switching.py 文件源码

def find_closest(t, v, t0, v0):
    """ Find the closest point on the curve f = a + b/x
    to the given point (t,v)
    """
    a = v0
    b = v0*t0
    # Solve for intersection points
    eqn_coefs = [1/b, -t/b, 0, v-a, -b]
    tis = np.roots(eqn_coefs)
    tis = tis[abs(tis.imag/tis.real)<0.01].real # We care only real solutions
    tis = tis[tis>0] # and positive ones
    # Choose the shortest among solutions
    ds = abs(tis-t)*np.sqrt(1 + np.power(tis,4)/(b*b)) # Distance from solutions to given point (t,v)
    idx = np.argmin(ds)
    ti = tis[idx]
    vi = a + b/ti
    return ti, vi