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);