import matplotlib.pyplot as plt
from matplotlib import rc
import matplotlib.path as path
from hermite_poly import Hermite, Poly
from models_and_functions import simulate, VAC, well_well, makegrid, fcn_weighting, L2subspaceProj_d, OU, dot
from mpl_toolkits import mplot3d
from basis_sets import indicator
from numpy import exp, arange
from pylab import meshgrid, cm, imshow, contour, clabel, colorbar, axis, title, show
import tables as tb
dimension = 1
fineness = 10
endpoint = 2.5
basis = [
indicator(fineness, endpoint, center=i).to_fcn()
for i in makegrid(endpoint, dimension=dimension, n=fineness)
]
basis = [Hermite(0).to_fcn()]
basis = basis + [
Hermite(n, d).to_fcn() for n in range(1, fineness)
for d in range(dimension)
]
basisSize = len(basis)
delta_t = .01
T = 1000
n = 160
length = round(T / delta_t)
print("Now opening trajectory data.")
h5 = tb.open_file(
"Trajectory_Data/OU_1D_delta_t={},T={},n={}.h5".format(delta_t, T, n), 'r')
from scipy.special import hermite
from scipy.linalg import eigh
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.path as path
from hermite_poly import Hermite
from simple_models import simulate, VAC, well_well, makegrid, fcn_weighting, L2subspaceProj_d
from mpl_toolkits import mplot3d
from basis_sets import indicator
from numpy import exp, arange
from pylab import meshgrid, cm, imshow, contour, clabel, colorbar, axis, title, show
m = 3
basis_H = [Hermite(n) for n in range(m)]
basis_I = [
indicator(fineness=5, endpoint=1, center=i)
for i in makegrid(endpoint=1, n=5)
]
x = simulate([0, 0], .1, 100)
# x.set_seed(5)
y = x.normal()
Y = VAC(basis_H, y, 1)
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)
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)
]
basis_I_40 = [
indicator(fineness=2 * m, endpoint=2, center=i)
for i in makegrid(endpoint=2, n=2 * m)
]
basis_I_80 = [
indicator(fineness=4 * m, endpoint=2, center=i)
for i in makegrid(endpoint=2, n=4 * m)
]
Z_20 = VAC(basis_I_20, z, 1)
Z_40 = VAC(basis_I_40, z, 1)
Z_80 = VAC(basis_I_80, z, 1)
delta_t = .001
T = 1000
n = 10
length = round(T / delta_t)
h5 = tb.open_file("Trajectory_Data/DW_1D_delta_t=.001,T=1000,n=10.h5", 'r')
a = h5.root.data
t = np.array([a[3,round(length * .05):round(length * .3)]])
print("Now getting eigenvalues.")
Phi_f = np.array([f(distribution) for f in basis_true])
evs = []
error = []
for l in fineness:
basis = [indicator(l, endpoint, center = i).to_fcn() for i in makegrid(endpoint, dimension = 1, n = l)]
ev = VAC(basis, t, time_lag, delta_t).find_eigen(4)
evs.append(ev)
Phi_g = np.array([f(distribution) for f in basis])
error.append(L2subspaceProj_d(w_f = w_f[2:], w_g = ev[1].T[2:][::-1],
distribution = distribution, Phi_f = Phi_f, Phi_g = Phi_g))
print("Now calculating error.")
plt.plot(fineness, error)
plt.xlabel("Number of basis functions")
plt.ylabel("Error in estimated subspaces")
plt.title("Error in estimation with varying basis size (Double Well, 1D)")
print([i for i in range(len(error)) if error[i] == min(error)])