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stl_multi.py
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stl_multi.py
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import torch
import numpy as np
# import signal_tl as stl
import sys
import rtamt
import time
from joblib import Parallel, delayed
trajs10 = torch.tensor([[-1.5650, 0.1290, 0.6401],
[-1.6037, 0.1343, 0.6401],
[-1.6423, 0.1390, 0.6401],
[-1.6807, 0.1431, 0.6401],
[-1.7189, 0.1467, 0.6401],
[-1.7569, 0.1497, 0.6401],
[-1.7947, 0.1521, 0.6401],
[-1.8323, 0.1539, 0.6401],
[-1.8697, 0.1552, 0.6401],
[-1.9069, 0.1559, 0.6401],
[-1.9440, 0.1561, 0.6401],
[-1.9808, 0.1556, 0.6401],
[-2.0175, 0.1546, 0.6401],
[-2.0539, 0.1531, 0.6401],
[-2.0902, 0.1509, 0.6401],
[-2.1262, 0.1482, 0.6401],
[-2.1621, 0.1449, 0.6401],
[-2.1978, 0.1411, 0.6401],
[-2.2333, 0.1366, 0.6401],
[-2.2686, 0.1316, 0.6401],
[-2.2686e+00, 1.3163e-01, 6.4008e-01],
[-2.3327e+00, 1.2163e-01, 6.4275e-01],
[-2.3964e+00, 1.0875e-01, 6.4542e-01],
[-2.4593e+00, 9.3034e-02, 6.4809e-01],
[-2.5216e+00, 7.4509e-02, 6.5077e-01],
[-2.5829e+00, 5.3213e-02, 6.5344e-01],
[-2.6432e+00, 2.9188e-02, 6.5611e-01],
[-2.7024e+00, 2.4827e-03, 6.5878e-01],
[-2.7603e+00, -2.6850e-02, 6.6145e-01],
[-2.8168e+00, -5.8750e-02, 6.6412e-01],
[-2.8719e+00, -9.3154e-02, 6.6680e-01],
[-2.9254e+00, -1.2999e-01, 6.6947e-01],
[-2.9771e+00, -1.6919e-01, 6.7214e-01],
[-3.0271e+00, -2.1067e-01, 6.7481e-01],
[-3.0751e+00, -2.5435e-01, 6.7748e-01],
[-3.1211e+00, -3.0014e-01, 6.8015e-01],
[-3.1650e+00, -3.4794e-01, 6.8283e-01],
[-3.2068e+00, -3.9767e-01, 6.8550e-01],
[-3.2462e+00, -4.4922e-01, 6.8817e-01],
[-3.2834e+00, -5.0248e-01, 6.9084e-01],
[-3.2834, -0.5025, 0.6908],
[-3.3077, -0.5383, 0.6908],
[-3.3296, -0.5757, 0.6908],
[-3.3490, -0.6144, 0.6908],
[-3.3657, -0.6544, 0.6908],
[-3.3796, -0.6954, 0.6908],
[-3.3908, -0.7372, 0.6908],
[-3.3992, -0.7797, 0.6908],
[-3.4046, -0.8227, 0.6908],
[-3.4072, -0.8659, 0.6908],
[-3.4069, -0.9092, 0.6908],
[-3.4036, -0.9524, 0.6908],
[-3.3975, -0.9953, 0.6908],
[-3.3885, -1.0377, 0.6908],
[-3.3767, -1.0793, 0.6908],
[-3.3621, -1.1201, 0.6908],
[-3.3448, -1.1598, 0.6908],
[-3.3248, -1.1983, 0.6908],
[-3.3024, -1.2353, 0.6908],
[-3.2774, -1.2707, 0.6908],
[-3.2774, -1.2707, 0.6908],
[-3.2595, -1.2978, 0.6922],
[-3.2413, -1.3247, 0.6935],
[-3.2227, -1.3513, 0.6948],
[-3.2039, -1.3777, 0.6962],
[-3.1847, -1.4039, 0.6975],
[-3.1652, -1.4299, 0.6989],
[-3.1454, -1.4556, 0.7002],
[-3.1253, -1.4811, 0.7015],
[-3.1050, -1.5064, 0.7029],
[-3.0843, -1.5314, 0.7042],
[-3.0633, -1.5562, 0.7055],
[-3.0421, -1.5808, 0.7069],
[-3.0206, -1.6051, 0.7082],
[-2.9987, -1.6291, 0.7095],
[-2.9766, -1.6529, 0.7109],
[-2.9543, -1.6764, 0.7122],
[-2.9316, -1.6997, 0.7136],
[-2.9087, -1.7227, 0.7149],
[-2.8855, -1.7454, 0.7162],
[-2.8855, -1.7454, 0.7162],
[-2.8624, -1.7680, 0.7189],
[-2.8390, -1.7904, 0.7216],
[-2.8153, -1.8126, 0.7242],
[-2.7914, -1.8344, 0.7269],
[-2.7673, -1.8559, 0.7296],
[-2.7429, -1.8772, 0.7323],
[-2.7182, -1.8982, 0.7349],
[-2.6933, -1.9189, 0.7376],
[-2.6681, -1.9393, 0.7403],
[-2.6428, -1.9594, 0.7429],
[-2.6171, -1.9792, 0.7456],
[-2.5913, -1.9987, 0.7483],
[-2.5652, -2.0179, 0.7510],
[-2.5389, -2.0368, 0.7536],
[-2.5124, -2.0554, 0.7563],
[-2.4857, -2.0736, 0.7590],
[-2.4587, -2.0916, 0.7616],
[-2.4316, -2.1092, 0.7643],
[-2.4042, -2.1266, 0.7670],
[-2.4042, -2.1266, 0.7670],
[-2.3768, -2.1439, 0.7683],
[-2.3491, -2.1610, 0.7697],
[-2.3213, -2.1777, 0.7710],
[-2.2933, -2.1941, 0.7723],
[-2.2651, -2.2101, 0.7737],
[-2.2367, -2.2259, 0.7750],
[-2.2081, -2.2413, 0.7763],
[-2.1793, -2.2563, 0.7777],
[-2.1504, -2.2710, 0.7790],
[-2.1213, -2.2854, 0.7803],
[-2.0920, -2.2995, 0.7817],
[-2.0626, -2.3132, 0.7830],
[-2.0330, -2.3265, 0.7843],
[-2.0033, -2.3395, 0.7857],
[-1.9734, -2.3522, 0.7870],
[-1.9433, -2.3645, 0.7884],
[-1.9132, -2.3765, 0.7897],
[-1.8828, -2.3881, 0.7910],
[-1.8524, -2.3993, 0.7924],
[-1.8524, -2.3993, 0.7924],
[-1.8219, -2.4106, 0.7937],
[-1.7914, -2.4215, 0.7950],
[-1.7606, -2.4320, 0.7964],
[-1.7298, -2.4422, 0.7977],
[-1.6989, -2.4520, 0.7990],
[-1.6678, -2.4614, 0.8004],
[-1.6366, -2.4705, 0.8017],
[-1.6054, -2.4793, 0.8031],
[-1.5740, -2.4876, 0.8044],
[-1.5425, -2.4956, 0.8057],
[-1.5110, -2.5032, 0.8071],
[-1.4793, -2.5105, 0.8084],
[-1.4476, -2.5173, 0.8097],
[-1.4158, -2.5239, 0.8111],
[-1.3839, -2.5300, 0.8124],
[-1.3520, -2.5358, 0.8137],
[-1.3200, -2.5411, 0.8151],
[-1.2879, -2.5462, 0.8164],
[-1.2558, -2.5508, 0.8177],
[-1.2558, -2.5508, 0.8177],
[-1.2236, -2.5554, 0.8191],
[-1.1915, -2.5597, 0.8204],
[-1.1592, -2.5636, 0.8218],
[-1.1270, -2.5671, 0.8231],
[-1.0946, -2.5702, 0.8244],
[-1.0623, -2.5730, 0.8258],
[-1.0299, -2.5754, 0.8271],
[-0.9975, -2.5774, 0.8284],
[-0.9651, -2.5790, 0.8298],
[-0.9327, -2.5802, 0.8311],
[-0.9002, -2.5811, 0.8324],
[-0.8677, -2.5816, 0.8338],
[-0.8353, -2.5817, 0.8351],
[-0.8028, -2.5814, 0.8364],
[-0.7704, -2.5807, 0.8378],
[-0.7379, -2.5797, 0.8391],
[-0.7055, -2.5783, 0.8405],
[-0.6731, -2.5765, 0.8418],
[-0.6407, -2.5743, 0.8431],
[-0.6407, -2.5743, 0.8431],
[-0.6083, -2.5721, 0.8445],
[-0.5759, -2.5696, 0.8458],
[-0.5436, -2.5666, 0.8471],
[-0.5113, -2.5633, 0.8485],
[-0.4790, -2.5596, 0.8498],
[-0.4468, -2.5556, 0.8511],
[-0.4147, -2.5511, 0.8525],
[-0.3826, -2.5463, 0.8538],
[-0.3505, -2.5411, 0.8551],
[-0.3185, -2.5355, 0.8565],
[-0.2866, -2.5296, 0.8578],
[-0.2548, -2.5233, 0.8592],
[-0.2230, -2.5166, 0.8605],
[-0.1913, -2.5096, 0.8618],
[-0.1597, -2.5021, 0.8632],
[-0.1282, -2.4943, 0.8645],
[-0.0968, -2.4862, 0.8658],
[-0.0655, -2.4776, 0.8672],
[-0.0342, -2.4688, 0.8685],
[-0.0342, -2.4688, 0.8685],
[ 0.0071, -2.4557, 0.8685],
[ 0.0474, -2.4400, 0.8685],
[ 0.0866, -2.4215, 0.8685],
[ 0.1245, -2.4005, 0.8685],
[ 0.1608, -2.3770, 0.8685],
[ 0.1955, -2.3511, 0.8685],
[ 0.2284, -2.3229, 0.8685],
[ 0.2593, -2.2925, 0.8685],
[ 0.2881, -2.2602, 0.8685],
[ 0.3147, -2.2260, 0.8685],
[ 0.3389, -2.1901, 0.8685],
[ 0.3607, -2.1526, 0.8685],
[ 0.3799, -2.1138, 0.8685],
[ 0.3964, -2.0737, 0.8685],
[ 0.4102, -2.0327, 0.8685],
[ 0.4212, -1.9908, 0.8685],
[ 0.5294, -1.9483, 0.8685],
[ 1.5347, -1.9053, 0.8685],
[ 3.5371, -1.8620, 0.8685]])
phi_1_x = [0.5, 2.50]
phi_1_y = [-2.5, -1.0]
phi_1_z = [0.5, 0.7]
phi_2_x = [2.5, 4.0]
phi_2_y = [-2.5, -1.0]
phi_2_z = [0.3, 0.5]
phi_3_x = [1.5, 4.0]# region 3 isolated for testing purposes
phi_3_y = [-0.5, 0.2]
phi_3_z = [0.3, 0.5]
psi_x = [0.0, 1.45]
psi_y = [-0.01, 0.01]
psi_z = [0.1, 0.6]
def monitor_R2(ways): # rtamt specs for runway R2
# data
# print("Hi", trajs0.shape)
trajs_x = ways[:,0].tolist()
trajs_y = ways[:,1].tolist()
trajs_z = ways[:,2].tolist()
r2 = np.array([[1.48,0.0,0.38]])
diff_trajs = np.diff(ways, axis = 0)
# print (diff_trajs,diff_trajs[:,1])
diff_angle = np.arctan2(diff_trajs[:,1],diff_trajs[:,0])
# print (diff_angle*180/np.pi)
# print (diff_angle.shape)
diff_angle_full = np.concatenate((diff_angle,diff_angle[-1:]))
# print (diff_angle_full*180/np.pi)
diff_angle_full = np.where(diff_angle_full < -1.57, diff_angle_full + 2 * np.pi, diff_angle_full)
# diff_angle_full = diff_angle_full.tolist()
phi_1u = 0.349066 - diff_angle_full
phi_1l = diff_angle_full + 0.349066
phi_2u = 2.00713 - diff_angle_full
phi_2l = diff_angle_full - 1.13446
phi_3u = 3.40339 - diff_angle_full
phi_3l = diff_angle_full - 2.87979
phi_1u = phi_1u.tolist()
phi_1l = phi_1l.tolist()
phi_2u = phi_2u.tolist()
phi_2l = phi_2l.tolist()
phi_3u = phi_3u.tolist()
phi_3l = phi_3l.tolist()
diff_trajs = np.concatenate((diff_trajs,diff_trajs[-1:]))
# print (diff_angle_full*180/np.pi)
# print('phi_3l',phi_3l)
vels_x = diff_trajs[:,0].tolist()
vels_y = diff_trajs[:,1].tolist()
vels_z = diff_trajs[:,2].tolist()
# print(len(vels_x))
# diff_from_runway = ways - r2
# print(diff_from_runway)
# print("ways",ways.shape,r2.shape)
if torch.is_tensor(ways):
ways = ways.numpy()
# sqrA = torch.sum(torch.pow(ways, 2), 1, keepdim=True).expand(ways.shape[0], r2.shape[0])
# sqrB = torch.sum(torch.pow(r2, 2), 1, keepdim=True).expand(r2.shape[0], ways.shape[0]).t()
sqrA = np.broadcast_to(np.sum(np.power(ways, 2), 1).reshape(ways.shape[0], 1), (ways.shape[0], r2.shape[0]))
sqrB = np.broadcast_to(np.sum(np.power(r2, 2), 1).reshape(r2.shape[0], 1), (r2.shape[0], ways.shape[0])).transpose()
#
L2_dist_runway = np.sqrt(sqrA - 2*np.matmul(ways, r2.transpose()) + sqrB)
#
# print(L2_dist_runway.shape)
L2_dist_runway = L2_dist_runway.squeeze().tolist()
# print(L2_dist_runway)
# print("trajs_x",trajs_x)
xl_r1 = np.array(trajs_x) - 0.5
xu_r1 = 2.5 - np.array(trajs_x)
yl_r1 = np.array(trajs_y) + 2.5
yu_r1 = -1.0 - np.array(trajs_y)
zl_r1 = np.array(trajs_z) - 0.5
zu_r1 = 0.7 - np.array(trajs_z)
xl_r2 = np.array(trajs_x) - 2.5
xu_r2 = 4.0 - np.array(trajs_x)
yl_r2 = np.array(trajs_y) + 2.5
yu_r2 = -0.08 - np.array(trajs_y)
zl_r2 = np.array(trajs_z) - 0.3
zu_r2 = 0.5 - np.array(trajs_z)
# print("sub",xl_r1)
# user_details = [{'name' : x, 'rank' : trajs_x.index(x)} for x in trajs_x]
xl_r1 = list(enumerate(xl_r1))
xu_r1 = list(enumerate(xu_r1))
yl_r1 = list(enumerate(yl_r1))
yu_r1 = list(enumerate(yu_r1))
# zl_r1 = list(enumerate(zl_r1))
# zu_r1 = list(enumerate(zu_r1))
xl_r2 = list(enumerate(xl_r2))
xu_r2 = list(enumerate(xu_r2))
yl_r2 = list(enumerate(yl_r2))
yu_r2 = list(enumerate(yu_r2))
trajs_x = list(enumerate(trajs_x))
trajs_y = list(enumerate(trajs_y))
trajs_z = list(enumerate(trajs_z))
phi_1u = list(enumerate(phi_1u))
phi_1l = list(enumerate(phi_1l))
phi_2u = list(enumerate(phi_2u))
phi_2l = list(enumerate(phi_2l))
phi_3u = list(enumerate(phi_3u))
phi_3l = list(enumerate(phi_3l))
# print('phi_3l',phi_3l)
vel_x = list(enumerate(vels_x))
vel_y = list(enumerate(vels_y))
vel_z = list(enumerate(vels_z))
# print('vel_z',vel_z)
L2_runway = list(enumerate(L2_dist_runway))
# print('trajs_z',trajs_z)
# # stl
spec = rtamt.STLDenseTimeSpecification(semantics=rtamt.Semantics.STANDARD)
# spec = rtamt.STLSpecification(language=rtamt.Language.PYTHON)
spec.name = 'runway r2'
spec.declare_var('iq', 'float')
spec.declare_var('up', 'float')
spec.declare_var('x', 'float')
spec.declare_var('xl_r1', 'float')
spec.declare_var('xu_r1', 'float')
spec.declare_var('yl_r1', 'float')
spec.declare_var('yu_r1', 'float')
spec.declare_var('zl_r1', 'float')
spec.declare_var('zu_r1', 'float')
spec.declare_var('xl_r2', 'float')
spec.declare_var('xu_r2', 'float')
spec.declare_var('yl_r2', 'float')
spec.declare_var('yu_r2', 'float')
spec.declare_var('y', 'float')
spec.declare_var('yl', 'float')
spec.declare_var('yu', 'float')
spec.declare_var('z', 'float')
spec.declare_var('zl', 'float')
spec.declare_var('zu', 'float')
spec.declare_var('final', 'float')
spec.declare_var('out', 'float')
spec.declare_var('phi_1u_head', 'float')
spec.declare_var('phi_1l_head', 'float')
spec.declare_var('phi_2u_head', 'float')
spec.declare_var('phi_2l_head', 'float')
spec.declare_var('phi_3u_head', 'float')
spec.declare_var('phi_3l_head', 'float')
# spec.set_var_io_type('xl', 'input')
# spec.set_var_io_type('xu', 'input')
spec.set_var_io_type('yl', 'input')
spec.set_var_io_type('yu', 'input')
spec.set_var_io_type('zl', 'input')
spec.set_var_io_type('zu', 'input')
spec.declare_var('vel_x', 'float')
spec.declare_var('vel_y', 'float')
spec.declare_var('vel_z', 'float')
spec.declare_const('threshold_1', 'float', '3')
spec.declare_const('threshold_2', 'float', '5')
# spec.declare_var('x', 'float')
# spec.declare_var('iq', 'float')
# spec.declare_var('up', 'float')
# spec.declare_var('xl', 'float')
# spec.declare_var('xu', 'float')
# spec.declare_var('y', 'float')
# spec.declare_var('yl', 'float')
# spec.declare_var('yu', 'float')
# spec.declare_var('z', 'float')
# spec.declare_var('zl', 'float')
# spec.declare_var('zu', 'float')
# spec.declare_var('out', 'float')
# spec.declare_var('out', 'float')
# spec.set_var_io_type('xl', 'input')
# spec.set_var_io_type('xu', 'input')
# spec.set_var_io_type('yl', 'input')
# spec.set_var_io_type('yu', 'input')
# spec.set_var_io_type('zl', 'input')
# spec.set_var_io_type('zu', 'input')
# spec.declare_var('phi_1', 'float')
# spec.declare_var('phi_2', 'float')
# spec.declare_var('phi_3', 'float')
# # spec.set_var_io_type('out', 'output')
# # spec.spec = '(eventually[0:0] ((always[0:0] (xl > 0.5)) and (always[0:0] (xu < 3.0))) )'
# spec.add_sub_spec = ('phi_1 = (eventually[0:0] (always[0:0]( (xl > 0.5) and (xu < 2.5) ) and ( (yl > -2.5) and (yu < -1.0) ) and ( (zl > 0.5) and (zu < 0.7) ) ) )')
# spec.add_sub_spec = ('phi_2 = (eventually[0:0] (always[0:0]( (xl > 2.5) and (xu < 4.0) ) and ( (yl > -2.5) and (yu < -0.08) ) and ( (zl > 0.3) and (zu < 0.5) ) ) )')
# spec.add_sub_spec = ('phi_3 = (eventually[0:0] (always[0:0]( (xl > 1.5) and (xu < 4.0) ) and ( (yl > -0.08) and (yu < 0.08) ) and ( (zl > 0.3) and (zu < 0.5) ) ) )')
# spec.spec = '( ((phi_1) until[0:0] (phi_2)) until[0:0] (phi_3) )'
# spec.spec = 'eventually(( ( (xl > 0.5) and (xu < 2.5) ) and ( (yl > -2.5) and (yu < -1.0) ) ) and eventually( ( (xl > 2.5) and (xu < 4.0) ) and ( (yl > -2.5) and (yu < -0.08) ) ) )'
# spec.spec ='eventually( (( (x >0.5) and (x < 2.5)) and ( (y > -2.5) and (y < -1.0) )) and eventually( ((x > 2.5) and (x < 4.0) ) and ((y > -2.5) and (y < -0.08)) ))'
# spec.spec =eventually( (( (x >0.5) and (x < 2.5)) and ( (y > -2.5) and (y < -1.0) )) and eventually( ((x > 2.5) and (x < 4.0) ) and ((y > -2.5) and (y < -0.08)) ))
# spec.spec ='eventually( (( (x >0.5) and (x < 2.5)) and ( (y > -2.5) and (y < -1.0) )) and eventually( ((x > 2.5) and (x < 4.0) ) and ((y > -2.5) and (y < -1.0)) and eventually( ((x > 1.5) and (x < 4.0) ) and ((y > -0.5) and (y < 0.2)) ) ))'
spec.spec ='eventually( (( (x >0.5) and (x < 2.5)) and ( (y > -2.5) and (y < -1.0) ) and ( (z > 0.6) and (z < 0.8) ) and ( (vel_x > 0) and (vel_y < 0.5) ) and ( (phi_1l_head) and (phi_1u_head) )) and eventually( ((x > 2.5) and (x < 4.0) ) and ((y > -2.5) and (y < -1.0)) and ( (z > 0.4) and (z< 0.6) ) and ( (vel_x < 0.5) and (vel_y >0) ) and ( (phi_2l_head) and (phi_2u_head) ) and eventually((final < 0.2) and ((y > -0.5) and (y < 0.2)) and ( (vel_x < 0) and (vel_y < 0.5) ) and ( (phi_3l_head) and (phi_3u_head) ) ) ))'
# spec.spec ='eventually( (( (x >0.5) and (x < 2.5)) and ( (y > -2.5) and (y < -1.0) ) and ( (z > 0.5) and (z < 0.7) )) and eventually( ((x > 2.5) and (x < 4.0) ) and ((y > -2.5) and (y < -0.08)) and ((z > 0.3) and (z < 0.5)) ))'
# spec.spec = '(eventually(always((( (x >0.5) and (x < 2.5)) and ( (y > -2.5) and (y < -1.0) ) and ( (z > 0.5) and (z < 0.7) ))))) until (eventually(always(( ((x > 2.5) and (x < 4.0) ) and ((y > -2.5) and (y < -0.08)) and ((z > 0.3) and (z < 0.5)) ))))'
# spec.spec = '(eventually(always((( (x >0.5) and (x < 2.5)) and ( (y > -2.5) and (y < -1.0) ) )))) until (eventually(always(( ((x > 2.5) and (x < 4.0) ) and ((y > -2.5) and (y < -0.08)) ))))'
# spec.add_sub_spec('iq = x>0.5')
# spec.add_sub_spec('up = x<2.5')
# spec.spec = 'out = ((iq) until (up) )'
# spec.spec = 'eventually(( ( (x > 0.5) and (x < 2.5) ) and ( (y > -2.5) and (y < -1.0) ) and ( (z > 0.5) and (z < 0.7) ) ) and eventually( ( (x > 2.5) and (x < 4.0) ) and ( (y > -2.5) and (y < -0.08) ) and ( (z > 0.3) and (z < 0.5) ) ) )'
try:
spec.parse()
# spec.pastify()
except rtamt.STLParseException as err:
print('STL Parse Exception: {}'.format(err))
sys.exit()
# out = spec.evaluate(['x', trajs_x],['y', trajs_y])
out = spec.evaluate(['xl_r1', xl_r1],['xu_r1', xu_r1],['yl_r1', yl_r1],['yu_r1', yu_r1],['zl_r1', zl_r1],['zu_r1', zu_r1],['xl_r2', xl_r2],['xu_r2', xu_r2],['yl_r2', yl_r2],['yu_r2', yu_r2],['xl', trajs_x],['xu',trajs_x],['yl', trajs_y],['yu',trajs_y],['zl', trajs_z],['zu',trajs_z],['x',trajs_x],['y',trajs_y],['z',trajs_z],['vel_x',vel_x],['vel_y',vel_y],['vel_z',vel_z],['final',L2_runway],['phi_1l_head',phi_1l],['phi_1u_head',phi_1u],['phi_2l_head',phi_2l],['phi_2u_head',phi_2u],['phi_3l_head',phi_3l],['phi_3u_head',phi_3u ])
# out = spec.evaluate(['x', trajs_x],['y', trajs_y],['z', trajs_z],['xl', trajs_x],['xu',trajs_x],['yl', trajs_y],['yu',trajs_y],['zl', trajs_z],['zu',trajs_z])
# print('Robustness offline: {}'.format(out))
return out[0][1]
print(trajs10.shape)
# trajs10 = trajs10[:,:]
print(trajs10.shape)
num_traj = 256
with Parallel(n_jobs=4) as parallel:
t = time.time()
for i in range(10):
parallel(delayed(monitor_R2)(trajs10) for i in range(num_traj))
print("time", time.time()-t)
t = time.time()
for i in range(10):
Parallel(n_jobs=4)(delayed(monitor_R2)(trajs10) for i in range(num_traj))
print("time", time.time()-t)
t = time.time()
for i in range(10):
for i in range(num_traj):
(monitor_R2(trajs10))
print("time", time.time()-t)