bessel_basis_test.cpp File Reference

#include <iostream>
#include <fstream>
#include <cmath>
#include <vector>
#include <map>
#include <unordered_map>
#include <string>
#include <cassert>
#include "../bessel_basis.h"
#include "../../source_cell/unitcell.h"
#include "../../source_estate/magnetism.h"
#include "gtest/gtest.h"
#include <mpi.h>

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Classes
class	TestBesselBasis

Functions
double	SimpsonIntegral (const std::vector< double > &x, const std::vector< double > &y)
	Simpson integral.
double	SphericalBessel (int l, double x)
	recursive definition of 1st-kind Spherical Bessel function of the first kind
std::vector< double >	CalculateSphericalBessel (int l, double q, const std::vector< double > &r)
	1st-kind Spherical Bessel function of the first kind mapped on realspace grid
std::vector< double >	GetSphericalBesselZeros (int order, int number)
	Get the first p zeros of 1st-kind, l-ordered Spherical Bessel function from a constant table.
std::vector< double >	GetqList (int order, int number, double rcut)
	Get mod of q vector of Spherical Bessel functions, all q satisfy when r=rcut, j_l(qr)=0.
std::vector< double >	operator* (const std::vector< double > &x, const std::vector< double > &y)
	overload operator * for vectors, elements will be multiplied one by one
std::vector< std::vector< std::vector< double > > >	GenerateTableOne (const bool smooth, const double sigma, const double ecutwfc, const double rcut, const int lmax, const double dr, const double dk)
	init_TableOne for unit test
std::unordered_map< std::string, double >	ReadinC4 (const std::string &FileName, const int &NumAtomType, const int &l, const int &NumChi, const int &NumBesselFunction)
	Improved version of source_io/bessel_basis::readin_C4 and allocate_C4 functions, for generating C4 matrix but now with a higher speed on accessing elements.
std::vector< std::vector< std::vector< std::vector< double > > > >	GenerateFaln (const std::string &FileName, const int &NumAtomType, const int &lmax, const int &NumChi, const int &NumBesselFunction, std::vector< std::vector< std::vector< double > > > vvv_d_TableOne)
	Generate F_{alpha, l, chi, k} matrix.
	TEST_F (TestBesselBasis, InitTest)
	TEST_F (TestBesselBasis, PolynomialInterpolation2Test)
	TEST_F (TestBesselBasis, PolynomialInterpolationTest)

Function Documentation

CalculateSphericalBessel()

std::vector< double > CalculateSphericalBessel	(	int	l,
		double	q,
		const std::vector< double > &	r
	)

1st-kind Spherical Bessel function of the first kind mapped on realspace grid

Attention

this function is a COMPLETE version, can replace the one in basic mathematical library

Parameters

l	order of 1st-kind spherical Bessel function
q	wave vector
r	realspace grid

Returns

function value on realspace grid

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GenerateFaln()

std::vector< std::vector< std::vector< std::vector< double > > > > GenerateFaln	(	const std::string &	FileName,
		const int &	NumAtomType,
		const int &	lmax,
		const int &	NumChi,
		const int &	NumBesselFunction,
		std::vector< std::vector< std::vector< double > > >	vvv_d_TableOne
	)

Generate F_{alpha, l, chi, k} matrix.

Parameters

FileName	name of external file where C4-stored file information is contained
NumAtomType	number of atom types
l	maximal angular momentum of localized orbitals
NumChi	number of contracted spherical bessel functions to fit one atomic orbital
NumBesselFunction	number of spherical bessel functions in one contracted spherical bessel function
vvv_d_TableOne	Integral table, has subscripts (l, q, k), whose element is the result of integral int{dr r^2 jle(r)*jlk(r)}. l runs over angular momentum, q runs over all spherical bessel functions, k runs over k points sampled controlled by ecutwfc and dk by sqrt(ecutwfc)/dk + 1 + 4.

Returns

F_{alpha, l, chi, k} matrix, whose element is the result of sum_{q}{C4(alpha, l, chi, q)*TableOne(l, q, k)}

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GenerateTableOne()

std::vector< std::vector< std::vector< double > > > GenerateTableOne	(	const bool	smooth,
		const double	sigma,
		const double	ecutwfc,
		const double	rcut,
		const int	lmax,
		const double	dr,
		const double	dk
	)

init_TableOne for unit test

Attention

this is a COMPLETE version of init_TableOne, can replace the one in source_io/bessel_basis.cpp

Parameters

smooth	whether to smooth the function (gaussian function)
sigma	stddev of gaussian function for smoothing
ecutwfc	control the number of Spheical Bessel functions
rcut	cutoff radius of Spherical Bessel functions, r>rcut, Spherical Bessel functions are zero
lmax	maximal angular momentum of Spherical Bessel functions
dr	grid spacing of r
dk	grid spacing of k

Returns

std::vector<std::vector<std::vector<double>>> TableOne[angular momentum][index of Spherical Bessel function][Arbitrary wave vector k]

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GetqList()

std::vector< double > GetqList	(	int	order,
		int	number,
		double	rcut
	)

Get mod of q vector of Spherical Bessel functions, all q satisfy when r=rcut, j_l(qr)=0.

first solve the equation j_l(x) = 0, therefore get the table (l, k) -> x, where l is the order of SBF and k is the k-th zero of j_l(x). Then let x = q*rcut, therefore q = x/rcut, return it.

Attention

this function itself is a COMPLETE version, while the function it called GetSphericalBesselZeros may be INCOMPLETE, due to limited support of numerical table.

Parameters

order	the angular momentum of Spherical Bessel functions
number	number of q to be returned
rcut	'cutoff radius' of Spherical Bessel functions. When r=rcut, Spherical Bessel functions are zero, and for r>rcut, they are zero as required by concept of constructing localized atomic orbital.

Returns

a vector of q, the q is from j_l(qr)

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GetSphericalBesselZeros()

std::vector< double > GetSphericalBesselZeros	(	int	order,
		int	number
	)

Get the first p zeros of 1st-kind, l-ordered Spherical Bessel function from a constant table.

Attention

this function is a INCOMPLETE version, due to limited support of numerical table.

Parameters

order	l, angular momentum
number	p, number of zeros needed

Returns

a vector of q, the q is from j_l(qr)

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operator*()

std::vector< double > operator*	(	const std::vector< double > &	x,
		const std::vector< double > &	y
	)

overload operator * for vectors, elements will be multiplied one by one

Parameters

x	one vector
y	another vector

Returns

vector after multiplication

ReadinC4()

std::unordered_map< std::string, double > ReadinC4	(	const std::string &	FileName,
		const int &	NumAtomType,
		const int &	l,
		const int &	NumChi,
		const int &	NumBesselFunction
	)

Improved version of source_io/bessel_basis::readin_C4 and allocate_C4 functions, for generating C4 matrix but now with a higher speed on accessing elements.

Attention

function will read in total number of chi-s both from file and from input, and assert that they are the same. It is also just a INCOMPLETE version, for a complete version, HTML parser library will be included and the other parameter, NumAtomType, will also be used for calibrating data.

Parameters

FileName	name of external file where C4-stored file information is contained
NumAtomType	number of atom types
l	maximal angular momentum of localized orbitals
NumChi	number of contracted spherical bessel functions to fit one atomic orbital
NumBesselFunction	number of spherical bessel functions in one contracted spherical bessel function

Returns

a map whose key is a string of "atomtype l chi q", and value is the corresponding C4 value

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SimpsonIntegral()

double SimpsonIntegral	(	const std::vector< double > &	x,
		const std::vector< double > &	y
	)

Simpson integral.

unit test for source_io/bessel_basis, not tested functions: readin_C4, allocate_C4

Attention

this function is a COMPLETE version, but there is no improvement in performance.

Parameters

x	variable stored in a vector
y	function value stored in a vector

Returns

integral value

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SphericalBessel()

double SphericalBessel	(	int	l,
		double	x
	)

recursive definition of 1st-kind Spherical Bessel function of the first kind

Attention

this function is a COMPLETE version, can replace the one in basic mathematical library

Parameters

l	order of 1st-kind spherical Bessel function
x	variable

Returns

value of 1st-kind spherical Bessel function

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TEST_F() [1/3]

TEST_F	(	TestBesselBasis	,
		InitTest
	)

TEST_F() [2/3]

TEST_F	(	TestBesselBasis	,
		PolynomialInterpolation2Test
	)

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TEST_F() [3/3]

TEST_F	(	TestBesselBasis	,
		PolynomialInterpolationTest
	)

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