Multiwavelet tutorial

Multiwavelet tutorial#

In this tutorial you will learn how to use the multiresolution analysis tools of the MRChem suite.

Using the VAMPyR Python package you will learn:

What a multiwavelet basis is and what it looks like.
How to use multiresolution analysis to represent functions and operators in 1D, 2D and 3D real space.

Prerequisites

Before attending this workshop, please make sure that you have the prerequisite software and hardware available.

We will work within Jupyter notebooks. We have set up this lesson such that it can be run entirely within your browser, using cloud infrastructure. You can also use your own computer, provided that it has the necessary tools installed. If that is not the case, please follow these detailed instructions.

	VAMPyR introduction
	Wavelet example: Haar
	Switching Representations via Two-Scale Relations
	Function projection in a MW basis
	Extension to many dimensions
	Separated representations of integral kernels
	Application of Poisson and Helmholtz operators
	Derivative operators
	Other operations on functions in the MW basis
	Basic Structures

Reference

Bibliography

Who is the course for?#

This lesson is for researchers and students that want to learn more about:

What are multiresolution analysis (MRA) and multiwavelets?
Which kind of operations can be performed with functions and operators using a Multiwalvelet representation?
What are the advantages and disadvantages of a Multiwavelet representation.

We assume that participants have knowledge of

calculus in one and several dimension
vector calculus
linear algebra
the Python programming language

About the course#

This lesson material is developed by the MRChem group at the Hylleraas Center for Quantum Molecular Sciences, in collaboration with Robert J. Harrison, Eduard Valeev, Florian Bischoff, Laura Ratcliff, Luigi Genovese.

Each lesson episode has clearly defined learning objectives and includes exercises and solutions, and is therefore also useful for self-learning. The lesson material is licensed under CC-BY-4.0 and can be reused in any form (with appropriate credit) in other courses and workshops.

Interacting with the notebooks#

MyBinder offers a free, customizable cloud computing environment and powers some of the contents of this lesson. You can run the entirety of Exercise 1 and most of Exercise 2 of this tutorial in the cloud.

The MyBinder web interface#

You can access the JupyterLab instance for this workshop by clicking the “launch binder” button at the top of the README file displayed at MRChemSoft/multiwavelet-tutorial

This will bring you to the loading page for the binder, which might take a few minutes to start up. Once loaded you will end up in a Jupyter-Lab environment with all necessary software packages installed. Bevare that the cloud instance runs on limited computational resources, so don’t expect awesome performance. Also, launching full-fledged MRChem calculations on molecules containing more than a few atoms is probably a bad idea.

Accessing a terminal#

From the “Launcher” tab, you can access terminal, Python interpreter, and notebook launchers:

You can open a text editor (for input files etc) by clicking “New” and select Text File. If you prefer a terminal editor, you can use nano or vim or emacs.

Starting the notebook from an episode#

You can run the notebook directly from an episode in the lesson. Click on the rocket icon on the top right of the page and select which launcher to use:

“Binder” will redirect you the binder instance. With “Live code”, you can run and modify the code cells within the webpage. The “Live code” option is powered by sphinx-thebe and, behind the scenes, MyBinder. Be aware that you will not be able to add new code cells in a live session.

Credits#

The lesson file structure and layout is heavily inspired by the VeloxChem workshop developed by EuroCC National Competence Center Sweden (ENCCS) and the PDC Center for High Performance Computing, which in turn is derived from work by CodeRefinery licensed under the MIT license. We have copied and adapted most of their license text.

Instructional Material#

This instructional material is made available under the Creative Commons Attribution license (CC-BY-4.0). The following is a human-readable summary of (and not a substitute for) the full legal text of the CC-BY-4.0 license. You are free:

to share - copy and redistribute the material in any medium or format
to adapt - remix, transform, and build upon the material for any purpose, even commercially.

The licensor cannot revoke these freedoms as long as you follow these license terms:

Attribution - You must give appropriate credit (mentioning that your work is derived from work that is Copyright (c) ENCCS and, where practical, linking to https://enccs.se), provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
No additional restrictions - You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits. With the understanding that:
- You do not have to comply with the license for elements of the material in the public domain or where your use is permitted by an applicable exception or limitation.
- No warranties are given. The license may not give you all of the permissions necessary for your intended use. For example, other rights such as publicity, privacy, or moral rights may limit how you use the material.

Software#

Except where otherwise noted, the example programs and other software provided with this repository are made available under the OSI-approved MIT license.