[R] matrix row product and cumulative product
Jeff Laake
Jeff.Laake at noaa.gov
Mon Aug 18 18:43:06 CEST 2008
Thanks for the tips on inline, jit and Reduce. The latter was exactly
what I wanted although the loop
is still the fastest for the simple product (accumulate=TRUE for
reduce). With regards to Moshe's comment,
I was just surprised by the timing difference. I tend to use apply
without giving it much thought. After profiling the code
it became apparent that a loop was better in this case. I was just
surprised that a loop was still as good
when the columns were 10 times the rows.
I'm very intrigued by the inline package but couldn't find any
documentation on the compiler I need with
a Windows machine to make it work. Any hints would be very much
appreciated especially in regards to
FORTRAN which was my first language some 35 years ago. I have MS
FORTRAN 90 although I've not touched
it for over 6 years thanks to the developers of R.
Thanks much for the help. --jeff
Elapsed times from system.time. see code below
Columns 10 100 1000 10000 100000
Rows 1000000 100000 10000 1000 100
cumprod Loop 1.0 1.0 1.3 1.2 3.0
Apply 27.3 3.4 1.8 1.2 1.4
Reduce 0.5 0.7 0.7 0.9 3.2
prod Loop 0.3 0.3 0.4 0.4 0.9
Apply 30.0 2.7 0.7 0.6 0.8
Reduce 0.6 0.6 0.8 1.0 4.7
N=10000000
xmat=matrix(runif(N),ncol=10)
system.time(cumprod.matrix(xmat))
system.time(t(apply(xmat,1,cumprod)))
system.time(Reduce("*",as.data.frame(xmat),accumulate=FALSE))
system.time(prod.matrix(xmat))
system.time(apply(xmat,1,prod))
system.time(Reduce("*",as.data.frame(xmat),accumulate=TRUE))
xmat=matrix(runif(N),ncol=100)
system.time(cumprod.matrix(xmat))
system.time(t(apply(xmat,1,cumprod)))
system.time(Reduce("*",as.data.frame(xmat),accumulate=FALSE))
system.time(prod.matrix(xmat))
system.time(apply(xmat,1,prod))
system.time(Reduce("*",as.data.frame(xmat),accumulate=TRUE))
xmat=matrix(runif(N),ncol=1000)
system.time(cumprod.matrix(xmat))
system.time(t(apply(xmat,1,cumprod)))
system.time(Reduce("*",as.data.frame(xmat),accumulate=FALSE))
system.time(prod.matrix(xmat))
system.time(apply(xmat,1,prod))
system.time(Reduce("*",as.data.frame(xmat),accumulate=TRUE))
xmat=matrix(runif(N),ncol=10000)
system.time(cumprod.matrix(xmat))
system.time(t(apply(xmat,1,cumprod)))
system.time(Reduce("*",as.data.frame(xmat),accumulate=FALSE))
system.time(prod.matrix(xmat))
system.time(apply(xmat,1,prod))
system.time(Reduce("*",as.data.frame(xmat),accumulate=TRUE))
xmat=matrix(runif(N),ncol=100000)
system.time(cumprod.matrix(xmat))
system.time(t(apply(xmat,1,cumprod)))
system.time(Reduce("*",as.data.frame(xmat),accumulate=FALSE))
system.time(prod.matrix(xmat))
system.time(apply(xmat,1,prod))
system.time(Reduce("*",as.data.frame(xmat),accumulate=TRUE))
Charles C. Berry wrote:
> On Sun, 17 Aug 2008, Jeff Laake wrote:
>
>> I spent a lot of time searching and came up empty handed on the
>> following query. Is there an equivalent to rowSums that does product
>> or cumulative product and avoids use of apply or looping? I found a
>> rowProd in a package but it was a convenience function for apply. As
>> part of a likelihood calculation called from optim, I’m computing
>> products and cumulative products of rows of matrices with far more
>> rows than columns. I started with apply and after some thought
>> realized that a loop of columns might be faster and it was
>> substantially faster (see below). Because the likelihood function is
>> called many times I’d like to speed it up even more if possible.
>
>
> You might check out the 'inline' or 'jit' packages.
>
> Otherwise, if you can as easily treat xmat as a list (or data.frame),
>
> Reduce( "*", xmat.data.frame, accumulate=want.cumprod )
>
> (where want.cumprod is FALSE for product, TRUE for cumulative product)
> will be a bit faster in many circumstances. However, this advantage is
> lost if you must retain xmat as a matrix since converting it to a
> data.frame seems to require more time than you save.
>
> HTH,
>
> Chuck
>
>>
>> Below is an example showing the cumprod.matrix and prod.matrix
>> looping functions that I wrote and some timing comparisons to the use
>> of apply for different column and row dimensions. At this point I’m
>> better off with looping but I’d like to hear of any further suggestions.
>>
>> Thanks –jeff
>>
>>> prod.matrix=function(x)
>> + {
>> + y=x[,1]
>> + for(i in 2:dim(x)[2])
>> + y=y*x[,i]
>> + return(y)
>> + }
>>
>>> cumprod.matrix=function(x)
>> + {
>> + y=matrix(1,nrow=dim(x)[1],ncol=dim(x)[2])
>> + y[,1]=x[,1]
>> + for (i in 2:dim(x)[2])
>> + y[,i]=y[,i-1]*x[,i]
>> + return(y)
>> + }
>>
>>> N=10000000
>>> xmat=matrix(runif(N),ncol=10)
>>> system.time(cumprod.matrix(xmat))
>> user system elapsed
>> 1.07 0.09 1.15
>>> system.time(t(apply(xmat,1,cumprod)))
>> user system elapsed
>> 29.27 0.21 29.50
>>> system.time(prod.matrix(xmat))
>> user system elapsed
>> 0.29 0.00 0.30
>>> system.time(apply(xmat,1,prod))
>> user system elapsed
>> 30.69 0.00 30.72
>>> xmat=matrix(runif(N),ncol=100)
>>> system.time(cumprod.matrix(xmat))
>> user system elapsed
>> 1.05 0.13 1.18
>>> system.time(t(apply(xmat,1,cumprod)))
>> user system elapsed
>> 3.55 0.14 3.70
>>> system.time(prod.matrix(xmat))
>> user system elapsed
>> 0.38 0.01 0.39
>>> system.time(apply(xmat,1,prod))
>> user system elapsed
>> 2.87 0.00 2.89
>>> xmat=matrix(runif(N),ncol=1000)
>>> system.time(cumprod.matrix(xmat))
>> user system elapsed
>> 1.30 0.18 1.46
>>> system.time(t(apply(xmat,1,cumprod)))
>> user system elapsed
>> 1.77 0.27 2.05
>>> system.time(prod.matrix(xmat))
>> user system elapsed
>> 0.46 0.00 0.47
>>> system.time(apply(xmat,1,prod))
>> user system elapsed
>> 0.7 0.0 0.7
>>> xmat=matrix(runif(N),ncol=10000)
>>> system.time(cumprod.matrix(xmat))
>> user system elapsed
>> 1.28 0.00 1.29
>>> system.time(t(apply(xmat,1,cumprod)))
>> user system elapsed
>> 1.19 0.08 1.26
>>> system.time(prod.matrix(xmat))
>> user system elapsed
>> 0.40 0.00 0.41
>>> system.time(apply(xmat,1,prod))
>> user system elapsed
>> 0.57 0.00 0.56
>>> xmat=matrix(runif(N),ncol=100000)
>>> system.time(cumprod.matrix(xmat))
>> user system elapsed
>> 3.18 0.00 3.19
>>> system.time(t(apply(xmat,1,cumprod)))
>> user system elapsed
>> 1.42 0.21 1.64
>>> system.time(prod.matrix(xmat))
>> user system elapsed
>> 1.05 0.00 1.05
>>> system.time(apply(xmat,1,prod))
>> user system elapsed
>> 0.82 0.00 0.81
>>> R.Version()
>> $platform
>> [1] "i386-pc-mingw32"
>> .
>> .
>> .
>> $version.string
>> [1] "R version 2.7.1 (2008-06-23)"
>>
>> ______________________________________________
>> R-help at 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.
>>
>
> Charles C. Berry (858) 534-2098
> Dept of Family/Preventive
> Medicine
> E mailto:cberry at tajo.ucsd.edu UC San Diego
> http://famprevmed.ucsd.edu/faculty/cberry/ La Jolla, San Diego
> 92093-0901
>
> ------------------------------------------------------------------------
>
> ______________________________________________
> R-help at 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.
>
More information about the R-help
mailing list