public MatrixValue Function(MatrixValue M)
{
var lu = new LUDecomposition(M);
return lu.U;
}
/// <summary>
/// Computes the determinant of the matrix.
/// </summary>
/// <returns>The value of the determinant.</returns>
public ScalarValue Det()
{
if (DimensionX == DimensionY)
{
var n = DimensionX;
if (n == 1)
{
return this[1, 1];
}
else if (n == 2)
{
return this[1, 1] * this[2, 2] - this[1, 2] * this[2, 1];
}
else if (n == 3)
{
return this[1, 1] * (this[2, 2] * this[3, 3] - this[2, 3] * this[3, 2]) +
this[1, 2] * (this[2, 3] * this[3, 1] - this[2, 1] * this[3, 3]) +
this[1, 3] * (this[2, 1] * this[3, 2] - this[2, 2] * this[3, 1]);
}
else if (n == 4)
{
//I guess that's right
return this[1, 1] * (this[2, 2] *
(this[3, 3] * this[4, 4] - this[3, 4] * this[4, 3]) + this[2, 3] *
(this[3, 4] * this[4, 2] - this[3, 2] * this[4, 4]) + this[2, 4] *
(this[3, 2] * this[4, 3] - this[3, 3] * this[4, 2])) -
this[1, 2] * (this[2, 1] *
(this[3, 3] * this[4, 4] - this[3, 4] * this[4, 3]) + this[2, 3] *
(this[3, 4] * this[4, 1] - this[3, 1] * this[4, 4]) + this[2, 4] *
(this[3, 1] * this[4, 3] - this[3, 3] * this[4, 1])) +
this[1, 3] * (this[2, 1] *
(this[3, 2] * this[4, 4] - this[3, 4] * this[4, 2]) + this[2, 2] *
(this[3, 4] * this[4, 1] - this[3, 1] * this[4, 4]) + this[2, 4] *
(this[3, 1] * this[4, 2] - this[3, 2] * this[4, 1])) -
this[1, 4] * (this[2, 1] *
(this[3, 2] * this[4, 3] - this[3, 3] * this[4, 2]) + this[2, 2] *
(this[3, 3] * this[4, 1] - this[3, 1] * this[4, 3]) + this[2, 3] *
(this[3, 1] * this[4, 2] - this[3, 2] * this[4, 1]));
}
var lu = new LUDecomposition(this);
return lu.Determinant();
}
return ScalarValue.Zero;
}
/// <summary>
/// Computes the inverse (if it exists).
/// </summary>
/// <returns>The inverse matrix.</returns>
public MatrixValue Inverse()
{
var target = One(DimensionX);
if (DimensionX < 24)
{
var lu = new YAMP.Numerics.LUDecomposition(this);
return lu.Solve(target);
}
else if (IsSymmetric)
{
var cho = new YAMP.Numerics.CholeskyDecomposition(this);
return cho.Solve(target);
}
var qr = YAMP.Numerics.QRDecomposition.Create(this);
return qr.Solve(target);
}
public ArgumentsValue Function(MatrixValue M)
{
var lu = new LUDecomposition(M);
return new ArgumentsValue(lu.L, lu.U, lu.Pivot);
}
