[](https://github.com/pyamg/pyamg/actions?query=workflow%3ACI-test+branch%3Amain)
[](https://github.com/pyamg/pyamg/actions?query=workflow%3ACI-lint+branch%3Amain)
[](https://pypi.org/project/pyamg/)
[](https://pypi.org/project/pyamg/)
[](https://app.codecov.io/gh/pyamg/pyamg)
[](https://doi.org/10.21105/joss.05495)
# Installation
PyAMG requires `numpy` and `scipy`
```
pip install pyamg
```
or from source:
```
pip install .
```
(`python setup.py install` will no longer work)
or with conda (see details below)
```
conda config --add channels conda-forge
conda install pyamg
```
# Introduction
PyAMG is a library of **Algebraic Multigrid (AMG)** solvers with a convenient Python interface.
PyAMG is currently developed and maintained by
[Luke Olson](http://lukeo.cs.illinois.edu),
[Jacob Schroder](https://www.unm.edu/~jbschroder), and
[Ben Southworth](https://arxiv.org/a/southworth_b_1.html).
The organization of the project can be found in [`organization.md`](organization.md) and
examples of use can be found in [`pyamg-examples`](https://github.com/pyamg/pyamg-examples).
**Acknowledgements:**
PyAMG was created by
[Nathan Bell](http://wnbell.com/),
[Luke Olson](http://lukeo.cs.illinois.edu), and
[Jacob Schroder](https://www.unm.edu/~jbschroder).
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/](http://pyamg.readthedocs.io/en/latest/).
- Create an [issue](https://github.com/pyamg/pyamg/issues).
- Look at the [Tutorial](https://github.com/pyamg/pyamg/wiki/Tutorial) or the [examples](https://github.com/pyamg/pyamg-examples) (for instance the [0_start_here](https://github.com/pyamg/pyamg-examples/blob/main/0_start_here/demo.py) example).
- Run the unit tests (`pip install pytest`):
- With PyAMG installed and from a non-source directory:
```python
import pyamg
pyamg.test()
```
- From the PyAMG source directory and installed (e.g. with `pip install -e .`):
```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.
````python
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>
multilevel_solver
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
</pre>
# Conda
More information can be found at [conda-forge/pyamg-feedstock](https://github.com/conda-forge/pyamg-feedstock).
*Linux:*
[](https://circleci.com/gh/conda-forge/pyamg-feedstock)
*OSX:*
[](https://travis-ci.org/conda-forge/pyamg-feedstock)
*Windows:*
[](https://ci.appveyor.com/project/conda-forge/pyamg-feedstock/branch/master)
*Version:*
[](https://anaconda.org/conda-forge/pyamg)
*Downloads:*
[](https://anaconda.org/conda-forge/pyamg)
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
```
Raw data
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"keywords": "algebraic multigrid,AMG,sparse matrix,preconditioning",
"author": "Nathan Bell, Luke Olson, and Jacob Schroder",
"author_email": "luke.olson@gmail.com",
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"description": "[](https://github.com/pyamg/pyamg/actions?query=workflow%3ACI-test+branch%3Amain)\n[](https://github.com/pyamg/pyamg/actions?query=workflow%3ACI-lint+branch%3Amain)\n[](https://pypi.org/project/pyamg/)\n[](https://pypi.org/project/pyamg/)\n[](https://app.codecov.io/gh/pyamg/pyamg)\n[](https://doi.org/10.21105/joss.05495)\n\n# Installation\nPyAMG requires `numpy` and `scipy`\n\n```\npip install pyamg\n```\n\nor from source:\n\n```\npip install .\n```\n\n(`python setup.py install` will no longer work)\n\nor with conda (see details below)\n\n```\nconda config --add channels conda-forge\nconda install pyamg\n```\n\n# Introduction\n\nPyAMG is a library of **Algebraic Multigrid (AMG)** solvers with a convenient Python interface.\n\n\n\nPyAMG is currently developed and maintained by\n[Luke Olson](http://lukeo.cs.illinois.edu),\n[Jacob Schroder](https://www.unm.edu/~jbschroder), and\n[Ben Southworth](https://arxiv.org/a/southworth_b_1.html).\nThe organization of the project can be found in [`organization.md`](organization.md) and\nexamples of use can be found in [`pyamg-examples`](https://github.com/pyamg/pyamg-examples).\n\n**Acknowledgements:**\nPyAMG was created by\n[Nathan Bell](http://wnbell.com/), \n[Luke Olson](http://lukeo.cs.illinois.edu), and\n[Jacob Schroder](https://www.unm.edu/~jbschroder).\nPortions of the project were partially supported by the NSF under award DMS-0612448.\n\n# Citing\n\nIf you use PyAMG in your work, please consider using the following citation:\n\n<pre>\n@article{pyamg2023,\n author = {Nathan Bell and Luke N. Olson and Jacob Schroder and Ben Southworth},\n title = {{PyAMG}: Algebraic Multigrid Solvers in Python},\n journal = {Journal of Open Source Software},\n year = {2023},\n publisher = {The Open Journal},\n volume = {8},\n number = {87},\n pages = {5495},\n doi = {10.21105/joss.05495},\n url = {https://doi.org/10.21105/joss.05495},\n}\n</pre>\n\n# Getting Help\n\n- For documentation see [http://pyamg.readthedocs.io/en/latest/](http://pyamg.readthedocs.io/en/latest/).\n\n- Create an [issue](https://github.com/pyamg/pyamg/issues).\n\n- Look at the [Tutorial](https://github.com/pyamg/pyamg/wiki/Tutorial) or the [examples](https://github.com/pyamg/pyamg-examples) (for instance the [0_start_here](https://github.com/pyamg/pyamg-examples/blob/main/0_start_here/demo.py) example).\n\n- Run the unit tests (`pip install pytest`):\n - With PyAMG installed and from a non-source directory:\n ```python\n import pyamg\n pyamg.test()\n ```\n - From the PyAMG source directory and installed (e.g. with `pip install -e .`):\n ```python\n pytest .\n ```\n\n# What is AMG?\n\n 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.\n\n# PyAMG Features\n\nPyAMG features implementations of:\n\n- **Ruge-Stuben (RS)** or *Classical AMG*\n- AMG based on **Smoothed Aggregation (SA)**\n\nand experimental support for:\n\n- **Adaptive Smoothed Aggregation (\u03b1SA)**\n- **Compatible Relaxation (CR)**\n\nThe predominant portion of PyAMG is written in Python with a smaller amount of supporting C++ code for performance critical operations.\n\n# Example Usage\n\nPyAMG is easy to use! The following code constructs a two-dimensional Poisson problem and solves the resulting linear system with Classical AMG.\n\n````python\nimport pyamg\nimport numpy as np\nA = pyamg.gallery.poisson((500,500), format='csr') # 2D Poisson problem on 500x500 grid\nml = pyamg.ruge_stuben_solver(A) # construct the multigrid hierarchy\nprint(ml) # print hierarchy information\nb = np.random.rand(A.shape[0]) # pick a random right hand side\nx = ml.solve(b, tol=1e-10) # solve Ax=b to a tolerance of 1e-10\nprint(\"residual: \", np.linalg.norm(b-A*x)) # compute norm of residual vector\n````\n\nProgram output:\n\n<pre>\nmultilevel_solver\nNumber of Levels: 9\nOperator Complexity: 2.199\nGrid Complexity: 1.667\nCoarse Solver: 'pinv2'\n level unknowns nonzeros\n 0 250000 1248000 [45.47%]\n 1 125000 1121002 [40.84%]\n 2 31252 280662 [10.23%]\n 3 7825 70657 [ 2.57%]\n 4 1937 17971 [ 0.65%]\n 5 483 4725 [ 0.17%]\n 6 124 1352 [ 0.05%]\n 7 29 293 [ 0.01%]\n 8 7 41 [ 0.00%]\n\nresidual: 1.24748994988e-08\n</pre>\n\n# Conda\n\nMore information can be found at [conda-forge/pyamg-feedstock](https://github.com/conda-forge/pyamg-feedstock).\n\n*Linux:*\n[](https://circleci.com/gh/conda-forge/pyamg-feedstock)\n\n*OSX:*\n[](https://travis-ci.org/conda-forge/pyamg-feedstock)\n\n*Windows:*\n[](https://ci.appveyor.com/project/conda-forge/pyamg-feedstock/branch/master)\n\n*Version:*\n[](https://anaconda.org/conda-forge/pyamg)\n\n*Downloads:*\n[](https://anaconda.org/conda-forge/pyamg)\n\nInstalling `pyamg` from the `conda-forge` channel can be achieved by adding `conda-forge` to your channels with:\n\n```\nconda config --add channels conda-forge\n```\n\nOnce the `conda-forge` channel has been enabled, `pyamg` can be installed with:\n\n```\nconda install pyamg\n```\n\nIt is possible to list all of the versions of `pyamg` available on your platform with:\n\n```\nconda search pyamg --channel conda-forge\n```\n",
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