Learning about 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

In [2]:
# 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).

In [3]:
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.

In [4]:
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
Maximum Number of UIDs       = 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
Maximum Number of UIDs       = 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

In [6]:
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
Maximum Number of UIDs       = 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).

In [9]:
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
Maximum Number of UIDs       = 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)

In [11]:
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
Maximum Number of UIDs       = 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")
In [ ]: