qics.cones.RenyiEntr¶

class qics.cones.RenyiEntr(n, alpha, iscomplex=False)[source]¶

A class representing the epigraph of the (homogenized) Renyi entropy, i.e., for some \(\alpha\in[0, 1)\),

\[\mathcal{RE}_{n} = \text{cl}\{ (t,u,X,Y) \in \mathbb{R} \times \mathbb{R}_{++} \times \mathbb{H}^n_{++} \times \mathbb{H}^n_{++} : t \geq u D_\alpha(u^{-1}X \| u^{-1}Y) \},\]

where

\[D_\alpha(X\|Y)=\frac{1}{\alpha-1}\log(\text{tr}[X^\alpha Y^{1-\alpha}]),\]

is the \(\alpha\)-Renyi entropy.

Parameters:

nint: Dimension of the matrices \(X\) and \(Y\).
alphafloat: The exponent \(\alpha\) used to parameterize the Renyi entropy.
iscomplexbool: Whether the matrices \(X\) and \(Y\) are defined over \(\mathbb{H}^n\) (True), or restricted to \(\mathbb{S}^n\) (False). The default is False.