An 𝒪(n) algorithm for generating uniform random vectors in n-dimensional cones
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Unbiased random vectors i.e. distributed uniformly in n-dimensional space, are widely applied and the computational cost of generating a vector increases only linearly with n. On the other hand, generating uniformly distributed random vectors in its subspaces typically involves the inefficiency of rejecting vectors falling outside, or re-weighting a non-uniformly distributed set of samples. Both approaches become severely ineffective as n increases. We present an efficient algorithm to generate uniform random directions in n-dimensional cones, to aid searching and sampling tasks in high dimensions.
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