[R] R emulation of FindRoot in Mathematica

[Valentin Petzel]

Hello Troels,

As fair as I understand you attempt to numerically solve a system of non linear equations 
in multiple variables in R. R does not provide this functionality natively, but have you tried 
multiroot from the rootSolve package:

https://cran.r-project.org/web/packages/rootSolve/rootSolve.pdf[1]

multiroot is called like

multiroot(f, start, ...)

where f is a function of one argument which is a vector of n values (representing the n 
variables) and returning a vector of d values (symbolising the d equations) and start is a 
vector of length n.

E.g. if we want so solve

x^2 + y^2 + z^2 = 1
x^3-y^3 = 0
x - z = 0

(which is of course equivalent to x = y = z, x^2 + y^2 + z^2 = 1, so x = y = z = ±sqrt(1/3) ~ 0.577)

we’d enter

f <- function(x) c(x[1]**2 + x[2]**2 + x[3]**2 - 1, x[1]**3 - x[2]**3, x[1] - x[3])

multiroot(f, c(0,0,0))

which yields

$root
[1] 0.5773502 0.5773505 0.5773502

$f.root
[1]  1.412261e-07 -2.197939e-07  0.000000e+00

$iter
[1] 31

$estim.precis
[1] 1.2034e-07

Best regards,
Valentin

Am Donnerstag, 19. Jänner 2023, 10:41:22 CET schrieb Troels Ring:
> Hi friends - I hope this is not a misplaced question. From the
> literature (Kushmerick AJP 1997;272:C1739-C1747) I have a series of
> Mathematica equations which are solved together to yield over different
> pH values the concentrations of metabolites in skeletal muscle using the
> Mathematica function FindRoot((E1,E2...),(V2,V2..)] where E is a list of
> equations and V list of variables.  Most of the equations are individual
> binding reactions of the form 10^6.494*atp*h == hatp and next
> 10^9.944*hatp*h ==hhatp describing binding of singe protons or Mg or K
> to ATP or creatin for example, but we also have constraints giving total
> concentrations of say ATP i.e. ATP + ATPH, ATPH2..ATP.Mg
> 
> I have, without success, tried to find ways to do this in R - I have 36
> equations on 36 variables and 8 equations on total concentrations. As
> far as I can see from the definition of FindRoot in Wolfram, Newton
> search or secant search is employed.
> 
> I'm on Windows R 4.2.2
> 
> Best wishes
> Troels Ring, MD
> Aalborg, Denmark
> 
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--------
[1] https://cran.r-project.org/web/packages/rootSolve/rootSolve.pdf

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