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

A Julia package for representing banded matrices
https://github.com/JuliaMatrices/BandedMatrices.jl

Last synced: 29 days ago
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A Julia package for representing banded matrices

• Host: GitHub
• URL: https://github.com/JuliaMatrices/BandedMatrices.jl
• Owner: JuliaLinearAlgebra
• License: other
• Created: 2016-03-23T23:44:12.000Z (over 8 years ago)
• Default Branch: master
• Last Pushed: 2024-11-08T12:09:45.000Z (about 1 month ago)
• Last Synced: 2024-11-13T05:35:48.131Z (about 1 month ago)
• Language: Julia
• Homepage: http://julialinearalgebra.github.io/BandedMatrices.jl/
• Size: 2.96 MB
• Stars: 129
• Watchers: 11
• Forks: 38
• Open Issues: 55
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# BandedMatrices.jl

A Julia package for representing banded matrices

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This package supports representing banded matrices by only the entries on the

bands.

One can create banded matrices of type `BandedMatrix` as follows:

```julia

BandedMatrix(-1=> 1:5, 2=>1:3)     # creates a 6 x 6 banded matrix version of diagm(-1=> 1:5, 2=>1:3)

BandedMatrix((-1=> 1:5, 2=>1:3), (n,m))     # creates an n x m banded matrix with 1 sub-diagonals and u super-diagonals with the specified diagonals

BandedMatrix((-1=> 1:5, 2=>1:3), (n,m), (l,u))     # creates an n x m banded matrix with l sub-diagonals and u super-diagonals with the specified diagonals

BandedMatrix(FillArrays.Zeros(m,n), (l,u))    # creates a banded matrix of zeros, with l sub-diagonals and u super-diagonals

BandedMatrix(FillArrays.Ones(m,n), (l,u))     # creates a banded matrix of ones, with l sub-diagonals and u super-diagonals

BandedMatrix(FillArrays.Eye(n), (l,u))        # creates a banded  n x n identity matrix, with l sub-diagonals and u super-diagonals

brand(m,n,l,u)     # creates a random banded matrix, with l sub-diagonals and u super-diagonals

```

For more examples, see [the documentation](https://julialinearalgebra.github.io/BandedMatrices.jl/dev/#Creating-banded-matrices).

Specialized algebra routines are overriden, include `*` and `\`:

```julia

A = brand(10000,10000,4,3)  # creates a 10000 x 10000 matrix with 4 sub-diagonals

                            # and 3 super-diagonals

b = randn(10000)

A*b  #   Calls optimized matrix*vector routine

A*A  #   Calls optimized matrix*matrix routine

A\b  #   Calls optimized matrix\vector routine

```