[R] Generate random vectors (continuous number) with a fixed sum
Rui Barradas
ru|pb@rr@d@@ @end|ng |rom @@po@pt
Wed Apr 23 07:26:57 CEST 2025
Hello,
Here are your tests and the random numbers' histograms.
one_vec <- function(a, b, s) {
repeat{
repeat{
u <- runif(1, a[1], b[1])
if(s - u > 0) break
}
v <- s - u
if(a[2] < v && v < b[2]) break
}
c(u, v)
}
gen_mat <- function(m, a, b, s) {
replicate(m, one_vec(a, b, s))
}
a <- c(0.015, 0.005)
b <- c(0.070, 0.045)
s <- 0.05528650577311
m <- 10000L
set.seed(2025)
res <- gen_mat(m, a, b, s)
apply(res, 1, min) > a
#> [1] TRUE TRUE
apply(res, 1, max) < b
#> [1] TRUE TRUE
# plot histograms of one million 2d vectors
system.time(
res1mil <- gen_mat(1e6, a, b, s)
)
#> user system elapsed
#> 3.01 0.06 3.86
old_par <- par(mfrow = c(1, 2))
hist(res1mil[1L,])
hist(res1mil[2L,])
par(old_par)
Hope this helps,
Rui Barradas
Às 23:31 de 22/04/2025, Rui Barradas escreveu:
> Hello,
>
> Inline.
>
> Às 17:55 de 22/04/2025, Brian Smith escreveu:
>> i.e. we should have
>>
>> all elements of Reduce("+", res) should be equal to s = 0.05528650577311
>>
>> My assertion is that it is not happing here.
>
> You are right, that's not what is happening. The output is n vectors of
> 2 elements each. It's each of these vectors that add up to s.
> Appparently I misunderstood the problem.
>
> Maybe this is what you want?
> (There is no n argument, the matrix is always 2*m)
>
>
> one_vec <- function(a, b, s) {
> repeat{
> repeat{
> u <- runif(1, a[1], b[1])
> if(s - u > 0) break
> }
> v <- s - u
> if(a[2] < v && v < b[2]) break
> }
> c(u, v)
> }
> gen_mat <- function(m, a, b, s) {
> replicate(m, one_vec(a, b, s))
> }
>
> set.seed(2025)
> res <- gen_mat(10000, a, b, s)
> colSums(res)
>
>
> Hope this helps,
>
> Rui Barradas
>
>
>>
>>
>> On Tue, 22 Apr 2025 at 22:20, Brian Smith <briansmith199312 using gmail.com>
>> wrote:
>>>
>>> Hi Rui,
>>>
>>> Thanks for the explanation.
>>>
>>> But in this case, are we looking at the correct solution at all?
>>>
>>> My goal is to generate random vector where:
>>> 1) the first element is bounded by (a[1], b[1]) and second element is
>>> bounded by (a[2], b[2])
>>> 2) sum of the element is s
>>>
>>> According to the outcome,
>>> The first matrix values are bounded by c(a[1], b[1]) & second matrix
>>> values are bounded by c(a[2], b[2])
>>>
>>> But,
>>> regarding the sum, I think we should have sum (element-wise) sum
>>> should be equal to s = 0.05528650577311.
>>>
>>> How could we achieve that then?
>>>
>>> On Tue, 22 Apr 2025 at 22:03, Rui Barradas <ruipbarradas using sapo.pt> wrote:
>>>>
>>>> Às 12:39 de 22/04/2025, Brian Smith escreveu:
>>>>> Hi Rui,
>>>>>
>>>>> Many thanks for your time and insight.
>>>>>
>>>>> However, I am not sure if I could understand the code. Below is what I
>>>>> tried based on your code
>>>>>
>>>>> library(Surrogate)
>>>>> a <- c(0.015, 0.005)
>>>>> b <- c(0.070, 0.045)
>>>>> set.seed(2025)
>>>>> res <- mapply(\(a, b, s, n, m) RandVec(a, b, s, n, m),
>>>>> MoreArgs = list(s = 0.05528650577311, n = 2, m =
>>>>> 10000), a, b)
>>>>>
>>>>> res1 = res[[1]]
>>>>> res2 = res[[2]]
>>>>>
>>>>> apply(res1, 1, min) > a ## [1] TRUE TRUE
>>>>> apply(res2, 1, min) > a ## [1] FALSE TRUE
>>>>>
>>>>> I could not understand what basically 2 blocks of res signify? Which
>>>>> one I should take as final simulation of the vector? If I take the
>>>>> first block then the lower bound condition is fulfilled, but not with
>>>>> the second block. However with the both blocks, the total equals s is
>>>>> satisfying.
>>>>>
>>>>> I appreciate your further insight.
>>>>>
>>>>> Thanks and regards,
>>>>>
>>>>> On Mon, 21 Apr 2025 at 20:43, Rui Barradas <ruipbarradas using sapo.pt>
>>>>> wrote:
>>>>>>
>>>>>> Hello,
>>>>>>
>>>>>> Inline.
>>>>>>
>>>>>> Às 16:08 de 21/04/2025, Rui Barradas escreveu:
>>>>>>> Às 15:27 de 21/04/2025, Brian Smith escreveu:
>>>>>>>> Hi,
>>>>>>>>
>>>>>>>> There is a function called RandVec in the package Surrogate
>>>>>>>> which can
>>>>>>>> generate andom vectors (continuous number) with a fixed sum
>>>>>>>>
>>>>>>>> The help page of this function states that:
>>>>>>>>
>>>>>>>> a
>>>>>>>>
>>>>>>>> The function RandVec generates an n by m matrix x. Each of the m
>>>>>>>> columns contain n random values lying in the interval [a,b]. The
>>>>>>>> argument a specifies the lower limit of the interval. Default 0.
>>>>>>>>
>>>>>>>> b
>>>>>>>>
>>>>>>>> The argument b specifies the upper limit of the interval.
>>>>>>>> Default 1.
>>>>>>>>
>>>>>>>> However in my case, the lower and upper limits are not same. For
>>>>>>>> example, if I need to draw a pair of number x, y, such that x +
>>>>>>>> y = 1,
>>>>>>>> then the lower and upper limits are different.
>>>>>>>>
>>>>>>>> I tried with below code
>>>>>>>>
>>>>>>>> library(Surrogate)
>>>>>>>>
>>>>>>>> RandVec(a=c(0.1, 0.2), b=c(0.2, 0.8), s=1, n=2, m=5)$RandVecOutput
>>>>>>>>
>>>>>>>> This generates error with message
>>>>>>>>
>>>>>>>> Error in if (b - a == 0) { : the condition has length > 1
>>>>>>>>
>>>>>>>> Is there any way to generate the numbers with different lower and
>>>>>>>> upper limits?
>>>>>>>>
>>>>>>>> ______________________________________________
>>>>>>>> R-help using r-project.org mailing list -- To UNSUBSCRIBE and more, see
>>>>>>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>>>>>>> PLEASE do read the posting guide https://www.R-project.org/posting-
>>>>>>>> guide.html
>>>>>>>> and provide commented, minimal, self-contained, reproducible code.
>>>>>>> Hello,
>>>>>>>
>>>>>>> Use ?mapply to cycle through all values of a and b.
>>>>>>> Note that the output matrices are transposed, the random vectors
>>>>>>> are the
>>>>>>> rows.
>>>>>> Sorry, this is not true. The columns are the random vectors, as
>>>>>> documented. An example setting the RNG seed, for reproducibility.
>>>>>>
>>>>>>
>>>>>> library(Surrogate)
>>>>>>
>>>>>> a <- c(0.1, 0.2)
>>>>>> b <- c(0.2, 0.8)
>>>>>> set.seed(2025)
>>>>>> res <- mapply(\(a, b, s, n, m) RandVec(a, b, s, n, m),
>>>>>> MoreArgs = list(s = 1, n = 2, m = 5), a, b)
>>>>>>
>>>>>> res
>>>>>> #> $RandVecOutput
>>>>>> #> [,1] [,2] [,3] [,4] [,5]
>>>>>> #> [1,] 0.146079 0.1649319 0.1413759 0.257086 0.1715478
>>>>>> #> [2,] 0.253921 0.2350681 0.2586241 0.142914 0.2284522
>>>>>> #>
>>>>>> #> $RandVecOutput
>>>>>> #> [,1] [,2] [,3] [,4] [,5]
>>>>>> #> [1,] 0.5930918 0.2154583 0.6915523 0.7167089 0.3617918
>>>>>> #> [2,] 0.4069082 0.7845417 0.3084477 0.2832911 0.6382082
>>>>>>
>>>>>> lapply(res, colSums)
>>>>>> #> $RandVecOutput
>>>>>> #> [1] 0.4 0.4 0.4 0.4 0.4
>>>>>> #>
>>>>>> #> $RandVecOutput
>>>>>> #> [1] 1 1 1 1 1
>>>>>>
>>>>>>
>>>>>> Hope this helps,
>>>>>>
>>>>>> Rui Barradas
>>>>>>>
>>>>>>>
>>>>>>> library(Surrogate)
>>>>>>>
>>>>>>> a <- c(0.1, 0.2)
>>>>>>> b <- c(0.2, 0.8)
>>>>>>> mapply(\(a, b, s, n, m) RandVec(a, b, s, n, m),
>>>>>>> MoreArgs = list(s = 1, n = 2, m = 5), a, b)
>>>>>>> #> $RandVecOutput
>>>>>>> #> [,1] [,2] [,3] [,4] [,5]
>>>>>>> #> [1,] 0.2004363 0.1552328 0.2391742 0.1744857 0.1949236
>>>>>>> #> [2,] 0.1995637 0.2447672 0.1608258 0.2255143 0.2050764
>>>>>>> #>
>>>>>>> #> $RandVecOutput
>>>>>>> #> [,1] [,2] [,3] [,4] [,5]
>>>>>>> #> [1,] 0.2157416 0.4691191 0.5067447 0.7749258 0.7728955
>>>>>>> #> [2,] 0.7842584 0.5308809 0.4932553 0.2250742 0.2271045
>>>>>>>
>>>>>>>
>>>>>>> Hope this helps,
>>>>>>>
>>>>>>> Rui Barradas
>>>>>>>
>>>>>>>
>>>>>>
>>>>>>
>>>>>> --
>>>>>> Este e-mail foi analisado pelo software antivírus AVG para
>>>>>> verificar a presença de vírus.
>>>>>> www.avg.com
>>>> Hello,
>>>>
>>>> The two blocks of res are the two random matrices, one for each
>>>> combination of (a,b). mapply passes each of the values in its arguments
>>>> list (the ellipses in the help page) and computes the anonymous
>>>> function
>>>> with the pairs (a[1], b[1]), (a[2], b[2]).
>>>>
>>>> Since a and b are two elements vectors the output res is a two members
>>>> named list. Your error is to compare the result of apply(res2, 1, min)
>>>> to a, when you should compare to a[2]. See the code below.
>>>>
>>>>
>>>> library(Surrogate)
>>>> a <- c(0.015, 0.005)
>>>> b <- c(0.070, 0.045)
>>>> set.seed(2025)
>>>> res <- mapply(\(a, b, s, n, m) RandVec(a, b, s, n, m),
>>>> MoreArgs = list(s = 0.05528650577311, n = 2, m =
>>>> 10000),
>>>> a, b)
>>>>
>>>> res1 = res[[1]]
>>>> res2 = res[[2]]
>>>>
>>>> # first check that the sums are correct
>>>> # these sums should be s = 0.05528650577311, up to floating-point
>>>> accuracy
>>>> lapply(res, \(x) colSums(x[, 1:5]) |> print(digits = 14L))
>>>> #> [1] 0.05528650577311 0.05528650577311 0.05528650577311
>>>> 0.05528650577311
>>>> #> [5] 0.05528650577311
>>>> #> [1] 0.05528650577311 0.05528650577311 0.05528650577311
>>>> 0.05528650577311
>>>> #> [5] 0.05528650577311
>>>> #> $RandVecOutput
>>>> #> [1] 0.05528651 0.05528651 0.05528651 0.05528651 0.05528651
>>>> #>
>>>> #> $RandVecOutput
>>>> #> [1] 0.05528651 0.05528651 0.05528651 0.05528651 0.05528651
>>>>
>>>> # now check the min and max
>>>> apply(res1, 1, min) > a[1L] ## [1] TRUE TRUE
>>>> #> [1] TRUE TRUE
>>>> apply(res2, 1, min) > a[2L] ## [1] TRUE TRUE
>>>> #> [1] TRUE TRUE
>>>>
>>>> apply(res1, 1, max) < b[1L] ## [1] TRUE TRUE
>>>> #> [1] TRUE TRUE
>>>> apply(res2, 1, max) < b[2L] ## [1] TRUE TRUE
>>>> #> [1] TRUE TRUE
>>>>
>>>>
>>>>
>>>> Which one should you take as final simulation of the vector? Both.
>>>> The first matrix values are bounded by c(a[1], b[1]) with column sums
>>>> equal to s.
>>>> The second matrix values are bounded by c(a[2], b[2]) with column sums
>>>> also equal to s.
>>>>
>>>> Hoep this helps,
>>>>
>>>> Rui Barradas
>>>>
>
> ______________________________________________
> R-help using r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide https://www.R-project.org/posting-
> guide.html
> and provide commented, minimal, self-contained, reproducible code.
--
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