# [R] Solve system of non linear equations using nasted loops

Berend Hasselman bhh at xs4all.nl
Thu May 11 10:12:42 CEST 2017

```Your code looks needlessly complicated and inefficient in my view.
Even if you don't need or use nested for loops it can still be simplified.

1: First define  some new constants to avoid the  the M? stuff in your function

<code>
pME <- ME[2:9]/ME
pMI <- MI[2:9]/MI
pMA <- MA[2:9]/MA
pMAE <- (MA-ME)/(MA[2:9]-ME[2:9])
pMAI <- (MA[2:9]-MI[2:9])/(MA-MI)
pMIA <- (MI[2:9]-MA[2:9])/(MI-MA)
</code>

2. Redefine your function and avoid silly and unnecessary  use of 1* and 2* and use a constant for log(.../...)
The vector pXX is a vector consisting of elements from the vector pME etc.

<code>
fun <- function(x,pXX) {
f <- numeric(length(x)) # read as:
pME <- pXX
pMI <- pXX
pMA <- pXX
pMAE <- pXX
pMAI <- pXX
pMIA <- pXX
const <- log(0.19245009/0.384900179)
f <- x - (log(pME)+(x+x)*2*(log(pMAE)))/const
f <- x - (log(pMI)-(x)*2*(log(pMAI)))/const
f <- x - (log(pMA)-(x)*2*(log(pMIA)))/const
f
}
</code>

This can be simplified further by doing the log(pXX) beforehand.

3. I'm not going to have a go at using expand.grid. Too lazy and more involved to get everything correct.
So use a nested loop as follows:

- prepare a result matrix of correct dimensions with7 columns: one for nleaslv termination code, 3 for the result x-vales and another 3 to store i,j,k.
- storing the termination code is a must to see if convergence was obtained.
- and before invoking nleqslv test if fun(startx) contains NA values. If it does fill the appropriate row of Result with NA.
- use an index counter (indx) to store the results in the rows of Result

<code>
Result <- matrix(0,nrow=9*9*9,ncol=7)

indx <- 1
for (i in 1:9) {
for (j in 1:9) {
for (k in 1:9) {
pXXijk <- c(pME[i],pMI[j],pMA[k],pMAE[i],pMAI[j],pMIA[k])
f.startx <- fun(startx,pXXijk)
if(anyNA(f.startx)) {
Result[indx,1:4] <- NA
} else {
z <- nleqslv(startx,fun,pXX=pXXijk)
Result[indx,1:4] <- c(z\$termcd,z\$x)
}
Result[indx,5:7] <- c(i,j,k)
indx <- indx+1
}
}
}
</code>

And now you can inspect Result, which contains 729 rows (and not 1000) and continue to make  a data.frame with column names.
The rest is up to you.

Berend

On 10 May 2017, at 20:20, Santiago Burone <santiago
burone at icloud.com> wrote:
>
> Hello,
>
> I'm new at R and I would like to use it in order to solve a system of non linear equations. I have the code that works but im not able to save the results.
>
>
>
> My system has three equations and i would like to solve this using three nested loops, becouse i need solutions for all the values combinations.
>
>
>
>
>
> The code im using is this:
>
>
>
> library(nleqslv)
> #x3 es gamma
> #x2 es alpha
> #x1 es beta
> MA <- c(50000, 43600, 40000, 38800, 37600, 34400, 31600, 27200, 24400, 20000)
> MI <- c(10000, 21800, 20000, 19400, 18800, 17200, 15800, 13600, 12200, 10000)
> ME <- c(30000, 32700, 30000, 29100, 28200, 25800, 23700, 20400, 18300, 15000)
> DE <- c(0.384900179, 0.19245009, 0.19245009, 0.19245009, 0.19245009, 0.19245009, 0.19245009, 0.19245009, 0.19245009, 0.19245009)
> for (i in 1:9) {
> for (j in 1:9){
> for (k in 1:9){
>
> fun <- function(x) {
> f <- numeric(length(x)) # read as:
> f <- 1*x - (log(ME[1+i]/ME)+(1*x+1*x)*(2)*(log((MA-ME)/(MA[i+1]-ME[i+1]))))/(log(0.19245009/0.384900179))
> f <- 1*x - (log(MI[1+j]/MI)-(1*x)*(2)*(log((MA[1+j]-MI[1+j])/(MA-MI))))/(log(0.19245009/0.384900179))
> f <- 1*x - (log(MA[1+k]/MA)-(1*x)*(2)*(log((MI[1+k]-MA[1+k])/(MI-MA))))/(log(0.19245009/0.384900179))
> f
> }
> startx <- c(1,1,1)
> assign(df.names[k+20], d.frame)
>
> }
> }
> }
>
>
>
>
> If im not wrong i should have 1000 different solutions but the data frame only save 10 results. I tried copying the last part of the code between the last two brackets (changing the name of the data frame despejes for despejes 1, 2 and 3 but i only get three data frames with exactly the same results. I dont know how could i save all the results of every combination. I mean, i need to solve for i=1, j=1 and the 9 diferent values of k and save those results, then i=1, j=2 and the 9 values of k..
>
>
>
> I know this might be a easy question but i have not been able to find a solution in the last days.
>
>
>
> Thanks in advance if you can help me.
>
>
> Santiago.
> 	[[alternative HTML version deleted]]
>
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