ellips_semiax takes as input an invertible matrix A
and returns the lengths of the semiaxes of the ellipsoidal cone given by
the image of the Lorentz cone under A.
ellips_semiax(A)
| A | matrix |
|---|
The output of ellips_semiax(A), A in Gl_d, is a positive
vector a in R^(d-1) such that the cone A*L, where
L={x in R^d | sqrt(2)*x_d >= ||x||},
is isometric to the cone {x in R^d | x_d >= sum_(j=1)^(d-1) x_j^2/a_j^2}.
See this vignette for further info.
Package: conivol
A <- matrix(c(2,3,5,7,11,13,17,19,23),3,3) ellips_semiax(A)#> [1] 0.10984660 0.03065619