calculate_igso3 函数旨在对 IGSO(3) 分布的概率密度函数 (PDF)、累积分布函数 (CDF)、以及相关统计量进行数值近似计算，特别用于预计算以加速后续操作（例如采样、反向扩散等）。

calculate_igso3函数源代码：

def calculate_igso3(*, num_sigma, num_omega, min_sigma, max_sigma):
    """calculate_igso3 pre-computes numerical approximations to the IGSO3 cdfs
    and score norms and expected squared score norms.

    Args:
        num_sigma: number of different sigmas for which to compute igso3
            quantities.
        num_omega: number of point in the discretization in the angle of
            rotation.
        min_sigma, max_sigma: the upper and lower ranges for the angle of
            rotation on which to consider the IGSO3 distribution.  This cannot
            be too low or it will create numerical instability.
    """
    # Discretize omegas for calculating CDFs. Skip omega=0.
    discrete_omega = np.linspace(0, np.pi, num_omega+1)[1:]

    # Exponential noise schedule.  This choice is closely tied to the
    # scalings used when simulating the reverse time SDE. For each step n,
    # discrete_sigma[n] = min_eps^(1-n/num_eps) * max_eps^(n/num_eps)
    discrete_sigma = 10 ** np.linspace(np.log10(min_sigma), np.log10(max_sigma), num_sigma + 1)[1:]

    # Compute the pdf and cdf values for the marginal distribution of the angle
    # of rotation (which is needed for sampling)
    pdf_vals = np.asarray(
        [igso3_density_angle(discrete_omega, sigma**2) for sigma in discrete_sigma])
    cdf_vals = np.asarray(
        [pdf.cumsum() / num_omega * np.pi for pdf in pdf_vals])

    # Compute the norms of the scores.  This are used to scale the rotation axis when
    # computing the score as a vector.
    score_norm = np.asarray(
        [d_logf_d_omega(discrete_omega, sigma**2)