svd of very large matrix in R program

large-data, matrix, r, svd

Solution

I think it's possible to compute (partial) `svd` using the `irlba` package and `bigmemory` and `bigalgebra` without using a lot of memory.

First let's create a 20000 * 20000 matrix and save it into a file

require(bigmemory)
require(bigalgebra)
require(irlba)

con <- file("mat.txt", open = "a")
replicate(20, {
    x <- matrix(rnorm(1000 * 20000), nrow = 1000)
    write.table(x, file  = 'mat.txt', append = TRUE,
            row.names = FALSE, col.names = FALSE)
})

file.info("mat.txt")$size
## [1] 7.264e+09   7.3 Gb
close(con)

Then you can read this matrix using `bigmemory::read.big.matrix`

bigm <- read.big.matrix("mat.txt", sep = " ",
                        type = "double",
                        backingfile = "mat.bk",
                        backingpath = "/tmp",
                        descriptorfile = "mat.desc")

str(bigm)
## Formal class 'big.matrix' [package "bigmemory"] with 1 slots
##   ..@ address:<externalptr>

dim(bigm)
## [1] 20000 20000

bigm[1:3, 1:3]
##            [,1]     [,2]     [,3]
## [1,] -0.3623255 -0.58463 -0.23172
## [2,] -0.0011427  0.62771  0.73589
## [3,] -0.1440494 -0.59673 -1.66319

Now we can use the use the excellent `irlba` package as explained in the package vignette.

The first step consist of defining matrix multiplication operator which can work with `big.matrix` object and then use the `irlba::irlba` function

### vignette("irlba", package = "irlba") # for more info

matmul <- function(A, B, transpose=FALSE) {
    ## Bigalgebra requires matrix/vector arguments
    if(is.null(dim(B))) B <- cbind(B)

    if(transpose)
        return(cbind((t(B) %*% A)[]))

    cbind((A %*% B)[])
}

dim(bigm)

system.time(
S <- irlba(bigm, nu = 2, nv = 2, matmul = matmul)
)

##    user  system elapsed 
## 169.820   0.923 170.194


str(S)
## List of 5
##  $ d    : num [1:2] 283 283
##  $ u    : num [1:20000, 1:2] -0.00615 -0.00753 -0.00301 -0.00615 0.00734 ...
##  $ v    : num [1:20000, 1:2] 0.020086 0.012503 0.001065 -0.000607 -0.006009 ...
##  $ iter : num 10
##  $ mprod: num 310

I forgot to set the seed to make it reproductible but I just wanted to show that it's possible to do that in R.

EDIT

If you are using a new version of the package `irlba`, the above code throw an error because the `matmult` parameter of the function `irlba` has been renamed to `mult`. Therefore, you should change this part of the code

S <- irlba(bigm, nu = 2, nv = 2, matmul = matmul)

By

S <- irlba(bigm, nu = 2, nv = 2, mult = matmul)

I want to thank @FrankD for pointing this out.

Problem

Original source