Defines an expression to be used as a kernel in 1D source model convolution.
sherpa> KERNEL [<dataset range> | ALLSETS [ID]] = <modelExpr>
<dataset range> = # (or more generally #:#,#:#, etc.) such that #
specifies a dataset number and #:# represents an inclusive range of
datasets; one may specify multiple inclusive ranges by separating them
with commas. The default dataset is dataset 1.
The model expression,
<modelExpr>,
is an algebraic combination of one or more of the following elements:
{<sherpa_modelname> | <sherpa_modelname>[modelname] |
<modelname> | <model_stack> | <nested_model>}
along with numerical values. The following operators are
recognized: + - * / ( ) { }.
See the CREATE command for further information.
Note that:
-
The documentation on
Sherpa Models contains a
summary list, and descriptions, of the models
that are available within Sherpa, which include models
from XSPEC, v. 11.3.
-
By default, if the model expression includes a model
component that has not previously been established, Sherpa
will prompt for the initial parameter values for that model component.
This prompting can be turned off using the
PARAMPROMPT OFF command.
To reset the kernel model stack, issue the command:
sherpa> KERNEL [<dataset range> | ALLSETS] =
The KERNEL model stack is used to convolve source model
expressions. As such, it has many uses, of which two are the following:
-
It can be used instead of an
INSTRUMENT model stack if the instrumental response
is representable by analytic functions (e.g., by a Gaussian).
-
It can be used to model circumstellar smearing of photon spectra; these
spectra may then be further smeared by the observing instrument.
Note that the parameter values of a KERNEL model stack are
frozen in fits; the kernel shape cannot be optimized.
The KERNEL model stack is evaluated on the same data grid
as the SOURCE model stack. In general, the data grid
will not be the correct grid for convolution; in the case of Gaussian
smoothing, the convolved spectrum may exhibit,
e.g., spectral lines that are
both dilated and translated. To prevent translation, the
user must set an origin for the convolution kernel using the command:
sherpa> KERNEL.ORIGIN [<dataset range> | ALLSETS] = <coordinate>
The example below will help illustrate this point.
Define SOURCE and KERNEL model stacks;
define the origin of the convolution kernel; and fit:
sherpa> SOURCE = GAUSS[modela]
modela.fwhm parameter value [19.3451]
modela.pos parameter value [804]
modela.ampl parameter value [126]
sherpa> KERNEL = NGAUSS[modelb]
modelb.fwhm parameter value [19.3451] 20
modelb.pos parameter value [804]
modelb.ampl parameter value [2594.62] 1:1:1
sherpa> KERNEL.ORIGIN = 804
sherpa> FIT
LVMQT: V2.0
LVMQT: initial statistic value = 578.346
LVMQT: final statistic value = 64.8424 at iteration 6
modela.fwhm 25.3426
modela.pos 807.882
modela.ampl 150.302
sherpa> KERNEL =
sherpa> FIT
LVMQT: V2.0
LVMQT: initial statistic value = 294.76
LVMQT: final statistic value = 64.3803 at iteration 7
modela.fwhm 32.3536
modela.pos 807.863
modela.ampl 117.826
The convolution kernel is a normalized Gaussian, with integrated area
set to 1 and full-width half-max of 20.
(For a normalized Gaussian, the integrated area equals the
amplitude.)
The kernel origin is set to be the centroid of the normalized Gaussian
(modelb.pos). Note the differences in the values of
modela.fwhm and modela.ampl between each fit.
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