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Just trying to understand why when I find the root of the following equation in excel I get a value however in R I get the "no sign change found error"

(-exp(-i*x))-x + 1

i = 1 in this case.

I'm plotting a graph where the value for i is 1:5. I've done this manually on excel and got a value of 0.003 when i = 1, here is the graph for all values of i: image 1

When try to find the root for when i = 1 in R though I get the error.

This is the code I am using to find the root:

func1 <- function(x) {

  (-exp(-1*x))-x+1 
}

root <- uniroot(func1, lower =0.5, upper = 1, extendInt = "yes")
print(root)
print(root$root)

}

Plotting the equation when i = 1 gives the following curve: image 2

Looking at the curve it doesn't seem like f(x) crosses 0 which explains the error, however, I get a value in excel.

Any help on this would be really appreciated

Thanks

Michael Skehan
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  • The function has a zero for `x=0` and it's always negative for any other value. What do you get in excel? – nicola Oct 12 '18 at 12:03
  • I originally got 0.003 for when i =1, however, I didn't expanding on my trial and error method enough, after doing so it looks like the value is 2.512E-08 – Michael Skehan Oct 12 '18 at 13:11

1 Answers1

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This is the best I can offer. It is using a method of derivatives I found at http://rpubs.com/wkmor1/simple-derivatives-in-r. It will allow you to get the roots from newtons method. 

options(scipen = 999)
f<-function(x) (-exp(-x)-x+1)
g<-function(x) { }
body(g)<-D(body(f),"x")
x <- 19
y<-vector()
y[1]<-x
for(i in 2:500) {
  y<-c(y, y[i-1] - (f(y[i-1])/g(y[i-1])))
  if(y[i]==y[i-1]) break
}
y

The output looks like this:

> y
 [1] 19.000000000000000  0.999999893546867  0.418023257075328  0.194491909332762
 [5]  0.094095681658666  0.046310116577025  0.022976345768161  0.011444180565743
 [9]  0.005711176200954  0.002852869974152  0.001425756748278  0.000712708975595
[13]  0.000356312158327  0.000178145499021  0.000089070105497  0.000044534390909
[17]  0.000022267031356  0.000011133470771  0.000005566723944  0.000002783342584
[21]  0.000001391644148  0.000000695821730  0.000000347990248  0.000000173795172
[25]  0.000000086916841  0.000000043487300  0.000000023063442  0.000000013435885
[29] -0.000000003090351 -0.000000003090351

I hope this helps.

Michael Vine
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