#include <gromacs/math/include/gromacs/math/gausstransform.h>

Description

Provide result of Gaussian function evaluation on a one-dimensional lattice.

This class owns the result of the operation and provides a view on it.

The distance between lattice points is one. Unit length is normalized by the lattice spacing, thus spreading width and range are given as multiples of lattice points distances.

This works well as approximation to piece-wise integration of a Gaussian on a lattice, when $\sigma > 1$ . The maximal relative error to evaluating erf differences for $\sigma = 1$ is 0.01602.

Public Member Functions
	GaussianOn1DLattice (int numGridPointsForSpreadingHalfWidth, real sigma)
	Construct Gaussian spreader with spreading range and Gaussian width. More...

	GaussianOn1DLattice (const GaussianOn1DLattice &other)
	Copy constructor.

GaussianOn1DLattice &	operator= (const GaussianOn1DLattice &other)
	Copy assignment.

	GaussianOn1DLattice (GaussianOn1DLattice &&other) noexcept
	Move constructor.

GaussianOn1DLattice &	operator= (GaussianOn1DLattice &&other) noexcept
	Move assignment.

void	spread (double amplitude, real latticeOffset)
	Spreads weight onto grid points in one dimension. More...

ArrayRef< const float >	view ()
	Returns view on spread result.

Constructor & Destructor Documentation

gmx::GaussianOn1DLattice::GaussianOn1DLattice	(	int	numGridPointsForSpreadingHalfWidth,
		real	sigma
	)

Construct Gaussian spreader with spreading range and Gaussian width.

Spread weights are distributed over a non-periodic lattice of length 2*numGridPointsForSpreadingHalfWidth+1. The lattice comprises a center point and spreadDistance points to the left and to the right.

Note: There is a maximum spreading width

Parameters

[in]	numGridPointsForSpreadingHalfWidth	maximum distance in number of gridpoints from 0
[in]	sigma	Gaussian width.

Member Function Documentation

void gmx::GaussianOn1DLattice::spread	(	double	amplitude,
		real	latticeOffset
	)

Spreads weight onto grid points in one dimension.

       .            :            |            :            .
       o            o            o            o            o
                             O---|
                     latticeOffset

O - atom position o - lattice positions . : | spreading value at grid points.

Note: Highest numerical accuracy is achieved when the spreading with offset to the nearest lattice coordinated < 0.5

Spreading on lattice coordinate $x_i$

$f(x_i) = \frac{\mathrm{amplitude}}{\sigma\sqrt{2\pi}}\exp(-\frac{\mathrm{offset}-x_i^2}{2 \sigma ^2})$

Parameters

[in]	amplitude	of the Gaussian spread.
[in]	latticeOffset	The distance to the nearest grid point in lattice coordinates.

The documentation for this class was generated from the following files:

src/gromacs/math/include/gromacs/math/gausstransform.h
src/gromacs/math/gausstransform.cpp

Description

Public Member Functions

Constructor & Destructor Documentation

Member Function Documentation