public QRArgs QR_Householder2()
{
QRArgs result = new QRArgs();
result.Hs = new Matrix[Columns];
result.Qs = new Matrix[Columns];
result.Rs = new Matrix[Columns];
Matrix Q = I(Rows);
Matrix R = this;
for (int k = 0; k < Columns; k++)
{
Vector x = R.GetColumn(k);
for (int i = 0; i < k; i++)
{
x.Data[i] = 0;
}
double[] w_array = new double[x.Data.Length];
w_array[k] = 1;
Vector e = new Vector(x.Rows, x.Columns, w_array);
double norm = x.Length;
double sign = System.Math.Sign(x.Data[k]);
Vector u = x + (sign == 0 ? 1 : sign) * norm * e;
Vector v = u / R.Data[k * Columns + k];
//Vector v = u / u.Length;
Vector vt = v.Transposed();
Matrix H = I(x.Data.Length) - 2 * ((v * vt) / (vt * v));
result.Hs[k] = H;
R = H * R;
result.Rs[k] = R;
Q = Q * H;
result.Qs[k] = H;
}
result.Q = Q;
result.R = R;
return(result);
}
public QRArgs QR_Householder()
{
QRArgs result = new QRArgs();
result.Hs = new Matrix[Columns];
result.Qs = new Matrix[Columns];
result.Rs = new Matrix[Columns];
Matrix Q = Matrix.I(Rows);
Matrix R = this;
for (int k = 0; k < Columns; k++)
{
Vector x = R.GetColumn(k);
for (int i = 0; i < k; i++)
{
x.Data[i] = 0;
}
double[] w_array = new double[x.Data.Length];
w_array[k] = x.Length;
Vector w = new Vector(x.Rows, x.Columns, w_array);
Vector v = w - x;
Matrix I = Matrix.I(v.Data.Length);
Vector vt = v.Transposed();
Matrix H = I - (2 * (v * vt)) * (1 / (vt * v));
result.Hs[k] = H;
R = H * R;
result.Rs[k] = R;
Q = Q * H;
result.Qs[k] = H;
}
result.Q = Q;
result.R = R;
return(result);
}
public QRArgs QR_Householder3()
{
QRArgs result = new QRArgs();
result.Hs = new Matrix[Columns];
result.Qs = new Matrix[Columns];
result.Rs = new Matrix[Columns];
Matrix Q = I(Rows);
Matrix R = this;
Matrix A = this;
for (int k = 0; k < Columns; k++)
{
if (k != 0)
{
A = A.Minor(0, 0);
}
Vector x = A.GetColumn(0);
Matrix B = Householder2(x);
Matrix H = I(Rows).Replace(k, k, B);
result.Hs[k] = H;
R = H * R;
result.Rs[k] = R;
Q = Q * H;
result.Qs[k] = H;
}
result.Q = Q;
result.R = R;
return(result);
}