Interpolations¶
This Tutorial is meant to give some hints about using Interpolation methods in gstlearn
In [1]:
import numpy as np
import pandas as pd
import sys
import os
import gstlearn as gl
import gstlearn.plot as gp
import matplotlib.pyplot as plt
Setting some global variables
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# Set the Global Options
verbose = True
flagGraphic = True
# Define the Space Dimension
ndim = 2
gl.defineDefaultSpace(gl.ESpaceType.RN, ndim)
# Set the Seed for the Random Number generator
gl.law_set_random_seed(32131)
Generating an initial square grid covering a 1 by 1 surface (100 meshes along each direction).
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grid = gl.DbGrid.create([100,100], [0.01,0.01])
Creating a Data Set. The set is generated using a non-conditional geostatistical simulation (performed using the Turning Bands method). This simulation is first performed on the grid which is then sampled to constitute the Point Data Set.
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model = gl.Model.createFromParam(gl.ECov.EXPONENTIAL, 0.1, 1.)
gl.simtub(None, grid, model)
if verbose:
grid.display()
np = 100
data = gl.Db.createSamplingDb(grid, 0., np, ["x1","x2","Simu"])
if verbose:
data.display()
Data Base Grid Characteristics ============================== Data Base Summary ----------------- File is organized as a regular grid Space dimension = 2 Number of Columns = 4 Total number of samples = 10000 Grid characteristics: --------------------- Origin : 0.000 0.000 Mesh : 0.010 0.010 Number : 100 100 Variables --------- Column = 0 - Name = rank - Locator = NA Column = 1 - Name = x1 - Locator = x1 Column = 2 - Name = x2 - Locator = x2 Column = 3 - Name = Simu - Locator = z1 Data Base Characteristics ========================= Data Base Summary ----------------- File is organized as a set of isolated points Space dimension = 2 Number of Columns = 4 Total number of samples = 100 Variables --------- Column = 0 - Name = rank - Locator = NA Column = 1 - Name = x1 - Locator = x1 Column = 2 - Name = x2 - Locator = x2 Column = 3 - Name = Simu - Locator = z1
In [5]:
if flagGraphic:
ax = data.plot()
ax.decoration(title="Data Set")
ax.geometry(xlim=[0,1],ylim=[0,1])
Interpolation using Moving Average technique¶
In this paragraph, we experiment an interpolation based on Moving average technique. We need to define a Moving Neighborhood first
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nmini = 5
nmaxi = 5
radius = 0.2
neigh = gl.NeighMoving.create(False, nmaxi, radius, nmini)
neigh.display()
Moving Neighborhood =================== Minimum number of samples = 5 Maximum number of samples = 5 Maximum horizontal distance = 0.2
In [7]:
gl.movingAverage(data, grid, neigh)
if verbose:
grid.display()
Data Base Grid Characteristics ============================== Data Base Summary ----------------- File is organized as a regular grid Space dimension = 2 Number of Columns = 5 Total number of samples = 10000 Grid characteristics: --------------------- Origin : 0.000 0.000 Mesh : 0.010 0.010 Number : 100 100 Variables --------- Column = 0 - Name = rank - Locator = NA Column = 1 - Name = x1 - Locator = x1 Column = 2 - Name = x2 - Locator = x2 Column = 3 - Name = Simu - Locator = NA Column = 4 - Name = MovAve.Simu.estim - Locator = z1
In [8]:
if flagGraphic:
ax = grid.plot()
ax.decoration(title="Moving Average")
Interpolation using Inverse Distance technique¶
In this paragraph, we experiment an interpolation based on Inverse Distance technique. We use the squared distance weighting function (default option).
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gl.inverseDistance(data, grid)
if verbose:
grid.display()
Data Base Grid Characteristics ============================== Data Base Summary ----------------- File is organized as a regular grid Space dimension = 2 Number of Columns = 6 Total number of samples = 10000 Grid characteristics: --------------------- Origin : 0.000 0.000 Mesh : 0.010 0.010 Number : 100 100 Variables --------- Column = 0 - Name = rank - Locator = NA Column = 1 - Name = x1 - Locator = x1 Column = 2 - Name = x2 - Locator = x2 Column = 3 - Name = Simu - Locator = NA Column = 4 - Name = MovAve.Simu.estim - Locator = NA Column = 5 - Name = InvDist.Simu.estim - Locator = z1
In [10]:
if flagGraphic:
ax = grid.plot()
ax.decoration(title="Inverse Squared Distance")
Least Square Polynomial Fit¶
In this paragraph, we experiment an interpolation based on Least Square Polynomial Fit technique. We use a polynomial of degree 1, fitted locally (on the samples neighboring the target grid node). Note that a bigger neighborhood had to be defined (more than 5 samples per neighborhood)
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nmini = 5
nmaxi = 10
radius = 0.5
neigh = gl.NeighMoving.create(False, nmaxi, radius, nmini)
neigh.display()
Moving Neighborhood =================== Minimum number of samples = 5 Maximum number of samples = 10 Maximum horizontal distance = 0.5
In [12]:
gl.leastSquares(data, grid, neigh, 1)
if verbose:
grid.display()
Data Base Grid Characteristics ============================== Data Base Summary ----------------- File is organized as a regular grid Space dimension = 2 Number of Columns = 7 Total number of samples = 10000 Grid characteristics: --------------------- Origin : 0.000 0.000 Mesh : 0.010 0.010 Number : 100 100 Variables --------- Column = 0 - Name = rank - Locator = NA Column = 1 - Name = x1 - Locator = x1 Column = 2 - Name = x2 - Locator = x2 Column = 3 - Name = Simu - Locator = NA Column = 4 - Name = MovAve.Simu.estim - Locator = NA Column = 5 - Name = InvDist.Simu.estim - Locator = NA Column = 6 - Name = LstSqr.Simu.estim - Locator = z1
In [13]:
if flagGraphic:
ax = grid.plot()
ax.decoration(title="Least Squares Polynomial Fit")
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