x = simulate([0], .1, 100)
x.set_seed(10)
z = x.potential(well_well)
f = simulate([0], .1, 1000)
f.set_seed(10)
y = f.potential(OU)
m = 3
basis_H = [Hermite(n) for n in range(m)]
Z = VAC(basis_H, y, 1)
ev_y_H = Z.find_eigen(3)
basis_H = [h.to_fcn() for h in basis_H]
H_fcns_y = [fcn_weighting(basis_H, v) for v in ev_y_H[1].T][::-1]
t = np.linspace(-1.7, 1.7, 100)
k = [h(z) for h in H_fcns_y]
plt.plot(z, k[0], "-m", label="First, H")
plt.plot(z, k[1], "-c", label="Second, H")
plt.plot(z, k[2], "-k", label="Third, H")
plt.legend(loc=8, prop={'size': 7})
plt.title("Estimated eigenfcns with indicator and Hermite bases")
plt.show()
m = 10
basis_I_20 = [
indicator(fineness=m, endpoint=2, center=i)
for i in makegrid(endpoint=2, n=m)
ev = [[ev[0][i] for ev in evs] for i in range(m - 1)]
[plt.plot(time_lag, ev[i]) for i in range(m - 1)]
plt.xlabel("Time Lag")
plt.ylabel("Eigenvalues")
plt.title("Eigenvalues vs. Time Lag (OU, 1-D)")
"""
The third eigenvalue is well approximated until around .41 seconds of time lag,
then the approximation gets dramatically worth.
"""
"""
CODE FOR PLOTTING BELOW
"""
ev = evs[0]
estimated = [fcn_weighting(basis, v) for v in ev[1].T][::-1]
true = [fcn_weighting(basis_true, v) for v in w_f][::-1]
if dimension == 1:
z = np.linspace(-1.5, 1.5, 20)
w = [h(z) for h in estimated]
y = [h(z) for h in true]
#
plt.plot(z, w[0], "-r", label="First")
plt.plot(z, w[1], "-b", label="Second")
plt.plot(z, w[2], "-g", label="Third")
# plt.plot(z[0],w[3], "-g", label = "Third")
# #
plt.plot(z, y[0], "-r", label="First")
plt.plot(z, y[1], "-b", label="Second")
plt.plot(z, y[2], "-g", label="Third")
ev_y_H = Y.find_eigen(3) z = x.potential(well_well) Z = VAC(basis_H, z, 1) ev_z_H = Z.find_eigen(3) Y = VAC(basis_I, y, 1) ev_y_I = Y.find_eigen(3) Z = VAC(basis_I, z, 1) ev_z_I = Z.find_eigen(3) basis_H = [h.to_fcn() for h in basis_H] basis_I = [i.to_fcn() for i in basis_I] H_fcns_y = [fcn_weighting(basis_H, v) for v in ev_y_H[1].T][::-1] H_fcns_z = [fcn_weighting(basis_H, v) for v in ev_z_H[1].T][::-1] I_fcns_y = [fcn_weighting(basis_I, v) for v in ev_y_I[1].T][::-1] I_fcns_z = [fcn_weighting(basis_I, v) for v in ev_z_I[1].T][::-1] print(L2subspaceProj_d(basis_H, H_fcns_y, endpoint=2.5, dimension=1, n=100)) # print( # L2subspaceProj_d(H_fcns_y, I_fcns_y, endpoint = 2.5, dimension = 1, n = 100), # L2subspaceProj_d(H_fcns_z, I_fcns_z, endpoint = 2.5, dimension = 1, n = 100) # ) z = np.linspace(-2.5, 2.5, 100) w = [h(z) for h in basis_H] l = [h(z) for h in H_fcns_y] e = [h(z) for h in I_fcns_y]
V = VAC(basis, trajectory, .385, delta_t)
ev = V.find_eigen(4)
time_lag = np.linspace(delta_t, .5, 40)
evs = np.array(
[VAC(basis, trajectory, l, delta_t).find_eigen(4)[0] for l in time_lag])
plt.plot(evs[:, 2])
plt.plot(evs[:, 1])
plt.plot(evs[:, 0])
s = evs[:, 2] - evs[:, 1]
print([i for i in range(len(s)) if s[i] == max(s)])
'''time_lag[i] = .385'''
H_fcns = [fcn_weighting(basis, v) for v in ev[1].T][::-1]
# z = np.array([np.linspace(-1.2,1.2,300)])
# w = [h(z) for h in H_fcns]
# plt.plot(z[0],w[0], "-r", label = "First")
# plt.plot(z[0],w[1], "-b", label = "Second")
# # plt.plot(z[0],w[2], "-g", label = "Third")
# # plt.plot(z[0],w[3], label = 'Fourth')
# # plt.plot(z[0],w[4], label = 'fifth')
# plt.legend()
# plt.title("Double well, estimated eigenfcns with indicator basis (n = 30,100)")
# plt.show()
#
h5.close()