[R] matrix row product and cumulative product

[Jeff Laake]

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.
>