bounding.py 文件源码

def make_eigvals_positive(am, targetprod):
    """For the symmetric square matrix `am`, increase any zero eigenvalues
    such that the total product of eigenvalues is greater or equal to
    `targetprod`. Returns a (possibly) new, non-singular matrix."""

    w, v = linalg.eigh(am)  # use eigh since a is symmetric
    mask = w < 1.e-10
    if np.any(mask):
        nzprod = np.product(w[~mask])  # product of nonzero eigenvalues
        nzeros = mask.sum()  # number of zero eigenvalues
        new_val = max(1.e-10, (targetprod / nzprod) ** (1. / nzeros))
        w[mask] = new_val  # adjust zero eigvals
        am_new = np.dot(np.dot(v, np.diag(w)), linalg.inv(v))  # re-form cov
    else:
        am_new = am

    return am_new