Element by element exponential of a sparse matrix in R

Question

I have a large sparse matrix (dgCMatrix) in R, and I would like to have the exponential of each element of this matrix. More precisely, I would like to do 1-exp(-x) to each element of the matrix. Unfortunately, when I do this in R, there is a sparse->dense coercion which takes a lot of time and memory (see example below).

library(Matrix)
i <- sample(20000, 20000); j <- sample(20000, 20000); x <- 7 * (1:20000)
A <- sparseMatrix(i, j, x = x)
1 - exp(-A)

Is there a way to avoid this coercion in R? As 1-exp(0) is 0, maybe sparsity can be preserved.

Do you wannt the elements equal zero to become `exp(0) == 1`? — Rui Barradas, Aug 29 '23 at 11:30
In python this is `expm1`, and is applied just to the nonzero elements, the `data` array of the `csr` format, — hpaulj, Aug 29 '23 at 14:10

ThomasIsCoding · Accepted Answer · 2023-08-29T12:14:35.900

5

Probably you can try

A@x <- 1 - exp(-A@x)

such that you update the non-sparse entries only.

For very small A@x, we can use

A@x <- -expm1(-A@x) # thanks for the comment from jblood94

or just simply

A <- -expm1(-A) # thanks for the comment from Ben Bolker

edited Aug 29 '23 at 12:14

answered Aug 29 '23 at 11:01

ThomasIsCoding

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It might also be good to keep `expm1` in mind in case `A@x` can get very small: `A@x <- -expm1(-A@x)`. – jblood94 Aug 29 '23 at 11:29
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@jblood94 yes, that's true, updated, thanks! – ThomasIsCoding Aug 29 '23 at 11:43
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In fact, `-expm1(-A)` works without any need to mess around with the slots. – Ben Bolker Aug 29 '23 at 12:08
@BenBolker aha, that's magic, cool! – ThomasIsCoding Aug 29 '23 at 12:12
@BenBolker, in the python version, `np.expm1` can be applied to dense arrays, and the sparse version just applies it to nonzeros `data` attribute. – hpaulj Aug 29 '23 at 17:07

Element by element exponential of a sparse matrix in R

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