berny.py 文件源码

def quadratic_step(g, H, w, trust, log=no_log):
    ev = np.linalg.eigvalsh((H+H.T)/2)
    rfo = np.vstack((np.hstack((H, g[:, None])),
                     np.hstack((g, 0))[None, :]))
    D, V = np.linalg.eigh((rfo+rfo.T)/2)
    dq = V[:-1, 0]/V[-1, 0]
    l = D[0]
    if norm(dq) <= trust:
        log('Pure RFO step was performed:')
        on_sphere = False
    else:
        def steplength(l):
            return norm(np.linalg.solve(l*eye(H.shape[0])-H, g))-trust
        l = Math.findroot(steplength, ev[0])  # minimization on sphere
        dq = np.linalg.solve(l*eye(H.shape[0])-H, g)
        on_sphere = False
        log('Minimization on sphere was performed:')
    dE = dot(g, dq)+0.5*dq.dot(H).dot(dq)  # predicted energy change
    log('* Trust radius: {:.2}'.format(trust))
    log('* Number of negative eigenvalues: {}'.format((ev < 0).sum()))
    log('* Lowest eigenvalue: {:.3}'.format(ev[0]))
    log('* lambda: {:.3}'.format(l))
    log('Quadratic step: RMS: {:.3}, max: {:.3}'.format(Math.rms(dq), max(abs(dq))))
    log('* Predicted energy change: {:.3}'.format(dE))
    return dq, dE, on_sphere