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bjarthurbjarthur
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add option for read-only off-diagonal elements
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‎README.md

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PackedArrays.jl defines the `SymmetricPacked` type which concatenates the
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columns of either the upper or lower triangle into a vector thereby using
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only a little more than half the memory.
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```
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julia> using PackedArrays
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julia> A = rand(5,5)
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5×5 Matrix{Float64}:
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0.364856 0.736451 0.704095 0.842738 0.207618
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0.0797498 0.63549 0.861638 0.834968 0.0660772
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0.152769 0.00271082 0.131074 0.727387 0.0995039
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0.201612 0.0429332 0.682401 0.96513 0.616451
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0.283603 0.818754 0.76548 0.284176 0.369353
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julia> AP = SymmetricPacked(A) # defaults to :U -- the upper triangle
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5×5 SymmetricPacked{Float64, Matrix{Float64}}:
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0.364856 0.736451 0.704095 0.842738 0.207618
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0.736451 0.63549 0.861638 0.834968 0.0660772
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0.704095 0.861638 0.131074 0.727387 0.0995039
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0.842738 0.834968 0.727387 0.96513 0.616451
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0.207618 0.0660772 0.0995039 0.616451 0.369353
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julia> AP.tri
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15-element Vector{Float64}:
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0.364855947737336
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0.7364505269442262
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0.63549015394607
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0.7040945131597321
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0.8616375176332387
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0.13107440168239382
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0.8427381656704127
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0.8349681382276347
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0.7273865854008484
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0.9651301546768161
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0.20761807799000453
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0.066077207744069
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0.09950392155913346
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0.6164510864085191
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0.3693525034730706
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julia> Base.summarysize(A)
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240
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julia> Base.summarysize(AP)
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184
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```
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Many BLAS routines input this packed storage format:
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```
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julia> using LinearAlgebra
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julia> y = rand(5)
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5-element Vector{Float64}:
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0.47717272627749296
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0.11563714323328722
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0.7096777607286059
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0.2632097580818683
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0.28688074092456195
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julia> x = rand(5)
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5-element Vector{Float64}:
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0.14292999002604434
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0.8641487402596497
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0.914860119103189
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0.06250499506408325
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0.14202984533447915
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julia> α = 0.5
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0.5
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julia> β = 0.5
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0.5
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julia> BLAS.spmv!(AP.uplo, α, AP.tri, x, β, copy(y)) # directly call BLAS
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5-element Vector{Float64}:
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0.946017838465631
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0.809954221322169
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0.867204761074523
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0.9592679333345454
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0.27783932357851576
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julia> mul!(copy(y), AP, x, α, β) # or use the equivalent julian interface
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5-element Vector{Float64}:
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0.946017838465631
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0.809954221322169
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0.867204761074523
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0.9592679333345454
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0.27783932357851576
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```
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`SymmetricPacked` differs in one important aspect to `LinearAlgebra.Symmetric`
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in that it optionally permits off diagonal elements to be set. Continuing
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from the example above:
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```
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julia> AP[1,1]=5
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5
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julia> AP
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5×5 SymmetricPacked{Float64, Matrix{Float64}, Val{:RO}()}:
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5.0 0.736451 0.704095 0.842738 0.207618
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0.736451 0.63549 0.861638 0.834968 0.0660772
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0.704095 0.861638 0.131074 0.727387 0.0995039
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0.842738 0.834968 0.727387 0.96513 0.616451
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0.207618 0.0660772 0.0995039 0.616451 0.369353
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julia> AP[1,5]=5
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ERROR: ArgumentError: Cannot set a non-diagonal index in a symmetric matrix
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Stacktrace:
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[1] setindex!(A::SymmetricPacked{Float64, Matrix{Float64}, Val{:RO}()}, v::Int64, i::Int64, j::Int64)
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@ PackedArrays ~/projects/darshan/PackedArrays/src/PackedArrays.jl:114
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[2] top-level scope
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@ REPL[7]:1
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julia> APRW = SymmetricPacked(A, :L, Val(:RW)) # default is :RO
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5×5 SymmetricPacked{Float64, Matrix{Float64}, Val{:RW}()}:
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0.364856 0.0797498 0.152769 0.201612 0.283603
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0.0797498 0.63549 0.00271082 0.0429332 0.818754
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0.152769 0.00271082 0.131074 0.682401 0.76548
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0.201612 0.0429332 0.682401 0.96513 0.284176
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0.283603 0.818754 0.76548 0.284176 0.369353
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julia> APRW[1,5]=5
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5
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julia> APRW
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5×5 SymmetricPacked{Float64, Matrix{Float64}, Val{:RW}()}:
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0.364856 0.0797498 0.152769 0.201612 5.0
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0.0797498 0.63549 0.00271082 0.0429332 0.818754
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0.152769 0.00271082 0.131074 0.682401 0.76548
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0.201612 0.0429332 0.682401 0.96513 0.284176
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5.0 0.818754 0.76548 0.284176 0.369353
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```

‎src/PackedArrays.jl

Lines changed: 22 additions & 14 deletions
Original file line numberDiff line numberDiff line change
@@ -7,15 +7,15 @@ import LinearAlgebra: mul!, BLAS, BlasFloat, generic_matvecmul!, MulAddMul
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export SymmetricPacked
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10-
struct SymmetricPacked{T,S<:AbstractMatrix{<:T}} <: AbstractMatrix{T}
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struct SymmetricPacked{T,S<:AbstractMatrix{<:T},V} <: AbstractMatrix{T}
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tri::Vector{T}
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n::Int
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uplo::Char
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function SymmetricPacked{T,S}(tri, n, uplo) where {T,S<:AbstractMatrix{<:T}}
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function SymmetricPacked{T,S,V}(tri, n, uplo) where {T,S<:AbstractMatrix{<:T},V}
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require_one_based_indexing(tri)
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uplo=='U' || uplo=='L' || throw(ArgumentError("uplo must be either 'U' (upper) or 'L' (lower)"))
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new{T,S}(tri, n, uplo)
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new{T,S,V}(tri, n, uplo)
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end
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end
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end
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"""
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SymmetricPacked(A, uplo=:U)
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SymmetricPacked(A, uplo=:U, offdiag=Val(:RO))
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Construct a `Symmetric` matrix in packed form of the upper (if `uplo = :U`)
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or lower (if `uplo = :L`) triangle of the matrix `A`.
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or lower (if `uplo = :L`) triangle of the matrix `A`. `offdiag` specifies
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whether elements not on the diagaonal can be set (if `:RW`) or not (if `:RO`).
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# Examples
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```jldoctest
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184
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```
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"""
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function SymmetricPacked(A::AbstractMatrix{T}, uplo::Symbol=:U) where {T}
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function SymmetricPacked(A::AbstractMatrix{T}, uplo::Symbol=:U, offdiag=Val(:RO)) where {T}
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n = checksquare(A)
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SymmetricPacked{T,typeof(A)}(pack(A, uplo), n, char_uplo(uplo))
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SymmetricPacked{T,typeof(A),offdiag}(pack(A, uplo), n, char_uplo(uplo))
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end
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function SymmetricPacked(x::SymmetricPacked{T,S}) where{T,S}
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SymmetricPacked{T,S}(T.(x.tri), x.n, x.uplo)
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function SymmetricPacked(x::SymmetricPacked{T,S,V}) where{T,S,V}
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SymmetricPacked{T,S,V}(T.(x.tri), x.n, x.uplo)
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end
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checksquare(x::SymmetricPacked) = x.n
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convert(::Type{SymmetricPacked{T,S}}, x::SymmetricPacked) where {T,S} = SymmetricPacked{T,S}(T.(x.tri), x.n, x.uplo)
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convert(::Type{SymmetricPacked{T,S,V}}, x::SymmetricPacked) where {T,S,V} = SymmetricPacked{T,S}(T.(x.tri), x.n, x.uplo)
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unsafe_convert(::Type{Ptr{T}}, A::SymmetricPacked{T,S}) where {T,S} = Base.unsafe_convert(Ptr{T}, A.tri)
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unsafe_convert(::Type{Ptr{T}}, A::SymmetricPacked{T,S,V}) where {T,S,V} = Base.unsafe_convert(Ptr{T}, A.tri)
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size(A::SymmetricPacked) = (A.n,A.n)
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return r
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end
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function setindex!(A::SymmetricPacked, v, i::Int, j::Int)
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function _setindex!(A::SymmetricPacked, v, i::Int, j::Int)
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@boundscheck checkbounds(A, i, j)
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if A.uplo=='U'
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i,j = minmax(i,j)
@@ -109,15 +110,22 @@ function setindex!(A::SymmetricPacked, v, i::Int, j::Int)
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return v
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end
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function setindex!(A::SymmetricPacked{T,S,Val(:RO)}, v, i::Int, j::Int) where {T,S}
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i!=j && throw(ArgumentError("Cannot set a non-diagonal index in a symmetric matrix"))
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_setindex!(A, v, i, j)
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end
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setindex!(A::SymmetricPacked{T,S,Val(:RW)}, v, i::Int, j::Int) where {T,S} = _setindex!(A, v, i, j)
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function copy(A::SymmetricPacked{T,S}) where {T,S}
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B = copy(A.tri)
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SymmetricPacked{T,S}(B, A.n, A.uplo)
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end
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@inline function mul!(y::StridedVector{T},
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AP::SymmetricPacked{T,<:StridedMatrix},
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AP::SymmetricPacked{T,<:StridedMatrix,V},
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x::StridedVector{T},
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α::Number, β::Number) where {T<:BlasFloat}
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α::Number, β::Number) where {T<:BlasFloat,V}
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alpha, beta = promote(α, β, zero(T))
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if alpha isa Union{Bool,T} && beta isa Union{Bool,T}
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BLAS.spmv!(AP.uplo, alpha, AP.tri, x, beta, y)

‎test/runtests.jl

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Original file line numberDiff line numberDiff line change
@@ -3,7 +3,7 @@ using PackedArrays, Test, LinearAlgebra
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A = collect(reshape(1:9.0,3,3))
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@testset "upper triangle" begin
6-
APU = SymmetricPacked(A, :U)
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APU = SymmetricPacked(A, :U, Val(:RW))
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@test APU[1,1] == A[1,1]
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@test APU[1,2] == A[1,2]
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2020
end
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2222
@testset "lower triangle" begin
23-
APL = SymmetricPacked(A, :L)
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APL = SymmetricPacked(A, :L, Val(:RW))
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2525
@test APL[1,1] == A[1,1]
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@test APL[1,2] == A[2,1]
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@test APL[2,1] == 0
3737
end
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39+
@testset "read-only" begin
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APL = SymmetricPacked(A, :L)
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APL[1,1]=3
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@test APL[1,1] == 3
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@test_throws ArgumentError APL[1,3]=3
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APL = SymmetricPacked(A, :L, Val(:RO))
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APL[1,1]=3
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@test APL[1,1] == 3
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@test_throws ArgumentError APL[1,3]=3
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end
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@testset "mul!" begin
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for uplo in [:U, :L]
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y = Float64[1,2,3]

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