pyuncertainnumber.pba.aggregation¶

Functions¶

`envelope`(...)	calculates the envelope of constructs only
`imposition`(...)	Returns the imposition/intersection of the list of p-boxes
`stochastic_mixture`(*l_uns[, weights])	it could work for either Pbox, distribution, DS structure or Intervals
`stacking`(→ pyuncertainnumber.pba.pbox_abc.Pbox)	stochastic mixture operation of Intervals with probability masses
`mixture_pbox`(→ pyuncertainnumber.pba.pbox_abc.Pbox)
`mixture_ds`(→ pyuncertainnumber.pba.dss.DempsterShafer)	mixture operation for DS structure
`env_samples`(data[, output_type, ecdf_choice])	nonparametric envelope function directly from data samples
`env_ecdf_sep`(*ecdfs[, output_type, ecdf_choice])	nonparametric envelope function for separate empirical CDFs
`env_am`(→ numpy.ndarray)	bespoke function used for am metric case
`env_pbox_am`(→ numpy.ndarray)	bespoke function used for am metric case

Module Contents¶

pyuncertainnumber.pba.aggregation.envelope(*l_uns: pyuncertainnumber.pba.pbox_abc.Pbox | pyuncertainnumber.pba.dss.DempsterShafer | numbers.Number | pyuncertainnumber.pba.intervals.Interval | pyuncertainnumber.pba.distributions.Distribution | pyuncertainnumber.characterisation.uncertainNumber.UncertainNumber, output_type='pbox') → pyuncertainnumber.pba.pbox_abc.Staircase | pyuncertainnumber.characterisation.uncertainNumber.UncertainNumber¶

calculates the envelope of constructs only

Parameters:

l_uns (list) – the components, constructs and uncertain numbers, on which the envelope operation applied on.
output_type (str) – {‘pbox’ or ‘uncertain_number’ or ‘un’} - default is pbox

Returns:

the envelope of the given arguments, either a p-box or an interval.

Example

>>> from pyuncertainnumber import envelope
>>> a = pba.normal(3, 1)
>>> b = pba.uniform(5, 8)
>>> c = pba.normal(13, 2)
>>> t = envelope(a, b, c, output_type='pbox') # or output_type='uncertain_number'

pyuncertainnumber.pba.aggregation.imposition(*l_uns: pyuncertainnumber.pba.pbox_abc.Pbox | pyuncertainnumber.pba.dss.DempsterShafer | numbers.Number | pyuncertainnumber.pba.intervals.Interval | pyuncertainnumber.pba.distributions.Distribution | pyuncertainnumber.characterisation.uncertainNumber.UncertainNumber, output_type='pbox') → pyuncertainnumber.pba.pbox_abc.Staircase | pyuncertainnumber.characterisation.uncertainNumber.UncertainNumber¶

Returns the imposition/intersection of the list of p-boxes

Parameters:

l_uns (list) – a list of constructs or UN objects to be mixed
output_type (str) – {‘pbox’ or ‘uncertain_number’ or ‘un’} - default is pbox

Returns:

Pbox or UncertainNumber

Example

>>> import pyuncertainnumber as pun
>>> from pyuncertainnumber import pba
>>> a = pba.normal([3, 7], 1)
>>> b = pba.uniform([3,5], [6,9])
>>> i = pun.imposition(a, b)

pyuncertainnumber.pba.aggregation.stochastic_mixture(*l_uns: pyuncertainnumber.pba.pbox_abc.Pbox | pyuncertainnumber.pba.dss.DempsterShafer | numbers.Number | pyuncertainnumber.pba.intervals.Interval | pyuncertainnumber.pba.distributions.Distribution | pyuncertainnumber.characterisation.uncertainNumber.UncertainNumber, weights=None)¶

it could work for either Pbox, distribution, DS structure or Intervals

Parameters:

l_uns (-) – list of constructs or uncertain numbers
weights (-) – list of weights

Example

>>> import pyuncertainnumber as pun
>>> p = pun.stochastic_mixture([[1,3], [2,4]])

pyuncertainnumber.pba.aggregation.stacking(vec_interval: pyuncertainnumber.pba.intervals.Interval | list[pyuncertainnumber.pba.intervals.Interval], *, weights=None, display=False, ax=None, return_type='pbox', **kwargs) → pyuncertainnumber.pba.pbox_abc.Pbox¶

stochastic mixture operation of Intervals with probability masses

Parameters:

vec_interval (-) – list of Intervals or a vectorised Interval
weights (-) – list of weights
display (-) – boolean for plotting
return_type (-) – {‘pbox’ or ‘ds’ or ‘bounds’}

Returns:

by default a p-box but can return the left and right bound F in eCDF_bundlebounds.

Note

For intervals specifically.
it takes a list of intervals or a single vectorised interval, which is

a different signature compared to the other aggregation functions. - together the interval and masses, it can be deemed that all the inputs required is jointly a DS structure

Example

>>> stacking([[1,3], [2,4]], weights=[0.5, 0.5], display=True)

pyuncertainnumber.pba.aggregation.mixture_pbox(*l_pboxes, weights=None, display=False) → pyuncertainnumber.pba.pbox_abc.Pbox¶

pyuncertainnumber.pba.aggregation.mixture_ds(*l_ds, display=False) → pyuncertainnumber.pba.dss.DempsterShafer¶: mixture operation for DS structure

pyuncertainnumber.pba.aggregation.env_samples(data: numpy.typing.ArrayLike, output_type='pbox', ecdf_choice='canonical')¶

nonparametric envelope function directly from data samples

Parameters:

data (ArrayLike) – Each row represents a distribution, on which the envelope operation applied.
output_type (str) – {‘pbox’ or ‘cdf’} default is pbox cdf is the CDF bundle
ecdf_choice (str) – {‘canonical’ or ‘staircase’}

Note

envelope on a set of empirical CDFs

pyuncertainnumber.pba.aggregation.env_ecdf_sep(*ecdfs, output_type='pbox', ecdf_choice='canonical')¶: nonparametric envelope function for separate empirical CDFs

pyuncertainnumber.pba.aggregation.env_am(n_pars: numpy.typing.ArrayLike) → numpy.ndarray¶

bespoke function used for am metric case

Parameters:: n_pars (ArrayLike) – (n_sam, 2) of tuple (mu, sigma) which may be a tensor

pyuncertainnumber.pba.aggregation.env_pbox_am(n_mean: numpy.typing.ArrayLike, n_std: numpy.typing.ArrayLike) → numpy.ndarray¶

bespoke function used for am metric case

Parameters:

n_mean (ArrayLike) – (n_sam,) of mean values which may be a tensor
n_std (ArrayLike) – (n_sam,) of standard deviation values which may be a tensor