freealg.distributions.ChiralBlock.matrix

ChiralBlock.matrix(size, seed=None)

Generate matrix with the spectral density of the distribution.

Parameters:

sizeint

Total size \(N = n + m\) of the returned matrix.

seedint, default=None

Seed for random number generator.

Returns:

Anumpy.ndarray

Symmetric matrix of shape \(N \times N\).

Notes

Generate a \((n+m) x (n+m)\) matrix

\[H = \begin{bmatrix} \alpha \mathbf{I}_n & (1/\sqrt{m})) \mathbf{X} \ (1/\sqrt{m})) \mathbf{X}^{\intercal} & \beta \mathbf{I}_m \end{bmatrix}\]

where \(\mathbf{X}\) has i.i.d. \(N(0,1)\) entries and \(n/m\) approximates \(c\).

Examples