numcertain 0.3.0

A python & numpy data type for floating point numbers with quantified uncertainity.

This package provides a python and numpy data type (uncertain) which implements a floating point value with quantified uncertainity, allowing for forward uncertainity propagation of uncorrelated values.

PyPI	pip install numcertain
Source code	https://github.com/DiamondLightSource/numcertain
Documentation	https://DiamondLightSource.github.io/numcertain
Releases	https://github.com/DiamondLightSource/numcertain/releases

Aritmatic Examples

A brief example of arithmatic with the provided uncertain data type is presented below:

a = uncertain(42.0, 5.0)
b = uncertain(36, 12)

print(a + b)
print(a - b)
print(a * b)
print(a / b)

>> 78.0±13.0
>> 6.0±13.0
>> 1512.0±535.1784749034662
>> 1.1666666666666667±0.41294635409218067

A brief example of arithmatic with numpy arrays with the uncertain dtype is presented below:

a = array([uncertain(5.0, 3.0), uncertain(7.0, 6.0)])
b = array([uncertain(12.0, 4.0), uncertain(24.0, 8.0)])

print(a + b)
print(a - b)
print(a * b)
print(a / b)

>> [uncertain(17.0, 5.0) uncertain(31.0, 10.0)]
>> [uncertain(-7.0, 5.0) uncertain(-17.0, 10.0)]
>> [uncertain(60.0, 41.182520563948) uncertain(168.0, 154.50566332662373)]
>> [uncertain(0.4166666666666667, 0.2859897261385278) uncertain(0.2916666666666667, 0.268238998830944)]

Alternative Methods

In order to accurately propagate uncertainties of related values the derivative of the computed expectation must be known with respect to expectations it is comprised of. Automatic differentiation (autodiff) provides a mechanism for computing the derivative of arbitrary functions with respect to their components by exploiting the fact that all codes, regardless of complexity, are reduced to a sequence of primative arithmetic operations during execution for which the derivatives are known, by applying the chain rule the overall derivative can be determined automatically.

The python package Uncertainties provides a python data type which performs autodiff to propagate the corresponding uncertainity, unforunately due to Implementation as a python object the library is non-performant when used for array math.

Whilst Propagation of Uncertainty with autodiff, describes the use of autodiff provided by the python package JAX in propagating uncertainities for array math.

See https://DiamondLightSource.github.io/numcertain for more detailed documentation.