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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 BARzero(w_F, w_R, DeltaF):
 """A function that when zeroed is equivalent to the solution of the Bennett acceptance ratio. from http://journals.aps.org/prl/pdf/10.1103/PhysRevLett.91.140601 D_F = M + w_F - Delta F D_R = M + w_R - Delta F we want: \sum_N_F (1+exp(D_F))^-1 = \sum N_R N_R <(1+exp(-D_R))^-1> ln \sum N_F (1+exp(D_F))^-1>_F = \ln \sum N_R exp((1+exp(-D_R))^(-1)>_R ln \sum N_F (1+exp(D_F))^-1>_F - \ln \sum N_R exp((1+exp(-D_R))^(-1)>_R = 0 Parameters w_F : np.ndarray w_F[t] is the forward work value from snapshot t. w_R : np.ndarray w_R[t] is the reverse work value from snapshot t. DeltaF : float Our current guess Returns ------- fzero : float a variable that is zeroed when DeltaF satisfies BAR. Examples -------- Compute free energy difference between two specified samples of work values. """


    np.seterr(over='raise')  # raise exceptions to overflows
    w_F = np.array(w_F, np.float64)
    w_R = np.array(w_R, np.float64)
    DeltaF = float(DeltaF)

    # Recommended stable implementation of BAR.

    # Determine number of forward and reverse work values provided.
    T_F = float(w_F.size)  # number of forward work values
    T_R = float(w_R.size)  # number of reverse work values

    # Compute log ratio of forward and reverse counts.
    M = np.log(T_F / T_R)

    # Compute log numerator. We have to watch out for overflows.  We
    # do this by making sure that 1+exp(x) doesn't overflow, choosing
    # to always exponentiate a negative number.

    # log f(W) = - log [1 + exp((M + W - DeltaF))]
    #          = - log ( exp[+maxarg] [exp[-maxarg] + exp[(M + W - DeltaF) - maxarg]] )
    #          = - maxarg - log(exp[-maxarg] + exp[(M + W - DeltaF) - maxarg])
    # where maxarg = max((M + W - DeltaF), 0)

    exp_arg_F = (M + w_F - DeltaF)
    # use boolean logic to zero out the ones that are less than 0, but not if greater than zero.
    max_arg_F = np.choose(np.less(0.0, exp_arg_F), (0.0, exp_arg_F))
    try:
        log_f_F = - max_arg_F - np.log(np.exp(-max_arg_F) + np.exp(exp_arg_F - max_arg_F))
    except:
        # give up; if there's overflow, return zero
        print("The input data results in overflow in BAR")
        return np.nan
    log_numer = logsumexp(log_f_F)

    # Compute log_denominator.
    # log f(R) = - log [1 + exp(-(M + W - DeltaF))]
    #          = - log ( exp[+maxarg] [exp[-maxarg] + exp[(M + W - DeltaF) - maxarg]] )
    #          = - maxarg - log[exp[-maxarg] + (T_F/T_R) exp[(M + W - DeltaF) - maxarg]]
    # where maxarg = max( -(M + W - DeltaF), 0)

    exp_arg_R = -(M - w_R - DeltaF)
    # use boolean logic to zero out the ones that are less than 0, but not if greater than zero.
    max_arg_R = np.choose(np.less(0.0, exp_arg_R), (0.0, exp_arg_R))
    try:
        log_f_R = - max_arg_R - np.log(np.exp(-max_arg_R) + np.exp(exp_arg_R - max_arg_R))
    except:
        print("The input data results in overflow in BAR")
        return np.nan
    log_denom = logsumexp(log_f_R)

    # This function must be zeroed to find a root
    fzero = log_numer - log_denom

    np.seterr(over='warn')  # return options to standard settings so we don't disturb other functionality.
    return fzero