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Re: st: Mata computes the second derivative of x^2 as 1.9.


From   Tirthankar Chakravarty <tirthankar.chakravarty@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Mata computes the second derivative of x^2 as 1.9.
Date   Sat, 4 Aug 2012 23:15:40 -0700

As with any numerical approximation procedure, there are tuning
parameters. Resetting the bounds for the optimal parameter (scale)
search works for your simple example

*---------------------------------------
mata:
mata clear
void f(p,v){
        v = p^2
}
D = deriv_init()
deriv_init_bounds(D, (1e-5, 1e-4))
deriv_init_evaluator(D, &f())
deriv_init_params(D, 0.5)
deriv(D,2)
deriv_result_delta(D)
end
*---------------------------------------

[M] and the references there contain more information. For more
complex multiparameter nonlinear problems, you should look at a
numerical analysis text.

T

On Sat, Aug 4, 2012 at 8:22 PM, Patrick Roland
<patrick.rolande@gmail.com> wrote:
> Perhaps someone might be able to explain this anomaly. The following
> code finds the second derivative of x^2 evaluated at 0.5, which should
> of course be 2.
>
>
> mata:
>
> void f(p,v){
>         v = p^2
> }
> D = deriv_init()
> deriv_init_evaluator(D, &f())
> deriv_init_params(D, 0.5)
> deriv(D,2)
>
> end
>
> Instead, in both Stata 11.2 and 12.1, the answer is 1.906569171.
>
> I'm trying to compute the Hessian of a complicated nonlinear function
> of several hundred arguments. It appears that Mata cannot correctly
> find the second derivative of x^2. This does not inspire confidence.
>
> Hopefully I'm overlooking something simple here, in which case I would
> greatly appreciate a correction.
> *
> *   For searches and help try:
> *   http://www.stata.com/help.cgi?search
> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/



-- 
Tirthankar Chakravarty
tchakravarty@ucsd.edu
tirthankar.chakravarty@gmail.com
*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/


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