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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 ORTHOGONAL POLYNOMIAL DENSITY ESTIMATION
Preliminaries
Imports
Step1:  Notebook settings
Step2:  Density Estimation
Initialize
Step3:  Create mock data streams
Step4:  Timings of density estimation
Step5:  Timings
33 ms per additive update with uniform distribution
31 ms per random update with uniform distribution
0.6 ms per evaluation at point
Plot final density
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Python Code:
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sbn
import pandas as pd
from uuid import uuid4
from lpde.geometry import WidthOf, Window, PointAt, BoundingBox, Mapper, Grid
from lpde.estimators import ParallelEstimator
from lpde.estimators.datatypes import Event, Degree, Action, Scalings, Signal
from lpde.producers import MockParams, MockProducer
from lpde.producers.distributions import gaussian
Explanation: ORTHOGONAL POLYNOMIAL DENSITY ESTIMATION
Preliminaries
Imports
End of explanation
%matplotlib notebook
Explanation: Notebook settings
End of explanation
legendre_width = WidthOf(1.8)
center = PointAt(0, 0)
window = Window(1.8, 1.8)
bounds = BoundingBox(center, window)
mapper = Mapper(bounds, legendre_width)
degree = Degree(20, 20)
params = MockParams(20, 100, 1, gaussian)
density = ParallelEstimator(degree, mapper, params)
action = Action.ADD
point = PointAt(0.5, 0.5)
event = Event(uuid4(), action, point)
grid = Grid(100, 100)
Explanation: Density Estimation
Initialize
End of explanation
def gaussian():
    x, y = np.random.multivariate_normal((0,0), ((0.1,0), (0,0.1)))
    if (-0.9 <= x <= 0.9) and (-0.9 <= y <= 0.9):
        return x, y
    else:
        return gaussian()
def uniform():
    return np.random.uniform(low=-0.9, high=0.9, size=2)
locations = []
def new_event(dist):
    location = dist()
    locations.append(location)
    point = PointAt(*location)
    return Event(uuid4(), Action(1), point)
def random_event(dist):
    event_type = np.random.randint(low=-1, high=2)
    if event_type == 1:
        location = dist()
        point = PointAt(*location)
        return Event(uuid4(), Action(1), point)
    elif event_type == 0:
        location = dist()
        point = PointAt(*location)
        column = density._phi.sample(1, axis=1).columns.values[0]
        return Event(column, Action(0), point)
    column = density._phi.sample(1, axis=1).columns.values[0]
    return Event(column, Action(-1))
density.controller.start(1, 1.0)
density.producer.start()
density.at(point)
density.controller.stop()
Explanation: Create mock data streams
End of explanation
#%%time
for i in range(100):
    density.update_with(new_event(gaussian))
#while not density.controller.phi_queue.empty():
#    pass
%%time
for i in range(1000):
    density.update_with(random_event(gaussian))
while not density._phi_queue_empty:
    pass
%%time
for i in range(1000):
    density.at(new_event(uniform).location)
while not density._phi_queue_empty:
    pass
Explanation: Timings of density estimation
End of explanation
n_hat = density.on(grid)
fig, ax = plt.subplots()
ax.set(xlabel=r'$x$', ylabel=r'$y$')
#ax.scatter(*zip(*locations), s=5, c='k')
contour = ax.imshow(n_hat,
                    cmap='viridis',
                    alpha=0.9,
                    extent=bounds.x_range+bounds.y_range,
                    origin='lower',
                    interpolation='bicubic')
cbar = plt.colorbar(contour, ax=ax, label=r'$n(x)$')
fig.tight_layout()
from bokeh.io import output_file, show
from bokeh.plotting import figure
from bokeh.tile_providers import STAMEN_TONER, STAMEN_TERRAIN
bound = 20000000 # meters
fig = figure(tools='pan, wheel_zoom', x_range=(-bound, bound), y_range=(-bound, bound))
fig.axis.visible = False
fig.add_tile(STAMEN_TERRAIN)
output_file("stamen_toner_plot.html")
show(fig)
from bokeh.plotting import figure, show, output_file
p = figure(x_range=bounds.x_range, y_range=bounds.y_range)
# must give a vector of image data for image parameter
p.image(image=[n_hat],
        x=bounds.x_range[0],
        y=bounds.y_range[0],
        dw=bounds.window[0],
        dh=bounds.window[1],
        palette="Spectral11",
        alpha=0.8)
output_file("image.html", title="image.py example")
show(p)  # open a browser
def f():
    pass
type(f)
callable(function)
Explanation: Timings
33 ms per additive update with uniform distribution
31 ms per random update with uniform distribution
0.6 ms per evaluation at point
Plot final density
End of explanation
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