[R] finding complex roots in R

Thu Sep 16 22:29:03 CEST 2010

Beware that you are likely to have multiple, or even infinitely many, roots
in the complex plane.  In the first example, there are infinitely many
roots, which are equal to +/- 1i  * (N * pi), where N = 1, 3, 5, ...

Similarly, there are infinitely many roots in my second example.

Therefore, I would suggest that you use the `multiStart' function in "BB" to
explore this in your problem.

Ravi.

-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On
Behalf Of Ravi Varadhan
Sent: Thursday, September 16, 2010 3:52 PM
To: 'Toros Caglar'; r-help at r-project.org
Subject: Re: [R] finding complex roots in R

Hi Toros,

It is actually quite easy to do this with existing real-root finders.  If
you want to solve for F(z) = 0, where z = x + iy, you simultaneously solve
for the zeros of the real and imaginary part of F.  

Here are a couple of examples using the package "BB":

fn1 <- function(x, a){
z <- x[1] + 1i * x[2]
f <- exp(z) + a
c(Re(f), Im(f))
}

fn2 <- function(x, a){
z <- x[1] + 1i * x[2]
f <- sin(z)^2 + sqrt(z) - log(z)
c(Re(f), Im(f))
}

require(BB)

# First example
> BBsolve(par=c(1,1), fn=fn1, a=1)
  Successful convergence.
$par
[1] -4.799024e-10  3.141593e+00

$residual
[1] 4.819472e-10

$fn.reduction
[1] 0.0002550771

$feval
[1] 81

$iter
[1] 5

$convergence
[1] 0

$message
[1] "Successful convergence"

$cpar
method      M     NM 
     2     50      1 

So, the complex root is: 0 + i*pi, as you might have guessed.

# Second example
> BBsolve(par=c(1,1), fn=fn2)
  Successful convergence.
$par
[1] 0.2555197 0.8948303

$residual
[1] 9.079212e-08

$fn.reduction
[1] 0.0002494436

$feval
[1] 168

$iter
[1] 92

$convergence
[1] 0

$message
[1] "Successful convergence"

$cpar
method      M     NM 
     2     50      1 

Here the complex root is: 0.2555 + i*0.8948.

In these two examples the function F(z) is scalar.  We can readily extend
this to vector F using the method that I just described.

Hope this helps,
Ravi.

-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On
Behalf Of Toros Caglar
Sent: Wednesday, September 15, 2010 11:33 PM
To: r-help at r-project.org
Subject: [R] finding complex roots in R

I am looking for a way to find the roots of a non-polynomial
expression. I know R has a few ways to deal with polynomials, but, I
could not find a method that deals with functions involving e^(x) type
arguments, that have complex roots as well as real roots.

Any ideas?

Thanks,

Toros

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