Random sample of matrices in SO(p)
Random sample of matrices in SO(p).
The sample size, the number of matrices you want to generate.
The dimensionality of the matrices.
The idea is very simple. Start with a unit vector pointing at the north pole (1,0,...,0). Then generate random numbers from a standard normal and scale them so that they have a unit length. To put it differently, a sample of n values from the uniform distribution on the sphere is generated. Then calculate the rotation matrix required to go from the north pole to each of a generated vector.
If n = 1 one matrix is returned. If n is greater than 1, an array with n matrices inside.
Michail Tsagris R implementation and documentation: Michail Tsagris <firstname.lastname@example.org> and Giorgos Athineou <email@example.com>
G. J. A. Amaral, I. L. Dryden & Andrew T. A. Wood (2007). Pivotal Bootstrap Methods for k-Sample Problems in Directional Statistics and Shape Analysis. Journal of the American Statistical Association, 102(478): 695-707.
rotation, Arotation, rot.matrix
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