public void MultiplicationInGaliosFieldShouldWorkCorrect(byte firstOperand, byte secondOperand, uint irreduciblePolynomial, byte expectedResult)
{
//arrange
var gfUnderTest = new GaloisField(irreduciblePolynomial);
//act
var actualResult = gfUnderTest.Multiply(firstOperand, secondOperand);
//assert
Assert.Equal(expectedResult, actualResult);
}
/// <summary>
/// Multiplies this matrix (the one on the left) by another matrix (the one on the right).
/// </summary>
public Matrix Multiply(Matrix right)
{
Throw.If(this.Columns != right.Rows, $"Columns on left ({this.Columns}) is different than rows on right ({right.Rows})");
Matrix result = new Matrix(this.Rows, right.Columns);
for (int r = 0; r < this.Rows; r++)
{
for (int c = 0; c < right.Columns; c++)
{
byte value = 0;
for (int i = 0; i < this.Columns; i++)
{
value ^= GaloisField.Multiply(Get(r, i), right.Get(i, c));
}
result.Set(r, c, value);
}
}
return(result);
}
/// <summary>
/// Does the work of matrix inversion. Assumes that this is an r by 2r matrix.
/// </summary>
private void GaussianElimination()
{
// Clear out the part below the main diagonal and scale the main diagonal to be 1.
for (int r = 0; r < Rows; r++)
{
// If the element on the diagonal is 0, find a row below
// that has a non-zero and swap them.
if (_data[r, r] == (byte)0)
{
for (int rowBelow = r + 1; rowBelow < Rows; rowBelow++)
{
if (_data[rowBelow, r] != 0)
{
SwapRows(r, rowBelow);
break;
}
}
}
// If we couldn't find one, the matrix is singular.
Throw.If(_data[r, r] == 0, "Matrix is singular");
// Scale to 1.
if (_data[r, r] != 1)
{
byte scale = GaloisField.Divide(1, _data[r, r]);
for (int c = 0; c < Columns; c++)
{
_data[r, c] = GaloisField.Multiply(_data[r, c], scale);
}
}
// Make everything below the 1 be a 0 by subtracting a multiple of it.
// Note: subtraction and addition are both exclusive or in the Galois field.
for (int rowBelow = r + 1; rowBelow < Rows; rowBelow++)
{
if (_data[rowBelow, r] != 0)
{
byte scale = _data[rowBelow, r];
for (int c = 0; c < Columns; c++)
{
_data[rowBelow, c] ^= GaloisField.Multiply(scale, _data[r, c]);
}
}
}
}
// Now clear the part above the main diagonal.
for (int d = 0; d < Rows; d++)
{
for (int rowAbove = 0; rowAbove < d; rowAbove++)
{
if (_data[rowAbove, d] != (byte)0)
{
byte scale = _data[rowAbove, d];
for (int c = 0; c < Columns; c++)
{
_data[rowAbove, c] ^= GaloisField.Multiply(scale, _data[d, c]);
}
}
}
}
}