iwish_ps function

Inverse of a Coefficient Matrix $\tilde{\mathcal{H}}_k$

This function computes the inverse of a coefficient matrix $\tilde{\mathcal{H}}_k$

that allows us to compute the expected value of a power-sum symmetric function of $W^{-1}$, where $W \sim W_m^{\beta}(n,\Sigma)$.

iwish_ps(k, alpha = 2)

Arguments

• k: The order of the $\tilde{\mathcal{H}}_k$ matrix (a positive integer)

• alpha: The type of Wishart distribution ($\alpha = 2/\beta$):

  • 1/2: Quaternion Wishart
  • 1: Complex Wishart
  • 2: Real Wishart (default)

Returns

Inverse of a coefficient matrix $\tilde{\mathcal{H}}_k$ that allows us to compute the expected value of a power-sum symmetric function of $W^{-1}$, where $W \sim W_m^{\beta}(n,\Sigma)$. The matrix is represented as a 3-dimensional array where each slice along the third dimension represents a coefficient matrix of the polynomial in descending powers of $\tilde{n}$.

Examples

# Example 1:
iwish_ps(3) # For real Wishart distribution with k = 3

# Example 2:
iwish_ps(4, 1) # For complex Wishart distribution with k = 4

# Example 3:
iwish_ps(2, 1/2) # For quaternion Wishart distribution with k = 2