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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def power_curve_density_correction(wind_speed, power_curve_wind_speeds, power_curve_values, density):
 r""" Calculates the turbine power output using a density corrected power curve. This function is carried out when the parameter `density_correction` of an instance of the :class:`~.modelchain.ModelChain` class is True. Parameters wind_speed : pandas.Series or numpy.array Wind speed at hub height in m/s. power_curve_wind_speeds : pandas.Series or numpy.array Wind speeds in m/s for which the power curve values are provided in `power_curve_values`. power_curve_values : pandas.Series or numpy.array Power curve values corresponding to wind speeds in `power_curve_wind_speeds`. density : pandas.Series or numpy.array Density of air at hub height in kg/m³. Returns ------- pandas.Series or numpy.array Electrical power output of the wind turbine in W. Data type depends on type of `wind_speed`. Notes ----- The following equation is used for the site specific power curve wind speeds [1]_, [2]_, [3]_: .. math:: v_{site}=v_{std}\cdot\left(\frac{\rho_0} {\rho_{site}}\right)^{p(v)} with: .. math:: p=\begin{cases} \frac{1}{3} & v_{std} \leq 7.5\text{ m/s}\\ \frac{1}{15}\cdot v_{std}-\frac{1}{6} & 7.5 \text{ m/s}<v_{std}<12.5\text{ m/s}\\ \frac{2}{3} & \geq 12.5 \text{ m/s} \end{cases}, v: wind speed [m/s], :math:`\rho`: density [kg/m³] :math:`v_{std}` is the standard wind speed in the power curve (:math:`v_{std}`, :math:`P_{std}`), :math:`v_{site}` is the density corrected wind speed for the power curve (:math:`v_{site}`, :math:`P_{std}`), :math:`\rho_0` is the ambient density (1.225 kg/m³) and :math:`\rho_{site}` the density at site conditions (and hub height). It is assumed that the power output for wind speeds above the maximum and below the minimum wind speed given in the power curve is zero. References .. [1] Svenningsen, L.: "Power Curve Air Density Correction And Other Power Curve Options in WindPRO". 1st edition, Aalborg, EMD International A/S , 2010, p. 4 .. [2] Svenningsen, L.: "Proposal of an Improved Power Curve Correction". EMD International A/S , 2010 .. [3] Biank, M.: "Methodology, Implementation and Validation of a Variable Scale Simulation Model for Windpower based on the Georeferenced Installation Register of Germany". Master's Thesis at Reiner Lemoine Institute, 2014, p. 13 """

    if density is None:
        raise TypeError("`density` is None. For the calculation with a " +
                        "density corrected power curve density at hub " +
                        "height is needed.")
    power_output = [(np.interp(
        wind_speed[i], power_curve_wind_speeds * (1.225 / density[i]) ** (
            np.interp(power_curve_wind_speeds, [7.5, 12.5], [1/3, 2/3])),
        power_curve_values, left=0, right=0)) for i in range(len(wind_speed))]

    # Power_output as pd.Series if wind_speed is pd.Series (else: np.array)
    if isinstance(wind_speed, pd.Series):
        power_output = pd.Series(data=power_output, index=wind_speed.index,
                                 name='feedin_power_plant')
    else:
        power_output = np.array(power_output)
    return power_output