SWHeart.py

import numpy as np

def SWHeart(u, v, alpha: float):
    """
        Calculate the heart of the Wilson function.

        Calculates the matrix H (Heart of the Wilson function) for maturities specified by vectors u and v.
        The formula is taken from the EIOPA technical specifications paragraph 132.

        Arguments:
            u: n_1 x 1 vector of maturities. Example: u = [1, 3]
            v: n_2 x 1 vector of maturities. Example: v = [1, 2, 3, 5]
            alpha: 1 x 1 floating number representing the convergence speed parameter alpha. Example: alpha = 0.05

        Returns:
            n_1 x n_2 matrix representing the Heart of the Wilson function for selected maturities and parameter alpha.
        H is calculated as described in paragraph 132 of the EIOPA documentation.

        For more information, see:
        https://www.eiopa.europa.eu/sites/default/files/risk_free_interest_rate/12092019-technical_documentation.pdf
        """
       
    u_Mat = np.tile(u, [v.size, 1]).transpose()
    v_Mat = np.tile(v, [u.size, 1])
    
    # Return the heart of the Wilson function from paragraph 132
    return 0.5 * (alpha * (u_Mat + v_Mat) + np.exp(-alpha * (u_Mat + v_Mat)) - alpha * np.absolute(u_Mat-v_Mat) - np.exp(-alpha * np.absolute(u_Mat-v_Mat)))