# [R] random numbers with constraints

Abby Spurdle @purd|e@@ @end|ng |rom gm@||@com
Thu Jan 28 20:58:03 CET 2021

```I recognize the problems with global data.
And my code could certainly be improved.

However, I also note that the random numbers (ignoring
transformations), need to be constant, while computing the rate.
Otherwise, my algorithm wouldn't work well.

As it is, rounding operations can cause "jumps".
Generating random numbers for each value of rate, would make those jumps bigger.

I'm thinking a better solution would be to put the entire code inside
a single function.

Although, in saying all of that, the uniroot approach, is not the best here.
A more "robust" root finding algorithm (or solver) would be far
better, but I'm not sure what that would mean, exactly...

Given the possible relevance of generating constrained samples, a
discussion on what a robust solver means, could be interesting...
Although, I'll leave it to you to agree or disagree, and if in
agreement, to suggest the best forum for such a discussion.

On Fri, Jan 29, 2021 at 4:42 AM Martin Maechler
<maechler using stat.math.ethz.ch> wrote:
>
> >>>>> Abby Spurdle
> >>>>>     on Thu, 28 Jan 2021 08:48:06 +1300 writes:
>
>     > I note that there's a possibility of floating point errors.
>     > If all values have one digit after the decimal point, you could replace:
>     > qexp (p, rate) with round (qexp (p, rate), 1).
>
>     > However, sometimes uniroot will fail, due to problems with input.
>
> I also think the  constrained.sample() function should not
> depend on the global variable 'u',
> but rather depend on 'n'   and construct 'u' from  runif(n).
>
> Martin
>
>     > On Thu, Jan 28, 2021 at 5:02 AM Denis Francisci
>     > <denis.francisci using gmail.com> wrote:
>     >>
>     >> Wonderful!
>     >> This is exactly what I need!
>     >> Thank you very much!!
>     >>
>     >> Denis
>     >>
>     >>
>     >>
>     >> Il giorno mer 27 gen 2021 alle ore 10:58 Abby Spurdle <spurdle.a using gmail.com> ha scritto:
>     >>>
>     >>> u <- runif (410)
>     >>> u <- (u - min (u) ) / diff (range (u) )
>     >>>
>     >>> constrained.sample <- function (rate)
>     >>> {   plim <- pexp (c (9.6, 11.6), rate)
>     >>> p <- plim [1] + diff (plim) * u
>     >>> qexp (p, rate)
>     >>> }
>     >>>
>     >>> diff.sum <- function (rate)
>     >>> sum (constrained.sample (rate) ) - 4200
>     >>>
>     >>> rate <- uniroot (diff.sum, c (1, 2) )\$root
>     >>> q <- constrained.sample (rate)
>     >>>
>     >>> length (q)
>     >>> range (q)
>     >>> sum (q)
>     >>>
>     >>>
>     >>> On Wed, Jan 27, 2021 at 9:03 PM Denis Francisci
>     >>> <denis.francisci using gmail.com> wrote:
>     >>> >
>     >>> > Hi,
>     >>> > I would like to generate random numbers in R with some constraints:
>     >>> > - my vector of numbers must contain 410 values;
>     >>> > - min value must be 9.6 and max value must be 11.6;
>     >>> > - sum of vector's values must be 4200.
>     >>> > Is there a way to do this in R?
>     >>> > And is it possible to generate this series in such a way that it follows a
>     >>> > specific distribution form (for example exponential)?
>     >>> > Thank you in advance,
>     >>> >
>     >>> > D.

```