# [R] numericDeriv

Peter Dalgaard p.dalgaard at biostat.ku.dk
Wed Nov 16 15:12:43 CET 2005

```(Ted Harding) <Ted.Harding at nessie.mcc.ac.uk> writes:

> 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

Oho. That had me baffled for a while... We should probably also
explain that x is a vector and differentiation of a vector w.r.t. a
vector is a matrix. If you want a 5x1 result you should likely use
something like

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

(I *hope* there's no way to get the result that Florent claims that he
expected...)

--
O__  ---- Peter Dalgaard             Øster Farimagsgade 5, Entr.B
c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
(*) \(*) -- University of Copenhagen   Denmark          Ph:  (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)                  FAX: (+45) 35327907

```