apply() is slow - how to make it faster or what are my alternatives?

Question

I have a quite large data frame, about 10 millions of rows. It has columns x and y, and what I want is to compute

hypot <- function(x) {sqrt(x[1]^2 + x[2]^2)}

for each row. Using apply it would take a lot of time (about 5 minutes, interpolating from lower sizes) and memory.

But it seems to be too much for me, so I've tried different things:

• compiling the hypot function reduces the time by about 10%
• using functions from plyr greatly increases the running time.

What's the fastest way to do this thing?

Answer 1

What about with(my_data,sqrt(x^2+y^2)) ?

set.seed(101)
d <- data.frame(x=runif(1e5),y=runif(1e5))

library(rbenchmark)

Two different per-line functions, one taking advantage of vectorization:

hypot <- function(x) sqrt(x[1]^2+x[2]^2)
hypot2 <- function(x) sqrt(sum(x^2))

Try compiling these too:

library(compiler)
chypot <- cmpfun(hypot)
chypot2 <- cmpfun(hypot2)

benchmark(sqrt(d[,1]^2+d[,2]^2),
          with(d,sqrt(x^2+y^2)),
          apply(d,1,hypot),
          apply(d,1,hypot2),
          apply(d,1,chypot),
          apply(d,1,chypot2),
          replications=50)

Results:

                       test replications elapsed relative user.self sys.self
5       apply(d, 1, chypot)           50  61.147  244.588    60.480    0.172
6      apply(d, 1, chypot2)           50  33.971  135.884    33.658    0.172
3        apply(d, 1, hypot)           50  63.920  255.680    63.308    0.364
4       apply(d, 1, hypot2)           50  36.657  146.628    36.218    0.260
1 sqrt(d[, 1]^2 + d[, 2]^2)           50   0.265    1.060     0.124    0.144
2  with(d, sqrt(x^2 + y^2))           50   0.250    1.000     0.100    0.144

As expected the with() solution and the column-indexing solution à la Tyler Rinker are essentially identical; hypot2 is twice as fast as the original hypot (but still about 150 times slower than the vectorized solutions). As already pointed out by the OP, compilation doesn't help very much.

Answer 2

While Ben Bolkers answer is comprehensive, I will explain other reasons to avoid apply on data.frames.

apply will convert your data.frame to a matrix. This will create a copy (waste of time and memory), as well as perhaps causing unintended type conversions.

Given that you have 10 million rows of data, I would suggest you look at the data.table package that will let you do things efficiently in terms of memory and time.

---

For example, using tracemem

x <- apply(d,1, hypot2)
tracemem[0x2f2f4410 -> 0x2f31b8b8]: as.matrix.data.frame as.matrix apply 

This is even worse if you then assign to a column in d

d$x <- apply(d,1, hypot2)
tracemem[0x2f2f4410 -> 0x2ee71cb8]: as.matrix.data.frame as.matrix apply 
tracemem[0x2f2f4410 -> 0x2fa9c878]: 
tracemem[0x2fa9c878 -> 0x2fa9c3d8]: $<-.data.frame $<- 
tracemem[0x2fa9c3d8 -> 0x2fa9c1b8]: $<-.data.frame $<- 

4 copies! -- with 10 million rows, that will probably come and bite you at somepoint.

If we use with, there is no copying involved, if we assign to a vector

y <- with(d, sqrt(x^2 + y^2))

But there will be if we assign to a column in the data.frame d

d$y <- with(d, sqrt(x^2 + y^2))
tracemem[0x2fa9c1b8 -> 0x2faa00d8]: 
tracemem[0x2faa00d8 -> 0x2faa0f48]: $<-.data.frame $<- 
tracemem[0x2faa0f48 -> 0x2faa0d08]: $<-.data.frame $<- 

Now, if you use data.table and := to assign by reference (no copying)

 library(data.table)
 DT <- data.table(d)



tracemem(DT)
[1] "<0x2d67a9a0>"
DT[,y := sqrt(x^2 + y^2)]

No copies!

---

Perhaps I will be corrected here, but another memory issue to consider is that sqrt(x^2+y^2)) will create 4 temporary variables (internally) x^2, y^2, x^2 + y^2 and then sqrt(x^2 + y^2))

The following will be slower, but only involve two variables being created.

 DT[, rowid := .I] # previous option: DT[, rowid := seq_len(nrow(DT))]
 DT[, y2 := sqrt(x^2 + y^2), by = rowid]

Answer 3

R is vectorised, so you could use the following, plugging in your own matrix of course

X = t(matrix(1:4, 2, 2))^2
>      [,1] [,2]
 [1,]    1    4
 [2,]    9   16

rowSums(X)^0.5

Nice and efficient :)