В Fri, 8 Dec 2023 08:21:16 +0100 Konrad via R-help <r-help@r-project.org> пишет:
> My problem is how to replicate the Eliminate function in R. While R does invite the user to "compute on the language", i.e. take R expressions and function calls and work with them as with ordinary variables [*], so far nobody wrote a complete computer algebra system in R. Interfaces for other CASes do exist, but I haven't tried them. > Or is it possible to solely solve the system numerically? While it's less efficient to do so, it must be possible. For example, the https://CRAN.R-project.org/package=nleqslv package does exactly that. > h0 = h + hd + hg, > d0 = d + hd, > ga0 = ga + hg, > kga = hg/(h*ga), > kd = hd/(h*d) > The aim is to fit a non-linear equation in the form: signal ~ I0 + > IHD * hd + ID * d. > The parameters which should be identified/optimized are: I0, ID, IHD > and kd. However, the only information known is kga (33600.0), h0 > (0.0000208), d0 (0.000079) and the guest concentration (= ga0). This doesn't quite agree with > 0 = h + hd + hga, > 33600. = d + hd, > 0.000079 = hga/(ga*h), ...that you gave to Mathematica. Is it d0 = d + hd or kga = 33600. = d + hd? kga = hg/(h*ga) or d0 = 0.000079 = hga/(ga*h)? What other equations are missing? The general approach is to take all the equations and write them down as a vector of expressions that should be evaluate to 0 at solution, then substitute() in the values of the constants and x[i] for sequential values of `i` for variables: fn <- function(x) NULL body(fn) <- substitute( c( # equations go here h0 - h + hd + hg, d0 - d + hd, ga0 - ga + hg, kga - hg/(h*ga), kd - hd/(h*d), # ...more equations... signal - I0 + IHD * hd + ID * d ), list( # knowns kga = 33600.0, h0 = 0.0000208, d0 = 0.000079, # assuming two more knowns live in same-named variables ga0 = ga0, signal = signal, # variables named so far I0 = quote(x[1]), ID = quote(x[2]), IHD = quote(x[3]), kd = quote(x[4]) # ...more variables... ) ) The resulting function fn() takes a vector of variables and should return a vector of zeroes at the solution. Try to solve it using nleqslv::nleqslv(starting_guess, fn) or some of the functions from the BB package. -- Best regards, Ivan [*] For example, see this R package automatically differentiate expressions when solving nonlinear least squares problems: https://cran.r-project.org/package=nlsr/vignettes/nlsr-derivs.pdf ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
