def expand_Q_from(Q, P):
'''
Q : k * 3
P : k+1 * 3
return
Q : k+1 * 3
'''
nr_points = Q.shape[0]
lengths = q_config[(nr_points - 2) % 3]["side_lengths"]
rad = q_config[(nr_points - 2) % 3]["rad"]
# center of circle of possible next points
center_para = lengths[1] * np.cos(rad) / lengths[0]
center_of_next_Q = Q[-1] * (1 - center_para) + Q[-2] * center_para
proj_para = np.dot(P[-1] - Q[-1],
Q[-1] - Q[-2]) / (lengths[0] * lengths[0])
proj = Q[-1] + proj_para * (Q[-1] - Q[-2])
new_q_point = center_of_next_Q + (
P[-1] - proj) * lengths[1] * np.sin(rad) / np.linalg.norm(P[-1] - proj)
Q = np.vstack([Q, new_q_point])
Q = kabsched_Q(Q, P)
return Q
def start_intensively_optimal_construct_Q_from(P, internal=5, rounds=5):
'''
construct a init Q for further refinement
'''
lengths = q_config[0]["side_lengths"]
p0 = P[0]
p1 = P[1]
q1 = p0 + (p1 - p0) / np.linalg.norm(p1 - p0) * lengths[0]
Q = np.array([P[0], q1])
Q = kabsched_Q(Q, P[0:2])
for i in range(2, P.shape[0]):
print 'now: ', i
tmp_p = P[0:i + 1]
Q = expand_Q_from(Q, tmp_p)
for _ in range(5):
Q = expand_Q_from(Q[0:-1], tmp_p)
if i < 500:
Q = optimize(Q, tmp_p, 5)
elif i % internal == 0:
Q = optimize(Q, tmp_p, rounds)
print rmsd(Q, P)
print "lower bound: ", lower_bound(Q, P)
return Q
def randomly_expand_Q_from(Q, P):
nr_points = Q.shape[0]
lengths = q_config[(nr_points - 2) % 3]["side_lengths"]
rad = q_config[(nr_points - 2) % 3]["rad"]
center_para = lengths[1] * np.cos(rad) / lengths[0]
center_of_next_Q = Q[-1] * (1 - center_para) + Q[-2] * center_para
u1 = (Q[-1] - Q[-2])
u1 = u1 / np.linalg.norm(u1)
u2 = np.array([1, 0, 0])
if np.abs(u1[1]) < np.abs(u1[0]):
u2 = np.array([0, 1, 0])
u2 = np.cross(u1, u2)
# u2 = np.array([u1[1] * u2[2] - u1[2] * u2[1], u1[2] * u2[0] - u1[0] * u2[2], u1[0] * u2[1] - u1[1] * u2[0]])
u2 = u2 / np.linalg.norm(u2)
# u3 = np.array([u1[1] * u2[2] - u1[2] * u2[1], u1[2] * u2[0] - u1[0] * u2[2], u1[0] * u2[1] - u1[1] * u2[0]])
u3 = np.cross(u1, u2)
U = np.array([u1, u2, u3])
next_rad = random.random() * np.pi * 2
radius = lengths[1] * np.sin(rad)
next_Q_point_in_U = np.array(
[0, radius * np.sin(next_rad), radius * np.cos(next_rad)])
next_Q_point = np.dot(next_Q_point_in_U, U) + center_of_next_Q
Q = np.vstack([Q, next_Q_point])
Q = kabsched_Q(Q, P)
return Q
def optimize_structure_by_pos(Q_origin, P_origin, k_pos):
assert k_pos > 1
assert k_pos < P_origin.shape[0] - 1
nr_P_row = P_origin.shape[0]
P = np.copy(P_origin)
Q = np.copy(Q_origin)
k = k_pos
v1 = (Q[k] - Q[k - 1])
u1 = v1 / np.linalg.norm(v1)
u2 = np.array([1, 0, 0])
if np.abs(u1[1]) < np.abs(u1[0]):
u2 = np.array([0, 1, 0])
u2 = np.cross(u1, u2)
# u2 = np.array([u1[1] * u2[2] - u1[2] * u2[1], u1[2] * u2[0] - u1[0] * u2[2], u1[0] * u2[1] - u1[1] * u2[0]])
u2 = u2 / np.linalg.norm(u2)
# u3 = np.array([u1[1] * u2[2] - u1[2] * u2[1], u1[2] * u2[0] - u1[0] * u2[2], u1[0] * u2[1] - u1[1] * u2[0]])
u3 = np.cross(u1, u2)
U = np.array([u1, u2, u3])
Qk = Q[k + 1:nr_P_row]
Pk = P[k + 1:nr_P_row]
q_point_k_wrap = np.copy(np.array([Q[k]]))
Qk = Qk - np.repeat(q_point_k_wrap, [Qk.shape[0]], axis=0)
Pk = Pk - np.repeat(q_point_k_wrap, [Qk.shape[0]], axis=0)
Qk_U = np.dot(Qk, U.transpose())
Pk_U = np.dot(Pk, U.transpose())
alpha = np.dot(Qk_U[:, 1], Pk_U[:, 2]) - np.dot(Qk_U[:, 2], Pk_U[:, 1])
beta = np.dot(Qk_U[:, 1], Pk_U[:, 1]) + np.dot(Qk_U[:, 2], Pk_U[:, 2])
cos_theta = beta / np.sqrt(alpha**2 + beta**2)
sin_theta = alpha / np.sqrt(alpha**2 + beta**2)
pre_A = np.array([[1, 0, 0], [0, cos_theta, sin_theta],
[0, -sin_theta, cos_theta]])
A = np.dot(np.dot(U.transpose(), pre_A), U)
Qk = np.dot(Qk, A)
Qk = Qk + np.repeat(q_point_k_wrap, [Qk.shape[0]], axis=0)
Q[k + 1:nr_P_row] = Qk
Q = kabsched_Q(Q, P)
return Q
def randomly_construct_Q_from(P):
'''
randomly generate initial state to test if the original algrithm can get the optimal result
'''
lengths = q_config[0]["side_lengths"]
p0 = P[0]
p1 = P[1]
q1 = p0 + (p1 - p0) / np.linalg.norm(p1 - p0) * lengths[0]
Q = np.array([P[0], q1])
Q = kabsched_Q(Q, P[0:2])
for i in range(2, P.shape[0]):
tmp_p = P[0:i + 1]
Q = randomly_expand_Q_from(Q, tmp_p)
print rmsd(Q, P)
return Q
def construct_Q_from(P):
'''
construct a init Q for further refinement
'''
lengths = q_config[0]["side_lengths"]
p0 = P[0]
p1 = P[1]
q1 = p0 + (p1 - p0) / np.linalg.norm(p1 - p0) * lengths[0]
Q = np.array([P[0], q1])
Q = kabsched_Q(Q, P[0:2])
for i in range(2, P.shape[0]):
tmp_p = P[0:i + 1]
Q = expand_Q_from(Q, tmp_p)
for _ in range(5):
Q = expand_Q_from(Q[0:-1], tmp_p)
print rmsd(Q, P)
print "lower bound: ", lower_bound(Q, P)
return Q