vnucso.cc File Reference

Solves the Hartree-Fock equation for the 2-cosh potential with spin-orbit in Nuclear Density Functional Theory without assumption of spatial symmetry. More...

#include <madness/mra/mra.h>
#include <madness/mra/vmra.h>
#include <madness/mra/operator.h>
#include <madness/constants.h>

Include dependency graph for vnucso.cc:

Classes
struct	Guess

Typedefs
typedef FunctionFactory< double_complex, 3 >	complex_factoryT
typedef Function< double_complex, 3 >	complex_functionT
typedef std::shared_ptr< FunctionFunctorInterface< double_complex, 3 > >	complex_functorT
typedef Vector< double, 3 >	coordT
typedef SeparatedConvolution< double, 3 >	operatorT
typedef std::shared_ptr< operatorT>	poperatorT
typedef FunctionFactory< double, 3 >	real_factoryT
typedef Function< double, 3 >	real_functionT
typedef std::shared_ptr< FunctionFunctorInterface< double, 3 > >	real_functorT

Functions
void	apply_potential (World &world, const real_functionT &V0, const real_functionT &V0x, const real_functionT &V0y, const real_functionT &V0z, const std::vector< complex_functionT > &u, const std::vector< complex_functionT > &v, std::vector< complex_functionT > &Vu, std::vector< complex_functionT > &Vv, std::vector< complex_functionT > du[3], std::vector< complex_functionT > dv[3], bool doso)
void	doit (World &world)
void	gaxpy1 (World &world, const double_complex alpha, std::vector< complex_functionT > &a, const double_complex beta, const std::vector< complex_functionT > &b, bool fence=true)
Tensor< double_complex >	hamiltonian_matrix (World &world, const std::vector< complex_functionT > &u, const std::vector< complex_functionT > &v, const std::vector< complex_functionT > &Vu, const std::vector< complex_functionT > &Vv, const std::vector< complex_functionT > du[3], const std::vector< complex_functionT > dv[3])
int	main (int argc, char **argv)
std::vector< poperatorT >	make_bsh_operators (World &world, const Tensor< double > &evals, double tol)
void	moments (World &world, const std::vector< complex_functionT > &u, const std::vector< complex_functionT > &v)
void	normalize2 (World &world, std::vector< complex_functionT > &u, std::vector< complex_functionT > &v)
static double	V (const coordT &r)

Variables
const double	a1 = 1.0
const double	a2 = 1.0
static const double	fac1 =exp(-R1/a1)
static const double	fac2 =exp(-R2/a2)
const double	L = 120.0
static double	lambda = lambda_correct
const double	lambda_correct = 0.0026608048208104861/reduced
const double	R1 = 2.0
const double	R2 = 2.0
const double	reduced = 0.04825964488415279478
const double	V1 = -50.0*reduced
const double	V2 = -50.0*reduced
const double	zeta = 7.5

Detailed Description

Solves the Hartree-Fock equation for the 2-cosh potential with spin-orbit in Nuclear Density Functional Theory without assumption of spatial symmetry.

Points of interest

• Forming a Hamiltonian and a Fock matrix
• Forming and solving a generalized eigensystem problem using LAPACK
• Refining the representation of real and complex functions
• Vectors of functions and operators, inner-product, gaxpy
• Application of the Helmholtz bound-state Green function as vector of operators and functions
• Projection and change of representation of functions from multiwavelets of degree k to k+1

The source is here.

This is a more involved example than the Hydrogen and Helium. This example couples the traditional diagonalization approach with that of the integral equation approach. The details are described in: G. I. Fann , J. Pei, R. J. Harrison1, J. Jia, J. Hill1 , M. Ou, W. Nazarewicz, W. A. Shelton and N. Schunck, "Fast multiresolution methods for density functional theory in nuclear physics," Journal of Physics, 180 (2009) 012080.

Typedef Documentation

complex_factoryT

typedef FunctionFactory<double_complex,3> complex_factoryT

complex_functionT

typedef Function<double_complex,3> complex_functionT

complex_functorT

typedef std::shared_ptr< FunctionFunctorInterface<double_complex,3> > complex_functorT

coordT

typedef Vector<double,3> coordT

operatorT

typedef SeparatedConvolution<double,3> operatorT

poperatorT

typedef std::shared_ptr<operatorT> poperatorT

real_factoryT

typedef FunctionFactory<double,3> real_factoryT

real_functionT

typedef Function<double,3> real_functionT

real_functorT

typedef std::shared_ptr< FunctionFunctorInterface<double,3> > real_functorT

Function Documentation

apply_potential()

void apply_potential	(	World &	world,
		const real_functionT &	V0,
		const real_functionT &	V0x,
		const real_functionT &	V0y,
		const real_functionT &	V0z,
		const std::vector< complex_functionT > &	u,
		const std::vector< complex_functionT > &	v,
		std::vector< complex_functionT > &	Vu,
		std::vector< complex_functionT > &	Vv,
		std::vector< complex_functionT >	du[3],
		std::vector< complex_functionT >	dv[3],
		bool	doso
	)

References madness::apply(), axis, madness::gaxpy(), I, lambda, madness::mul(), madness::Function< T, NDIM >::reconstruct(), madness::reconstruct(), u(), and v.

Referenced by doit().

doit()

void doit

(

World &

world

)

References madness::_(), madness::add(), madness::apply(), apply_potential(), axis, c, e(), e1(), madness::WorldGopInterface::fence(), madness::World::gop, hamiltonian_matrix(), k, L, make_bsh_operators(), madness::matrix_inner(), max, moments(), madness::norm2s(), normalize2(), madness::print(), madness::project(), madness::World::rank(), madness::reconstruct(), reduced, madness::FunctionDefaults< NDIM >::set_autorefine(), madness::FunctionDefaults< NDIM >::set_cubic_cell(), madness::FunctionDefaults< NDIM >::set_initial_level(), madness::FunctionDefaults< NDIM >::set_k(), madness::FunctionDefaults< NDIM >::set_refine(), madness::FunctionDefaults< NDIM >::set_thresh(), madness::FunctionDefaults< NDIM >::set_truncate_mode(), madness::sygv(), thresh, madness::transform(), madness::truncate(), u(), v, V(), w(), madness::wall_time(), and zeta.

Referenced by main().

gaxpy1()

void gaxpy1	(	World &	world,
		const double_complex	alpha,
		std::vector< complex_functionT > &	a,
		const double_complex	beta,
		const std::vector< complex_functionT > &	b,
		bool	fence = true
	)

References a, alpha, b, beta, madness::WorldGopInterface::fence(), madness::World::gop, and MADNESS_ASSERT.

hamiltonian_matrix()

Tensor<double_complex> hamiltonian_matrix	(	World &	world,
		const std::vector< complex_functionT > &	u,
		const std::vector< complex_functionT > &	v,
		const std::vector< complex_functionT > &	Vu,
		const std::vector< complex_functionT > &	Vv,
		const std::vector< complex_functionT >	du[3],
		const std::vector< complex_functionT >	dv[3]
	)

References axis, madness::matrix_inner(), madness::reconstruct(), u(), and v.

Referenced by doit().

main()

int main	(	int	argc,
		char **	argv
	)

References SafeMPI::COMM_WORLD, doit(), e(), madness::error(), madness::finalize(), madness::initialize(), madness::print(), and madness::startup().

make_bsh_operators()

std::vector<poperatorT> make_bsh_operators	(	World &	world,
		const Tensor< double > &	evals,
		double	tol
	)

References madness::BSHOperatorPtr3D(), madness::BaseTensor::dim(), and lo.

Referenced by doit().

moments()

void moments	(	World &	world,
		const std::vector< complex_functionT > &	u,
		const std::vector< complex_functionT > &	v
	)

References madness::Function< T, NDIM >::compress(), madness::conj(), madness::Function< T, NDIM >::gaxpy(), madness::inner(), madness::print(), madness::World::rank(), madness::reconstruct(), madness::scale(), madness::FunctionDefaults< NDIM >::set_autorefine(), madness::Function< T, NDIM >::trace(), u(), and v.

Referenced by doit().

normalize2()

void normalize2	(	World &	world,
		std::vector< complex_functionT > &	u,
		std::vector< complex_functionT > &	v
	)

References madness::norm2s(), u(), and v.

Referenced by doit().

V()

static double V ( const coordT &  r )

static

References a1, a2, fac1, fac2, V1, V2, and zeta.

Referenced by doit().

Variable Documentation

a1

const double a1 = 1.0

Referenced by madness::poly4erfc::poly4erfc(), madness::WorldTaskQueue::add(), c_uks_vwn5__(), madness::c_uks_vwn5__(), check_multiplication_table_c2v(), dumb(), madness::SRConf< T >::emul(), madness::TensorTrain< T >::emul(), madness::fast_transpose(), Foo::get1(), Foo::get1c(), Foo::get2(), Foo::get2c(), Foo::get3(), Foo::get3c(), Foo::get4(), Foo::get4c(), Foo::get5(), Foo::get5c(), madness::CCPairFunction< T, NDIM >::inner_internal(), is_aligned(), QuasiNewton::line_search(), madness::QuasiNewton::line_search(), madness::detail::run_function(), madness::poly4erfc::S(), madness::WorldObject< Derived >::send(), madness::WorldObject< Derived >::send_am(), madness::WorldObject< Derived >::send_task(), madness::WorldTaskQueue::send_task(), madness::WorldObject< Derived >::task(), test_accessors(), test_compress(), test_constructor(), test_inner(), test_truncation(), test_XCOperator(), and V().

a2

const double a2 = 1.0

Referenced by madness::poly4erfc::poly4erfc(), madness::WorldTaskQueue::add(), c_rks_vwn5__(), madness::c_rks_vwn5__(), c_uks_vwn5__(), madness::c_uks_vwn5__(), check_multiplication_table_c2v(), dumb(), exact_energy(), madness::fast_transpose(), Foo::get2(), Foo::get2c(), Foo::get3(), Foo::get3c(), Foo::get4(), Foo::get4c(), Foo::get5(), Foo::get5c(), madness::CCPairFunction< T, NDIM >::inner_internal(), is_aligned(), QuasiNewton::line_search(), madness::QuasiNewton::line_search(), madness::detail::run_function(), madness::poly4erfc::S(), madness::WorldObject< Derived >::send(), madness::WorldObject< Derived >::send_am(), madness::WorldObject< Derived >::send_task(), madness::WorldTaskQueue::send_task(), madness::GradientalGaussSlater::Spp_div_S(), madness::WorldObject< Derived >::task(), test_accessors(), test_compress(), test_inner(), test_truncation(), test_XCOperator(), madness::GradientalGaussSlater::U2X_spherical(), madness::Slater::U2X_spherical(), and V().

fac1

const double fac1 =exp(-R1/a1)

static

Referenced by V().

fac2

const double fac2 =exp(-R2/a2)

static

Referenced by V().

L

const double L = 120.0

Referenced by doit().

lambda

double lambda = lambda_correct

static

Referenced by apply_potential(), sympgrad4(), and sympgrad6().

lambda_correct

const double lambda_correct = 0.0026608048208104861/reduced

R1

const double R1 = 2.0

Referenced by madness::apply(), and madness::rank_revealing_decompose().

R2

const double R2 = 2.0

Referenced by madness::apply(), compute_energy(), madness::MP3::compute_mp3_cd(), madness::MP3::compute_mp3_ef(), madness::MP3::compute_mp3_ef_low_scaling(), madness::MP3::compute_mp3_ef_with_permutational_symmetry(), madness::MP3::compute_mp3_ghij(), madness::MP3::compute_mp3_ghij_fast(), madness::MP3::compute_mp3_klmn(), madness::MP3::compute_mp3_klmn_fast(), guess(), madness::CCPairFunction< T, NDIM >::inner_internal(), main(), madness::MP3::mp3_test(), madness::CCPairFunction< T, NDIM >::norm2(), madness::NuclearCorrelationFactor::square(), madness::NuclearCorrelationFactor::square_times_V_derivative(), and test_swap_particles().

reduced

const double reduced = 0.04825964488415279478

Referenced by doit(), and madness::TDHF::make_guess_from_initial_diagonalization().

V1

const double V1 = -50.0*reduced

Referenced by make_Hd(), make_Hdiag(), make_Hv(), nuclear_anchor_test(), and V().

V2

const double V2 = -50.0*reduced

Referenced by make_Hd(), nuclear_anchor_test(), and V().

zeta

const double zeta = 7.5

Referenced by c_uks_vwn5__(), madness::c_uks_vwn5__(), doit(), madness::XCOperator< T, NDIM >::prep_xc_args_response(), and V().