PyAMG 5.1.0.post1.dev1+ge1fe54c#

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PyAMG requires numpy and scipy

pip install pyamg

or from source:

pip install .

(python install will no longer work)

or with conda (see details below)

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


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 ``` <>`_ and examples of use can be found in ``pyamg-examples` <pyamg/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.


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

  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       = {},

Getting Help#

  • For documentation see

  • Create an issue.

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

  • Run the unit tests (pip install pytest):

    • With PyAMG installed and from a non-source directory: .. code-block:: python

      import pyamg pyamg.test()

    • From the PyAMG source directory and installed (e.g. with pip install -e .): .. code-block:: python

      pytest .

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.

import pyamg
import numpy as np
A =,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:

Number of Levels:     9
Operator Complexity:  2.199
Grid Complexity:      1.667
Coarse Solver:        'pinv2'
  level   unknowns     nonzeros
    0       250000      1248000 [45.47%]
    1       125000      1121002 [40.84%]
    2        31252       280662 [10.23%]
    3         7825        70657 [ 2.57%]
    4         1937        17971 [ 0.65%]
    5          483         4725 [ 0.17%]
    6          124         1352 [ 0.05%]
    7           29          293 [ 0.01%]
    8            7           41 [ 0.00%]

residual:  1.24748994988e-08


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


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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