Linearity analysis determines which variables depend on which other variables and whether the dependence is linear or nonlinear. One of the many applications of this analysis is determining whether a loop involves only linear loop-carried dependences and therefore the adjoint of the loop may be reversed and fused with the computation of the original function. This paper specifies the data-flow equations that compute linearity analysis. In addition, the paper describes using linearity analysis with array dependence analysis to determine whether a loop-carried dependence is linear or nonlinear. © Springer-Verlag Berlin Heidelberg 2006.
CITATION STYLE
Strout, M. M., & Hovland, P. (2006). Linearity analysis for automatic differentiation. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 3994 LNCS-IV, pp. 574–581). Springer Verlag. https://doi.org/10.1007/11758549_79
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