Using Deriv package for derivative wrt vector-CodePudding

I am exploring autodiff, and I would like to use Deriv for computing a derivative of a function wrt to a vector. I write

library(numDeriv)
library(Deriv)
h = function(x) c(1,2)%*%x
grad(h,c(1,2)) #ok
#[1] 1 2
dh=Deriv(h,x='x')
#Error in c(1, 2) %*% 1 : non-conformable arguments
dh(c(1,2))

Does anyone have a good way to do this?

From help(Deriv), it seems like one should be able to let the argument be a vector

here is a side effect with vector length. E.g. in Deriv(~a bx, c("a", "b")) the result is c(a = 1, b = x). To avoid the difference in lengths of a and b components (when x is a vector), one can use an optional parameter combine Deriv(~a bx, c("a", "b"), combine="cbind") which gives cbind(a = 1, b = x) producing a two column matrix which is probably the desired result here.

I would like to avoid making each of the vector components a different argument to the function.

For example numDeriv above lets us easily take a derivative wrt vector x

CodePudding user response：

This is an answer; The to packages handles multiple dimensions differently.


library(numDeriv)
library(Deriv)
h = function(x,y) c(1,2) %*% c(x,y)
grad(\(x) h(x[1], x[2]),c(1,2))
dh = Deriv(h)
dh(c(1,2))

CodePudding user response：

Here is a solution using not Deriv but madness, a really neat package.

We basically create an object that is the thing we would like to take the derivative with respect to (in this case x), and then as we apply functions to that object, the derivatives are collected.

We get the evaluated derivative using this function, as we do with grad in numDeriv.

library(madness)

h = function(x){t(x)%*%matrix(c(2,1),nrow=2,ncol=1)}
x=matrix(c(1,1),nrow=2,ncol=1)

gd=function(h,x){
x=madness(val=x)
z=h(x)
attr(z,"dvdx")
}
gd(h,x)
#     [,1] [,2]
#[1,]    2    1