
Tangent: Automatic differentiation using sourcecode transformation for dynamically typed array programming
The need to efficiently calculate first and higherorder derivatives of...
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DiffSharp: Automatic Differentiation Library
In this paper we introduce DiffSharp, an automatic differentiation (AD) ...
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Binomial Checkpointing for Arbitrary Programs with No User Annotation
Heretofore, automatic checkpointing at procedurecall boundaries, to red...
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Don't Unroll Adjoint: Differentiating SSAForm Programs
This paper presents reversemode algorithmic differentiation (AD) based ...
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Automatic Differentiation in PCF
We study the correctness of automatic differentiation (AD) in the contex...
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A Succinct Multivariate Lazy Multivariate Tower AD for Weil Algebra Computation
We propose a functional implementation of Multivariate Tower Automatic D...
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DivideandConquer Checkpointing for Arbitrary Programs with No User Annotation
Classical reversemode automatic differentiation (AD) imposes only a sma...
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Automatic Differentiation in ROOT
In mathematics and computer algebra, automatic differentiation (AD) is a set of techniques to evaluate the derivative of a function specified by a computer program. AD exploits the fact that every computer program, no matter how complicated, executes a sequence of elementary arithmetic operations (addition, subtraction, multiplication, division, etc.), elementary functions (exp, log, sin, cos, etc.) and control flow statements. AD takes source code of a function as input and produces source code of the derived function. By applying the chain rule repeatedly to these operations, derivatives of arbitrary order can be computed automatically, accurately to working precision, and using at most a small constant factor more arithmetic operations than the original program. This paper presents AD techniques available in ROOT, supported by Cling, to produce derivatives of arbitrary C/C++ functions through implementing source code transformation and employing the chain rule of differential calculus in both forward mode and reverse mode. We explain its current integration for gradient computation in TFormula. We demonstrate the correctness and performance improvements in ROOT's fitting algorithms.
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