One-Dimensional Functions

Analytic one-dimensional functions

Function available for use when, e.g., applying broadening to calculated structure factors, radial distribution functions etc.

Keyword Parameters FT1 DKN2 Description
None – ✓ ✓ No broadening function
Gaussian FWHM ✓ ✓ Un-normalised Gaussian with no prefactor $$ f(x) = \exp\left(-\frac{x^2}{2c^2}\right), c = \frac{\textrm{FWHM}}{2 \sqrt{2 \ln(2)}} $$
ScaledGaussian A
FWHM		 ✓ ✓ Un-normalised Gaussian with prefactor $$ f(x) = A\exp\left(-\frac{x^2}{2c^2}\right), c = \frac{\textrm{FWHM}}{2 \sqrt{2 \ln(2)}} $$
OmegaDependentGaussian FWHM ✓ ✓ Un-normalised Gaussian with variable FWHM and no prefactor - note that the parameter $\omega$ is set implicitly by the context using the broadening function $$ f(x) = \exp\left(-\frac{x^2}{2(c\omega)^2}\right), c = \frac{\textrm{FWHM}}{2 \sqrt{2 \ln(2)}} $$
GaussianC2 FWHM1
FWHM2		 ✓ ✓ Un-normalised Gaussian with constant and variable FWHM components and no prefactor - note that the parameter $\omega$ is set implicitly by the context using the broadening function $$ f(x) = \exp\left(-\frac{x^2}{2(c_1 + c_2\omega)^2}\right), c_n = \frac{\textrm{FWHM}_n}{2 \sqrt{2 \ln(2)}} $$

1Whether an analytic Fourier transform is defined

2Whether discrete kernel normalisation is defined (function sums to 1.0)

Last modified February 24, 2023: Docs 1.0 (#1221) (6f6c04b7e)