NDArray<T> Householder<T>::evalHHmatrix(const NDArray<T>& x) {
// input validation
if(!x.isVector() && !x.isScalar())
throw "ops::helpers::Householder::evalHHmatrix method: input array must be vector or scalar!";
NDArray<T> w((int)x.lengthOf(), 1, x.ordering(), x.getWorkspace()); // column-vector
NDArray<T> wT(1, (int)x.lengthOf(), x.ordering(), x.getWorkspace()); // row-vector (transposed w)
T coeff;
T normX = x.template reduceNumber<simdOps::Norm2<T>>();
const T min = DataTypeUtils::min<T>();
if(normX*normX - x(0)*x(0) <= min) {
normX = x(0);
coeff = (T)0.;
w = (T)0.;
}
else {
if(x(0) >= (T)0.)
normX = -normX; // choose opposite sign to lessen roundoff error
T u0 = x(0) - normX;
coeff = -u0 / normX;
w.assign(x / u0);
}
w(0) = (T)1.;
wT.assign(&w);
NDArray<T> identity((int)x.lengthOf(), (int)x.lengthOf(), x.ordering(), x.getWorkspace());
identity.setIdentity(); // identity matrix
return identity - mmul(w, wT) * coeff;
}
void Householder<T>::evalHHmatrixDataI(const NDArray<T>& x, T& coeff, T& normX) {
int rows = (int)x.lengthOf()-1;
int num = 1;
if(rows == 0) {
rows = 1;
num = 0;
}
NDArray<T> tail(rows, 1, x.ordering(), x.getWorkspace());
evalHHmatrixData(x, tail, coeff, normX);
if(x.isRowVector()) {
NDArray<T>* temp = x.subarray({{}, {num, x.sizeAt(1)}});
temp->assign(tail);
delete temp;
}
else {
NDArray<T>* temp = x.subarray({{num, x.sizeAt(0)}, {}});
temp->assign(tail);
delete temp;
}
}
