setTimeStepper( stepper) 40 41 def slowTimeStep( self, dt= 0.0): 42 '''Takes a time step using straight forward Python loops.''' 43 g = self. dot( v, v)) 32 33 34 class LaplaceSolver: 35 '''A simple Laplacian solver that can use different schemes to 36 solve the problem.''' 37 def _init_( self, grid, stepper= ' numeric '): 38 self. 28 This requires that self.u and self.old_u must be appropriately 29 setup.''' 30 v = ( self. u = func( x, ymax) 25 26 def computeError( self): 27 '''Computes absolute error using an L2 norm for the solution. copy() 14 15 def setBCFunc( self, func): 16 '''Sets the BC given a function of two variables.''' 17 xmin, ymin = self. zeros(( nx, ny), ' d ') 12 # used to compute the change in solution in some of the methods. dy = float( ymax- ymin)/( ny- 1) 11 self. dx = float( xmax- xmin)/( nx- 1) 10 self. The solution can be obtained by iterating in the following manner.ġ import numpy 2 3 class Grid: 4 '''A simple grid class that stores the details and solution of the 5 computational grid.''' 6 def _init_( self, nx= 10, ny= 10, xmin= 0.0, xmax= 1.0, 7 ymin= 0.0, ymax= 1.0): 8 self. The values of u along the sides of the rectangle are given.

Then the function u can be represented as a 2 dimensional array - u(nx, ny). Discretise the domain into an (nx x ny) grid of points. It can be shown that this problem can be solved using a simple four point averaging scheme as follows. For convenience the domain of interest is considered to be a rectangle and the boundary values at the sides of this rectangle are given.

We are required to solve for some unknown function u(x,y) such that ∇ 2u = 0 with a boundary condition specified. The formal specification of the problem is as follows. The example we will consider is a very simple (read, trivial) case of solving the 2D Laplace equation using an iterative finite difference scheme (four point averaging, Gauss-Seidel or Gauss-Jordan). We will also use this opportunity to benchmark the various ways to solve a particular numerical problem in Python and compare them to an implementation of the algorithm in C++. We will also show how to use f2py to wrap a Fortran subroutine and call it from within Python.

We'll use NumPy, SciPy's weave (using both weave.blitz and weave.inline) and Pyrex. This is a simple introductory document to using Python for performance computing. The source tarball ( perfpy_2.tgz ) contains in addition the Fortran code, the pure C++ code, the Pyrex sources and a setup.py script to build the f2py and Pyrex module. Laplace.py is the complete Python code discussed below. This article was originally written by Prabhu Ramachandran. A beginners guide to using Python for performance computingĪ beginners guide to using Python for performance computingĪ comparison of weave with NumPy, Pyrex, Psyco, Fortran (77 and 90) and C++ for solving Laplace's equation.

Scipy performance python gauss seidel