Actually, it's very easy to integrate a function of two variables in a
single variable for a given value of the other variable.

Using your example:

MySum <- function(x,y) {
     ans = x + y
     return(ans)
}

Note a things about how I wrote this. One, I broke the function out and used
curly braces to enclose the body of the expression; secondly, I kept the
body of the function at a constant indent level using spaces, not hard tabs;
thirdly, I gave it a meaningful (if somewhat silly) name. (There are so many
things that have names like "func" or "f" in R that you really don't want to
risk overloading something important) Finally, I used the (technically
unnecessary) return() command to say specifically what values my function
will be return. The use of "ans" is a personal preference, but I think it
makes clear what the function is aiming at.

Suppose I want to integrate this over [0,1] with y = 3. This can be coded

R> integrate(MySum, 0, 1, 3)
3.5

If you read the documentation for integrate (? integrate) you'll see that
there is an optional "..." argument that allows further parameters to be
passed to the integrand. Here, this is only the value of y.

Now suppose I want to define a function that integrates over that same unit
interval but takes y as an argument. This can be done as

BadIntegrateMySum <- function(y) {
     ans = integrate(MySum, 0, 1, y)
     return(ans)
}

However, this is a potentially dangerous thing to do because it requires
MySum to just show up inside of BadIntegrateMySum. R is able to try to help
you out, but really it's very dangerous so don't rely on it. Rather, define
MySum inside of the first function as a helper inside of the larger
function:

GoodIntegrateMySum <- function(y) {

    MySumHelper <- function(x,y) {
        ans = x + y
        return(ans)
    }

    ans = integrate(MySumHelper, 0, 1, y)
    return(ans)
}

Hopefully this is much clearer. There's a slightly contentious stylistic
point here -- whether it's ok to use y in the definition of the helper and
in the bigger function -- but I think it's ok in this circumstance because
the two instances specifically correspond to each other.

A more general form of this could take in "MySumHelper" as an argument (yes
functions can be passed like that)

# MySum as above

GoodIntegrateUnitInterval <- function(xIntegrand, yParameter) {
    # Requires xIntegrand to be a function of two variables x,y
    # You can actually do this in the code, but for now let's just assume no
user error and that xIntegrand is the right sort of thing.
    ans = integrate(xIntegrand, 0, 1, yParameter)
    return(ans)
}

R> GoodIntegrateUnitInverval(MySum, 3)
3.5

as before.

There's nothing wrong with using "result" like I've used "ans," but I do
hesitate to see it used as a function rather than a variable. A good rule of
thumb is to check if a variable is already defined as a function name using
the apropos() command.

I don't have time or inclination to rework your whole code right now, but
take a stab at formatting it with consistent+informative variable and
function names, a well reasoned use of scoping, and appropriate use of
integrate() and I'll happily comment on it.

Hope this helps,

Michael Weylandt

On Thu, Sep 1, 2011 at 8:57 PM, . . <xkziloj@gmail.com> wrote:

> 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.
>
> Thanks in advance.
>
> On Thu, Sep 1, 2011 at 2:44 PM, R. Michael Weylandt
> <michael.weylandt@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.
> >
> >
> >
> > On another basis, please, please read this:
> > http://google-styleguide.googlecode.com/svn/trunk/google-r-style.html
> > or this
> > http://had.co.nz/stat405/resources/r-style-guide.html
> >
> > 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@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
> >> suggestions are welcome, please.
> >>
> >> Again, appologies for my previous mistake. It was not my intention to
> >> blame about "integrate".
> >>
> >> On Thu, Sep 1, 2011 at 11:49 AM, R. Michael Weylandt
> >> <michael.weylandt@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@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
> >> >> #     adaptIntegrate(f1,0,2000)$integral
> >> >>
> >> >> #     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.
> >> >>
> >> >> Thanks in advance.
> >> >>
> >> >> On Thu, Sep 1, 2011 at 10:55 AM, R. Michael Weylandt
> >> >> <michael.weylandt@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@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@r-project.org mailing list
> >> >> >> > https://stat.ethz.ch/mailman/listinfo/r-help
> >> >> >> > PLEASE do read the posting guide
> >> >> >> > 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@r-project.org mailing list
> >> >> >> https://stat.ethz.ch/mailman/listinfo/r-help
> >> >> >> PLEASE do read the posting guide
> >> >> >> http://www.R-project.org/posting-guide.html
> >> >> >> and provide commented, minimal, self-contained, reproducible code.
> >> >> >
> >> >> >
> >> >
> >> >
> >
> >
>

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