void Householder<T>::evalHHmatrixData(const NDArray<T>& x, NDArray<T>& tail, T& coeff, T& normX) {
// input validation
if(!x.isVector() && !x.isScalar())
throw "ops::helpers::Householder::evalHHmatrixData method: input array must be vector or scalar!";
if(!x.isScalar() && x.lengthOf() != tail.lengthOf() + 1)
throw "ops::helpers::Householder::evalHHmatrixData method: input tail vector must have length less than unity compared to input x vector!";
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.;
tail = (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;
if(x.isRowVector())
tail.assign(x({{}, {1, -1}}) / u0);
else
tail.assign(x({{1, -1}, {}}) / u0);
}
}
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;
}
