test_mul_sparse.cc File Reference

#include <madness/mra/mra.h>
#include <madness/mra/vmra.h>
#include <madness/world/test_utilities.h>
#include <cmath>
#include <cstdio>
#include <string>
#include <vector>

Include dependency graph for test_mul_sparse.cc:

Classes
class	Gauss
	exp(-a |r-R|^2) More...
struct	operand_pair
	an operand pair plus the independently projected analytic product More...
class	Slater
	c * exp(-a |r|), cusped at the origin: this is what drives the tree deep More...

Functions
static std::string	fmt_tol (double tol)
static long	interior_nodes_with_coeffs (World &world, const Function< double, D > &f)
int	main (int argc, char **argv)
static std::vector< operand_pair >	make_pairs (World &world)
static Function< double, D >	project (World &world, const std::shared_ptr< FunctionFunctorInterface< double, D > > &functor)
int	test_dot (World &world, std::vector< operand_pair > &pairs)
	T5: dot routes through the screened kernel; check it against the analytic sum.
int	test_exact (World &world, std::vector< operand_pair > &pairs)
	T1: the exact path reproduces the analytic product.
int	test_screening_accuracy (World &world, std::vector< operand_pair > &pairs)
int	test_self_consistency (World &world, std::vector< operand_pair > &pairs)
int	test_tree_state (World &world, std::vector< operand_pair > &pairs)
	T2: the result is a reconstructed tree, both scalar and vector entry points.

Variables
static const double	C_MAX = 100.0
	err <= C_MAX*tol; measured max 34
static const std::size_t	D = 3
static const double	EXACT_FLOOR = 1.e-7
static const double	P_MIN = 0.4
	err ~ tol^p; measured p = 0.58 .. 0.75
static const double	THRESH_REF = 1.e-9
	projection threshold of the reference

Function Documentation

fmt_tol()

static std::string fmt_tol ( double  tol )

static

References madness::nonlinear_vector_solver().

Referenced by test_dot(), test_self_consistency(), and test_tree_state().

interior_nodes_with_coeffs()

static long interior_nodes_with_coeffs ( World &  world, const Function< double, D > &  f  )

static

number of nodes violating the reconstructed layout: coefficients live on the leaves only

References madness::f, madness::World::gop, madness::nonlinear_vector_solver(), and madness::WorldGopInterface::sum().

Referenced by test_tree_state().

main()

int main	(	int	argc,
		char **	argv
	)

References madness::WorldGopInterface::fence(), madness::finalize(), madness::World::gop, madness::initialize(), make_pairs(), madness::nonlinear_vector_solver(), 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::startup(), test_dot(), test_exact(), test_screening_accuracy(), test_self_consistency(), test_tree_state(), and THRESH_REF.

make_pairs()

static std::vector< operand_pair > make_pairs ( World &  world )

static

coincident Gaussians, separated Gaussians (where the screening actually fires, as it does for distant localized orbitals), and a Slater cusp

References a, madness::nonlinear_vector_solver(), and madness::project().

Referenced by main().

project()

static Function< double, D > project ( World &  world, const std::shared_ptr< FunctionFunctorInterface< double, D > > &  functor  )

static

References madness::f, madness::nonlinear_vector_solver(), and madness::Function< T, NDIM >::truncate().

test_dot()

int test_dot	(	World &	world,
		std::vector< operand_pair > &	pairs
	)

T5: dot routes through the screened kernel; check it against the analytic sum.

References a, b, C_MAX, madness::test_output::checkpoint(), madness::copy(), madness::dot(), madness::test_output::end(), EXACT_FLOOR, madness::f, fmt_tol(), madness::g, madness::nonlinear_vector_solver(), madness::norm2(), q(), madness::World::rank(), and madness::test_output::set_do_print().

Referenced by main().

test_exact()

int test_exact	(	World &	world,
		std::vector< operand_pair > &	pairs
	)

T1: the exact path reproduces the analytic product.

References madness::test_output::checkpoint(), madness::test_output::end(), EXACT_FLOOR, madness::mul_sparse(), madness::nonlinear_vector_solver(), madness::norm2(), p(), q(), madness::World::rank(), and madness::test_output::set_do_print().

Referenced by main().

test_screening_accuracy()

int test_screening_accuracy	(	World &	world,
		std::vector< operand_pair > &	pairs
	)

T3: the screening error over a tol ladder, against the analytic product.

The bounds are measured, not derived: err ~ tol^p with p short of 1, and tree quantization (adjacent tol yielding the same tree) leaves err flat and inflates err/tol by up to a decade. Hence a loose C_MAX plus two tighter statements – err falls monotonically with tol, and its decay exponent does not collapse.

References C_MAX, madness::test_output::checkpoint(), madness::test_output::end(), madness::mul_sparse(), madness::nonlinear_vector_solver(), madness::norm2(), p(), P_MIN, q(), madness::World::rank(), and madness::test_output::set_do_print().

Referenced by main().

test_self_consistency()

int test_self_consistency	(	World &	world,
		std::vector< operand_pair > &	pairs
	)

T4: screened and exact multiplication agree to within tol, no analytic reference needed

References C_MAX, madness::test_output::checkpoint(), madness::test_output::end(), exact, fmt_tol(), madness::mul_sparse(), madness::nonlinear_vector_solver(), madness::norm2(), p(), q(), madness::World::rank(), and madness::test_output::set_do_print().

Referenced by main().

test_tree_state()

int test_tree_state	(	World &	world,
		std::vector< operand_pair > &	pairs
	)

T2: the result is a reconstructed tree, both scalar and vector entry points.

References madness::test_output::checkpoint(), madness::test_output::end(), madness::WorldGopInterface::fence(), fmt_tol(), madness::get_tree_state(), madness::World::gop, interior_nodes_with_coeffs(), L, madness::mul_sparse(), madness::nonlinear_vector_solver(), p(), q(), madness::World::rank(), madness::reconstructed, madness::test_output::set_do_print(), and v.

Referenced by main().

Variable Documentation

C_MAX

const double C_MAX = 100.0

static

err <= C_MAX*tol; measured max 34

Bounds on the screening error over the tol ladder, all measured, see the header of test_screening_accuracy.

Referenced by test_dot(), test_screening_accuracy(), and test_self_consistency().

D

const std::size_t D = 3

static

Referenced by Gauss::operator()().

EXACT_FLOOR

const double EXACT_FLOOR = 1.e-7

static

Error floor of the exact path (tol=0): the product of two order-k polynomials is not representable at order k, and multiplication does not autorefine. Measured max 2.3e-8 over the pairs below.

Referenced by test_dot(), and test_exact().

P_MIN

const double P_MIN = 0.4

static

err ~ tol^p; measured p = 0.58 .. 0.75

Referenced by test_screening_accuracy().

THRESH_REF

const double THRESH_REF = 1.e-9

static

projection threshold of the reference

Referenced by main().