# Calling rdiff() with a function¶

Calling syntax:

rdiff( func::Function, init::Tuple; order::Int)


## Arguments¶

func: is a Julia generic function. is a tuple containing the types for each parameter of func. These types are necessary to pick a the right method of the given function. By default the generated expression will yield the derivative for each variable given unless the variable is listed in the ignore argument. (keyword arg, default = 1) is an integer indicating the derivation order (1 for 1st order, etc.). Order 0 is allowed and will produce a function that is a processed version of ex with some variables names rewritten and possibly some optimizations. (default=Main) module where the expression is meant to be evaluated. External variables and functions should be evaluable in this module. (default=false) if true rdiff dumps the graph of the generating expression, instead of the expression. (default=true) tells rdiff whether to generate the code for all orders up to order (true) or only the last order. (default=[]) do not differentiate against the listed variables (identified by their position index), useful if you are not interested in having the derivative of one of several variables in init.

## Output¶

A function, evaluated in the same module that func is from and returning a tuple containing the expression value and the derivative at first, second , etc.. order.

## Usage¶

rdiff takes a function defined with the same subset of Julia statements ( assigments, getindex, setindex!, for loops, function calls ) as the Expression variant of rdiff() and transforms it into another function whose call will return the derivatives at all orders between 0 and the order specified:

julia> rosenbrock(x) = (1 - x[1])^2 + 100(x[2] - x[1]^2)^2   # function to be derived
julia> rosen2 = rdiff(rosenbrock, (Vector{Float64},), order=2)       # orders up to 2
(anonymous function)
julia> rosen2([1,2])
(100,[-400.0,200.0],
2x2 Array{Float64,2}:
402.0  -400.0
-400.0   200.0)


The generated function will attempt to remove all uneeded calculations (e.g. x + 0) and factorize repeated function calls as much as possible.

All the variables appearing in the init argument are considered as the expression’s arguments and a derivative is calculated for it (and cross derivatives if order is >= 2), unless they are listed in the ignore argument.

For orders >= 2 only a single variable, of type Real or Vector, is allowed. For orders 0 and 1 variables can be of type Real, Vector or Matrix and can be in an unlimited number. If you are dealing with a function of several (scalar) variables you will have you aggregate them into a vector (as in the example above).

## Limitations¶

• The function should have a single return statement positioned at the end. Functions exiting before the end (conditionally or not) cannot be differentiated.
• All variables should be type-stable (not change from a scalar to a vector for example).
• Only a limited set of Julia semantics are supported at this stage. Some frequently used statements such as comprehensions, if else, while loops cannot be used in the expression.
• Mutating functions cannot be used (with the exception of setindex! and setfield!).