[R] Help with multidimensional array

[Bert Gunter]

Folks:

1. Well, should have known better... I was wrong about what I said in
my earlier post below.

2. Here's yet another way to skin the cat using matrix multiplication
that is, maybe, a bit faster than using reduce.

First, the three methods (left as a homework exercise to see how/why they work):

## Originally proposed: d = dim of array test; xx is vector
e1 <- quote(Reduce('+', lapply(seq_len(d[3]), function(j) xx[j] *
test[, , j])))

## my earlier "better" (Ha!) way
e2 <- quote(apply(test*rep.int(xx, rep.int(d[1]*d[2],d[3])),1:2,sum))

## Using matrix multiplication
e3 <- quote(sapply(1:d[2],function(i)test[,i,]%*%xx))

Let's first try it with something simple to verify that the
expressions are "equivalent":

d <- 2:4
test <- array(1:24,dim=d)
xx <- 1:4

eval(e1)
eval(e2)
eval(e3)

IMPORTANT NOTE: This will **not** give identical() = TRUE results. e1
and e2 give integer results and e3 gives numeric. In general, floating
point arithmetic will defeat identical(). Instead, use  all.equal()


Now here's a test bed.

d <- 10*c(50,50,4)  ## dimensions of test array
test<- array(rnorm(prod(d)),dim=d)
xx <- runif(d[3])

results <- lapply(list(e1,e2,e3),function(e)system.time(eval(e)))

results

[[1]]
   user  system elapsed
   0.34    0.01    0.36

[[2]]
   user  system elapsed
   3.08    0.08    3.16

[[3]]
   user  system elapsed
   0.27    0.00    0.26


##Try it with different dim

d <- 10*c(5,10,100)  ## dimensions of test array
test<- array(rnorm(prod(d)),dim=d)
xx <- runif(d[3])

results <- lapply(list(e1,e2,e3),function(e)system.time(eval(e)))

results
[[1]]
   user  system elapsed
   0.20    0.02    0.22

[[2]]
   user  system elapsed
   0.25    0.01    0.27

[[3]]
   user  system elapsed
   0.12    0.00    0.13

So I was dead wrong below; but matrix multiplication seems a tad
faster than Reduce.

Cheers to all,

-- Bert


On Mon, Mar 28, 2011 at 8:00 PM, Bert Gunter <bgunter at gene.com> wrote:
> Arrays are vectors stored in column major order. Hence
>
> H <- apply( H12*rep(hessian_lambda,e = n*k), 1:2, sum)
> ## but check that this gives what you want
>
> I'm pretty sure this is faster than the alternatives that were
> proposed, but whether it's much (or even noticeably)  faster, I don't
> know.
>
>
>
> -- Bert
>
>
> On Mon, Mar 28, 2011 at 5:56 PM, Giuseppe <neox86 at gmail.com> wrote:
>> Dennis,
>>
>> Yes, Reduce works, but unfortunately it does not speed up the
>> evaluation time (actually, it makes it a little bit slower).
>>
>> Thank you anyway.
>>
>>
>>
>> On Tue, Mar 29, 2011 at 2:21 AM, Dennis Murphy <djmuser at gmail.com> wrote:
>>> Hi:
>>>
>>> Is this what you're after?
>>>
>>> m <- array(1:27, c(3, 3, 3))
>>> xx <- 1:3
>>> Reduce('+', lapply(xx, function(k) xx[k] * m[, , k]))
>>>
>>>> m
>>> , , 1
>>>
>>>      [,1] [,2] [,3]
>>> [1,]    1    4    7
>>> [2,]    2    5    8
>>> [3,]    3    6    9
>>>
>>> , , 2
>>>
>>>      [,1] [,2] [,3]
>>> [1,]   10   13   16
>>> [2,]   11   14   17
>>> [3,]   12   15   18
>>>
>>> , , 3
>>>
>>>      [,1] [,2] [,3]
>>> [1,]   19   22   25
>>> [2,]   20   23   26
>>> [3,]   21   24   27
>>>
>>>> xx <- 1:3
>>>> Reduce('+', lapply(xx, function(k) xx[k] * m[, , k]))
>>>      [,1] [,2] [,3]
>>> [1,]   78   96  114
>>> [2,]   84  102  120
>>> [3,]   90  108  126
>>>
>>> HTH,
>>> Dennis
>>>
>>>
>>> On Mon, Mar 28, 2011 at 4:10 PM, Giuseppe <neox86 at gmail.com> wrote:
>>>>
>>>> I have the following situation.
>>>>
>>>> H12 is an array of dimension (n,k,m) and hessian_lambda is a numeric
>>>> of length m.
>>>>
>>>> I need to multiply each matrix H12[,,1], H12[,,2], ..., H12[,m] by
>>>> hessian_lambda[1], hessian_lambda[2], ..., hessian_lambda[m],
>>>> respectively, and then add the resulting (n,k) matrices. What I am
>>>> using at the moment is the following code:
>>>>
>>>> H <- matrix(0, n, k)
>>>>  for(j in 1:(m)) {
>>>>        H <- H + H12[,,j]*hessian_lambda[j]
>>>>  }
>>>>
>>>> Does anybody see a way to speed up this without using loop? (The
>>>> output needs to be a matrix).
>>>>
>>>> Thank you for your time.
>>>>
>>>> ______________________________________________
>>>> 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.
>>>
>>>
>>
>> ______________________________________________
>> 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.
>>
>
>
>
> --
> Bert Gunter
> Genentech Nonclinical Biostatistics
> 467-7374
> http://devo.gene.com/groups/devo/depts/ncb/home.shtml
>



-- 
Bert Gunter
Genentech Nonclinical Biostatistics
467-7374
http://devo.gene.com/groups/devo/depts/ncb/home.shtml