Apply function on multiple rows of matrix

Question

If I have a matrix, does there exist a way to apply a function on the rows of a matrix in such way that a certain number of rows are grouped?

As an example: I might like to solve a least squares problem using QR decomposition on a matrix for every ten of my hundred rows. This might look like:

set.seed(128)
f <- function(x) x^2 -x + 1
x <- runif(1000, -1, 1)
y <- f(x) + rnorm(1000, 0, 0.2)

morpheus <- cbind(1,x,x^2)
# apply qr.solve(morpheus, y) 100 times on 10 rows at a time 
# in such way that the correspondence between morpheus and y is not broken

Would anybody now how this problem could be solved? If it would be possible, I'd prefer an approach using any form of apply or other functional solution, but still any help is welcome

Answer 1

Using dplyr

library(dplyr)
morpheus %>% group_by(rep(1:10, 100)) %>% do(as.data.frame(rbind(qr.solve(cbind(.$const, .$x, .$x_sq), .$y))))
Source: local data frame [10 x 4]
Groups: rep(1:10, 100)

   rep(1:10, 100)        V1         V2        V3
1               1 1.0410480 -0.9616138 0.8777193
2               2 0.9883532 -0.9751688 1.0431504
3               3 1.0263414 -1.0053184 0.8811848
4               4 1.0114099 -1.0024364 0.9341063
5               5 1.0059417 -0.9694164 0.9322200
6               6 1.0501467 -1.0186771 0.9048468
7               7 0.9748101 -1.0045796 1.0932815
8               8 0.9784629 -0.9572418 1.0008312
9               9 0.9559010 -1.0271767 1.0823086
10             10 0.9435522 -1.0583352 1.0804009

Answer 2

I think the simplest solution, apart from for loop, would be using by

f <- function(x) x^2 -x + 1
x <- runif(1000, -1, 1)
y <- f(x) + rnorm(1000, 0, 0.2)

morpheus <- cbind(1,x,x^2,y, rep(1:100,each=10))

by(morpheus[,1:4], morpheus[,5], function(x)qr.solve(x[,1:3],x[,4]))

     INDICES: 1
        V1          x         V3 
     1.1359248 -0.7800506  0.6642460 
    --------------------------------------------------------------------------------- 
    INDICES: 2
       V1          x         V3 
     0.9156199 -1.0999112  1.0019637 
    --------------------------------------------------------------------------------- 
    INDICES: 3
       V1          x         V3 
     0.9901892 -0.8275427  1.2576495 

### etc.

UPDATE: you can use do.call to get the results into a matrix for further use:

do.call('rbind',as.list(
  by(morpheus[,1:4], morpheus[,5], function(x){
    qr.solve(x[,1:3],x[,4])
  })
))

# results:

          V1          x        V3
1   0.9445907 -1.0655362 0.9471155
2   1.0370279 -0.8100258 0.7440526
3   0.9681344 -0.7442517 0.9108040
### etc.

Answer 3

If you have an additional variable that labels the set of rows you want to independently apply your function on, you may want to try

 library('data.table')
 iris <- as.data.table(iris)
 iris[,
      apply(.SD,1, mean),
      by = Species
      ]

       Species    V1
  1:    setosa 2.550
  2:    setosa 2.375
  3:    setosa 2.350
  4:    setosa 2.350
  5:    setosa 2.550
 ---                
146: virginica 4.300
147: virginica 3.925
148: virginica 4.175
149: virginica 4.325
150: virginica 3.950

and replace mean with any other function of your choice, by = variable being the variable allowing you to group by ten rows at a time.