BandMatrix Tweaks

Banded matrices

Banded matrices are important as they naturally arise from discretising 1-dimensional PDEs and can be efficiently solved via LU and Cholesky decomposition.

Eigen has some support for banded matrices via the Eigen::internal::BandMatrix class. This class stores banded matrices as their diagonals, allowing efficient storage of these sparse matrices.

For details on the storage format see http://www.netlib.org/lapack/lug/node124.html.

What tweaks?

Since the operations implemented for the BandMatrix class are somewhat lacking, the purpose of this library is to add some of those missing features. All contributions are welcome.

Current capabilities are:

• Element access via the item function: B(i, j) is item(B, i, j)
• Row and column access with the slice function: B(i, j:k) is slice(B, i, {j, k}), B(i:j, k) is slice(B, {i, j}, k)
• Multiplication via the mult function: B*b is mult(B, b)
• Transposition via the transpose function: B^T is transpose(B)
• Conversion from dense format via the fromDenseMatrix function: use either fromDenseMatrix(A, supers, subs) or fromDenseMatrix(A) for a dense matrix A.

Please see tutorial.cpp a more complete introduction.