solving simultaneous Equations in R
On 11-12-2013, at 23:56, eliza botto <eliza_botto at hotmail.com> wrote:
Dear Berend, Thankyou very much indeed for you reply. By taking help from your previous reply @ http://r.789695.n4.nabble.com/Simultaneous-equations-td2524645.html i was able to generate the following loop for the calculation of x=x[1] and y=x[2]. fun <- function(x) { f <- numeric(length(x)) # read as: f[1] <- 1-0.514-(gamma(1/x[1])*gamma(2/x[1]-1/x[2]))/(gamma(2/x[1])*gamma(1/x[1]-1/x[2])) f[2] <- 0.57- (gamma(1/x[1]-1/x[2])/gamma(1/x[1])-3*gamma(2/x[1]-1/x[2])/gamma(2/x[1])+2*gamma(3/x[1]-1/x[2])/gamma(3/x[1]))/(gamma(1/x[1]-1/x[2])/gamma(1 /x[1])-gamma(2/x[1]-1/x[2])/gamma(2/x[1])) f } startx <- c(0.1,0.15) # start the answer search here answers<-as.data.frame(nleqslv(startx,fun)) answers What i cant understand is the concept involved for setting "startx". my x[1] should always be smaller than x[2] and they both should be less than 1. how can i demonstrate it to startx command line?
I don?t quite understand what you you mean. Your starting values obey the restrictions you specify (if that is what you meant). The solution vector has all elements > 1. But it is a solution. Do you mean that you want a solution satisfying the constraints you mention? I cannot tell if that is possible. Generally speaking a square system of equations is solved or not. Sometimes you can vary the starting values to get a different solution that obeys the specified constraints. If these constraints are necessary you are not solving a system of equations but trying to find a parameter set that satisfies certain criteria. Together with a criterion (sum of squares of function values for example) you could use an optimizing algorithm (optim, nlmin, constrOptim to name a few). Berend
thanks for your help. I m grateful. Eliza
Subject: Re: [R] solving simultaneous Equations in R From: bhh at xs4all.nl Date: Wed, 11 Dec 2013 12:43:02 +0100 CC: r-help at r-project.org To: eliza_botto at hotmail.com On 11-12-2013, at 12:16, eliza botto <eliza_botto at hotmail.com> wrote:
Dear users of R,
I'm trying to solve the following 2 equations simultaneously in R for "x" and "y". I couldn't get through due to my limited knowledge of R.
3=1-[(x-1)!(2x-y-1)!/(2x-1)!(x-y-1)!]
6={[(x-y-1)!/(x-1)!]-[3(2x-y-1)!/(2x-1)!]+[2(3x-y-1)!/(3x-1)!]}/{[(x-y-1)!/(x-1)!]-[(2x-y-1)!/(2x-1)!]}
obviously, ! is factorial.
kindly help me out on it or at least suggest something.
I'll be extremely grateful.
There are several packages that solve a system of equations. ktsolve, nleqslv, BB, which you can find in CRAN Task views: "Numerical Mathematics? and ?Optimization?. You will have to write your equations in standard R notation. I can?t tell if your system is solvable. Berend
Eliza [[alternative HTML version deleted]]
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