# [R] numericDeriv

(Ted Harding) Ted.Harding at nessie.mcc.ac.uk
Wed Nov 16 14:11:51 CET 2005

```On 16-Nov-05 Florent Bresson wrote:
> I have to compute some standard errors using the delta
> method and so have to use the command "numericDeriv"
> to get the desired gradient. Befor using it on my
> complicated function, I've done a try with a simple
> exemple :
>
> x <- 1:5
> numericDeriv(quote(x^2),"x")
>
> and i get :
>
> [1]   1   8  27  64 125 216
>      [,1] [,2] [,3] [,4] [,5] [,6]
> [1,]  Inf    0    0  NaN    0    0
> [2,]    0    0    0  NaN    0    0
> [3,]    0  Inf    0  NaN    0    0
> [4,]    0    0    0  NaN    0    0
> [5,]    0    0  Inf  NaN    0    0
> [6,]    0    0    0  NaN    0    0
>
> I don't understand the result. I thought I will get :
>
> [1]   1   8  27  64 125 216
>      [,1]
> [1,]  1
> [2,]  4
> [3,]  6
> [4,]  8
> [5,]  10
> [6,]  12
>
> The derivative of x^2 is still 2x, isn't it ?

The trap you've fallen into is that "x <- 1:5" makes x of
integer type, and (believe it or not) you cannot differentiate
when the support of a function is the integers. Wrong topology
(though I'm not sure that this is quite how R thinks about it).

So give x a bit of elbow-room ("numeric" type has "continous"
-- well, nearly -- topology):

> x <- as.numeric(1:5)
> numericDeriv(quote(x^2),"x")
[1]  1  4  9 16 25
[,1] [,2] [,3] [,4] [,5]
[1,]    2    0    0    0    0
[2,]    0    4    0    0    0
[3,]    0    0    6    0    0
[4,]    0    0    0    8    0
[5,]    0    0    0    0   10

Cheers,
Ted.

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Date: 16-Nov-05                                       Time: 13:11:49
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