Interpolation of geo-referenced data for Python.

## Project description

# pangeo-pyinterp

Python library for optimized geo-referenced interpolation.

## About

The motivation of this project is to provide tools for interpolating geo-referenced data used in the field of geosciences. Other libraries cover this problem, but written entirely in Python, the performance of these projects was not quite sufficient for our needs. That is why this project started.

With this library, you can interpolate
2D,
3D,
or
4D
fields using `n-variate`

and `bicubic`

interpolators
and unstructured
grids.
You can also apply for a data
binning on
the bivariate area by simple or linear binning.

The library core is written in C++ using the Boost C++ Libraries, Eigen3, GNU Scientific Library, and pybind11 libraries.

This software also uses CMake to configure the project and Googletest to perform unit testing of the library kernel.

## Fill undefined values

The undefined values in the grids do not allow interpolation of values located in the neighborhood. This behavior is a concern when you need to interpolate values near the mask of some fields. The library provides utilities to fill the undefined values:

- loess to fill the undefined values on the boundary between the defined/undefined values using local regression.
- gauss_seidel to fill all undefined values in a grid using the Gauss-Seidel method by relaxation.

## Geographic indexers

### N-Dimensional Grids

N-dimensional grid is a grid defined by a matrix, in a 2D space, by a cube in a 3D space, etc. Each dimension of the grid is associated with a vector corresponding to its coordinates or axes. Axes used to locate a pixel in the grid from the coordinates of a point. These axes are either:

*regular*: a vector of 181 latitudes spaced a degree from -90 to 90 degrees;*irregular*: a vector of 109 latitudes irregularly spaced from -90 to 89.940374 degrees.

These objects are manipulated by the class pyinterp.Axis, which will choose, according to Axis definition, the best implementation. This object will allow you to find the two indexes framing a given value. This operating mode allows better performance when searching for a regular axis (a simple calculation will enable you to see the index of a point immediately). In contrast, in the case of an irregular axis, the search will be performed using a binary search.

Finally, this class can define a circular axis from a vector to correctly locate a value on the circle. This type of Axis will is used handling longitudes.

### Temporal Axes

The pyinterp.TemporalAxis class handles temporal axes, i.e., axes defined by 64-bit integer vectors, which is the encoding used by numpy to control dates. This class allows handling dates without loss of information when the precision of the times is the nanosecond. These objects are used by spatiotemporal grids to perform temporal interpolations.

### Unstructured Grids

In the case of unstructured grids, the index used is a *R*Tree*. These trees
have better performance than the *KDTree* generally found in Python library
implementations.

The tree used here is the implementation provided by the C++ Boost library.

An adaptation has introduced to address spherical equatorial coordinates
effectively. Although the Boost library allows these coordinates to manipulated
natively, the performance is lower than in the case of Cartesian space. Thus, we
have chosen to implement a conversion of Longitude Latitude Altitude (*LLA*)
coordinates into Earth-Centered, Earth-Fixed (*ECEF*) coordinates transparently
for the user to ensure that we can preserve excellent performance. The
disadvantage of this implementation is that it requires a little more memory, as
one more element gets used to index the value of the Cartesian space.

The management of the LLA/ECEF coordinate conversion is managed to use the Olson, D.K. algorithm. It has excellent performance with an accuracy of 1e-8 meters for altitude.

### Geohash

Geohashing is a geocoding method used to encode geographic coordinates (latitude and longitude) into a short string of digits and letters delineating an area on a map, which is called a cell, with varying resolutions. The more characters in the string, the more precise the location.

Geohashes use Base-32 alphabet encoding (characters can be `0`

to `9`

and `A`

to `Z`

, excl `A`

, `I`

, `L`

and `O`

).

This method is used to build a geographic index, possibly stored on disk, for the purpose of indexing data.

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