Dear All,
I am solving equation F(x) = A, e.g. F(x) = -0.065
It took me 26 iterations (computations of F) to solve it manually to 8
digits precision:
. F 0.1 -.03582777
. F 0.2 -.08729092
. F 0.15 -.06267811
. F 0.16 -.06777041
. F 0.155 -.06523528
. F 0.153 -.06421507
. F 0.154 -.06472562
. F 0.1545 -.06498056
. F 0.15456 -.06501114
. F 0.15455 -.06500604
. F 0.15454 -.06500095
. F 0.15453 -.06499585
. F 0.154536 -.06499891
. F 0.1545367 -.06499927
. F 0.1545368 -.06499932
. F 0.1545369 -.06499937
. F 0.15453698 -.06499941
. F 0.154537 -.06499942
. F 0.1545375 -.06499967
. F 0.15453778 -.06499982
. F 0.1545379 -.06499988
. F 0.154538 -.06499993
. F 0.1545383 -.06500008
. F 0.1545382 -.06500003
. F 0.1545381 -.06499998
. F 0.15453816 -.06500001
. F 0.15453815 -.065
I have also checked that I can solve it similarly to a couple of other
randomly chosen reasonable values, e.g. -0.071.
I am using Stata's -ml- command to maximize -(F(x)+0.065)^2 but it
gets stuck even after thousands of evaluations of F:
8947.Requested F(.1054786)=-.0623424094117909
8948.Requested F(.1054786)=-.0623424094117909
8949.Requested F(.1054786)=-.0623424094117909
8950.Requested F(-2.634596)=.2516850686732928
8951.Requested F(2.845553)=-.4834788090804468
numerical derivatives are approximate
flat or discontinuous region encountered
Iteration 55: log likelihood = -.05241295 (backed up)
8952.Requested F(-.2668051)=.1354119673051408
8953.Requested F(-.0806633)=.0490795853955872
8954.Requested F(.0124076)=-.0080075923011136
8955.Requested F(.0589431)=-.036368878923033
8956.Requested F(.0822108)=-.0496348343265961
8957.Requested F(.0938447)=-.0560561994045774
8958.Requested F(.0996616)=-.0592159036741122
8959.Requested F(.1025701)=-.060783280290728
8960.Requested F(.1040243)=-.0615638449113507
8961.Requested F(.1047514)=-.061953356620413
8962.Requested F(.105115)=-.0621479470183188
8963.Requested F(.1052968)=-.0622451942077213
8964.Requested F(.1053877)=-.0622938058069336
8965.Requested F(.1054331)=-.0623180818738749
8966.Requested F(.1054558)=-.0623302191596138
8967.Requested F(.1054672)=-.0623363143485496
8968.Requested F(.1054729)=-.0623393618959092
8969.Requested F(.1054757)=-.0623408589251915
8970.Requested F(.1054771)=-.0623416074369894
8971.Requested F(.1054778)=-.0623419816921718
8972.Requested F(.1054782)=-.0623421955520671
8973.Requested F(.1054784)=-.0623423024819647
8974.Requested F(.1054785)=-.0623423559468972
8975.Requested F(.1054785)=-.0623423559468972
8976.Requested F(.1054785)=-.0623423559468972
8977.Requested F(.1054785)=-.0623423559468972
(8977 is number of computations of F() )
I am using option difficult already.
I wonder if there is any way to tell Stata to stop requesting F(x)
over and over again with the same x.
F is quite computationally intensive, and I would like to have a very
low number of calls to it.
The graph of F looks like this:
http://img217.imageshack.us/my.php?image=functionfffpd8.png
And I need to be able to solve F(x)=A for (A<0) , which is a "good"
part of the graph.
Here is a part of my code:
/*
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------*/
program define myfunction
args lnf Xb
/* ----- all this mess just to get the only parameter beta
----- */
summarize $ADEPT_ELAST_Income, meanonly
local beta= r(mean)
summarize `Xb', meanonly
local beta=r(mean)-`beta'
/* -------------- determined parameter beta
------------------- */
/* could I just use local beta = ML_b[1,1] here ?? didn't
work for some reason ??? */
F `beta'
local result =-(r(result)-${target})^2
quietly replace `lnf' = `result'
global MyIter = 0$MyIter + 1
end
/*
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------*/
ml model lf myfunction (irrelevant_var = )
ml init 27401, copy /* 27401 is about mean of irrelevant_var
I would like to initialize close to zero, say in [0;0.5] */
global MyIter =0
ml maximize , difficult
mat B=e(b)
summarize irrelevant_var, meanonly
local solution = B[1,1] - r(mean)
I am also looking for a tutorial on optimization in Stata of functions
(of one or more variables). I could find plenty of ML tutorials, but
very few info on how to max(F(x)-A) numerically w.r.t x.
I have a "ML estimation with Stata" book by Gould, Pitblado and
Sribney, so any references to it are welcomed.
And most important is that the solution must work in Stata 9. I know
Mata 10 has optimize() engine. But it was not available in Stata 9.
Also is there a list and description of all the globals, that
-maximize- passes to -myfunction-, available somewhere? I did a search
in Google and I found that some of them are not mentioned anywhere in
the www. (eg: ML_tn1 etc)
Thank you,
Sergiy Radyakin
PS: seems like I am crunching nonlinear equations faster than 8x3GHz
machine. Just passed 18,500 requests to F() and hopelessly continuing
:)
*
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