Generate random correlation matrices, for some definition of random. Currently supports just one definition/method:
Lewandowski, Daniel, Dorota Kurowicka, and Harry Joe. "Generating random correlation matrices based on vines and extended onion method." Journal of multivariate analysis 100.9 (2009): 1989-2001. doi:10.1016/j.jmva.2009.04.008
This package has two functions, randcormatrix(d, η) and randcovmatrix(d, η, σ) . d is the dimension, and η is a parameter that controls the distribution of the off-diagonal terms. randcovmatrix is used to generate a covariance matrix from the output of randcormatrix, where the standard deviation of each component is controlled by σ.
To get a feel for how to set η, consider the following output from test/runtests.jl, which shows some example matrices and the average range of off-diagonals:
η => 2
1.00 0.07 0.59 0.78
0.07 1.00 0.28 -0.03
0.59 0.28 1.00 0.69
0.78 -0.03 0.69 1.00
mean(ranges) => 0.9609607012737842
median(ranges) => 0.9522641114303307
η => 8
1.00 -0.24 0.15 0.18
-0.24 1.00 -0.10 -0.06
0.15 -0.10 1.00 0.02
0.18 -0.06 0.02 1.00
mean(ranges) => 0.5846747844778034
median(ranges) => 0.5787807331445632
η => 32
1.00 -0.06 0.08 -0.11
-0.06 1.00 -0.05 0.12
0.08 -0.05 1.00 -0.14
-0.11 0.12 -0.14 1.00
mean(ranges) => 0.3094525766085337
median(ranges) => 0.3050648782864559
η => 128
1.00 0.05 -0.00 -0.02
0.05 1.00 -0.05 0.07
-0.00 -0.05 1.00 0.03
-0.02 0.07 0.03 1.00
mean(ranges) => 0.15721653854980638
median(ranges) => 0.15120529987720227
Pull requests welcome for additional methods of generating random correlation matrices that are described in the literature.