st: passing extra information to function evaluator program nl

[Ben Zipperer <benzipperer@gmail.com>]

I am interested in using Stata to find a real roots to a single
polynomial several times, where the coefficients vary each time.  I
basically want to apply Newton's method or something else to vectors
of coefficients. I originally planned to restrict the solver at
http://www.stata.com/support/faqs/lang/nl.html to a single polynomial
and then iterate it, changing the coefficients at each iteration.
However, I can't figure out how to pass the coefficients to the
function evaluator program. How do I do this? Do I modify the syntax
statement of the program? Or should I try a different strategy?

For example, let's say the rows of the following matrix form the
coefficients for a quadratic polynomial

mat def M = (1,2,3\ 4,5,6\ 7,8,9)

Then the nl program evaluator program is something like

capture program drop nlpolysolve
program nlpolysolve

        syntax varlist(min=1 max=1) [if], at(name)

        tempname x z
        scalar `x' = `at'[1, 1]
        scalar `z' = `at'[1, 2]

        tempvar yh
	// the real polynomial
        gen double `yh' = a_`i' * x^2 + b_`i' * `x' + c_`i' + 1 in 1

        replace `yh' = 1 - `z' in 2
        replace `varlist' = `yh'

end

And my iterations are something like

forvalues i=1/3 {
 preserve
 clear
 set obs 2
 gen y = 0
 replace y = 1 in 1

 local a_`i' = M[`i',1]
 local b_`i' = M[`i',2]
 local c_`i' = M[`i',3]

 nl polysolve @ y, parameters(A B) initial(A 0.5 B 1)
stuffiwanttopass(a_`i' b_`i' c_i')

 restore
}

How do I pass the entries of the matrix to the nlpolysolve program above?

thanks,
Ben
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