def computeGeodesicMap(V, F, gt_interest_points, max_dist):
distances = geodesic.geodesic([item for v in V for item in v], [item for f in F for item in f], gt_interest_points, max_dist)
distances = np.array(distances).reshape(len(gt_interest_points), len(V))
distances_map = {}
for i in range(0, len(gt_interest_points)):
distances_map[gt_interest_points[i]] = distances[i];
return distances_map
# Integrate until the norm of the velocity has grown by a factor of 10
# and print out some diagnotistic along the way
print("Iteration: %i, tau: %f, |v| = %f" %
(len(geo.vs), geo.ts[-1], np.linalg.norm(geo.vs[-1])))
return np.linalg.norm(geo.vs[-1]) < 25.0 * np.linalg.norm(geo.vs[0])
# Calculate initial velocity
v = InitialVelocity(x, jacobian, Avv)
# Calculate geodesic
geo = geodesic(func,
jacobian,
Avv,
M,
N,
x,
v,
atol=1e-2,
rtol=1e-2,
callback=callback)
geo.integrate(5.0)
print('Got to t={0}'.format(geo.ts[-1]))
Plotting.figure(2)
plt.plot(geo.ts, geo.xs)
# Calculate jtj approximation to hessian (in log params) and plot eigenvalue
# spectrum
j = model5_fit.m.jacobian_log_params_sens(geo.xs[-1, :])
jtj = np.dot(np.transpose(j), j)
e, v = Utility.eig(jtj)
# and print out some diagnotistic along the way
print("Iteration: %i, tau: %f, |v| = %f" %
(len(geo.vs), geo.ts[-1], np.linalg.norm(geo.vs[-1])))
return np.linalg.norm(geo.vs[-1]) < 25.0 * np.linalg.norm(geo.vs[0])
# Calculate initial velocity
v = InitialVelocity(x, jacobian, Avv)
# Calculate geodesic
geo = geodesic(func,
jacobian,
Avv,
M,
N,
x,
-v,
atol=1e-2,
rtol=1e-2,
callback=callback,
invSVD=True)
geo.integrate(15.0)
print('Got to t={0}'.format(geo.ts[-1]))
Plotting.figure(2)
plt.plot(geo.ts, geo.xs)
# Calculate jtj approximation to hessian (in log params) and plot eigenvalue
# spectrum
j = model42_fit.m.jacobian_log_params_sens(geo.xs[-1, :])
jtj = np.dot(np.transpose(j), j)
# Choose starting parameters
x = np.log([1.0, 1.0])
v = InitialVelocity(x, j, Avv)
# Callback function used to monitor the geodesic after each step
def callback(geo):
# Integrate until the norm of the velocity has grown by a factor of 10
# and print out some diagnotistic along the way
print("Iteration: %i, tau: %f, |v| = %f" %(len(geo.vs), geo.ts[-1], np.linalg.norm(geo.vs[-1])))
return np.linalg.norm(geo.vs[-1]) < 100.0
# Construct the geodesic
# It is usually not necessary to be very accurate here, so we set small tolerances
geo_forward = geodesic(r, j, Avv, 2, 2, x, v, atol = 1e-2, rtol = 1e-2, callback = callback)
# Integrate
geo_forward.integrate(25.0)
import pylab
# plot the geodesic path to find the limit
# This should show the singularity at the "fold line" x[0] = x[1]
pylab.figure()
pylab.plot(geo_forward.ts, geo_forward.xs)
pylab.xlabel("tau")
pylab.ylabel("Parameter Values")
pylab.show()
## Now do opposite direction
return (r(x + h * v) + r(x - h * v) - 2 * r(x)) / h / h
# Choose starting parameters
x = np.log([1.0, 2.0])
v = InitialVelocity(x, j, Avv)
# Callback function used to monitor the geodesic after each step
def callback(geo):
# Integrate until the norm of the velocity has grown by a factor of 10
# and print out some diagnotistic along the way
print("Iteration: %i, tau: %f, |v| = %f" %
(len(geo.vs), geo.ts[-1], np.linalg.norm(geo.vs[-1])))
return np.linalg.norm(geo.vs[-1]) < 10.0
# Construct the geodesic
# It is usually not necessary to be very accurate here, so we set small tolerances
geo = geodesic(r, j, Avv, 2, 2, x, v, atol=1e-2, rtol=1e-2, callback=callback)
# Integrate
geo.integrate(25.0)
import pylab
# plot the geodesic path to find the limit
# This should show the singularity at the "fold line" x[0] = x[1]
pylab.plot(geo.ts, geo.xs)
pylab.xlabel("tau")
pylab.ylabel("Parameter Values")
pylab.show()
