# [R] Latin Hypercube with condition sum = 1

Rainer M Krug r.m.krug at gmail.com
Sun Nov 23 18:59:29 CET 2008

```On Sun, Nov 23, 2008 at 7:43 PM, Ben Bolker <bolker at ufl.edu> wrote:
> Rainer M Krug <r.m.krug <at> gmail.com> writes:
>
>>
>> Hi
>>
>> I want to du a sensitivity analysis using Latin Hypercubes. But my
>> parameters have to fulfill two conditions:
>>
>> 1) ranging from 0 to 1
>> 2) have to sum up to 1
>>
>
>  Perhaps I'm missing something, but it seems that there's
> only one vector that satisfies these two conditions simultaneously,
> which is x={0,1} ... ???  (Actually, technically speaking
> you could have as many zeros as you wanted -- x = {0,0,0,1}
> would also work -- but I don't think that's going to help much.)
> If min(x)=0 and max(x)=1, then x must contain 0 and 1.  If x
> contains any other non-zero values, and no negative
> ones, then sum(x)>1 ...

You are absolutely right - but when you look at the example, I want
that the FINAL latin hypercube sets sum up to one, and the values
RANGING from 0 to 1, i.e. (0.5, 0.5) would also satisfy the condition.

>
>   You seem to have a problem either in your definitions,
> or in your communication of those definitions to us ...

Probably both - but to try again:

1) values ranging between 0 and 1 (0 <= x <= 1)
2) all elements in one set of the lLatin Hypercube should add to one.

Assuming two dimensions, (1,0) & (0,1) & (0.3, 0.7) , ... would all
satisfy the condition 1 and 2;

(0.8, 0.3) would satisfy 1, but not 2;
(-1, 2) would satisfy 2, but not 1

Hope this clarifies my question,

Rainer

>
>  cheers
>   Ben Bolker
>
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--
Rainer M. Krug, PhD (Conservation Ecology, SUN), MSc (Conservation
Biology, UCT), Dipl. Phys. (Germany)

Centre of Excellence for Invasion Biology
Faculty of Science
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```