static type call(A0& a0, I const& indices)
{
Idx idx = nt2::function_index(indices, a0.extent(), meta::as_<typename A0::indexes_type>());
std::size_t b = nt2::run(idx, 0u, meta::as_<std::size_t>());
std::size_t e = nt2::run(idx, nt2::numel(idx.extent())-1u, meta::as_<std::size_t>())+1u;
typename A0::value_type* p = const_cast<typename A0::value_type*>(a0.raw());
return type(expr::make(container_ref(boost::make_shared<container>(idx.extent(), nt2::share(p+b, p+e)))));
}
BOOST_FORCEINLINE void
combine_eigens(const T& wr, const T& wi, A0& w)
{
typedef typename A0::value_type type_t;
int n = numel(wr);
w.resize(of_size(n, 1));
nt2::container::table<type_t, nt2::shared_> sw(of_size(n, 1), share(w.data(), w.data()+n));
sw = tocomplex(wr, wi);
}
BOOST_FORCEINLINE result_type operator()(A0& a0, A1 const& a1) const
{
result_type that;
nt2_la_int n = nt2::width(a0);
nt2_la_int lda = a0.leading_size();
NT2_F77NAME(zpotrf) (&a1,&n,a0.raw(),&lda,&that);
return that;
}
BOOST_FORCEINLINE result_type operator()(A0& a0, A1 const a1) const
{
result_type that;
nt2_la_int n = nt2::width(a0);
nt2_la_int lda = a0.leading_size();
magma_zpotrf(a1,n,(cuDoubleComplex*)a0.raw(),lda,&that);
return that;
}
BOOST_FORCEINLINE result_type operator()(A0& a0, A1& a1) const
{
result_type that;
nt2_la_int m = nt2::height(a0);
nt2_la_int n = nt2::width(a0);
nt2_la_int ld = a0.leading_size();
a1.resize( nt2::of_size(std::min(n, m), 1) );
magma_cgetrf(m, n, (cuFloatComplex*)a0.data(), ld, a1.data(), &that);
return that;
}
BOOST_FORCEINLINE result_type operator()( A0& a, A1& scale
, A2& ilo, A3& ihi, C0 job) const
{
result_type info;
nt2_la_int n = nt2::width(a);
BOOST_ASSERT_MSG(n == nt2_la_int(nt2::height(a)), "input must be square");
nt2_la_int lda = nt2::max(a.leading_size(), One<size_t>());
NT2_F77NAME(cgebal) (&job, &n
, a.raw(), &lda
, &ilo, &ihi
, scale.raw(), &info);
return info;
}
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 result_type operator()(A0& a0, A1& a1) const
{
result_type that;
nt2_la_int n = nt2::width(a0);
nt2_la_int ld = a0.leading_size();
nt2_la_int ldb = a1.leading_size();
nt2_la_int nhrs = nt2::width(a1);
char uplo = 'L';
NT2_F77NAME(zposv) ( &uplo, &n, &nhrs, a0.data(), &ld, a1.data(), &ldb
, &that
);
return that;
}
BOOST_FORCEINLINE result_type operator()( A0& a0, A1& s, A2& u,A3 &vt, A4 const jobu
, A5 const jobvt) const
{
result_type that;
details::workspace<typename A0::value_type> w;
nt2_la_int m = nt2::height(a0);
nt2_la_int n = nt2::width(a0);
nt2_la_int ld = a0.leading_size();
nt2_la_int ldu = u.leading_size() > 1 ? u.leading_size() : 1 ;
nt2_la_int ldvt= vt.leading_size() > 1 ? vt.leading_size() : 1 ;
nt2_la_int lwork_query = -1;
char c = std::toupper(jobu);
magma_vec_t magma_jobu = c == 'A' ? MagmaAllVec : c == 'S' ? MagmaSomeVec : c == 'O' ? MagmaOverwriteVec : c == 'N' ? MagmaNoVec : (magma_vec_t)0;
c = std::toupper(jobvt);
magma_vec_t magma_jobvt = c == 'A' ? MagmaAllVec : c == 'S' ? MagmaSomeVec : c == 'O' ? MagmaOverwriteVec : c == 'N' ? MagmaNoVec : (magma_vec_t)0;
magma_sgesvd(magma_jobu,magma_jobvt,m, n, 0, ld, 0, 0, ldu
, 0, ldvt, w.main()
, lwork_query, &that
);
w.prepare_main();
nt2::gesvd(a0,s,u,vt,jobu,jobvt,w);
return that;
}
//==========================================================================
/// INTERNAL ONLY - X = LINSOLVE(A,B) -- symmetric shape
BOOST_FORCEINLINE
void eval ( A0 const& a0, A1 const& a1 , A2 const& a2 ,boost::mpl::long_<1> const
, nt2::symmetric_ const&) const
{
type_t rcond;
nt2::container::table<nt2_la_int> piv = nt2::zeros(a0.leading_size(), 1
, nt2::meta::as_<nt2_la_int>() );
boost::proto::child_c<0>(a2).resize(nt2::of_size(a0.leading_size(),1));
NT2_AS_TERMINAL_IN(desired_semantic1,a,a0);
NT2_AS_TERMINAL_IN(desired_semantic,b,a1);
nt2_la_int iter = nt2::sysvx( boost::proto::value(a),boost::proto::value(piv)
, boost::proto::value(b)
, boost::proto::value(boost::proto::child_c<0>(a2))
, rcond);
boost::ignore_unused(iter);
}
result_type operator()(A0& yi, A1& inputs) const
{
yi.resize(inputs.extent());
const child0 & x = boost::proto::child_c<0>(inputs);
if (numel(x) <= 1)
BOOST_ASSERT_MSG(numel(x) > 1, "Interpolation requires at least two sample points in each dimension.");
else
{
BOOST_ASSERT_MSG(issorted(x, 'a'), "for 'nearest' interpolation x values must be sorted in ascending order");
const child1 & y = boost::proto::child_c<1>(inputs);
BOOST_ASSERT_MSG(numel(x) == numel(y), "The grid vectors do not define a grid of points that match the given values.");
const child2 & xi = boost::proto::child_c<2>(inputs);
bool extrap = false;
value_type extrapval = Nan<value_type>();
choices(inputs, extrap, extrapval, N1());
table<index_type> index = bsearch (x, xi);
table<value_type> dx = xi-x(index);
table<index_type> indexp1 = oneplus(index);
yi = y(nt2::if_else(lt(nt2::abs(xi-x(index)), nt2::abs(xi-x(indexp1))), index, indexp1));
value_type b = value_type(x(begin_));
value_type e = value_type(x(end_));
if (!extrap) yi = nt2::if_else(nt2::logical_or(boost::simd::is_nge(xi, b),
boost::simd::is_nle(xi, e)), extrapval, yi);
}
return yi;
}
static type call(A0& a0, I const& indices)
{
return boost::proto::make_expr<tag::function_,container::domain>
( boost::reference_wrapper<A0>(a0)
, function_index(indices, a0.extent(), meta::as_<typename A0::indexes_type>())
);
}
static type call(A0& a0, I const& indices)
{
Idx idx = nt2::function_index(indices, a0.extent(), meta::as_<typename A0::indexes_type>());
std::size_t b = nt2::run(idx, 0u, meta::as_<std::size_t>());
return nt2_expr(basic_expr::make(container_ref(boost::proto::value(a0), boost::proto::value(a0).begin()+b, idx.extent())));
}
BOOST_FORCEINLINE result_type operator()( A0& a, A1& b, A2& alpha, A3& beta, A4& vr, A5& vl) const
{
result_type info = 0;
char jobvr = 'V';
char jobvl = 'V';
details::workspace<typename A0::value_type> wk;
nt2_la_int n = nt2::width(a);
BOOST_ASSERT_MSG( (n == nt2_la_int(nt2::height(a)))
&&(n == nt2_la_int(nt2::height(b))) , "inputs must be square");
nt2_la_int lda = nt2::max(a.leading_size(), One<size_t>());
nt2_la_int ldb = nt2::max(b.leading_size(), One<size_t>());
nt2_la_int ldvl = n;
nt2_la_int ldvr = n;
NT2_F77NAME(zggev) ( &jobvl, &jobvr
, &n
, 0 /*a*/, &lda
, 0 /*b*/, &ldb
, 0/*alpha*/
, 0/*beta*/
, 0/*vl*/, &ldvl
, 0/*vr*/, &ldvr
, wk.main(), details::query()
, wk.reals()
, &info);
info = nt2::ggev_wvrvl(a, b, alpha, beta, vr, vl, wk);
return info;
}
BOOST_FORCEINLINE
result_type operator()(A0 const& a0, A1 ind, A2 dim) const
{
std::size_t along = dim-1;
typename A0::extent_type ex1 = a0.extent();
ex1[along] = 1;
return boost::proto::make_expr< nt2::tag::line_
, container::domain
> ( boost::cref(a0)
, along
, as_index( a0.extent()
, as_subscript(ex1, ind)
)
, nt2::linesstride(a0, dim)
);
}
result_type operator()(A0& out, const A1& in) const
{
size_t n = boost::proto::child_c<0>(in);
out.resize(nt2::of_size(n, n));
nt2::table<value_type, _2D> l = nt2::abs(nt2::pascal(n, 1, nt2::meta::as_<value_type>()));
nt2::table<value_type, _2D> u = nt2::fliplr(nt2::flipud(l));
nt2::table<value_type, _2D> d = nt2::from_diag(nt2::pow(value_type(-2), nt2::_(value_type(0), value_type(n-1))));
out = nt2::round2even(nt2::mtimes(l, nt2::mtimes(d, u)));
return out;
}
BOOST_FORCEINLINE result_type operator()(A0& a0, A1 a1, nt2::symmetric_ const&) const
{
result_type norm;
char uplo = 'L';
nt2_la_int n = nt2::width(a0);
nt2_la_int ld = n;
if(a1 =='I'|| a1 =='1'|| a1 =='O')
{
nt2::memory::container<tag::table_, result_type, nt2::_2D> work(nt2::of_size(n,1));
norm = NT2_F77NAME(zlansy)( &a1, &uplo, &n, a0.raw(), &ld, work.raw());
}
else
{
norm = NT2_F77NAME(zlansy)( &a1, &uplo, &n, a0.raw(), &ld, 0);
}
return norm;
}
BOOST_FORCEINLINE void
combine_vects(const T1& rv, const T2& wi, A0& v)
{
typedef typename A0::value_type type_t;
int n = height(rv);
v.resize(of_size(n, n));
nt2::container::table<type_t, nt2::shared_> sv(of_size(n, n), share(v.data(), v.data()+numel(v)));
for(int j=1; j <= n; ++j)
{
if(wi(j))
{
sv(nt2::_, j ) = tocomplex(rv(nt2::_, j), rv(nt2::_, j+1));
sv(nt2::_, j+1) = conj(sv(nt2::_, j));
++j;
}
else
sv(nt2::_, j) = rv(nt2::_, j);
}
}
void foo (int x)
{
// This should be a single variable declaration, but instead it is two seperate declarations.
// this is OK here, but a bug when it is handled this way inside of a for loop initialization.
// See test2012_106.C.
// #if 1
// class A0 {public: int foo (int x) {return x;}} x2;
// #else
for (class A0 {public: int foo (int x) {return x;}} x2; x2.foo (0); x) {}
// #endif
}
result_type operator()(A0& out, const A1& in) const
{
BOOST_AUTO_TPL(x,boost::proto::child_c<0>(in));
_2D siz = boost::proto::value(boost::proto::child_c<1>(in));
size_t n = siz[0];
size_t m = siz[1];
tab_t rnd = nt2::rand(n*m, 1, nt2::meta::as_<value_t>());
value_t p = nt2::numel(x);
out.resize(siz);
out(nt2::_) = x(nt2::iceil(rnd*p));
return out;
}
//==========================================================================
/// INTERNAL ONLY - X = LINSOLVE(A,B) -- positive definite shape
BOOST_FORCEINLINE
void eval ( A0 const& a0, A1 const& a1 , A2 const& a2 ,boost::mpl::long_<1> const
, nt2::positive_definite_ const&) const
{
type_t rcond;
boost::proto::child_c<0>(a2).resize(nt2::of_size(a0.leading_size(),1));
NT2_AS_TERMINAL_IN(desired_semantic1,a,a0);
NT2_AS_TERMINAL_IN(desired_semantic,b,a1);
nt2_la_int iter = nt2::posvx( boost::proto::value(a), boost::proto::value(b)
, boost::proto::value(boost::proto::child_c<0>(a2))
, rcond);
boost::ignore_unused(iter);
}
result_type operator()(A0& out, const A1& in) const
{
size_t n = boost::proto::child_c<0>(in);
value_type fn = value_type(n);
table<value_type> ns = nt2::cons(of_size(1, 3), fn, fn/12, fn/20);
table<i_type> ee(nt2::of_size(1, 3));
table<value_type> ff(nt2::of_size(1, 3));
// nt2::frexp(ns, ff, ee);
nt2::frexp(ns(1), ff(1), ee(1));
nt2::frexp(ns(2), ff(2), ee(2));
nt2::frexp(ns(3), ff(3), ee(3));
BOOST_AUTO_TPL(kk, nt2::find(nt2::logical_and(eq(ff, nt2::Half<value_type>()), is_gtz(ee))));
BOOST_ASSERT_MSG(!nt2::isempty(kk), "n must be of form 2^m or 12*2^m or 20*2^m");
size_t k = kk(1);
i_type e = nt2::minusone(ee(k));
out.resize(nt2::of_size(n, n));
table<value_type> h;
if (k == 1) // n = 1 * 2^e;
{
h = nt2::One<value_type>();
}
else if ( k == 2) // N = 12 * 2^e;
{
h = nt2::vertcat(nt2::ones(1,12,meta::as_<value_type>()),
nt2::horzcat(nt2::ones(11,1,meta::as_<value_type>()),
nt2::toeplitz(cons<value_type>(of_size(1, 11), -1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1),
cons<value_type>(of_size(1, 11), -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1)
)
)
);
}
else if ( k == 3) // N = 20 * 2^e;
{
h = vertcat(nt2::ones(1,20,meta::as_<value_type>()),
nt2::horzcat(nt2::ones(19,1,meta::as_<value_type>()),
nt2::hankel(cons<value_type>(of_size(1, 19),-1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1, 1),
cons<value_type>(of_size(1, 19),1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1)
)
)
);
}
// Kronecker product construction.
for (i_type i = 1; i <= e; ++i)
{
table<value_type> h1 = nt2::vertcat(nt2::horzcat(h, h), nt2::horzcat(h, -h));
h = h1; //ALIASING
}
out = h;
return out;
}
BOOST_FORCEINLINE result_type operator()(A0& a0, A1& a1, A2& a2) const
{
result_type that;
nt2_la_int n = std::min(nt2::height(a0),nt2::width(a0));
nt2_la_int lda = n;
nt2_la_int nhrs = nt2::width(a2);
nt2_la_int ldb = a2.leading_size();
a1.resize(nt2::of_size(n,1));
magma_zgesv(n,nhrs,(cuDoubleComplex*)a0.data(),lda,a1.data()
,(cuDoubleComplex*)a2.data(),ldb,&that);
return that;
}
BOOST_FORCEINLINE result_type operator()(A0 const& a0, A1 const&a1, A2 const& a2) const
{
result_type rcond;
nt2_la_int n = nt2::height(a0);
nt2_la_int ld = n;
nt2_la_int info;
char uplo = 'L';
nt2::memory::container<tag::table_, v_t, nt2::_2D> work(nt2::of_size(2*n,1));
NT2_F77NAME(zsycon) ( &uplo, &n, a0.raw(), &ld, a1.raw(), &a2, &rcond
, work.raw(), &info
);
return rcond;
}
BOOST_FORCEINLINE result_type operator()(A0& a0, A1& a1, A2& a2) const
{
result_type that;
details::workspace<typename A0::value_type> w;
nt2_la_int m = nt2::height(a0);
nt2_la_int n = nt2::width(a0);
nt2_la_int ld = a0.leading_size();
nt2_la_int lwork_query = -1;
magma_sgeqp3 (m, n, 0, ld, 0, 0, w.main()
, lwork_query, &that
);
w.prepare_main();
nt2::geqp3(a0,a1,a2,w);
return that;
}
BOOST_FORCEINLINE result_type operator()(A0& a0, A1& a1, A2& a2) const
{
result_type that;
details::workspace<typename A0::value_type> w;
nt2_la_int m = nt2::height(a0);
nt2_la_int n = nt2::width(a0);
nt2_la_int ld = a0.leading_size();
NT2_F77NAME(sgeqp3) (&m, &n, 0, &ld, 0, 0, w.main()
, details::query(), &that
);
w.prepare_main();
nt2::geqp3(a0,a1,a2,w);
return that;
}
BOOST_FORCEINLINE result_type operator()(A0& a0, A1& a1,A2& a2) const
{
result_type that;
details::workspace<typename A2::value_type> w;
nt2_la_int m = nt2::height(a0);
nt2_la_int ld = a0.leading_size();
nt2_la_int k = a1.leading_size();
char side = 'L';
char trans = 'N';
NT2_F77NAME(sormqr) (&side,&trans,&m, &m, &k, 0, &ld, 0, 0, &m, w.main()
, details::query(), &that
);
w.prepare_main();
nt2::mqr(a0,a1,a2,w);
return that;
}
result_type operator()(A0& out, const A1& in) const
{
size_t n = boost::proto::child_c<0>(in);
BOOST_ASSERT_MSG(n!= 2, "There is no 2x2 magic matrix");
out.resize(nt2::of_size(n, n));
if(n%2 == 1) //Odd order
{
oddOrderMagicSquare(out,n);
}
else if(n%4 == 0)
{
evenx2(out,n);
}
else
{
evenx1(out,n);
}
return out;
}
BOOST_FORCEINLINE result_type operator()(A0& a0, A1& s, A2& u,A3 &vt, A4 jobu, A5 jobvt) const
{
result_type that;
details::workspace<typename A0::value_type> w;
nt2_la_int m = nt2::height(a0);
nt2_la_int n = nt2::width(a0);
nt2_la_int ld = a0.leading_size();
nt2_la_int ldu = u.leading_size() > 1 ? u.leading_size() : 1 ;
nt2_la_int ldvt= vt.leading_size() > 1 ? vt.leading_size() : 1 ;
NT2_F77NAME(sgesvd) (&jobu,&jobvt,&m, &n, 0, &ld, 0, 0, &ldu
, 0, &ldvt, w.main()
, details::query(), &that
);
w.resize_main(5*nt2::max(m, n));
nt2::gesvd(a0,s,u,vt,jobu,jobvt,w);
return that;
}
BOOST_FORCEINLINE result_type operator()(A0& a0, A1& s) const
{
result_type info;
details::workspace<typename A0::value_type> w;
nt2_la_int m = nt2::height(a0);
nt2_la_int n = nt2::width(a0);
nt2_la_int ld = a0.leading_size();
nt2_la_int ldu = 1 ;
nt2_la_int ldvt= 1 ;
char job = 'N';
NT2_F77NAME(sgesvd) (&job, &job, &m, &n, 0, &ld, 0, 0, &ldu
, 0, &ldvt, w.main()
, details::query(), &info
);
w.prepare_main();
w.resize_main(5*nt2::max(m, n));
nt2::gesvd_w(a0,s,w);
return info;
}