spkf

def mk_spk(self, i, eta=1e-2):
    """
    It's possible to plot the approximate spectral functions by broadening
    the delta functions of A_{ij}(k, w) and summing them

    Args:
        i (int) : the entry of the diagonal spectral function A_{ii}
        eta (float) : artificial broadening of the delta function
    """

    """
    # A delta function is the limit eta->0+ of a lorentzian
    def lorentzian(w, a, eta=eta):
        return 1 / np.pi * eta / ((w - a)**2 + eta**2)
    """

    # fetch problem
    prb = self.SPC.PRB

    # avoid computing _constants_ repeatedly
    LZ0 = 1.0 / np.pi * eta
    ETA_2 = eta**2

    # initialize `spkf`
    spkf = np.zeros(len(self.SPC.ax_W))

    # for all momenta
    for k_vec in prb.k_grid:

        # diagonalize
        hamiltonian = prb.get_hamiltonian(k_vec)
        eigvals, eigvecs = LA.eigh(hamiltonian)

        # benefit from Numpy's SIMD vectorization
        # assumed `ax_W` is a vector like `eigvals`
        lorentzians = LZ0 / ( (self.SPC.ax_W - eigvals)**2 + ETA_2 )

        # update `spkf` by adding E^\dagger . L . E
        spkf += np.linalg.multi_dot(eigvects.conjugate(), lorentzians, eigvecs).real

    #END for


    #? WHY PLOT HERE?
    # plot
    fig, ax = plt.subplots()
    ax.plot(self.SPC.ax_W, spkf)
    fig.tight_layout()