Point Process¶
In [1]:
import numpy as np
import gstlearn as gl
import gstlearn.plot as gp
import matplotlib.pyplot as plt
This file provides some illustration of the generation of sets of Points. We can create the set of Points which covers a Box (in any space dimension). For sake of demonstration, this is demonstrated in 2-D.
We can create the set by drawing samples at random within the Box extension
In [2]:
nech = 1000
db = gl.Db.createFromBox(nech,[0,0],[100,100],4324);
ax = db.plot(size=5)
ax.decoration(title="Uniform Poisson")
print(f"The number of samples = {db.getSampleNumber()}")
The number of samples = 1000
We now generate a positive Regionalized variable over a grid that will serve as a density.
In [3]:
# Creating a Grid
grid = gl.DbGrid.create(nx=[100,100])
# Creating the isotropic Model
m = gl.Model()
cov = gl.CovAniso.createIsotropic(ctxt=m.getContext(),type=gl.ECov.MATERN,range=20,param=2)
m.addCov(cov)
# Simulating a Gaussian variable using an isotropic Model then turn positive (exponentiation)
gl.simtub(None,grid,m,nbtuba=400)
a = grid["Simu"]
a[np.where(a < 0)[0]] = 0
grid["Simu"] = a
ax = grid.plot()
ax.decoration(title="Density variable")
Now we define the set of Points according to different models. The first one is according to Poisson process (i.e. points randomly located within a Box.
In [4]:
db = gl.Db.createFromDbGrid(nech,grid,4324)
ax = db.plot(size=5)
ax.decoration(title="Regionalized Poisson")
print(f"Number of samples = {db.getSampleNumber()}")
Number of samples = 910
We now try the repulsion on the Uniform Poisson
In [5]:
db = gl.Db.createFromBox(nech,[0,0],[100,100],seed=43243,flag_exact=True,flag_repulsion=True,range=5.,beta=100);
ax = db.plot(size=5)
ax.decoration(title="Uniform Poisson with Repulsion")
print(f"The number of samples = {db.getSampleNumber()}")
The number of samples = 200
Combining the repulsion with the regionalized Poisson internsity
In [6]:
db = gl.Db.createFromDbGrid(nech,grid,seed=43243,flag_exact=True,flag_repulsion=True,range=5.,beta=100)
ax = db.plot(size=5)
ax.decoration(title="Regionalized Poisson with Repulsion")
print(f"Number of samples = {db.getSampleNumber()}")
Number of samples = 145
