My goal is to "sum" two not compatible matrices (matrices with different dimensions) using (and preserving) row and column names.

I've figured this approach: convert the matrices to data.table objects, join them and then sum columns vectors.

An example:

> M1
  1 3 4 5 7 8
1 0 0 1 0 0 0
3 0 0 0 0 0 0
4 1 0 0 0 0 0
5 0 0 0 0 0 0
7 0 0 0 0 1 0
8 0 0 0 0 0 0
> M2
  1 3 4 5 8
1 0 0 1 0 0
3 0 0 0 0 0
4 1 0 0 0 0
5 0 0 0 0 0
8 0 0 0 0 0
> M1 %ms% M2
  1 3 4 5 7 8
1 0 0 2 0 0 0
3 0 0 0 0 0 0
4 2 0 0 0 0 0
5 0 0 0 0 0 0
7 0 0 0 0 1 0
8 0 0 0 0 0 0

This is my code:

M1 <- matrix(c(0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0), byrow = TRUE, ncol = 6)
colnames(M1) <- c(1,3,4,5,7,8)
M2 <- matrix(c(0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0), byrow = TRUE, ncol = 5)
colnames(M2) <- c(1,3,4,5,8)
# to data.table objects
DT1 <- data.table(M1, keep.rownames = TRUE, key = "rn")
DT2 <- data.table(M2, keep.rownames = TRUE, key = "rn")
# join and sum of common columns
if (nrow(DT1) > nrow(DT2)) {
    A <- DT2[DT1, roll = TRUE]
    A[, list(X1 = X1 + X1.1, X3 = X3 + X3.1, X4 = X4 + X4.1, X5 = X5 + X5.1, X7, X8 = X8 + X8.1), by = rn]
}

That outputs:

   rn X1 X3 X4 X5 X7 X8
1:  1  0  0  2  0  0  0
2:  3  0  0  0  0  0  0
3:  4  2  0  0  0  0  0
4:  5  0  0  0  0  0  0
5:  7  0  0  0  0  1  0
6:  8  0  0  0  0  0  0

Then I can convert back this data.table to a matrix and fix row and column names.

The questions are:

• how to generalize this procedure?

  I need a way to automatically create list(X1 = X1 + X1.1, X3 = X3 + X3.1, X4 = X4 + X4.1, X5 = X5 + X5.1, X7, X8 = X8 + X8.1) because i want to apply this function to matrices which dimensions (and row/columns names) are not known in advance.

  In summary I need a merge procedure that behaves as described.

• there are other strategies/implementations that achieve the same goal that are, at the same time, faster and generalized? (hoping that some data.table monster help me)

• to what kind of join (inner, outer, etc. etc.) is assimilable this procedure?

Thanks in advance.

p.s.: I'm using data.table version 1.8.2

EDIT - SOLUTIONS

@Aaron solution. No external libraries, only base R. It works also on list of matrices.

add_matrices_1 <- function(...) {
  a <- list(...)
  cols <- sort(unique(unlist(lapply(a, colnames))))
  rows <- sort(unique(unlist(lapply(a, rownames))))
  out <- array(0, dim = c(length(rows), length(cols)), dimnames = list(rows,cols))
  for (m in a) out[rownames(m), colnames(m)] <- out[rownames(m), colnames(m)] + m
  out
}

@MadScone solution. Used reshape2 package. It works only on two matrices per call.

add_matrices_2 <- function(m1, m2) {
  m <- acast(rbind(melt(M1), melt(M2)), Var1~Var2, fun.aggregate = sum)
  mn <- unique(colnames(m1), colnames(m2))
  rownames(m) <- mn
  colnames(m) <- mn
  m
}

BENCHMARK (100 runs with microbenchmark package)

Unit: microseconds
   expr                min         lq    median         uq       max
1 add_matrices_1   196.009   257.5865   282.027   291.2735   549.397
2 add_matrices_2 13737.851 14697.9790 14864.778 16285.7650 25567.448

No need to comment the benchmark: @Aaron solution wins.

I'll continue to investigate a similar solution for data.table objects.

I'll add other solutions eventually reported or discovered.