PyAMG 5.2.1.post1.dev29+g7e5b79d#
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, Jacob Schroder, and Ben Southworth. The organization of the project can be found in ``organization.md` <organization.md>`_ 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.
Citing#
If you use PyAMG in your work, please consider using the following citation:
@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}, }
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
):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:: pythonpytest .
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 = 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:
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
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
Reference#
- PyAMG Reference
- Multigrid data structure (“The Multilevel Hierarchy”)
- Core AMG Methods
- Common AMG Components
- Helper Routings
- Krylov Methods
- Gallery Problems
- amg_core
- pyamg.amg_core
apply_absolute_distance_filter()
apply_distance_filter()
apply_givens()
apply_householders()
approx_ideal_restriction_pass1()
approx_ideal_restriction_pass2()
bellman_ford()
block_approx_ideal_restriction_pass2()
block_gauss_seidel()
block_jacobi()
block_jacobi_indexed()
breadth_first_search()
bsr_gauss_seidel()
bsr_jacobi()
bsr_jacobi_indexed()
calc_BtB()
classical_strength_of_connection_abs()
classical_strength_of_connection_min()
cljp_naive_splitting()
cluster_center()
cluster_node_incidence()
connected_components()
cr_helper()
csc_scale_columns()
csc_scale_rows()
evolution_strength_helper()
extract_subblocks()
filter_matrix_rows()
fit_candidates()
gauss_seidel()
gauss_seidel_indexed()
gauss_seidel_ne()
gauss_seidel_nr()
householder_hornerscheme()
incomplete_mat_mult_bsr()
incomplete_mat_mult_csr()
jacobi()
jacobi_indexed()
jacobi_ne()
lloyd_cluster()
lloyd_cluster_exact()
maximal_independent_set_k_parallel()
maximal_independent_set_parallel()
maximal_independent_set_serial()
maximum_row_value()
min_blocks()
naive_aggregation()
one_point_interpolation()
overlapping_schwarz_csr()
pairwise_aggregation()
pinv_array()
remove_strong_FF_connections()
rs_cf_splitting()
rs_cf_splitting_pass2()
rs_classical_interpolation_pass1()
rs_classical_interpolation_pass2()
rs_direct_interpolation_pass1()
rs_direct_interpolation_pass2()
satisfy_constraints_helper()
standard_aggregation()
symmetric_strength_of_connection()
truncate_rows_csr()
vertex_coloring_LDF()
vertex_coloring_jones_plassmann()
vertex_coloring_mis()
- pyamg.amg_core