public MatrixMethods(Fixed <Q>[,] matrix)
{
this.matrix = matrix;
rows = matrix.GetLength(0);
columns = matrix.GetLength(1);
delta = (Fixed <Q>) 1 / 100;
}
private static void addRowToRow(int row1, int row2, bool negative)
{
for (int i = 0; i < Matrix.GetLength(1); i++)
{
if (negative)
{
Matrix[row2, i] -= Matrix[row1, i];
}
else
{
Matrix[row2, i] += Matrix[row1, i];
}
}
}
public static Fixed <Q>[,] MatrixMult(Fixed <Q>[,] A, Fixed <Q>[,] B)
{
Fixed <Q>[,] matrix = new Fixed <Q> [A.GetLength(0), B.GetLength(1)];
for (int row = 0; row < matrix.GetLength(0); row++)
{
for (int col = 0; col < matrix.GetLength(1); col++)
{
for (int i = 0; i < A.GetLength(1); i++)
{
matrix[row, col] += A[row, i] * B[i, col];
}
}
}
return(matrix);
}
public static void Eliminate(Fixed <Q>[,] matrix)
{
Matrix = matrix;
for (int j = 0; j < Matrix.GetLength(1); j++)
{
for (int i = 1 + j; i < Matrix.GetLength(0); i++)
{
var multiplier = Matrix[j, j];
multiplyRow(j, Matrix[i, j]);
multiplyRow(i, multiplier);
addRowToRow(j, i, true);
multiplyRow(j, 1 / multiplier);
}
}
}
static void AddRow(int iTargetRow, int iSecondRow, Fixed <Q> iMultiple, ref Fixed <Q>[,] reducedMatrix)
{
for (int j = 0; j < reducedMatrix.GetLength(1); j++)
{
reducedMatrix[iTargetRow, j] += (reducedMatrix[iSecondRow, j] * iMultiple);
}
}
static void MultiplyRow(int iRow, Fixed <Q> num, ref Fixed <Q>[,] reducedMatrix)
{
for (int j = 0; j < reducedMatrix.GetLength(1); j++)
{
reducedMatrix[iRow, j] *= num;
}
}
static void InterchangeRow(int iRow1, int iRow2, ref Fixed <Q>[,] reducedMatrix)
{
for (int j = 0; j < reducedMatrix.GetLength(1); j++)
{
Fixed <Q> temp = reducedMatrix[iRow1, j];
reducedMatrix[iRow1, j] = reducedMatrix[iRow2, j];
reducedMatrix[iRow2, j] = temp;
}
}
public static Fixed <Q>[,] AddCol(Fixed <Q>[,] A, Fixed <Q>[,] b)
{
Fixed <Q>[,] matrix = new Fixed <Q> [A.GetLength(0), A.GetLength(1) + 1];
for (int row = 0; row < matrix.GetLength(0); row++)
{
for (int col = 0; col < matrix.GetLength(1); col++)
{
if (col < A.GetLength(1))
{
matrix[row, col] = A[row, col];
}
else
{
matrix[row, col] = b[row, 0];
}
}
}
return(matrix);
}
public static Fixed <Q>[,] ReducedEchelonForm(Fixed <Q>[,] M)
{
Fixed <Q>[,] reducedMatrix = M;
for (int i = 0; i < M.GetLength(0); i++)
{
if (reducedMatrix[i, i] == 0)
{
for (int j = i + 1; j < reducedMatrix.GetLength(0); j++)
{
if (reducedMatrix[j, i] != 0)
{
InterchangeRow(i, j, ref reducedMatrix);
}
}
}
if (reducedMatrix[i, i] == 0)
{
continue;
}
if (reducedMatrix[i, i] != 1)
{
for (int j = i + 1; j < reducedMatrix.GetLength(0); j++)
{
if (reducedMatrix[j, i] == 1)
{
InterchangeRow(i, j, ref reducedMatrix);
}
}
}
MultiplyRow(i, 1 / reducedMatrix[i, i], ref reducedMatrix);
for (int j = i + 1; j < reducedMatrix.GetLength(0); j++)
{
AddRow(j, i, -reducedMatrix[j, i], ref reducedMatrix);
}
for (int j = i - 1; j >= 0; j--)
{
AddRow(j, i, -reducedMatrix[j, i], ref reducedMatrix);
}
}
return(reducedMatrix);
}