BandedMatrices.jl
A Julia package for representing banded matrices
This package supports representing banded matrices by only the entries on the bands.
One can create banded matrices of type BandedMatrix as follows:
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
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.
Specialized algebra routines are overriden, include * and \:
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
# 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