Directional (version 6.8)

Random sample of matrices in SO(p): Random sample of matrices in SO(p)

Description

Random sample of matrices in SO(p).

Usage

rsop(n, p)

Value

If n = 1 one matrix is returned. If n is greater than 1, an array with n matrices inside.

Arguments

n

The sample size, the number of matrices you want to generate.

p

The dimensionality of the matrices.

Author

Michail Tsagris.

R implementation and documentation: Michail Tsagris and Giorgos Athineou <[e-mail]>.

Details

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.

References

Amaral G.J.A., Dryden I.L. and Wood A.T.A. (2007). Pivotal Bootstrap Methods for k-Sample Problems in Directional Statistics and Shape Analysis. Journal of the American Statistical Association, 102(478): 695--707.

See Also

rotation, Arotation, rot.matrix

Examples

x1 <- rsop(1, 3)
x2 <- rsop(10, 3)
x3 <- rsop(100, 10)