def create_node_from_list(self, t_list, ind_list):
"""Returns a node, using the t_list and ind_list to specify the path.
Args:
t_list (list): Epochs (MJD) of depart/approach.
ind_list (list): Indices of the asteroids to approach or depart from
Returns:
Node: Node that contains the full history of the path.
"""
# create the initial orbit:
initial = Orbit(name='Initial', index=ind_list[0])
rv = select_asteroid(ind_list[0]).rv(t_list[0])
initial.from_rv(t_list[0], *rv)
# create the initial node:
node = Node(t_list[0],
index=ind_list[0],
approach_orbit=initial,
parent=None)
# create all the legs:
for t, ind in zip(t_list[1:], ind_list[1:]):
node = node.create_next_node(target_ind=ind, target_epoch=t)
return node
def test_errors(requests_mock):
client = Orbit(auth="f4k3")
requests_mock.get("https://app.orbit.love/api/v1/workspaces",
status_code=400)
with pytest.raises(OrbitException):
location = client.get_workspaces()
def __init__(self, weather, orbit_details):
self.orbit1 = Orbit(config.ORBIT1_LENGTH, config.ORBIT1_CRATERS, "Orbit1", orbit_details["Orbit1"])
self.orbit2 = Orbit(config.ORBIT2_LENGTH, config.ORBIT2_CRATERS, "Orbit2", orbit_details["Orbit2"])
try:
self.weather = config.WEATHER_CONDITIONS[weather.lower()]
except KeyError:
raise KeyError
def get_flyby_orbit(a, ecc, body, inOutDir, nDir, isOut=False):
periapsis = a * (1 - ecc)
tempOrb = Orbit(a, ecc, 0, 0, 0, 0, 0, body)
delta = tempOrb.get_flight_angle_at_soi(isOut)
rpDir = rodrigues_rotate(inOutDir, nDir, delta)
vpDir = cross(nDir, rpDir)
rp = rpDir * periapsis
vp = vpDir * math.sqrt(body.mu * (2 / periapsis - 1 / a))
return Orbit.from_state_vector(rp, vp, 0, body)
def load_dataset(file = '../gtoc4_problem_data.txt'):
df = pd.read_csv(file, skiprows=2,delimiter= '\s+',header=None)
df.columns = ['Name','Epoch','a','e','i','LAN','omega','M0']
asteroids = set()
for i in range(len(df)):
o = Orbit(index=i)
o.from_gtoc(*df.iloc[i])
asteroids.add(o)
earth = create_earth()
return asteroids, earth
def dict_to_body(body_dict, system_list):
name = body_dict['name']
mu = float(body_dict['gm']) * 1E9
eqr = float(body_dict['radius']) * 1000
rotPeriod = float(body_dict['rotperiod'])
rotIni = float(body_dict['rotini']) * pi/180
a = float(body_dict['sma']) * 1000
ecc = float(body_dict['ecc'])
inc = float(body_dict['inc']) * pi/180
argp = float(body_dict['arg']) * pi/180
lan = float(body_dict['raan']) * pi/180
mo = float(body_dict['mean']) * pi/180
epoch = float(body_dict['epoch'])
primName = body_dict['parent']
if primName == '':
orb = None
else:
prim = [bd for bd in system_list if bd.name == primName][0]
orb = Orbit(a, ecc, inc, argp, lan, mo, epoch, prim)
try:
colorStr = body_dict['color']
color = eval(colorStr)
except:
color = (255, 255, 255)
ref = int(body_dict['id'])
return Body(name, eqr, mu, None, rotPeriod, rotIni, orb, ref, None, color)
def test_client_workspaces_request(requests_mock):
expected_json = {
"data": [{
"id": "650",
"type": "workspace",
"attributes": {},
"relationships": {}
}]
}
requests_mock.get("https://app.orbit.love/api/v1/workspaces",
json=expected_json)
client = Orbit(auth="f4k3")
workspaces = client.get_workspaces()
assert workspaces[0]["id"] == "650"
def create_next_node(self, target_ind, target_epoch):
"""Function creates next node to be visited by solving Lambert, updating current sc mass
Args:
target_ind (int): next asteroid to be visited
target_epoch (float): epoch at which next asteroid is to be visited [MJD]
Returns:
(node): node object of input asteroid to be visited at input epoch
"""
t0 = self.epoch
r0, v0 = self.approach_orbit.rv()
# find next ast and get its position (vel not needed)
ast = select_asteroid(target_ind)
r_target, v_target = ast.rv(target_epoch)
# solve lamberts problem
v1, v2 = lb.lambert(mu, r0, r_target, (target_epoch - t0) * day2s)
# note that a maneouver is needed at the initial epoch to set us on a rendevousz path with target ast
dv = v1 - v0 # only the initial change in velocity needed
#incrememental cost (delta V, mass)
if self.parent_node is None:
# starting at earth
inc_cost = max(0, norm(dv) - 4.0)
# call mass_at_node to compute remaining mass after maneuver
#m_node = mass_at_node(1500, inc_cost) # FIXME - SAYS THAT mass_at_node() is not defined...
else:
inc_cost = norm(dv)
# call mass_at_node?
# create new orbit, index=-2 since it is a transfer
o_new = Orbit(name=f'Trx{self.len_of_chain()+1:2.0f}')
o_new.from_rv(target_epoch, r_target, v2)
# create new node
new_Node = Node(epoch=target_epoch,
index=target_ind,
approach_orbit=o_new,
parent=self)
# update cost and manouever history
new_Node.maneuvers = self.maneuvers + [(t0, dv)]
new_Node.cost = self.cost + inc_cost
return new_Node
def init_patched_conic(x,
rf=1837400.0,
r0=6371000.0 + 185000.0,
phi0=0.0,
D=384402000.0,
V=2.649e-6 * 384402000.0):
"""Generic objective function. x is [lam1, v0]."""
lam1 = x[0]
v0 = x[1]
r_soi = PatchedConic.r_soi
r1 = np.sqrt(D**2 + r_soi**2 - 2.0 * D * r_soi * np.cos(lam1))
depart = Orbit(PatchedConic.mu_earth, r0, v0, phi0)
intercept = depart.at(r1, sign='+')
if np.isnan(intercept.v):
raise ValueError("expected radius is not reached")
elif depart.energy >= 0:
raise ValueError("expected elliptical orbit")
return PatchedConic(depart, intercept, lam1=lam1, rf=rf)
def alter_orbits(self, orbit_list):
modified_orbit = []
for iter in orbit_list:
name = iter._name
distance = iter._distance
no_of_craters = iter._no_of_craters + (self._crater_effect *
iter._no_of_craters / 100)
orbit_speed = iter._speed
orb_temp = Orbit(name, distance, no_of_craters)
modified_orbit.append(OrbitWithTraffic(orb_temp, orbit_speed))
return modified_orbit
def populate_face_orbits(self):
orbits = []
faces = self.faces[:]
for i in range(72):
orbit = Orbit()
face = faces[0]
seed = faces.pop()
orbit.add_line(seed)
moves = list(seed.moves)
axis = moves[0]
for j in range(9):
face_centers = [face.center() for face in faces]
mirror_index = face_centers.index(seed.center().mirror_around(self.cells[axis]))
seed = faces.pop(mirror_index)
orbit.add_line(seed)
moves = list(seed.moves)
moves.remove(axis)
axis = moves[0]
orbits.append(orbit)
return orbits
def initialize_orbit(self):
QApplication.instance().processEvents(
) #Need to call processEvents to make the status bar message show up before the live orbit connection stuff starts.
orbit = Orbit.lcls_bpms(auto_connect=False, parent=self)
self.x_magnet_list = MagnetList("X", "xcor_list.json", parent=self)
self.total_progress = orbit.progress_total(
) + self.x_magnet_list.progress_total()
num_pvs = orbit.pv_count() + self.x_magnet_list.pv_count()
self.loading_label.setText("Connecting to {} PVs...".format(num_pvs))
self.loading_label.setAlignment(Qt.AlignCenter)
self.progress_bar.setMaximum(self.total_progress)
orbit.connectionProgress.connect(self.increment_progress)
self.x_magnet_list.connectionProgress.connect(self.increment_progress)
orbit.connect()
orbit.name = "Live Orbit"
self.live_orbit = orbit
self.initialize_magnet_lists()
self.connection_complete()
def flyby_height_objective(periapsis, *params):
aIn, aOut, deltaAngle, body = params
eccIn = 1 - periapsis / aIn
eccOut = 1 - periapsis / aOut
inOrb = Orbit(aIn, eccIn, 0, 0, 0, 0, 0, body)
outOrb = Orbit(aOut, eccOut, 0, 0, 0, 0, 0, body)
deltaIn = inOrb.get_flight_angle_at_soi()
deltaOut = outOrb.get_flight_angle_at_soi()
return abs(deltaAngle - deltaIn - deltaOut)
def project_to_surface(orb, times):
"""Takes list of positions and times and projects to body's surface."""
bd = orb.prim
positions = orb.get_positions(times=times)[0]
bodyThetas = 2*np.pi/bd.rotPeriod * np.array(times) + bd.rotIni
sphericalPositions = cartesian_to_spherical(positions)
surfaceCoords = sphericalPositions[:,1:]
for ii in range(len(times)):
longitude = surfaceCoords[ii,0] - Orbit.map_angle(bodyThetas[ii])
count = 0
while abs(longitude) > np.pi:
longitude = longitude - np.sign(longitude) * 2*np.pi
count = count+1
if count > 10:
print('Why?')
break
surfaceCoords[ii,0] = longitude
return surfaceCoords
from grid import Grid
from orbit import Orbit
import matplotlib.pyplot as plt
# Set up grid
Z = 1
G = Grid(Z, 0.0001 / Z, 80, 0.002)
# Set up orbit
n = 2
l = 0
expected_nodes = n - l - 1
orb = Orbit(G, n, l)
# Shoot with a guess E
E = -0.8
orb.shoot(E)
eps = 0.0001
if n - l - 1 == 0:
while abs(orb.delt_E) > eps:
E += orb.delt_E * 1e-4
orb.shoot(E)
print(E)
else:
while abs(orb.delt_E) > eps or orb.node != n - l - 1:
E += orb.delt_E * 1e-4
if abs(orb.delt_E) < eps:
E -= .3 * E
orb.shoot(E)
print(E)
print("Number of nodes ", orb.node)
#print(orb.tp)
def create_earth():
# create Earth
earth = Orbit(name='Earth', index=-1)
earth.from_gtoc('Earth',54000,0.999988049532578, 1.671681163160e-2, 0.8854353079654e-3, 175.40647696473, 287.61577546182, 257.60683707535)
return earth
from weather import Weather
from vehicle import Vehicle
from orbit import Orbit
from orbitwithtraffic import OrbitWithTraffic
from decisionmaker import DecisionMaker
from console import Console
from vehicletype import VehicleType
from orbitname import OrbitName
from weather import WeatherFactory
from weather import WeatherType
if __name__ == '__main__':
orb1 = Orbit("Orbit1", 18, 20)
orb2 = Orbit("Orbit2", 20, 10)
#orb1 = Orbit(OrbitName.Orbit1, 18, 20)
#orb2 = Orbit(OrbitName.Orbit2, 20, 10)
bike = Vehicle(VehicleType.Bike, 10, 1)
tuktuk = Vehicle(VehicleType.TukTuk, 12, 1)
car = Vehicle(VehicleType.Car, 20, 1)
vehicle_list=[tuktuk,bike,car]
#---------------------------
console=Console()
inputs=console.getuserinput()
#------------------------------
option = WeatherType(inputs[0])
weather = WeatherFactory.get_weather(option)
orbit1 = OrbitWithTraffic(orb1, inputs[1])
orbit2 = OrbitWithTraffic(orb2, inputs[2])
orbit_list=[orbit1,orbit2]
def __init__(self, arrival_time):
# Start with earth parking orbit
leo = Orbit.circular(PatchedConic.mu_earth, 6378136.6 + 185000.0)
# Get the state of the moon at arrival so we know how far out
# we need to go and how fast.
x_moon_arrive = spice.spkez(301, arrival_time, 'J2000', 'NONE',
399)[0] * 1000.0
# Produce patched conic
x, pcx = pc.optimize_deltav(np.array(
[49.9 * np.pi / 180.0, leo.v + 3200.0]),
1837400.0,
leo.r,
leo.phi,
norm(x_moon_arrive[0:3]),
norm(x_moon_arrive[3:6]),
conjugate=True)
depart_time = arrival_time - pcx.tof
free_flight_sweep_angle = pcx.nu1 - pcx.nu0
# Get state of moon at departure so we can figure out the
# plane of our trajectory.
x_moon_depart = spice.spkez(301, depart_time, 'J2000', 'NONE',
399)[0] * 1000.0
# Get earth--moon frame at SOI arrival time
rm0 = x_moon_depart[:3]
rm0hat = rm0 / norm(rm0)
rm1 = x_moon_arrive[:3]
rm1hat = rm1 / norm(rm1)
hhat = np.cross(rm0hat, rm1hat)
hhat /= norm(hhat)
T_eci_to_pqw = spice.twovec(rm1hat, 1, hhat, 3)
# Get directions to initial and final vectors
r1hat = T_eci_to_pqw.T.dot(
rotate_z(pcx.gam1).dot(np.array([1.0, 0, 0])))
r0hat = T_eci_to_pqw.T.dot(
rotate_z(pcx.gam1 - free_flight_sweep_angle).dot(
np.array([1.0, 0.0, 0.0])))
v0hat = np.cross(hhat, r0hat)
# post delta-v state:
r0 = r0hat * leo.r
v0 = v0hat * x[1]
# pre delta-v state:
v0m = v0hat * leo.v
# arrival state:
# r1 = r1hat * pcx.arrive.r
# v1 = ?
self.free_flight_sweep_angle = free_flight_sweep_angle
self.depart_time = depart_time
self.arrival_time = arrival_time
self.x_depart_post = np.hstack((r0, v0))
self.x_depart_pre = np.hstack((r0, v0m))
self.x_moon_depart = x_moon_depart
self.x_moon_arrive = x_moon_arrive
self.deltav = v0 - v0m
from grid import Grid
from orbit import Orbit
import matplotlib.pyplot as plt
Z = 1
G = Grid(Z, 0.0001 / Z, 50, 0.002)
orb = Orbit(G, 3, 0)
# That’s it!
# Print resulting E
#print(orb.E)
#print(orb.Vh)
# Plot
#plt.plot(G.r, orb.u, linewidth =2)
#plt.title(r"Numerical solution $u_{30}$")
plt.plot(G.r, orb.vreal, "y-", linewidth=4, label="Analytical")
plt.plot(G.r, orb.Vh, "k--", linewidth=1, label="Numerical")
plt.legend(loc="best")
plt.savefig("num30.png")
plt.show()
max = orbit.max_anomaly * 0.95
thetas = [(2 * i / 100 - 1) * max for i in range(101)]
data = [orbit.position_at(t).measure(1000 * METERS) for t in thetas]
transpose = [[p[i] for p in data] for i in range(3)]
ax.plot3D(*transpose)
# Set boundaries
SIZE = 10000
ax.set(xlim=(-SIZE, SIZE), ylim=(-SIZE, SIZE))
# Plot Kerbin itself
ax.scatter3D(0, 0, 0)
# Plot some orbits
geosync = Orbit.circular_with_period(KERBIN, 21549.425 * SECS)
radius = geosync.semimajor_axis
sat = Satellite(KERBIN, radius * Vec3.X, geosync.speed_at(radius) * Vec3.Y)
plot_orbit(sat.orbit)
BoostPrograde(200 * METERS / SECS).apply(sat)
plot_orbit(sat.orbit)
WaitTime(sat.orbit.period / 4).apply(sat)
BoostPrograde(200 * METERS / SECS).apply(sat)
plot_orbit(sat.orbit)
sat.wait_time(sat.orbit.period / 5)
BoostPrograde(-50 * METERS / SECS).apply(sat)
plot_orbit(sat.orbit)
def add_orbit(figure, orb, startTime, endTime=None, numPts=201,
dateFormat=None, apses=False, nodes=False, fullPeriod=True,
color=(255,255,255), name='', style='solid', fade=True,):
if fade:
fadedColor = fade_color(color,3)
else:
fadedColor = color
period = orb.get_period()
if fullPeriod and (endTime is None):
endTime = startTime + period
# start and end mean anomalies
mStart = orb.get_mean_anomaly(startTime)
if (period < (endTime-startTime) or fullPeriod) and (orb.ecc < 1):
mEnd = mStart + 2*math.pi
else:
mEnd = mStart + 2*math.pi/period * (endTime-startTime)
# get points clustered around apoapsis and periapsis
if orb.ecc < 1:
a = mStart - (mStart%math.pi)
b = a + math.pi
else:
if mStart < 0:
a = mStart
b = 0
else:
a = 0
b = mEnd
# orbit crosses two apo/peri-apses
if ((mEnd >= b + math.pi) and (orb.ecc < 1)):
c = b + math.pi
d = c + math.pi
n = math.ceil(math.pi/(mEnd-mStart)*numPts)
kStart = n*math.acos((a+b-2*mStart)/(b-a))/math.pi
kEnd = n*math.acos((c+d-2*mEnd)/(d-c))/math.pi
ks1 = [[kStart]]
ks1.append([*range(math.ceil(kStart), n)])
ks1 = [k for sublist in ks1 for k in sublist]
meanAnoms1 = \
[0.5*(a+b) + 0.5*(b-a) *math.cos((n-k)/n*math.pi) for k in ks1];
ks2 = [*range(0,n)]
meanAnoms2 = \
[0.5*(b+c) + 0.5*(c-b) *math.cos((n-k)/n*math.pi) for k in ks2];
ks3 = [*range(0,math.ceil(kEnd))]
ks3.append(kEnd)
meanAnoms3 = \
[0.5*(c+d) + 0.5*(d-c) *math.cos((n-k)/n*math.pi) for k in ks3];
meanAnoms = np.append(meanAnoms1, meanAnoms2)
meanAnoms = np.append(meanAnoms, meanAnoms3)
times = startTime + period/(2*math.pi) * (meanAnoms - mStart)
# orbit crosses one apo/peri-apsis
elif mEnd > b:
if orb.ecc < 1:
c = b + math.pi
n1 = math.ceil(math.pi/(mEnd-mStart)*numPts)
n2 = n1
else:
c = mEnd
n1 = math.ceil(abs(mStart/(mEnd-mStart))*numPts)
n2 = math.ceil(abs(mEnd/(mEnd-mStart))*numPts)
kStart = n1*math.acos((a+b-2*mStart)/(b-a))/math.pi
kEnd = n2*math.acos((b+c-2*mEnd)/(c-b))/math.pi
ks1 = [[kStart]]
ks1.append([*range(math.ceil(kStart), n1)])
ks1 = [k for sublist in ks1 for k in sublist]
meanAnoms1 = \
[0.5*(a+b) + 0.5*(b-a) *math.cos((n1-k)/n1*math.pi) for k in ks1];
ks2 = [*range(0,math.ceil(kEnd))]
ks2.append(kEnd)
meanAnoms2 = \
[0.5*(b+c) + 0.5*(c-b) *math.cos((n2-k)/n2*math.pi) for k in ks2];
meanAnoms = np.append(meanAnoms1, meanAnoms2)
times = startTime + period/(2*math.pi) * (meanAnoms - mStart)
# orbit crosses no apo/peri-apses
else:
if orb.ecc < 1:
n = math.ceil(2*math.pi/(mEnd-mStart)*numPts)
else:
n = numPts
kStart = n*math.acos((a+b-2*mStart)/(b-a))/math.pi
kEnd = n*math.acos((a+b-2*mEnd)/(b-a))/math.pi
ks = [[kStart]]
ks.append([*range(math.ceil(kStart), math.ceil(kEnd))])
ks.append([kEnd])
ks = [k for sublist in ks for k in sublist]
meanAnoms = np.array( \
[0.5*(a+b) + 0.5*(b-a) *math.cos((n-k)/n*math.pi) for k in ks]);
meanAnoms = meanAnoms.flatten()
times = startTime + period/(2*math.pi) * (meanAnoms - mStart)
pos, vel = orb.get_positions(times = times)
pos = np.transpose(pos)
vel = np.transpose(vel)
if orb.ecc<1:
for ii, m in enumerate(meanAnoms):
meanAnoms[ii] = Orbit.map_angle(m)
if not dateFormat is None:
day = dateFormat['day']
year = dateFormat['year']
cData = np.stack((norm(pos, axis = 0)/1000,
norm(vel, axis = 0),
np.floor(times/(3600*day*year))+1,
np.floor(times%(3600*day*year)/(day*3600)+1),
np.floor((times%(3600*day))/3600),
np.floor(((times%(3600*day))%3600)/60),
np.floor(((times%(3600*day))%3600)%60),
times,
meanAnoms),
axis=1);
hoverLabel = "r = %{customdata[0]:.3e} km" + "<br>" +\
"v = %{customdata[1]:.3e} m/s" + "<br>" + "<br>" +\
"Year %{customdata[2]:.0f}, " +\
"Day %{customdata[3]:.0f} " +\
"%{customdata[4]:0>2d}" + ":" +\
"%{customdata[5]:0>2d}" + ":" +\
"%{customdata[6]:0>2d}" + "<br>" +\
"UT: %{customdata[7]:.3f} s" + "<br>" +\
"Mean Anomaly: %{customdata[8]:.5f} rad" + "<br>" + "<br>" +\
"Semi-major Axis = " + "{:.0f}".format(orb.a) + " m" + "<br>" +\
"Eccentricity = " + "{:.4f}".format(orb.ecc) + "<br>" +\
"Inclination = " + "{:.4f}".format(orb.inc*180/math.pi) + "°" + "<br>" +\
"Argument of the Periapsis = " + "{:.4f}".format(orb.argp*180/math.pi) + "°" + "<br>" +\
"Longitude of Ascending Node = " + "{:.4f}".format(orb.lan*180/math.pi) + "°" + "<br>" +\
"Mean Anomaly at Epoch = " + "{:.4f}".format(orb.mo) + " rad" + "<br>" +\
"Epoch = " + "{:.2f}".format(orb.epoch) + " s"
else:
cData = norm(pos, axis = 0)/1000
hoverLabel = "r = %{customdata:.4e} km"
figure.add_trace(go.Scatter3d(
x = pos[0],
y = pos[1],
z = pos[2],
customdata = cData,
mode = "lines",
line = dict(
color = times,
colorscale = [[0, 'rgb'+str(fadedColor)],
[1, 'rgb'+str(color)]],
dash = style
),
hovertemplate = hoverLabel,
name = name,
showlegend = False,
))
if nodes:
add_nodes(figure, orb)
if apses:
add_apses(figure, orb)
import os
import json
from orbit import Orbit, OrbitException
client = Orbit(auth=os.environ['ORBIT_API_KEY'])
repo_activities = {}
activities = client.get_activities('650',
items=250,
start_date='2020-12-01',
end_date='2021-02-08',
direction="ASC",
auto_paginated=True)
for activity in activities:
repo = activity['attributes']['tags'][1]
last_activity = activity['attributes']['occurred_at']
print(activity['attributes']['type'])
if not repo in repo_activities:
repo_activities[repo] = {'count': 0, 'last_activity': None}
else:
repo_activities[repo]['count'] += 1
repo_activities[repo]['last_activity'] = last_activity
print(json.dumps(repo_activities, indent=4, sort_keys=True))
def orbit(self) -> Orbit:
return Orbit.from_cartesian(self.body, self.pos, self.vel)
Z = 1
g = Grid(Z, 0.0001 / Z, 110., 0.001)
n = 1
epsilon = 0.0001
colors = ["black", "red", "blue", "green", "purple", "orange"]
styles = ["-", "-.", "-", "--"]
if n <= 6:
factor = 0.3
else:
factor = 0.1
for l in range(0, n):
orb = Orbit(g, n, l)
E = -0.45
orb.shoot(E)
if n - l - 1 == 0:
while abs(orb.delta_E) > epsilon:
E += 1e-4 * orb.delta_E
orb.shoot(E)
print "----->" + str(E)
else:
while abs(orb.delta_E) > epsilon or orb.node != n - l - 1:
E += 1e-4 * orb.delta_E
if abs(orb.delta_E) < epsilon:
E -= factor * E
print "--------->" + str(E)
orb.shoot(E)
#print "I have done l="+str(l)
conjugate=conjugate,
maxiter=alpha_maxiter,
alphatol=alphatol,
plot=plot_alpha,
disp=disp)
print("Warning: exceeded max iterations (gradient phase)")
return x, pcx
if __name__ == '__main__':
D = 384402000.0
V = 2.649e-6 * D
leo = Orbit.circular(PatchedConic.mu_earth,
6378136.6 + 185000.0) # earth parking
XS = []
YS = []
optimize_deltav(np.array([49.9 * np.pi / 180.0, leo.v + 3200.0]),
1837400.0,
leo.r,
leo.phi,
D,
V,
conjugate=True)
YS = np.vstack(YS)
import matplotlib.pyplot as plt
fig = plt.figure()
