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


From   Patrick Roland <patrick.rolande@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Mata computes the second derivative of x^2 as 1.9.
Date   Sun, 5 Aug 2012 12:09:41 -0700

Sure, but i) it is disturbing that the default parameters work so
poorly on such a simple problem and ii) in more problems where the
derivatives are not known, one does not have the option of choosing
the tuning parameters so that the procedure matches the known results
as closely as possible.

On Sat, Aug 4, 2012 at 11:15 PM, Tirthankar Chakravarty
<tirthankar.chakravarty@gmail.com> wrote:
> 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/
*
*   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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