[R] Questions about lexical scope

[Laurent Gautier]

Dear Joseph,


Did you get any answer about your problem ?

I have been toying with your examples and get a bit scared of what
is happening with lexical scoping...


I edited your function bv.integrate to have some informations about
what was going on.

bv.integrate <- function(f, a, b, n=100, rule=midpoint) {
  assign("count", 0, envir=.GlobalEnv)
  g <- function(y) {
    assign("count", get("count", envir=.GlobalEnv)+1, envir=.GlobalEnv
    fx <- function(x) f(x, y)
    rule(fx, a[2], b[2], n)
  }
  cat("# times in g:", get("count", envir=.GlobalEnv), "\n")
  rule(g, a[1], b[1])
}

my R sesssion gave the following:

> bv.integrate(function(x, y) sin(x + y), c(0,0), c(1,1), rule=trapezoidal)
# times in g: 0 
[1] 0.007080675
> print(count)
[1] 2

> bv.integrate(function(x, y) sin(x + y), c(0,0), c(1,1), rule=midpoint)
# times in g: 0 
[1] 0.773651
> print(count)
[1] 100


For some reason the function 'g' defined in bv.integrate is applied only
2 times when the rule is trapezoidal and 100 times when the rule is
midpoint (?!)... and the variable 'count' I defined in '.GlobalEnv' has
different values (depending on whether I am in '.GlobalEnv' or in
'bv.integrate'....


I must have missed something obvious somewhere... but where ?




L.





-- 
--------------------------------------------------------------
Laurent Gautier			CBS, Building 208, DTU
PhD. Student			DK-2800 Lyngby,Denmark	
tel: +45 45 25 24 89		http://www.cbs.dtu.dk/laurent




On Wed, Aug 07, 2002 at 12:28:28AM +0900, Lu Chi-Hsien Joseph wrote:
> Dear R-users,
> 
> The numerical integration example given in Gentleman and Ihaka (2000), 
> "Lexical Scope and Statistical Computing," JCGS, 9, 491-508,
> is very interesting and helpful in understanding how lexical scope 
> is about.
> However, I got some questions that I just can't figure out.
> First all, allow me to copy the two functions given by the authors:
> 
> midpoint <- function(f, a, b, n=100) {
>     h <- (b - a)/n
>     (b - a)*mean(sapply(seq(a + h/2, b - h/2, length=n), f))
> }
> 
> bv.integrate <- function(f, a, b, n=100, rule=midpoint) {
>     g <- function(y) {
>         fx <- function(x) f(x, y)
>         rule(fx, a[2], b[2], n)
>     }
>     rule(g, a[1], b[1])
> }
> 
> I modified the function name from "integrate" to "bv.integrate".
> To integrate f(x,y)=sin(x + y) over the unit square,
> it works:
> > bv.integrate(function(x, y) sin(x + y), c(0,0), c(1,1))
> [1] 0.773651
> (compare with .7736445 calculated from 2sin(1)*(1 - cos(1)))
> 
> Then I write a function using trapezoidal rule as follows:
> 
> trapezoidal <- function(f, a, b, n=100) {
>     h <- (b - a)/n
>     i <- 1:n
>     sum(f(a + (i - 1)*h), f(a + i*h))*h/2
> }
> 
> I checked with
> > trapezoidal(sin, 0, 1)
> [1] 0.4596939
> > 1 - cos(1)
> [1] 0.4596977
> 
> and
> > trapezoidal(dnorm, -3, 3)
> [1] 0.9972922
> > diff(pnorm(c(-3, 3)))
> [1] 0.9973002
> 
> Then, this is what I got by plugged in "trapezoidal" for the "rule" 
> in bv.integrate():
> > bv.integrate(function(x, y) sin(x + y), c(0,0), c(1,1), rule=trapezoidal)
> [1] 0.007080675
> 
> Hundred time smaller! 
> Answer can be "improved" by increasing n, but always 100 times smaller.
> 
> Anything wrong with the way I wrote trapezoidal()?
> I just can't figure out any difference, in terms of input/output,
> between midpoint() and trapezoidal().
> 
> Then I tried to use integrate() as the rule in bv.integrate(),
> by defining a wrap-up function:
> 
> intg <- function(f, a, b, n=100) integrate(f, a, b, n)$value
> 
> to have the value as the only output.
> But, I got
> > bv.integrate(function(x, y) sin(x + y), c(0,0), c(1,1), rule=intg)
> Error in integrate(f, a, b, n) : evaluation of function gave a result 
> of wrong length
> 
> I tried to use debugger() to find out what's wrong,
> but not succeeded.
> There must be something I missed in understanding the lexical scope,
> however, what's going on with the function I wrote?
> What should be the way to correct them?
> 
> Certainly, I know integrate() should be the one to use.
> These are questions from my preparation of programming exercise 
> of using R in my statistical computation class.
> 
> I'll be very appreciated for anyone who might help me on these
> questions.
> 
> Best regards,
> 
> C. Joseph Lu
> Department of Statistics
> National Cheng-Kung University
> Tainan, Taiwan, ROC
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