st: Mata: trouble with nested optimize()

[Matthew J Baker <matthew.baker@hunter.cuny.edu>]

I think the problem with the example is that the "q" term, which 
is set as an external in the first function, is not getting there! So, 
the problem is that the q value is not being passed along. 
Therefore, one can make two modifications to the code given to 
get it to run:
1) allow invobj to be a function of q directly, and get rid of the 
external call, 
and
2) use the function invd to formally set the q argument of invobj. 
If I make these two modifications, the program runs. The 
modified example: 

clear
mata: mata clear

mata:
void invobj(todo,p,q,f,S,H) //allow function to depend on q 
explicitly
{
//Trivial inversion: assume that I cannot invert q=10-p 
analytically:
f=(q-(10-p))^2
}

real scalar function invd(real scalar q)
{
       transmorphic I
       I=optimize_init()
       optimize_init_evaluator(I,&invobj())
       optimize_init_evaluatortype(I,"d0")
       optimize_init_params(I,(3))
       optimize_init_argument(I,1,q)   // pass q to invobj
       optimize_init_which(I,"min")
       p=optimize(I)
       return(p)
}

void objftn(todo,q,f,S,H)
{
real scalar p
p=invd(q);

f=q*(p-1)
}

S=optimize_init()
optimize_init_evaluator(S,&objftn())
optimize_init_evaluatortype(S,"d0")
optimize_init_params(S,(1))
optimize_init_which(S,"max")
s=optimize(S)
s
end


Hope that helps!

Matt Baker

- Hide quoted text -

On Mon, May 9, 2011 at 7:20 PM, Lydia Pikyi Cheung 
<cheun073@umn.edu> wrote:
Dear Statalist users,

I would like to maximize a function F(q1,q2) that involves terms
p1(q1,q2), p2(q1,q2) that do not have analytical forms. I.e., 
every
time a trial value (q1,q2) is used to evaluate F(), Mata needs to
solve a system of equations to back out the corresponding 
p1(q1,q2)
and p2(q1,q2), in order to evaluate F(). I solve this system of
equations using optimize(), following
http://www.stata.com/support/faqs/lang/nl.html (bottom of 
page). As a
result, I have an inner optimize() routine to solve the system of
equations inside the main optimize() routine to maximize F().

Is this possible? I have attached my code below with simplified
functions. (I have simplified both p,q be scalars, i.e. F(q,p) is a
function of scalars, and p(q) takes a scalar argument.) I keep
getting:

: s=optimize(S)
initial values not feasible
(1 line skipped)
----------------------------------------
r(1400);

I do not think initial values are the problem. After running the
following code, I checked:

: S
 0x5ac5bdc

: I
                <istmt>:  3499  I not found
r(3499);

Thus S was initialized successfully while I was not. Is it because
objftn() fails to invoke function invd()?

Any better way to code this problem is appreciated as well.

= = = = = = = = = = = = = = = = = = =
clear
mata: mata clear

mata:
void invobj(todo,p,f,S,H)
{
external real scalar q
//Trivial inversion: assume that I cannot invert q=10-p 
analytically:
f=(q-(10-p))^2
}

real scalar function invd(real scalar q)
{
       transmorphic I
       I=optimize_init()
       optimize_init_evaluator(I,&invobj())
       optimize_init_evaluatortype(I,"d0")
       optimize_init_params(I,(3))
       optimize_init_which(I,"min")
       p=optimize(I)
       return(p)
}

void objftn(todo,q,f,S,H)
{
real scalar p
p=invd(q);

f=q*(p-1)
}

S=optimize_init()
optimize_init_evaluator(S,&objftn())
optimize_init_evaluatortype(S,"d0")
optimize_init_params(S,(1))
optimize_init_which(S,"max")
s=optimize(S)
s
end
*
*   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/



-- 
Dr. Matthew J. Baker
Department of Economics
Hunter College and the Graduate Center, CUNY
*
*   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/