On Automatic Diierentiation of Codes with Complex Arithmetic with Respect to Real Variables on Automatic Diierentiation of Codes with Complex Arithmetic with Respect to Real Variables
نویسندگان
چکیده
We explore what it means to apply automatic diierentiation with respect to a set of real variables to codes containing complex arithmetic. That is, both dependent and independent variables with respect to diierentiation are real variables, but in order to exploit features of complex mathematics, part of the code is expressed by employing complex arithmetic. We investigate how one can apply automatic diierentiation to complex variables if one exploits the homomorphism of the complex numbers C onto R 2. It turns out that, by and large, the usual rules of diierentiation apply, but subtle diierences in special cases arise for sqrt(), abs(), and the power operator.
منابع مشابه
On Automatic Diierentiation of Codes with Complex Arithmetic with Respect to Real Variables Contents Abstract 1 1 Introduction 1 2 Complex Numbers and Functions 2 2.1 Complex Arithmetic Rules
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