pyuncertainnumber.pba.utils¶

Exceptions¶

NotIncreasingError

Common base class for all non-exit exceptions.

Classes¶

CustomEdgeRectHandler

Functions¶

`extend_ecdf`(cdf)	add zero and one to the ecdf
`sorting`(list1, list2)
`reweighting`(*masses)	reweight the masses to sum to 1
`uniform_reparameterisation`(a, b)	reparameterise the uniform distribution to a, b
`find_nearest`(array, value)	Find index/indices of nearest value(s) in array to each value.
`plot_intervals`(vec_interval[, ax])	plot the intervals in a vectorised form
`read_json`(file_name)
`is_increasing`(arr)	check if 'arr' is increasing
`condensation`(bound, number)	a joint implementation for condensation
`condensation_bounds`(bounds, number)	condense the bounds of number pbox
`condensation_bound`(bound, number)	condense the bounds of number pbox
`smooth_condensation`(bounds[, number])
`equi_selection`(arr, n)	draw n equidistant points from the array
`create_colored_edge_box`(x0, y0, width, height[, linewidth])
`expose_functions_as_public`(mapping, wrapper)	expose private functions as public APIs
`left_right_switch`(left, right)
`build_constraints_from_pbox_robust`(q_a, p_a, q_b, p_b, ...)	Returns x, L, U, n and also the envelopes F_L, F_U on x_grid.
`variance_bounds_via_lp`(q_a, p_a, q_b, p_b, x_grid[, ...])
`get_mean_var_from_ecdf`(q, p)	Numerically estimate the mean and var from ECDF data
`sample_ecdf_in_pbox`(q_a, p_a, q_b, p_b[, x_grid, n, ...])	Sample a random ECDF (quantile & probability vectors) lying inside the p-box
`area_between_ecdfs`(x_upper, p_upper, x_lower, p_lower)	Compute the area between two ECDFs defined by (x_upper, p_upper) and (x_lower, p_lower).
`_ecdf_value_on_left_of_intervals`(x, p, grid_left)	Right-continuous ECDF value used on [grid_left[k], grid_right[k]).

Module Contents¶

pyuncertainnumber.pba.utils.extend_ecdf(cdf)¶

add zero and one to the ecdf

Parameters:: CDF_bundle

pyuncertainnumber.pba.utils.sorting(list1, list2)¶

pyuncertainnumber.pba.utils.reweighting(*masses)¶: reweight the masses to sum to 1

pyuncertainnumber.pba.utils.uniform_reparameterisation(a, b)¶: reparameterise the uniform distribution to a, b

pyuncertainnumber.pba.utils.find_nearest(array, value)¶

Find index/indices of nearest value(s) in array to each value.

Efficient for both scalar and array inputs.

pyuncertainnumber.pba.utils.plot_intervals(vec_interval: list[pyuncertainnumber.pba.intervals.number.Interval], ax=None, **kwargs)¶: plot the intervals in a vectorised form :param vec_interval: vectorised interval objects

pyuncertainnumber.pba.utils.read_json(file_name)¶

pyuncertainnumber.pba.utils.is_increasing(arr)¶: check if ‘arr’ is increasing

exception pyuncertainnumber.pba.utils.NotIncreasingError¶

Bases: Exception

Common base class for all non-exit exceptions.

pyuncertainnumber.pba.utils.condensation(bound, number: int)¶

a joint implementation for condensation

Parameters:

number (int) – the number to be reduced
bound (array-like) – either the left or right bound to be reduced

Note

It will keep the first and last from the bound

pyuncertainnumber.pba.utils.condensation_bounds(bounds, number)¶

condense the bounds of number pbox

Parameters:

number (int) – the number to be reduced
bounds (list or tuple) – the left and right bound to be reduced

pyuncertainnumber.pba.utils.condensation_bound(bound, number)¶

condense the bounds of number pbox

Parameters:

number (int) – the number to be reduced
bound (array-like) – either the left or right bound to be reduced

pyuncertainnumber.pba.utils.smooth_condensation(bounds, number=200)¶

pyuncertainnumber.pba.utils.equi_selection(arr, n)¶: draw n equidistant points from the array

pyuncertainnumber.pba.utils.create_colored_edge_box(x0, y0, width, height, linewidth=1)¶

class pyuncertainnumber.pba.utils.CustomEdgeRectHandler¶

Bases: matplotlib.legend_handler.HandlerBase

create_artists(legend, orig_handle, xdescent, ydescent, width, height, fontsize, trans)¶

pyuncertainnumber.pba.utils.expose_functions_as_public(mapping, wrapper)¶

expose private functions as public APIs

Parameters:

mapping (dict) – a dictionary containing private function names mapped to public APIs
wrapper (callable) – a function that wraps the original functions (e.g., the decorator UNtoUN)

Note

the decorator which wraps the original function returning Pbox into returning UN, hence making the public UN API

pyuncertainnumber.pba.utils.left_right_switch(left, right)¶: Note

right quantile should be greater and equal than left quantile

pyuncertainnumber.pba.utils.build_constraints_from_pbox_robust(q_a, p_a, q_b, p_b, x_grid, n=None, eps=1e-12)¶: Returns x, L, U, n and also the envelopes F_L, F_U on x_grid. If F_L==F_U (degenerate p-box), we set L=U=round(n*F) exactly to avoid infeasibility.

pyuncertainnumber.pba.utils.variance_bounds_via_lp(q_a, p_a, q_b, p_b, x_grid, n=None, mu_grid=101)¶

pyuncertainnumber.pba.utils.get_mean_var_from_ecdf(q, p)¶

Numerically estimate the mean and var from ECDF data

Parameters:

q (array-like) – quantiles
p (array-like) – probabilities

Example

>>> # Given ECDF data an example
>>> q = [1, 2, 3, 4]
>>> p = [0.25, 0.5, 0.75, 1.0]
>>> mean, var = get_mean_var_from_ecdf(q, p)

pyuncertainnumber.pba.utils.sample_ecdf_in_pbox(q_a, p_a, q_b, p_b, x_grid=None, n=None, rng=None, eps=1e-12)¶

Sample a random ECDF (quantile & probability vectors) lying inside the p-box defined by lower envelope (q_a, p_a) and upper envelope (q_b, p_b).

Parameters:

q_a – arrays Lower (left) bounding quantile function sampled at probabilities p_a.
p_a – arrays Lower (left) bounding quantile function sampled at probabilities p_a.
q_b – arrays Upper (right) bounding quantile function sampled at probabilities p_b.
p_b – arrays Upper (right) bounding quantile function sampled at probabilities p_b.
x_grid – array or None Discrete support where ECDF masses are allowed to sit. If None, uses the union of q_a and q_b sorted and uniqued. You can also pass a custom grid (e.g., np.linspace(min(q_a), max(q_b), 200)).
n – int or None ECDF size (number of jumps). If None, defaults to len(p_a).
rng – numpy.random.Generator or None Random generator to control reproducibility.
eps – float Small tolerance to avoid rounding issues in DP bounds.

Returns

qndarray (length n): Quantile vector (nondecreasing), values taken from x_grid.
pndarray (length n): Probability vector for the ECDF: p[r] = (r+1)/n.

Note

Choose an x-grid (or let the function use the union of q_a and q_b). # x_grid = np.linspace(min(q_a), max(q_b), 200) # e.g., a uniform 200-point support

Example

>>> p = pba.normal([4, 6], 1)
>>> ecdf_q, ecdf_p = sample_ecdf_in_pbox(p.left, p.p_values, p.right, p.p_values)

pyuncertainnumber.pba.utils.area_between_ecdfs(x_upper, p_upper, x_lower, p_lower)¶

Compute the area between two ECDFs defined by (x_upper, p_upper) and (x_lower, p_lower).

Parameters:

x_upper – arrays defining the upper ECDF
p_upper – arrays defining the upper ECDF
x_lower – arrays defining the lower ECDF
p_lower – arrays defining the lower ECDF

pyuncertainnumber.pba.utils._ecdf_value_on_left_of_intervals(x, p, grid_left)¶: Right-continuous ECDF value used on [grid_left[k], grid_right[k]). For values below the first x, value is 0. For above the last x, value stays at p[-1].