the cuspy half of the nemo tau decomposition, supplied pointwise More...

#include <xcfunctional.h>

Collaboration diagram for madness::nemo_u1_functors:

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Public Types
typedef madness::FunctionFunctorInterface< double, 3 >	functorT

Public Member Functions
	nemo_u1_functors ()

	nemo_u1_functors (const std::vector< std::shared_ptr< functorT > > &u1)

bool	active () const

void	append (const madness::Key< 3 > &key, std::vector< madness::Tensor< double > > &t) const
	write U1 and \|U1\|^2 at this box's quadrature points into t[enum_u1*]

Public Attributes
madness::FunctionCommonData< double, 3 >	cdata

std::vector< std::shared_ptr< functorT > >	f

Detailed Description

the cuspy half of the nemo tau decomposition, supplied pointwise

Holds the four analytic ncf quantities that must never become MRA functions – $U_{1,x}, U_{1,y}, U_{1,z}, |\mathbf U_1|^2$ – and writes their values into the argument vector at the quadrature points of whatever box the caller is operating on. Empty unless a nuclear correlation factor is in play, in which case active() is true and the four enum_u1* slots are filled.

The point is that nothing is projected. A product of U1 with anything, formed as a Function, has to be represented on some tree; on a tree too coarse for U1's eprec-scale structure the polynomial fit rings across the whole box. Evaluating U1 here instead means its values go straight into the functional's pointwise arithmetic and only the potential is ever projected – which the existing machinery already does, and already has to.

$|\mathbf U_1|^2$ comes from its own functor rather than from summing the squares of the three components: that functor treats its diagonal specially, because smoothed_unitvec has norm < 1 inside eprec while the exact diagonal is $ (S'/S)^2 $ .