// PLUDecomposition (PLU): Returns the Permutation Matrix, Lower Triangular Matrix, and Upper Triangular Matrix decomposition of a given Matrix as a tuple
public static (Matrix, Matrix, Matrix) PLUDecomposition(Matrix matrix)
{
Matrix PermutationMatrix = Identity(matrix.rows);
Matrix LowerTriangularMatrix;
if (matrix.rows > matrix.columns)
{
LowerTriangularMatrix = new Matrix(matrix.rows, matrix.columns);
}
else
{
LowerTriangularMatrix = new Matrix(matrix.rows, matrix.rows);
}
Matrix UpperTriangularMatrix = Copy(matrix);
for (uint colIndex = 0; colIndex < LowerTriangularMatrix.columns; colIndex++)
{
uint pivotIndex = colIndex;
double pivotValue = UpperTriangularMatrix.values[colIndex, colIndex];
if (pivotValue < 0)
{
pivotValue = pivotValue * -1;
}
for (uint rowIndex = colIndex + 1; rowIndex < LowerTriangularMatrix.rows; rowIndex++)
{
double rowValue = UpperTriangularMatrix.values[rowIndex, colIndex];
if (rowValue < 0)
{
rowValue = rowValue * -1;
}
if (pivotValue < rowValue)
{
pivotIndex = rowIndex;
pivotValue = rowValue;
}
}
if (pivotIndex != colIndex)
{
PermutationMatrix.SwapRows(colIndex, pivotIndex);
LowerTriangularMatrix.SwapRows(colIndex, pivotIndex);
UpperTriangularMatrix.SwapRows(colIndex, pivotIndex);
}
LowerTriangularMatrix.values[colIndex, colIndex] = 1;
if (UpperTriangularMatrix.values[colIndex, colIndex] == 0)
{
continue;
}
for (uint rowIndex = colIndex + 1; rowIndex < LowerTriangularMatrix.rows; rowIndex++)
{
double operation = -(UpperTriangularMatrix.values[rowIndex, colIndex] / UpperTriangularMatrix.values[colIndex, colIndex]);
LowerTriangularMatrix.values[rowIndex, colIndex] = -operation;
UpperTriangularMatrix.SwapRows(rowIndex, AddArrays(MultiplyArray(UpperTriangularMatrix.RowValues(colIndex), operation), UpperTriangularMatrix.RowValues(rowIndex)));
}
}
for (uint rowIndex = (uint)matrix.columns; rowIndex < matrix.rows; rowIndex++)
{
UpperTriangularMatrix.RemoveRow((uint)matrix.columns);
}
PermutationMatrix = Transpose(PermutationMatrix);
return(PermutationMatrix, LowerTriangularMatrix, UpperTriangularMatrix);
}
