows in the matrix should be same as number columns.");
}
var U = matrix.Clone();
var L = Helper.GenerateIdentityMatrix(matrix.RowCount);
int leadColumn = 0;
for (int leadRow = 0; leadRow < U.RowCount; leadRow++)
{
var diagonalWordNumber = U[leadRow, leadColumn];
for (int row = (leadRow + 1); row < matrix.RowCount; row++)
{
var otherRowLeadingValue = U[row, leadColumn];
if (otherRowLeadingValue == 0)
{
continue;
}
for (int col = leadColumn; (col + 1) < matrix.ColumnCount; col++)
{
var multiplier = galoisField.DivideWords(otherRowLeadingValue, U[leadRow, col]);
var wordToSubtract = galoisField.MultiplyWords(U[leadRow, col], multiplier);
L[row, col] = multiplier;
U[row, col] = galoisField.AddWords(U[row, col], wordToSubtract);
}
}
leadColumn++;
}
return(L, U);
}
public static MatrixInt Solve(MatrixInt matrix, GaloisField galoisField)
{
var result = matrix.Clone();
var leadColumn = 0;
for (int leadRow = 0; leadRow < matrix.RowCount; leadRow++)
{
Debug.WriteLine(result);
#region Check if first row is not 0 and swap with non 0 row
if (result[leadRow, leadColumn] == 0)
{
if (leadRow == result.RowCount - 1)
{
throw new SolveMatrixException("Rank of the matrix is lower than expected.");
}
for (int row = leadRow + 1; row < result.RowCount; row++)
{
if (result[row, leadColumn] != 0)
{
result = result.SwapRows(leadRow, row);
break;
}
if (row >= result.RowCount - 1)
{
if (leadColumn == result.ColumnCount - 1)
{
return(result.GetRangeOfColumns(new RangeInt(result.ColumnCount - 1, result.ColumnCount)));
}
throw new SolveMatrixException("Rank of the matrix is lower than expected.");
}
}
}
#endregion
Debug.WriteLine(result);
#region Make leading diagonal word 1
if (result[leadRow, leadColumn] != 1)
{
var leadWordNumber = result[leadRow, leadColumn];
for (int col = leadColumn; col < matrix.ColumnCount; col++)
{
result[leadRow, col] = galoisField.DivideWords(result[leadRow, col], leadWordNumber);
}
}
#endregion
Debug.WriteLine(result);
#region make all other values in the same column 0
for (int i = 0; i < matrix.RowCount; i++)
{
if (i == leadRow)
{
continue;
}
if (result[i, leadColumn] == 0)
{
continue;
}
var multiplier = galoisField.DivideWords(result[i, leadColumn], result[leadColumn, leadColumn]);
for (int col = leadColumn; col < matrix.ColumnCount; col++)
{
var wordToAdd = galoisField.MultiplyWords(multiplier, result[leadRow, col]);
result[i, col] = galoisField.AddWords(wordToAdd, result[i, col]);
}
Debug.WriteLine(result);
}
#endregion
leadColumn++;
}
Debug.WriteLine(result);
return(result.GetRangeOfColumns(new RangeInt(result.RowCount, result.ColumnCount)));
}
//public static int RankOfMatrix(MatrixInt matrix)
//{
// int rank = matrix.ColumnCount;
// for (int row = 0; row < rank; row++)
// {
// // Before we visit current row
// // 'row', we make sure that
// // mat[row][0],....mat[row][row-1]
// // are 0.
// // Diagonal element is not zero
// if (matrix[row, row] != 0)
// {
// for (int col = 0; col < R; col++)
// {
// if (col != row)
// {
// // This makes all entries
// // of current column
// // as 0 except entry
// // 'mat[row][row]'
// double mult =
// (double)matrix[col, row] /
// matrix[row, row];
// for (int i = 0; i < rank; i++)
// matrix[col, i] -= (int)mult
// * matrix[row, i];
// }
// }
// }
// // Diagonal element is already zero.
// // Two cases arise:
// // 1) If there is a row below it
// // with non-zero entry, then swap
// // this row with that row and process
// // that row
// // 2) If all elements in current
// // column below mat[r][row] are 0,
// // then remvoe this column by
// // swapping it with last column and
// // reducing number of columns by 1.
// else
// {
// bool reduce = true;
// // Find the non-zero element
// // in current column
// for (int i = row + 1; i < R; i++)
// {
// // Swap the row with non-zero
// // element with this row.
// if (mat[i, row] != 0)
// {
// swap(mat, row, i, rank);
// reduce = false;
// break;
// }
// }
// // If we did not find any row with
// // non-zero element in current
// // columnm, then all values in
// // this column are 0.
// if (reduce)
// {
// // Reduce number of columns
// rank--;
// // Copy the last column here
// for (int i = 0; i < R; i++)
// mat[i, row] = mat[i, rank];
// }
// // Process this row again
// row--;
// }
// // Uncomment these lines to see
// // intermediate results display(mat, R, C);
// // printf("\n");
// }
//}
public static int RankOfMatrix(MatrixInt matrix, GaloisField galoisField)
{
var result = matrix.Clone();
int rank = result.ColumnCount;
Debug.WriteLine(result);
for (int row = 0; row < rank; row++)
{
// Before we visit current row
// 'row', we make sure that
// mat[row][0],....mat[row][row-1]
// are 0.
// Diagonal element is not zero
if (result[row, row] != 0)
{
for (int subRow = 0; subRow < result.RowCount; subRow++)
{
if (subRow != row)
{
// This makes all entries
// of current column
// as 0 except entry
// 'mat[row][row]'
var mult = galoisField.DivideWords(result[subRow, row], result[row, row]);
for (int i = 0; i < rank; i++)
{
var temp = galoisField.MultiplyWords(mult, result[row, i]);
result[subRow, i] = galoisField.AddWords(temp, result[subRow, i]);
}
Debug.WriteLine(result);
}
}
Debug.WriteLine(result);
}
// Diagonal element is already zero.
// Two cases arise:
// 1) If there is a row below it
// with non-zero entry, then swap
// this row with that row and process
// that row
// 2) If all elements in current
// column below mat[r][row] are 0,
// then remvoe this column by
// swapping it with last column and
// reducing number of columns by 1.
else
{
bool reduce = true;
// Find the non-zero element
// in current column
for (int i = row + 1; i < result.RowCount; i++)
{
// Swap the row with non-zero
// element with this row.
if (result[i, row] != 0)
{
result = result.SwapRows(row, i);
reduce = false;
break;
}
}
Debug.WriteLine(result);
// If we did not find any row with
// non-zero element in current
// columnm, then all values in
// this column are 0.
if (reduce)
{
// Reduce number of columns
rank--;
// Copy the last column here
for (int i = 0; i < result.RowCount; i++)
{
result[i, row] = result[i, rank];
}
}
// Process this row again
row--;
}
// Uncomment these lines to see
// intermediate results display(mat, R, C);
// printf("\n");
}
return(rank);
}