tzu - 5 months ago 29

R Question

To simplify the question, I will use a toy example here. I want to derive the gradient and Hessian of a polynomial function such as

library(pracma)

`dummy <- function(x) {`

z <- x[1]; y <- x[2]

rez <- (z^2)*(y^3)+3

rez

}

grad(dummy, c(1,2))

hessian(dummy, c(1,2))

M question is that is there an efficient way so I can derive the gradient and Hessian from different constant terms in

`dummy`

`(z^2)*(y^3)+a`

`z=1`

`y=2`

`a=[0.01,3]`

Thanks!

Answer

Both `pracma::hessian`

and `pracma::grad`

take `...`

as "variables to be passed to `f`

". If you want `a`

to be a variable, you just need your `dummy`

function to take it as an argument:

```
dummy <- function(x, a) {
z <- x[1]; y <- x[2]
rez <- (z^2)*(y^3)+a
rez
}
grad(dummy, c(1,2), a = 0.01)
# [1] 16 12
hessian(dummy, c(1,2), a = 3)
# [,1] [,2]
# [1,] 16 24
# [2,] 24 12
sapply(seq(0.01, 3, length.out = 10), function(a) grad(dummy, c(1, 2), a = a))
# [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
# [1,] 16 16 16 16 16 16 16 16 16 16
# [2,] 12 12 12 12 12 12 12 12 12 12
```

Of course the results are all the same, you are changing a constant term and then taking derivatives; the derivative of any constant is 0. But the idea will generalize to more interesting cases.