[R] Generate random vectors (continuous number) with a fixed sum
Brian Smith
br|@n@m|th199312 @end|ng |rom gm@||@com
Thu Apr 24 19:33:03 CEST 2025
Hi Rui,
This code is able to generate absolutely correct random sample vector
based on the applicable constraints.
I have one question though.
If I understood the R code correctly then, the first element is
drawing random number from Uniform distribution unconditionally,
however drawing of sample point for the second element is conditional
to the first one. Therefore if we have large vector size instead of
current 2, I guess the feasible region for the last few elements will
be very small.
Will that be any problem? does there any algorithm exist where all
(n-1) elements would be drawn unconditionally assuming our vector has
n elements?
Thanks and regards,
On Wed, 23 Apr 2025 at 10:57, Rui Barradas <ruipbarradas using sapo.pt> wrote:
>
> 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.
>
>
> --
> Este e-mail foi analisado pelo software antivírus AVG para verificar a presença de vírus.
> www.avg.com
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