How to combine columns with identical names in a large sparse Matrix

Question

I have a sparse dgTMatrix from the Matrix package, that has picked up some duplicate colnames. I want to combine these by summing the columns with the same names, forming a reduced Matrix.

I found this post, which I adapted for sparse matrix operations. But: It's still very slow on large objects. I am wondering if someone has a better solution that operates directly on the indexed elements of the sparse matrix that would be faster. For instance, A@j indexes (from zero) the labels in A@Dimnames[[2]], which could be compacted and used to reindex A@j. (Note: This is why I used the triplet sparse matrix form rather than the Matrix default of column-sparse matrixes since figuring out that p value makes my head hurt every time.)

require(Matrix)

# set up a (triplet) sparseMatrix
A <- sparseMatrix(i = c(1, 2, 1, 2, 1, 2), j = 1:6, x = rep(1:3, 2), 
                  giveCsparse = FALSE,
                  dimnames = list(paste0("r", 1:2), rep(letters[1:3], 2)))
A
## 2 x 6 sparse Matrix of class "dgTMatrix"
##    a b c a b c
## r1 1 . 3 . 2 .
## r2 . 2 . 1 . 3

str(A)
## Formal class 'dgTMatrix' [package "Matrix"] with 6 slots
##   ..@ i       : int [1:6] 0 1 0 1 0 1
##   ..@ j       : int [1:6] 0 1 2 3 4 5
##   ..@ Dim     : int [1:2] 2 6
##   ..@ Dimnames:List of 2
##   .. ..$ : chr [1:2] "r1" "r2"
##   .. ..$ : chr [1:6] "a" "b" "c" "a" ...
##   ..@ x       : num [1:6] 1 2 3 1 2 3
##   ..@ factors : list()

# my matrix-based attempt
OP1 <- function(x) {
    nms <- colnames(x)
    if (any(duplicated(nms))) 
        x <- x %*% Matrix(sapply(unique(nms),"==", nms))
    x
} 
OP1(A)
## 2 x 3 sparse Matrix of class "dgCMatrix"
##    a b c
## r1 1 2 3
## r2 1 2 3

It worked fine, but seems quite slow on the huge sparse objects on which I intend to use it. Here's a larger item:

# now something bigger, for testing
set.seed(10)
nr <- 10000     # rows
nc <- 26*100    # columns - 100 repetitions of a-z
nonZeroN <- round(nr * nc / 3)  # two-thirds sparse
B <- sparseMatrix(i = sample(1:nr, size = nonZeroN, replace = TRUE), 
                  j = sample(1:nc, size = nonZeroN, replace = TRUE),
                  x = round(runif(nonZeroN)*5+1),
                  giveCsparse = FALSE, 
                  dimnames =  list(paste0("r", 1:nr), rep(letters, nc/26)))
print(B[1:5, 1:10], col.names = TRUE)
## 5 x 10 sparse Matrix of class "dgTMatrix"
##     a b c  d e f g h i  j
## r1  . . 5  . . 2 . . .  .
## r2  . . .  . . . . . .  4
## r4  . . .  . . . . 3 3  .
## r3  2 2 .  3 . . . 3 .  .
## r5  3 . .  1 . . . . .  5

require(microbenchmark)
microbenchmark(OPmatrixCombine1 = OP1(B), times = 30)
## Unit: milliseconds
##             expr      min       lq     mean   median       uq      max neval
## OPmatrixCombine1 578.9222 619.3912 665.6301 631.4219 646.2716 1013.777    30

Is there a better way, where better means faster and, if possible, not requiring the construction of additional large objects?

Answer 1

Here's an attempt using the index reindexing I had in mind, which I figured out with a friend's help (Patrick is that you?). It reindexes the j values, and uses the very handy feature of sparseMatrix() that adds the x values together for elements whose index positions are the same.

OP2 <- function(x) {
    nms <- colnames(x)
    uniquenms <- unique(nms)
    # build the sparseMatrix again: x's with same index values are automatically
    # added together, keeping in mind that indexes stored from 0 but built from 1
    sparseMatrix(i = x@i + 1, 
                 j = match(nms, uniquenms)[x@j + 1],
                 x = x@x,
                 dimnames = list(rownames(x), uniquenms),
                 giveCsparse = FALSE)
}

Results are the same:

OP2(A)
## 2 x 3 sparse Matrix of class "dgCMatrix"
##    a b c
## r1 1 2 3
## r2 1 2 3

all.equal(as(OP1(B), "dgTMatrix"), OP2(B))
## [1] TRUE

But faster:

require(microbenchmark)
microbenchmark(OPmatrixCombine1 = OP1(B), 
               OPreindexSparse = OP2(B),
               times = 30)
## Unit: relative
##              expr      min       lq     mean   median       uq      max neval
##  OPmatrixCombine1 1.756769 1.307651 1.360487 1.341814 1.346864 1.460626    30
##   OPreindexSparse 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000    30