Synopsis
One-dimensional normalized beta model function.
Syntax
normbeta1d
Description
This is the same model as the beta1d model but with a different slope parameter and normalisation.
Example
>>> create_model_component("normbeta1d", "mdl")
>>> print(mdl)Create a component of the normbeta1d model and display its default parameters. The output is:
mdl Param Type Value Min Max Units ----- ---- ----- --- --- ----- mdl.pos thawed 0 -3.40282e+38 3.40282e+38 mdl.width thawed 1 1.17549e-38 3.40282e+38 mdl.index thawed 2.5 0.5 1000 mdl.ampl thawed 1 0 3.40282e+38
ATTRIBUTES
The attributes for this object are:
| Attribute | Definition |
|---|---|
| pos | The center of the line. |
| w | The line width. |
| alpha | The slope of the profile at large radii. |
| ampl | The amplitude refers to the integral of the model. |
Notes
The functional form of the model for points is:
f(x) = A * (1 + ((x - pos) / w)^2)^(-alpha) A = ampl / integral f(x) dx
The grid version is evaluated by numerically intgerating the function over each bin using a non-adaptive Gauss-Kronrod scheme suited for smooth functions [1] , falling over to a simple trapezoid scheme if this fails.
References
- [1] https://www.gnu.org/software/gsl/manual/html_node/QNG-non_002dadaptive-Gauss_002dKronrod-integration.html
Bugs
See the bugs pages on the Sherpa website for an up-to-date listing of known bugs.