FillArrays.jl

Julia package to lazily represent matrices filled with a single entry, as well as identity matrices. This package exports the following types: Eye, Fill, Ones, Zeros, Trues and Falses.

The primary purpose of this package is to present a unified way of constructing matrices. For example, to construct a 5-by-5 CLArray of all zeros, one would use

julia> CLArray(Zeros(5,5))

Because Zeros is lazy, this can be accomplished on the GPU with no memory transfer. Similarly, to construct a 5-by-5 BandedMatrix of all zeros with bandwidths (1,2), one would use

julia> BandedMatrix(Zeros(5,5), (1, 2))

Usage

Here are the matrix types:

julia> Zeros(5, 6)
5×6 Zeros{Float64}

julia> Zeros{Int}(2, 3)
2×3 Zeros{Int64}

julia> Ones{Int}(5)
5-element Ones{Int64}

julia> Eye{Int}(5)
 5×5 Diagonal{Int64,Ones{Int64,1,Tuple{Base.OneTo{Int64}}}}:
  1  ⋅  ⋅  ⋅  ⋅
  ⋅  1  ⋅  ⋅  ⋅
  ⋅  ⋅  1  ⋅  ⋅
  ⋅  ⋅  ⋅  1  ⋅
  ⋅  ⋅  ⋅  ⋅  1

julia> Fill(7.0f0, 3, 2)
3×2 Fill{Float32}: entries equal to 7.0

julia> Trues(2, 3)
2×3 Ones{Bool}

julia> Falses(2)
2-element Zeros{Bool}

They support conversion to other matrix types like Array, SparseVector, SparseMatrix, and Diagonal:

julia> Matrix(Zeros(5, 5))
5×5 Array{Float64,2}:
 0.0  0.0  0.0  0.0  0.0
 0.0  0.0  0.0  0.0  0.0
 0.0  0.0  0.0  0.0  0.0
 0.0  0.0  0.0  0.0  0.0
 0.0  0.0  0.0  0.0  0.0

julia> SparseMatrixCSC(Zeros(5, 5))
5×5 SparseMatrixCSC{Float64,Int64} with 0 stored entries

julia> Array(Fill(7, (2,3)))
2×3 Array{Int64,2}:
 7  7  7
 7  7  7

There is also support for offset index ranges, and the type includes the axes:

julia> Ones((-3:2, 1:2))
6×2 Ones{Float64,2,Tuple{UnitRange{Int64},UnitRange{Int64}}} with indices -3:2×1:2

julia> Fill(7, ((0:2), (-1:0)))
3×2 Fill{Int64,2,Tuple{UnitRange{Int64},UnitRange{Int64}}} with indices 0:2×-1:0: entries equal to 7

julia> typeof(Zeros(5,6))
Zeros{Float64,2,Tuple{Base.OneTo{Int64},Base.OneTo{Int64}}}

These types have methods that perform many operations efficiently, including elementary algebra operations like multiplication and addition, as well as linear algebra methods like norm, adjoint, transpose and vec.