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st: nonlinear equation: finding zeros


From   "Luigi Pinoni" <gipino9@gmail.com>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: nonlinear equation: finding zeros
Date   Fri, 24 Jun 2011 00:19:26 +0200

Dear all, 

I have an apparently simple problem of finding zeros to nonlinear equations.
I was told that mata can easily do the trick but I must say that I am
completely new to it and struggling to enter its programming language. I
have also searched the statalist but either I am left with most of my doubts
or I keep finding reference to the FAQ:
http://www.stata.com/support/faqs/lang/nl.html, which I am struggling to
implement (so, please, do not redirect me to it again?).

Let me now explain my problem. I need a command to numerically computes the
zeroes of one equation. For instance, consider the single equation:

0=exp(-R*w)-exp(-R*(w+5000))/2-exp(-R*(w-z))/2

Assume that (for instance) w=1000 and z=10. Can Stata tell me what is the
value of the scalar R that make the RHS of the equation above equal to zero
(in my example it is R=0.06931471806)?

Actually, all variables mentioned above (w,z) are Nx1 vectors, i.e. w and z
are three variables in a Stata data set and I need to generate the Nx1
vector of solutions, row by row. In other words, the actual problem I have
is to find the N zeros of equations:

0=exp(-R[i]*w[i])-exp(-R[i]*(w[i]+5000))/2-exp(-R[i]*(w[i]-z[i]))/2

Knowing the value of w[i] and z[i], for all i=1,?,N.

I have tried to find this R following the FAQ mentioned above (using mata)
but Stata issues some mistakes that I am unable to interpret. Could you
please tell me where I am going wrong?

I do appreciate your help and please accept my apologies for the naivety of
my mata coding. 

All the best! 

********** BEGINNING OF MY EXAMPLE
clear all
set obs 10
gen w=.
replace w=915000 in 1
replace w=1000 in 2
replace w=4000 in 3
replace w=250000 in 4
replace w=280000 in 5
replace w=330000 in 6
replace w=500 in 7
replace w=498000 in 8
replace w=410000 in 9
replace w=520000 in 10
gen z=.
replace z=500 in 1
replace z=10 in 2
replace z=1000 in 3
replace z=1000 in 4
replace z=100 in 5
replace z=5000 in 6
replace z=1000 in 7
replace z=5000 in 8
replace z=100 in 9
replace z=2000 in 10

mata
void mysolver(todo, p, lnf, S, H)  {
                     p=(1..10)
                     lnf=(
exp(-R*w[1])-exp(-R*(w[1]+5000))/2-exp(-R*(w[1]-z[1]))/2)^2 
         }

S = optimize_init()
optimize_init_evaluator(S, &mysolver())
optimize_init_evaluatortype(S, "v0")
optimize_init_params(S, (1))
optimize_init_which(S,  "min" )
optimize_init_tracelevel(S,"none")
optimize_init_conv_ptol(S, 1e-16)
optimize_init_conv_vtol(S, 1e-16)
p = optimize(S)
p 
end
********** END OF MY EXAMPLE





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