This work reproduces the differential affine velocity estimator for vector magnetograms (DAVE4VM) developed by dr. P.W. Shuck. At first this work was published in The Astrophysical Journal 683:1134Y1152, 2008 August 20 - TRACKING VECTOR MAGNETOGRAMS WITH THE MAGNETIC INDUCTION EQUATION - P.W. Shuck. Essentially it is a working version in python of dave4vm that was originally written in IDL.

The goal of this work is not only to re-design an existing tool to better suit the needs of my current work but also to ultimately deliver a tool that can be used by the solar physics community for free.

Currently, the version within the Jupyter Notebook was already tested for some magnetograms and is capable of reproducing the IDL version results.

Description of the modules: - call_v1.py: This module organize a pair of fits using the cubitos.py module and should be, when the code is properly done, where the user will interact with the algorithm to personalize the size of the spatial grid, time difference and what data will be used. The other versions can loop over multiple files and insert the results in a database however they have extra functionalities that rely in some scripts that are not here.

• cubitos.py: This module scan a folder for the Br, Btheta, Bphi .fits files and create data cubes with them using Sunpy.
• do_dave4vm_and.py: Here data is pre-processed to be fed on the dave4vm call using the odiffxy.py module and calculating

averages between the .fits files. This module returns the dictionary with the variables that are fed into dave4vm.py (magvm), the velocities calculated with dave4vm (vel4vm) and the trace of the main matrix used to perform the calculations (trc).

• odiffxy5.py: This module will calculate the spatial derivatives of dx and dy and return those results to the

do_dave4vm_and.py module.

• dave4vm.py: In this module the main calculations are done. At first the kernel that will be used to calculate

the convolution integrals in the dave4vm_matrix.py module is created. Then, the output matrix (AM) is used to calculate the velocities leading to the final product (vel4vm).

-dave4vm_matrix.py: This module calculates the convolution integrals between the data stored in the dictionary (magvm) and the kernel (psf, psfx, psfy, psfxx, psfyy, psfxy)

Changes: 2018-02-12: The first working version was added on this repository. It was written in a way that is as faithful as possible to the original code. Testing and comparing the performance of this version against the original code is ongoing.

2018-01-05: Ipython notebook and test data added. Some bugs were corrected but the major problems still persists.

2018-05-10: New Ipython notebook added with a working version.

2018-05-24: Scipy.signal convolve and numpy solve introduced improving the code speed.

2018-08-06: Documentation improvements in some codes and reorganization of github folder.

Original License:

AUTHORIZATION TO USE AND DISTRIBUTE

I hereby agree to the following terms governing the use and redistribution of the DAVE/DAVE4VM software release originally written and developed by Dr. Schuck.

Redistribution and use in source and binary forms, with or without modification, are permitted provided that (1) source code distributions retain this paragraph in its entirety, (2) distributions including binary code include this paragraph in its entirety in the documentation or other materials provided with the distribution, (3) improvements, additions and upgrades to the software will be provided to NRL Authors in computer readable form, with an unlimited, royalty-free license to use these improvements, additions and upgrades, and the authority to grant unlimited royalty-free sublicenses to these improvements and (4) all published research using this software display the following acknowledgment ``This work uses the DAVE/DAVE4VM codes written and developed by the Naval Research Laboratory.''

Neither the name of NRL or its contributors, nor any entity of the United States Government may be used to endorse or promote products derived from this software, nor does the inclusion of the NRL written and developed software directly or indirectly suggest NRL's or the United States Government's endorsement of this product.

THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.

Link for download the original code written in IDL: https://ccmc.gsfc.nasa.gov/lwsrepository/index.php