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Made IPNewton() compatible with alternate types (e.g. sparse) of hess…
…ians and jacobians
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test/multivariate/solvers/constrained/ipnewton/matrixtypes.jl
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
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| using Optim, Test | ||
| import SparseArrays: sparse | ||
| import LinearAlgebra: Tridiagonal | ||
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| let | ||
| # Why do the tests fail when this function is defined inside the @testset? | ||
| """ | ||
| Create TwiceDifferentiable objective and TwiceDifferentiableConstraints | ||
| representing | ||
| min x'A*x s.t. x[i]^2 + x[i+1]^2 = 1 for i=1:2:(n-1) | ||
| """ | ||
| function problem(A::AbstractMatrix) | ||
| n = size(A,1) | ||
| (mod(n,2) == 0) || error("size(A,1) must be even") | ||
| ncon = n ÷ 2 | ||
| h0 = A | ||
| g0 = zeros(eltype(A),n) | ||
| x0 = zeros(n) | ||
| function grad!(g,x) | ||
| for i in 1:n | ||
| g[i] = 2*x'*A[:,i] | ||
| end | ||
| end | ||
| function hess!(h,x) | ||
| copyto!(h,A) | ||
| end | ||
| function obj(x) | ||
| return(x'*A*x) | ||
| end | ||
| f = Optim.TwiceDifferentiable(obj, grad!, | ||
| hess!, x0, zero(eltype(A)), g0, h0 ) | ||
| function con_c!(c,x) | ||
| for i in 1:ncon | ||
| c[i] = x[2*i-1]^2 + x[2*i]^2 | ||
| end | ||
| c | ||
| end | ||
| Jstore = similar(A,n÷2,n) | ||
| Jstore .= zero(eltype(A)) | ||
| function con_j!(J,x) | ||
| for i in 1:ncon | ||
| J[i,2*i-1] = 2x[2*i-1] | ||
| J[i,2*i] = 2x[2*i] | ||
| end | ||
| end | ||
| function con_hl!(h,x,λ) | ||
| for i in 1:n | ||
| h[i,i] += 2λ[(i+1)÷2] | ||
| end | ||
| end | ||
| lx = fill(-Inf,n) | ||
| ux = fill(Inf,n) | ||
| lc = ones(n÷2) | ||
| uc = ones(n÷2) | ||
| fc = Optim.TwiceDifferentiableConstraints(con_c!, con_j!, con_hl!, lx, ux, lc, uc) | ||
| return(f, fc, Jstore) | ||
| end | ||
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| @testset "hessian and jacobian alternate types" begin | ||
| n = 8 | ||
| A = zeros(n,n) | ||
| x0 = ones(n) | ||
| for i in 1:n | ||
| A[i,i] = 2.0 | ||
| if (i>1) | ||
| A[i-1,i] = 1.0 | ||
| A[i,i-1] = 1.0 | ||
| end | ||
| end | ||
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| f,con,J = problem(A) | ||
| dense_sol = Optim.optimize(f,con,x0,Optim.IPNewton(conJstorage=J)) | ||
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| @testset "sparse" begin | ||
| f,con,J = problem(sparse(A)) | ||
| sparse_sol = Optim.optimize(f,con,x0,Optim.IPNewton(conJstorage=J)) | ||
| @test dense_sol.minimum ≈ sparse_sol.minimum | ||
| @test dense_sol.minimizer ≈ sparse_sol.minimizer | ||
| end | ||
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| @testset "tridiagonal" begin | ||
| f,con,J = problem(Tridiagonal(A)) | ||
| tridiagonal_sol = Optim.optimize(f,con,x0,Optim.IPNewton(conJstorage=J)) | ||
| @test dense_sol.minimum ≈ tridiagonal_sol.minimum | ||
| @test dense_sol.minimizer ≈ tridiagonal_sol.minimizer | ||
| end | ||
| end | ||
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||
| end |