ORTHOGONAL POLYNOMIAL DENSITY ESTIMATION

Preliminaries

Imports



In [1]:

    
from numpy import seterr
from mkl import set_num_threads
from uuid import uuid4

from lpde.geometry import WidthOf, Window, PointAt, BoundingBox, Mapper, Grid
from lpde.estimators import ParallelEstimator
from lpde.estimators.datatypes import Degree
from lpde.producers import MockParams
from lpde.producers.distributions import gaussian
from lpde.visualizers import Visualize

Notebook settings



In [2]:

    
%matplotlib qt5

_ = seterr(over='ignore')

set_num_threads(1)

Density Estimation

Initialize



In [3]:

    
legendre_width = WidthOf(1.8)

center = PointAt(51.375, 35.675)
window = Window(0.55, 0.35)
bounds = BoundingBox(center, window)

mapper = Mapper(bounds, legendre_width)

degree = Degree(20, 20)
params = MockParams(100, 1000, gaussian)
demand = ParallelEstimator(degree, mapper, params)

Start, check, and stop



In [4]:

    
demand.controller.start(16, 1.0)



In [5]:

    
demand.controller.alive









    Out[5]:





{'Datagate': True,
 'Minimizers': (True,
  True,
  True,
  True,
  True,
  True,
  True,
  True,
  True,
  True,
  True,
  True,
  True,
  True,
  True,
  True),
 'Producer': True,
 'Smoother': True}



In [6]:

    
demand.controller.open









    Out[6]:





{'Coefficients': True, 'Events in': True, 'Events out': True, 'Points': True}



In [9]:

    
demand.controller.qsize









    Out[9]:





{'Coefficients': 0, 'Points': 0}



In [10]:

    
demand.controller.stop()

Query density at a specific point



In [ ]:

    
point = PointAt(51.4, 35.7)

demand.at(point)

Plot the density

With the default settings ...



In [ ]:

    
visulization = Visualize(demand)
animation = visulization.show(cartopy=True, zoom=11)

... and with a different grid.



In [ ]:

    
demand.grid = Grid(50, 150)

visulization = Visualize(demand)
animation = visulization.show(cartopy=True)

Plot the gradient of the density



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import matplotlib.pyplot as plt

demand.grid = Grid(50, 50)

fig, ax = plt.subplots(figsize=(5.5, 5),)
ax.quiver(*demand.grid, *demand.gradient_on_grid, demand.on_grid, angles='xy', pivot='middle')
fig.tight_layout()

Query density gradient at a specific point



In [ ]:

    
demand.gradient_at(PointAt(51.4, 35.7))



In [ ]: