Inf +1i vs 1+Inf*1i

Robin,

You could try

b <- complex(real=1, im=Inf)



------------------------------------------
?scar Manuel Rueda Palacio
Viceintervenci?n
Consejer?a de Hacienda 
Junta de Castilla y Le?n
Tfno: 983414092   e-mail: ruepalos at jcyl.es
------------------------------------------

-----Mensaje original-----
De: r-help-bounces at stat.math.ethz.ch
[mailto:r-help-bounces at stat.math.ethz.ch]En nombre de Robin Hankin
Enviado el: mi?rcoles, 13 de abril de 2005 9:51
Para: R-help at stat.math.ethz.ch
Asunto: [R] Inf +1i vs 1+Inf*1i


Hi

If I have

a <- Inf + 1i

then

Re(a) is Inf, and Im(a) is 1, as expected.

But if

b <- 1 + Inf * 1i,

then

Im(b) = Inf ,  as expected,   but Re(b) = NaN, which I didn't expect.


Why this asymmetry?   How to define an object with Re(b)=1, Im(b)=Inf?


--
Robin Hankin
Uncertainty Analyst
Southampton Oceanography Centre
European Way, Southampton SO14 3ZH, UK
  tel  023-8059-7743

______________________________________________
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"Robin" == Robin Hankin <r.hankin at soc.soton.ac.uk>
    on Wed, 13 Apr 2005 08:51:19 +0100 writes:

Robin> Hi
    Robin> If I have

    Robin> a <- Inf + 1i

    Robin> then

    Robin> Re(a) is Inf, and Im(a) is 1, as expected.

    Robin> But if

    Robin> b <- 1 + Inf * 1i,

    Robin> then

    Robin> Im(b) = Inf ,  as expected,   but Re(b) = NaN, which I didn't expect.

    Robin> Why this asymmetry?

I think this is a (very long standing) buglet in our complex
arithmetic, since you can directly see

  > 1+ 1i*Inf
  [1] NaN+Infi

    Robin> How to define an object with Re(b)=1, Im(b)=Inf?

{Oscar already mentioned    b <- complex(real=1, im=Inf) }

Martin Maechler, ETH Zurich

Actually, the problem comes from  "Inf * 1i" (or 1i * Inf)
and the 
	  0 * Inf |-> NaN
which of course is `correct' in general, but a bit undesirable
in the rule

   (a + bi) * (c + di)  =  (ac - bd) + (ad + bc)i

{and similarly in complex division}.

Note that the same problem also leads to

  > 1 * complex(re=0, im=Inf)
  [1] NaN+Infi

which is even more ugly,  
since  '1 * z' really should return 'z' for all z.

Martin

BTW:  S-plus (6.2.1) also returns NaN 
      (printing "NA".  S+ has no complex versions of 'NaN')

"MM" == Martin Maechler <maechler at stat.math.ethz.ch>
    on Wed, 13 Apr 2005 10:17:00 +0200 writes:

"Robin" == Robin Hankin <r.hankin at soc.soton.ac.uk>
    on Wed, 13 Apr 2005 08:51:19 +0100 writes:

Robin> Hi
    Robin> If I have

    Robin> a <- Inf + 1i

    Robin> then

    Robin> Re(a) is Inf, and Im(a) is 1, as expected.

    Robin> But if

    Robin> b <- 1 + Inf * 1i,

    Robin> then

    Robin> Im(b) = Inf ,  as expected,   but Re(b) = NaN, which I didn't expect.

    Robin> Why this asymmetry?

    MM> I think this is a (very long standing) buglet in our complex
    MM> arithmetic, since you can directly see

    >> 1+ 1i*Inf
    MM> [1] NaN+Infi

    Robin> How to define an object with Re(b)=1, Im(b)=Inf?

    MM> {Oscar already mentioned    b <- complex(real=1, im=Inf) }

    MM> Martin Maechler, ETH Zurich

    MM> ______________________________________________
    MM> R-help at stat.math.ethz.ch mailing list
    MM> https://stat.ethz.ch/mailman/listinfo/r-help
    MM> PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html

Actually, the problem comes from  "Inf * 1i" (or 1i * Inf)
and the
	  0 * Inf |-> NaN
which of course is `correct' in general, but a bit undesirable
in the rule

   (a + bi) * (c + di)  =  (ac - bd) + (ad + bc)i

thanks for this Martin.

Now I see what is going on, I wouldn't describe this as "undesirable" 
because
"(1+0i) * (0 + Inf i)"  depends  on the behaviour of the infinite limit
in the second bracket compared with the zero limit in the first.

To wit, f() and g() both calculate 1*(Inf i):



 >  f <- function(n){(1+1i/sqrt(n))*(0+n*1i)}
 > g <- function(n){(1+1i/n)*(0+sqrt(n)*1i)}
 > f(1e8)
[1] -10000+1e+08i
 > g(1e8)
[1] -1e-04+10000i
 >


So perhaps it's unreasonable to expect complex arithmetic to guess what 
I want.


very best wishes

rksh



Robin Hankin
Uncertainty Analyst
Southampton Oceanography Centre
European Way, Southampton SO14 3ZH, UK
  tel  023-8059-7743