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 |
AFWHM |
✓ | ✓ | 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 |
FWHM1FWHM2 |
✓ | ✓ | 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)