[R] Generate random vectors (continuous number) with a fixed sum
Rui Barradas
ru|pb@rr@d@@ @end|ng |rom @@po@pt
Tue Apr 22 18:32:55 CEST 2025
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
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