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#127 fix: support cones for generic number types. #136

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#127 fix: support cones for generic number types. #136

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4e135d8
Adding support for BigFLoat cones
lrnv Jun 29, 2021
8607081
removing completely the typecheck
lrnv Jun 29, 2021
75dc3a0
Better dispatch
lrnv Jun 29, 2021
2421625
Remove D
lrnv Jun 29, 2021
337a365
formula was false
lrnv Jun 30, 2021
3e25ee5
Tring MutableArithmetics + small change.
lrnv Jun 30, 2021
c5b1f70
Move to mutable arithmetics for aribitrary type PSD projections
lrnv Jun 30, 2021
edfcbe9
Change comment
lrnv Jul 1, 2021
ae81709
Temporary fix
lrnv Jul 1, 2021
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9 changes: 6 additions & 3 deletions src/convexset.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -205,6 +205,7 @@ end

function _project!(X::AbstractMatrix{T}, ws::PsdBlasWorkspace{T}) where {T}
w,Z = GenericLinearAlgebra.eigen(GenericLinearAlgebra.Hermitian(X))
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This reallocates w and Z at every iteration. Is there a non-allocating version of GenericAlgebra.eigen ? eigen! perhaps?

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There is a function with that name but I do not understand how it works (and where it stores the result). I tried several things and no luck yet :/

#X .= MutableArithmetics.mul!(Z,LinearAlgebra.Diagonal(max.(w,0)),Z') " does not work.
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@blegat blegat Jun 30, 2021 •
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Multiplication with Diagonal is not implemented yet. You can do broadcast instead

julia> g(n) = (x = big.(ones(n)); A = big.(ones(n, n)); @time A .* x)
g (generic function with 1 method)

julia> j(n) = (x = big.(ones(n)); A = big.(ones(n, n)); @time MA.mul!.(A, x))
j (generic function with 1 method)

julia> g(1000);
  0.138854 seconds (2.00 M allocations: 114.441 MiB)

julia> g(1000);
  0.294522 seconds (2.00 M allocations: 114.441 MiB, 48.67% gc time)

julia> g(1000);
  0.139574 seconds (2.00 M allocations: 114.441 MiB)

julia> j(1000);
  0.182560 seconds (2 allocations: 7.629 MiB, 54.97% gc time)

julia> j(1000);
  0.082594 seconds (2 allocations: 7.629 MiB)

Note that here it will modify the entries of Z so of Z' as well. You can see that it still allocates 7MB because it still needs to allocate the resulting matrix.

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Here is what I would do

julia> X = big.(rand(3,3))
3×3 Matrix{BigFloat}:
 0.867983  0.677627  0.457641
 0.42301   0.29595   0.787097
 0.531521  0.938297  0.101263

julia> MA.mutable_operate!(zero, X)

julia> X
3×3 Matrix{BigFloat}:
 0.0  0.0  0.0
 0.0  0.0  0.0
 0.0  0.0  0.0

julia> w = big.([-3.0, 0.0, 2.0])
3-element Vector{BigFloat}:
  3.0
  0.0
  2.0

julia> Z = BigFloat.(reshape(1:9, 3, 3))
3×3 Matrix{BigFloat}:
 1.0  4.0  7.0
 2.0  5.0  8.0
 3.0  6.0  9.0

julia> buffer = zero(X)
3×3 Matrix{BigFloat}:
 0.0  0.0  0.0
 0.0  0.0  0.0
 0.0  0.0  0.0

julia> for i in 1:3
           w[i] <= 0 && continue
           z = view(Z, i, :)
           MA.mutable_operate_to!(buffer, *, z, z')
           for I in eachindex(X)
               X[I] = MA.add_mul!(X[I], w[i], buffer[I])
           end
       end

julia> X
3×3 Matrix{BigFloat}:
 21.0   48.0   75.0
 48.0  120.0  192.0
 75.0  192.0  309.0

julia> Z' * Diagonal(w) * Z
3×3 Matrix{BigFloat}:
 21.0   48.0   75.0
 48.0  120.0  192.0
 75.0  192.0  309.0

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@lrnv lrnv Jun 30, 2021 •
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Your code and outputs are not concordant, however your algorithm is OK. Sadly i needed Z*D*Z' and not Z'*D*Z, but i can translate.
Thanks :)

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Looks like the code I wrote is what it should be, however i have a bug on my machine :

ERROR: MethodError: mutable_operate!(::typeof(MutableArithmetics.add_mul), ::BigFloat, ::BigFloat, ::BigFloat) is ambiguous. Candidates:
  mutable_operate!(op::Union{typeof(MutableArithmetics.add_mul), typeof(MutableArithmetics.sub_mul)}, x, y, 
z, args::Vararg{Any, N}) where N in MultivariatePolynomials at C:\Users\u009192\.julia\packages\MultivariatePolynomials\kvnmd\src\operators.jl:357
  mutable_operate!(op::Function, x::BigFloat, args::Vararg{Any, N}) where N in MutableArithmetics at C:\Users\u009192\.julia\packages\MutableArithmetics\8xkW3\src\bigfloat.jl:87
Possible fix, define
  mutable_operate!(::Union{typeof(MutableArithmetics.add_mul), typeof(MutableArithmetics.sub_mul)}, ::BigFloat, ::Any, ::Any, ::Vararg{Any, N}) where N
Stacktrace:

Looks like MultivariatePolynomials defined mutability in a way that was too greedy. @blegat what do you think ?

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@lrnv lrnv Jun 30, 2021 •
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For other types than BigFloat, say Double64 from DoubleFloats.jl, it works correctly however.

X .= Z*LinearAlgebra.Diagonal(max.(w,0))*Z'
end

Expand Down Expand Up @@ -279,9 +280,11 @@ function project!(x::AbstractVector{T}, cone::Union{PsdCone{T}, DensePsdCone{T}}
symmetrize_upper!(X)
_project!(X, cone.work)

#fill in the lower triangular part
for j=1:n, i=1:(j-1)
X[j,i] = X[i,j]
#fill in the lower triangular part, only needed when calling BLAS.
if T <: Union{Float32,Float64}
for j=1:n, i=1:(j-1)
X[j,i] = X[i,j]
end
end
end
return nothing
Expand Down