How to use the forcebalance.nifty.statisticalInefficiency function in forcebalance

def mean_stderr(ts):
    """Return mean and standard deviation of a time series ts."""
    return np.mean(ts), \
      np.std(ts)*np.sqrt(statisticalInefficiency(ts, warn=False)/len(ts))

def mean_stderr(ts):
    """ Get mean and standard deviation of a time series. """
    return np.mean(ts), np.std(ts)*np.sqrt(statisticalInefficiency(ts, warn=False)/len(ts))

v_ = kwargs['v_']
        b0 = np.ones(L,dtype=float)
        dx = d_[:,0]
        dy = d_[:,1]
        dz = d_[:,2]
        D2  = bzavg(dx**2,b)-bzavg(dx,b)**2
        D2 += bzavg(dy**2,b)-bzavg(dy,b)**2
        D2 += bzavg(dz**2,b)-bzavg(dz,b)**2
        return prefactor*D2/bzavg(v_,b)/T
    Eps0 = calc_eps0(None,**{'d_':Dips, 'v_':V})
    Eps0boot = []
    for i in range(numboots):
        boot = np.random.randint(L,size=L)
        Eps0boot.append(calc_eps0(None,**{'d_':Dips[boot], 'v_':V[boot]}))
    Eps0boot = np.array(Eps0boot)
    Eps0_err = np.std(Eps0boot)*np.sqrt(np.mean([statisticalInefficiency(Dips[:,0]),statisticalInefficiency(Dips[:,1]),statisticalInefficiency(Dips[:,2])]))
 
    # Dielectric constant analytic derivative
    Dx = Dips[:,0]
    Dy = Dips[:,1]
    Dz = Dips[:,2]
    D2 = avg(Dx**2)+avg(Dy**2)+avg(Dz**2)-avg(Dx)**2-avg(Dy)**2-avg(Dz)**2
    GD2  = 2*(flat(np.dot(GDx,col(Dx)))/L - avg(Dx)*(np.mean(GDx,axis=1))) - Beta*(covde(Dx**2) - 2*avg(Dx)*covde(Dx))
    GD2 += 2*(flat(np.dot(GDy,col(Dy)))/L - avg(Dy)*(np.mean(GDy,axis=1))) - Beta*(covde(Dy**2) - 2*avg(Dy)*covde(Dy))
    GD2 += 2*(flat(np.dot(GDz,col(Dz)))/L - avg(Dz)*(np.mean(GDz,axis=1))) - Beta*(covde(Dz**2) - 2*avg(Dz)*covde(Dz))
    GEps0 = prefactor*(GD2/avg(V) - mBeta*covde(V)*D2/avg(V)**2)/T
    Sep = printcool("Dielectric constant:           % .4e +- %.4e\nAnalytic Derivative:" % (Eps0, Eps0_err))
    FF.print_map(vals=GEps0)
    if FDCheck:
        GEps0_fd = property_derivatives(Liquid, FF, mvals, h, pgrad, kT, calc_eps0, {'d_':Dips,'v_':V})
        Sep = printcool("Numerical Derivative:")
        FF.print_map(vals=GEps0_fd)

#----
    # Isothermal compressibility
    #----
    def calc_kappa(b=None, **kwargs):
        if b is None: b = np.ones(L,dtype=float)
        if 'v_' in kwargs:
            v_ = kwargs['v_']
        return bar_unit / kT * (bzavg(v_**2,b)-bzavg(v_,b)**2)/bzavg(v_,b)
    Kappa = calc_kappa(None,**{'v_':V})
    Kappaboot = []
    for i in range(numboots):
        boot = np.random.randint(L,size=L)
        Kappaboot.append(calc_kappa(None,**{'v_':V[boot]}))
    Kappaboot = np.array(Kappaboot)
    Kappa_err = np.std(Kappaboot) * np.sqrt(statisticalInefficiency(V))

    # Isothermal compressibility analytic derivative
    Sep = printcool("Isothermal compressibility:  % .4e +- %.4e bar^-1\nAnalytic Derivative:" % (Kappa, Kappa_err))
    GKappa1 = +1 * Beta**2 * avg(V**2) * deprod(V) / avg(V)**2
    GKappa2 = -1 * Beta**2 * avg(V) * deprod(V**2) / avg(V)**2
    GKappa3 = +1 * Beta**2 * covde(V)
    GKappa  = bar_unit*(GKappa1 + GKappa2 + GKappa3)
    FF.print_map(vals=GKappa)
    if FDCheck:
        GKappa_fd = property_derivatives(Lipid, FF, mvals, h, pgrad, kT, calc_kappa, {'v_':V})
        Sep = printcool("Numerical Derivative:")
        FF.print_map(vals=GKappa_fd)
        Sep = printcool("Difference (Absolute, Fractional):")
        absfrac = ["% .4e  % .4e" % (i-j, (i-j)/j) for i,j in zip(GKappa, GKappa_fd)]
        FF.print_map(vals=absfrac)

v_ = kwargs['v_']
        b0 = np.ones(L,dtype=float)
        dx = d_[:,0]
        dy = d_[:,1]
        dz = d_[:,2]
        D2  = bzavg(dx**2,b)-bzavg(dx,b)**2
        D2 += bzavg(dy**2,b)-bzavg(dy,b)**2
        D2 += bzavg(dz**2,b)-bzavg(dz,b)**2
        return prefactor*D2/bzavg(v_,b)/T
    Eps0 = calc_eps0(None,**{'d_':Dips, 'v_':V})
    Eps0boot = []
    for i in range(numboots):
        boot = np.random.randint(L,size=L)
        Eps0boot.append(calc_eps0(None,**{'d_':Dips[boot], 'v_':V[boot]}))
    Eps0boot = np.array(Eps0boot)
    Eps0_err = np.std(Eps0boot)*np.sqrt(np.mean([statisticalInefficiency(Dips[:,0]),statisticalInefficiency(Dips[:,1]),statisticalInefficiency(Dips[:,2])]))
 
    # Dielectric constant analytic derivative
    Dx = Dips[:,0]
    Dy = Dips[:,1]
    Dz = Dips[:,2]
    D2 = avg(Dx**2)+avg(Dy**2)+avg(Dz**2)-avg(Dx)**2-avg(Dy)**2-avg(Dz)**2
    GD2  = 2*(flat(np.dot(GDx,col(Dx)))/L - avg(Dx)*(np.mean(GDx,axis=1))) - Beta*(covde(Dx**2) - 2*avg(Dx)*covde(Dx))
    GD2 += 2*(flat(np.dot(GDy,col(Dy)))/L - avg(Dy)*(np.mean(GDy,axis=1))) - Beta*(covde(Dy**2) - 2*avg(Dy)*covde(Dy))
    GD2 += 2*(flat(np.dot(GDz,col(Dz)))/L - avg(Dz)*(np.mean(GDz,axis=1))) - Beta*(covde(Dz**2) - 2*avg(Dz)*covde(Dz))
    GEps0 = prefactor*(GD2/avg(V) - mBeta*covde(V)*D2/avg(V)**2)/T
    Sep = printcool("Dielectric constant:           % .4e +- %.4e\nAnalytic Derivative:" % (Eps0, Eps0_err))
    FF.print_map(vals=GEps0)
    if FDCheck:
        GEps0_fd = property_derivatives(Lipid, FF, mvals, h, pgrad, kT, calc_eps0, {'d_':Dips,'v_':V})
        Sep = printcool("Numerical Derivative:")
        FF.print_map(vals=GEps0_fd)

#----
    # Isothermal compressibility
    #----
    def calc_kappa(b=None, **kwargs):
        if b is None: b = np.ones(L,dtype=float)
        if 'v_' in kwargs:
            v_ = kwargs['v_']
        return bar_unit / kT * (bzavg(v_**2,b)-bzavg(v_,b)**2)/bzavg(v_,b)
    Kappa = calc_kappa(None,**{'v_':V})
    Kappaboot = []
    for i in range(numboots):
        boot = np.random.randint(L,size=L)
        Kappaboot.append(calc_kappa(None,**{'v_':V[boot]}))
    Kappaboot = np.array(Kappaboot)
    Kappa_err = np.std(Kappaboot) * np.sqrt(statisticalInefficiency(V))

    # Isothermal compressibility analytic derivative
    Sep = printcool("Isothermal compressibility:  % .4e +- %.4e bar^-1\nAnalytic Derivative:" % (Kappa, Kappa_err))
    GKappa1 = +1 * Beta**2 * avg(V**2) * deprod(V) / avg(V)**2
    GKappa2 = -1 * Beta**2 * avg(V) * deprod(V**2) / avg(V)**2
    GKappa3 = +1 * Beta**2 * covde(V)
    GKappa  = bar_unit*(GKappa1 + GKappa2 + GKappa3)
    FF.print_map(vals=GKappa)
    if FDCheck:
        GKappa_fd = property_derivatives(Liquid, FF, mvals, h, pgrad, kT, calc_kappa, {'v_':V})
        Sep = printcool("Numerical Derivative:")
        FF.print_map(vals=GKappa_fd)
        Sep = printcool("Difference (Absolute, Fractional):")
        absfrac = ["% .4e  % .4e" % (i-j, (i-j)/j) for i,j in zip(GKappa, GKappa_fd)]
        FF.print_map(vals=absfrac)

def mean_stderr(ts):
    """ Get mean and standard deviation of a time series. """
    if ts.ndim == 1:
        return np.mean(ts, axis = 0), np.std(ts, axis = 0)*np.sqrt(statisticalInefficiency(ts, warn=False)/len(ts))
    else:
        return np.mean(ts, axis = 0), np.std(ts, axis = 0)*np.sqrt(multiD_statisticalInefficiency(ts, warn=False)/len(ts))

def mean_stderr(ts):
    """ Get mean and standard deviation of a time series. """
    return np.mean(ts), np.std(ts)*np.sqrt(statisticalInefficiency(ts, warn=False)/len(ts))