/// <summary>
/// Reduces matrix to row-echelon (REF/Gauss) or reduced row-echelon (RREF/Gauss-Jordan) form and solves for augmented columns (if any.)
/// </summary>
public static MatrixEliminationResult Eliminate(double[,] input, MatrixReductionForm form, int augmentedCols = 0)
{
int totalRowCount = input.GetLength(0);
int totalColCount = input.GetLength(1);
if (augmentedCols >= totalColCount)
{
throw new ArgumentException(nameof(augmentedCols), Properties.Resources.Exception_TooMuchAugmentedColumns);
}
MatrixEliminationResult result = new MatrixEliminationResult();
double[,] output = CreateCopy(input);
// number of pivots found
int numPivots = 0;
// loop through columns, exclude augmented columns
for (int col = 0; col < totalColCount - augmentedCols; col++)
{
int?pivotRow = FindPivot(output, numPivots, col, totalRowCount);
if (pivotRow == null)
{
continue; // no pivots, go to another column
}
ReduceRow(output, pivotRow.Value, col, totalColCount);
SwitchRows(output, pivotRow.Value, numPivots, totalColCount);
pivotRow = numPivots;
numPivots++;
// Eliminate Previous Rows
if (form == MatrixReductionForm.ReducedRowEchelonForm)
{
for (int tmpRow = 0; tmpRow < pivotRow; tmpRow++)
{
EliminateRow(output, tmpRow, pivotRow.Value, col, totalColCount);
}
}
// Eliminate Next Rows
for (int tmpRow = pivotRow.Value; tmpRow < totalRowCount; tmpRow++)
{
EliminateRow(output, tmpRow, pivotRow.Value, col, totalColCount);
}
}
result.Rank = numPivots;
result.FullMatrix = output;
result.AugmentedColumnCount = augmentedCols;
if (augmentedCols > 0 && form == MatrixReductionForm.ReducedRowEchelonForm) // matrix has solution
{
result.Solution = ExtractColumns(output, totalColCount - augmentedCols, totalColCount - 1);
}
return(result);
}
/// <summary>
/// Reduces matrix to row-echelon (REF/Gauss) or reduced row-echelon (RREF/Gauss-Jordan) form.
/// Accepts the number of augmeted columns. If the number specified is null, the default number specified in the matrix is used.
/// </summary>
/// <remarks>
/// If <param name="augmentedColCount">augmentedColCount</param> is null, <seealso cref="Elsheimy.Components.Linears.Matrix.AugmentedColumnCount"/> is used.
/// </remarks>
public virtual Matrix Reduce(MatrixReductionForm form, int?augmentedColCount = null)
{
int augmentedCols = augmentedColCount ?? this.AugmentedColumnCount;
return(new Matrix(MatrixFunctions.Eliminate(this.InnerMatrix, form, augmentedCols).FullMatrix));
}
/// <summary>
/// Reduces matrix to row-echelon (REF/Gauss) or reduced row-echelon (RREF/Gauss-Jordan) form.
/// </summary>
public static double[,] Reduce(double[,] input, MatrixReductionForm form)
{
return(Eliminate(input, form, 0).FullMatrix);
}
