[R] Need help to understand integrate function

[Ravi Varadhan]

The magic is not in setting options(digits=10).  I did that just to show you the accuracy of the answer.  The magic is in setting a more stringent error tolerance,  rel.tol=1.e-10.

The divergent error is due to the fact that the default tolerance of (roughly) 1.e-04 is too large.

Ravi.

____________________________________________________________________

Ravi Varadhan, Ph.D.
Assistant Professor,
Division of Geriatric Medicine and Gerontology
School of Medicine
Johns Hopkins University

Ph. (410) 502-2619
email: rvaradhan at jhmi.edu


----- Original Message -----
From: R_help Help <rhelpacc at gmail.com>
Date: Thursday, August 12, 2010 9:23 pm
Subject: Re: [R] Need help to understand integrate function
To: Ravi Varadhan <rvaradhan at jhmi.edu>
Cc: r-help at r-project.org


> Hi Ravi - Thank you. I'm wondering how the magic happens here with
>  options(digits=10)? And the most important point, I do not quite
>  understand why divergent error could occur. In this case, the function
>  is analytically integrable. Any insight would be greatly appreciated
>  so that I learn something out of this. Thank you.
>  
>  Rob
>  
>  On Wed, Aug 11, 2010 at 11:46 PM, Ravi Varadhan <rvaradhan at jhmi.edu> 
> wrote:
>  > Try this:
>  >
>  > options(digits=10)
>  >
>  >> integrate(f=powerLaw2, lower=0, upper=Inf, l1=1.8980185, 
> l2=-0.0804259, c0=1, t0=259.78, rel.tol=1.e-10)
>  > 0.01089019946 with absolute error < 3.7e-11
>  >
>  >
>  > Ravi.
>  > ____________________________________________________________________
>  >
>  > Ravi Varadhan, Ph.D.
>  > Assistant Professor,
>  > Division of Geriatric Medicine and Gerontology
>  > School of Medicine
>  > Johns Hopkins University
>  >
>  > Ph. (410) 502-2619
>  > email: rvaradhan at jhmi.edu
>  >
>  >
>  > ----- Original Message -----
>  > From: R_help Help <rhelpacc at gmail.com>
>  > Date: Wednesday, August 11, 2010 9:44 pm
>  > Subject: [R] Need help to understand integrate function
>  > To: r-help at r-project.org
>  >
>  >
>  >> Hi,
>  >>
>  >>  I'm running into a wall when trying to use the integrate 
> function. I
>  >>  have the following setting:
>  >>
>  >>  powerLaw2 <- function(x,l1,l2,c0,t0) {
>  >>
>  >>     idx <- which(x <= 0);
>  >>     if (length(idx) > 0) {
>  >>        x[idx] <- 0;
>  >>     }
>  >>
>  >>     xl <- (-l1+l2)*log(x/t0);
>  >>     L <- log(c0)-l1*log(x)-log(1+exp(xl));
>  >>     L <- exp(L);
>  >>     return(L);
>  >>  }
>  >>
>  >>  plCDF2 <- function(x,l1,l2,c0,t0) {
>  >>
>  >>     print(c(l1,l2,c0,t0));
>  >>     cdf <- integrate(f=powerLaw2,lower=x,upper=Inf,l1=l1,l2=l2,c0=c0,t0=t0,stop.on.error=T);
>  >>     return(cdf$value);
>  >>
>  >>  }
>  >>
>  >>  I know that as long as my l1 > 1 and l2 < 1 the integration above
>  >>  should converge. However, this doesn't seem to be the case when I 
> call
>  >>  integrate function with the following parameter:
>  >>
>  >>
>  >>  Browse[1]> integrate(f=powerLaw2,lower=1e-09,upper=Inf,l1=1.8980185,l2=-0.0804259,c0=1,t0=259.78,stop.on.error=T)
>  >>  failed with message 'the integral is probably divergent'
>  >>
>  >>  Would you please shed some light? And how could I prevent this
>  >>  situation? Thank you.
>  >>
>  >>  Rgds,
>  >>
>  >>  Rob
>  >>
>  >>  ______________________________________________
>  >>  R-help at r-project.org mailing list
>  >>
>  >>  PLEASE do read the posting guide
>  >>  and provide commented, minimal, self-contained, reproducible code.
>  >