pyamg 1.0.0

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

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.

Objectives

 * ease of use
 o interface is accessible to non-experts
 o extensive documentation and references
 * speed
 o solves problems with millions of unknowns efficiently
 o core multigrid algorithms are implemented in C++ and translated through SWIG
 o sparse matrix support provided by scipy.sparse
 * readability
 o source code is organized into intuitive components
 * extensibility
 o core components can be reused to implement additional techniques
 o new features are easy integrated
 * experimentation
 o facilitates rapid prototyping and analysis of multigrid methods
 * portability
 o tested on several platforms
 o 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


Product's homepage

Here are some key features of "pyamg":

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)

Requirements:

· Python