PyAMG is developed by Nathan Bell, Luke Olson, and Jacob Schroder, in the Deparment of Computer Science at the University of Illinois at Urbana-Champaign. Portions of the project were partially supported by the NSF under award DMS-0612448.

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Introduction

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

Citing

@MISC{BeOlSc2011,
      author = "Bell, W. N. and Olson, L. N. and Schroder, J. B.",
      title = "{PyAMG}: Algebraic Multigrid Solvers in {Python} v2.0",
      year = "2011",
      url = "http://www.pyamg.org",
      note = "Release 2.0"
      }

Getting Help

Contact the pyamg-user group

Look at the Tutorial or the Examples (for instance the 0STARTHERE example)

Read the documentation (TODO: new link coming)

or

Try the docstrings: for example

print pyamg.strength.__doc__

or

pyamg.strength?

in ipython

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.

PyAMG Objectives

ease of use

• interface is accessible to non-experts
• extensive documentation and references

speed

• solves problems with millions of unknowns efficiently
• core multigrid algorithms are implemented in C++ and translated through SWIG
• sparse matrix support provided by scipy.sparse

readability

• source code is organized into intuitive components

extensibility

• core components can be reused to implement additional techniques
• new features are easy integrated

experimentation

• facilitates rapid prototyping and analysis of multigrid methods

portability

• tested on several platforms
• relies only on Python, NumPy, and SciPy

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.

from scipy import *
from scipy.linalg import *
from pyamg import *
from pyamg.gallery import *
A = poisson((500,500), format='csr')     # 2D Poisson problem on 500x500 grid
ml = ruge_stuben_solver(A)               # construct the multigrid hierarchy
print ml                                 # print hierarchy information
b = 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-8
print "residual norm is", norm(b - A*x)  # compute norm of residual vector

Program output:

    multilevel_solver
    Number of Levels:     6
    Operator Complexity:  2.198
    Grid Complexity:      1.666
    Coarse Solver:        'pinv2'
      level   unknowns     nonzeros
        0       250000      1248000 [45.50%]
        1       125000      1121002 [40.87%]
        2        31252       280662 [10.23%]
        3         7825        70657 [ 2.58%]
        4         1937        17973 [ 0.66%]
        5          484         4728 [ 0.17%]
    
    residual norm is 1.86112114946e-06