RadialProjection Namespace Reference

Classes
class	RadialProjector
	RadialProjector is for projecting a function who has seperatable radial and angular parts: f(r) = f(|r|) * Ylm(theta, phi) onto planewave basis. More...

Functions
void	_mask_func (std::vector< double > &mask)
	get the mask function for SBFFT
void	_do_mask_on_radial (const int nr1, const double *r, const double *in, const int nr2, const double *mask, double *out)
	do operation w(r)/m(r) on a radial function. The cutoff radius of w(r) is smaller than the cutoff radius of m(r). The m(r) has been rescaled so that r ranges from 0 to 1.

Function Documentation

_do_mask_on_radial()

void RadialProjection::_do_mask_on_radial	(	const int	nr1,
		const double *	r,
		const double *	in,
		const int	nr2,
		const double *	mask,
		double *	out
	)

do operation w(r)/m(r) on a radial function. The cutoff radius of w(r) is smaller than the cutoff radius of m(r). The m(r) has been rescaled so that r ranges from 0 to 1.

Parameters

nr1	number of grid points of function to operate
r	grid points of function to operate
in	function to operate
nr2	number of grid points of mask function
mask	mask function
out	output value

_mask_func()

void RadialProjection::_mask_func

(

std::vector< double > &

mask

)

get the mask function for SBFFT

====================================================================================

                 Small box Fast-Fourier-Transform (SBFFT)

==================================================================================== Small box FFT is a technique for quickly intergrating real-space localized functions , or say perform FFT in a small box defined by a "mask function" with relatively low time complexity, will be out-performing in system where number of atoms are larger than ten. For details please refer to the work: Mask-function real-space implementations of nonlocal pseudopotentials by Wang, L.-W., PHYSICAL REVIEW B, VOLUME64,201107(R)

Following are the brief technical review of this technique. Given the function to be transformed w(r):

1. Generate the q-grid in range |q| < 2qmax - qc, in which the qmax is the one defined by ecutrho, and qc is the cutoff defined by ecutwfc.
2. With mask function m(r) generated, make division of w(r) by m(r). The real space cutoff (or the radius that w(r) vanishes), r0, must be smaller than the cutoff of m(r) to ensure the convergence of the division. Denote wm(r) = w(r)/m(r).
3. Make FT on wm(r) to get wm(q)
4. Make inverse FT with only the q-grid in range |q| < 2qmax - qc to get the wm'(r).
5. Perform real-space integration on function w'(r)*m(r)*exp(iqr).

Parameters

mask	mask function

Here is the caller graph for this function: