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Compressed LBFGS (forward) operator #258
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1b4244d
CompressedLBFGS structure + Matrix interface + mul! (first version)
647b19e
allocation free for the core of the mul! method
5ca9000
circular push!
3ff759b
add documentation
7d0ef3d
add tests + change to satisfy the tests
28fdfc0
Reduce allocations in push! + modify tests
050d219
improve circular shift in push! (faster update than LBFGSOperator)
f0884c8
m -> mem, CompressedLBFGS -> CompressedLBFGSOperator + add vectorshift!
4a293cc
new module ModCompressedLBFGSOperator + remove CUDA + add Requires + fix
f447c62
test using CUDA#master
cf114e0
fix CUDA types + adapt tests
d80a7d8
Update src/compressed_lbfgs.jl
paraynaud 11e3b34
Update src/compressed_lbfgs.jl
paraynaud 341332f
Update src/compressed_lbfgs.jl
paraynaud b82c99e
apply correction from the review
b211db5
restore buildkite + add CompressedLBFGData + prod!
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,270 @@ | ||
| #= | ||
| Compressed LBFGS implementation from: | ||
| REPRESENTATIONS OF QUASI-NEWTON MATRICES AND THEIR USE IN LIMITED MEMORY METHODS | ||
| Richard H. Byrd, Jorge Nocedal and Robert B. Schnabel (1994) | ||
| DOI: 10.1007/BF01582063 | ||
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| Implemented by Paul Raynaud (supervised by Dominique Orban) | ||
| =# | ||
|
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| using LinearAlgebra, LinearAlgebra.BLAS | ||
| using Requires | ||
|
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| export CompressedLBFGSOperator, CompressedLBFGSData | ||
| # export default_matrix_type, default_vector_type | ||
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| default_matrix_type(; T::DataType=Float64) = Matrix{T} | ||
| default_vector_type(; T::DataType=Float64) = Vector{T} | ||
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| @init begin | ||
| @require CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba" begin | ||
| default_matrix_type(; T::DataType=Float64) = CUDA.functional() ? CUDA.CuMatrix{T, CUDA.Mem.DeviceBuffer} : Matrix{T} | ||
| default_vector_type(; T::DataType=Float64) = CUDA.functional() ? CUDA.CuVector{T, CUDA.Mem.DeviceBuffer} : Vector{T} | ||
| end | ||
| # this scheme may be extended to other GPU backend modules | ||
| end | ||
|
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| function columnshift!(A::AbstractMatrix{T}; direction::Int=-1, indicemax::Int=size(A)[1]) where T | ||
| map(i-> view(A,:,i+direction) .= view(A,:,i), 1-direction:indicemax) | ||
| return A | ||
| end | ||
|
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| function vectorshift!(v::AbstractVector{T}; direction::Int=-1, indicemax::Int=length(v)) where T | ||
| view(v, 1:indicemax+direction) .= view(v,1-direction:indicemax) | ||
| return v | ||
| end | ||
|
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||
| """ | ||
| CompressedLBFGSData{T, M<:AbstractMatrix{T}, V<:AbstractVector{T}} | ||
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| A LBFGS limited-memory operator. | ||
| It represents a linear application Rⁿˣⁿ, considering at most `mem` BFGS updates. | ||
| This implementation considers the bloc matrices reoresentation of the BFGS (forward) update. | ||
| It follows the algorithm described in [REPRESENTATIONS OF QUASI-NEWTON MATRICES AND THEIR USE IN LIMITED MEMORY METHODS](https://link.springer.com/article/10.1007/BF01582063) from Richard H. Byrd, Jorge Nocedal and Robert B. Schnabel (1994). | ||
| This operator considers several fields directly related to the bloc representation of the operator: | ||
| - `mem`: the maximal memory of the operator; | ||
| - `n`: the dimension of the linear application; | ||
| - `k`: the current memory's size of the operator; | ||
| - `α`: scalar for `B₀ = α I`; | ||
| - `Sₖ`: retain the `k`-th last vectors `s` from the updates parametrized by `(s,y)`; | ||
| - `Yₖ`: retain the `k`-th last vectors `y` from the updates parametrized by `(s,y)`;; | ||
| - `Dₖ`: a diagonal matrix mandatory to perform the linear application and to form the matrix; | ||
| - `Lₖ`: a lower diagonal mandatory to perform the linear application and to form the matrix. | ||
| In addition to this structures which are circurlarly update when `k` reaches `mem`, we consider other intermediate data structures renew at each update: | ||
| - `chol_matrix`: a matrix required to store a Cholesky factorization of a Rᵏˣᵏ matrix; | ||
| - `intermediate_1`: a R²ᵏˣ²ᵏ matrix; | ||
| - `intermediate_2`: a R²ᵏˣ²ᵏ matrix; | ||
| - `inverse_intermediate_1`: a R²ᵏˣ²ᵏ matrix; | ||
| - `inverse_intermediate_2`: a R²ᵏˣ²ᵏ matrix; | ||
| - `intermediary_vector`: a vector ∈ Rᵏ to store intermediate solutions; | ||
| - `sol`: a vector ∈ Rᵏ to store intermediate solutions; | ||
| This implementation is designed to work either on CPU or GPU. | ||
| """ | ||
| mutable struct CompressedLBFGSData{T, M<:AbstractMatrix{T}, V<:AbstractVector{T}, I <: Integer} | ||
| mem::Int # memory of the operator | ||
| n::I # vector size | ||
| k::I # k ≤ mem, active memory of the operator | ||
| α::T # B₀ = αI | ||
| Sₖ::M # gather all sₖ₋ₘ : n * mem | ||
| Yₖ::M # gather all yₖ₋ₘ : n * mem | ||
| Dₖ::Diagonal{T,V} # mem * mem | ||
| Lₖ::LowerTriangular{T,M} # mem * mem | ||
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| chol_matrix::M # 2mem * 2mem | ||
| intermediate_diagonal::Diagonal{T,V} # mem * mem | ||
| intermediate_1::UpperTriangular{T,M} # 2mem * 2mem | ||
| intermediate_2::LowerTriangular{T,M} # 2mem * 2mem | ||
| inverse_intermediate_1::UpperTriangular{T,M} # 2mem * 2mem | ||
| inverse_intermediate_2::LowerTriangular{T,M} # 2mem * 2mem | ||
| intermediary_vector::V # 2mem | ||
| sol::V # 2mem | ||
|
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| nprod::I | ||
| end | ||
|
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| """ | ||
| CompressedLBFGSData(n::Int; [T=Float64, mem=5], gpu:Bool) | ||
|
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| A implementation of a LBFGS operator (forward), representing a `nxn` linear application. | ||
| It considers at most `k` BFGS iterates, and fit the architecture depending if it is launched on a CPU or a GPU. | ||
| """ | ||
| function CompressedLBFGSData(n::I; mem::I=5, T=Float64, M=default_matrix_type(; T), V=default_vector_type(; T)) where {I<:Integer} | ||
| α = (T)(1) | ||
| k = 0 | ||
| Sₖ = M(undef, n, mem) | ||
| Yₖ = M(undef, n, mem) | ||
| Dₖ = Diagonal(V(undef, mem)) | ||
| Lₖ = LowerTriangular(M(undef, mem, mem)) | ||
| Lₖ.data .= zero(T) | ||
|
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| chol_matrix = M(undef, mem, mem) | ||
| intermediate_diagonal = Diagonal(V(undef, mem)) | ||
| intermediate_1 = UpperTriangular(M(undef, 2*mem, 2*mem)) | ||
| intermediate_2 = LowerTriangular(M(undef, 2*mem, 2*mem)) | ||
| inverse_intermediate_1 = UpperTriangular(M(undef, 2*mem, 2*mem)) | ||
| inverse_intermediate_2 = LowerTriangular(M(undef, 2*mem, 2*mem)) | ||
| intermediary_vector = V(undef, 2*mem) | ||
| sol = V(undef, 2*mem) | ||
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| nprod = 0 | ||
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| return CompressedLBFGSData{T,M,V,I}(mem, n, k, α, Sₖ, Yₖ, Dₖ, Lₖ, chol_matrix, intermediate_diagonal, intermediate_1, intermediate_2, inverse_intermediate_1, inverse_intermediate_2, intermediary_vector, sol, nprod) | ||
| end | ||
|
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| mutable struct CompressedLBFGSOperator{T, M<:AbstractMatrix{T}, V<:AbstractVector{T}, F, I <: Integer} <: AbstractQuasiNewtonOperator{T} | ||
| nrow::I | ||
| ncol::I | ||
| symmetric::Bool | ||
| hermitian::Bool | ||
| Bv::V | ||
| data::CompressedLBFGSData{T,M,V} | ||
| prod!::F # apply the operator to a vector | ||
| tprod!::F # apply the transpose operator to a vector | ||
| ctprod!::F # apply the transpose conjugate operator to a vector | ||
| end | ||
|
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| function CompressedLBFGSOperator(n::I; mem::I=5, T=Float64, M=default_matrix_type(; T), V=default_vector_type(; T)) where {I <: Integer} | ||
| nrow = n | ||
| ncol = n | ||
| symmetric = true | ||
| hermitian = true | ||
| Bv = V(undef, n) | ||
| data = CompressedLBFGSData(n; mem, T, M, V) | ||
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| prod! = @closure (res, v, α, β) -> begin | ||
| mul!(Bv, data, v) | ||
| if β == zero(T) | ||
| res .= α .* Bv | ||
| else | ||
| res .= α .* Bv .+ β .* res | ||
| end | ||
| end | ||
|
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| F = typeof(prod!) | ||
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| return CompressedLBFGSOperator{T,M,V,F,I}(nrow, ncol, symmetric, hermitian, Bv, data, prod!, prod!, prod!) | ||
| end | ||
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| has_args5(op::CompressedLBFGSOperator) = true | ||
| use_prod5!(op::CompressedLBFGSOperator) = true | ||
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| Base.push!(op::CompressedLBFGSOperator{T,M,V}, s::V, y::V) where {T,M,V<:AbstractVector{T}} = Base.push!(op.data, s, y) | ||
| function Base.push!(data::CompressedLBFGSData{T,M,V}, s::V, y::V) where {T,M,V<:AbstractVector{T}} | ||
| if data.k < data.mem # still some place in the structures | ||
| data.k += 1 | ||
| view(data.Sₖ, :, data.k) .= s | ||
| view(data.Yₖ, :, data.k) .= y | ||
| view(data.Dₖ.diag, data.k) .= dot(s, y) | ||
| mul!(view(data.Lₖ.data, data.k, 1:data.k-1), transpose(view(data.Yₖ, :, 1:data.k-1)), view(data.Sₖ, :, data.k) ) | ||
| else # k == mem update circurlarly the intermediary structures | ||
| columnshift!(data.Sₖ; indicemax=data.k) | ||
| columnshift!(data.Yₖ; indicemax=data.k) | ||
| # data.Dₖ .= circshift(data.Dₖ, (-1, -1)) | ||
| vectorshift!(data.Dₖ.diag; indicemax=data.k) | ||
| view(data.Sₖ, :, data.k) .= s | ||
| view(data.Yₖ, :, data.k) .= y | ||
| view(data.Dₖ.diag, data.k) .= dot(s, y) | ||
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| map(i-> view(data.Lₖ, i:data.mem-1, i-1) .= view(data.Lₖ, i+1:data.mem, i), 2:data.mem) | ||
| mul!(view(data.Lₖ.data, data.k, 1:data.k-1), transpose(view(data.Yₖ, :, 1:data.k-1)), view(data.Sₖ, :, data.k) ) | ||
| end | ||
|
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| # step 4 and 6 | ||
| precompile_iterated_structure!(data) | ||
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| # secant equation fails if uncommented | ||
| # data.α = dot(y,s)/dot(s,s) | ||
| return data | ||
| end | ||
|
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| # Algorithm 3.2 (p15) | ||
| # Theorem 2.3 (p6) | ||
| Base.Matrix(op::CompressedLBFGSOperator{T,M,V}) where {T,M,V} = Base.Matrix(op.data) | ||
| function Base.Matrix(data::CompressedLBFGSData{T,M,V}) where {T,M,V} | ||
| B₀ = M(undef, data.n, data.n) | ||
| map(i -> B₀[i, i] = data.α, 1:data.n) | ||
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| BSY = M(undef, data.n, 2*data.k) | ||
| (data.k > 0) && (BSY[:, 1:data.k] = B₀ * data.Sₖ[:, 1:data.k]) | ||
| (data.k > 0) && (BSY[:, data.k+1:2*data.k] = data.Yₖ[:, 1:data.k]) | ||
| _C = M(undef, 2*data.k, 2*data.k) | ||
| (data.k > 0) && (_C[1:data.k, 1:data.k] .= transpose(data.Sₖ[:, 1:data.k]) * data.Sₖ[:, 1:data.k]) | ||
| (data.k > 0) && (_C[1:data.k, data.k+1:2*data.k] .= data.Lₖ[1:data.k, 1:data.k]) | ||
| (data.k > 0) && (_C[data.k+1:2*data.k, 1:data.k] .= transpose(data.Lₖ[1:data.k, 1:data.k])) | ||
| (data.k > 0) && (_C[data.k+1:2*data.k, data.k+1:2*data.k] .-= data.Dₖ[1:data.k, 1:data.k]) | ||
| C = inv(_C) | ||
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| Bₖ = B₀ .- BSY * C * transpose(BSY) | ||
| return Bₖ | ||
| end | ||
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| # Algorithm 3.2 (p15) | ||
| # step 4, Jₖ is computed only if needed | ||
| function inverse_cholesky(data::CompressedLBFGSData{T,M,V}) where {T,M,V} | ||
| view(data.intermediate_diagonal.diag, 1:data.k) .= inv.(view(data.Dₖ.diag, 1:data.k)) | ||
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| mul!(view(data.inverse_intermediate_1, 1:data.k, 1:data.k), view(data.intermediate_diagonal, 1:data.k, 1:data.k), transpose(view(data.Lₖ, 1:data.k, 1:data.k))) | ||
| mul!(view(data.chol_matrix, 1:data.k, 1:data.k), view(data.Lₖ, 1:data.k, 1:data.k), view(data.inverse_intermediate_1, 1:data.k, 1:data.k)) | ||
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| mul!(view(data.chol_matrix, 1:data.k, 1:data.k), transpose(view(data.Sₖ, :, 1:data.k)), view(data.Sₖ, :, 1:data.k), data.α, (T)(1)) | ||
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| cholesky!(Symmetric(view(data.chol_matrix, 1:data.k, 1:data.k))) | ||
| Jₖ = transpose(UpperTriangular(view(data.chol_matrix, 1:data.k, 1:data.k))) | ||
| return Jₖ | ||
| end | ||
|
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| # step 6, must be improve | ||
| function precompile_iterated_structure!(data::CompressedLBFGSData) | ||
| Jₖ = inverse_cholesky(data) | ||
|
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| # constant update | ||
| view(data.intermediate_1, data.k+1:2*data.k, 1:data.k) .= 0 | ||
| view(data.intermediate_2, 1:data.k, data.k+1:2*data.k) .= 0 | ||
| view(data.intermediate_1, data.k+1:2*data.k, data.k+1:2*data.k) .= transpose(Jₖ) | ||
| view(data.intermediate_2, data.k+1:2*data.k, data.k+1:2*data.k) .= Jₖ | ||
|
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| # updates related to D^(1/2) | ||
| view(data.intermediate_diagonal.diag, 1:data.k) .= sqrt.(view(data.Dₖ.diag, 1:data.k)) | ||
| view(data.intermediate_1, 1:data.k,1:data.k) .= .- view(data.intermediate_diagonal, 1:data.k, 1:data.k) | ||
| view(data.intermediate_2, 1:data.k, 1:data.k) .= view(data.intermediate_diagonal, 1:data.k, 1:data.k) | ||
|
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| # updates related to D^(-1/2) | ||
| view(data.intermediate_diagonal.diag, 1:data.k) .= (x -> 1/sqrt(x)).(view(data.Dₖ.diag, 1:data.k)) | ||
| mul!(view(data.intermediate_1, 1:data.k,data.k+1:2*data.k), view(data.intermediate_diagonal, 1:data.k, 1:data.k), transpose(view(data.Lₖ, 1:data.k, 1:data.k))) | ||
| mul!(view(data.intermediate_2, data.k+1:2*data.k, 1:data.k), view(data.Lₖ, 1:data.k, 1:data.k), view(data.intermediate_diagonal, 1:data.k, 1:data.k)) | ||
| view(data.intermediate_2, data.k+1:2*data.k, 1:data.k) .= view(data.intermediate_2, data.k+1:2*data.k, 1:data.k) .* -1 | ||
|
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| view(data.inverse_intermediate_1, 1:2*data.k, 1:2*data.k) .= inv(data.intermediate_1[1:2*data.k, 1:2*data.k]) | ||
| view(data.inverse_intermediate_2, 1:2*data.k, 1:2*data.k) .= inv(data.intermediate_2[1:2*data.k, 1:2*data.k]) | ||
| end | ||
|
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| # Algorithm 3.2 (p15) | ||
| LinearAlgebra.mul!(Bv::V, op::CompressedLBFGSOperator{T,M,V}, v::V) where {T,M,V<:AbstractVector{T}} = LinearAlgebra.mul!(Bv, op.data, v) | ||
| function LinearAlgebra.mul!(Bv::V, data::CompressedLBFGSData{T,M,V}, v::V) where {T,M,V<:AbstractVector{T}} | ||
| data.nprod += 1 | ||
| # step 1-4 and 6 mainly done by Base.push! | ||
| # step 5 | ||
| mul!(view(data.sol, 1:data.k), transpose(view(data.Yₖ, :, 1:data.k)), v) | ||
| mul!(view(data.sol, data.k+1:2*data.k), transpose(view(data.Sₖ, :, 1:data.k)), v) | ||
| # scal!(data.α, view(data.sol, data.k+1:2*data.k)) # more allocation, slower | ||
| view(data.sol, data.k+1:2*data.k) .*= data.α | ||
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| mul!(view(data.intermediary_vector, 1:2*data.k), view(data.inverse_intermediate_2, 1:2*data.k, 1:2*data.k), view(data.sol, 1:2*data.k)) | ||
| mul!(view(data.sol, 1:2*data.k), view(data.inverse_intermediate_1, 1:2*data.k, 1:2*data.k), view(data.intermediary_vector, 1:2*data.k)) | ||
|
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| # step 7 | ||
| mul!(Bv, view(data.Yₖ, :, 1:data.k), view(data.sol, 1:data.k)) | ||
| mul!(Bv, view(data.Sₖ, :, 1:data.k), view(data.sol, data.k+1:2*data.k), - data.α, (T)(-1)) | ||
| Bv .+= data.α .* v | ||
| return Bv | ||
| end | ||
|
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| """ | ||
| reset!(op) | ||
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| Resets the CompressedLBFGS data of the given operator. | ||
| """ | ||
| function reset!(op::CompressedLBFGSOperator) | ||
| op.data.nprod = 0 | ||
| return op | ||
| end | ||
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
|
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@@ -5,3 +5,5 @@ import LinearAlgebra.diag | |
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| include("lbfgs.jl") | ||
| include("lsr1.jl") | ||
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| include("compressed_lbfgs.jl") | ||
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -1,15 +1,16 @@ | ||
| using Arpack, Test, TestSetExtensions, LinearOperators | ||
| using LinearAlgebra, SparseArrays | ||
| include("test_aux.jl") | ||
| # include("test_aux.jl") | ||
|
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| include("test_linop.jl") | ||
| include("test_linop_allocs.jl") | ||
| include("test_adjtrans.jl") | ||
| include("test_cat.jl") | ||
| include("test_lbfgs.jl") | ||
| include("test_lsr1.jl") | ||
| include("test_kron.jl") | ||
| include("test_callable.jl") | ||
| include("test_deprecated.jl") | ||
| include("test_normest.jl") | ||
| include("test_diag.jl") | ||
| # include("test_linop.jl") | ||
| # include("test_linop_allocs.jl") | ||
| # include("test_adjtrans.jl") | ||
| # include("test_cat.jl") | ||
| # include("test_lbfgs.jl") | ||
| include("test_clbfgs.jl") | ||
| # include("test_lsr1.jl") | ||
| # include("test_kron.jl") | ||
| # include("test_callable.jl") | ||
| # include("test_deprecated.jl") | ||
| # include("test_normest.jl") | ||
| # include("test_diag.jl") |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,21 @@ | ||
| @testset "CompressedLBFGSOperator operator" begin | ||
| iter=50 | ||
| n=100 | ||
| n=5 | ||
| types = [Float32, Float64] | ||
| for T in types | ||
| lbfgs = CompressedLBFGSOperator(n; T) # mem=5 | ||
| V = LinearOperators.default_vector_type(;T) | ||
| Bv = V(rand(T, n)) | ||
| s = V(rand(T, n)) | ||
| mul!(Bv, lbfgs, s) # warm-up | ||
| for i in 1:iter | ||
| s = V(rand(T, n)) | ||
| y = V(rand(T, n)) | ||
| push!(lbfgs, s, y) | ||
| allocs = @allocated mul!(Bv, lbfgs, s) | ||
| @test allocs == 0 | ||
| @test Bv ≈ y | ||
| end | ||
| end | ||
| end |
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invhas been used to wait until a better solution is found.The function is performed only when an update occurs.
The dimension of the matrix inverted is related to
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You could use
LAPACK.getrf!andLAPACK.getri!ondata.intermediate_1[1:2*data.k, 1:2*data.k]anddata.intermediate_1[1:2*data.k, 1:2*data.k].getrf!computes a dense LU decomposition in-place.getri!uses the factors of the LU decomposition to compute the inverse.I added a dispatch in CUDA.jl and AMDGPU.jl for these LAPACK calls.
https://github.com/JuliaGPU/CUDA.jl/blob/master/lib/cusolver/dense.jl#L895-L926