# Path: blond/utils/bmath.py
# def use_mpi():
# def mpiMode():
# def use_fftw():
# def use_precision(_precision='double'):
# def update_active_dict(new_dict):


from builtins import range, object
from scipy.integrate import cumtrapz
from ..utils import bmath as bm
import numpy as np
import ctypes
import warnings
                self.omega_rf[:, index], self.phi_rf[:, index],
                self.charge, self.n_rf, self.acceleration_kick[index])

    def drift(self, beam_dt, beam_dE, index):
        """Function updating the particle arrival time to the RF station
        (drift). If only the zeroth order slippage factor is given, 'simple'
        and 'exact' solvers are available. The 'simple' solver is somewhat
        faster. Otherwise, the solver is automatically 'exact' and calculates
        the frequency slippage up to second order. The corresponding equations
        are (nb: the n indices correspond to the turn number):

        .. math::
            \\Delta t^{n+1} = \\Delta t^{n} + \\frac{L}{C} T_0^{n+1} \\left[ \\left(1+\\sum_{i=0}^{2}{\\alpha_i\\left(\\delta^{n+1}\\right)^{i+1}}\\right)   \\frac{1+\\left(\\Delta E/E_s\\right)^{n+1}}{1+\\delta^{n+1}}    - 1\\right] \quad \\text{(exact)}

        .. math::
            \\Delta t^{n+1} = \\Delta t^{n} + \\frac{L}{C} T_0^{n+1} \\left(\\frac{1}{1 - \\eta(\\delta^{n+1})\\delta^{n+1}} - 1\\right) \quad \\text{(legacy)}

        .. math::
            \\Delta t^{n+1} = \\Delta t^{n} + \\frac{L}{C} T_0^{n+1}\\eta_0\\delta^{n+1} \quad \\text{(simple)}

        The relative momentum needs to be calculated from the relative energy
        and is obtained as follow:

        .. math::
            \\delta = \\sqrt{1+\\beta_s^{-2}\\left[\\left(\\frac{\\Delta E}{E_s}\\right)^2 + 2\\frac{\\Delta E}{E_s}\\right]} - 1 \quad \\text{(exact)}

        .. math::
            \\delta = \\frac{\\Delta E}{\\beta_s^2 E_s} \quad \\text{(simple, legacy)}

        """

# Path: blond/utils/bmath.py
# def use_mpi():
# def mpiMode():
# def use_fftw():
# def use_precision(_precision='double'):
# def update_active_dict(new_dict):


# Path: blond/trackers/tracker.py
from builtins import range, object
from scipy.integrate import cumtrapz
from ..utils import bmath as bm
import numpy as np
import ctypes
import warnings

                self.omega_rf[:, index], self.phi_rf[:, index],
                self.charge, self.n_rf, self.acceleration_kick[index])

    def drift(self, beam_dt, beam_dE, index):
        """Function updating the particle arrival time to the RF station
        (drift). If only the zeroth order slippage factor is given, 'simple'
        and 'exact' solvers are available. The 'simple' solver is somewhat
        faster. Otherwise, the solver is automatically 'exact' and calculates
        the frequency slippage up to second order. The corresponding equations
        are (nb: the n indices correspond to the turn number):

        .. math::
            \\Delta t^{n+1} = \\Delta t^{n} + \\frac{L}{C} T_0^{n+1} \\left[ \\left(1+\\sum_{i=0}^{2}{\\alpha_i\\left(\\delta^{n+1}\\right)^{i+1}}\\right)   \\frac{1+\\left(\\Delta E/E_s\\right)^{n+1}}{1+\\delta^{n+1}}    - 1\\right] \quad \\text{(exact)}

        .. math::
            \\Delta t^{n+1} = \\Delta t^{n} + \\frac{L}{C} T_0^{n+1} \\left(\\frac{1}{1 - \\eta(\\delta^{n+1})\\delta^{n+1}} - 1\\right) \quad \\text{(legacy)}

        .. math::
            \\Delta t^{n+1} = \\Delta t^{n} + \\frac{L}{C} T_0^{n+1}\\eta_0\\delta^{n+1} \quad \\text{(simple)}

        The relative momentum needs to be calculated from the relative energy
        and is obtained as follow:

        .. math::
            \\delta = \\sqrt{1+\\beta_s^{-2}\\left[\\left(\\frac{\\Delta E}{E_s}\\right)^2 + 2\\frac{\\Delta E}{E_s}\\right]} - 1 \quad \\text{(exact)}

        .. math::
            \\delta = \\frac{\\Delta E}{\\beta_s^2 E_s} \quad \\text{(simple, legacy)}

        """

        bm.drift(beam_dt, beam_dE, self.solver, self.t_rev[index],