GaussianJacobi produces wrong eigenvalues

[jiahao]

As reported by @dlfivefifty,

eigvalrand(GaussianJacobi(2,0,0),100)

produces eigenvalues shown in the plot. They should be symmetrically distributed around 1/2, so the heavy clustering should be present both at 0 and 1. Instead, the clustering only happens near 1.

[amerberg]

Right now, eigvalrand is returning the singular values of a bidiagonal matrix. My (limited) understanding of the paper of Edelman and Sutton is that the square of these values should follow the law of the Jacobi ensemble. Squaring the values returned by eigvalrand(GaussianJacobi(2,0,0),100) does give me something very nearly symmetric. Could that be the problem?