https://github.com/JuliaMatrices/BlockBandedMatrices.jl

A Julia package for representing block-banded matrices and banded-block-banded matrices
https://github.com/JuliaMatrices/BlockBandedMatrices.jl

Last synced: about 2 months ago
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A Julia package for representing block-banded matrices and banded-block-banded matrices

• Host: GitHub
• URL: https://github.com/JuliaMatrices/BlockBandedMatrices.jl
• Owner: JuliaLinearAlgebra
• License: mit
• Created: 2016-12-10T03:10:30.000Z (over 8 years ago)
• Default Branch: master
• Last Pushed: 2024-04-17T12:29:16.000Z (12 months ago)
• Last Synced: 2024-04-17T14:12:06.267Z (12 months ago)
• Language: Julia
• Homepage: https://julialinearalgebra.github.io/BlockBandedMatrices.jl/
• Size: 880 KB
• Stars: 56
• Watchers: 8
• Forks: 13
• Open Issues: 20
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# BlockBandedMatrices.jl

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

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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](https://github.com/JuliaArrays/BlockArrays.jl)

whose layout of non-zero blocks is banded. We can construct a `BlockBandedMatrix` as follows:

```julia

using FillArrays, LinearAlgebra

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](https://github.com/JuliaLinearAlgebra/BandedMatrices.jl).

We can construct a `BandedBlockBandedMatrix` as follows:

```julia

using FillArrays, LinearAlgebra

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

```