sample_photon_flux¶

sherpa.astro.ui.sample_photon_flux(lo=None, hi=None, id=None, num=1, scales=None, correlated=False, numcores=None, bkg_id=None, model=None, otherids=())

Return the photon flux distribution of a model.

For each iteration, draw the parameter values of the model from a normal distribution, evaluate the model, and sum the model over the given range (the flux). The return array contains the flux and parameter values for each iteration. The units for the flux are as returned by calc_photon_flux.

Changed in version 4.12.2: The model and otherids parameters were added.

Parameters
• lo (number, optional) – The lower limit to use when summing up the signal. If not given then the lower value of the data grid is used.

• hi (optional) – The upper limit to use when summing up the signal. If not given then the upper value of the data grid is used.

• id (int or string, optional) – The identifier of the data set to use. If None, the default value, then all datasets with associated models are used to calculate the errors and the model evaluation is done using the default dataset.

• num (int, optional) – The number of samples to create. The default is 1.

• scales (array, optional) – The scales used to define the normal distributions for the parameters. The size and shape of the array depends on the number of free parameters in the fit (n) and the value of the correlated parameter. When the parameter is True, scales must be given the covariance matrix for the free parameters (a n by n matrix that matches the parameter ordering used by Sherpa). For un-correlated parameters the covariance matrix can be used, or a one-dimensional array of n elements can be used, giving the width (specified as the sigma value of a normal distribution) for each parameter (e.g. the square root of the diagonal elements of the covariance matrix). If the scales parameter is not given then the covariance matrix is evaluated for the current model and best-fit parameters.

• correlated (bool, optional) – Should the correlation between the parameters be included when sampling the parameters? If not, then each parameter is sampled from independent distributions. In both cases a normal distribution is used.

• numcores (optional) – The number of CPU cores to use. The default is to use all the cores on the machine.

• bkg_id (int or string, optional) – The identifier of the background component to use. This should only be set when the line to be measured is in the background model.

• model (model, optional) – The model to integrate. If left as None then the source model for the dataset will be used. This can be used to calculate the unabsorbed flux, as shown in the examples. The model must be part of the source expression.

• otherids (sequence of integer and string ids, optional) – The list of other datasets that should be included when calculating the errors to draw values from.

Returns

The return array has the shape (num, N+1), where N is the number of free parameters in the fit and num is the num parameter. The rows of this array contain the flux value, as calculated by calc_photon_flux, followed by the values of the thawed parameters used for that iteration. The order of the parameters matches the data returned by get_fit_results.

Return type

vals

calc_photon_flux()

Integrate the unconvolved source model over a pass band.

calc_energy_flux()

Integrate the unconvolved source model over a pass band.

covar()

Estimate the confidence intervals using the confidence method.

plot_cdf()

Plot the cumulative density function of an array.

plot_pdf()

Plot the probability density function of an array.

plot_energy_flux()

Display the energy flux distribution.

plot_photon_flux()

Display the photon flux distribution.

plot_trace()

Create a trace plot of row number versus value.

sample_energy_flux()

Return the energy flux distribution of a model.

sample_flux()

Return the flux distribution of a model.

Notes

There are two ways to use this function to calculate fluxes from multiple sources. The first is to leave the id argument as None, in which case all available datasets will be used. Alternatively, the id and otherids arguments can be set to list the exact datasets to use, such as id=1, otherids=(2,3,4).

The returned value contains all free parameters in the fit, even if they are not included in the model argument (e.g. when calculating an unabsorbed flux).

Examples

Calculate the photon flux distribution for the range 0.5 to 7, and plot up the resulting flux distribution (as a cumulative distribution):

>>> vals = sample_photon_flux(0.5, 7, num=1000)
>>> plot_cdf(vals[:, 0], name='flux')


Repeat the above, but allowing the parameters to be correlated, and then calculate the 5, 50, and 95 percent quantiles of the photon flux distribution:

>>> cvals = sample_photon_flux(0.5, 7, num=1000, correlated=True)
>>> np.percentile(cvals[:, 0], [5, 50, 95])


The photon flux of a component (or sub-set of components) can be calculated using the model argument. For the following case, an absorbed power-law was used to fit the data - xsphabs.gal * powerlaw.pl - and then the flux of just the power-law component is calculated. Note that the returned array has columns ‘flux’, ‘gal.nh’, ‘pl.gamma’, and ‘pl.ampl’ (that is flux and then the free parameters in the full model).

>>> vals = sample_photon_flux(0.5, 7, model=pl, num=1000, correlated=True)


Calculate the 2-10 keV flux for the pl model using a joint fit to the datasets 1, 2, 3, and 4:

>>> vals = sample_photon_flux(2, 10, model=pl, id=1, otherids=(2,3,4),
...                           num=1000)


Use the given parameter errors for sampling the parameter distribution. The fit must have three free parameters, and each parameter is sampled independently (in this case parerrs gives the sigma values for each parameter):

>>> parerrs = [0.25, 1.22, 1.04e-4]
>>> vals = sample_photon_flux(2, 10, num=5000, scales=parerrs)


In this case the parameter errors are taken from the covariance analysis, using the parmaxes field since these are positive.

>>> covar()
>>> parerrs = get_covar_results().parmaxes
>>> vals = sample_photon_flux(0.5, 2, num=1000, scales=parerrs)


Run covariance to estimate the parameter errors and then extract the covariance matrix from the results (as the cmat variable). This matrix is then used to define the parameter widths - including correlated terms - in the flux sampling, after being increased by ten percent. This is used to calculate both the absorbed (vals1) and unabsorbed (vals2) fluxes. Both arrays have columns: flux, gal.nh, pl.gamma, and pl.ampl.

>>> set_source(xsphabs.gal * powlaw1d.pl)
>>> fit()
>>> covar()
>>> cmat = get_covar_results().extra_output
>>> vals1 = sample_photon_flux(2, 10, num=5000, correlated=True,
...                            scales=1.1 * cmat)
>>> vals2 = sample_photon_flux(2, 10, num=5000, correlated=True,
...                            model=pl, scales=1.1 * cmat)


Calculate the flux and error distribution using fits to all datasets:

>>> set_source(xsphabs.gal * xsapec.clus)
>>> set_source(2, gal * clus)
>>> set_source(3, gal * clus)
... fit the data
>>> vals = sample_photon_flux(0.5, 10, model=clus, num=10000)


Calculate the flux and error distribution using fits to an explicit set of datasets (in this case datasets 1 and 2):

>>> vals = sample_photon_flux(0.5, 10, id=1, otherids=[2],
...                           model=clus, num=10000)