Best way to store a sparse matrix in .NET

Question

We have an application that stores a sparse matrix. This matrix has entries that mostly exist around the main diagonal of the matrix. I was wondering if there were any efficie

Answer 1

There are two questions here:

• "Mostly around the main diagonal" is too vague. If the elements lie in bands, then use banded storage of the bands themselves, as vectors offset from the main diagonal. If the elements are scattered randomly in the vicinity of the main diagonal, then either use a banded form that may include some zeros in the bands, or use a pure sparse form that stores only the elements and their positions in the array.

• What will you do with the matrix? If your goal is merely efficient storage, then a banded form will be efficient, with fast access to any element. If you will do linear algebra with the matrix, but never more than matrixvector multiplies, then the banded form will still work splendidly. If you work with matrixmatrix multiplies or matrix factorizations, where fill-in becomes a problem, then a pure sparse form may be more appropriate. For example, the product of two banded matrices will have additional bands, so the product of two tridiagonal matrices will be pentadiagonal. For a factorization, reorderings will sometimes be useful to minimize fill-in. (AMD is one choice, Approximate Minimum Degree permutation, but there are other schemes.)