#!/usr/bin/env python3
# -*- coding: utf-8 -*-
import numpy as np
import scipy as sp
import scipy.io
import matplotlib.pyplot as plt
import d3s.domain as domain
import d3s.kernels as kernels
import d3s.algorithms as algorithms
import d3s.systems as systems
plt.ion()
#%% Ornstein-Uhlenbeck process
Omega = domain.discretization(np.array([[-2, 2]]), np.array([50]))
f = systems.OrnsteinUhlenbeck(0.001, 500)
X = Omega.randPerBox(100)
Y = f(X)
sigma = np.sqrt(0.3)
epsilon = 0.1
k = kernels.gaussianKernel(sigma)
evs = 4 # number of eigenfunctions to be computed
# Perron-Frobenius
d, V = algorithms.kedmd(X, Y, k, epsilon=epsilon, evs=evs, operator='P')
for i in range(evs):
plt.figure()
a = s @ s.T
tra = np.trace(a)
for i in range(m):
for j in range(m):
G_10[i, j] = -1/k.sigma**2 * (B[i, i] - B[i, j]) \
+ 0.5*(1/k.sigma**4 * np.dot(X[:, i]-X[:, j], a @ (X[:, i]-X[:, j])) - 1/k.sigma**2 * tra )
G_10 = G_10 * G_00
return (G_00, G_10)
#%% Ornstein-Uhlenbeck process --------------------------------------------------------------------
#%% define domain
bounds = np.array([[-2, 2]])
boxes = np.array([100])
Omega = domain.discretization(bounds, boxes)
#%% define system
alpha = 1
beta = 4
def b(x):
return -alpha * x
def sigma(x):
return np.sqrt(2 / beta) * np.ones((1, 1, x.shape[1]))
#%% generate data
import d3s.kernels as kernels import d3s.domain as domain import d3s.ceig as ceig import d3s.antisymmetricKernels as akernels #%% two electrons in a box # define parameters h = 1 m0 = 1 L = np.pi # define domain bounds = np.array([[0, L], [0, L]]) boxes = np.array([31, 31]) Omega = domain.discretization(bounds, boxes) # generate data X, isBoundary = Omega.vertexGrid() m = Omega.numVertices() # replace regular grid nr = np.count_nonzero(isBoundary) n_new = 1000 X = np.hstack( (X[:, isBoundary], Omega.rand(n_new)) ) isBoundary = np.hstack( (np.ones(nr, dtype='bool'), np.zeros(n_new, dtype='bool') )) m = X.shape[1] #%% plot boundary