template < class S > void compute(const size_t & n, const S& t, S& r) const
{
typedef typename S::value_type v_type;
if (nt2::isdiagonal(t))
{
r = nt2::from_diag(nt2::sqrt(nt2::diag_of(t)));
}
else
{
// Compute upper triangular square root R of T, a column at a time.
r = nt2::zeros(n, n, meta::as_<v_type>());
for (size_t j=1; j <= n; ++j)
{
r(j,j) = nt2::sqrt(t(j,j));
for (size_t i=j-1; i >= 1; --i)
{
//itab_ k = _(i+1, j-1);
v_type s = nt2::globalsum(nt2::multiplies(colvect(r(i,_(i+1, j-1))),
colvect(r(_(i+1, j-1),j))));
// value_type s = nt2::mtimes(r(i,_(i+1, j-1)), r(_(i+1, j-1),j));
r(i,j) = (t(i,j) - s)/(r(i,i) + r(j,j));
}
}
}
}
static void evenx2(A0& out, std::size_t n)
{
value_type nn = n;
BOOST_AUTO_TPL(p, nt2::_(value_type(1), nn));
BOOST_AUTO_TPL(j, nt2::trunc(nt2::mod(p,nt2::Four<value_type>())*nt2::Half<value_type>()));
BOOST_AUTO_TPL(k, nt2::sx(nt2::tag::is_equal_(), j, nt2::colvect(j)));
BOOST_AUTO_TPL(p1, colvect(nt2::_(value_type(1), nn, nt2::sqr(nn))));
out = nt2::sx(nt2::tag::plus_(),p1,nt2::minusone(p));
out(k) = nt2::oneplus(sqr(nn)) - out(k);
}
template <class XPR> vtab_t eval(const XPR & xxi){
vtab_t xi = rowvect(xxi);
itab_t index = nt2::bsearch (breaks, xi);
vtab_t val = coefs(index, 1);
for(size_t i=2; i <= order; ++i){
val = mul(colvect(xi-breaks(index)), val) + coefs(index,i);
}
val = nt2::reshape(val, size(xxi));
return val;
}
BOOST_AUTO_TPL(p, nt2::_(value_type(1), nn));
BOOST_AUTO_TPL(j, nt2::trunc(nt2::mod(p,nt2::Four<value_type>())*nt2::Half<value_type>()));
BOOST_AUTO_TPL(k, nt2::sx(nt2::tag::is_equal_(), j, nt2::colvect(j)));
BOOST_AUTO_TPL(p1, colvect(nt2::_(value_type(1), nn, nt2::sqr(nn))));
out = nt2::sx(nt2::tag::plus_(),p1,nt2::minusone(p));
out(k) = nt2::oneplus(sqr(nn)) - out(k);
}
static void evenx1(A0& out, std::size_t n)
{
std::size_t m = n >> 1; //m is odd.
oddOrderMagicSquare(out, m);
value_type m2 = sqr(m);
container::table<value_type> t = nt2::catv(cath(out, out+Two<value_type>()*m2),
cath(out+Three<value_type>()*m2, out+m2));
BOOST_AUTO_TPL(i, colvect(nt2::_(1, m)));
std::size_t k = (n-2) >> 2;
BOOST_AUTO_TPL(j, nt2::cath(nt2::_(std::size_t(1), k), nt2::_(n-k+2, n)));
swap_lines(t, i, i+m, j);
std::size_t k1 = k+1;
BOOST_AUTO_TPL(ii, nt2::_(k1, k1));
BOOST_AUTO_TPL(jj, nt2::_(std::size_t(1), k+1));
swap_lines(t, ii, ii+m, jj);
out = t;
}
template < class M, class I1, class I2, class IDX > static
void swap_lines(M& m, I1 i1, I2 i2, const IDX & j)
{
container::table<value_type> tmp = m(i1, j);//buggy if i1 i2 are integers
m(i1, j) = m(i2, j);
