Re: [R] matrix row product and cumulative product

Mon, 18 Aug 2008 09:45:07 -0700

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)"

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Charles C. Berry                            (858) 534-2098
Dept of Family/Preventive Medicine 
E mailto:[EMAIL PROTECTED]                UC San Diego
http://famprevmed.ucsd.edu/faculty/cberry/ La Jolla, San Diego 92093-0901 

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and provide commented, minimal, self-contained, reproducible code.



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PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

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