Function compute_next_removal

ot/regpath.py:357–403

r""" This function computes the next gamma value if a variable is removed at the next iteration of the regularization path. We look for the largest value of the regularization parameter such that an element of the current solution vanishes .. math:: \max_{j \in A} \frac{\ph

(phi, delta, current_gamma)

def compute_next_removal(phi, delta, current_gamma):
    r""" This function computes the next gamma value if a variable
    is removed at the next iteration of the regularization path.

    We look for the largest value of the regularization parameter such that
    an element of the current solution vanishes

    .. math::
        \max_{j \in A} \frac{\phi_j}{\delta_j}

    where :

    - A is the current active set
    - :math:`\phi_j` is the :math:`j` th element of the intercept of the \
      current solution
    - :math:`\delta_j` is the :math:`j` th element of the slope of the \
      current solution


    Parameters
    ----------
    phi : ndarray, shape (size(A), )
        Intercept of the solution at the current iteration
    delta : ndarray, shape (size(A), )
        Slope of the solution at the current iteration
    current_gamma : float
        Value of the regularization parameter at the beginning of the \
        current iteration

    Returns
    -------
    next_removal_gamma : float
        Gamma value if a variable is removed at the next iteration
    next_removal_index : int
        Index of the variable to be removed at the next iteration


    .. _references-regpath:
    References
    ----------
    .. [41] Chapel, L., Flamary, R., Wu, H., Févotte, C., and Gasso, G. (2021).
        Unbalanced optimal transport through non-negative penalized
        linear regression. NeurIPS.
    """
    r_candidate = phi / (delta - 1e-16)
    r_candidate[r_candidate >= (1 - 1e-8) * current_gamma] = 0
    return np.max(r_candidate), np.argmax(r_candidate)


def complement_schur(M_current, b, d, id_pop):