//==========================================================================
// null space basis up to epsi
//==========================================================================
tab_t null(base_t epsi = -1 )const
{
epsi = epsi < 0 ? nt2::eps(w_(1)) : epsi;
int j = numel(w_);
for(; (j > 0) && (w_(j)<= epsi); j--);
j++;
return nt2::fliplr(trans(vt()(_(j, last_index<1>(vt_)), _)));
}
// /////////////////////////////////////////////////////////////////////////////
// return rank up to epsi
// /////////////////////////////////////////////////////////////////////////////
size_t rank(base_t epsi = Eps<base_t>())
{
size_t r = 0;
base_t thresh = n_*epsi*nt2::max(nt2::abs(w_(_)));
for(int i=1; i <= n_; ++i)
{
if(nt2::abs(w_(i)) > thresh) ++r;
}
return r;
}
extern "C" void* call_poll_cq_w_wrap(void* wrap_)
{
wrap_Connector* w_(static_cast<wrap_Connector*>(wrap_) );
w_->connector_->poll_cq(w_->s_ctx_);
delete w_;
return 0;
}
void ftrl_proximal::update(SparseVector<float> x, float p, float y)
{
for (SparseVector<float>::InnerIterator it(x); it; ++it)
{
int i = it.index();
float x_i = it.value();
float g = (p - y) * x_i;
float sigma = (sqrt(n_(i) + g * g) - sqrt(n_(i))) / alpha_;
z_(i) += g - sigma * w_(i);
n_(i) += g * g;
}
}
//==========================================================================
// Return matrix rank up to epsi
//==========================================================================
size_t rank(base_t epsi = -1) const
{
epsi = (epsi < 0) ? nt2::max(n_, m_)*nt2::eps(w_(1)): epsi;
// size_t r = 0;
// for(int i=1; i <= numel(w_); ++i)
// {
// if (w_(i) > epsi)
// ++r;
// else
// return r;
// }
// return r;
return size_t(sum(if_one_else_zero(gt(w_, epsi))(_)));
}
float ftrl_proximal::predict(SparseVector<float> x)
{
double wTx = 0.0;
for (SparseVector<float>::InnerIterator it(x); it; ++it)
{
int i = it.index();
int sign = 0;
if(z_(i) < 0)
sign =-1;
else
sign = 1;
if(z_(i) * sign <= lambda1_)
w_(i) = 0.0;
else
w_(i) = (sign * lambda1_ - z_(i)) / ((beta_ + sqrt(n_(i))) / alpha_ + lambda2_);
wTx += w_(i) * it.value();
}
return 1.0 / (1.0 + exp(-max(min(wTx, 35.0), -35.0)));
}
void FEM::init_localmass(double localmass[][4], int cells){
const double h = 1./cells;
int dim, num;
ELEMENTS::Interval Element;
dim = Element.dimension();
num = Element.getNumberOfCorners();
std::vector<std::vector<double> > Stencil;
std::vector<double> data(num*dim,0.);
for(int i = 0; i < cells; ++i)
{
data[0] = i*h;
data[1] = (i+1)*h;
Element(data);
Stencil = Element.integrate(C_(1) * v_()*w_());
localmass[i][0] = Stencil[0][0];
localmass[i][1] = Stencil[0][1];
localmass[i][2] = Stencil[1][0];
localmass[i][3] = Stencil[1][1];
}
}
tab_t pinv(base_t epsi = -1 )const
{
epsi = epsi < 0 ? nt2::eps(w_(1)) : epsi;
tab_t w1 = nt2::if_else( gt(w_, length(a_)*epsi), nt2::rec(w_), Zero<base_t>());
return mtimes(trans(vt_), mtimes(from_diag(w1), trans(u_)));
}
template<class XPR> result_type solve(const XPR & b,
base_t epsi = Mone<base_t>() )const{
epsi = epsi < 0 ? nt2::eps(w_(1)) : epsi;
tab_t w1 = nt2::if_else( gt(w_, length(a_)*epsi), nt2::rec(w_), Zero<base_t>());
return mtimes(trans(vt_), mtimes(from_diag(w1), mtimes(trans(u_), b)));
}
//==========================================================================
// Return matrix norm
//==========================================================================
base_t norminv() const { return nt2::rec(w_(nt2::min(m_, n_))); }
//==========================================================================
// Return matrix norm
//==========================================================================
base_t norm() const { return w_(1); }
//==========================================================================
// Return matrix condition number
//==========================================================================
base_t cond() const
{
base_t r = w_(1)/w_(nt2::min(m_, n_));
return is_nan(r) ? Inf<base_t>() : r;
}
void operator()(nt2::blocked_range<std::size_t> const& r)
{
out_ = w_(out_,r.begin(),r.size());
};
// /////////////////////////////////////////////////////////////////////////////
// return condition number
// /////////////////////////////////////////////////////////////////////////////
base_t cond() const {return nt2::abs(w_(1)/w_(numel(w_))); }