Symbolic Differentiation

R-based solution for symbolic differentiation. It admits user-defined function as well as function substitution in arguments of functions to be differentiated. Some symbolic simplification is part of the work.

Deriv

Symbolic differentiation

The original version of this software was written in R by Andrew Clausen (clausen at econ.upenn.edu) in 2007.

Mark Reid (mark.reid at anu.edu.au) sent a patch, applied 21/2/2009.

In 2014, Andrew has passed the maintenance to Serguei Sokol (sokol at insa-toulouse.fr). Since then, the software was deeply rewritten and completed.

Main new features include:

• new derivative engine allowing simple syntaxe for differentiation rules;
• many new functions are added to the rule table;
• custom differentiation rules can be added by user;
• automatic differentiation (AD) of a code with multiple assignement operators;
• when taking derivative of a function Deriv() returns a function too. The later can be called with the same arguments as the original function;
• can differentiate by variables stored in vectors or lists, e.g. param$theta or x[1], x[2] etc.
• simplifications are extended to rational expressions and factorizations;
• expression caching is enabled by default;
• Deriv() is made the only entry point for all types of entries:
  • expression
  • language
  • function
  • right hand side of a formula
  • character string
  • plain unevaluated code
• few unit tests were added to the package

Installation

> devtools::install_github("sgsokol/Deriv")

Usage

In R session do:

> library(Deriv)
> f <- function(x, n=2) x^n+sin(n*x)     # user defined function to diffierentiate
> (df <- Deriv(f))                       # -> c(x = n * x^(n - 1) + n * cos(n * x), n = log(x) * x^n + x * cos(n * x))
> df(2, 3)                               # ->         x         n
                                         # -> 14.880511  7.465518

> Deriv(expression(f(y, 3)), "y")        # -> expression(3 * y^2 + 3 * cos(3 * y))
> Deriv(~ f(y, 3), "y")                  # -> 3 * y^2 + 3 * cos(3 * y)
> y <- 2; eval(Deriv(~ f(y, 3), "y"))    # -> 14.88051

For more information and examples:

> ?Deriv