    Integrate a model across each bin (one dimensional).

integrate1d

Numerically integrate a one-dimensional model across each bin of a "histogram" dataset - that is one with low and high edges for each bin. The model to be integrated is supplied as an input to this model and any attribute changes must be made before this.

>>> create_model_component("integrate1d", "mdl")
>>> print(mdl)

Create a component of the integrate1d model and display its default parameters. The output is:

mdl Param Type Value Min Max Units ----- ---- ----- --- --- ----- mdl.epsabs frozen 2.22045e-16 -3.40282e+38 3.40282e+38 mdl.epsrel frozen 0 -3.40282e+38 3.40282e+38 mdl.maxeval frozen 10000 -3.40282e+38 3.40282e+38

The Integrate1D model lets you use a one-dimensional model which can only be evaluated at a point in a case where the dataset has a low and high edge for the independent axis - such as a Data1DInt object. The Scale1D model is used as an example of a model which only evaluates at a point (as it always returns the scale value), but in actual code you should use the Const1D model rather than apply Integrate1D to Scale1D. The evaluation of the `smdl`

instance returns the `c0` parameter value (set to 10) at each point, whereas the `mdl` instance integrates this across each bin, and so returning the bin width times `c0` for each bin. Note that the tolerance for the integration:

was changed from the default (tolerance for 64-bit float) to the 32-bit float tolerance (to avoid a warning message when evaluating mdl);
and must be changed before being applied to the model to integrate (smdl) in this case.
>>> import numpy as np >>> from sherpa.models.basic import Scale1D, Integrate1D >>> xlo, xhi = [2, 5, 8], [4, 8, 12] >>> imdl = Integrate1D(name='imdl') >>> imdl.epsabs = np.finfo(np.float32).eps >>> smdl = Scale1D(name='smdl') >>> mdl = imdl(smdl) >>> smdl.c0 = 10 >>> print(mdl) integrate1d(smdl) Param Type Value Min Max Units ----- ---- ----- --- --- ----- smdl.c0 thawed 10 -3.40282e+38 3.40282e+38 >>> print(smdl(xlo, xhi)) [10. 10. 10.] >>> print(mdl(xlo, xhi)) [20. 30. 40.]

ATTRIBUTES

The attributes for this object are:

Attribute
Definition
epsabs
The maximum absolute difference allowed when integrating the model. This parameter is always frozen.
epsrel
The maximum relative difference allowed when integrating the model. This parameter is always frozen.
maxeval
The maximum number of iterations allowed per bin. This parameter is always frozen.

Notes

If `imdl` is an instance of `Integrate1D` and `omdl` the model to integrate, then `imdl(omdl)` creates the integrated form. Note that changes to the `Integrate1D` parameters - such as `epsabs` - must be made before creating this integrated form. For example, to change the absolute tolerance to a value appropriate for 32-bit floats:

>>> import numpy as np >>> omdl = Polynom1D() # note: this class already supports integration >>> imdl = Integrate1D(name='imdl') >>> imdl.epsabs = np.finfo(np.float32).eps >>> mdl = imdl(omdl)

See the bugs pages on the Sherpa website for an up-to-date listing of known bugs.

December 2023