In R, change the values of some items in a matrix without causing a copy of the entire matrix?

I have a "small" square matrix that I want to add to a "big" matrix. The big matrix contains all the rows and columns of the small matrix plus extras. I want to add the values where the indices are in common and just keep the values from the big one where that index is not contained in the small one. Unfortunately, all the data is copied on the addition so it takes a long time and can temporarily spike memory when the matrices are large.

I have tried adding subsets using matrices and data.frames, as well as a data.table method using rbindlist. Both the data.frame and matrix methods seem to cause a memory copy (why?) and the rbindlist method is not ideal because it requires a melt and dcast and temporarily spiking the memory by spiking the number of rows.

Is there any way to just change the values of some items in a matrix without causing a copy of the entire matrix?

Here are my attempts:

MList <- list(M1,M2)
unionCols <- Reduce(union, lapply(MList, colnames))
MTotal <- matrix(as.double(rep(0,(length(unionCols))^2)), nrow = length(unionCols))
rownames(MTotal) <- colnames(MTotal) <- unionCols
DFTotal <- as.data.frame(MTotal)
DFList <- lapply(MList, as.data.frame)
for(i in 1:length(MList)){
  tracemem(MTotal)
  tracemem(DFTotal)
  mCol <- match(colnames(MList[[i]]), colnames(MTotal))
  MTotal[mCol,mCol] <- MTotal[mCol,mCol] + MList[[i]] # this causes a copy
  DFTotal[mCol,mCol] <- DFTotal[mCol,mCol] + DFList[[i]] # this causes a copy
}
M1
M2
MTotal

# rbindlist method
.AggDMCMatsSingleM2 <- function(M1, M2){
  .MyMelt <- function(M){
    DT <- setnames(reshape2::melt(M, id.vars = colnames(M)), c('Var1','Var2'), c('row','col'))
  }
  M_total <- as.matrix(data.table::dcast(rbindlist(lapply(list(M1,M2), .MyMelt)),
                                         formula = as.formula(row ~ col),
                                         value.var = 'value',
                                         fun.aggregate = sum,
                                         fill = 0),
                       rownames = 'row')
  return(M_total)
}
M1
M2
.AggDMCMatsSingleM2(M1,M2)

If I follow what you are asking we can directly add and write to the big matrix using the bracket notation row/col names of the small matrix:

big_matrix<-matrix(data=rep(1, 25), nrow=5, 
                   dimnames = list(c(LETTERS[1:5]), 
                                   c(letters[1:5])))
#  a b c d e
#A 1 1 1 1 1
#B 1 1 1 1 1
#C 1 1 1 1 1
#D 1 1 1 1 1
#E 1 1 1 1 1
small_matrix<-matrix(data=c(1:9), nrow=3, 
                     dimnames = list(c(LETTERS[2:4]), 
                                     c(letters[2:4])))
#  b c d
#B 1 4 7
#C 2 5 8
#D 3 6 9    
big_matrix[rownames(small_matrix), colnames(small_matrix)] <- 
  big_matrix[rownames(small_matrix), colnames(small_matrix)] + small_matrix

#  a b c  d e
#A 1 1 1  1 1
#B 1 2 5  8 1
#C 1 3 6  9 1
#D 1 4 7 10 1
#E 1 1 1  1 1

More complex test:

big_matrix<-matrix(data=rep(1, 25), nrow=5, 
                   dimnames = list(c(LETTERS[1:5]), 
                                   c(letters[1:5])))
#  a b c d e
#A 1 1 1 1 1
#B 1 1 1 1 1
#C 1 1 1 1 1
#D 1 1 1 1 1
#E 1 1 1 1 1
small_matrix<-matrix(data=c(1:9), nrow=3, 
                     dimnames = list(c("A", "D", "C"), 
                                     c(letters[c(2:4)])))
#  b c d
#A 1 4 7
#D 2 5 8
#C 3 6 9

    big_matrix[rownames(small_matrix), colnames(small_matrix)] <- 
      big_matrix[rownames(small_matrix), colnames(small_matrix)] + small_matrix
big_matrix
#  a b c  d e
#A 1 2 5  8 1
#B 1 1 1  1 1
#C 1 4 7 10 1
#D 1 3 6  9 1
#E 1 1 1  1 1