Spatial interpolation Python module

## Project description      ## version 0.2.5 - Huygens Crater

PyInterpolate is designed as the Python library for geostatistics. Its role is to provide access to spatial statistics tools used in many studies. This package helps you interpolate spatial data with the Kriging technique.

If you’re:

• GIS expert,
• geologist,
• mining engineer,
• ecologist,
• public health specialist,
• data scientist.

Then this package may be helpful for you. You could use it for:

• spatial interpolation and spatial prediction,
• alone or with machine learning libraries,
• for point and areal datasets.

Pyinterpolate allows you to perform:

1. Ordinary Kriging and Simple Kriging (spatial interpolation from points),
2. Centroid-based Kriging of Polygons (spatial interpolation from blocks and areas),
3. Area-to-area and Area-to-point Poisson Kriging of Polygons (spatial interpolation and data deconvolution from areas to points).

## How it works

The package performs multiple spatial interpolation tasks. The flow of analysis is usually the same for each interpolation method:

from pyinterpolate.io_ops import read_point_data



[2.] Analyze data, Semivariance calculation.

from pyinterpolate.semivariance import calculate_semivariance

max_range = 0.32

experimental_semivariogram = calculate_semivariance(
data=point_data,
max_range=max_range)


[3.] Data transformation, theoretical semivariogram.

from pyinterpolate.semivariance impJezero Craterort TheoreticalSemivariogram
semivar = TheoreticalSemivariogram(points_array=point_data, empirical_semivariance=experimental_semivariogram)
number_of_ranges = 32

semivar.find_optimal_model(weighted=False, number_of_ranges=number_of_ranges)


[4.] Interpolation.

from pyinterpolate.kriging import Krige

model = Krige(semivariogram_model=semivar, known_points=point_data)
unknown_point = (12.1, -5.9)

ok_pred = model.ordinary_kriging(unknown_location=unknown_point, number_of_neighbours=32)


[5.] Error and uncertainty analysis.

real_val = 10  # Some real, known observation at a given point
squared_error = (real_val - ok_pred)**2
print(squared_error)

>> 48.72


With pyinterpolate, you can retrieve the point support model from areal aggregates. Example from Tick-borne Disease Detector study for European Space Agency - COVID-19 population at risk mapping. It was done with the Area-to-Point Poisson Kriging technique from the package. Countries worldwide present infections as areal sums to protect the privacy of infected people. But this kind of representation introduces bias to the decision-making process. To overcome this bias, you may use Poisson Kriging. Areal aggregates of COVID-19 infection rate are transformed to new point support semivariogram created from population density blocks. As an output, we get a population at risk map: ## Status

Beta version: the package is tested, and the main structure is preserved, but future changes are likely to occur.

## Setup

Setup by pip: pip install pyinterpolate / Python 3.7 is required!

Detailed instructions on setting up the package are presented in the file SETUP.md. We pointed out there most common problems related to third-party packages.

You may follow those setup steps to create a conda environment with a package for your tests:

### Recommended - conda installation

[1.] First, install system dependencies to use package (libspatialindex_c.so):

LINUX:

sudo apt install libspatialindex-dev


MAC OS:

brew install spatialindex


[2.] Next step is to create conda environment with Python 3.7, pip, and notebook packages and activate your environment:

conda create -n [YOUR NAME] -c conda-forge python=3.7 pip notebook

conda activate [YOUR NAME]


[3.] In the next step, install pyinterpolate and its dependencies with pip:

pip install pyinterpolate


[4.] You are ready to use the package!

### pip installation

With Python==3.7 and system libspatialindex_c.so dependencies, you may install the package by simple command:

pip install pyinterpolate


Always use Virtual Environment for the installation.

## Tests and contribution

All tests are grouped in the test directory. To run them, you must have installed the unittest package. More about test and contribution is here: CONTRIBUTION.md

## Commercial and scientific projects where the library has been used

• Tick-Borne Disease Detector (Data Lions) for the European Space Agency (2019-2020).
• B2C project related to the prediction of demand for specific flu medications,
• B2G project related to large-scale infrastructure maintenance.

## Bibliography

PyInterpolate is developed thanks to many resources, and some of them are pointed out here:

• Armstrong M., Basic Linear Geostatistics, Springer 1998,
• GIS Algorithms by Ningchuan Xiao: https://uk.sagepub.com/en-gb/eur/gis-algorithms/book241284
• Pardo-Iguzquiza E., VARFIT: a Fortran-77 program for fitting variogram models by weighted least squares, Computers & Geosciences 25, 251-261, 1999,
• Goovaerts P., Kriging and Semivariogram Deconvolution in the Presence of Irregular Geographical Units, Mathematical Geology 40(1), 101-128, 2008
• Deutsch C.V., Correcting for Negative Weights in Ordinary Kriging, Computers & Geosciences Vol.22, No.7, pp. 765-773, 1996

## Requirements and dependencies (v 0.2.5)

• Python 3.7.6

• Numpy 1.18.3

• Scipy 1.4.1

• GeoPandas 0.7.0

• Fiona 1.18.13.post1 (Mac OS) / Fiona 1.8 (Linux)

• Rtree 0.9.4 (Mac OS), Rtree >= 0.8 & < 0.9 (Linux)

• Descartes 1.1.0

• Pyproj 2.6.0

• Shapely 1.7.0

• Matplotlib 3.2.1

## Package structure

High level overview:

• pyinterpolate
• distance - distance calculation,
• idw - inverse distance weighting interpolation,
• io_ops - reads and prepares input spatial datasets,
• transform - transforms spatial datasets,
• viz - interpolation of smooth surfaces from points into rasters,
• kriging - Ordinary Kriging, Simple Kriging, Poisson Kriging: centroid based, area-to-area, area-to-point,
• misc - compare different kriging techniques,
• semivariance - calculate semivariance, fit semivariograms and regularize semivariogram,
• tutorials - tutorials (Basic, Intermediate and Advanced)

## Development

• v 0.3 of the package that runs on the Linux, Mac, and Windows OS; updated and extended variance modeling and analysis.

## Known Bugs

• Package may crash with a huge dataset (memory issues). Operations are performed with numpy arrays, and for datasets larger than 10 000 points, there could be a memory issue (Issue page)

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