Re: [Rd] R-devel (r81196) hanging at dchisq(large) (PR#13309)

2021-11-16 Thread Martin Maechler
> Avraham Adler 
> on Tue, 16 Nov 2021 02:35:56 + writes:

> I am building r-devel on Windows 10 64bit using Jeroen's mingw system,
> and I am finding that my make check-devel hangs on the above issue.
> Everything is vanila except that I am using OpenBLAS 0.3.18. I have
> been using OpenBLAS for over a decade and have not had this issue
> before. Is there anything I can do to dig deeper into this issue from
> my end? Could there be anything that changed in R-devel that may have
> triggered this? The bugzilla report doesn't have any code attached to
> it.

> Thank you,
> Avi

Hmm.. it would've be nice to tell a bit more, instead of having all
your readers to search links, etc.

In the bugzilla bug report PR#13309
https://bugs.r-project.org/show_bug.cgi?id=13309 ,the example was

 dchisq(x=Inf, df=10, ncp=1)

I had fixed the bug 13 years ago, in svn rev 47005
with regression test in /tests/d-p-q-r-tests.R :


## Non-central Chi^2 density for large x
stopifnot(0 == dchisq(c(Inf, 1e80, 1e50, 1e40), df=10, ncp=1))
## did hang in 2.8.0 and earlier (PR#13309).


and you are seeing your version of R hanging at exactly this
location?


I'd bet quite a bit that the underlying code in these
non-central chi square computations *never* calls BLAS and hence
I cannot imagine how openBLAS could play a role.

However, there must be something peculiar in your compiler setup,
compilation options, 
as of course the above regression test has been run 100s of
1000s of times also under Windows in the last 13 years ..

Last but not least (but really only vaguely related):
   There is still a FIXME in the source code (but not about
hanging, but rather of loosing some accuracy in border cases),
see e.g. https://svn.r-project.org/R/trunk/src/nmath/dnchisq.c
and for that reason I had written an R version of that C code
even back in 2008 which I've made available in  CRAN package
DPQ  a few years ago (together with many other D/P/Q
distribution computations/approximations).
 -> https://cran.r-project.org/package=DPQ

Best,
Martin


> sessionInfo:
> R Under development (unstable) (2021-11-15 r81196)
> Platform: x86_64-w64-mingw32/x64 (64-bit)
> Running under: Windows 10 x64 (build 19043)

> Matrix products: default

> locale:
> [1] LC_COLLATE=English_United States.1252
> [2] LC_CTYPE=English_United States.1252
> [3] LC_MONETARY=English_United States.1252
> [4] LC_NUMERIC=C
> [5] LC_TIME=English_United States.1252

> attached base packages:
> [1] stats graphics  grDevices utils datasets  methods   base

> loaded via a namespace (and not attached):
> [1] compiler_4.2.0 tools_4.2.0

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[Rd] Inconsistent is.list results on 'by' objects

2021-11-16 Thread Ofek Shilon
Take this toy code:
df   <- data.frame(a=seq(10), b=rep(1:2, 5))
df.empty <- subset(df, a>10)
byy   <- by(data=df,   INDICES=df$b, FUN=function(x) x[1,])
byy.empty <- by(data=df.empty, INDICES=df.empty$b, FUN=function(x) x[1,])

class(byy)   # "by"
class(byy.empty) # "by"

is.list(byy)# TRUE
is.list(byy.empty)  # FALSE!


This behavior already messed up stuff elsewhere:
https://github.com/Rdatatable/data.table/issues/5258

I'd say any questions about the class of an object (whether 'class' or
indirectly by 'is.**')
should not have the answers depend on the specific contents of the object.

Does this qualify as an R bug? Am I missing something?

[[alternative HTML version deleted]]

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Re: [Rd] R-devel (r81196) hanging at dchisq(large) (PR#13309)

2021-11-16 Thread Avraham Adler
On Tue, Nov 16, 2021 at 8:43 AM Martin Maechler
 wrote:
>
> > Avraham Adler
> > on Tue, 16 Nov 2021 02:35:56 + writes:
>
> > I am building r-devel on Windows 10 64bit using Jeroen's mingw system,
> > and I am finding that my make check-devel hangs on the above issue.
> > Everything is vanila except that I am using OpenBLAS 0.3.18. I have
> > been using OpenBLAS for over a decade and have not had this issue
> > before. Is there anything I can do to dig deeper into this issue from
> > my end? Could there be anything that changed in R-devel that may have
> > triggered this? The bugzilla report doesn't have any code attached to
> > it.
>
> > Thank you,
> > Avi
>
> Hmm.. it would've be nice to tell a bit more, instead of having all
> your readers to search links, etc.
>
> In the bugzilla bug report PR#13309
> https://bugs.r-project.org/show_bug.cgi?id=13309 ,the example was
>
>  dchisq(x=Inf, df=10, ncp=1)
>
> I had fixed the bug 13 years ago, in svn rev 47005
> with regression test in /tests/d-p-q-r-tests.R :
>
>
> ## Non-central Chi^2 density for large x
> stopifnot(0 == dchisq(c(Inf, 1e80, 1e50, 1e40), df=10, ncp=1))
> ## did hang in 2.8.0 and earlier (PR#13309).
>
>
> and you are seeing your version of R hanging at exactly this
> location?
>
>
> I'd bet quite a bit that the underlying code in these
> non-central chi square computations *never* calls BLAS and hence
> I cannot imagine how openBLAS could play a role.
>
> However, there must be something peculiar in your compiler setup,
> compilation options, 
> as of course the above regression test has been run 100s of
> 1000s of times also under Windows in the last 13 years ..
>
> Last but not least (but really only vaguely related):
>There is still a FIXME in the source code (but not about
> hanging, but rather of loosing some accuracy in border cases),
> see e.g. https://svn.r-project.org/R/trunk/src/nmath/dnchisq.c
> and for that reason I had written an R version of that C code
> even back in 2008 which I've made available in  CRAN package
> DPQ  a few years ago (together with many other D/P/Q
> distribution computations/approximations).
>  -> https://cran.r-project.org/package=DPQ
>
> Best,
> Martin
>

Hello, Martin.

Apologies, I thought the PR # was sufficient. Yes, I am seeing this at
this exact location. This is what I saw in d-p-q-r-tst-2.Rout.fail and
I then ran d-p-q-r-tst.R line-by-line and R hung precisely after
`stopifnot(0 == dchisq(c(Inf, 1e80, 1e50, 1e40), df=10, ncp=1))`.

Is it at all possible that this has to do with the recent change from
bd0 to ebd0 (PR #15628) [1]?

For completeness, I ran all the code _beneath_ the call, and while
nothing else cause an infinite loop, I posted what I believe may be
unexpected results below,

Thank you,

Avi

[1]: https://bugs.r-project.org/show_bug.cgi?id=15628

> ## FIXME ?!:  MxM/2 seems +- ok ??
> (dLmM <- dnbinom(xL, mu = 1, size = MxM))  # all NaN but the last
Warning in dnbinom(xL, mu = 1, size = MxM) : NaNs produced
 [1] NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN   0
> (dLpI <- dnbinom(xL, prob=1/2, size = Inf))#  ditto
Warning in dnbinom(xL, prob = 1/2, size = Inf) : NaNs produced
 [1] NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN   0
> (dLpM <- dnbinom(xL, prob=1/2, size = MxM))#  ditto
Warning in dnbinom(xL, prob = 1/2, size = MxM) : NaNs produced
 [1] NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN   0

> d <- dnbinom(x,  mu = mu, size = Inf) # gave NaN (for 0 and L), now all 0
Warning in dnbinom(x, mu = mu, size = Inf) : NaNs produced
> p <- pnbinom(x,  mu = mu, size = Inf) # gave all NaN, now uses ppois(x, mu)
Warning in pnbinom(x, mu = mu, size = Inf) : NaNs produced

> pp <- (0:16)/16
> q <- qnbinom(pp, mu = mu, size = Inf) # gave all NaN
> set.seed(1); NI <- rnbinom(32, mu = mu, size = Inf)# gave all NaN
> set.seed(1); N2 <- rnbinom(32, mu = mu, size = L  )
> stopifnot(exprs = {
+ all.equal(d, c(0.006737947, 0.033689735, 0.0842243375,
0.140373896, 0,0,0,0), tol = 9e-9)# 7.6e-10
+ all.equal(p, c(0.006737947, 0.040427682, 0.1246520195,
0.265025915, 1,1,1,1), tol = 9e-9)# 7.3e-10
+ all.equal(d, dpois(x, mu))# current implementation: even identical()
+ all.equal(p, ppois(x, mu))
+ q == c(0, 2, 3, 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 7, 8, 9, Inf)
+ q == qpois(pp, mu)
+ identical(NI, N2)
+ })
Error: d and c(0.006737947, 0.033689735, 0.0842243375, 0.140373896, 0,
0,   are not equal:
  'is.NA' value mismatch: 0 in current 1 in target

> if(!(onWindows && arch == "x86")) {
+  ## This gave a practically infinite loop (on 64-bit Lnx, Windows;
not in 32-bit)
+ tools::assertWarning(p <- pchisq(1.0012e200, df=1e200, ncp=100),
+  "simpleWarning", verbose=TRUE)
+ stopifnot(p == 1)
+ 

Re: [Rd] Inconsistent is.list results on 'by' objects

2021-11-16 Thread Bill Dunlap
Try adding simplify=FALSE to the call to by().

-Bill

On Tue, Nov 16, 2021 at 4:04 AM Ofek Shilon  wrote:

> Take this toy code:
> df   <- data.frame(a=seq(10), b=rep(1:2, 5))
> df.empty <- subset(df, a>10)
> byy   <- by(data=df,   INDICES=df$b, FUN=function(x) x[1,])
> byy.empty <- by(data=df.empty, INDICES=df.empty$b, FUN=function(x) x[1,])
>
> class(byy)   # "by"
> class(byy.empty) # "by"
>
> is.list(byy)# TRUE
> is.list(byy.empty)  # FALSE!
>
>
> This behavior already messed up stuff elsewhere:
> https://github.com/Rdatatable/data.table/issues/5258
>
> I'd say any questions about the class of an object (whether 'class' or
> indirectly by 'is.**')
> should not have the answers depend on the specific contents of the object.
>
> Does this qualify as an R bug? Am I missing something?
>
> [[alternative HTML version deleted]]
>
> __
> R-devel@r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-devel
>

[[alternative HTML version deleted]]

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[Rd] LOGNAME env var in the check code

2021-11-16 Thread Gábor Csárdi
While trying to reproduce a NOTE for

* checking for new files in some other directories ... NOTE

I noticed that the check code uses

Sys.getenv("LOGNAME")

to query the name of the current user. However on many systems this is
not set, so this is the empty string, and then no NOTE is shown. (Only
files owned by the current user generate a NOTE.)

An alternative would be to call `id -un` to query the username, or
create a file and then use `file.info()` to query its owner. Using one
of these alternatives would make this check more reproducible.

Thanks,
Gabor

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Re: [Rd] R-devel (r81196) hanging at dchisq(large) (PR#13309)

2021-11-16 Thread Kevin Ushey
Do you see this same hang in a build of R with debug symbols? Can you
try running R with GDB, or even WinDbg or another debugger, to see
what the call stack looks like when the hang occurs? Does the hang
depend on the number of threads used by OpenBLAS?

On the off chance it's relevant, I've seen hangs / crashes when using
a multithreaded OpenBLAS with R on some Linux systems before, but
never found the time to isolate a root cause.

Best,
Kevin

On Tue, Nov 16, 2021 at 5:12 AM Avraham Adler  wrote:
>
> On Tue, Nov 16, 2021 at 8:43 AM Martin Maechler
>  wrote:
> >
> > > Avraham Adler
> > > on Tue, 16 Nov 2021 02:35:56 + writes:
> >
> > > I am building r-devel on Windows 10 64bit using Jeroen's mingw system,
> > > and I am finding that my make check-devel hangs on the above issue.
> > > Everything is vanila except that I am using OpenBLAS 0.3.18. I have
> > > been using OpenBLAS for over a decade and have not had this issue
> > > before. Is there anything I can do to dig deeper into this issue from
> > > my end? Could there be anything that changed in R-devel that may have
> > > triggered this? The bugzilla report doesn't have any code attached to
> > > it.
> >
> > > Thank you,
> > > Avi
> >
> > Hmm.. it would've be nice to tell a bit more, instead of having all
> > your readers to search links, etc.
> >
> > In the bugzilla bug report PR#13309
> > https://bugs.r-project.org/show_bug.cgi?id=13309 ,the example was
> >
> >  dchisq(x=Inf, df=10, ncp=1)
> >
> > I had fixed the bug 13 years ago, in svn rev 47005
> > with regression test in /tests/d-p-q-r-tests.R :
> >
> >
> > ## Non-central Chi^2 density for large x
> > stopifnot(0 == dchisq(c(Inf, 1e80, 1e50, 1e40), df=10, ncp=1))
> > ## did hang in 2.8.0 and earlier (PR#13309).
> >
> >
> > and you are seeing your version of R hanging at exactly this
> > location?
> >
> >
> > I'd bet quite a bit that the underlying code in these
> > non-central chi square computations *never* calls BLAS and hence
> > I cannot imagine how openBLAS could play a role.
> >
> > However, there must be something peculiar in your compiler setup,
> > compilation options, 
> > as of course the above regression test has been run 100s of
> > 1000s of times also under Windows in the last 13 years ..
> >
> > Last but not least (but really only vaguely related):
> >There is still a FIXME in the source code (but not about
> > hanging, but rather of loosing some accuracy in border cases),
> > see e.g. https://svn.r-project.org/R/trunk/src/nmath/dnchisq.c
> > and for that reason I had written an R version of that C code
> > even back in 2008 which I've made available in  CRAN package
> > DPQ  a few years ago (together with many other D/P/Q
> > distribution computations/approximations).
> >  -> https://cran.r-project.org/package=DPQ
> >
> > Best,
> > Martin
> >
>
> Hello, Martin.
>
> Apologies, I thought the PR # was sufficient. Yes, I am seeing this at
> this exact location. This is what I saw in d-p-q-r-tst-2.Rout.fail and
> I then ran d-p-q-r-tst.R line-by-line and R hung precisely after
> `stopifnot(0 == dchisq(c(Inf, 1e80, 1e50, 1e40), df=10, ncp=1))`.
>
> Is it at all possible that this has to do with the recent change from
> bd0 to ebd0 (PR #15628) [1]?
>
> For completeness, I ran all the code _beneath_ the call, and while
> nothing else cause an infinite loop, I posted what I believe may be
> unexpected results below,
>
> Thank you,
>
> Avi
>
> [1]: https://bugs.r-project.org/show_bug.cgi?id=15628
>
> > ## FIXME ?!:  MxM/2 seems +- ok ??
> > (dLmM <- dnbinom(xL, mu = 1, size = MxM))  # all NaN but the last
> Warning in dnbinom(xL, mu = 1, size = MxM) : NaNs produced
>  [1] NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
> NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN   0
> > (dLpI <- dnbinom(xL, prob=1/2, size = Inf))#  ditto
> Warning in dnbinom(xL, prob = 1/2, size = Inf) : NaNs produced
>  [1] NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
> NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN   0
> > (dLpM <- dnbinom(xL, prob=1/2, size = MxM))#  ditto
> Warning in dnbinom(xL, prob = 1/2, size = MxM) : NaNs produced
>  [1] NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
> NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN   0
>
> > d <- dnbinom(x,  mu = mu, size = Inf) # gave NaN (for 0 and L), now all 0
> Warning in dnbinom(x, mu = mu, size = Inf) : NaNs produced
> > p <- pnbinom(x,  mu = mu, size = Inf) # gave all NaN, now uses ppois(x, mu)
> Warning in pnbinom(x, mu = mu, size = Inf) : NaNs produced
>
> > pp <- (0:16)/16
> > q <- qnbinom(pp, mu = mu, size = Inf) # gave all NaN
> > set.seed(1); NI <- rnbinom(32, mu = mu, size = Inf)# gave all NaN
> > set.seed(1); N2 <- rnbinom(32, mu = mu, size = L  )
> > stopifnot(exprs = {
> + all.equal(d, c(0.006737947, 0.033689735, 0.0842243375,
> 0.140373896, 0,0,0,0), tol = 9e-9)# 7.6e-10
> + all.equal(p, c(0.006737947, 0.040427682,

Re: [Rd] Inconsistent is.list results on 'by' objects

2021-11-16 Thread Kevin Ushey
You can see this a bit more clearly with e.g.

> storage.mode(byy)
[1] "list"
> storage.mode(byy.empty)
[1] "logical"

So even though both objects have S3 class "by", they have a different
underlying internal storage mode (as simplifying the result of 'by'
has given you a 0-length logical, instead of a 0-length list).

Best,
Kevin

On Tue, Nov 16, 2021 at 10:21 AM Bill Dunlap  wrote:
>
> Try adding simplify=FALSE to the call to by().
>
> -Bill
>
> On Tue, Nov 16, 2021 at 4:04 AM Ofek Shilon  wrote:
>
> > Take this toy code:
> > df   <- data.frame(a=seq(10), b=rep(1:2, 5))
> > df.empty <- subset(df, a>10)
> > byy   <- by(data=df,   INDICES=df$b, FUN=function(x) x[1,])
> > byy.empty <- by(data=df.empty, INDICES=df.empty$b, FUN=function(x) x[1,])
> >
> > class(byy)   # "by"
> > class(byy.empty) # "by"
> >
> > is.list(byy)# TRUE
> > is.list(byy.empty)  # FALSE!
> >
> >
> > This behavior already messed up stuff elsewhere:
> > https://github.com/Rdatatable/data.table/issues/5258
> >
> > I'd say any questions about the class of an object (whether 'class' or
> > indirectly by 'is.**')
> > should not have the answers depend on the specific contents of the object.
> >
> > Does this qualify as an R bug? Am I missing something?
> >
> > [[alternative HTML version deleted]]
> >
> > __
> > R-devel@r-project.org mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-devel
> >
>
> [[alternative HTML version deleted]]
>
> __
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Re: [Rd] R-devel (r81196) hanging at dchisq(large) (PR#13309)

2021-11-16 Thread Avraham Adler
On Tue, Nov 16, 2021 at 10:42 PM Kevin Ushey  wrote:
>
> Do you see this same hang in a build of R with debug symbols? Can you
> try running R with GDB, or even WinDbg or another debugger, to see
> what the call stack looks like when the hang occurs? Does the hang
> depend on the number of threads used by OpenBLAS?
>
> On the off chance it's relevant, I've seen hangs / crashes when using
> a multithreaded OpenBLAS with R on some Linux systems before, but
> never found the time to isolate a root cause.
>


This last was a good thought, Kevin, as I had just compiled OpenBLAS
3.18 multi-threaded, but I recompiled it single threaded and it still
crashes. The version of R I built from source last time, (2021-05-20
r80347), does not hang when calling `dchisq(c(Inf, 1e80, 1e50, 1e40),
df=10, ncp=1)`. I think I built that with OpenBLAS 3.15. I can try
doing that here. As for building with debug symbols, I have never done
that before, so if you could provide some guidance (off-list if you
think it is inappropriate to keep it here) or point me in the
direction of some already posted advice, I would appreciate it!

Avi



> Best,
> Kevin
>
> On Tue, Nov 16, 2021 at 5:12 AM Avraham Adler  wrote:
> >
> > On Tue, Nov 16, 2021 at 8:43 AM Martin Maechler
> >  wrote:
> > >
> > > > Avraham Adler
> > > > on Tue, 16 Nov 2021 02:35:56 + writes:
> > >
> > > > I am building r-devel on Windows 10 64bit using Jeroen's mingw 
> > > system,
> > > > and I am finding that my make check-devel hangs on the above issue.
> > > > Everything is vanila except that I am using OpenBLAS 0.3.18. I have
> > > > been using OpenBLAS for over a decade and have not had this issue
> > > > before. Is there anything I can do to dig deeper into this issue 
> > > from
> > > > my end? Could there be anything that changed in R-devel that may 
> > > have
> > > > triggered this? The bugzilla report doesn't have any code attached 
> > > to
> > > > it.
> > >
> > > > Thank you,
> > > > Avi
> > >
> > > Hmm.. it would've be nice to tell a bit more, instead of having all
> > > your readers to search links, etc.
> > >
> > > In the bugzilla bug report PR#13309
> > > https://bugs.r-project.org/show_bug.cgi?id=13309 ,the example was
> > >
> > >  dchisq(x=Inf, df=10, ncp=1)
> > >
> > > I had fixed the bug 13 years ago, in svn rev 47005
> > > with regression test in /tests/d-p-q-r-tests.R :
> > >
> > >
> > > ## Non-central Chi^2 density for large x
> > > stopifnot(0 == dchisq(c(Inf, 1e80, 1e50, 1e40), df=10, ncp=1))
> > > ## did hang in 2.8.0 and earlier (PR#13309).
> > >
> > >
> > > and you are seeing your version of R hanging at exactly this
> > > location?
> > >
> > >
> > > I'd bet quite a bit that the underlying code in these
> > > non-central chi square computations *never* calls BLAS and hence
> > > I cannot imagine how openBLAS could play a role.
> > >
> > > However, there must be something peculiar in your compiler setup,
> > > compilation options, 
> > > as of course the above regression test has been run 100s of
> > > 1000s of times also under Windows in the last 13 years ..
> > >
> > > Last but not least (but really only vaguely related):
> > >There is still a FIXME in the source code (but not about
> > > hanging, but rather of loosing some accuracy in border cases),
> > > see e.g. https://svn.r-project.org/R/trunk/src/nmath/dnchisq.c
> > > and for that reason I had written an R version of that C code
> > > even back in 2008 which I've made available in  CRAN package
> > > DPQ  a few years ago (together with many other D/P/Q
> > > distribution computations/approximations).
> > >  -> https://cran.r-project.org/package=DPQ
> > >
> > > Best,
> > > Martin
> > >
> >
> > Hello, Martin.
> >
> > Apologies, I thought the PR # was sufficient. Yes, I am seeing this at
> > this exact location. This is what I saw in d-p-q-r-tst-2.Rout.fail and
> > I then ran d-p-q-r-tst.R line-by-line and R hung precisely after
> > `stopifnot(0 == dchisq(c(Inf, 1e80, 1e50, 1e40), df=10, ncp=1))`.
> >
> > Is it at all possible that this has to do with the recent change from
> > bd0 to ebd0 (PR #15628) [1]?
> >
> > For completeness, I ran all the code _beneath_ the call, and while
> > nothing else cause an infinite loop, I posted what I believe may be
> > unexpected results below,
> >
> > Thank you,
> >
> > Avi
> >
> > [1]: https://bugs.r-project.org/show_bug.cgi?id=15628
> >
> > > ## FIXME ?!:  MxM/2 seems +- ok ??
> > > (dLmM <- dnbinom(xL, mu = 1, size = MxM))  # all NaN but the last
> > Warning in dnbinom(xL, mu = 1, size = MxM) : NaNs produced
> >  [1] NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
> > NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN   0
> > > (dLpI <- dnbinom(xL, prob=1/2, size = Inf))#  ditto
> > Warning in dnbinom(xL, prob = 1/2, size = Inf) : NaNs produced
> >  [1] NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
> > NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN   0