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sparseLRMatrix provides a single matrix S4 class called sparseLRMatrix which represents matrices that can be expressed as the sum of sparse matrix and a low rank matrix. We also provide an efficient SVD method for these matrices by wrapping the RSpectra SVD implementation.

Eventually, we will fully subclass Matrix::Matrix objects, but the current implementation is extremely minimal.


You can install the released version of sparseLRMatrix from CRAN with:

# install.packages("remotes")


#> Loading required package: Matrix


n <- 50
m <- 40
k <- 3

A <- rsparsematrix(n, m, 0.1)

U <- Matrix(rnorm(n * k), nrow = n, ncol = k)
V <- Matrix(rnorm(m * k), nrow = m, ncol = k)

# construct the matrix, which represents A + U %*% t(V)
X <- sparseLRMatrix(sparse = A, U = U, V = V)

s <- svds(X, 5)  # efficient

And a quick sanity check

Y <- A + tcrossprod(U, V)
s2 <- svds(Y, 5)  # inefficient, but same calculation

# singular values match up, you can check for yourself
# that the singular vectors do as well!
all.equal(s$d, s2$d)
#> [1] TRUE