autodiffr: Automatic Differentiation in R through 'Julia'

The package need to deal with derivatives and second-order (or higher-order) derivatives of R1 -> R1 functions gradients and hessians of Rn(n>1) -> R1 functions * jacobians of Rn(n>1) -> Rm(m>1) functions

And the package will provide separate functions, like deriv for derivatives, and grad for gradients.

It is expected that users understand the difference and use corresponding functions when dealing with problems in different dimensionality.

Maybe we can include some error messages like "grad is not for R1 -> R1 functions, maybe you want to use deriv?" if the user uses grad for a scalar function of one variable.

The arguments to the interface functions will look like: grad(func, x = NULL, mode = c("forward", "reverse"), ...) where func is the original function. x is where the gradient is calculated, and it should be the first argument to func except the arguments matched by .... If it is NULL, then a gradient function will be returned. mode is whether forward or reverse mode automatic differentiation is used, And ... are other arguments to the function func.