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phase_plane.py
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phase_plane.py
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from tvb.basic.neotraits.api import HasTraits, Attr, NArray, List
from ipywidgets import interact, FloatSlider, Dropdown, ToggleButton
import numpy as np
import matplotlib.pylab as plt
import matplotlib.gridspec as gridspec
from tvb.simulator.lab import integrators
def phase_plane_interactive(model, integrator):
NUMBEROFGRIDPOINTS = 42
TRAJ_STEPS = 4096
def plot_phase_plane(**param_kwargs):
# defaults, to be changed
svx = param_kwargs.pop('svx') #x-axis: 1st state variable
svy = param_kwargs.pop('svy') #y-axis: 2nd state variable
mode = param_kwargs.pop('mode')
# set model params
for k, v in param_kwargs.items():
setattr(model, k, np.r_[v])
# state vector
sv_mean = np.array([param_kwargs[key] for key in model.state_variables])
sv_mean = sv_mean.reshape((model.nvar, 1, 1))
default_sv = sv_mean.repeat(model.number_of_modes, axis=2)
no_coupling = np.zeros((model.nvar, 1, model.number_of_modes))
# mesh grid
xlo = model.state_variable_range[svx][0]
xhi = model.state_variable_range[svx][1]
ylo = model.state_variable_range[svy][0]
yhi = model.state_variable_range[svy][1]
X = np.mgrid[xlo:xhi:(NUMBEROFGRIDPOINTS*1j)]
Y = np.mgrid[ylo:yhi:(NUMBEROFGRIDPOINTS*1j)]
# Calculate the vector field.
svx_ind = model.state_variables.index(svx)
svy_ind = model.state_variables.index(svy)
#Calculate the vector field discretely sampled at a grid of points
grid_point = default_sv.copy()
U = np.zeros((NUMBEROFGRIDPOINTS, NUMBEROFGRIDPOINTS,
model.number_of_modes))
V = np.zeros((NUMBEROFGRIDPOINTS, NUMBEROFGRIDPOINTS,
model.number_of_modes))
for ii in range(NUMBEROFGRIDPOINTS):
grid_point[svy_ind] = Y[ii]
for jj in range(NUMBEROFGRIDPOINTS):
#import pdb; pdb.set_trace()
grid_point[svx_ind] = X[jj]
d = model.dfun(grid_point, no_coupling)
for kk in range(model.number_of_modes):
U[ii, jj, kk] = d[svx_ind, 0, kk]
V[ii, jj, kk] = d[svy_ind, 0, kk]
# plot
f = plt.figure( figsize=(10,8+model.nvar))
gs0 = gridspec.GridSpec(2,1, figure=f, wspace=0.1, height_ratios=(8,model.nvar))
gs = gridspec.GridSpecFromSubplotSpec(1, 1, subplot_spec=gs0[0], hspace=0.05)
# Top (unshared) axes
ax = f.add_subplot(gs[0])
ax.set(
xlabel = "State Variable " + svx,
ylabel = "State Variable " + svy,
title = model.__class__.__name__ + " mode " + str(mode)
)
if np.all(U[:, :, mode] + V[:, :, mode] == 0):
ax.set(title = model_name + " mode " + mode + ": NO MOTION IN THIS PLANE")
X, Y = np.meshgrid(X, Y)
pp_quivers = ax.scatter(X, Y, s=8, marker=".", c="k")
else:
pp_quivers = ax.quiver(X, Y,
U[:, :, mode],
V[:, :, mode],
width=0.001, headwidth=8)
#Plot the nullclines
nullcline_x = ax.contour(X, Y,
U[:, :, mode],
[0], colors="r")
nullcline_y = ax.contour(X, Y,
V[:, :, mode],
[0], colors="g")
if param_kwargs['trajectory']:
if isinstance(integrator, integrators.IntegratorStochastic):
if integrator.noise.ntau > 0.0:
integrator.noise.configure_coloured(integrator.dt,
(1, model.nvar, 1,
model.number_of_modes))
else:
integrator.noise.configure_white(integrator.dt,
(1, model.nvar, 1,
model.number_of_modes))
svx_ind = model.state_variables.index(svx)
svy_ind = model.state_variables.index(svy)
#Calculate an example trajectory
state = default_sv.copy()
integrator.clamped_state_variable_indices = np.setdiff1d(
np.r_[:len(model.state_variables)], np.r_[svx_ind, svy_ind])
integrator.clamped_state_variable_values = default_sv[integrator.clamped_state_variable_indices]
scheme = integrator.scheme
traj = np.zeros((TRAJ_STEPS+1, model.nvar, 1,
model.number_of_modes))
traj[0, :] = state
for step in range(TRAJ_STEPS):
state = scheme(state, model.dfun, no_coupling, 0.0, 0.0)
traj[step+1, :] = state
ax.scatter(default_sv[svx_ind], default_sv[svy_ind], s=42, c='g', marker='o', edgecolor=None)
ax.plot(traj[:, svx_ind, 0, mode],
traj[:, svy_ind, 0, mode])
#Plot the selected state variable trajectories as a function of time
gs = gridspec.GridSpecFromSubplotSpec(model.nvar, 1, subplot_spec=gs0[1], hspace=0.1)
for i, svar in enumerate(model.state_variables):
ax = f.add_subplot(gs[i])
ax.plot(np.arange(TRAJ_STEPS+1) * integrator.dt, traj[:, i, 0, mode])
ax.set(ylabel=svar)
if i < model.nvar-1:
ax.axes.xaxis.set_ticks([])
else:
ax.set(xlabel="time (ms)")
# setup widgets
param_kwargs = {}
for param_name in type(model).declarative_attrs:
param_def = getattr(type(model), param_name)
if not isinstance(param_def, NArray) or not param_def.dtype == np.float :
continue
param_range = param_def.domain
if param_range is None:
continue
param_value = getattr(model, param_name).item()
param_kwargs[param_name] = FloatSlider(
min=param_range.lo, max=param_range.hi, value=param_value)
for svar, svar_range in model.state_variable_range.items():
param_kwargs[svar] = FloatSlider(
min=svar_range[0], max=svar_range[1], value=np.mean(svar_range)
)
param_kwargs['svx'] = Dropdown(
#options=[(v,i) for i, v in enumerate(model.state_variables)],
options = model.state_variables,
value=model.state_variables[0],
description='X axis'
)
param_kwargs['svy'] = Dropdown(
#options=[(v,i) for i, v in enumerate(model.state_variables)],
options = model.state_variables,
value=model.state_variables[1],
description='Y axis'
)
param_kwargs['mode'] = Dropdown(
options=list(range(model.number_of_modes)),
value=0,
description='Mode'
)
param_kwargs['trajectory'] = ToggleButton(
value=False,
description='Show trajectory'
)
w = interact(plot_phase_plane, **param_kwargs)
return w