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# 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`.

11/20/2017

19 days ago

115 commits