/// <summary>
/// Gets the leading (first non-zero) column in each row of the matrix.
/// </summary>
/// <param name="matrix">The <see cref="MatrixByRow"/> to determine leading columns for.</param>
/// <returns>An array containing the leading columns of each row.</returns>
public static int[] GetLeadingColumns(MatrixByRow matrix)
{
int[] leadingPositions = new int[matrix.Height];
for (int i = 0; i < matrix.Height; i++)
{
int pos = GetLeadingColumn(matrix[i]);
leadingPositions[i] = pos;
}
return(leadingPositions);
}
/// <inheritdoc/>
public override ExpNode Execute(RowElimOperNode node)
{
// Ensure matrix.
if (node.Child is TensorNode tensorNode && tensorNode.TensorType == TensorType.Matrix)
{
MatrixByRow matrix = new MatrixByRow(tensorNode);
int[] leadingPositions = RefHelpers.GetLeadingColumns(matrix);
// Put in row-echelon form
for (int i = 0; i < matrix.Height; i++)
{
int leftMostCol = RefHelpers.GetLeftMostColumn(leadingPositions, i);
matrix.SwapRows(i, leftMostCol);
Common.Swap(ref leadingPositions[i], ref leadingPositions[leftMostCol]);
if (leadingPositions[i] == -1)
{
continue;
}
matrix[i].MultiplyRow(QuickOpers.Reciprical(matrix[i][leadingPositions[i]]));
for (int j = i + 1; j < matrix.Height; j++)
{
matrix[j].AddRowToRow(matrix[i], QuickOpers.Negative(matrix[j][leadingPositions[i]]));
leadingPositions[j] = RefHelpers.GetLeadingColumn(matrix[j]);
}
}
if (node.EliminationMethod == RowElimMethod.GaussJordan)
{
// Put in reduced row-echelon form
for (int i = matrix.Height - 1; i > 0; i--)
{
for (int j = i - 1; j >= 0; j--)
{
matrix[j].AddRowToRow(matrix[i], QuickOpers.Negative(matrix[j][leadingPositions[i]]));
leadingPositions[j] = RefHelpers.GetLeadingColumn(matrix[j]);
}
}
}
return(matrix.AsExpNode());
}
return(HandleError(new CannotReduceNonMatrix(this, node.Child)));
}
