R help - Oct 2009 - generalization of tabulate()

Hi

I want a generalization of tabulate() which works on rows of a matrix.
Suppose I have an integer matrix 'observation':

 > observation

y1 y2 y3
1 4 0
1 4 0
2 0 3
4 1 0
0 5 0
0 1 4
2 0 3

Each row corresponds to a (multivariate) observation.  Note that the
first two rows are identical: this means that data "c(1,4,0)" was
observed twice.

Now suppose I can list the sample space:

 > S
          
 [1,] 5 0 0
 [2,] 4 1 0
 [3,] 3 2 0
 [4,] 2 3 0
 [5,] 1 4 0
 [6,] 0 5 0
 [7,] 4 0 1
 [8,] 3 1 1
 [9,] 2 2 1
[10,] 1 3 1
[11,] 0 4 1
[12,] 3 0 2
[13,] 2 1 2
[14,] 1 2 2
[15,] 0 3 2
[16,] 2 0 3
[17,] 1 1 3
[18,] 0 2 3
[19,] 1 0 4
[20,] 0 1 4
[21,] 0 0 5

(thus each row corresponds to a point in my sample space).

 Now what I need to do is to construct a new matrix, which uses the
 'observation' matrix above, which is a sort of table:

 > desired

      y1 y2 y3 d
 [1,] 5 0 0 0
 [2,] 4 1 0 1
 [3,] 3 2 0 0
 [4,] 2 3 0 0
 [5,] 1 4 0 2
 [6,] 0 5 0 1
 [7,] 4 0 1 0
 [8,] 3 1 1 0
 [9,] 2 2 1 0
[10,] 1 3 1 0
[11,] 0 4 1 0
[12,] 3 0 2 0
[13,] 2 1 2 0
[14,] 1 2 2 0
[15,] 0 3 2 0
[16,] 2 0 3 2
[17,] 1 1 3 0
[18,] 0 2 3 0
[19,] 1 0 4 0
[20,] 0 1 4 1
[21,] 0 0 5 0


Thus the 'd' column counts the number of times that each row occurs in
variable 'observation'.  So desired[5,4]=2 because the observation
corresponding to desired[5,1:3] (viz c(1,4,0)) occurred twice.  And
desired[1,4]=0 because the observation corresponding to desired[1,1:3]
(viz c(5,0,0)) did not occur once (it was not observed).

In my application I have dim(S) ~= c(5,4e6).

I've tried merge(), stack(),  reshape(), but the best I can do
is the (derisory):

require(partitions)


obs <- matrix(as.integer(c(
                1, 4, 0,
                1, 4, 0,
                2, 0, 3,
                4, 1, 0,
                0, 5, 0,
                0, 1, 4,
                2, 0, 3
                )),ncol=3,byrow=TRUE)

S <- t(compositions(5,3))
d <- rep(0,nrow(S))


for(i in seq_len(nrow(obs))){
  for(j in seq_len(nrow(S))){
    if(all(obs[i,,drop=TRUE] == S[j,,drop=TRUE])){
      d[j] <- d[j]+1
    }
  }
}

S <- cbind(S,d)


Anyone got anything better before I try C?


-- 
Robin K. S. Hankin
Uncertainty Analyst
University of Cambridge
19 Silver Street
Cambridge CB3 9EP
01223-764877

Using the generalized inner product defined in this post:

   https://www.stat.math.ethz.ch/pipermail/r-help/2006-July/109311.html

try this:

   cbind(S, d = rowSums(inner(S, obs, identical)))


On Fri, Oct 16, 2009 at 4:29 AM, Robin Hankin <rksh1 at cam.ac.uk>
wrote:
> Hi
>
> I want a generalization of tabulate() which works on rows of a matrix.
> Suppose I have an integer matrix 'observation':
>
>> observation
>
> y1 y2 y3
> 1 4 0
> 1 4 0
> 2 0 3
> 4 1 0
> 0 5 0
> 0 1 4
> 2 0 3
>
> Each row corresponds to a (multivariate) observation. ?Note that the
> first two rows are identical: this means that data "c(1,4,0)" was
> observed twice.
>
> Now suppose I can list the sample space:
>
>> S
> ? ? ? ? [1,] 5 0 0
> [2,] 4 1 0
> [3,] 3 2 0
> [4,] 2 3 0
> [5,] 1 4 0
> [6,] 0 5 0
> [7,] 4 0 1
> [8,] 3 1 1
> [9,] 2 2 1
> [10,] 1 3 1
> [11,] 0 4 1
> [12,] 3 0 2
> [13,] 2 1 2
> [14,] 1 2 2
> [15,] 0 3 2
> [16,] 2 0 3
> [17,] 1 1 3
> [18,] 0 2 3
> [19,] 1 0 4
> [20,] 0 1 4
> [21,] 0 0 5
>
> (thus each row corresponds to a point in my sample space).
>
> Now what I need to do is to construct a new matrix, which uses the
> 'observation' matrix above, which is a sort of table:
>
>> desired
>
> ? ? y1 y2 y3 d
> [1,] 5 0 0 0
> [2,] 4 1 0 1
> [3,] 3 2 0 0
> [4,] 2 3 0 0
> [5,] 1 4 0 2
> [6,] 0 5 0 1
> [7,] 4 0 1 0
> [8,] 3 1 1 0
> [9,] 2 2 1 0
> [10,] 1 3 1 0
> [11,] 0 4 1 0
> [12,] 3 0 2 0
> [13,] 2 1 2 0
> [14,] 1 2 2 0
> [15,] 0 3 2 0
> [16,] 2 0 3 2
> [17,] 1 1 3 0
> [18,] 0 2 3 0
> [19,] 1 0 4 0
> [20,] 0 1 4 1
> [21,] 0 0 5 0
>
>
> Thus the 'd' column counts the number of times that each row occurs
in
> variable 'observation'. ?So desired[5,4]=2 because the observation
> corresponding to desired[5,1:3] (viz c(1,4,0)) occurred twice. ?And
> desired[1,4]=0 because the observation corresponding to desired[1,1:3]
> (viz c(5,0,0)) did not occur once (it was not observed).
>
> In my application I have dim(S) ~= c(5,4e6).
>
> I've tried merge(), stack(), ?reshape(), but the best I can do
> is the (derisory):
>
> require(partitions)
>
>
> obs <- matrix(as.integer(c(
> ? ? ? ? ? ? ? 1, 4, 0,
> ? ? ? ? ? ? ? 1, 4, 0,
> ? ? ? ? ? ? ? 2, 0, 3,
> ? ? ? ? ? ? ? 4, 1, 0,
> ? ? ? ? ? ? ? 0, 5, 0,
> ? ? ? ? ? ? ? 0, 1, 4,
> ? ? ? ? ? ? ? 2, 0, 3
> ? ? ? ? ? ? ? )),ncol=3,byrow=TRUE)
>
> S <- t(compositions(5,3))
> d <- rep(0,nrow(S))
>
>
> for(i in seq_len(nrow(obs))){
> ?for(j in seq_len(nrow(S))){
> ? if(all(obs[i,,drop=TRUE] == S[j,,drop=TRUE])){
> ? ? d[j] <- d[j]+1
> ? }
> ?}
> }
>
> S <- cbind(S,d)
>
>
> Anyone got anything better before I try C?
>
>
> --
> Robin K. S. Hankin
> Uncertainty Analyst
> University of Cambridge
> 19 Silver Street
> Cambridge CB3 9EP
> 01223-764877
>
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