AlmostBlockDiagonal{T, I <: Integer, V <: AbstractMatrix{T}} <: AbstractMatrix{T}

A matrix with block matrices on the diagonal, but not strictly has their corner against each other.

For example:

A 10 x 10 matrix:

x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x

can be abstracted as:

julia> AlmostBlockDiagonal([rand(3,4),rand(2,4),rand(2,4),rand(3,4)], [2,2,2,4])

Here, the first argument is the fillers in the almost block diagonal matrix, the second argument is the offset of each adjacent block in the diagonal.

! note The column of block ncol and row of block nrow must satisfy: ncol ≥ nrow.

The implementation mainly comes from the paper: SOLVEBLOK: A Package for Solving Almost Block Diagonal Linear Systems which is originally a FORTRAN program for the solution of an almost block diagonal system by gaussian elimination with scale row pivoting.

Intermediate matrix used for the representation of modified almost block diagonals mainly use for pivoting LU factorization.

Convert a AlmostBlockDiagonal matrix to an intermediate form to do the factorization and solving

! note Only for the square almost diagonal matrix of course

nblocks(A::AlmostBlockDiagonal[, dim])

Return the number of on-diagonal blocks.

nblocks(A::IntermediateAlmostBlockDiagonal[, dim])