def create_ephem_paths():
# sensor design
n = 60
omega = 56
theta, phi, fit = angles_distribution(n, float(omega))
theta_t, phi_t = 0., 0.
# ant-world
noise = 0.0
ttau = .06
dx = 1e-02 # meters
dt = 2. / 60. # min
delta = timedelta(minutes=dt)
routes = load_routes()
flow = dx * np.ones(2) / np.sqrt(2)
max_theta = 0.
def encode(theta, phi, Y, P, A, theta_t=0., phi_t=0., d_phi=0., nb_tcl=8, sigma=np.deg2rad(13),
shift=np.deg2rad(40)):
alpha = (phi + np.pi / 2) % (2 * np.pi) - np.pi
phi_tcl = np.linspace(0., 2 * np.pi, nb_tcl, endpoint=False) # TB1 preference angles
phi_tcl = (phi_tcl + d_phi) % (2 * np.pi)
# Input (POL) layer -- Photo-receptors
s_1 = Y * (np.square(np.sin(A - alpha)) + np.square(np.cos(A - alpha)) * np.square(1. - P))
s_2 = Y * (np.square(np.cos(A - alpha)) + np.square(np.sin(A - alpha)) * np.square(1. - P))
r_1, r_2 = np.sqrt(s_1), np.sqrt(s_2)
r_pol = (r_1 - r_2) / (r_1 + r_2 + eps)
# Tilting (CL1) layer
d_cl1 = (np.sin(shift - theta) * np.cos(theta_t) +
np.cos(shift - theta) * np.sin(theta_t) *
np.cos(phi - phi_t))
gate = np.power(np.exp(-np.square(d_cl1) / (2. * np.square(sigma))), 1)
w = -float(nb_tcl) / (2. * float(n)) * np.sin(phi_tcl[np.newaxis] - alpha[:, np.newaxis]) * gate[:, np.newaxis]
r_tcl = r_pol.dot(w)
R = r_tcl.dot(np.exp(-np.arange(nb_tcl) * (0. + 1.j) * 2. * np.pi / float(nb_tcl)))
res = np.clip(3.5 * (np.absolute(R) - .53), 0, 2) # certainty of prediction
ele_pred = 26 * (1 - 2 * np.arcsin(1 - res) / np.pi) + 15
d_phi += np.deg2rad(9 + np.exp(.1 * (54 - ele_pred))) / (60. / float(dt))
return r_tcl, d_phi
stats = {
"max_alt": [],
"noise": [],
"opath": [],
"ipath": [],
"d_x": [],
"d_c": [],
"tau": []
}
avg_time = timedelta(0.)
terrain = z_terrain.copy()
for enable_ephemeris in [False, True]:
if enable_ephemeris:
print "Foraging with the time compensation mechanism."
else:
print "Foraging without the time compensation mechanism."
# stats
d_x = [] # logarithmic distance
d_c = []
tau = [] # tortuosity
ri = 0
print "Routes: ",
for route in routes[::2]:
net = CX(noise=0., pontin=False)
net.update = True
# sun position
cur = datetime(2018, 6, 21, 10, 0, 0)
seville_obs.date = cur
sun.compute(seville_obs)
theta_s = np.array([np.pi / 2 - sun.alt])
phi_s = np.array([(sun.az + np.pi) % (2 * np.pi) - np.pi])
sun_azi = []
sun_ele = []
time = []
# outward route
route.condition = Hybrid(tau_x=dx)
oroute = route.reverse()
x, y, yaw = [(x0, y0, yaw0) for x0, y0, _, yaw0 in oroute][0]
opath = [[x, y, yaw]]
v = np.zeros(2)
tb1 = []
d_phi = 0.
for _, _, _, yaw in oroute:
theta_n, phi_n = tilt(theta_t, phi_t, theta, phi + yaw)
sun_ele.append(theta_s[0])
sun_azi.append(phi_s[0])
time.append(cur)
sky.theta_s, sky.phi_s = theta_s, phi_s
Y, P, A = sky(theta_n, phi_n, noise=noise)
if enable_ephemeris:
r_tb1, d_phi = encode(theta, phi, Y, P, A, d_phi=d_phi)
else:
r_tb1, d_phi = encode(theta, phi, Y, P, A, d_phi=0.)
yaw0 = yaw
_, yaw = np.pi - decode_sph(r_tb1) + phi_s
net(yaw, flow)
yaw = (yaw + np.pi) % (2 * np.pi) - np.pi
v = np.array([np.sin(yaw), np.cos(yaw)]) * route.dx
opath.append([opath[-1][0] + v[0], opath[-1][1] + v[1], yaw])
tb1.append(net.tb1)
cur += delta
seville_obs.date = cur
sun.compute(seville_obs)
theta_s = np.array([np.pi / 2 - sun.alt])
phi_s = np.array([(sun.az + np.pi) % (2 * np.pi) - np.pi])
opath = np.array(opath)
yaw -= phi_s
# inward route
ipath = [[opath[-1][0], opath[-1][1], opath[-1][2]]]
L = 0. # straight distance to the nest
C = 0. # distance towards the nest that the agent has covered
SL = 0.
TC = 0.
tb1 = []
tau.append([])
d_x.append([])
d_c.append([])
while C < 15:
theta_n, phi_n = tilt(theta_t, phi_t, theta, phi + yaw)
sun_ele.append(theta_s[0])
sun_azi.append(phi_s[0])
time.append(cur)
sky.theta_s, sky.phi_s = theta_s, phi_s
Y, P, A = sky(theta_n, phi_n, noise=noise)
if enable_ephemeris:
r_tb1, d_phi = encode(theta, phi, Y, P, A, d_phi=d_phi)
else:
r_tb1, d_phi = encode(theta, phi, Y, P, A, d_phi=0.)
_, yaw = np.pi - decode_sph(r_tb1) + phi_s
motor = net(yaw, flow)
yaw = (ipath[-1][2] + motor + np.pi) % (2 * np.pi) - np.pi
v = np.array([np.sin(yaw), np.cos(yaw)]) * route.dx
ipath.append([ipath[-1][0] + v[0], ipath[-1][1] + v[1], yaw])
tb1.append(net.tb1)
L = np.sqrt(np.square(opath[0][0] - ipath[-1][0]) + np.square(opath[0][1] - ipath[-1][1]))
C += route.dx
d_x[-1].append(L)
d_c[-1].append(C)
tau[-1].append(L / C)
if C <= route.dx:
SL = L
if TC == 0. and len(d_x[-1]) > 50 and d_x[-1][-1] > d_x[-1][-2]:
TC = C
cur += delta
seville_obs.date = cur
sun.compute(seville_obs)
theta_s = np.array([np.pi / 2 - sun.alt])
phi_s = np.array([(sun.az + np.pi) % (2 * np.pi) - np.pi])
ipath = np.array(ipath)
d_x[-1] = np.array(d_x[-1]) / SL * 100
d_c[-1] = np.array(d_c[-1]) / TC * 100
tau[-1] = np.array(tau[-1])
ri += 1
avg_time += cur - datetime(2018, 6, 21, 10, 0, 0)
stats["max_alt"].append(0.)
stats["noise"].append(noise)
stats["opath"].append(opath)
stats["ipath"].append(ipath)
stats["d_x"].append(d_x[-1])
stats["d_c"].append(d_c[-1])
stats["tau"].append(tau[-1])
print ".",
print ""
print "average time:", avg_time / ri # 1:16:40
np.savez_compressed("data/pi-stats-ephem.npz", **stats)
from compoundeye.geometry import angles_distribution
from comp_model_plots import evaluate
import matplotlib.pyplot as plt
import numpy as np
if __name__ == "__main__":
tilt = False
samples = 1000
nb_noise = 1
max_noise = 1
theta, phi, fit = angles_distribution(60, 60)
alpha = (phi - np.pi / 2) % (2 * np.pi) - np.pi
noises = np.linspace(0, max_noise, int(max_noise * 2) + 1, endpoint=True)
costs, d_effs, eles = [], [], []
x = []
for noise in noises:
costs.append([])
d_effs.append([])
eles.append([])
x.append([])
for _ in xrange(nb_noise):
n = np.absolute(np.random.randn(*theta.shape)) < noise
cloud = 100. * n.sum() / np.float32(n.size)
x[-1].append(cloud)
d_err, d_eff, tau = evaluate(noise=noise, tilting=False)
costs[-1].append(d_err)
d_effs[-1].append(d_eff)
eles[-1].append(tau.flatten())
def create_paths(noise_type="uniform"):
global seville_obs, sun, dx
# sensor design
n = 60
omega = 56
theta, phi, fit = angles_distribution(n, float(omega))
theta_t, phi_t = 0., 0.
# sun position
seville_obs.date = datetime(2018, 6, 21, 9, 0, 0)
sun.compute(seville_obs)
theta_s = np.array([np.pi / 2 - sun.alt])
phi_s = np.array([(sun.az + np.pi) % (2 * np.pi) - np.pi])
# ant-world
noise = 0.0
ttau = .06
dx = 1e-02
routes = load_routes()
flow = dx * np.ones(2) / np.sqrt(2)
max_theta = 0.
stats = {
"max_alt": [],
"noise": [],
"opath": [],
"ipath": [],
"d_x": [],
"d_c": [],
"tau": []
}
for max_altitude in [.0, .1, .2, .3, .4, .5]:
for ni, noise in enumerate([0.0, 0.2, 0.4, 0.6, 0.8, .97]):
# stats
d_x = [] # logarithmic distance
d_c = []
tau = [] # tortuosity
ri = 0
for route in routes[::2]:
dx = route.dx
net = CX(noise=0., pontin=False)
net.update = True
# outward route
route.condition = Hybrid(tau_x=dx)
oroute = route.reverse()
x, y, yaw = [(x0, y0, yaw0) for x0, y0, _, yaw0 in oroute][0]
opath = [[x, y, yaw]]
v = np.zeros(2)
tb1 = []
for _, _, _, yaw in oroute:
theta_t, phi_t = get_3d_direction(opath[-1][0], opath[-1][1], yaw, tau=ttau)
max_theta = max_theta if max_theta > np.absolute(theta_t) else np.absolute(theta_t)
theta_n, phi_n = tilt(theta_t, phi_t, theta, phi + yaw)
sky.theta_s, sky.phi_s = theta_s, phi_s
Y, P, A = sky(theta_n, phi_n, noise=get_noise(theta_n, phi_n, noise, mode=noise_type))
r_tb1 = encode(theta, phi, Y, P, A)
yaw0 = yaw
_, yaw = np.pi - decode_sph(r_tb1) + phi_s
net(yaw, flow)
yaw = (yaw + np.pi) % (2 * np.pi) - np.pi
v = np.array([np.sin(yaw), np.cos(yaw)]) * route.dx
opath.append([opath[-1][0] + v[0], opath[-1][1] + v[1], yaw])
tb1.append(net.tb1)
opath = np.array(opath)
yaw -= phi_s
# inward route
ipath = [[opath[-1][0], opath[-1][1], opath[-1][2]]]
L = 0. # straight distance to the nest
C = 0. # distance towards the nest that the agent has covered
SL = 0.
TC = 0.
tb1 = []
tau.append([])
d_x.append([])
d_c.append([])
while C < 15:
theta_t, phi_t = get_3d_direction(ipath[-1][0], ipath[-1][1], yaw, tau=ttau)
theta_n, phi_n = tilt(theta_t, phi_t, theta, phi + yaw)
sky.theta_s, sky.phi_s = theta_s, phi_s
Y, P, A = sky(theta_n, phi_n, noise=noise)
r_tb1 = encode(theta, phi, Y, P, A)
_, yaw = np.pi - decode_sph(r_tb1) + phi_s
motor = net(yaw, flow)
yaw = (ipath[-1][2] + motor + np.pi) % (2 * np.pi) - np.pi
v = np.array([np.sin(yaw), np.cos(yaw)]) * route.dx
ipath.append([ipath[-1][0] + v[0], ipath[-1][1] + v[1], yaw])
tb1.append(net.tb1)
L = np.sqrt(np.square(opath[0][0] - ipath[-1][0]) + np.square(opath[0][1] - ipath[-1][1]))
C += route.dx
d_x[-1].append(L)
d_c[-1].append(C)
tau[-1].append(L / C)
if C <= route.dx:
SL = L
if TC == 0. and len(d_x[-1]) > 50 and d_x[-1][-1] > d_x[-1][-2]:
TC = C
ipath = np.array(ipath)
d_x[-1] = np.array(d_x[-1]) / SL * 100
d_c[-1] = np.array(d_c[-1]) / TC * 100
tau[-1] = np.array(tau[-1])
ri += 1
stats["max_alt"].append(max_altitude)
stats["noise"].append(noise)
stats["opath"].append(opath)
stats["ipath"].append(ipath)
stats["d_x"].append(d_x[-1])
stats["d_c"].append(d_c[-1])
stats["tau"].append(tau[-1])
np.savez_compressed("../data/pi-stats-%s.npz" % noise_type, **stats)
_, _, vh = np.linalg.svd(points - points.mean(axis=0))
# unitary normal vector
u = vh.conj().transpose()[:, -1]
p = sph2vec(np.pi / 2, yaw, zenith=True)
pp = p - p.dot(u) / np.square(np.linalg.norm(u)) * u
theta_p, phi_p, _ = vec2sph(pp, zenith=True)
return theta_p - np.pi / 2, phi_p - yaw
if __name__ == "__main__":
from notebooks.plots import plot_sky
# sensor design
n = 60
omega = 56
theta, phi, fit = angles_distribution(n, float(omega))
theta_t, phi_t = 0., 0.
# sun position
seville = ephem.Observer()
seville.lat = '37.392509'
seville.lon = '-5.983877'
seville.date = datetime(2018, 6, 21, 9, 0, 0)
sun = ephem.Sun()
sun.compute(seville)
theta_s = np.array([np.pi / 2 - sun.alt])
phi_s = np.array([(sun.az + np.pi) % (2 * np.pi) - np.pi])
theta_sky, phi_sky = fibonacci_sphere(1000, 180)
# ant-world
def evaluate_old(
n=60,
omega=56,
noise=0.,
nb_cl1=16,
sigma=np.deg2rad(13),
shift=np.deg2rad(40),
nb_tb1=8,
use_default=False,
weighted=True,
fibonacci=False,
simple_pol=False,
uniform_poliriser=False,
# single evaluation
sun_azi=None,
sun_ele=None,
# data parameters
tilting=True,
samples=1000,
show_plots=False,
show_structure=False,
verbose=False):
# default parameters
tau_L = 2.
c1 = .6
c2 = 4.
eps = np.finfo(float).eps
AA, BB, CC, DD, EE = T_L.dot(np.array([tau_L, 1.])) # sky parameters
T_T = np.linalg.pinv(T_L)
tau_L, c = T_T.dot(np.array([AA, BB, CC, DD, EE]))
tau_L /= c # turbidity correction
# Prez. et. al. Luminance function
def L(cchi, zz):
ii = zz < (np.pi / 2)
ff = np.zeros_like(zz)
if zz.ndim > 0:
ff[ii] = (1. + AA * np.exp(BB / (np.cos(zz[ii]) + eps)))
elif ii:
ff = (1. + AA * np.exp(BB / (np.cos(zz) + eps)))
pphi = (1. + CC * np.exp(DD * cchi) + EE * np.square(np.cos(cchi)))
return ff * pphi
if tilting:
angles = np.array([[0., 0.], [np.pi / 6, 0.], [np.pi / 6, np.pi / 4],
[np.pi / 6, 2 * np.pi / 4],
[np.pi / 6, 3 * np.pi / 4],
[np.pi / 6, 4 * np.pi / 4],
[np.pi / 6, 5 * np.pi / 4],
[np.pi / 6, 6 * np.pi / 4],
[np.pi / 6, 7 * np.pi / 4], [np.pi / 3, 0.],
[np.pi / 3, np.pi / 4], [np.pi / 3, 2 * np.pi / 4],
[np.pi / 3, 3 * np.pi / 4],
[np.pi / 3, 4 * np.pi / 4],
[np.pi / 3, 5 * np.pi / 4],
[np.pi / 3, 6 * np.pi / 4],
[np.pi / 3, 7 * np.pi / 4]]) # 17
if samples == 1000:
samples /= 2
else:
angles = np.array([[0., 0.]]) # 1
# generate the different sun positions
if sun_azi is not None or sun_ele is not None:
theta_s = sun_ele if type(sun_ele) is np.ndarray else np.array(
[sun_ele])
phi_s = sun_azi if type(sun_azi) is np.ndarray else np.array([sun_azi])
else:
theta_s, phi_s = fibonacci_sphere(samples=samples, fov=161)
phi_s = phi_s[theta_s <= np.pi / 2]
theta_s = theta_s[theta_s <= np.pi / 2]
samples = theta_s.size
# generate the properties of the sensor
try:
theta, phi, fit = angles_distribution(n, float(omega))
except ValueError:
theta = np.empty(0, dtype=np.float32)
phi = np.empty(0, dtype=np.float32)
fit = False
if not fit or n > 100 or fibonacci:
theta, phi = fibonacci_sphere(n, float(omega))
# theta, phi, fit = angles_distribution(n, omega)
# if not fit:
# print theta.shape, phi.shape
theta = (theta - np.pi) % (2 * np.pi) - np.pi
phi = (phi + np.pi) % (2 * np.pi) - np.pi
alpha = (phi + np.pi / 2) % (2 * np.pi) - np.pi
# computational model parameters
phi_cl1 = np.linspace(0., 4 * np.pi, nb_cl1,
endpoint=False) # CL1 preference angles
phi_tb1 = np.linspace(0., 2 * np.pi, nb_tb1,
endpoint=False) # TB1 preference angles
# initialise lists for the statistical data
d = np.zeros((samples, angles.shape[0]), dtype=np.float32)
t = np.zeros_like(d)
d_eff = np.zeros((samples, angles.shape[0]), dtype=np.float32)
a_ret = np.zeros_like(t)
tb1 = np.zeros((samples, angles.shape[0], nb_tb1), dtype=np.float32)
# iterate through the different tilting angles
for j, (theta_t, phi_t) in enumerate(angles):
# transform relative coordinates
theta_s_, phi_s_ = tilt(theta_t, phi_t, theta=theta_s, phi=phi_s)
theta_, phi_ = tilt(theta_t, phi_t + np.pi, theta=theta, phi=phi)
_, alpha_ = tilt(theta_t, phi_t + np.pi, theta=np.pi / 2, phi=alpha)
for i, (e, a, e_org,
a_org) in enumerate(zip(theta_s_, phi_s_, theta_s, phi_s)):
# SKY INTEGRATION
gamma = np.arccos(
np.cos(theta_) * np.cos(e_org) +
np.sin(theta_) * np.sin(e_org) * np.cos(phi_ - a_org))
# Intensity
I_prez, I_00, I_90 = L(gamma, theta_), L(0., e_org), L(
np.pi / 2, np.absolute(e_org - np.pi / 2))
# influence of sky intensity
I = (1. / (I_prez + eps) - 1. /
(I_00 + eps)) * I_00 * I_90 / (I_00 - I_90 + eps)
chi = (4. / 9. - tau_L / 120.) * (np.pi - 2 * e_org)
Y_z = (4.0453 * tau_L -
4.9710) * np.tan(chi) - 0.2155 * tau_L + 2.4192
if uniform_poliriser:
Y = np.maximum(np.full_like(I_prez, Y_z), 0.)
else:
Y = np.maximum(Y_z * I_prez / (I_00 + eps), 0.) # Illumination
# Degree of Polarisation
M_p = np.exp(-(tau_L - c1) / (c2 + eps))
LP = np.square(np.sin(gamma)) / (1 + np.square(np.cos(gamma)))
if uniform_poliriser:
P = np.ones_like(LP)
elif simple_pol:
P = np.clip(2. / np.pi * M_p * LP, 0., 1.)
else:
P = np.clip(
2. / np.pi * M_p * LP * (theta_ * np.cos(theta_) +
(np.pi / 2 - theta_) * I), 0., 1.)
# Angle of polarisation
if uniform_poliriser:
A = np.full_like(P, a_org + np.pi)
else:
_, A = tilt(e_org, a_org + np.pi, theta_, phi_)
# create cloud disturbance
if noise > 0:
eta = np.absolute(np.random.randn(*P.shape)) < noise
if verbose:
print "Noise level: %.4f (%.2f %%)" % (
noise, 100. * eta.sum() / float(eta.size))
P[eta] = 0. # destroy the polarisation pattern
else:
eta = np.zeros(1)
# COMPUTATIONAL MODEL
# Input (POL) layer -- Photo-receptors
s_1 = 15. * (np.square(np.sin(A - alpha_)) +
np.square(np.cos(A - alpha_)) * np.square(1. - P))
s_2 = 15. * (np.square(np.cos(A - alpha_)) +
np.square(np.sin(A - alpha_)) * np.square(1. - P))
r_1, r_2 = np.sqrt(s_1), np.sqrt(s_2)
# r_1, r_2 = np.log(s_1 + 1.), np.log(s_2 + 1.)
r_pol = (r_1 - r_2) / (r_1 + r_2 + eps)
# Tilting (CL1) layer
d_cl1 = (
np.sin(shift - theta) * np.cos(theta_t) +
np.cos(shift - theta) * np.sin(theta_t) * np.cos(phi - phi_t))
gate = np.power(
np.exp(-np.square(d_cl1) / (2. * np.square(sigma))), 1)
w_cl1 = float(nb_cl1) / float(n) * np.sin(
alpha[:, np.newaxis] - phi_cl1[np.newaxis]) * gate[:,
np.newaxis]
r_cl1 = r_pol.dot(w_cl1)
# Output (TB1) layer
w_tb1 = float(nb_tb1) / float(
2 * nb_cl1) * np.cos(phi_tb1[np.newaxis] -
phi_cl1[:, np.newaxis])
r_tb1 = r_cl1.dot(w_tb1)
if use_default:
w = -float(nb_tb1) / (2. * float(n)) * np.sin(phi_tb1[
np.newaxis] - alpha[:, np.newaxis]) * gate[:, np.newaxis]
r_tb1 = r_pol.dot(w)
# decode response - FFT
R = r_tb1.dot(
np.exp(-np.arange(nb_tb1) * (0. + 1.j) * np.pi /
(float(nb_tb1) / 2.)))
a_pred = (np.pi - np.arctan2(R.imag, R.real)) % (
2. * np.pi) - np.pi # sun azimuth (prediction)
tau_pred = np.absolute(R) # certainty of prediction
d[i, j] = np.absolute(
azidist(np.array([e, a]), np.array([0., a_pred])))
t[i, j] = tau_pred if weighted else 1.
a_ret[i, j] = a_pred
tb1[i, j] = r_tb1
# effective degree of polarisation
M = r_cl1.max() - r_cl1.min()
# M = t[i, j] * 2.
p = np.power(10, M / 2.)
d_eff[i, j] = np.mean((p - 1.) / (p + 1.))
if show_plots:
plt.figure("sensor-noise-%2d" %
(100. * eta.sum() / float(eta.size)),
figsize=(18, 4.5))
ax = plt.subplot(1, 12, 10)
plt.imshow(w_cl1, cmap="coolwarm", vmin=-1, vmax=1)
plt.xlabel("CBL", fontsize=16)
plt.xticks([0, 15], ["1", "16"])
plt.yticks([0, 59], ["1", "60"])
ax.tick_params(axis='both', which='major', labelsize=16)
ax.tick_params(axis='both', which='minor', labelsize=16)
ax = plt.subplot(1, 6, 6) # , sharey=ax)
plt.imshow(w_tb1, cmap="coolwarm", vmin=-1, vmax=1)
plt.xlabel("TB1", fontsize=16)
plt.xticks([0, 7], ["1", "8"])
plt.yticks([0, 15], ["1", "16"])
cbar = plt.colorbar(ticks=[-1, 0, 1])
cbar.ax.set_yticklabels([r'$\leq$ -1', r'0', r'$\geq$ 1'])
ax.tick_params(axis='both', which='major', labelsize=16)
ax.tick_params(axis='both', which='minor', labelsize=16)
ax = plt.subplot(1, 4, 1, polar=True)
ax.scatter(phi,
theta,
s=150,
c=r_pol,
marker='o',
cmap="coolwarm",
vmin=-1,
vmax=1)
ax.scatter(a,
e,
s=100,
marker='o',
edgecolor='black',
facecolor='yellow')
ax.scatter(phi_t + np.pi,
theta_t,
s=200,
marker='o',
edgecolor='black',
facecolor='yellowgreen')
ax.set_theta_zero_location("N")
ax.set_theta_direction(-1)
ax.set_ylim([0, np.deg2rad(40)])
ax.set_yticks([])
ax.set_xticks(
np.linspace(-3 * np.pi / 4,
5 * np.pi / 4,
8,
endpoint=False))
ax.set_title("POL Response", fontsize=16)
ax.tick_params(axis='both', which='major', labelsize=16)
ax.tick_params(axis='both', which='minor', labelsize=16)
ax = plt.subplot(1, 4, 2, polar=True)
ax.scatter(phi,
theta,
s=150,
c=r_pol * gate,
marker='o',
cmap="coolwarm",
vmin=-1,
vmax=1)
ax.scatter(a,
e,
s=100,
marker='o',
edgecolor='black',
facecolor='yellow')
ax.scatter(phi_t + np.pi,
theta_t,
s=200,
marker='o',
edgecolor='black',
facecolor='yellowgreen')
ax.set_theta_zero_location("N")
ax.set_theta_direction(-1)
ax.set_ylim([0, np.deg2rad(40)])
ax.set_yticks([])
ax.set_xticks(
np.linspace(-3 * np.pi / 4,
5 * np.pi / 4,
8,
endpoint=False))
ax.set_title("Gated Response", fontsize=16)
ax.tick_params(axis='both', which='major', labelsize=16)
ax.tick_params(axis='both', which='minor', labelsize=16)
ax = plt.subplot(1, 4, 3, polar=True)
x = np.linspace(0, 2 * np.pi, 721)
# CBL
ax.fill_between(x,
np.full_like(x, np.deg2rad(60)),
np.full_like(x, np.deg2rad(90)),
facecolor="C1",
alpha=.5,
label="CBL")
ax.scatter(phi_cl1[:nb_cl1 / 2] - np.pi / 24,
np.full(nb_cl1 / 2, np.deg2rad(75)),
s=600,
c=r_cl1[:nb_cl1 / 2],
marker='o',
edgecolor='red',
cmap="coolwarm",
vmin=-1,
vmax=1)
ax.scatter(phi_cl1[nb_cl1 / 2:] + np.pi / 24,
np.full(nb_cl1 / 2, np.deg2rad(75)),
s=600,
c=r_cl1[nb_cl1 / 2:],
marker='o',
edgecolor='green',
cmap="coolwarm",
vmin=-1,
vmax=1)
for ii, pp in enumerate(phi_cl1[:nb_cl1 / 2] - np.pi / 24):
ax.text(pp - np.pi / 20,
np.deg2rad(75),
"%d" % (ii + 1),
ha="center",
va="center",
size=10,
bbox=dict(boxstyle="circle", fc="w", ec="k"))
for ii, pp in enumerate(phi_cl1[nb_cl1 / 2:] + np.pi / 24):
ax.text(pp + np.pi / 20,
np.deg2rad(75),
"%d" % (ii + 9),
ha="center",
va="center",
size=10,
bbox=dict(boxstyle="circle", fc="w", ec="k"))
# TB1
ax.fill_between(x,
np.full_like(x, np.deg2rad(30)),
np.full_like(x, np.deg2rad(60)),
facecolor="C2",
alpha=.5,
label="TB1")
ax.scatter(phi_tb1,
np.full_like(phi_tb1, np.deg2rad(45)),
s=600,
c=r_tb1,
marker='o',
edgecolor='blue',
cmap="coolwarm",
vmin=-1,
vmax=1)
for ii, pp in enumerate(phi_tb1):
ax.text(pp,
np.deg2rad(35),
"%d" % (ii + 1),
ha="center",
va="center",
size=10,
bbox=dict(boxstyle="circle", fc="w", ec="k"))
ax.arrow(pp,
np.deg2rad(35),
0,
np.deg2rad(10),
fc='k',
ec='k',
head_width=.1,
overhang=.3)
# Sun position
ax.scatter(a,
e,
s=500,
marker='o',
edgecolor='black',
facecolor='yellow')
# Decoded TB1
# ax.plot([0, a_pred], [0, e_pred], 'k--', lw=1)
ax.plot([0, a_pred], [0, np.pi / 2], 'k--', lw=1)
ax.arrow(a_pred,
0,
0,
np.deg2rad(20),
fc='k',
ec='k',
head_width=.3,
head_length=.2,
overhang=.3)
ax.legend(ncol=2, loc=(-.55, -.1), fontsize=16)
ax.set_theta_zero_location("N")
ax.set_theta_direction(-1)
ax.set_ylim([0, np.pi / 2])
ax.set_yticks([])
ax.set_xticks([])
ax.set_title("Sensor Response", fontsize=16)
plt.subplots_adjust(left=.02, bottom=.12, right=.98, top=.88)
ax.tick_params(axis='both', which='major', labelsize=16)
ax.tick_params(axis='both', which='minor', labelsize=16)
plt.show()
d_deg = np.rad2deg(d)
if show_structure:
plt.figure("sensor-structure", figsize=(4.5, 4.5))
ax = plt.subplot(111, polar=True)
ax.scatter(phi, theta, s=150, c="black", marker='o')
ax.set_theta_zero_location("N")
ax.set_theta_direction(-1)
ax.set_ylim([0, np.deg2rad(50)])
ax.set_yticks([])
ax.set_xticks(
np.linspace(-3 * np.pi / 4, 5 * np.pi / 4, 8, endpoint=False))
ax.set_title("POL Response")
plt.show()
return d_deg, d_eff, t, a_ret, tb1
def evaluate_slow(
n=60,
omega=56,
noise=0.,
nb_cl1=8,
sigma_pol=np.deg2rad(13),
shift_pol=np.deg2rad(40),
nb_tb1=8,
sigma_sol=np.deg2rad(13),
shift_sol=np.deg2rad(40),
use_default=False,
weighted=True,
fibonacci=False,
uniform_polariser=False,
# single evaluation
sun_azi=None,
sun_ele=None,
# data parameters
tilting=True,
samples=1000,
show_plots=False,
show_structure=False,
verbose=False):
if tilting:
angles = np.array([[0., 0.], [np.pi / 6, 0.], [np.pi / 6, np.pi / 4],
[np.pi / 6, 2 * np.pi / 4],
[np.pi / 6, 3 * np.pi / 4],
[np.pi / 6, 4 * np.pi / 4],
[np.pi / 6, 5 * np.pi / 4],
[np.pi / 6, 6 * np.pi / 4],
[np.pi / 6, 7 * np.pi / 4], [np.pi / 3, 0.],
[np.pi / 3, np.pi / 4], [np.pi / 3, 2 * np.pi / 4],
[np.pi / 3, 3 * np.pi / 4],
[np.pi / 3, 4 * np.pi / 4],
[np.pi / 3, 5 * np.pi / 4],
[np.pi / 3, 6 * np.pi / 4],
[np.pi / 3, 7 * np.pi / 4]]) # 17
if samples == 1000:
samples /= 2
else:
angles = np.array([[0., 0.]]) # 1
# generate the different sun positions
if sun_azi is not None or sun_ele is not None:
theta_s = sun_ele if type(sun_ele) is np.ndarray else np.array(
[sun_ele])
phi_s = sun_azi if type(sun_azi) is np.ndarray else np.array([sun_azi])
else:
theta_s, phi_s = fibonacci_sphere(samples=samples, fov=161)
phi_s = phi_s[theta_s <= np.pi / 2]
theta_s = theta_s[theta_s <= np.pi / 2]
samples = theta_s.size
# generate the properties of the sensor
try:
theta, phi, fit = angles_distribution(n, float(omega))
except ValueError:
theta = np.empty(0, dtype=np.float32)
phi = np.empty(0, dtype=np.float32)
fit = False
if not fit or n > 100 or fibonacci:
theta, phi = fibonacci_sphere(n, float(omega))
# theta, phi, fit = angles_distribution(n, omega)
# if not fit:
# print theta.shape, phi.shape
theta = (theta - np.pi) % (2 * np.pi) - np.pi
phi = (phi + np.pi) % (2 * np.pi) - np.pi
alpha = (phi + np.pi / 2) % (2 * np.pi) - np.pi
# computational model parameters
phi_cl1 = np.linspace(0., 2 * np.pi, nb_cl1,
endpoint=False) # CL1 preference angles
phi_tb1 = np.linspace(0., 2 * np.pi, nb_tb1,
endpoint=False) # TB1 preference angles
# initialise lists for the statistical data
d = np.zeros((samples, angles.shape[0]), dtype=np.float32)
t = np.zeros_like(d)
d_eff = np.zeros((samples, angles.shape[0]), dtype=np.float32)
a_ret = np.zeros_like(t)
tb1 = np.zeros((samples, angles.shape[0], nb_tb1), dtype=np.float32)
# iterate through the different tilting angles
for j, (theta_t, phi_t) in enumerate(angles):
# transform relative coordinates
theta_s_, phi_s_ = tilt(theta_t, phi_t, theta=theta_s, phi=phi_s)
_, alpha_ = tilt(theta_t, phi_t + np.pi, theta=np.pi / 2, phi=alpha)
for i, (e, a, e_org,
a_org) in enumerate(zip(theta_s_, phi_s_, theta_s, phi_s)):
sky = Sky(theta_s=e_org, phi_s=a_org, theta_t=theta_t, phi_t=phi_t)
sky.verbose = verbose
# COMPUTATIONAL MODEL
# Input (POL) layer -- Photo-receptors
dra = POLCompassDRA(n=n, omega=omega)
dra.theta_t = theta_t
dra.phi_t = phi_t
r_pol = dra(sky, noise=noise, uniform_polariser=uniform_polariser)
r_sol = dra.r_po
# Tilting (SOL) layer
d_pol = (np.sin(shift_pol - theta) * np.cos(theta_t) +
np.cos(shift_pol - theta) * np.sin(theta_t) *
np.cos(phi - phi_t))
gate_pol = np.power(
np.exp(-np.square(d_pol) / (2. * np.square(sigma_pol))), 1)
z_pol = -float(nb_cl1) / float(n)
w_cl1_pol = z_pol * np.sin(phi_cl1[
np.newaxis] - alpha[:, np.newaxis]) * gate_pol[:, np.newaxis]
d_sol = (np.sin(shift_sol - theta) * np.cos(theta_t) +
np.cos(shift_sol - theta) * np.sin(theta_t) *
np.cos(phi - phi_t))
gate_sol = np.power(
np.exp(-np.square(d_sol) / (2. * np.square(sigma_sol))), 1)
z_sol = float(nb_cl1) / float(n)
w_cl1_sol = z_sol * np.sin(phi_cl1[
np.newaxis] - alpha[:, np.newaxis]) * gate_sol[:, np.newaxis]
o = 1. / 64.
f_pol, f_sol = .5 * np.power(2 * theta_t / np.pi, o), .5 * (
1 - np.power(2 * theta_t / np.pi, o))
r_cl1_pol = r_pol.dot(w_cl1_pol)
r_cl1_sol = r_sol.dot(w_cl1_sol)
r_cl1 = f_pol * r_cl1_pol + f_sol * r_cl1_sol
# r_cl1 = r_cl1_sol
# Output (TCL) layer
# w_tb1 = np.eye(nb_tb1)
w_tb1 = float(nb_tb1) / float(nb_cl1) * np.cos(
phi_tb1[np.newaxis] - phi_cl1[:, np.newaxis])
r_tb1 = r_cl1.dot(w_tb1)
if use_default:
w = -float(nb_tb1) / (2. * float(n)) * np.sin(
phi_tb1[np.newaxis] -
alpha[:, np.newaxis]) * gate_pol[:, np.newaxis]
r_tb1 = r_pol.dot(w)
# decode response - FFT
R = r_tb1.dot(
np.exp(-np.arange(nb_tb1) * (0. + 1.j) * np.pi /
(float(nb_tb1) / 2.)))
a_pred = (np.pi - np.arctan2(R.imag, R.real)) % (
2. * np.pi) - np.pi # sun azimuth (prediction)
tau_pred = np.maximum(np.absolute(R), 0) # certainty of prediction
d[i, j] = np.absolute(
azidist(np.array([e, a]), np.array([0., a_pred])))
t[i, j] = tau_pred if weighted else 1.
a_ret[i, j] = a_pred
tb1[i, j] = r_tb1
# effective degree of polarisation
M = r_cl1.max() - r_cl1.min()
# M = t[i, j] * 2.
p = np.power(10, M / 2.)
d_eff[i, j] = np.mean((p - 1.) / (p + 1.))
if show_plots:
plt.figure("sensor-noise-%2d" %
(100. * sky.eta.sum() / float(sky.eta.size)),
figsize=(18, 4.5))
ax = plt.subplot(1, 12, 10)
plt.imshow(w_cl1_pol, cmap="coolwarm", vmin=-1, vmax=1)
plt.xlabel("CBL", fontsize=16)
plt.xticks([0, 15], ["1", "16"])
plt.yticks([0, 59], ["1", "60"])
ax.tick_params(axis='both', which='major', labelsize=16)
ax.tick_params(axis='both', which='minor', labelsize=16)
ax = plt.subplot(1, 6, 6) # , sharey=ax)
plt.imshow(w_tb1, cmap="coolwarm", vmin=-1, vmax=1)
plt.xlabel("TB1", fontsize=16)
plt.xticks([0, 7], ["1", "8"])
plt.yticks([0, 15], ["1", "16"])
cbar = plt.colorbar(ticks=[-1, 0, 1])
cbar.ax.set_yticklabels([r'$\leq$ -1', r'0', r'$\geq$ 1'])
ax.tick_params(axis='both', which='major', labelsize=16)
ax.tick_params(axis='both', which='minor', labelsize=16)
ax = plt.subplot(1, 4, 1, polar=True)
ax.scatter(phi,
theta,
s=150,
c=r_pol,
marker='o',
cmap="coolwarm",
vmin=-1,
vmax=1)
ax.scatter(a,
e,
s=100,
marker='o',
edgecolor='black',
facecolor='yellow')
ax.scatter(phi_t + np.pi,
theta_t,
s=200,
marker='o',
edgecolor='black',
facecolor='yellowgreen')
ax.set_theta_zero_location("N")
ax.set_theta_direction(-1)
ax.set_ylim([0, np.deg2rad(40)])
ax.set_yticks([])
ax.set_xticks(np.linspace(0, 2 * np.pi, 8, endpoint=False))
ax.set_xticklabels([
r'$0^\circ$', r'$45^\circ$', r'$90^\circ$', r'$135^\circ$',
r'$180^\circ$', r'$-135^\circ$', r'$-90^\circ$',
r'$-45^\circ$'
])
ax.set_title("POL Response", fontsize=16)
ax.tick_params(axis='both', which='major', labelsize=16)
ax.tick_params(axis='both', which='minor', labelsize=16)
ax = plt.subplot(1, 4, 2, polar=True)
ax.scatter(phi,
theta,
s=150,
c=r_pol * gate_pol,
marker='o',
cmap="coolwarm",
vmin=-1,
vmax=1)
ax.scatter(a,
e,
s=100,
marker='o',
edgecolor='black',
facecolor='yellow')
ax.scatter(phi_t + np.pi,
theta_t,
s=200,
marker='o',
edgecolor='black',
facecolor='yellowgreen')
ax.set_theta_zero_location("N")
ax.set_theta_direction(-1)
ax.set_ylim([0, np.deg2rad(40)])
ax.set_yticks([])
ax.set_xticks(np.linspace(0, 2 * np.pi, 8, endpoint=False))
ax.set_xticklabels([
r'$0^\circ$', r'$45^\circ$', r'$90^\circ$', r'$135^\circ$',
r'$180^\circ$', r'$-135^\circ$', r'$-90^\circ$',
r'$-45^\circ$'
])
ax.set_title("Gated Response", fontsize=16)
ax.tick_params(axis='both', which='major', labelsize=16)
ax.tick_params(axis='both', which='minor', labelsize=16)
ax = plt.subplot(1, 4, 3, polar=True)
x = np.linspace(0, 2 * np.pi, 721)
# CBL
ax.fill_between(x,
np.full_like(x, np.deg2rad(60)),
np.full_like(x, np.deg2rad(90)),
facecolor="C1",
alpha=.5,
label="CBL")
ax.scatter(phi_cl1[:nb_cl1 / 2] - np.pi / 24,
np.full(nb_cl1 / 2, np.deg2rad(75)),
s=600,
c=r_cl1[:nb_cl1 / 2],
marker='o',
edgecolor='red',
cmap="coolwarm",
vmin=-1,
vmax=1)
ax.scatter(phi_cl1[nb_cl1 / 2:] + np.pi / 24,
np.full(nb_cl1 / 2, np.deg2rad(75)),
s=600,
c=r_cl1[nb_cl1 / 2:],
marker='o',
edgecolor='green',
cmap="coolwarm",
vmin=-1,
vmax=1)
for ii, pp in enumerate(phi_cl1[:nb_cl1 / 2] - np.pi / 24):
ax.text(pp - np.pi / 20,
np.deg2rad(75),
"%d" % (ii + 1),
ha="center",
va="center",
size=10,
bbox=dict(boxstyle="circle", fc="w", ec="k"))
for ii, pp in enumerate(phi_cl1[nb_cl1 / 2:] + np.pi / 24):
ax.text(pp + np.pi / 20,
np.deg2rad(75),
"%d" % (ii + 9),
ha="center",
va="center",
size=10,
bbox=dict(boxstyle="circle", fc="w", ec="k"))
# TB1
ax.fill_between(x,
np.full_like(x, np.deg2rad(30)),
np.full_like(x, np.deg2rad(60)),
facecolor="C2",
alpha=.5,
label="TB1")
ax.scatter(phi_tb1,
np.full_like(phi_tb1, np.deg2rad(45)),
s=600,
c=r_tb1,
marker='o',
edgecolor='blue',
cmap="coolwarm",
vmin=-1,
vmax=1)
for ii, pp in enumerate(phi_tb1):
ax.text(pp,
np.deg2rad(35),
"%d" % (ii + 1),
ha="center",
va="center",
size=10,
bbox=dict(boxstyle="circle", fc="w", ec="k"))
ax.arrow(pp,
np.deg2rad(35),
0,
np.deg2rad(10),
fc='k',
ec='k',
head_width=.1,
overhang=.3)
# Sun position
ax.scatter(a,
e,
s=500,
marker='o',
edgecolor='black',
facecolor='yellow')
# Decoded TB1
# ax.plot([0, a_pred], [0, e_pred], 'k--', lw=1)
ax.plot([0, a_pred], [0, np.pi / 2], 'k--', lw=1)
ax.arrow(a_pred,
0,
0,
np.deg2rad(20),
fc='k',
ec='k',
head_width=.3,
head_length=.2,
overhang=.3)
ax.legend(ncol=2, loc=(-.55, -.1), fontsize=16)
ax.set_theta_zero_location("N")
ax.set_theta_direction(-1)
ax.set_ylim([0, np.pi / 2])
ax.set_yticks([])
ax.set_xticks([])
ax.set_title("Sensor Response", fontsize=16)
plt.subplots_adjust(left=.02, bottom=.12, right=.98, top=.88)
ax.tick_params(axis='both', which='major', labelsize=16)
ax.tick_params(axis='both', which='minor', labelsize=16)
plt.show()
d_deg = np.rad2deg(d)
if show_structure:
plt.figure("sensor-structure", figsize=(4.5, 4.5))
ax = plt.subplot(111, polar=True)
ax.scatter(phi, theta, s=150, c="black", marker='o')
ax.set_theta_zero_location("N")
ax.set_theta_direction(-1)
ax.set_ylim([0, np.deg2rad(50)])
ax.set_yticks([])
ax.set_xticks(
np.linspace(-3 * np.pi / 4, 5 * np.pi / 4, 8, endpoint=False))
ax.set_title("POL Response")
plt.show()
return d_deg, d_eff, t, a_ret, tb1
def noise_test(save=None, mode=0, repeats=10, **kwargs):
from sphere.transform import sph2vec
print "Running noise test:", kwargs
modes = ['normal', 'corridor', 'side']
print "Mode:", modes[mode]
plt.figure("noise-%s" % modes[mode], figsize=(5, 5))
n, omega = 60, 56
etas = np.linspace(0, 1, 21)
taus = np.zeros_like(etas)
means = np.zeros_like(etas)
ses = np.zeros_like(etas)
for i in xrange(10):
noise = np.ones(n, int)
if mode > 0:
theta, phi, fit = angles_distribution(n, float(omega))
x, _, _ = sph2vec(theta, phi)
else:
x = np.argsort(np.absolute(np.random.randn(n)))
for ii, eta in enumerate(etas):
if mode == 0:
noise[:] = 0
noise[x[:int(eta * float(n))]] = 1
else:
noise[:] = 0
if mode > 1:
noise[x > (1 - 2 * eta)] = 1
else:
noise[np.abs(x) > (1 - eta)] = 1
d_err, d_eff, tau, _, _ = evaluate(n=n,
omega=omega,
noise=noise,
verbose=False,
tilting=True,
**kwargs)
means[ii] = (means[ii] * i + d_err.mean()) / (i + 1)
ses[ii] = (ses[ii] * i + d_err.std() / np.sqrt(d_err.size)) / (i +
1)
taus[ii] = (taus[ii] * i + tau.mean()) / (i + 1)
print "Noise level: %.2f (%03d) | Mean cost: %.2f +/- %.4f" % (
eta, np.sum(noise), means[ii], ses[ii])
plt.fill_between(etas * 100, means - ses, means + ses, facecolor="grey")
plt.plot(etas * 100, means, color="red", linestyle="-", label="tilting")
plt.plot(etas * 100,
taus * 45,
color="red",
linestyle="--",
label="tau-tilting")
taus = np.zeros_like(etas)
means = np.zeros_like(etas)
ses = np.zeros_like(etas)
for i in xrange(repeats):
noise = np.ones(n, int)
if mode > 0:
theta, phi, fit = angles_distribution(n, float(omega))
x, _, _ = sph2vec(theta, phi)
else:
x = np.argsort(np.absolute(np.random.randn(n)))
for ii, eta in enumerate(etas):
if mode == 0:
noise[:] = 0
noise[x[:int(eta * float(n))]] = 1
else:
noise[:] = 0
if mode > 1:
noise[x > (1 - 2 * eta)] = 1
else:
noise[np.abs(x) > (1 - eta)] = 1
d_err, d_eff, tau, _, _ = evaluate(n=n,
omega=omega,
noise=noise,
verbose=False,
tilting=False,
**kwargs)
means[ii] = (means[ii] * i + d_err.mean()) / (i + 1)
ses[ii] = (ses[ii] * i + d_err.std() / np.sqrt(d_err.size)) / (i +
1)
taus[ii] = (taus[ii] * i + tau.mean()) / (i + 1)
print "Noise level: %.2f (%03d) | Mean cost: %.2f +/- %.4f" % (
eta, np.sum(noise), means[ii], ses[ii])
plt.fill_between(etas * 100,
means - ses,
means + ses,
facecolor="grey",
alpha=.5)
plt.plot(etas * 100, means, color="black", linestyle="-", label="plane")
plt.plot(etas * 100,
taus * 45,
color="black",
linestyle="--",
label="tau-plane")
plt.ylim([0, 90])
plt.yticks([0, 30, 60, 90], [r'%d$^\circ$' % o for o in [0, 30, 60, 90]])
plt.xlim([0, 100])
plt.xlabel(r'noise ($\eta$)')
plt.ylabel("MAE ($^\circ$)")
# plt.legend()
if save:
plt.savefig(save)
plt.show()
def noise_test(save=None, mode=0, repeats=10, **kwargs):
from sphere.transform import sph2vec
print "Running noise test:", kwargs
modes = ['uniform', 'corridor', 'canopy']
print "Mode:", modes[mode]
plt.figure("noise-%s" % modes[mode], figsize=(4, 3))
n, omega = 60, 56
etas = np.linspace(0, 1, 21)
taus = np.zeros_like(etas)
means = np.zeros_like(etas)
ses = np.zeros_like(etas)
data = []
theta, phi, fit = angles_distribution(n, float(omega))
for i in xrange(repeats):
for ii, eta in enumerate(etas):
noise = get_noise(theta, phi, eta, mode=modes[mode])
d_err, d_eff, tau, _, _ = evaluate(n=n,
omega=omega,
noise=noise,
verbose=False,
tilting=True,
**kwargs)
data.append([tau, d_err])
means[ii] = (means[ii] * i + d_err.mean()) / (i + 1)
ses[ii] = (ses[ii] * i + d_err.std() / np.sqrt(d_err.size)) / (i +
1)
taus[ii] = (taus[ii] * i + tau.mean()) / (i + 1)
print "Noise level: %.2f (%03d) | Mean cost: %.2f +/- %.4f | tau: %.2f --> sigma: %2f" % (
eta, np.sum(noise), means[ii], ses[ii], taus[ii],
6. / taus[ii] + 6)
np.savez_compressed("../data/noise-%s.npz" % modes[mode],
x=np.array(data)[:, 0],
y=np.array(data)[:, 1])
sigmas = 6. / taus + 6.
plt.fill_between(etas * 100, means - ses, means + ses, facecolor="grey")
plt.plot(etas * 100, means, color="red", linestyle="-", label="tilting")
plt.plot(etas * 100,
taus * 45,
color="red",
linestyle="--",
label="tau-tilting")
plt.plot(etas * 100,
sigmas,
color="red",
linestyle="--",
label="sigma-tilting")
taus = np.zeros_like(etas)
means = np.zeros_like(etas)
ses = np.zeros_like(etas)
for i in xrange(repeats):
for ii, eta in enumerate(etas):
noise = get_noise(theta, phi, eta, mode=modes[mode])
d_err, d_eff, tau, _, _ = evaluate(n=n,
omega=omega,
noise=noise,
verbose=False,
tilting=False,
**kwargs)
data.append([tau, d_err])
means[ii] = (means[ii] * i + d_err.mean()) / (i + 1)
ses[ii] = (ses[ii] * i + d_err.std() / np.sqrt(d_err.size)) / (i +
1)
taus[ii] = (taus[ii] * i + tau.mean()) / (i + 1)
print "Noise level: %.2f (%03d) | Mean cost: %.2f +/- %.4f | tau: %.2f --> sigma: %2f" % (
eta, np.sum(noise), means[ii], ses[ii], taus[ii],
4. / taus[ii] + 2)
np.savez_compressed("../data/noise-%s.npz" % modes[mode],
x=np.array(data)[:, 0],
y=np.array(data)[:, 1])
sigmas = 4. / taus - 2.
plt.fill_between(etas * 100,
means - ses,
means + ses,
facecolor="grey",
alpha=.5)
plt.plot(etas * 100, means, color="black", linestyle="-", label="plane")
plt.plot(etas * 100,
taus * 45,
color="black",
linestyle="--",
label="tau-plane")
plt.plot(etas * 100,
sigmas,
color="black",
linestyle="--",
label="sigma-plane")
plt.ylim([0, 90])
plt.yticks([0, 30, 60, 90], [r'%d$^\circ$' % o for o in [0, 30, 60, 90]])
plt.xlim([0, 100])
plt.xlabel(r'noise ($\eta$)')
plt.ylabel("MAE ($^\circ$)")
# plt.legend()
if save:
plt.savefig(save)
plt.show()