Combining the product of matrix columns into a new matrix-CodePudding

I have a 10 by 6 matrix and I'd like to multiply columns 2:6 by column 1, then columns 3:6 by column 2, and so on until I'm left with column 5 * column 6. The matrix is below.

    M12.7 <- matrix(data = 1:60, nrow = 10, ncol = 6)
       [,1] [,2] [,3] [,4] [,5] [,6]
 [1,]    1   11   21   31   41   51
 [2,]    2   12   22   32   42   52
 [3,]    3   13   23   33   43   53
 [4,]    4   14   24   34   44   54
 [5,]    5   15   25   35   45   55
 [6,]    6   16   26   36   46   56
 [7,]    7   17   27   37   47   57
 [8,]    8   18   28   38   48   58
 [9,]    9   19   29   39   49   59
[10,]   10   20   30   40   50   60

This should result in 5 matrices for a total of 15 columns. I want to then combine those matrices into a 10 by 15 matrix. I've written a function that sort of gets me there. But I can't apply it to a whole reference matrix, M12.7 in this case. The function is:

function(datamatrix, column, colz) { 
   datamatrix[, column] * datamatrix[, (column 1):colz]
}

datamatrix in the function is not data.matrix. Any help is greatly appreciated

CodePudding user response：

s <- seq(ncol(M12.7)-1)
do.call(cbind, lapply(s, function(x)M12.7[,x]*M12.7[, -seq(x)]))

      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14] [,15]
 [1,]   11   21   31   41   51  231  341  451  561   651   861  1071  1271  1581  2091
 [2,]   24   44   64   84  104  264  384  504  624   704   924  1144  1344  1664  2184
 [3,]   39   69   99  129  159  299  429  559  689   759   989  1219  1419  1749  2279
 [4,]   56   96  136  176  216  336  476  616  756   816  1056  1296  1496  1836  2376
 [5,]   75  125  175  225  275  375  525  675  825   875  1125  1375  1575  1925  2475
 [6,]   96  156  216  276  336  416  576  736  896   936  1196  1456  1656  2016  2576
 [7,]  119  189  259  329  399  459  629  799  969   999  1269  1539  1739  2109  2679
 [8,]  144  224  304  384  464  504  684  864 1044  1064  1344  1624  1824  2204  2784
 [9,]  171  261  351  441  531  551  741  931 1121  1131  1421  1711  1911  2301  2891
[10,]  200  300  400  500  600  600  800 1000 1200  1200  1500  1800  2000  2400  3000

Another way:

s <- seq(ncol(M12.7) -1)
n <- sequence(rev(s)) 1
p <- cumsum(n==2)

M12.7[, p] *M12.7[, n p-1]

CodePudding user response：

If I'm understanding correctly, we can use the cumulative product cumprod function applied to each row:

t(apply(M12.7, MARGIN = 1, FUN = cumprod))
      [,1] [,2] [,3]   [,4]     [,5]      [,6]
 [1,]    1   11  231   7161   293601  14973651
 [2,]    2   24  528  16896   709632  36900864
 [3,]    3   39  897  29601  1272843  67460679
 [4,]    4   56 1344  45696  2010624 108573696
 [5,]    5   75 1875  65625  2953125 162421875
 [6,]    6   96 2496  89856  4133376 231469056
 [7,]    7  119 3213 118881  5587407 318482199
 [8,]    8  144 4032 153216  7354368 426553344
 [9,]    9  171 4959 193401  9476649 559122291
[10,]   10  200 6000 240000 12000000 720000000

CodePudding user response：

There is rowCumprods in matrixStats

library(matrixStats)
rowCumprods(M12.7)
      [,1] [,2] [,3]   [,4]     [,5]      [,6]
 [1,]    1   11  231   7161   293601  14973651
 [2,]    2   24  528  16896   709632  36900864
 [3,]    3   39  897  29601  1272843  67460679
 [4,]    4   56 1344  45696  2010624 108573696
 [5,]    5   75 1875  65625  2953125 162421875
 [6,]    6   96 2496  89856  4133376 231469056
 [7,]    7  119 3213 118881  5587407 318482199
 [8,]    8  144 4032 153216  7354368 426553344
 [9,]    9  171 4959 193401  9476649 559122291
[10,]   10  200 6000 240000 12000000 720000000