Symbolic Differentiation.

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