Sigma is a header-only C++ library for uncertainty propagation throughout mathematical operations on floating point values, inspired by uncertainties for Python and Measurements.jl for Julia.

Statement of Need

Scientific analysis, whether based on experiment or simulation, often uses values that are paired with some representation of their accuracy or reliability. Oftentimes, this representation is a value's standard deviation or a similar metric. The uncertainty in a value can be derived from a number of sources, including instrument accuracy, limitations from approximations, or the statistical nature of the value itself. New values resulting from operations on uncertain inputs will have uncertainties derived from the input uncertainties, but the process of propagating those relationships can become tedious and complicated. To the best of our knowledge, there is no currently maintained C++ library to facilitate this kind of uncertainty propagation. As C++ is an important language in the development of scientific software and high-performance computing, Sigma has been developed in an attempt to fill this gap.

See Background for methodological details.

Features

Propagate uncertainty throughout calculations
Track dependent variable correlation to independent variables
Support for common mathematical operations.
Limited compatibility with Eigen for linear algebra support.

See here for examples.

Installation

Sigma is header-only, so installation is not strictly required for usage. The files simply need to be locatable by your project, as well the dependencies required by Sigma itself (e.g. Eigen if support is configured). Dependency gathering, testing, building of the documentation, and installation are all handled with CMake and the CMaize Framework.

# -- Configuration Step --
# Should the tests be built? BUILD_TESTING=ON Default: OFF
# Should we build the documentation? BUILD_DOCS=ON Default: OFF
# Include Eigen compatibility headers? ENABLE_EIGEN_SUPPORT=ON Default: ON
cmake -Bbuild -H. \
    -DCMAKE_CXX_STANDARD=17 \
    -DCMAKE_INSTALL_PREFIX=/path/to/install \
    -DBUILD_TESTING=ON \
    -DBUILD_DOCS=ON \
    -DENABLE_EIGEN_SUPPORT=ON
 
# -- Build Documentation --
cmake --build build --target sigma_cxx_api
# Documentation will be in ./build/html
 
# -- Build and Run Tests --
cmake --build build --parallel
cd build
ctest -VV
 
# -- Install Library --
cmake --build build --target install

Contributing

Acknowledgments

This work was supported by the Ames National Laboratory's Laboratory Directed Research and Development (LDRD) program. The Ames Laboratory is operated for the U.S. DOE by Iowa State University under contract # DE-AC02-07CH11358.