Random sample of matrices in SO(p)
Random sample of matrices in SO(p).
rsop(n, p)
n |
The sample size, the number of matrices you want to generate. |
p |
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 mtsagris@uoc.gr and Giorgos Athineou <gioathineou@gmail.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.
x1 <- rsop(1, 3) x2 <- rsop(10, 3) x3 <- rsop(100, 10)
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