/**
* Create a Vandermonde matrix, which is guaranteed to have the
* property that any subset of rows that forms a square matrix
* is invertible.
*
* @param rows Number of rows in the result.
* @param cols Number of columns in the result.
* @return A Matrix.
*/
private static Matrix vandermonde(int rows, int cols)
{
Matrix result = new Matrix(rows, cols);
try
{
for (int r = 0; r < rows; r++)
{
for (int c = 0; c < cols; c++)
{
result.set(r, c, Galois.exp((byte)r, c));
}
}
}
catch (Exception e)
{
Console.WriteLine(e);
throw;
}
return(result);
}
/**
* Multiplies this matrix (the one on the left) by another
* matrix (the one on the right).
*/
public Matrix times(Matrix right)
{
if (getColumns() != right.getRows())
{
throw new Exception(
"Columns on left (" + getColumns() + ") " +
"is different than rows on right (" + right.getRows() + ")");
}
Matrix result = new Matrix(getRows(), right.getColumns());
for (int r = 0; r < getRows(); r++)
{
for (int c = 0; c < right.getColumns(); c++)
{
byte value = 0;
for (int i = 0; i < getColumns(); i++)
{
value ^= Galois.multiply(get(r, i), right.get(i, c));
}
result.set(r, c, value);
}
}
return(result);
}
/**
* Does the work of matrix inversion.
*
* Assumes that this is an r by 2r matrix.
*/
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] == 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.
if (data[r][r] == 0)
{
throw new Exception("Matrix is singular");
}
// Scale to 1.
if (data[r][r] != 1)
{
byte scale = Galois.divide(1, data[r][r]);
for (int c = 0; c < columns; c++)
{
data[r][c] = Galois.multiply(data[r][c], scale);
}
}
// Make everything below the 1 be a 0 by subtracting
// a multiple of it. (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] ^= Galois.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] != 0)
{
byte scale = data[rowAbove][d];
for (int c = 0; c < columns; c++)
{
data[rowAbove][c] ^= Galois.multiply(scale, data[d][c]);
}
}
}
}
}