pipes.py 文件源码

def _F_mk(Q_p, P, n_p, J, r_b, r_p, z, pikg, sigma):
    """
    Complex matrix F_mk from Claesson and Hellstrom (2011), EQ. 34
    """
    F = np.zeros((n_p, J), dtype=np.cfloat)
    for m in range(n_p):
        for k in range(J):
            fmk = 0. + 0.j
            for n in range(n_p):
                # First term
                if m != n:
                    fmk += Q_p[n]*pikg/(k+1)*(r_p[m]/(z[n] - z[m]))**(k+1)
                # Second term
                fmk += sigma*Q_p[n]*pikg/(k+1)*(r_p[m]*np.conj(z[n])/(
                        r_b**2 - z[m]*np.conj(z[n])))**(k+1)
                for j in range(J):
                    # Third term
                    if m != n:
                        fmk += P[n,j]*binom(j+k+1, j) \
                                *r_p[n]**(j+1)*(-r_p[m])**(k+1) \
                                /(z[m] - z[n])**(j+k+2)
                    # Fourth term
                    j_pend = np.min((k, j)) + 1
                    for jp in range(j_pend):
                        fmk += sigma*np.conj(P[n,j])*binom(j+1, jp) \
                                *binom(j+k-jp+1, j)*r_p[n]**(j+1) \
                                *r_p[m]**(k+1)*z[m]**(j+1-jp) \
                                *np.conj(z[n])**(k+1-jp) \
                                /(r_b**2 - z[m]*np.conj(z[n]))**(k+j+2-jp)
            F[m,k] = fmk

    return F