Multiplying elements of a matrix depending on numbers and strings of the row names and column names (2)

Question

This question is similar to the one I asked here. I again have a very large matrix with row and column names that are identical. These names are a three letter string followed by a number. The three letter string repeats itself and only the number changes. After several repetitions, the string changes and the number starts from 1 again.

Basically what I'm looking for is doing specific calculations based on each element's row name and column name.

I will give a small example of what I'm looking for. Here is a matrix a:

matrix <- matrix(c(1:36), nrow = 6, byrow = TRUE)

names <- paste(rep(c("aaa" , "bbb", "ccc"), each = 2) , rep(c(1:2) , times = 3))

rownames(matrix) <- names
colnames(matrix) <- names

that gives:

      aaa 1 aaa 2 bbb 1 bbb 2 ccc 1 ccc 2
aaa 1     1     2     3     4     5     6
aaa 2     7     8     9    10    11    12
bbb 1    13    14    15    16    17    18
bbb 2    19    20    21    22    23    24
ccc 1    25    26    27    28    29    30
ccc 2    31    32    33    34    35    36

For each element of this matrix I would like to do a multiplication. It's a bit hard to explain with words.

If an element of a matrix has a row name with a different three letter string than its column name, I would match the number appearing after the string and multiply "first 3 letter string number" with "second three letter string with same number".

If "aaa" is matched with "bbb" then:

matrix[aaa (number n), aaa (number m)] * matrix[bbb (number n), bbb (number m)]

if "aaa" is equal to "aaa" then

matrix[aaa (number n), aaa (number m)] * matrix[aaa (number n), aaa (number m)]

or basically the element squared.

So I will give some examples of what I am looking for:

• in matrix["aaa 1", "aaa 2"] I would multiply matrix["aaa 1", "aaa 2"] with matrix["aaa 1", "aaa 2"] (2*2) giving 4

• in matrix["aaa 1", "bbb 2"] I would multiply matrix["aaa 1", "aaa 2"] with matrix["bbb 1", "bbb 2"] (2*16) giving 32

• in matrix["bbb 2", "ccc 1"] I would multiply matrix["bbb 2", "bbb 1"] with matrix["ccc 2", "ccc 1"] (21*35) giving 735

In the end, the matrix (called d) should give:

      aaa 1 aaa 2 bbb 1 bbb 2 ccc 1 ccc 2
aaa 1     1     4    15    32    29    60
aaa 2    49    64   147   176   245   288
bbb 1    15    32   225   256   435   480
bbb 2   147   176   441   484   735   792
ccc 1    29    60   435   480   841   900
ccc 2   245   288   735   792  1225  1296

which I got by using horrible code:

d <- matrix^2

d[1,3] <- matrix[1,1] * matrix[3,3]
d[1,4] <- matrix[1,2] * matrix[3,4]
d[1,5] <- matrix[1,1] * matrix[5,5]
d[1,6] <- matrix[1,2] * matrix[5,6]
d[2,3] <- matrix[2,1] * matrix[4,3]
d[2,4] <- matrix[2,2] * matrix[4,4]
d[2,5] <- matrix[2,1] * matrix[6,5]
d[2,6] <- matrix[2,2] * matrix[6,6]

d[3,1] <- matrix[3,3] * matrix[1,1]
d[3,2] <- matrix[3,4] * matrix[1,2]
d[3,5] <- matrix[3,3] * matrix[5,5]
d[3,6] <- matrix[3,4] * matrix[5,6]
d[4,1] <- matrix[4,3] * matrix[2,1] 
d[4,2] <- matrix[4,4] * matrix[2,2]
d[4,5] <- matrix[4,3] * matrix[6,5]
d[4,6] <- matrix[4,4] * matrix[6,6]

d[5,1] <- matrix[5,5] * matrix[1,1]
d[5,2] <- matrix[5,6] * matrix[1,2]
d[5,3] <- matrix[5,5] * matrix[3,3]
d[5,4] <- matrix[5,6] * matrix[3,4]
d[6,1] <- matrix[6,5] * matrix[2,1]
d[6,2] <- matrix[6,6] * matrix[2,2]
d[6,3] <- matrix[6,5] * matrix[4,3]
d[6,4] <- matrix[6,6] * matrix[4,4]

Is there a code than can solve this more efficiently with loops or some other way?

Answer 1

Dirty with loops:

d2 <- matrix^2
for (i in rownames(matrix)) {
  for (j in colnames(matrix)) {
    i1 <- strsplit(i, ' ', fixed = T)[[1]]
    j1 <- strsplit(j, ' ', fixed = T)[[1]]
    ni <- c(i1[2], j1[2])
    n1 <- paste(i1[1], ni)
    n2 <- paste(j1[1], ni)
    d2[i, j] <- matrix[n1[1], n1[2]] * matrix[n2[1], n2[2]]
  }
}

d2
#       aaa 1 aaa 2 bbb 1 bbb 2 ccc 1 ccc 2
# aaa 1     1     4    15    32    29    60
# aaa 2    49    64   147   176   245   288
# bbb 1    15    32   225   256   435   480
# bbb 2   147   176   441   484   735   792
# ccc 1    29    60   435   480   841   900
# ccc 2   245   288   735   792  1225  1296
all.equal(d2, d)
# [1] TRUE

This will be faster (without loops):

require(data.table)
require(Hmisc)
mat <- matrix # rename matrix variable,
# it is bad practice to name variables the same as internal functions
rn <- rownames(mat)
nn <- data.table(expand.grid(rn, rn, stringsAsFactors = F)) # all combinations of names
# split into parts:
nn[, Cs(v1, s1) := tstrsplit(Var1, ' ', fixed = T)]
nn[, Cs(v2, s2) := tstrsplit(Var2, ' ', fixed = T)]

# make respective new names:
nn[, a1 := paste(v1, s1)]
nn[, a2 := paste(v1, s2)]
nn[, b1 := paste(v2, s1)]
nn[, b2 := paste(v2, s2)]

index <- as.matrix(nn[, lapply(.SD, match, rn),
                      .SDcols = Cs(a1, a2, b1, b2)]) # get indexes of elements

d3 <- mat[index[, 1:2]] * mat[index[, 3:4]] # selection of elements and multiplication
d3 <- matrix(d3, ncol = ncol(mat)) # convert to matrix
rownames(d3) <- rn
colnames(d3) <- rn

all.equal(d3, d2)
# [1] TRUE

Answer 2

We can use mapply here

#Get all the possible combination of rownames and column names
all_combns <- expand.grid(rownames(matrix), colnames(matrix),
                   stringsAsFactors = FALSE)

matrix[] <- mapply(function(x, y) {
        #Extract first three letters
        first_group <- substr(x, 1, 3)
        second_group <- substr(y, 1, 3)

        #Extract the numeric part which could also be done in this example by
        #substr(x, 5, 5)
        #I am just extracting the numeric part in the string.
        first_num <- sub("[^\\d]+", "", x, perl = TRUE)
        second_num <- sub("[^\\d]+", "", y, perl = TRUE)

        #Construct element 1 and multiply it by elemnt 2
        matrix[paste(first_group, first_num),paste(first_group, second_num)] *
        matrix[paste(second_group, first_num),paste(second_group, second_num)]
        } , all_combns[, 1], all_combns[, 2])

matrix

#      aaa 1 aaa 2 bbb 1 bbb 2 ccc 1 ccc 2
#aaa 1     1     4    15    32    29    60
#aaa 2    49    64   147   176   245   288
#bbb 1    15    32   225   256   435   480
#bbb 2   147   176   441   484   735   792
#ccc 1    29    60   435   480   841   900
#ccc 2   245   288   735   792  1225  1296