BOOST_FORCEINLINE static void doit2(const T& a, value_type& b, Out0& r)
{
r.resize(extent(a));
typedef typename A0::index_type index_type;
typedef table<value_type, index_type> result_type;
bool is_ltz_b = is_ltz(b);
if(is_ltz(b)) b = -b;
value_type m = nt2::trunc(b);
value_type f = b-m;
result_type q, t;
// tie(q, t) = schur(a,'N'/*"complex"*/); // t is complex schur form. result_type e, v;
if (false && isdiagonal(t))
{
t = nt2::from_diag(nt2::pow(diag_of(t), m));
if(is_ltz_b) t = nt2::inv(t);
r = nt2::mtimes(q, nt2::mtimes(t, nt2::trans(nt2::conj(q))));
return;
}
else
{ //use iterative method
r = nt2::eye(nt2::size(a), meta::as_<value_type>());
result_type rf = r;
if (m)
{
result_type a00 = a;
while (m >= nt2::One<value_type>())
{
if (nt2::is_odd(m))
{
r = nt2::mtimes(a00, r);
}
a00 = nt2::mtimes(a00, a00);
m = nt2::trunc(m/2); //Half<value_type>(); or >> 1
}
}
if(!f)
{
if(is_ltz_b) r = nt2::inv(r);
return;
}
else
{
result_type a00 = nt2::sqrtm(a);
value_type thresh = nt2::Half<value_type>();
while (f > Zero<value_type>())
{
if (f >= thresh)
{
rf = nt2::mtimes(rf, a00);
f -= thresh;
}
thresh *= nt2::Half<value_type>();
a00 = nt2::sqrtm(a00);
}
}
r= nt2::mtimes(r, rf);
if(is_ltz_b) r = nt2::inv(r);
}
}
BOOST_FORCEINLINE static void conf_bounds(const A0& a0, A1& a1,
const M2x2 pcov,
const value_type& normz,
Out0 & p)
{
typedef typename boost::proto::result_of::child_c<A1&,1>::type Out1;
typedef typename boost::proto::result_of::child_c<A1&,2>::type Out2;
// NT2_DISPLAY(a0.extent()); NT2_DISPLAY(a1.extent());
p.resize(a0.extent());
const In0& x = boost::proto::child_c<0>(a0);
// NT2_DISPLAY(x);
const In1& a = boost::proto::child_c<1>(a0);
// NT2_DISPLAY(a);
const In2& b = boost::proto::child_c<2>(a0);
// NT2_DISPLAY(b);
BOOST_AUTO_TPL(z, x/b);
// NT2_DISPLAY(z);
// NT2_DISPLAY(nt2::gammainc(z, a));
// NT2_DISPLAY(size(p));
p = nt2::exp(z); //nt2::gammainc(z, a);
// NT2_DISPLAY(p);
// Out0& p = boost::proto::child_c<0>(a1);
// NT2_DISPLAY(p);
BOOST_AUTO_TPL(itp, (p/nt2::oneminus(p)));
// NT2_DISPLAY(itp);
BOOST_AUTO_TPL(dp, nt2::rec(p*oneminus(p))); // derivative of logit(p) w.r.t. p
// NT2_DISPLAY(dp);
BOOST_AUTO_TPL(da, dgammainc(z,a)*dp); // dlogitp/da = dp/da * dlogitp/dp
// NT2_DISPLAY(da);
BOOST_AUTO_TPL(db, -nt2::exp(a*nt2::log(z)-z-nt2::gammaln(a)-nt2::log(b))* dp); // dlogitp/db = dp/db * dlogitp/dp
// NT2_DISPLAY(db);
BOOST_AUTO_TPL(varLogitp, pcov(1,1)*sqr(da) + (Two<value_type>()*pcov(1,2)*da + pcov(2,2)*db)*db);
// NT2_DISPLAY(varLogitp);
// NT2_DISPLAY(normz);
BOOST_AUTO_TPL(exp_halfwidth, nt2::exp(normz*nt2::sqrt(varLogitp)));
// NT2_DISPLAY(exp_halfwidth);
Out1 & plo = boost::proto::child_c<1>(a1);
Out2 & pup = boost::proto::child_c<2>(a1);
plo.resize(a0.extent());
pup.resize(a0.extent());
// std::cout << "1" << std::endl;
plo = itp*exp_halfwidth;
// std::cout << "2" << std::endl;
pup = itp/exp_halfwidth;
// std::cout << "3" << std::endl;
plo /= nt2::oneplus(plo);
// std::cout << "4" << std::endl;
pup /= nt2::oneplus(pup);
// std::cout << "5" << std::endl;
}
BOOST_FORCEINLINE static void doit1(const value_type& a, T& b, Out0& r)
{
r.resize(extent(b));
r = nt2::expm(nt2::log(a)*b);
}
