def optim_fun(p):
np.random.seed(SEED)
start_pos = np.array([
np.random.uniform(*BOUNDS[0]),
np.random.uniform(*BOUNDS[1]),
np.random.uniform(*BOUNDS[2]),
])
# make agent and trajectory
ag = CenterlineInferringAgent(
tau=p[0], noise=p[1], bias=p[2], threshold=np.inf,
hit_trigger='peak', hit_influence=0,
k_0=np.eye(2), k_s=np.eye(2), tau_memory=1, bounds=BOUNDS)
traj = ag.track(pl, start_pos, DURATION, DT)
speeds = np.linalg.norm(traj['vs'], axis=1)
ws = np.linalg.norm(angular_velocity(traj['vs'], DT), axis=1)
ws = ws[~np.isnan(ws)]
ys = traj['xs'][:, 1]
ks_speeds = stats.ks_2samp(speeds, empirical['speeds'])[0]
ks_ws = stats.ks_2samp(ws, empirical['ws'])[0]
ks_ys = stats.ks_2samp(ys, empirical['ys'])[0]
val = ks_speeds + ks_ws + ks_ys
# punish unallowable values
if np.any(p < 0):
val += 10000
return val
def crossing_triggered_headings_early_late_vary_param(
SEED, SAVE_FILE, N_TRAJS, DURATION, DT, TAU, NOISE, BIAS,
HIT_INFLUENCE, SQRT_K_0, VARIABLE_PARAMS, BOUNDS, PL_CONC, PL_MEAN,
PL_STD, H_MIN_PEAK, H_MAX_PEAK, X_MIN_PEAK, X_MAX_PEAK,
EARLY_LESS_THAN, SUBTRACT_PEAK_HEADING, T_BEFORE, T_AFTER, T_INT_START,
T_INT_END, AX_GRID):
"""
Fly several agents through a simulated plume and plot their plume-crossing-triggered
headings.
"""
# try to open saved results
if os.path.isfile(SAVE_FILE):
print('Results file found. Loading results file.')
results = np.load(SAVE_FILE)
else:
print('Results file not found. Running analysis...')
np.random.seed(SEED)
# build plume
pl = GaussianLaminarPlume(PL_CONC, PL_MEAN, PL_STD)
# loop over all parameter sets
varying_params = []
fixed_params = []
early_late_heading_diffs_all = []
early_late_heading_diffs_lb_all = []
early_late_heading_diffs_ub_all = []
for variable_params in VARIABLE_PARAMS:
print('Variable params: {}'.format(variable_params))
assert set(variable_params.keys()) == set(
['threshold', 'tau_memory', 'sqrt_k_s'])
# identify which parameter is varying
for key, vals in variable_params.items():
if isinstance(vals, list):
varying_params.append((key, vals))
fixed_params.append(([(k, v)
for k, v in variable_params.items()
if k != key]))
n_param_sets = len(vals)
break
# make other parameters into lists so they can all be looped over nicely
for key, vals in variable_params.items():
if not isinstance(vals, list):
variable_params[key] = [vals for _ in range(n_param_sets)]
early_late_heading_diffs = []
early_late_heading_diffs_lb = []
early_late_heading_diffs_ub = []
for param_set_ctr in range(len(variable_params.values()[0])):
threshold = variable_params['threshold'][param_set_ctr]
hit_influence = HIT_INFLUENCE
tau_memory = variable_params['tau_memory'][param_set_ctr]
k_0 = np.array([
[SQRT_K_0**2, 0],
[0, SQRT_K_0**2],
])
k_s = np.array([
[variable_params['sqrt_k_s'][param_set_ctr]**2, 0],
[0, variable_params['sqrt_k_s'][param_set_ctr]**2],
])
# build tracking agent
ag = CenterlineInferringAgent(tau=TAU,
noise=NOISE,
bias=BIAS,
threshold=threshold,
hit_trigger='peak',
hit_influence=hit_influence,
tau_memory=tau_memory,
k_0=k_0,
k_s=k_s,
bounds=BOUNDS)
trajs = []
for _ in range(N_TRAJS):
# choose random start position
start_pos = np.array([
np.random.uniform(*BOUNDS[0]),
np.random.uniform(*BOUNDS[1]),
np.random.uniform(*BOUNDS[2]),
])
# make trajectory
traj = ag.track(plume=pl,
start_pos=start_pos,
duration=DURATION,
dt=DT)
traj['headings'] = heading(traj['vs'])[:, 2]
trajs.append(traj)
crossings_early = []
crossings_late = []
ts_before = int(T_BEFORE / DT)
ts_after = int(T_AFTER / DT)
for traj in trajs:
starts, onsets, peak_times, offsets, ends = \
segment_by_threshold(traj['odors'], threshold)[0].T
for ctr, (start, peak_time,
end) in enumerate(zip(starts, peak_times, ends)):
if not (H_MIN_PEAK <= traj['headings'][peak_time] <
H_MAX_PEAK):
continue
if not (X_MIN_PEAK <= traj['xs'][peak_time, 0] <
X_MAX_PEAK):
continue
crossing = np.nan * np.zeros((ts_before + ts_after, ))
ts_before_crossing = peak_time - start
ts_after_crossing = end - peak_time
if ts_before_crossing >= ts_before:
crossing[:ts_before] = traj['headings'][
peak_time - ts_before:peak_time]
else:
crossing[ts_before - ts_before_crossing:ts_before] = \
traj['headings'][start:peak_time]
if ts_after_crossing >= ts_after:
crossing[ts_before:] = traj['headings'][
peak_time:peak_time + ts_after]
else:
crossing[ts_before:ts_before + ts_after_crossing] = \
traj['headings'][peak_time:end]
if SUBTRACT_PEAK_HEADING:
crossing -= crossing[ts_before]
if ctr < EARLY_LESS_THAN:
crossings_early.append(crossing)
else:
crossings_late.append(crossing)
crossings_early = np.array(crossings_early)
crossings_late = np.array(crossings_late)
t = np.arange(-ts_before, ts_after) * DT
h_mean_early = np.nanmean(crossings_early, axis=0)
h_mean_late = np.nanmean(crossings_late, axis=0)
h_sem_early = nansem(crossings_early, axis=0)
h_sem_late = nansem(crossings_late, axis=0)
h_mean_diff = h_mean_late - h_mean_early
h_mean_diff_lb = h_mean_late - h_sem_late - (h_mean_early +
h_sem_early)
h_mean_diff_ub = h_mean_late + h_sem_late - (h_mean_early -
h_sem_early)
early_late_heading_diff = \
h_mean_diff[(t > T_INT_START) * (t <= T_INT_END)].mean()
early_late_heading_diff_lb = \
h_mean_diff_lb[(t > T_INT_START) * (t <= T_INT_END)].mean()
early_late_heading_diff_ub = \
h_mean_diff_ub[(t > T_INT_START) * (t <= T_INT_END)].mean()
early_late_heading_diffs.append(early_late_heading_diff)
early_late_heading_diffs_lb.append(early_late_heading_diff_lb)
early_late_heading_diffs_ub.append(early_late_heading_diff_ub)
early_late_heading_diffs_all.append(
np.array(early_late_heading_diffs))
early_late_heading_diffs_lb_all.append(
np.array(early_late_heading_diffs_lb))
early_late_heading_diffs_ub_all.append(
np.array(early_late_heading_diffs_ub))
# save results
results = np.array([{
'varying_params':
varying_params,
'fixed_params':
fixed_params,
'early_late_heading_diffs_all':
early_late_heading_diffs_all,
'early_late_heading_diffs_lb_all':
early_late_heading_diffs_lb_all,
'early_late_heading_diffs_ub_all':
early_late_heading_diffs_ub_all,
}])
np.save(SAVE_FILE, results)
results = results[0]
## MAKE PLOTS
fig_size = (5 * AX_GRID[1], 4 * AX_GRID[0])
fig, axs = plt.subplots(*AX_GRID, figsize=fig_size, tight_layout=True)
for ax_ctr in range(len(results['varying_params'])):
ax = axs.flatten()[ax_ctr]
ys_plot = results['early_late_heading_diffs_all'][ax_ctr]
ys_err = [
ys_plot - results['early_late_heading_diffs_lb_all'][ax_ctr],
results['early_late_heading_diffs_ub_all'][ax_ctr] - ys_plot
]
xs_name = results['varying_params'][ax_ctr][0]
xs_plot = np.arange(len(ys_plot))
ax.errorbar(xs_plot, ys_plot, yerr=ys_err, color='k', fmt='--o')
ax.axhline(0, color='gray')
if np.max(results['early_late_heading_diffs_ub_all'][ax_ctr]) > 0:
y_range = np.max(results['early_late_heading_diffs_ub_all'][ax_ctr]) - \
np.min(results['early_late_heading_diffs_lb_all'][ax_ctr])
else:
y_range = -np.min(
results['early_late_heading_diffs_lb_all'][ax_ctr])
y_min = np.min(
results['early_late_heading_diffs_lb_all'][ax_ctr]) - 0.1 * y_range
y_max = max(np.max(results['early_late_heading_diffs_ub_all'][ax_ctr]),
0) + 0.1 * y_range
ax.set_xlim(-1, len(ys_plot))
ax.set_xticks(xs_plot)
x_ticklabels = results['varying_params'][ax_ctr][1]
if xs_name == 'threshold':
x_ticklabels = [
'{0:.4f}'.format(xtl * (0.0476 / 526)) for xtl in x_ticklabels
]
ax.set_xticklabels(x_ticklabels)
ax.set_ylim(y_min, y_max)
if xs_name == 'tau_memory': x_label = 'tau_m (s)'
elif xs_name == 'threshold': x_label = 'threshold (% ethanol)'
else: x_label = xs_name
ax.set_xlabel(x_label)
ax.set_ylabel('mean heading difference\nfor late vs. early crossings')
for ax in axs.flatten():
set_font_size(ax, 16)
return fig
def example_trajectory_centerline_with_plume(SEED, DURATION, DT, TAU, NOISE,
BIAS, THRESHOLD, HIT_INFLUENCE,
TAU_MEMORY, K_0, K_S, BOUNDS,
PL_CONC, PL_MEAN, PL_STD):
"""
Create an example trajectory and plot some of the resulting covariates.
"""
# build plume and agent
pl = GaussianLaminarPlume(PL_CONC, PL_MEAN, PL_STD)
k_0 = K_0 * np.eye(2)
k_s = K_S * np.eye(2)
ag = CenterlineInferringAgent(tau=TAU,
noise=NOISE,
bias=BIAS,
threshold=THRESHOLD,
hit_trigger='peak',
hit_influence=HIT_INFLUENCE,
k_0=k_0,
k_s=k_s,
tau_memory=TAU_MEMORY,
bounds=BOUNDS)
# generate the trajectory
np.random.seed(SEED)
start_pos = np.array([
np.random.uniform(*BOUNDS[0]),
np.random.uniform(*BOUNDS[1]),
np.random.uniform(*BOUNDS[2]),
])
traj = ag.track(pl, start_pos, DURATION, DT)
# plot trajectory
fig = plt.figure(figsize=(15, 10), tight_layout=True)
axs = [fig.add_subplot(4, 1, 1)]
axs[-1].plot(traj['xs'][:, 0], traj['xs'][:, 1], lw=2, color='k', zorder=0)
axs[-1].scatter(traj['xs'][0, 0],
traj['xs'][0, 1],
lw=0,
c='r',
zorder=1,
s=100)
axs[-1].set_xlim(*BOUNDS[0])
axs[-1].set_ylim(*BOUNDS[1])
axs[-1].set_xlabel('x (m)')
axs[-1].set_ylabel('y (m)')
axs[-1].set_title('example trajectory')
# plot some histograms
speeds = np.linalg.norm(traj['vs'], axis=1)
ws = np.linalg.norm(angular_velocity(traj['vs'], DT), axis=1)
ws = ws[~np.isnan(ws)]
axs.append(fig.add_subplot(4, 2, 3))
axs.append(fig.add_subplot(4, 2, 4))
axs[-2].hist(speeds, bins=30, lw=0, normed=True)
axs[-1].hist(ws, bins=30, lw=0, normed=True)
axs[-2].set_xlabel('speed (m/s)')
axs[-1].set_xlabel('ang. vel (rad/s)')
axs[-2].set_ylabel('relative counts')
axs.append(fig.add_subplot(4, 1, 3))
axs.append(axs[-1].twinx())
ts = traj['ts']
odors = traj['odors']
cl_vars = np.trace(traj['centerline_ks'], axis1=1, axis2=2)
axs[-2].plot(ts, odors, color='r', lw=2)
axs[-1].plot(ts, cl_vars, color='k', lw=2)
axs[-2].set_xlabel('time (s)')
axs[-2].set_ylabel('odor')
axs[-1].set_ylabel('centerline var')
axs.append(fig.add_subplot(4, 1, 4))
axs.append(axs[-1].twinx())
bs = traj['bs']
axs[-2].plot(ts, odors, color='r', lw=2)
axs[-1].plot(ts, bs[:, 0], color='k', lw=2)
axs[-2].set_xlabel('time (s)')
axs[-2].set_ylabel('odor')
axs[-1].set_ylabel('upwind bias')
for ax in axs:
set_font_size(ax, 16)
return fig
def crossing_triggered_headings_early_late_centerline(
SEED, N_TRAJS, DURATION, DT, TAU, NOISE, BIAS, AGENT_THRESHOLD,
HIT_INFLUENCE, TAU_MEMORY, K_0, K_S, BOUNDS, PL_CONC, PL_MEAN, PL_STD,
ANALYSIS_THRESHOLD, H_MIN_PEAK, H_MAX_PEAK, X_MIN_PEAK, X_MAX_PEAK,
EARLY_LESS_THAN, SUBTRACT_PEAK_HEADING, T_BEFORE, T_AFTER, SAVE_FILE):
"""
Fly several agents through a simulated plume and plot their plume-crossing-triggered
headings.
"""
# build plume and agent
pl = GaussianLaminarPlume(PL_CONC, PL_MEAN, PL_STD)
k_0 = K_0 * np.eye(2)
k_s = K_S * np.eye(2)
ag = CenterlineInferringAgent(tau=TAU,
noise=NOISE,
bias=BIAS,
threshold=AGENT_THRESHOLD,
hit_trigger='peak',
hit_influence=HIT_INFLUENCE,
k_0=k_0,
k_s=k_s,
tau_memory=TAU_MEMORY,
bounds=BOUNDS)
# GENERATE TRAJECTORIES
np.random.seed(SEED)
trajs = []
for _ in range(N_TRAJS):
# choose random start position
start_pos = np.array([
np.random.uniform(*BOUNDS[0]),
np.random.uniform(*BOUNDS[1]),
np.random.uniform(*BOUNDS[2]),
])
# make trajectory
traj = ag.track(plume=pl,
start_pos=start_pos,
duration=DURATION,
dt=DT)
traj['headings'] = heading(traj['vs'])[:, 2]
trajs.append(traj)
# ANALYZE TRAJECTORIES
n_crossings = []
# collect early and late crossings
crossings_early = []
crossings_late = []
ts_before = int(T_BEFORE / DT)
ts_after = int(T_AFTER / DT)
for traj in trajs:
starts, onsets, peak_times, offsets, ends = \
segment_by_threshold(traj['odors'], ANALYSIS_THRESHOLD)[0].T
n_crossings.append(len(peak_times))
for ctr, (start, peak_time,
end) in enumerate(zip(starts, peak_times, ends)):
if not (H_MIN_PEAK <= traj['headings'][peak_time] < H_MAX_PEAK):
continue
if not (X_MIN_PEAK <= traj['xs'][peak_time, 0] < X_MAX_PEAK):
continue
crossing = np.nan * np.zeros((ts_before + ts_after, ))
ts_before_crossing = peak_time - start
ts_after_crossing = end - peak_time
if ts_before_crossing >= ts_before:
crossing[:ts_before] = traj['headings'][peak_time -
ts_before:peak_time]
else:
crossing[ts_before - ts_before_crossing:ts_before] = \
traj['headings'][start:peak_time]
if ts_after_crossing >= ts_after:
crossing[ts_before:] = traj['headings'][peak_time:peak_time +
ts_after]
else:
crossing[ts_before:ts_before + ts_after_crossing] = \
traj['headings'][peak_time:end]
if SUBTRACT_PEAK_HEADING:
crossing -= crossing[ts_before]
if ctr + 1 < EARLY_LESS_THAN:
crossings_early.append(crossing)
else:
crossings_late.append(crossing)
n_crossings = np.array(n_crossings)
crossings_early = np.array(crossings_early)
crossings_late = np.array(crossings_late)
t = np.arange(-ts_before, ts_after) * DT
p_vals = get_ks_p_vals(crossings_early, crossings_late)
h_mean_early = np.nanmean(crossings_early, axis=0)
h_sem_early = nansem(crossings_early, axis=0)
h_mean_late = np.nanmean(crossings_late, axis=0)
h_sem_late = nansem(crossings_late, axis=0)
save_data = {'t': t, 'early': h_mean_early, 'late': h_mean_late}
np.save(SAVE_FILE, np.array([save_data]))
fig, axs = plt.figure(figsize=(15, 15), tight_layout=True), []
axs.append(fig.add_subplot(3, 2, 1))
axs.append(fig.add_subplot(3, 2, 2))
handles = []
try:
handles.append(axs[0].plot(t,
h_mean_early,
lw=3,
color='b',
label='early')[0])
axs[0].fill_between(t,
h_mean_early - h_sem_early,
h_mean_early + h_sem_early,
color='b',
alpha=0.2)
except:
pass
try:
handles.append(axs[0].plot(t,
h_mean_late,
lw=3,
color='g',
label='late')[0])
axs[0].fill_between(t,
h_mean_late - h_sem_late,
h_mean_late + h_sem_late,
color='g',
alpha=0.2)
except:
pass
axs[0].set_xlabel('time since peak (s)')
## get y-position to plot p-vals at
y_min, y_max = axs[0].get_ylim()
y_range = y_max - y_min
y_p_vals = (y_min + 0.02 * y_range) * np.ones(len(p_vals))
y_p_vals_10 = y_p_vals.copy()
y_p_vals_05 = y_p_vals.copy()
y_p_vals_01 = y_p_vals.copy()
y_p_vals_10[p_vals > 0.1] = np.nan
y_p_vals_05[p_vals > 0.05] = np.nan
y_p_vals_01[p_vals > 0.01] = np.nan
axs[0].plot(t, y_p_vals_10, lw=4, color='gray')
axs[0].plot(t, y_p_vals_05, lw=4, color=(1, 0, 0))
axs[0].plot(t, y_p_vals_01, lw=4, color=(.25, 0, 0))
print('min p-value = {}'.format(np.nanmin(p_vals)))
if SUBTRACT_PEAK_HEADING:
axs[0].set_ylabel('change in heading (deg)')
else:
axs[0].set_ylabel('heading (deg)')
# axs[0].legend(handles=handles, fontsize=16)
bin_min = -0.5
bin_max = n_crossings.max() + 0.5
bins = np.linspace(bin_min, bin_max, bin_max - bin_min + 1, endpoint=True)
axs[1].hist(n_crossings, bins=bins, lw=0, normed=True)
axs[1].set_xlim(bin_min, bin_max)
axs[1].set_xlabel('number of crossings')
axs[1].set_ylabel('proportion of trajectories')
axs.append(fig.add_subplot(3, 1, 2))
axs[2].plot(trajs[0]['xs'][:, 0], trajs[0]['xs'][:, 1])
axs[2].axhline(0, color='gray', ls='--')
axs[2].set_xlabel('x (m)')
axs[2].set_ylabel('y (m)')
axs.append(fig.add_subplot(3, 1, 3))
all_xy = np.concatenate([traj['xs'][:, :2] for traj in trajs[:3000]],
axis=0)
x_bins = np.linspace(BOUNDS[0][0], BOUNDS[0][1], 66, endpoint=True)
y_bins = np.linspace(BOUNDS[1][0], BOUNDS[1][1], 30, endpoint=True)
axs[3].hist2d(all_xy[:, 0], all_xy[:, 1], bins=(x_bins, y_bins))
axs[3].set_xlabel('x (m)')
axs[3].set_ylabel('y (m)')
for ax in axs:
set_font_size(ax, 20)
return fig
def crossing_triggered_headings_all(
SEED, N_TRAJS, DURATION, DT, TAU, NOISE, BIAS, AGENT_THRESHOLD,
HIT_INFLUENCE, TAU_MEMORY, K_0, K_S, BOUNDS, PL_CONC, PL_MEAN, PL_STD,
ANALYSIS_THRESHOLD, H_MIN_PEAK, H_MAX_PEAK, SUBTRACT_PEAK_HEADING,
T_BEFORE, T_AFTER, Y_LIM):
"""
Fly several agents through a simulated plume and plot their plume-crossing-triggered
headings.
"""
# build plume and agent
pl = GaussianLaminarPlume(PL_CONC, PL_MEAN, PL_STD)
k_0 = K_0 * np.eye(2)
k_s = K_S * np.eye(2)
ag = CenterlineInferringAgent(tau=TAU,
noise=NOISE,
bias=BIAS,
threshold=AGENT_THRESHOLD,
hit_trigger='peak',
hit_influence=HIT_INFLUENCE,
k_0=k_0,
k_s=k_s,
tau_memory=TAU_MEMORY,
bounds=BOUNDS)
# generate trajectories
np.random.seed(SEED)
trajs = []
for _ in range(N_TRAJS):
# choose random start position
start_pos = np.array([
np.random.uniform(*BOUNDS[0]),
np.random.uniform(*BOUNDS[1]),
np.random.uniform(*BOUNDS[2]),
])
# make trajectory
traj = ag.track(plume=pl,
start_pos=start_pos,
duration=DURATION,
dt=DT)
traj['headings'] = heading(traj['vs'])[:, 2]
trajs.append(traj)
crossings = []
ts_before = int(T_BEFORE / DT)
ts_after = int(T_AFTER / DT)
for traj in trajs:
starts, onsets, peak_times, offsets, ends = \
segment_by_threshold(traj['odors'], ANALYSIS_THRESHOLD)[0].T
for start, peak_time, end in zip(starts, peak_times, ends):
if not (H_MIN_PEAK <= traj['headings'][peak_time] < H_MAX_PEAK):
continue
crossing = np.nan * np.zeros((ts_before + ts_after, ))
ts_before_crossing = peak_time - start
ts_after_crossing = end - peak_time
if ts_before_crossing >= ts_before:
crossing[:ts_before] = traj['headings'][peak_time -
ts_before:peak_time]
else:
crossing[ts_before - ts_before_crossing:ts_before] = \
traj['headings'][start:peak_time]
if ts_after_crossing >= ts_after:
crossing[ts_before:] = traj['headings'][peak_time:peak_time +
ts_after]
else:
crossing[ts_before:ts_before + ts_after_crossing] = \
traj['headings'][peak_time:end]
if SUBTRACT_PEAK_HEADING:
crossing -= crossing[ts_before]
crossings.append(crossing)
crossings = np.array(crossings)
t = np.arange(-ts_before, ts_after) * DT
fig, ax = plt.subplots(1, 1, figsize=(8, 6), tight_layout=True)
h_mean = np.nanmean(crossings, axis=0)
h_sem = nansem(crossings, axis=0)
ax.plot(t, crossings.T, lw=0.5, alpha=0.5, color='c', zorder=0)
ax.plot(t, h_mean, lw=3, color='k')
ax.fill_between(t, h_mean - h_sem, h_mean + h_sem, color='k', alpha=0.2)
ax.axvline(0, ls='--', color='gray')
ax.set_ylim(*Y_LIM)
ax.set_xlabel('time since peak (s)')
if SUBTRACT_PEAK_HEADING:
ax.set_ylabel('change in heading (deg)')
else:
ax.set_ylabel('heading (deg)')
set_font_size(ax, 16)
return fig
def example_trajectory_centerline_no_plume(SEED, DURATION, DT, TAU, NOISE,
BIAS, BOUNDS):
"""
Create an example trajectory and plot some of the resulting covariates.
"""
# build plume and agent
pl = GaussianLaminarPlume(0, np.array([0., 0]), [1., 1.])
ag = CenterlineInferringAgent(tau=TAU,
noise=NOISE,
bias=BIAS,
threshold=np.inf,
hit_trigger='peak',
hit_influence=0,
k_0=np.eye(2),
k_s=np.eye(2),
tau_memory=1,
bounds=BOUNDS)
# generate the trajectory
np.random.seed(SEED)
start_pos = np.array([
np.random.uniform(*BOUNDS[0]),
np.random.uniform(*BOUNDS[1]),
np.random.uniform(*BOUNDS[2]),
])
traj = ag.track(pl, start_pos, DURATION, DT)
# plot trajectory
fig = plt.figure(figsize=(15, 10), tight_layout=True)
axs = []
axs.append(fig.add_subplot(2, 1, 1))
axs[0].plot(traj['xs'][:, 0], traj['xs'][:, 1], lw=2, color='k', zorder=0)
axs[0].scatter(traj['xs'][0, 0],
traj['xs'][0, 1],
lw=0,
c='r',
zorder=1,
s=100)
axs[0].set_xlim(*BOUNDS[0])
axs[0].set_ylim(*BOUNDS[1])
axs[0].set_xlabel('x (m)')
axs[0].set_ylabel('y (m)')
axs[0].set_title('example trajectory')
# plot some histograms
speeds = np.linalg.norm(traj['vs'], axis=1)
ws = np.linalg.norm(angular_velocity(traj['vs'], DT), axis=1)
ws = ws[~np.isnan(ws)]
axs.append(fig.add_subplot(2, 2, 3))
axs.append(fig.add_subplot(2, 2, 4))
axs[1].hist(speeds, bins=30, lw=0, normed=True)
axs[2].hist(ws, bins=30, lw=0, normed=True)
axs[1].set_xlabel('speed (m/s)')
axs[2].set_xlabel('ang. vel (rad/s)')
axs[1].set_ylabel('relative counts')
for ax in axs:
set_font_size(ax, 16)
return fig
def example_trajectory_with_plume(
SEED, DURATION, DT, TAU, NOISE, BIAS, THRESHOLD, HIT_INFLUENCE,
TAU_MEMORY, K_0, K_S, BOUNDS,
PL_CONC, PL_MEAN, PL_STD):
"""
Create an example trajectory and plot some of the resulting covariates.
"""
# build plume and agent
pl = GaussianLaminarPlume(PL_CONC, PL_MEAN, PL_STD)
k_0 = K_0 * np.eye(2)
k_s = K_S * np.eye(2)
ag = CenterlineInferringAgent(
tau=TAU, noise=NOISE, bias=BIAS, threshold=THRESHOLD,
hit_trigger='peak', hit_influence=HIT_INFLUENCE,
k_0=k_0, k_s=k_s, tau_memory=TAU_MEMORY, bounds=BOUNDS)
# generate the trajectory
np.random.seed(SEED)
start_pos = np.array([
np.random.uniform(*BOUNDS[0]),
np.random.uniform(*BOUNDS[1]),
np.random.uniform(*BOUNDS[2]),
])
traj = ag.track(pl, start_pos, DURATION, DT)
# plot trajectory
fig = plt.figure(figsize=(15, 10), tight_layout=True)
axs = [fig.add_subplot(4, 1, 1)]
axs[-1].plot(traj['xs'][:, 0], traj['xs'][:, 1], lw=2, color='k', zorder=0)
axs[-1].scatter(traj['xs'][0, 0], traj['xs'][0, 1], lw=0, c='r', zorder=1, s=100)
axs[-1].set_xlim(*BOUNDS[0])
axs[-1].set_ylim(*BOUNDS[1])
axs[-1].set_xlabel('x (m)')
axs[-1].set_ylabel('y (m)')
axs[-1].set_title('example trajectory')
# plot some histograms
speeds = np.linalg.norm(traj['vs'], axis=1)
ws = np.linalg.norm(angular_velocity(traj['vs'], DT), axis=1)
ws = ws[~np.isnan(ws)]
axs.append(fig.add_subplot(4, 2, 3))
axs.append(fig.add_subplot(4, 2, 4))
axs[-2].hist(speeds, bins=30, lw=0, normed=True)
axs[-1].hist(ws, bins=30, lw=0, normed=True)
axs[-2].set_xlabel('speed (m/s)')
axs[-1].set_xlabel('ang. vel (rad/s)')
axs[-2].set_ylabel('relative counts')
axs.append(fig.add_subplot(4, 1, 3))
axs.append(axs[-1].twinx())
ts = traj['ts']
odors = traj['odors']
cl_vars = np.trace(traj['centerline_ks'], axis1=1, axis2=2)
axs[-2].plot(ts, odors, color='r', lw=2)
axs[-1].plot(ts, cl_vars, color='k', lw=2)
axs[-2].set_xlabel('time (s)')
axs[-2].set_ylabel('odor')
axs[-1].set_ylabel('centerline var')
axs.append(fig.add_subplot(4, 1, 4))
axs.append(axs[-1].twinx())
bs = traj['bs']
axs[-2].plot(ts, odors, color='r', lw=2)
axs[-1].plot(ts, bs[:, 0], color='k', lw=2)
axs[-2].set_xlabel('time (s)')
axs[-2].set_ylabel('odor')
axs[-1].set_ylabel('upwind bias')
for ax in axs:
set_font_size(ax, 16)
return fig
def crossing_triggered_headings_early_late_vary_param(
SEED, SAVE_FILE, N_TRAJS, DURATION, DT,
TAU, NOISE, BIAS, HIT_INFLUENCE, SQRT_K_0,
VARIABLE_PARAMS, BOUNDS,
PL_CONC, PL_MEAN, PL_STD,
H_MIN_PEAK, H_MAX_PEAK,
X_MIN_PEAK, X_MAX_PEAK,
EARLY_LESS_THAN,
SUBTRACT_PEAK_HEADING, T_BEFORE, T_AFTER,
T_INT_START, T_INT_END, AX_GRID):
"""
Fly several agents through a simulated plume and plot their plume-crossing-triggered
headings.
"""
# try to open saved results
if os.path.isfile(SAVE_FILE):
print('Results file found. Loading results file.')
results = np.load(SAVE_FILE)
else:
print('Results file not found. Running analysis...')
np.random.seed(SEED)
# build plume
pl = GaussianLaminarPlume(PL_CONC, PL_MEAN, PL_STD)
# loop over all parameter sets
varying_params = []
fixed_params = []
early_late_heading_diffs_all = []
early_late_heading_diffs_lb_all = []
early_late_heading_diffs_ub_all = []
for variable_params in VARIABLE_PARAMS:
print('Variable params: {}'.format(variable_params))
assert set(variable_params.keys()) == set(
['threshold', 'tau_memory', 'sqrt_k_s'])
# identify which parameter is varying
for key, vals in variable_params.items():
if isinstance(vals, list):
varying_params.append((key, vals))
fixed_params.append((
[(k, v) for k, v in variable_params.items() if k != key]))
n_param_sets = len(vals)
break
# make other parameters into lists so they can all be looped over nicely
for key, vals in variable_params.items():
if not isinstance(vals, list):
variable_params[key] = [vals for _ in range(n_param_sets)]
early_late_heading_diffs = []
early_late_heading_diffs_lb = []
early_late_heading_diffs_ub = []
for param_set_ctr in range(len(variable_params.values()[0])):
threshold = variable_params['threshold'][param_set_ctr]
hit_influence = HIT_INFLUENCE
tau_memory = variable_params['tau_memory'][param_set_ctr]
k_0 = np.array([
[SQRT_K_0 ** 2, 0],
[0, SQRT_K_0 ** 2],
])
k_s = np.array([
[variable_params['sqrt_k_s'][param_set_ctr] ** 2, 0],
[0, variable_params['sqrt_k_s'][param_set_ctr] ** 2],
])
# build tracking agent
ag = CenterlineInferringAgent(
tau=TAU, noise=NOISE, bias=BIAS, threshold=threshold,
hit_trigger='peak', hit_influence=hit_influence, tau_memory=tau_memory,
k_0=k_0, k_s=k_s, bounds=BOUNDS)
trajs = []
for _ in range(N_TRAJS):
# choose random start position
start_pos = np.array([
np.random.uniform(*BOUNDS[0]),
np.random.uniform(*BOUNDS[1]),
np.random.uniform(*BOUNDS[2]),
])
# make trajectory
traj = ag.track(plume=pl, start_pos=start_pos, duration=DURATION, dt=DT)
traj['headings'] = heading(traj['vs'])[:, 2]
trajs.append(traj)
crossings_early = []
crossings_late = []
ts_before = int(T_BEFORE / DT)
ts_after = int(T_AFTER / DT)
for traj in trajs:
starts, onsets, peak_times, offsets, ends = \
segment_by_threshold(traj['odors'], threshold)[0].T
for ctr, (start, peak_time, end) in enumerate(zip(starts, peak_times, ends)):
if not (H_MIN_PEAK <= traj['headings'][peak_time] < H_MAX_PEAK):
continue
if not (X_MIN_PEAK <= traj['xs'][peak_time, 0] < X_MAX_PEAK):
continue
crossing = np.nan * np.zeros((ts_before + ts_after,))
ts_before_crossing = peak_time - start
ts_after_crossing = end - peak_time
if ts_before_crossing >= ts_before:
crossing[:ts_before] = traj['headings'][peak_time - ts_before:peak_time]
else:
crossing[ts_before - ts_before_crossing:ts_before] = \
traj['headings'][start:peak_time]
if ts_after_crossing >= ts_after:
crossing[ts_before:] = traj['headings'][peak_time:peak_time + ts_after]
else:
crossing[ts_before:ts_before + ts_after_crossing] = \
traj['headings'][peak_time:end]
if SUBTRACT_PEAK_HEADING:
crossing -= crossing[ts_before]
if ctr < EARLY_LESS_THAN:
crossings_early.append(crossing)
else:
crossings_late.append(crossing)
crossings_early = np.array(crossings_early)
crossings_late = np.array(crossings_late)
t = np.arange(-ts_before, ts_after) * DT
h_mean_early = np.nanmean(crossings_early, axis=0)
h_mean_late = np.nanmean(crossings_late, axis=0)
h_sem_early = nansem(crossings_early, axis=0)
h_sem_late = nansem(crossings_late, axis=0)
h_mean_diff = h_mean_late - h_mean_early
h_mean_diff_lb = h_mean_late - h_sem_late - (h_mean_early + h_sem_early)
h_mean_diff_ub = h_mean_late + h_sem_late - (h_mean_early - h_sem_early)
early_late_heading_diff = \
h_mean_diff[(t > T_INT_START) * (t <= T_INT_END)].mean()
early_late_heading_diff_lb = \
h_mean_diff_lb[(t > T_INT_START) * (t <= T_INT_END)].mean()
early_late_heading_diff_ub = \
h_mean_diff_ub[(t > T_INT_START) * (t <= T_INT_END)].mean()
early_late_heading_diffs.append(early_late_heading_diff)
early_late_heading_diffs_lb.append(early_late_heading_diff_lb)
early_late_heading_diffs_ub.append(early_late_heading_diff_ub)
early_late_heading_diffs_all.append(np.array(early_late_heading_diffs))
early_late_heading_diffs_lb_all.append(np.array(early_late_heading_diffs_lb))
early_late_heading_diffs_ub_all.append(np.array(early_late_heading_diffs_ub))
# save results
results = np.array([
{
'varying_params': varying_params,
'fixed_params': fixed_params,
'early_late_heading_diffs_all': early_late_heading_diffs_all,
'early_late_heading_diffs_lb_all': early_late_heading_diffs_lb_all,
'early_late_heading_diffs_ub_all': early_late_heading_diffs_ub_all,
}])
np.save(SAVE_FILE, results)
results = results[0]
## MAKE PLOTS
fig_size = (5 * AX_GRID[1], 4 * AX_GRID[0])
fig, axs = plt.subplots(*AX_GRID, figsize=fig_size, tight_layout=True)
for ax_ctr in range(len(results['varying_params'])):
ax = axs.flatten()[ax_ctr]
ys_plot = results['early_late_heading_diffs_all'][ax_ctr]
ys_err = [
ys_plot - results['early_late_heading_diffs_lb_all'][ax_ctr],
results['early_late_heading_diffs_ub_all'][ax_ctr] - ys_plot
]
xs_name = results['varying_params'][ax_ctr][0]
xs_plot = np.arange(len(ys_plot))
ax.errorbar(
xs_plot, ys_plot, yerr=ys_err, color='k', fmt='--o')
ax.axhline(0, color='gray')
if np.max(results['early_late_heading_diffs_ub_all'][ax_ctr]) > 0:
y_range = np.max(results['early_late_heading_diffs_ub_all'][ax_ctr]) - \
np.min(results['early_late_heading_diffs_lb_all'][ax_ctr])
else:
y_range = -np.min(results['early_late_heading_diffs_lb_all'][ax_ctr])
y_min = np.min(
results['early_late_heading_diffs_lb_all'][ax_ctr]) - 0.1 * y_range
y_max = max(np.max(
results['early_late_heading_diffs_ub_all'][ax_ctr]), 0) + 0.1 * y_range
ax.set_xlim(-1, len(ys_plot))
ax.set_xticks(xs_plot)
x_ticklabels = results['varying_params'][ax_ctr][1]
if xs_name == 'threshold':
x_ticklabels = ['{0:.4f}'.format(xtl * (0.0476/526)) for xtl in x_ticklabels]
ax.set_xticklabels(x_ticklabels)
ax.set_ylim(y_min, y_max)
if xs_name == 'tau_memory': x_label = 'tau_m (s)'
elif xs_name == 'threshold': x_label = 'threshold (% ethanol)'
else: x_label = xs_name
ax.set_xlabel(x_label)
ax.set_ylabel('mean heading difference\nfor late vs. early crossings')
for ax in axs.flatten():
set_font_size(ax, 16)
return fig
def crossing_triggered_headings_early_late(
SEED, N_TRAJS, DURATION, DT,
TAU, NOISE, BIAS, AGENT_THRESHOLD,
HIT_INFLUENCE, TAU_MEMORY,
K_0, K_S, BOUNDS,
PL_CONC, PL_MEAN, PL_STD,
ANALYSIS_THRESHOLD,
H_MIN_PEAK, H_MAX_PEAK,
X_MIN_PEAK, X_MAX_PEAK,
EARLY_LESS_THAN,
SUBTRACT_PEAK_HEADING, T_BEFORE, T_AFTER):
"""
Fly several agents through a simulated plume and plot their plume-crossing-triggered
headings.
"""
# build plume and agent
pl = GaussianLaminarPlume(PL_CONC, PL_MEAN, PL_STD)
k_0 = K_0 * np.eye(2)
k_s = K_S * np.eye(2)
ag = CenterlineInferringAgent(
tau=TAU, noise=NOISE, bias=BIAS, threshold=AGENT_THRESHOLD,
hit_trigger='peak', hit_influence=HIT_INFLUENCE,
k_0=k_0, k_s=k_s, tau_memory=TAU_MEMORY, bounds=BOUNDS)
# GENERATE TRAJECTORIES
np.random.seed(SEED)
trajs = []
for _ in range(N_TRAJS):
# choose random start position
start_pos = np.array([
np.random.uniform(*BOUNDS[0]),
np.random.uniform(*BOUNDS[1]),
np.random.uniform(*BOUNDS[2]),
])
# make trajectory
traj = ag.track(plume=pl, start_pos=start_pos, duration=DURATION, dt=DT)
traj['headings'] = heading(traj['vs'])[:, 2]
trajs.append(traj)
# ANALYZE TRAJECTORIES
n_crossings = []
# collect early and late crossings
crossings_early = []
crossings_late = []
ts_before = int(T_BEFORE / DT)
ts_after = int(T_AFTER / DT)
for traj in trajs:
starts, onsets, peak_times, offsets, ends = \
segment_by_threshold(traj['odors'], ANALYSIS_THRESHOLD)[0].T
n_crossings.append(len(peak_times))
for ctr, (start, peak_time, end) in enumerate(zip(starts, peak_times, ends)):
if not (H_MIN_PEAK <= traj['headings'][peak_time] < H_MAX_PEAK):
continue
if not (X_MIN_PEAK <= traj['xs'][peak_time, 0] < X_MAX_PEAK):
continue
crossing = np.nan * np.zeros((ts_before + ts_after,))
ts_before_crossing = peak_time - start
ts_after_crossing = end - peak_time
if ts_before_crossing >= ts_before:
crossing[:ts_before] = traj['headings'][peak_time - ts_before:peak_time]
else:
crossing[ts_before - ts_before_crossing:ts_before] = \
traj['headings'][start:peak_time]
if ts_after_crossing >= ts_after:
crossing[ts_before:] = traj['headings'][peak_time:peak_time + ts_after]
else:
crossing[ts_before:ts_before + ts_after_crossing] = \
traj['headings'][peak_time:end]
if SUBTRACT_PEAK_HEADING:
crossing -= crossing[ts_before]
if ctr < EARLY_LESS_THAN:
crossings_early.append(crossing)
else:
crossings_late.append(crossing)
n_crossings = np.array(n_crossings)
crossings_early = np.array(crossings_early)
crossings_late = np.array(crossings_late)
t = np.arange(-ts_before, ts_after) * DT
h_mean_early = np.nanmean(crossings_early, axis=0)
h_sem_early = nansem(crossings_early, axis=0)
h_mean_late = np.nanmean(crossings_late, axis=0)
h_sem_late = nansem(crossings_late, axis=0)
fig, axs = plt.figure(figsize=(15, 15), tight_layout=True), []
axs.append(fig.add_subplot(3, 2, 1))
axs.append(fig.add_subplot(3, 2, 2))
handles = []
try:
handles.append(axs[0].plot(t, h_mean_early, lw=3, color='b', label='early')[0])
axs[0].fill_between(t, h_mean_early - h_sem_early, h_mean_early + h_sem_early,
color='b', alpha=0.2)
except:
pass
try:
handles.append(axs[0].plot(t, h_mean_late, lw=3, color='g', label='late')[0])
axs[0].fill_between(t, h_mean_late - h_sem_late, h_mean_late + h_sem_late,
color='g', alpha=0.2)
except:
pass
axs[0].axvline(0, ls='--', color='gray')
axs[0].set_xlabel('time since peak (s)')
if SUBTRACT_PEAK_HEADING:
axs[0].set_ylabel('change in heading (deg)')
else:
axs[0].set_ylabel('heading (deg)')
axs[0].legend(handles=handles, fontsize=16)
bin_min = -0.5
bin_max = n_crossings.max() + 0.5
bins = np.linspace(bin_min, bin_max, bin_max - bin_min + 1, endpoint=True)
axs[1].hist(n_crossings, bins=bins, lw=0, normed=True)
axs[1].set_xlim(bin_min, bin_max)
axs[1].set_xlabel('number of crossings')
axs[1].set_ylabel('proportion of trajectories')
axs.append(fig.add_subplot(3, 1, 2))
axs[2].plot(trajs[0]['xs'][:, 0], trajs[0]['xs'][:, 1])
axs[2].axhline(0, color='gray', ls='--')
axs[2].set_xlabel('x (m)')
axs[2].set_ylabel('y (m)')
axs.append(fig.add_subplot(3, 1, 3))
all_xy = np.concatenate([traj['xs'][:, :2] for traj in trajs[:3000]], axis=0)
x_bins = np.linspace(BOUNDS[0][0], BOUNDS[0][1], 66, endpoint=True)
y_bins = np.linspace(BOUNDS[1][0], BOUNDS[1][1], 30, endpoint=True)
axs[3].hist2d(all_xy[:, 0], all_xy[:, 1], bins=(x_bins, y_bins))
axs[3].set_xlabel('x (m)')
axs[3].set_ylabel('y (m)')
for ax in axs:
set_font_size(ax, 20)
return fig
def crossing_triggered_headings_all(
SEED,
N_TRAJS, DURATION, DT,
TAU, NOISE, BIAS, AGENT_THRESHOLD,
HIT_INFLUENCE, TAU_MEMORY, K_0, K_S,
BOUNDS,
PL_CONC, PL_MEAN, PL_STD,
ANALYSIS_THRESHOLD, H_MIN_PEAK, H_MAX_PEAK,
SUBTRACT_PEAK_HEADING, T_BEFORE, T_AFTER, Y_LIM):
"""
Fly several agents through a simulated plume and plot their plume-crossing-triggered
headings.
"""
# build plume and agent
pl = GaussianLaminarPlume(PL_CONC, PL_MEAN, PL_STD)
k_0 = K_0 * np.eye(2)
k_s = K_S * np.eye(2)
ag = CenterlineInferringAgent(
tau=TAU, noise=NOISE, bias=BIAS, threshold=AGENT_THRESHOLD,
hit_trigger='peak', hit_influence=HIT_INFLUENCE,
k_0=k_0, k_s=k_s, tau_memory=TAU_MEMORY, bounds=BOUNDS)
# generate trajectories
np.random.seed(SEED)
trajs = []
for _ in range(N_TRAJS):
# choose random start position
start_pos = np.array([
np.random.uniform(*BOUNDS[0]),
np.random.uniform(*BOUNDS[1]),
np.random.uniform(*BOUNDS[2]),
])
# make trajectory
traj = ag.track(plume=pl, start_pos=start_pos, duration=DURATION, dt=DT)
traj['headings'] = heading(traj['vs'])[:, 2]
trajs.append(traj)
crossings = []
ts_before = int(T_BEFORE / DT)
ts_after = int(T_AFTER / DT)
for traj in trajs:
starts, onsets, peak_times, offsets, ends = \
segment_by_threshold(traj['odors'], ANALYSIS_THRESHOLD)[0].T
for start, peak_time, end in zip(starts, peak_times, ends):
if not (H_MIN_PEAK <= traj['headings'][peak_time] < H_MAX_PEAK):
continue
crossing = np.nan * np.zeros((ts_before + ts_after,))
ts_before_crossing = peak_time - start
ts_after_crossing = end - peak_time
if ts_before_crossing >= ts_before:
crossing[:ts_before] = traj['headings'][peak_time - ts_before:peak_time]
else:
crossing[ts_before - ts_before_crossing:ts_before] = \
traj['headings'][start:peak_time]
if ts_after_crossing >= ts_after:
crossing[ts_before:] = traj['headings'][peak_time:peak_time + ts_after]
else:
crossing[ts_before:ts_before + ts_after_crossing] = \
traj['headings'][peak_time:end]
if SUBTRACT_PEAK_HEADING:
crossing -= crossing[ts_before]
crossings.append(crossing)
crossings = np.array(crossings)
t = np.arange(-ts_before, ts_after) * DT
fig, ax = plt.subplots(1, 1, figsize=(8, 6), tight_layout=True)
h_mean = np.nanmean(crossings, axis=0)
h_sem = nansem(crossings, axis=0)
ax.plot(t, crossings.T, lw=0.5, alpha=0.5, color='c', zorder=0)
ax.plot(t, h_mean, lw=3, color='k')
ax.fill_between(t, h_mean - h_sem, h_mean + h_sem, color='k', alpha=0.2)
ax.axvline(0, ls='--', color='gray')
ax.set_ylim(*Y_LIM)
ax.set_xlabel('time since peak (s)')
if SUBTRACT_PEAK_HEADING:
ax.set_ylabel('change in heading (deg)')
else:
ax.set_ylabel('heading (deg)')
set_font_size(ax, 16)
return fig
def optimize_model_params(
SEED,
DURATION, DT, BOUNDS,
EXPERIMENT, ODOR_STATE,
MAX_TRAJS_EMPIRICAL,
N_TIME_POINTS_EMPIRICAL,
SAVE_FILE_PREFIX,
INITIAL_PARAMS, MAX_ITERS):
"""
Find optimal model parameters by fitting speed and angular velocity distributions of empirical
data.
"""
# check to see if empirical time points have already been saved
file_name = '{}_{}_odor_{}.npy'.format(SAVE_FILE_PREFIX, EXPERIMENT, ODOR_STATE)
if os.path.isfile(file_name):
empirical = np.load(file_name)[0]
else:
print('extracting time points from data')
# get all trajectories
trajs = session.query(models.Trajectory).filter_by(
experiment_id=EXPERIMENT, odor_state=ODOR_STATE, clean=True).\
limit(MAX_TRAJS_EMPIRICAL).all()
# get all speeds and angular velocities
cc = np.concatenate
speeds_empirical = cc([traj.velocities_a(session) for traj in trajs])
ws_empirical = cc([traj.angular_velocities_a(session) for traj in trajs])
ys_empirical = cc([traj.timepoint_field(session, 'position_y') for traj in trajs])
# sample a set of speeds and ws
np.random.seed(SEED)
speeds_empirical = np.random.choice(speeds_empirical, N_TIME_POINTS_EMPIRICAL, replace=False)
ws_empirical = np.random.choice(ws_empirical, N_TIME_POINTS_EMPIRICAL, replace=False)
ys_empirical = np.random.choice(ys_empirical, N_TIME_POINTS_EMPIRICAL, replace=False)
empirical = {'speeds': speeds_empirical, 'ws': ws_empirical, 'ys': ys_empirical}
# save them for easy access next time
np.save(file_name, np.array([empirical]))
print('performing optimization')
# make a plume
pl = GaussianLaminarPlume(0, np.zeros((2,)), np.ones((2,)))
# define function to be optimized
def optim_fun(p):
np.random.seed(SEED)
start_pos = np.array([
np.random.uniform(*BOUNDS[0]),
np.random.uniform(*BOUNDS[1]),
np.random.uniform(*BOUNDS[2]),
])
# make agent and trajectory
ag = CenterlineInferringAgent(
tau=p[0], noise=p[1], bias=p[2], threshold=np.inf,
hit_trigger='peak', hit_influence=0,
k_0=np.eye(2), k_s=np.eye(2), tau_memory=1, bounds=BOUNDS)
traj = ag.track(pl, start_pos, DURATION, DT)
speeds = np.linalg.norm(traj['vs'], axis=1)
ws = np.linalg.norm(angular_velocity(traj['vs'], DT), axis=1)
ws = ws[~np.isnan(ws)]
ys = traj['xs'][:, 1]
ks_speeds = stats.ks_2samp(speeds, empirical['speeds'])[0]
ks_ws = stats.ks_2samp(ws, empirical['ws'])[0]
ks_ys = stats.ks_2samp(ys, empirical['ys'])[0]
val = ks_speeds + ks_ws + ks_ys
# punish unallowable values
if np.any(p < 0):
val += 10000
return val
# optimize it
p_best = optimize.fmin(optim_fun, np.array(INITIAL_PARAMS), maxiter=MAX_ITERS)
# generate one final trajectory
np.random.seed(SEED)
start_pos = np.array([
np.random.uniform(*BOUNDS[0]),
np.random.uniform(*BOUNDS[1]),
np.random.uniform(*BOUNDS[2]),
])
ag = CenterlineInferringAgent(
tau=p_best[0], noise=p_best[1], bias=p_best[2], threshold=np.inf,
hit_trigger='peak', hit_influence=0,
k_0=np.eye(2), k_s=np.eye(2), tau_memory=1, bounds=BOUNDS)
traj = ag.track(pl, start_pos, DURATION, DT)
speeds = np.linalg.norm(traj['vs'], axis=1)
ws = np.linalg.norm(angular_velocity(traj['vs'], DT), axis=1)
ws = ws[~np.isnan(ws)]
ys = traj['xs'][:, 1]
# make plots of things that have been optimized
## get bins
speed_max = max(speeds.max(), empirical['speeds'].max())
bins_speed = np.linspace(0, speed_max, 41, endpoint=True)
bincs_speed = 0.5 * (bins_speed[:-1] + bins_speed[1:])
w_max = max(ws.max(), empirical['ws'].max())
bins_w = np.linspace(0, w_max, 41, endpoint=True)
bincs_w = 0.5 * (bins_w[:-1] + bins_w[1:])
bins_y = np.linspace(BOUNDS[1][0], BOUNDS[1][1], 41, endpoint=True)
bincs_y = 0.5 * (bins_y[:-1] + bins_y[1:])
cts_speed, _ = np.histogram(speeds, bins=bins_speed, normed=True)
cts_speed_empirical, _ = np.histogram(empirical['speeds'], bins=bins_speed, normed=True)
cts_w, _ = np.histogram(ws, bins=bins_w, normed=True)
cts_w_empirical, _ = np.histogram(empirical['ws'], bins=bins_w, normed=True)
cts_y, _ = np.histogram(ys, bins=bins_y, normed=True)
cts_y_empirical, _ = np.histogram(empirical['ys'], bins=bins_y, normed=True)
fig = plt.figure(figsize=(15, 8), tight_layout=True)
axs = []
axs.append(fig.add_subplot(2, 3, 1))
axs.append(fig.add_subplot(2, 3, 2))
axs.append(fig.add_subplot(2, 3, 3))
axs[0].plot(bincs_speed, cts_speed_empirical, lw=2, color='k')
axs[0].plot(bincs_speed, cts_speed, lw=2, color='r')
axs[0].set_xlabel('speed (m/s)')
axs[0].set_ylabel('rel. counts')
axs[0].legend(['data', 'model'], fontsize=16)
axs[1].plot(bincs_w, cts_w_empirical, lw=2, color='k')
axs[1].plot(bincs_w, cts_w, lw=2, color='r')
axs[1].set_xlabel('ang. vel. (rad/s)')
axs[2].plot(bincs_y, cts_y_empirical, lw=2, color='k')
axs[2].plot(bincs_y, cts_y, lw=2, color='r')
axs[2].set_xlabel('y (m)')
axs.append(fig.add_subplot(2, 1, 2))
axs[3].plot(traj['xs'][:500, 0], traj['xs'][:500, 1], lw=2, color='k', zorder=0)
axs[3].scatter(traj['xs'][0, 0], traj['xs'][0, 1], lw=0, c='r', zorder=1, s=100)
axs[3].set_xlim(*BOUNDS[0])
axs[3].set_ylim(*BOUNDS[1])
axs[3].set_xlabel('x (m)')
axs[3].set_ylabel('y (m)')
axs[3].set_title('example trajectory')
for ax in axs:
set_font_size(ax, 16)
# print out parameters
print('best params:')
print('tau = {}'.format(p_best[0]))
print('noise = {}'.format(p_best[1]))
print('bias = {}'.format(p_best[2]))
return fig
def example_trajectory_no_plume(SEED, DURATION, DT, TAU, NOISE, BIAS, BOUNDS):
"""
Create an example trajectory and plot some of the resulting covariates.
"""
# build plume and agent
pl = GaussianLaminarPlume(0, np.array([0., 0]), np.eye(2))
ag = CenterlineInferringAgent(
tau=TAU, noise=NOISE, bias=BIAS, threshold=np.inf,
hit_trigger='peak', hit_influence=0,
k_0=np.eye(2), k_s=np.eye(2), tau_memory=1, bounds=BOUNDS)
# generate the trajectory
np.random.seed(SEED)
start_pos = np.array([
np.random.uniform(*BOUNDS[0]),
np.random.uniform(*BOUNDS[1]),
np.random.uniform(*BOUNDS[2]),
])
traj = ag.track(pl, start_pos, DURATION, DT)
# plot trajectory
fig = plt.figure(figsize=(15, 10), tight_layout=True)
axs = []
axs.append(fig.add_subplot(2, 1, 1))
axs[0].plot(traj['xs'][:, 0], traj['xs'][:, 1], lw=2, color='k', zorder=0)
axs[0].scatter(traj['xs'][0, 0], traj['xs'][0, 1], lw=0, c='r', zorder=1, s=100)
axs[0].set_xlim(*BOUNDS[0])
axs[0].set_ylim(*BOUNDS[1])
axs[0].set_xlabel('x (m)')
axs[0].set_ylabel('y (m)')
axs[0].set_title('example trajectory')
# plot some histograms
speeds = np.linalg.norm(traj['vs'], axis=1)
ws = np.linalg.norm(angular_velocity(traj['vs'], DT), axis=1)
ws = ws[~np.isnan(ws)]
axs.append(fig.add_subplot(2, 2, 3))
axs.append(fig.add_subplot(2, 2, 4))
axs[1].hist(speeds, bins=30, lw=0, normed=True)
axs[2].hist(ws, bins=30, lw=0, normed=True)
axs[1].set_xlabel('speed (m/s)')
axs[2].set_xlabel('ang. vel (rad/s)')
axs[1].set_ylabel('relative counts')
for ax in axs:
set_font_size(ax, 16)
return fig
