Laplacian in 1D, 2D, or 3D

Sparse (1-3)D Laplacian on a rectangular grid with exact eigenpairs.

The code computes the exact eigenpairs of (1-3)D negative Laplacian on a rectangular finite-difference grid for combinations of Dirichlet, Neumann, and Periodic boundary conditions using explicit formulas from
http://en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors_of_the_second_derivative
The code can also compute the sparse matrix itself, using Kronecker sums of 1D Laplacians. For more information on tensor sums, see
http://en.wikipedia.org/wiki/Kronecker_sum_of_discrete_Laplacians

Example, compute everything for 3D negative Laplacian with mixed boundary conditions:
[lambda,V,A] = laplacian([100,45,55],{'DD' 'NN' 'P'}, 20);
Compute only the eigenvalues:
lambda = laplacian([100,45,55],{'DD' 'NN' 'P'}, 20);
Compute the matrix only:
[~,~,A] = laplacian([100,45,55],{'DD' 'NN' 'P'});

GNU OCTAVE compatible.

This code is a part of the BLOPEX eigensolver package, see
http://en.wikipedia.org/wiki/BLOPEX
or go directly to
http://code.google.com/p/blopex/

Copyright owners: Bryan C. Smith and Andrew V. Knyazev