/// <summary>
/// Calculates the LU-decomposition of the given matrix.
/// </summary>
/// <param name="matrix">The matrix to decompose.</param>
/// <exception cref="NonSquareMatrixException"> if matrix is not square</exception>
public FieldLUDecomposition(FieldMatrix <T> matrix)
{
if (!matrix.isSquare())
{
throw new NonSquareMatrixException(matrix.getRowDimension(), matrix.getColumnDimension());
}
int m = matrix.getColumnDimension();
field = matrix.getField();
lu = matrix.getData();
pivot = new int[m];
cachedL = null;
cachedU = null;
cachedP = null;
// Initialize permutation array and parity
for (int row = 0; row < m; row++)
{
pivot[row] = row;
}
even = true;
singular = false;
// Loop over columns
for (int col = 0; col < m; col++)
{
T sum = field.getZero();
// upper
for (int row = 0; row < col; row++)
{
T[] luRow = lu[row];
sum = luRow[col];
for (int i = 0; i < row; i++)
{
sum = sum.subtract(luRow[i].multiply(lu[i][col]));
}
luRow[col] = sum;
}
// lower
int nonZero = col; // permutation row
for (int row = col; row < m; row++)
{
T[] luRow = lu[row];
sum = luRow[col];
for (int i = 0; i < col; i++)
{
sum = sum.subtract(luRow[i].multiply(lu[i][col]));
}
luRow[col] = sum;
if (lu[nonZero][col].Equals(field.getZero()))
{
// try to select a better permutation choice
++nonZero;
}
}
// Singularity check
if (nonZero >= m)
{
singular = true;
return;
}
// Pivot if necessary
if (nonZero != col)
{
T tmp = field.getZero();
for (int i = 0; i < m; i++)
{
tmp = lu[nonZero][i];
lu[nonZero][i] = lu[col][i];
lu[col][i] = tmp;
}
int temp = pivot[nonZero];
pivot[nonZero] = pivot[col];
pivot[col] = temp;
even = !even;
}
// Divide the lower elements by the "winning" diagonal elt.
T luDiag = lu[col][col];
for (int row = col + 1; row < m; row++)
{
T[] luRow = lu[row];
luRow[col] = luRow[col].divide(luDiag);
}
}
}