/**
* Compute the search direction based on the current (inverse) Hessian
* approximation and given gradient.
*
* @param[out] pk The negative product of the inverse Hessian and gradient
* direction gk.
* @param[in] gk Gradient direction.
**/
inline void search_direction(VectorT &pk, const VectorT &gk) const {
std::vector<Scalar> alphas(_buf.size());
typename
boost::circular_buffer<UpdateT>::const_reverse_iterator buf_rit;
typename boost::circular_buffer<UpdateT>::const_iterator buf_it;
typename std::vector<Scalar>::const_iterator alpha_it;
typename std::vector<Scalar>::reverse_iterator alpha_rit;
pk.noalias() = -gk;
for (buf_rit = _buf.rbegin(), alpha_rit = alphas.rbegin();
buf_rit != _buf.rend();
buf_rit++, alpha_rit++) {
Scalar alpha;
const Scalar &rhoi(boost::get<0>(*buf_rit));
const VectorT &yi(boost::get<1>(*buf_rit));
const VectorT &si(boost::get<2>(*buf_rit));
alpha = rhoi * si.dot(pk);
pk -= alpha * yi;
*alpha_rit = alpha;
}
pk *= _gammak;
for (buf_it = _buf.begin(), alpha_it = alphas.begin();
buf_it != _buf.end();
buf_it++, alpha_it++) {
Scalar beta;
const Scalar &rhoi(boost::get<0>(*buf_it));
const VectorT &yi(boost::get<1>(*buf_it));
const VectorT &si(boost::get<2>(*buf_it));
beta = rhoi*yi.dot(pk);
pk += (*alpha_it - beta)*si;
}
}
