Automatic Differentiation with Dual Numbers
Arithmetic Operators
Dual object class An S4 Class for dual numbers
tools:::Rd_package_title("dual")
Special Functions of Mathematics
Hyperbolic Functions
Logarithms and Exponentials
Logic Operators for Comparing Dual Numbers
Miscellaneous Mathematical Functions
Special Functions of Mathematics
Trigonometric Functions
Automatic differentiation is achieved by using dual numbers without providing hand-coded gradient functions. The output value of a mathematical function is returned with the values of its exact first derivative (or gradient). For more details see Baydin, Pearlmutter, Radul, and Siskind (2018) <https://jmlr.org/papers/volume18/17-468/17-468.pdf>.