Python tools for interpolating 3D or 4D fields

Forked from https://github.com/DurhamDecLab/ARBInterp

Python tools for interpolation of gridded data, either:

Tricubic interpolation of 3D gridded data, based on the scheme by Lekien and Marsden: https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.1296

Further details on this code here: https://openresearchsoftware.metajnl.com/articles/10.5334/jors.258/

Takes in gridded data from comma-separated input file, either a scalar field U as an N x 4 (x,y,z,U) array or a vector field B as an N x 6 (x, y, z, Bx, By, Bz) array.

or:

Quadcubic interpolation of 4D gridded data. Takes in gridded data from comma-separated input file, either a scalar field U as an N x 5 (x,y,z,t,U) array or a vector field B as an N x 7 (x, y, z, t, Bx, By, Bz) array.

Background and 4D method see: https://arxiv.org/abs/1904.09869

$ pip install git+https://github.com/cmordini/qinterp.git

As of version 1.8 I have tested on Python 3.9.6 and numpy 1.21.1. All Python 2 support is dropped.

• numpy

Note: Due to the boundary conditions the interpolatable volume is slightly smaller than the input field. A query at the edge will return a 'nan'. Further work will implement boundary conditions of the Neumann or Dirichlet types.

Instantiate the 'tricubic' / 'quadcubic' class by passing a loaded field to it. It is not necessary to order the (x,y,z) / (x,y,z,t) coordinates - the code will do that itself.

NOTE: a regular field (i.e. with equal grid spacing in all dimensions) must be supplied. The spacing along all axes does not have to match, only be consistent along each.

The (3D) interpolant field does not have to be cubic, only cuboid.

If an Nx4 (3D) or Nx5 (4D) array is passed the tricubic / quadcubic class will operate in scalar mode and return both the interpolated field magnitude and partial derivatives.

If an Nx6 (3D) or Nx7 (4D) array is passed the tricubic / quadcubic class will accept an optional kword argument 'mode' with one of the following switches:

'norm' - this takes the norm of the vector field as the interpolant. Magnitude and gradient returned. 'vector' - interpolates the x, y and z field components separately and returns them together. 'both' - returns the interpolated magnitude and gradients of the norm of the field, AND the vector components.

If no argument is passed it will default to 'vector'. If a 'mode' kword is passed but an N x 4 array is detected, the kword will be ignored.

The optional argument "quiet" can be passed, which suppresses screen print messages when the interpolation is activated.

To query the interpolant field call the "Query" method. Input can be a single set of Cartesian coordinates (x,y,z) / (x,y,z,t) or a range of points as an array. If a range, the first 3/4 columns are assumed to be the (x,y,z) / (x,y,z,t) coordinates. Further columns can be present e.g. velocity components - these are ignored.

ARBInterp.py - contains tricubic and quadcubic classes and methods for querying interpolant field.

ARB3DInterpExample.py - loads an example 3D field and queries it with sample coordinates.

Example3DVectorField.csv - part of a magnetic field, as vector components, (x, y, z, Bx, By, Bz).

Example3DScalarField.csv - the same field as Example3DVectorField, but the norm / magnitude, (x,y,z,U).

ARB4DInterpExample.py - loads an example time-varying 4D field and queries it with sample coordinates.

Example4DVectorField.csv - part of a magnetic field, as vector components, (x, y, z, t, Bx, By, Bz).

Example4DScalarField.csv - the same field as Example4DVectorField, but the norm / magnitude, (x,y,z,t,U).

B_Matrix_3D.csv - This is the 64 x 64 interpolation matrix as described by Lekien and Marsden. Code to generate this is included in the tricubic class in ARBInterp.py. NB: this assumes components of b-vector are ordered f,df/dx,df/dy,df/dz,d2f/dxdy,d2f/dxdz,d2f/dydz,d3f/dxdydz.

B_Matrix_4D.csv - this is the 256 x 256 interpolation matrix - paper to follow. Also included in ARBInterp.py, in the quadcubic class. NB: this assumes components of b-vector are ordered f,df/dx,df/dy,df/dz,df/dt,d2f/dxdy,d2f/dxdz,d2f/dxdt,d2f/dydz,d2f/dydt,d2x/dzdt,d3f/dxdydz,d3f/dxdydt,d3f/dxdzdt,d3f/dydzdt,d4f/dxdydzdt.

Interested in contributing? Check out the contributing guidelines. Please note that this project is released with a Code of Conduct. By contributing to this project, you agree to abide by its terms.

ARBInterp was created by Paul Walker. It is licensed under the terms of the GNU General Public License v3.0 license.

ARBInterp was created by Paul Walker. Packaged by Carmelo Mordini as qinterp with cookiecutter and the py-pkgs-cookiecutter template.