Generate random vectors (continuous number) with a fixed sum

Hello,

Inline.

?s 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 at 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 at sapo.pt> wrote:

?s 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 at sapo.pt> 
wrote:

Hello,

Inline.

?s 16:08 de 21/04/2025, Rui Barradas escreveu:

?s 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?

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

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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