R help - Dec 2012 - efficiently multiply different matrices in 3-d array with different vectors?

Hello,

I have been wondering of an efficient way to do this:

I have an n x m x p array Z and a p x n matrix Y.

I want to multiply each of the n matrices with the corresponding column
vector of Y.

In other words, I am wanting to matrix multiply: 

Z[i, ,] %*% Y[, i]

which will give me a (two-dimensional) array or matrix of dimension n x
p with the i'th row storing the above.

Any pointers on an efficient way of doing this? I considered using
apply, but was not successful. 

Many thanks again and best wishes,
Ranjan



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I think what you are doing is a tensor algebra. You may want to try tensorA:

http://cran.r-project.org/web/packages/tensorA/index.html

On 28 December 2012 06:33, Ranjan Maitra <maitra.mbox.ignored at
inbox.com> wrote:
> Any pointers on an efficient way of doing this? I considered using
> apply, but was not successful.
please post that code. Why it was not successful? What was the error message?

HI,

Not sure if this is what you wanted:
set.seed(14)
Z<-array(sample(1:100,80,replace=TRUE),dim=c(5,2,8))
set.seed(21)
Y<-matrix(sample(1:40,40,replace=TRUE),nrow=8)
do.call(cbind,lapply(seq_len(dim(Z)[1]),function(i) Z[i,,]%*%Y[,i]))
#???? [,1] [,2]? [,3]? [,4]? [,5]
#[1,] 5065 6070 12328 11536 13678
#[2,] 6152 9878 11161 13777? 7991
A.K.




----- Original Message -----
From: Ranjan Maitra <maitra.mbox.ignored at inbox.com>
To: r-help at r-project.org
Cc: 
Sent: Friday, December 28, 2012 12:33 AM
Subject: [R] efficiently multiply different matrices in 3-d array with different
vectors?

Hello,

I have been wondering of an efficient way to do this:

I have an n x m x p array Z and a p x n matrix Y.

I want to multiply each of the n matrices with the corresponding column
vector of Y.

In other words, I am wanting to matrix multiply: 

Z[i, ,] %*% Y[, i]

which will give me a (two-dimensional) array or matrix of dimension n x
p with the i'th row storing the above.

Any pointers on an efficient way of doing this? I considered using
apply, but was not successful. 

Many thanks again and best wishes,
Ranjan



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What I had in mind was a tensor multiplication.
I think,  using tensor arithmetic for multidimensional arrays looks
more compacts
and efficient (~ 2-3 times). I am guessing that performance will be much more
pronounced for n-D arrays (n>3).

# Component Wise
set.seed(14)
Z<-array(sample(1:1000000,800000,replace=TRUE),dim=c(50000,2,8))
set.seed(21)
Y<-matrix(sample(1:400000,400000,replace=TRUE),nrow=8)
system.time(X<-do.call(cbind,lapply(seq_len(dim(Z)[1]),function(i)
Z[i,,]%*%Y[,i])))
#   user  system elapsed
#   0.58    0.00    0.58
R<-cbind(sum(X[1,]), sum(X[2,]))
# Tensor multiply
library(tensorA)
set.seed(14)
Zt <-to.tensor(sample(1:1000000,800000,replace=TRUE), c(a=50000, b=2, c=8))
set.seed(21)
Yt <-to.tensor(sample(1:400000,400000,replace=TRUE), c(c=8, a=50000))
system.time(Rt<-Zt %e% Yt)
#   user  system elapsed
#  0.124   0.000   0.126
# correct results?
R
#            [,1]         [,2]
#[1,] 4.00595e+16 3.997387e+16
Rt
#[1] 4.005950e+16 3.997387e+1

On 30 December 2012 20:21, arun <smartpink111 at yahoo.com>
wrote:
> HI,
> I was not aware of the algebraic relationship.
> Tx for the explanation.
For the record; the simple example I have shown can be reproduced with
Einstein's summation rule as well. While A and x tensors have
covariant (lower) indices *only*.
So using %r%  may make sense only if we have contravariant (upper)
indices as well (mixed-variant).
Just to clarify my previous post to avoid any confusion.