Creating Kronecker product in R-CodePudding

Let the following be the dataset:

What I need to do is to create new columns wherein I need to multiply all a columns with b columns and name the newly created column as a1_b1, a1_b2........ a1_b4, a2_b1, a2_b2 as shown in the figure.

I am using R for data analysis. Even though I have stated only two columns by two columns, in reality, it is 1600 by 25. Hence the question.

CodePudding user response：

This might be fast enough:

set.seed(42)
DF <- data.frame(a1 = sample(1:10), 
                 a2 = sample(1:10),
                 b1 = sample(1:10),
                 b2 = sample(1:10))

a <- grep("a", names(DF))
b <- grep("b", names(DF))
combs <- expand.grid(a, b)

res <- do.call(mapply, c(list(FUN = \(...) do.call(`*`, DF[, c(...)])), combs))
colnames(res) <- paste(names(DF)[combs[[1]]], names(DF)[combs[[2]]], sep = "_")

cbind(DF, res)
#   a1 a2 b1 b2 a1_b1 a2_b1 a1_b2 a2_b2
#1   1  8  9  3     9    72     3    24
#2   5  7 10  1    50    70     5     7
#3  10  4  3  2    30    12    20     8
#4   8  1  4  6    32     4    48     6
#5   2  5  5 10    10    25    20    50
#6   4 10  6  8    24    60    32    80
#7   6  2  1  4     6     2    24     8
#8   9  6  2  5    18    12    45    30
#9   7  9  8  7    56    72    49    63
#10  3  3  7  9    21    21    27    27

CodePudding user response：

The operation in the question is the transpose of the KhatriRao product. We use the Matrix package which comes with R so it does not have to be installed. Using the input in the Note at the end, pick out the two portions, transpose them, use KhatriRao and transpose back giving a sparse matrix (class "dgCMatrix"). We can use as.matrix to convert to a dense matrix as shown or as.data.frame(as.matrix(...)) to convert to a data.frame.

library(Matrix)

rownames(dat) <- 1:nrow(dat)
ix <- grep("a", colnames(dat))
as.matrix(t(KhatriRao(t(dat[, -ix]), t(dat[, ix]), make.dimnames = TRUE)))

giving:

  a1:b1  a2:b1 a1:b2   a2:b2
1   101  838.3 108.3  898.89
2   204 1050.6 220.6 1136.09
3   309 1957.0 357.0 2261.00
4   416 1664.0 464.0 1856.00
5   525 1638.0 578.0 1803.36
6   749 2118.6 838.6 2372.04

Note

dat <- setNames(cbind(BOD, BOD   100), c("a1", "a2", "b1", "b2"))
dat

giving

  a1   a2  b1    b2
1  1  8.3 101 108.3
2  2 10.3 102 110.3
3  3 19.0 103 119.0
4  4 16.0 104 116.0
5  5 15.6 105 115.6
6  7 19.8 107 119.8