qnbinom with small size is slow

?? I can reproduce this on

R Under development (unstable) (2020-07-24 r78910)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Pop!_OS 18.04 LTS

 ? In my opinion this is worth reporting, but discussing it here first 
was a good idea.? Many more people read this list than watch the bug 
tracker, so it will get more attention here; once the excitement has 
died down here (which might be almost immediately!), if no-one has 
already volunteered to post it to the bug tracker, request an account 
(as specified at https://www.r-project.org/bugs.html )

 ? Thanks!

 ?? Ben Bolker


For what it's worth it doesn't seem to be a threshold effect: approximately

log10(time[seconds]) ~ -8 - log10(-size)

over the range from 1e-6 to 1e-9


ff <- function(x) {
 ?? system.time(qnbinom(0.5, mu=3, size=10^x))[["elapsed"]]
}
svec <- seq(-5,-9,by=-0.2)
res <- lapply(svec, function(x) {
 ??? cat(x,"\n")
 ??? replicate(10,ff(x))
 ??? })

dd <- data.frame(size=rep(svec,each=10),
 ???????????????? time=unlist(res))
boxplot(log10(time)~size, dd)
summary(lm(log10(time)~size, data=dd, subset=time>0))

Hi all,

I recently noticed that `qnbinom()` can take a long time to calculate
a result if the `size` argument is very small.
For example
    qnbinom(0.5, mu = 3, size = 1e-10)
takes ~30 seconds on my computer.

I used gdb to step through the qnbinom.c implementation and noticed
that in line 106
(https://github.com/wch/r-source/blob/f8d4d7d48051860cc695b99db9be9cf439aee743/src/nmath/qnbinom.c#L106)
`y` becomes a very large negative number. Later in the function `y` is
(as far as I can see) only used as input for `pnbinom()` which is why
I would assume that it should be a non-negative integer.

I was wondering if this behavior could be considered a bug and should
be reported on the bugzilla? I read the instructions at
https://www.r-project.org/bugs.html and wasn't quite sure, so I
decided to ask here first :)

Best,
Constantin




PS: I tested the code with R 4.0.0 on macOS and the latest unstable
version using docker (https://github.com/wch/r-debug). The session
info is

sessionInfo()

R Under development (unstable) (2020-08-06 r78973)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Ubuntu 20.04 LTS

Matrix products: default
BLAS:   /usr/local/RD/lib/R/lib/libRblas.so
LAPACK: /usr/local/RD/lib/R/lib/libRlapack.so

locale:
  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C
  [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8
  [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8
  [7] LC_PAPER=en_US.UTF-8       LC_NAME=C
  [9] LC_ADDRESS=C               LC_TELEPHONE=C
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C

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

loaded via a namespace (and not attached):
[1] compiler_4.1.0

______________________________________________
R-devel at r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-devel

Thanks Ben for verifying the issue. It is always reassuring to hear
when others can reproduce the problem.

I wrote a small patch that fixes the issue
(https://github.com/r-devel/r-svn/pull/11):

diff --git a/src/nmath/qnbinom.c b/src/nmath/qnbinom.c
index b313ce56b2..d2e8d98759 100644
--- a/src/nmath/qnbinom.c
+++ b/src/nmath/qnbinom.c
@@ -104,6 +104,7 @@ double qnbinom(double p, double size, double prob,
int lower_tail, int log_p)
     /* y := approx.value (Cornish-Fisher expansion) :  */
     z = qnorm(p, 0., 1., /*lower_tail*/TRUE, /*log_p*/FALSE);
     y = R_forceint(mu + sigma * (z + gamma * (z*z - 1) / 6));
+    y = fmax2(0.0, y);

     z = pnbinom(y, size, prob, /*lower_tail*/TRUE, /*log_p*/FALSE);

I used the https://github.com/r-devel/r-svn repo and its continuous
integration tools to check that it doesn't break any existing tests:
https://github.com/r-devel/r-svn/actions/runs/201327042

I have also requested a Bugzilla-account, but haven't heard anything back yet.

Best,
Constantin

Am Fr., 7. Aug. 2020 um 21:41 Uhr schrieb Ben Bolker <bbolker at gmail.com>:

    I can reproduce this on

R Under development (unstable) (2020-07-24 r78910)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Pop!_OS 18.04 LTS

   In my opinion this is worth reporting, but discussing it here first
was a good idea.  Many more people read this list than watch the bug
tracker, so it will get more attention here; once the excitement has
died down here (which might be almost immediately!), if no-one has
already volunteered to post it to the bug tracker, request an account
(as specified at https://www.r-project.org/bugs.html )

   Thanks!

    Ben Bolker


For what it's worth it doesn't seem to be a threshold effect: approximately

log10(time[seconds]) ~ -8 - log10(-size)

over the range from 1e-6 to 1e-9


ff <- function(x) {
    system.time(qnbinom(0.5, mu=3, size=10^x))[["elapsed"]]
}
svec <- seq(-5,-9,by=-0.2)
res <- lapply(svec, function(x) {
     cat(x,"\n")
     replicate(10,ff(x))
     })

dd <- data.frame(size=rep(svec,each=10),
                  time=unlist(res))
boxplot(log10(time)~size, dd)
summary(lm(log10(time)~size, data=dd, subset=time>0))




On 8/7/20 2:01 PM, Constantin Ahlmann-Eltze via R-devel wrote:

Hi all,

I recently noticed that `qnbinom()` can take a long time to calculate
a result if the `size` argument is very small.
For example
    qnbinom(0.5, mu = 3, size = 1e-10)
takes ~30 seconds on my computer.

I used gdb to step through the qnbinom.c implementation and noticed
that in line 106
(https://github.com/wch/r-source/blob/f8d4d7d48051860cc695b99db9be9cf439aee743/src/nmath/qnbinom.c#L106)
`y` becomes a very large negative number. Later in the function `y` is
(as far as I can see) only used as input for `pnbinom()` which is why
I would assume that it should be a non-negative integer.

I was wondering if this behavior could be considered a bug and should
be reported on the bugzilla? I read the instructions at
https://www.r-project.org/bugs.html and wasn't quite sure, so I
decided to ask here first :)

Best,
Constantin




PS: I tested the code with R 4.0.0 on macOS and the latest unstable
version using docker (https://github.com/wch/r-debug). The session
info is

sessionInfo()

R Under development (unstable) (2020-08-06 r78973)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Ubuntu 20.04 LTS

Matrix products: default
BLAS:   /usr/local/RD/lib/R/lib/libRblas.so
LAPACK: /usr/local/RD/lib/R/lib/libRlapack.so

locale:
  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C
  [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8
  [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8
  [7] LC_PAPER=en_US.UTF-8       LC_NAME=C
  [9] LC_ADDRESS=C               LC_TELEPHONE=C
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C

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

loaded via a namespace (and not attached):
[1] compiler_4.1.0

______________________________________________
R-devel at r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-devel

______________________________________________
R-devel at r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-devel

Constantin Ahlmann-Eltze via R-devel 
    on Mon, 10 Aug 2020 10:05:36 +0200 writes:

> Thanks Ben for verifying the issue. It is always reassuring to hear
    > when others can reproduce the problem.

    > I wrote a small patch that fixes the issue
    > (https://github.com/r-devel/r-svn/pull/11):

    > diff --git a/src/nmath/qnbinom.c b/src/nmath/qnbinom.c
    > index b313ce56b2..d2e8d98759 100644
    > --- a/src/nmath/qnbinom.c
    > +++ b/src/nmath/qnbinom.c
    > @@ -104,6 +104,7 @@ double qnbinom(double p, double size, double prob,
    > int lower_tail, int log_p)
    > /* y := approx.value (Cornish-Fisher expansion) :  */
    > z = qnorm(p, 0., 1., /*lower_tail*/TRUE, /*log_p*/FALSE);
    > y = R_forceint(mu + sigma * (z + gamma * (z*z - 1) / 6));
    > +    y = fmax2(0.0, y);

    > z = pnbinom(y, size, prob, /*lower_tail*/TRUE, /*log_p*/FALSE);

    > I used the https://github.com/r-devel/r-svn repo and its continuous
    > integration tools to check that it doesn't break any existing tests:
    > https://github.com/r-devel/r-svn/actions/runs/201327042

    > I have also requested a Bugzilla-account, but haven't heard anything back yet.

    > Best,
    > Constantin

Thank you for the report, and Ben for his experiment.

And, indeed in this case, this returns  0  much more  quickly.

Note that this could be even much more quickly: The
Cornish-Fisher expansion is not really of much use here, ...
and quick check would just see that pnbinom(0, size, prob) > 

Note however, that in other cases, results for  small 'size'
are *still* not good  (and *not* influenced by your patch !!),
e.g.,

## Other examples, not giving 0, are fast already but  *in*accurate:
qnbinom(.9999, mu=3, size=1e-4)
## [1] 8044

## but
str(ur1 <- uniroot(function(q) pnbinom(q, mu=3, size=1e-4) - 0.9999, c(7000,8000)))
## List of 5
##  $ root      : num 7942
##  $ f.root    : num 1.52e-09
##  $ iter      : int 18
##  $ init.it   : int NA
##  $ estim.prec: num 6.49e-05

## and this of course does not change when asking for more precision :

str(ur2 <- uniroot(function(q) pnbinom(q, mu=3, size=1e-4) - 0.9999, c(7000,8000), tol=1e-12))
## List of 5
##  $ root      : num 7942  <<< correct is 7942, not 8044 !!!
##  $ f.root    : num 1.52e-09
##  $ iter      : int 47
##  $ init.it   : int NA
##  $ estim.prec: num 7.28e-12

----------

so, in principle the C-internal  search() function really should be
improved for such  ( somewhat extreme!! )  cases.
or ... ?? ... a different approximation should be used for such
extreme small 'size' (and  prob := size/(size+mu)  ) ...

Martin Maechler
ETH Zurich   and  R Core team

Hi Martin,

thanks for verifying. I agree that the Cornish-Fisher seems to struggle
with the small size parameters, but I also don't have a good idea how to
replace it.

But I think fixing do_search() is possible:

I think the problem is that when searching to the left y is decremented
only if `pnbinom(y - incr, n, pr, /*l._t.*/TRUE, /*log_p*/FALSE)) < p` is
FALSE. I think the solution is to move the update of y before the if.
However, I need to make this slightly awkward check if incr == 1, so that
the return in line 123 and the do-while block at the end of qnbinom() do
not need to be modified.

diff --git a/src/nmath/qnbinom.c b/src/nmath/qnbinom.c
index b313ce56b2..16845d9373 100644
--- a/src/nmath/qnbinom.c
+++ b/src/nmath/qnbinom.c
@@ -49,10 +49,18 @@ do_search(double y, double *z, double p, double n,
double pr, double incr)
 {
     if(*z >= p) {	/* search to the left */
 	for(;;) {
+        y = fmax2(0, y - incr);
 	    if(y == 0 ||
-	       (*z = pnbinom(y - incr, n, pr, /*l._t.*/TRUE, /*log_p*/FALSE)) < p)
-		return y;
-	    y = fmax2(0, y - incr);
+	       (*z = pnbinom(y, n, pr, /*l._t.*/TRUE, /*log_p*/FALSE)) < p){
+            if(incr == 1){
+                // we know that the search is stopped if incr == 1
+                // and we know that the correct result is just right
+                // of the current y
+                return y + 1;
+            }else{
+                return y;
+            }
+        }
 	}
     }
     else {		/* search to the right */


With this patch, we get the expected result

qnbinom(0.9999, mu = 3, size = 1e-4)

[1] 7942

I have updated the pull request at https://github.com/r-devel/r-svn/pull/11
and it is currently checking if the change breaks anything.

Best,
Constantin


Am 20.08.20 um 22:27 schrieb Martin Maechler:

Constantin Ahlmann-Eltze via R-devel
    on Mon, 10 Aug 2020 10:05:36 +0200 writes:

    > Thanks Ben for verifying the issue. It is always reassuring to hear
    > when others can reproduce the problem.

    > I wrote a small patch that fixes the issue
    > (https://github.com/r-devel/r-svn/pull/11):

    > diff --git a/src/nmath/qnbinom.c b/src/nmath/qnbinom.c
    > index b313ce56b2..d2e8d98759 100644
    > --- a/src/nmath/qnbinom.c
    > +++ b/src/nmath/qnbinom.c
    > @@ -104,6 +104,7 @@ double qnbinom(double p, double size, double prob,
    > int lower_tail, int log_p)
    > /* y := approx.value (Cornish-Fisher expansion) :  */
    > z = qnorm(p, 0., 1., /*lower_tail*/TRUE, /*log_p*/FALSE);
    > y = R_forceint(mu + sigma * (z + gamma * (z*z - 1) / 6));
    > +    y = fmax2(0.0, y);

    > z = pnbinom(y, size, prob, /*lower_tail*/TRUE, /*log_p*/FALSE);

    > I used the https://github.com/r-devel/r-svn repo and its continuous
    > integration tools to check that it doesn't break any existing tests:
    > https://github.com/r-devel/r-svn/actions/runs/201327042

    > I have also requested a Bugzilla-account, but haven't heard
anything back yet.

    > Best,
    > Constantin

Thank you for the report, and Ben for his experiment.

And, indeed in this case, this returns  0  much more  quickly.

Note that this could be even much more quickly: The
Cornish-Fisher expansion is not really of much use here, ...
and quick check would just see that pnbinom(0, size, prob) >

Note however, that in other cases, results for  small 'size'
are *still* not good  (and *not* influenced by your patch !!),
e.g.,

## Other examples, not giving 0, are fast already but  *in*accurate:
qnbinom(.9999, mu=3, size=1e-4)
## [1] 8044

## but
str(ur1 <- uniroot(function(q) pnbinom(q, mu=3, size=1e-4) - 0.9999,
c(7000,8000)))
## List of 5
##  $ root      : num 7942
##  $ f.root    : num 1.52e-09
##  $ iter      : int 18
##  $ init.it   : int NA
##  $ estim.prec: num 6.49e-05

## and this of course does not change when asking for more precision :

str(ur2 <- uniroot(function(q) pnbinom(q, mu=3, size=1e-4) - 0.9999,
c(7000,8000), tol=1e-12))
## List of 5
##  $ root      : num 7942  <<< correct is 7942, not 8044 !!!
##  $ f.root    : num 1.52e-09
##  $ iter      : int 47
##  $ init.it   : int NA
##  $ estim.prec: num 7.28e-12

----------

so, in principle the C-internal  search() function really should be
improved for such  ( somewhat extreme!! )  cases.
or ... ?? ... a different approximation should be used for such
extreme small 'size' (and  prob := size/(size+mu)  ) ...

Martin Maechler
ETH Zurich   and  R Core team

Constantin Ahlmann-Eltze 
    on Fri, 21 Aug 2020 11:51:13 +0200 writes:

> Hi Martin, thanks for verifying. I agree that the
    > Cornish-Fisher seems to struggle with the small size
    > parameters, but I also don't have a good idea how to
    > replace it.

    > But I think fixing do_search() is possible:

Yes,  but your fix was not correct..
(and I used time to find out)

Note that do_search()  is used in all three of

qnbinom()
 qbinom()
  qpois()

If a change was correct and an improvement, it will be an
improvement for all three cases; if it is only sometimes good,
it may also be sometimes bad for the other two cases.

Note that running the checks on the current R sources makes
almost no sense: Of course the new bugs (your: "slow"; mine:
inaccurate when result is quite larger than 0) are *NOT* yet in
the regression tests.

And it's really not worth doing experiments on the cloud ("QI"
is really increasing the climate change, by each time installing
tons (=> bandwidth) and running 1.5 hours ..):

I don't know what big a part of tree is killed by the bandwith
  (==> electricity of internet routers, cooling, ...)
and the 1.5 hour run
  (==> electricity of the CPUs; cooling; ...)
but I'd rather do test such small changes on my small desktop
where I don't need to install anything etc
(*and* I know that the Swiss electricity is almost exclusively
  produced from no-Carbon-emission plants).

--------

I'm busy for another 1-3 days (taking & grading exams),
but really do want to address this myself, rather than trying
these proposals (and having you burn electricity on routers and
CPUs and coolers) ...

Martin