# BlockBandedMatrices.jl

A Julia package for representing block-block-banded matrices and banded-block-banded matrices

This package supports representing block-banded and banded-block-banded matrices by only storing the entries in the non-zero bands.

A `BlockBandedMatrix`

is a subtype of `BlockMatrix`

of BlockArrays.jl
whose non-zero blocks are banded. We can construct a `BlockBandedMatrix`

as follows:

```
l,u = 2,1 # block bandwidths
N = M = 4 # number of row/column blocks
cols = rows = 1:N # block sizes
BlockBandedMatrix(Zeros(sum(rows),sum(cols)), rows,cols, (l,u)) # creates a block-banded matrix of zeros
BlockBandedMatrix(Ones(sum(rows),sum(cols)), rows,cols, (l,u)) # creates a block-banded matrix with ones in the non-zero entries
BlockBandedMatrix(I, rows,cols, (l,u)) # creates a block-banded identity matrix
```

A `BandedBlockBandedMatrix`

has the added structure that the blocks themselves are
banded, and conform to the banded matrix interface of BandedMatrices.jl.
We can construct a `BandedBlockBandedMatrix`

as follows:

```
l,u = 2,1 # block bandwidths
λ,μ = 1,2 # sub-block bandwidths: the bandwidths of each block
N = M = 4 # number of row/column blocks
cols = rows = 1:N # block sizes
BandedBlockBandedMatrix(Zeros(sum(rows),sum(cols)), rows,cols, (l,u), (λ,μ)) # creates a banded-block-banded matrix of zeros
BandedBlockBandedMatrix(Ones(sum(rows),sum(cols)), rows,cols, (l,u), (λ,μ)) # creates a banded-block-banded matrix with ones in the non-zero entries
BandedBlockBandedMatrix(I, rows,cols, (l,u), (λ,μ))) # creates a banded-block-banded identity matrix
```