public Matrix GetInverse()
{
// using Adjoint method
// https://www.mathwords.com/i/inverse_of_a_matrix.htm
return(Matrices.Divide(
GetAdjugate(),
GetDeterminant()));
}
public Matrix GetHouseholder()
{
// https://en.wikipedia.org/wiki/QR_decomposition#Using_Householder_reflections
// creating a new alias to match commonly used algorithm variables
Matrix A = this;
// don't alter a1 or it will alter A
ColumnVector a1 = A.GetColumnVector(
0,
0,
A.Height);
decimal norm = a1.GetNorm();
// create copy of vector that can be edited
Matrix u = a1.AsMatrix();
// subtract norm * e vector
// the sign is selected so it has the opposite sign of u1
decimal u1 = u[0, 0];
//u[0, 0] -= Math.Sign(u1) * norm;
u[0, 0] -= norm;
u.DivideBy(2);
Matrix uT = u.GetTranspose();
Matrix uuT = Matrices.Multiply(
u,
uT);
Matrix I = Matrices.GetIdentity(
uuT.Width);
uuT.MultiplyBy(
2 / norm);
Matrix H = Matrices.Subtract(
I,
uuT);
return(H);
}
