Integrate1D

class sherpa.models.basic.Integrate1D(name='integrate1d')[source] [edit on github]

Bases: RegriddableModel1D

Integrate a model across each bin (one dimensional).

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.

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)

Examples

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 Summary

cache

The maximum size of the cache.

lpars

Return any linked parameters.

ndim

A one-dimensional model.

pars

Return the parameters of the model.

thawedparhardmaxes

The hard maximum values for the thawed parameters.

thawedparhardmins

The hard minimum values for the thawed parameters.

thawedparmaxes

The maximum limits of the thawed parameters.

thawedparmins

The minimum limits of the thawed parameters.

thawedpars

The thawed parameters of the model.

Methods Summary

apply(outer, *otherargs, **otherkwargs)

cache_clear()

Clear the cache.

cache_status()

Display the cache status.

calc(p, *args, **kwargs)

Evaluate the model on a grid.

freeze()

Freeze any thawed parameters of the model.

get_center()

get_thawed_pars()

Return the thawed parameter objects.

guess(dep, *args, **kwargs)

Set an initial guess for the parameter values.

regrid(*args, **kwargs)

The class RegriddableModel1D allows the user to evaluate in the requested space then interpolate onto the data space.

reset()

Reset the parameter values.

set_center(*args, **kwargs)

startup([cache])

Called before a model may be evaluated multiple times.

teardown()

Called after a model may be evaluated multiple times.

thaw()

Thaw any frozen parameters of the model.

Attributes Documentation

cache = 5

The maximum size of the cache.

lpars

Return any linked parameters.

This only returns linked parameters that are not related to the model, and each parameter is not repeated.

New in version 4.16.1.

See also

pars

Examples

By default there are no linked parameters:

>>> from sherpa.models.basic import Gauss2D
>>> mdl = Gauss2D("mdl")
>>> len(mdl.pars)
6
>>> mdl.lpars
()

Force the model to have identical xpos and ypos parameters. Since the linked parameter value (mdl.xpos) is part of the model it is not included in lpars:

>>> mdl.ypos = mdl.xpos
>>> len(mdl.pars)
6
>>> mdl.lpars
()

Add a link to allow the sigma term to be fit rather than FWHM. Since the linked parameter - here from the Const1D model - is not a part of the model it is included in lpars:

>>> import numpy as np
>>> from sherpa.models.basic import Const1D
>>> sigma = Const1D("sigma")
>>> mdl.fwhm = 2 * np.sqrt(2 * np.log(2)) * sigma.c0
>>> len(mdl.pars)
6
>>> mdl.lpars
(<Parameter 'c0' of model 'sigma'>,)
ndim: int | None = 1

A one-dimensional model.

pars

Return the parameters of the model.

This does not include any linked parameters.

Changed in version 4.16.1: The pars field can no-longer be set directly. Individual elements can still be changed.

See also

lpars

thawedparhardmaxes

The hard maximum values for the thawed parameters.

The minimum and maximum range of the parameters can be changed with thawedparmins and thawedparmaxes but only within the range given by thawedparhardmins to thawparhardmaxes.

thawedparhardmins

The hard minimum values for the thawed parameters.

The minimum and maximum range of the parameters can be changed with thawedparmins and thawedparmaxes but only within the range given by thawedparhardmins to thawparhardmaxes.

thawedparmaxes

The maximum limits of the thawed parameters.

Get or set the maximum limits of the thawed parameters of the model as a list of numbers. If there are no thawed parameters then [] is used. The ordering matches that of the pars attribute.

See also

thawedpars, thawedarhardmaxes, thawedparmins

thawedparmins

The minimum limits of the thawed parameters.

Get or set the minimum limits of the thawed parameters of the model as a list of numbers. If there are no thawed parameters then [] is used. The ordering matches that of the pars attribute.

See also

thawedpars, thawedarhardmins, thawedparmaxes

thawedpars

The thawed parameters of the model.

Get or set the thawed parameters of the model as a list of numbers. If there are no thawed parameters then [] is used. The ordering matches that of the pars attribute.

Methods Documentation

apply(outer, *otherargs, **otherkwargs) [edit on github]
cache_clear() None [edit on github]

Clear the cache.

cache_status() None [edit on github]

Display the cache status.

Information on the cache - the number of “hits”, “misses”, and “requests” - is displayed at the INFO logging level.

Example

>>> pl.cache_status()
 powlaw1d.pl                size:    5  hits:   633  misses:   240  check=  873
calc(p: Sequence[SupportsFloat], *args, **kwargs) ndarray [edit on github]

Evaluate the model on a grid.

Parameters:
  • p (sequence of numbers) – The parameter values to use. The order matches the pars field.

  • *args – The model grid. The values can be scalar or arrays, and the number depends on the dimensionality of the model and whether it is being evaluated over an integrated grid or at a point (or points).

  • **kwargs – Any model-specific values that are not parameters.

freeze() None [edit on github]

Freeze any thawed parameters of the model.

get_center() [edit on github]
get_thawed_pars() list[Parameter] [edit on github]

Return the thawed parameter objects.

This includes linked parameters, which complicates the min/max settings, since the range on the components of a linked parameter does not match that of the original parameter, which is an issue when the limits are exceeded.

New in version 4.16.1.

guess(dep, *args, **kwargs) [edit on github]

Set an initial guess for the parameter values.

Attempt to set the parameter values, and ranges, for the model to match the data values. This is intended as a rough guess, so it is expected that the model is only evaluated a small number of times, if at all.

regrid(*args, **kwargs) [edit on github]

The class RegriddableModel1D allows the user to evaluate in the requested space then interpolate onto the data space. An optional argument ‘interp’ enables the user to change the interpolation method.

Examples

>>> import numpy as np
>>> from sherpa.models.basic import Box1D
>>> from sherpa.utils import linear_interp
>>> mybox = Box1D()
>>> request_space = np.arange(1, 10, 0.1)
>>> regrid_model = mybox.regrid(request_space, interp=linear_interp)
reset() None [edit on github]

Reset the parameter values.

Restores each parameter to the last value it was set to. This allows the parameters to be easily reset after a fit.

set_center(*args, **kwargs) [edit on github]
startup(cache: bool = False) None [edit on github]

Called before a model may be evaluated multiple times.

Parameters:

cache (bool, optional) – Should a cache be used when evaluating the models.

See also

teardown

teardown() None [edit on github]

Called after a model may be evaluated multiple times.

See also

startup

thaw() None [edit on github]

Thaw any frozen parameters of the model.

Those parameters that are marked as “always frozen” are skipped.