Same Seed, Different Os, Different Random Numbers in R

Same seed, different OS, different random numbers in R

From docs:

Random docs:

RNGversion can be used to set the random generators as they were in an earlier R version (for reproducibility).

So try this on all systems:

set.seed(10, kind = "Mersenne-Twister", normal.kind = "Inversion"); rnorm(1)
[1] 0.01874617

First two values in .Random.seed are always the same with different set.seed()s

Expanding helpful comments from @r2evans and @Dave2e into an answer.

1) .Random.seed[1]

From ?.Random.seed, it says:

".Random.seed is an integer vector whose first element codes the
kind of RNG and normal generator. The lowest two decimal digits are in
0:(k-1) where k is the number of available RNGs. The hundreds
represent the type of normal generator (starting at 0), and the ten
thousands represent the type of discrete uniform sampler."

Therefore the first value doesn't change unless one changes the generator method (RNGkind).

Here is a small demonstration of this for each of the available RNGkinds:

library(tidyverse)

# available RNGkind options
kinds <- c(
  "Wichmann-Hill",
  "Marsaglia-Multicarry",
  "Super-Duper",
  "Mersenne-Twister",
  "Knuth-TAOCP-2002",
  "Knuth-TAOCP",
  "L'Ecuyer-CMRG"
)
# test over multiple seeds
seeds <- c(1:3)

f <- function(kind, seed) {
  # set seed with simulation parameters
  set.seed(seed = seed, kind = kind)
  # check value of first element in .Random.seed
  return(.Random.seed[1])
}

# run on simulated conditions and compare value over different seeds
expand_grid(kind = kinds, seed = seeds) %>%
  pmap(f) %>%
  unlist() %>%
  matrix(
    ncol = length(seeds),
    byrow = T,
    dimnames = list(kinds, paste0("seed_", seeds))
  )

#>                      seed_1 seed_2 seed_3
#> Wichmann-Hill         10400  10400  10400
#> Marsaglia-Multicarry  10401  10401  10401
#> Super-Duper           10402  10402  10402
#> Mersenne-Twister      10403  10403  10403
#> Knuth-TAOCP-2002      10406  10406  10406
#> Knuth-TAOCP           10404  10404  10404
#> L'Ecuyer-CMRG         10407  10407  10407

^{Created on 2022-01-06 by the reprex package (v2.0.1)}

2) .Random.seed[2]

At least for the default "Mersenne-Twister" method, .Random.seed[2] is an index that indicates the current position in the random set. From the docs:

The ‘seed’ is a 624-dimensional set of 32-bit integers plus a current
position in that set.

This is updated when random processes using the seed are executed. However for other methods it the documentation doesn't mention something like this and there doesn't appear to be a clear trend in the same way.

See below for an example of changes in .Random.seed[2] over iterative random process after set.seed().

library(tidyverse)

# available RNGkind options
kinds <- c(
  "Wichmann-Hill",
  "Marsaglia-Multicarry",
  "Super-Duper",
  "Mersenne-Twister",
  "Knuth-TAOCP-2002",
  "Knuth-TAOCP",
  "L'Ecuyer-CMRG"
)

# create function to run random process and report .Random.seed[2]
t <- function(n = 1) {
  p <- .Random.seed[2]
  runif(n)
  p
}

# create function to set seed and iterate a random process
f2 <- function(kind, seed = 1, n = 5) {
  
  set.seed(seed = seed,
           kind = kind)

  replicate(n, t())
}

# set simulation parameters
trials <- 5
seeds <- 1:2
x <- expand_grid(kind = kinds, seed = seeds, n = trials) 

# evaluate and report
x %>% 
  pmap_dfc(f2) %>% 
  mutate(n = paste0("trial_", 1:trials)) %>% 
  pivot_longer(-n, names_to = "row") %>% 
  pivot_wider(names_from = "n") %>% 
  select(-row) %>% 
  bind_cols(x[,1:2], .)

#> # A tibble: 14 x 7
#>    kind                  seed    trial_1     trial_2     trial_3 trial_4 trial_5
#>    <chr>                <int>      <int>       <int>       <int>   <int>   <int>
#>  1 Wichmann-Hill            1      23415        8457       23504  2.37e4  2.28e4
#>  2 Wichmann-Hill            2      21758       27800        1567  2.58e4  2.37e4
#>  3 Marsaglia-Multicarry     1 1280795612   945095059    14912928  1.34e9  2.23e8
#>  4 Marsaglia-Multicarry     2 -897583247 -1953114152  2042794797  1.39e9  3.71e8
#>  5 Super-Duper              1 1280795612 -1162609806 -1499951595  5.51e8  6.35e8
#>  6 Super-Duper              2 -897583247   224551822     -624310 -2.23e8  8.91e8
#>  7 Mersenne-Twister         1        624           1           2  3       4     
#>  8 Mersenne-Twister         2        624           1           2  3       4     
#>  9 Knuth-TAOCP-2002         1  166645457   504833754   504833754  5.05e8  5.05e8
#> 10 Knuth-TAOCP-2002         2  967462395   252695483   252695483  2.53e8  2.53e8
#> 11 Knuth-TAOCP              1 1050415712   999978161   999978161  1.00e9  1.00e9
#> 12 Knuth-TAOCP              2  204052929   776729829   776729829  7.77e8  7.77e8
#> 13 L'Ecuyer-CMRG            1 1280795612  -169270483  -442010614  4.71e8  1.80e9
#> 14 L'Ecuyer-CMRG            2 -897583247 -1619336578  -714750745  2.10e9 -9.89e8

^{Created on 2022-01-06 by the reprex package (v2.0.1)}

Here you can see that from the Mersenne-Twister method, .Random.seed[2] increments from it's maximum of 624 back to 1 and increased by the size of the random draw and that this is the same for set.seed(1) and set.seed(2). However the same trend is not seen in the other methods. To illustrate the last point, see that runif(1) increments .Random.seed[2] by 1 while runif(2) increments it by 2:

# create function to run random process and report .Random.seed[2]
t <- function(n = 1) {
  p <- .Random.seed[2]
  runif(n)
  p
}

set.seed(1, kind = "Mersenne-Twister")
replicate(9, t(1))
#> [1] 624   1   2   3   4   5   6   7   8

set.seed(1, kind = "Mersenne-Twister")
replicate(5, t(2))
#> [1] 624   2   4   6   8

^{Created on 2022-01-06 by the reprex package (v2.0.1)}

3) Sequential Randoms

Because the index or state of .Random.seed (apparently for all the RNG methods) advances according to the size of the 'random draw' (number of random values genearted from the .Random.seed), it is possible to generate the same series of random numbers from the same seed in different sized increments. Furthermore, as long as you run the same random process at the same point in the sequence after setting the same seed, it seems that you will get the same result. Observe the following example:

# draw 3 at once
set.seed(1, kind = "Mersenne-Twister")
sample(100, 3, T)
#> [1] 68 39  1

# repeat single draw 3 times
set.seed(1, kind = "Mersenne-Twister")
sample(100, 1)
#> [1] 68
sample(100, 1)
#> [1] 39
sample(100, 1)
#> [1] 1

# draw 1, do something else, draw 1 again
set.seed(1, kind = "Mersenne-Twister")
sample(100, 1)
#> [1] 68
runif(1)
#> [1] 0.5728534
sample(100, 1)
#> [1] 1

^{Created on 2022-01-06 by the reprex package (v2.0.1)}

4) Correlated Randoms

As we saw above, two random processes run at the same point after setting the same seed are expected to give the same result. However, even when you provide constraints on how similar the result can be (e.g. by changing the mean of rnorm() or even by providing different functions) it seems that the results are still perfectly correlated within their respective ranges.

# same function with different constraints
set.seed(1, kind = "Mersenne-Twister")
a <- runif(50, 0, 1)

set.seed(1, kind = "Mersenne-Twister")
b <- runif(50, 10, 100)

plot(a, b)

Sample Image

# different functions
set.seed(1, kind = "Mersenne-Twister")
d <- rnorm(50)

set.seed(1, kind = "Mersenne-Twister")
e <- rlnorm(50)

plot(d, e)

Sample Image

^{Created on 2022-01-06 by the reprex package (v2.0.1)}

Different samples despite same seed in R

Setting the seed allows R to generate the same series of random numbers. So when you call sample() for the second time, it's using the second number in that series.

If you want the same results from both calls to sample() you need to set the seed before each call:

    a = 1:10

    set.seed(1)
    sample(a, 1)

    set.seed(1)
    sample(a, 1)

See for example how the random number generator works

Different Set.seed sample function results with same versions of R in different OS

You have to set also the kind:

set.seed(1, "Mersenne-Twister", sample.kind="Rounding")
sample(100,3)
#[1] 27 37 57

set.seed(1, "Mersenne-Twister", sample.kind="Rejection")
sample(100,3)
#[1] 68 39  1

Is set.seed consistent over different versions of R (and Ubuntu)?

Cross-OS consistency: yes

If you installed R on two different operating systems without manually changing defaults or the RProfile, you should get the same results when using set.seed().

Consistency over versions of R: not necessarily

It used to be the case that set.seed() would give the same results across R versions, but that's no longer generally true thanks to a little-announced update in R 3.6.0. So you can get cross version consistency comparing results before R 3.6.0, but if you compare a post-3.6.0 use of set.seed() to a pre-3.6.0 use of set.seed(), you will get different results.

You can see that in the examples below:

R 3.2.0

> set.seed(1999)
> sample(LETTERS, 3)
[1] "T" "N" "L"

R 3.5.3

> set.seed(1999)
> sample(LETTERS, 3)
[1] "T" "N" "L"

R 3.6.0

set.seed(1999)
sample(LETTERS, 3)
[1] "D" "Z" "R"

The reason for the inconsistency is that in R 3.6.0, the default kind of under-the-hood random-number generator was changed. Now, in order to get the results from set.seed() to match, you have to first call the function RNGkind(sample.kind = "Rounding").

R 3.6.0

> RNGkind(sample.kind = "Rounding")
Warning message:
In RNGkind(sample.kind = "Rounding") : non-uniform 'Rounding' sampler used
> set.seed(1999)
> sample(Letters, 3)
[1] "T" "N" "L"

Same Seed, Different Os, Different Random Numbers in R