pyuncertainnumber.pba.operation¶

Classes¶

`Vector`
`Matrix`
`iVector`	Independent Vector of Pboxes
`iMatrix`	Independent Matrix of Pboxes
`Vector_pbox`	Vector of Pboxes

Functions¶

`frechet_op`(x, y[, op])	Frechet operation on two pboxes
`naive_frechet_op`(x, y, op)	The real naive Frechet bounds implementation
`new_naive_frechet_op`(x, y, op[, n_sam])	this is a slow version
`perfect_op`(x, y[, op])	perfect operation on two pboxes
`opposite_op`(x, y[, op])	opposite operation on two pboxes
`independent_op`(x, y[, op])	independent operation on two pboxes
`copula_op`(→ pyuncertainnumber.pba.pbox_abc.Pbox)	Bivariate operation on two pboxes with a given copula
`copula_dss_op`(→ pyuncertainnumber.pba.pbox_abc.Pbox)	Bivariate operation on two DSS with a given copula
`C_func`(u, v, copula)
`copula_mass`(C_func, u, v[, eps])	Compute the discrete copula mass matrix p_ij from grids u, v on [0,1].
`positiveconv_pbox`(a, b[, op])	positive dependence (PQD) convolution of two pboxes
`new_vectorised_naive_frechet_op`(x, y, op)	independent operation on two pboxes
`vectorized_cartesian_op`(a, b, op)	vectorised cartesian operation for the bounds of pboxes
`isum`(l_p)	Sum of pboxes indepedently
`convert`(un)	Convert any input un into a Pbox object
`p_backcalc`(a, c, ops)	backcal for p-boxes
`adec`(a, c)	Additive deconvolution: returns b such that a + b ≈ c
`i_mul`(a, b)	bivariate independent multiplication of pboxes

Module Contents¶

pyuncertainnumber.pba.operation.frechet_op(x: pyuncertainnumber.pba.pbox_abc.Pbox, y: pyuncertainnumber.pba.pbox_abc.Pbox, op=operator.add)¶: Frechet operation on two pboxes

Note

this corresponds to the Frank, Nelson and Sklar Frechet bounds implementation

pyuncertainnumber.pba.operation.naive_frechet_op(x: pyuncertainnumber.pba.pbox_abc.Pbox, y: pyuncertainnumber.pba.pbox_abc.Pbox, op)¶

The real naive Frechet bounds implementation

Note

counterpart of naivefrechetpbox in pba.r

Parameters:

x (Pbox) – pboxes to be operated on
y (Pbox) – pboxes to be operated on
op (function) – arithemtic operator to be applied, e.g. operator.add

Returns:

left and right bounds of the pbox - Zu: lower bound of the pbox - Zd: upper bound of the pbox

Return type:

Zu, Zd (tuple)

Example

>>> from pyuncertainnumber import pba
>>> a = pba.normal([4,5], 1)
>>> b = pba.uniform([3,4], [7,8])
>>> left_bound, right_bound = pba.naive_frechet_op(a, b, operator.add)

pyuncertainnumber.pba.operation.new_naive_frechet_op(x: pyuncertainnumber.pba.pbox_abc.Pbox, y: pyuncertainnumber.pba.pbox_abc.Pbox, op, n_sam=Params.steps)¶: this is a slow version

pyuncertainnumber.pba.operation.perfect_op(x: pyuncertainnumber.pba.pbox_abc.Pbox, y: pyuncertainnumber.pba.pbox_abc.Pbox, op=operator.add)¶: perfect operation on two pboxes

Note

defined for addition and multiplication. Different for subtraction and division.

pyuncertainnumber.pba.operation.opposite_op(x: pyuncertainnumber.pba.pbox_abc.Pbox, y: pyuncertainnumber.pba.pbox_abc.Pbox, op=operator.add)¶: opposite operation on two pboxes

Note

defined for addition and multiplication. Different for subtraction and division.

pyuncertainnumber.pba.operation.independent_op(x: pyuncertainnumber.pba.pbox_abc.Pbox, y: pyuncertainnumber.pba.pbox_abc.Pbox, op=operator.add)¶: independent operation on two pboxes

Note

defined for addition and multiplication. Different for subtraction and division.

pyuncertainnumber.pba.operation.copula_op(x: pyuncertainnumber.pba.pbox_abc.Pbox, y: pyuncertainnumber.pba.pbox_abc.Pbox, dependency: pyuncertainnumber.pba.dependency.Dependency, op=operator.add) → pyuncertainnumber.pba.pbox_abc.Pbox¶

Bivariate operation on two pboxes with a given copula

Returns:: resulting pbox after applying the operation with the copula
Return type:: Pbox

pyuncertainnumber.pba.operation.copula_dss_op(x: pyuncertainnumber.pba.dss.DempsterShafer, y: pyuncertainnumber.pba.dss.DempsterShafer, dependency, op=operator.add) → pyuncertainnumber.pba.pbox_abc.Pbox¶

Bivariate operation on two DSS with a given copula

Note

This is a temporary function until DSS is fully integrated with Pbox operations

Returns:: resulting DSS after applying the operation with the copula
Return type:: Pbox

pyuncertainnumber.pba.operation.C_func(u, v, copula)¶

pyuncertainnumber.pba.operation.copula_mass(C_func, u, v, eps=1e-12)¶: Compute the discrete copula mass matrix p_ij from grids u, v on [0,1]. C: callable taking arrays (same shape) and returning C(u,v) u, v: 1D arrays (ascending) of points in [0,1] eps: small value to avoid ±inf when calling C near 0 or 1

pyuncertainnumber.pba.operation.positiveconv_pbox(a, b, op=operator.add)¶

positive dependence (PQD) convolution of two pboxes

Example

>>> X = pba.uniform(1, 24)
>>> Y = X
>>> p_ = positiveconv_pbox(X, Y)

pyuncertainnumber.pba.operation.new_vectorised_naive_frechet_op(x: pyuncertainnumber.pba.pbox_abc.Pbox, y: pyuncertainnumber.pba.pbox_abc.Pbox, op)¶: independent operation on two pboxes

Note

defined for addition and multiplication. Different for subtraction and division.

pyuncertainnumber.pba.operation.vectorized_cartesian_op(a, b, op)¶

vectorised cartesian operation for the bounds of pboxes

Note

used on self.left, other.left

Example

>>> nleft = vectorized_cartesian_op(self.left, other.left, operator.add)
>>> nright = vectorized_cartesian_op(self.right, other.right, operator.add)

pyuncertainnumber.pba.operation.isum(l_p)¶

Sum of pboxes indepedently

Parameters:: l_p (list) – list of Pbox objects

Note

Same signature with Python sum which takes a list of inputs

Tip

Python sum accomplishes sum of Frechet case.

pyuncertainnumber.pba.operation.convert(un)¶

Convert any input un into a Pbox object

Note

theorically ‘un’ can be {Interval, DempsterShafer, Distribution, float, int}

pyuncertainnumber.pba.operation.p_backcalc(a, c, ops)¶: backcal for p-boxes #! incorrect implementation :param a: probability box objects :type a: Pbox :param c: probability box objects :type c: Pbox :param ops: {‘additive_bcc’, ‘multiplicative_bcc’} whether additive or multiplicative :type ops: object

pyuncertainnumber.pba.operation.adec(a, c)¶: Additive deconvolution: returns b such that a + b ≈ c Assumes a, b, c are instances of RandomNbr.

Note

implmentation from Scott

pyuncertainnumber.pba.operation.i_mul(a, b)¶: bivariate independent multiplication of pboxes

class pyuncertainnumber.pba.operation.Vector(components)¶

components¶

__iter__()¶

__len__()¶

__repr__()¶

__getitem__(index)¶

__setitem__(index, value)¶

__add__(other)¶

__sub__(other)¶

__mul__(other)¶

__rmul__(other)¶

__truediv__(other)¶

__matmul__(other)¶

tanh()¶: Pbox tanh operation elemenwise

class pyuncertainnumber.pba.operation.Matrix(rows)¶

__getitem__(index)¶

__len__()¶

shape()¶

__repr__()¶

__setitem__(index, value)¶

__add__(other)¶

__sub__(other)¶

__mul__(other)¶

__rmul__(other)¶

__truediv__(other)¶

__matmul__(other)¶

tanh()¶

class pyuncertainnumber.pba.operation.iVector(components)¶

Bases: Vector

Independent Vector of Pboxes

__add__(other)¶

__matmul__(other)¶

class pyuncertainnumber.pba.operation.iMatrix(rows)¶

Bases: Matrix

Independent Matrix of Pboxes

__add__(other)¶

__matmul__(other)¶

class pyuncertainnumber.pba.operation.Vector_pbox(components)¶

Bases: Vector

Vector of Pboxes

__matmul__(other)¶