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A package for uncertainty propagation

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Measurements are precise only up to a particular uncertainty. Such measurement results are thus called uncertain quantities. When performing calculations with uncertain quantities, the uncertainties of the results depend on the uncertainties of the operands involved. The quantification of uncertainties resulting from a mathematical operation involving uncertain operands is called uncertainty propagation. From a programmer’s point of view, uncertainties might be associated with the respective nominal values, such that the propagation of uncertainties happens automatically, and existing algorithms can be re-used with the uncertain quantities as arguments. Here I am proposing a Python package to define uncertain operands, to carry out calculations using such operands with uncertainty propagation, and to provide string representations of uncertain quantities involved. Complex numbers can be used to define uncertain quantities; for such complex-valued uncertainties no net uncertainty can be calculated. The objects holding uncertain values have array properties, though scalar arrays can be used; elements of an uncertain array behave as if they were uncertain quantities on their own. When requesting a string representation of an uncertain quantity, the typeset result depends on the number of standard deviations to use and on the chosen precision, given by the number of digits with respect to the uncertainty. Furthermore, when typesetting multidimensional arrays with uncertainty, the decimal fractions are aligned to improve readability of the results. upy uses algorithmic differentiation (also known as automatic differentation) to track uncertainties through the operations. Uncertain values might be used in calculations together with other uncertain values as well as with any numeric Python or numpy objects. A range of mathematical functions is supported. upy provides several syntactic conventions appropriate to the subject. For instance, defining uncertain quantities is possible by writing:

uvalue = nominal +- u(uncertainty)

where u is a function provided by upy. Uncertain values constructed in this way will be independent of each other with respect to their uncertainties; upy will keep track of the correlations arising from combination of uncertain quantities in mathematical operations. All functionality is suited both for use in the interactive Python shell as well as in programs for numerical analysis.

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