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<p>Random vectors distributed uniformly in the direction space are widely used, and the computational cost of generating a vector in <i>n</i> dimensions increases only linearly with <i>n</i>. 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 <i>n</i> increases. We present an efficient algorithm to generate uniformly distributed random directions in <i>n</i>-dimensional cones, to aid sampling, searching and optimization tasks in high dimensions.</p>

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An \(\mathcal {O}\)(n) Algorithm for Generating Uniform Random Vectors in n-dimensional Cones

  • 期刊论文

  • 发表日期：

    2025年5月31日

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  • Arun I.,
  • Murugesan Venkatapathi

摘要

Random vectors distributed uniformly in the direction space are widely used, and the computational cost of generating a vector in n dimensions 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 uniformly distributed random directions in n-dimensional cones, to aid sampling, searching and optimization tasks in high dimensions.