# [R] Alternatives to integrate?

. . xkziloj at gmail.com
Fri Sep 2 02:57:28 CEST 2011

```Thanks for your reply Michael, it seems I have a lot of things to
learn yet but for sure, your response is being very helpful in this
proccess. I will try to explore every point you said:

A doubt I have is, if I define "func <- function(x,y) x + y" how can I
integrate it only in "x"? My solution for this would be to define
"func <- function(x) x + y". Is not ok?

Also, with respect to the helper functions I'd created, I am wondering
if you can see a better organization for my code. It is so because
this is the only way I can see. Particularly I do not like how I am
using "results", but I can not think in another form.

On Thu, Sep 1, 2011 at 2:44 PM, R. Michael Weylandt
<michael.weylandt at gmail.com> wrote:
> Leaving aside some other issues that this whole email chain has opened up,
>
> I'd guess that your most immediate problem is that you are trying to
> numerically integrate the PMF of a discrete distribution but you are
> treating it as a continuous distribution. If you took the time to properly
> debug (as you were instructed yesterday) you'd probably find that whenever
> you call dpois(x, lambda) for x not an integer you get a warning message.
>
> Specifically, check this out
>
>> integrate(dpois,0,Inf,1)
> 9.429158e-13 with absolute error < 1.7e-12
>
>> n = 0:1000; sum(dpois(n,1))
> 1
>
> I could be entirely off base here, but I'm guessing that many of your
> problems derive from this.
>
>
>
> or this
>
> And, perhaps most importantly, don't rely on the black magic of values
> moving in and out of functions (lexical scoping). Seriously, just don't do
> it.
>
> If you have helper functions that need values, actively pass them: you will
> save yourself hours of trouble when (not if) you debug your functions. I'm
> looking, for example, at g() in the first big block of code you provided.
> Call it g(a,n) and spend the extra 4 keystrokes to pass the values. It makes
> everyone happier.
>
> Michael
>
> On Thu, Sep 1, 2011 at 12:37 PM, . . <xkziloj at gmail.com> wrote:
>>
>> So, please excuse me Michael, you are completely sure. I will try
>> describe I am trying to do, please let me know if I can provide more
>> info.
>>
>> The idea is provide to "func" two probability density functions(PDFs)
>> and obtain another PDF that is a compound of them. In a final analysis
>> this characterize an abundance distribution for me. The two PDFs are
>> provided through "f" and "g" and there is some manipulation here
>> because I need flexibility to easily change this two funcions.
>>
>> In the code provided, "f" is the Exponential distribution and "g" is
>> the Poisson distribution. For this case, I have the analytical
>> solution, below. This way I can check the result. But I am also
>> considering other combinations of  "f" and "g" that have difficult, or
>> even does not have analitical solution. This is the reason why I am
>> trying to develop "func".
>>
>> func2 <- function(y, frac, rate, trunc=0, log=FALSE) {
>>    is.wholenumber <- function(x, tol = .Machine\$double.eps^0.5)
>>        abs(x - round(x)) < tol
>>    if(FALSE %in% sapply(y,is.wholenumber))
>>        print("y must be integer because dpoix is a discrete PDF.")
>>    else {
>>        f <- function(y){
>>            b <- y*log(frac)
>>            m <- log(rate)
>>            n <- (y+1)*log(rate+frac)
>>            if(log)b+m-n else exp(b+m-n)
>>        }
>>        f(y)/(1-f(trunc))
>>    }
>> }
>> > func2(200,0.05,0.001)
>> [1] 0.000381062
>>
>> In theory, the interval of integration is 0 to Inf, but for some tests
>> I did, go up to 2000 may still provide reasonable results.
>>
>> Also, as it seems, I am still writing my first functions in R and
>>
>> Again, appologies for my previous mistake. It was not my intention to
>>
>> On Thu, Sep 1, 2011 at 11:49 AM, R. Michael Weylandt
>> <michael.weylandt at gmail.com> wrote:
>> > I'm going to try to put this nicely:
>> >
>> > What you provided is not a problem with integrate. Instead, you provided
>> > a
>> > rather unintelligible and badly-written piece of code that
>> > (miraculously)
>> > seems to work, though it's not well documented so I have no idea if
>> > 1.3e-21
>> > is what you want to get.
>> >
>> > Let's try this again: per your original request, what is the problem
>> > with
>> > integrate?
>> >
>> > If instead you feel there's something wrong with your code, might I
>> > suggest
>> > you just say that and ask for help, rather than passing the blame onto a
>> > perfectly useful base function.
>> >
>> > Oh, and since you asked that I propose something: comment your code.
>> >
>> > Michael
>> >
>> > On Thu, Sep 1, 2011 at 10:33 AM, . . <xkziloj at gmail.com> wrote:
>> >>
>> >> Hi Michael,
>> >>
>> >> This is the problem:
>> >>
>> >> func <- Vectorize(function(x, a, sad, samp="pois", trunc=0, ...) {
>> >>  result <- function(x) {
>> >>    f1 <- function(n) {
>> >>                        f <- function() {
>> >>        dcom <- paste("d", sad, sep="")
>> >>        dots <- c(as.name("n"), list(...))
>> >>        do.call(dcom, dots)
>> >>                        }
>> >>      g <- function() {
>> >>        dcom <- paste("d", samp, sep="")
>> >>        lambda <- a * n
>> >>        dots <- c(as.name("x"), as.name("lambda"))
>> >>        do.call(dcom, dots)
>> >>      }
>> >>      f() * g()
>> >>    }
>> >>    integrate(f1,0,2000)\$value
>> >>
>> >> #     n <- 0:2000
>> >> #     trapz(n,f1(n))
>> >>
>> >> #     area(f1, 0, 2000, limit=10000, eps=1e-100)
>> >>  }
>> >>  return(result(x) / (1 - result(trunc)))
>> >> }, "x")
>> >> func(200, 0.05, "exp", rate=0.001)
>> >>
>> >> If you could propose something I will be gratefull.
>> >>
>> >>
>> >> On Thu, Sep 1, 2011 at 10:55 AM, R. Michael Weylandt
>> >> <michael.weylandt at gmail.com> wrote:
>> >> > Mr ". .",
>> >> >
>> >> > MASS::area comes to mind but it may be more helpful if you could say
>> >> > what
>> >> > you are looking for / why integrate is not appropriate it is for
>> >> > whatever
>> >> > you are doing.
>> >> >
>> >> > Strictly speaking, I suppose there are all sorts of "alternatives" to
>> >> > integrate() if you are willing to be really creative and build
>> >> > something
>> >> > from scratch: diff(), cumsum(), lm(), hist(), t(), c(), ....
>> >> >
>> >> > Michael Weylandt
>> >> >
>> >> > On Thu, Sep 1, 2011 at 9:53 AM, B77S <bps0002 at auburn.edu> wrote:
>> >> >>
>> >> >> package "caTools"
>> >> >> see ?trapz
>> >> >>
>> >> >>
>> >> >> . wrote:
>> >> >> >
>> >> >> > Hi all,
>> >> >> >
>> >> >> > is there any alternative to the function integrate?
>> >> >> >
>> >> >> > Any comments are welcome.
>> >> >> >
>> >> >> > Thanks in advance.
>> >> >> >
>> >> >> > ______________________________________________
>> >> >> > R-help at r-project.org mailing list
>> >> >> > https://stat.ethz.ch/mailman/listinfo/r-help
>> >> >> > http://www.R-project.org/posting-guide.html
>> >> >> > and provide commented, minimal, self-contained, reproducible code.
>> >> >> >
>> >> >>
>> >> >> --
>> >> >> View this message in context:
>> >> >>
>> >> >>
>> >> >> http://r.789695.n4.nabble.com/Alternatives-to-integrate-tp3783624p3783645.html
>> >> >> Sent from the R help mailing list archive at Nabble.com.
>> >> >>
>> >> >> ______________________________________________
>> >> >> R-help at r-project.org mailing list
>> >> >> https://stat.ethz.ch/mailman/listinfo/r-help