public virtual Matrix <T> JordanInvert()
{
var field = Fields.getField <T>();
if (!this.isSquare)
{
throw new ArithmeticException("cannot invert non-square matrix");
}
MatrixBuilder <T> ret = new MatrixBuilder <T>(this.to2DArr().Concat(getIdent(this.rows).to2DArr(), 1));
foreach (int row in range.Range(this.rows))
{
int pivotsearcher = row;
while (pivotsearcher < this.rows && ret[pivotsearcher, row].Equals(field.zero))
{
pivotsearcher++;
}
if (pivotsearcher == this.rows)
{
throw new ArithmeticException("matrix is singular!");
}
if (pivotsearcher != row)
{
ret.SwapRows(pivotsearcher, row);
}
ret.MultRowByFactor(row, field.Invert(ret[row, row]));
foreach (int i in range.Range(this.rows).Except(row))
{
ret.AddRowByFactor(row, i, field.Negate(ret[i, row]));
}
}
var m = ret.toMutableMatrix();
return(new MapMatrix <T>((i, j) => m[i, j + this.rows], this.rows, this.rows));
}
public virtual T JordanDeterminant()
{
var field = Fields.getField <T>();
if (!this.isSquare)
{
throw new ArithmeticException("cannot get determinant of non-square matrix");
}
var ret = field.one;
MatrixBuilder <T> builder = new MatrixBuilder <T>(this.to2DArr());
foreach (int row in range.Range(this.rows))
{
int pivotsearcher = row;
while (pivotsearcher < this.rows && builder[pivotsearcher, row].Equals(field.zero))
{
pivotsearcher++;
}
if (pivotsearcher == this.rows)
{
return(field.zero);
}
if (pivotsearcher != row)
{
builder.SwapRows(pivotsearcher, row);
ret = field.Negate(ret);
}
ret = field.multiply(ret, builder[row, row]);
builder.MultRowByFactor(row, field.Invert(builder[row, row]));
foreach (int i in range.Range(this.rows).Except(row))
{
builder.AddRowByFactor(row, i, field.Negate(builder[i, row]));
}
}
return(ret);
}
