Installation

PyAMG requires numpy and scipy

pip install pyamg

or from source:

pip install .

or with conda (see details below)

conda config --add channels conda-forge
conda install pyamg

For an editable install use:

pip install meson-python meson ninja pybind11 versioningit pytest
pip install --no-build-isolation -e .

Introduction

PyAMG is a library of Algebraic Multigrid (AMG) solvers with a convenient Python interface.

PyAMG is currently developed and maintained by
Luke Olson,
Jacob Schroder, and
Ben Southworth.
The organization of the project can be found in organization.md and
examples of use can be found in pyamg-examples.

Acknowledgements:
PyAMG was created by
Nathan Bell,
Luke Olson, and
Jacob Schroder.
Portions of the project were partially supported by the NSF under award DMS-0612448.

Citing

If you use PyAMG in your work, please consider using the following citation:

<pre> @article{pyamg2023, author = {Nathan Bell and Luke N. Olson and Jacob Schroder and Ben Southworth}, title = {{PyAMG}: Algebraic Multigrid Solvers in Python}, journal = {Journal of Open Source Software}, year = {2023}, publisher = {The Open Journal}, volume = {8}, number = {87}, pages = {5495}, doi = {10.21105/joss.05495}, url = {https://doi.org/10.21105/joss.05495}, } </pre>

Getting Help

• For documentation see http://pyamg.readthedocs.io/en/latest/.

• Create an issue.

• Look at the Tutorial or the examples (for instance the 0_start_here example).

• Run the unit tests (pip install pytest):

  • From Python with PyAMG installed and from a non-source directory:

  pythonCopy
  import pyamg
  pyamg.test()

  • From the PyAMG source directory and an editable install:
    (e.g. with pip install -e .):

  bashCopy
  pip install --no-build-isolation -e ".[test]"
  pytest .

  • From the PyAMG source directory and a regular install:
    (e.g. with pip install -e .):

  bashCopy
  pip install ".[test]"
  pytest --pyargs pyamg --basetemp=temp

What is AMG?

AMG is a multilevel technique for solving large-scale linear systems with optimal or near-optimal efficiency. Unlike geometric multigrid, AMG requires little or no geometric information about the underlying problem and develops a sequence of coarser grids directly from the input matrix. This feature is especially important for problems discretized on unstructured meshes and irregular grids.

PyAMG Features

PyAMG features implementations of:

• Ruge-Stuben (RS) or Classical AMG
• AMG based on Smoothed Aggregation (SA)

and experimental support for:

• Adaptive Smoothed Aggregation (αSA)
• Compatible Relaxation (CR)

The predominant portion of PyAMG is written in Python with a smaller amount of supporting C++ code for performance critical operations.

Example Usage

PyAMG is easy to use! The following code constructs a two-dimensional Poisson problem and solves the resulting linear system with Classical AMG.

pythonCopy
import pyamg
import numpy as np
A = pyamg.gallery.poisson((500,500), format='csr')  # 2D Poisson problem on 500x500 grid
ml = pyamg.ruge_stuben_solver(A)                    # construct the multigrid hierarchy
print(ml)                                           # print hierarchy information
b = np.random.rand(A.shape[0])                      # pick a random right hand side
x = ml.solve(b, tol=1e-10)                          # solve Ax=b to a tolerance of 1e-10
print("residual: ", np.linalg.norm(b-A@x))          # compute norm of residual vector

Program output:

<pre> MultilevelSolver Number of Levels: 9 Operator Complexity: 2.198 Grid Complexity: 1.667 Coarse Solver: 'pinv' level unknowns nonzeros 0 250000 1248000 [45.50%] 1 125000 1121002 [40.87%] 2 31372 280840 [10.24%] 3 7814 69818 [2.55%] 4 1953 17559 [0.64%] 5 481 4421 [0.16%] 6 123 1145 [0.04%] 7 30 282 [0.01%] 8 10 76 [0.00%] residual: 4.772211803542084e-09 </pre>

Conda

More information can be found at conda-forge/pyamg-feedstock.

Linux:

OSX:

Windows:

Version:

Downloads:

Installing pyamg from the conda-forge channel can be achieved by adding conda-forge to your channels with:

conda config --add channels conda-forge

Once the conda-forge channel has been enabled, pyamg can be installed with:

conda install pyamg

It is possible to list all of the versions of pyamg available on your platform with:

conda search pyamg --channel conda-forge