Scott Chamberlain
blogged about faster creation of
binomial matrices the other day, and even referred to our
RcppArmadillo
package as a possible solution (though claiming he didn't get it to work, tst tst -- that is what the
rcpp-devel list is here to help with).
The post also fell short of a good
aggregated timing comparison for which we love the
rbenchmark package. So in order to rectify this, and to see
what we can do here with
Rcpp, a quick post revisiting the
issue.
As preliminaries, we need to load three packages:
inline to
create compiled code on the fly (which, I should mention, is also used together with
Rcpp by the
Stan / RStan MCMC sampler which is creating some buzz this week), the compiler
package included with R to create byte-compiled code and lastly the aforementioned
rbenchmark package to do the timings. We also set row and
column dimension, and set them a little higher than the original example to actually have something measurable:
library(inline)
library(compiler)
library(rbenchmark)
n <- 500
k <- 100
The first suggestion was the one by Scott himself. We will wrap this one, and all the following ones, in a function so
that all approaches are comparable as being in a function of two dimension arguments:
scott <- function(N, K)
mm <- matrix(0, N, K)
apply(mm, c(1, 2), function(x) sample(c(0, 1), 1))
scottComp <- cmpfun(scott)
We also immediatly compute a byte-compiled version (just because we now can) to see if this helps at all with the code.
As there are no (explicit !) loops, we do not expect a big pickup. Scott's function works, but sweeps the
sample() function across all rows and columns which is probably going to be (relatively) expensive.
Next is the first improvement suggested to Scott which came from Ted Hart.
ted <- function(N, K)
matrix(rbinom(N * K, 1, 0.5), ncol = K, nrow = N)
This is quite a bit smarter as it vectorises the approach, generating N times K elements at once which are then reshaped into
a matrix.
Another suggestion came from David Smith as well as Rafael Maia. We rewrite it slightly to make it a function with two
arguments for the desired dimensions:
david <- function(m, n)
matrix(sample(0:1, m * n, replace = TRUE), m, n)
This is very clever as it uses
sample() over zero and one rather than making (expensive) draws from random
number generator.
Next we have a version from Luis Apiolaza:
luis <- function(m, n)
round(matrix(runif(m * n), m, n))
It draws from a random uniform and rounds to zero and one, rather than deploying the binomial.
Then we have the version using
RcppArmadillo
hinted at by Scott, but with actual arguments and a correction for row/column dimensions. Thanks to
inline we can write the C++ code as an R character string;
inline takes care of everything and we end up with C++-based
solution directly callable from R:
arma <- cxxfunction(signature(ns="integer", ks="integer"), plugin = "RcppArmadillo", body='
int n = Rcpp::as<int>(ns);
int k = Rcpp::as<int>(ks);
return wrap(arma::randu(n, k));
')
This works, and is pretty fast. The only problem is that
it answers the wrong question as it returns U(0,1) draws and
not binomials. We need to truncate or round. So a corrected version is
armaFloor <- cxxfunction(signature(ns="integer", ks="integer"), plugin = "RcppArmadillo", body='
int n = Rcpp::as<int>(ns);
int k = Rcpp::as<int>(ks);
return wrap(arma::floor(arma::randu(n, k) + 0.5));
')
which uses the the old rounding approximation of adding 1/2 before truncating.
With Armadillo in the picture, we do wonder how Rcpp sugar would do. Rcpp sugar, described in one of the eight vignettes
of the
Rcpp package, is using template meta-programming to
provide R-like expressiveness (aka "syntactic sugar") at the C++ level. In particular, it gives access to R's RNG
functions
using the exact same RNGs as R making the results directly substitutable (whereas Armadillo uses its
own RNG).
sugar <- cxxfunction(signature(ns="integer", ks="integer"), plugin = "Rcpp", body='
int n = Rcpp::as<int>(ns);
int k = Rcpp::as<int>(ks);
Rcpp::RNGScope tmp;
Rcpp::NumericVector draws = Rcpp::runif(n*k);
return Rcpp::NumericMatrix(n, k, draws.begin());
')
Here
Rcpp::RNGScope deals with setting/resetting the R RNG state. This draws a vector of N time K uniforms
similar to Luis' function -- and just like Luis' R function does so without looping -- and then shapes a matrix of dimension N by K from it.
And it does of course have the same problem as the
RcppArmadillo approach
earlier and we can use the same solution:
sugarFloor <- cxxfunction(signature(ns="integer", ks="integer"), plugin = "Rcpp", body='
int n = Rcpp::as<int>(ns);
int k = Rcpp::as<int>(ks);
Rcpp::RNGScope tmp;
Rcpp::NumericVector draws = Rcpp::floor(Rcpp::runif(n*k)+0.5);
return Rcpp::NumericMatrix(n, k, draws.begin());
')
Now that we have all the pieces in place, we can compare:
res <- benchmark(scott(n, k), scottComp(n,k),
ted(n, k), david(n, k), luis(n, k),
arma(n, k), sugar(n,k),
armaFloor(n, k), sugarFloor(n, k),
order="relative", replications=100)
print(res[,1:4])
With all the above code example in a small R script we call via
littler, we get
edd@max:~/svn/rcpp/pkg$ r /tmp/scott.r
Loading required package: methods
test replications elapsed relative
7 sugar(n, k) 100 0.072 1.000000
9 sugarFloor(n, k) 100 0.088 1.222222
6 arma(n, k) 100 0.126 1.750000
4 david(n, k) 100 0.136 1.888889
8 armaFloor(n, k) 100 0.138 1.916667
3 ted(n, k) 100 0.384 5.333333
5 luis(n, k) 100 0.410 5.694444
1 scott(n, k) 100 33.045 458.958333
2 scottComp(n, k) 100 33.767 468.986111
We can see several takeaways:
- Rcpp sugar wins, which is something we have seen in previous posts on this blog. One hundred replication take only
72 milliseconds (or 88 in the corrected version) --- less than one millisecond per matrix creation.
- RcppArmadillo does well too, and I presume
that the small difference is due not to code in Armadillo but the fact that we need one more 'mapping' of data types
on the way back to R
- The
sample() idea by David and Rafael is very, very fast too. This proves once again that
well-written R code can be competitive. It also suggest how to make the C++ solution by foregoing (expensive)
RNG draws in favour of sampling
- The approaches by Ted and Luis are also pretty good. In practice, the are probably good enough.
- Scott's function is not looking so hot (particularly as we increased the problem dimensions) and byte-compilation
does not help at all.
Thanks to Scott and everybody for suggesting this interesting problem. Trying the
rbinom() Rcpp sugar
function, or implementing
sample() at the C++ level is, as the saying goes, left as an exercise to the reader.
What, haven't you heard about the WikiLovesMonuments photo contest around cultural heritage? Copying from its web page,
tmperamental found either on 
I tried to continue 
Next weekend I will hold an advanced Haskell talk at the 
In late July, the 
For about the past three months I've been conducting a small experiment.
When I've seen people misbehave on the Debian development mailing list,
I've sent a private e-mail to them suggesting they should avoid
some specific behavior, in the hope of getting them to stop.
My success has been varied. A few have thanked me, and changed their
behavior. A couple have taken offense. Some have ignored me.
I've noticed a correlation between how much effort I put into the
letter and how successful it. Broadly speaking, if I send anything
earlier than the sixth version, it fails. Getting the message exactly
right is not easy, for me, and takes quite some effort and time.
I'm happy about my successes, but on the whole, I fear my experiment
is a failure. It's too much effort to do this in the long term,
and it's too chancy. Someone else might be able to do it better,
but this is not something I can keep on doing.
I think we need some better solution to keep discussions in Debian
on track and not have them blow up. We have a systemic problem where
contentious issues, such as choice of init system, is quite hard
for us to deal with. We're also not very good at dealing with
situations where a few individuals are dominating the discussion
by being loud, insistent, and unwilling to budge or to give any
credence to opposing views. I don't know what to do about that,
but we clearly need social and possibly technical tools for this.
This article documents how I'm currently building my firewalls. It
builds on 
Today, 
This module allows you to be notified via 
Here s a second post on the subject of 
Arundina Sans font from 
But for legacy fonts without OpenType features, it renders badly:
In addition, according to Behdad, PUA glyphs in legacy fonts are not supported yet. This means there will be regression on fonts designed for Windows XP or below. But modern fonts designed for Windows 7 should be fine.
Changes on Bugs
The engine replacement from scratch certainly affects existing bugs. Some become obsolete, some still remain. Here are the summary for Thai/Lao engine, as resolved upstream:
Closed bugs:
One can easily spot the dotted circle glitches. And here is how I workaround it, which is like how it's rendered on other terminals:
With the HarfBuzz replacement, here is how it renders:
That is, although it s still wrong, it s more tolerable. So, the question for users is: Could they tolerate this until VTE is redesigned for Indic scripts supports? 
The unstoppable PostgreSQL team just 
FreedomBox 0.1
Ian Sullivan posted a release announcement today regarding the first
