"""Calculate group velocity matrix."""
# Copyright (C) 2021 Atsushi Togo
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import numpy as np
from phonopy.phonon.thermal_properties import mode_cv
from phonopy.units import Kb


def mode_cv_matrix(temp, freqs, cutoff=1e-4):
    r"""Calculate mode heat capacity matrix, Cqjj'.

    C_{\mathbf{q}jj'} = K_B \frac{e^{x_{\mathbf{q}j} - x_{\mathbf{q}j'}} - 1}
    {x_{\mathbf{q}j} - x_{\mathbf{q}j'}} \left( \frac{
    x_{\mathbf{q}j} + x_{\mathbf{q}j'}}{2}
    \right)^2 n_{\mathbf{q}j}(n_{\mathbf{q}j'} + 1)

    Note
    ----
    Diagonal (j=j') terms reduce to normal mode heat capacity.

    Parameters
    ----------
    temp : float
        Temperature in K.
    freqs : ndarray
        Phonon frequencies at a q-point in eV.
    cutoff : float
        This is used to check the degeneracy.

    Returns
    -------
    ndarray
        Heat capacity matrix in eV/K.
        shape=(num_band, num_band), dtype='double', order='C'.

    """
    x = freqs / Kb / temp
    shape = (len(freqs), len(freqs))
    cvm = np.zeros(shape, dtype="double", order="C")
    for i, j in np.ndindex(shape):
        if abs(freqs[i] - freqs[j]) < cutoff:
            cvm[i, j] = mode_cv(temp, freqs[i])
            continue
        sub = x[i] - x[j]
        add = x[i] + x[j]
        n_inv = np.exp([x[i], x[j], sub]) - 1
        cvm[i, j] = Kb * n_inv[2] / sub * (add / 2) ** 2 / n_inv[0] * (1 / n_inv[1] + 1)
    return cvm
