solve

solve, a Python code which solves a linear system of equations A*x=b using Gauss elimination.

In Python, there are a number of high quality functions, such as the numpy.linalg.solve() function, which could be used for this purpose. Nonetheless, this code may be useful because:

• it shows the steps involved in a simple Gauss-elimination procedure;
• it can be used to count the number of operations in Gauss-elimination;
• it can be used as a guide for writing a corresponding program in a non-Python environment;
• its performance can be compared to corresponding versions in C, C++, Fortran and MATLAB;
• it can be used as a starting point for exploring band storage, sparse storage, iterative solutions and other topics in linear algebra.

Licensing:

The computer code and data files made available on this web page are distributed under the MIT license

Languages:

solve is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

cg, a Python code which implements a simple version of the conjugate gradient (CG) method for solving a system of linear equations of the form A*x=b, suitable for situations in which the matrix A is positive definite (only real, positive eigenvalues) and symmetric.

gmgsolve, a Python code which can apply one step of the V-cycle of the geometric multigrid method, by Mike Sussman.

r8ge, a Python code which contains linear algebra functions for R8GE matrices (real, 64 bit General storage format).

r8lib, a Python code which contains many utility routines using double precision real (R8) arithmetic.

Source Code:

• solve.py, the source code.
• solve.sh, calls the tests.
• solve.txt, the output file.