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Thread: Generating random vectors

  1. #1
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    Generating random vectors

    Hey folks,

    I need an algorithm to generate random vectors. Restriction on vectors $\displaystyle $x=(x_1,\ldots,x_n)$$ are as follows:

    a) $\displaystyle $x_1 + x_2 + \ldots + x_n$ = 0$ so they lie in an $\displaystyle n-1$ dimensional hyperplane going through zero.
    b) $\displaystyle $x_i \in [-1,1] \forall i$$
    c) The density is uniform, e.g. each vector satisfying conditions a) and b) is picked with equal probability.

    Example: $\displaystyle $(1,-1/2,-1/2)$$ and $\displaystyle $(0,0,0)$$ are both OK as long as they are generated with the same probability.

    Thanks
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  2. #2
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    Re: Generating random vectors

    Use whatever random number generator you like to get values for $\displaystyle x_1$, $\displaystyle x_2$, ..., $\displaystyle x_{n-1}$ between -1 and 1, then calculate $\displaystyle x_n= -x_1- x_2- x_3- \cdot\cdot\cdot - x_{n-1}$.
    Last edited by HallsofIvy; Aug 29th 2013 at 02:56 PM.
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  3. #3
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    Re: Generating random vectors

    Sorry, but your method does not neccessarily guarantee that $\displaystyle $x_n \in [-1,1]$$ is satisfied, for example if all your draws from $\displaystyle $1$$ to $\displaystyle $n-1$$ are equal to one and $\displaystyle $n\geq 3$$.
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  4. #4
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    Re: Generating random vectors

    @HallsofIvy any other ideas? I would be really thankful since I think this one is easy and it's just me who's stupid
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