Reconsider caching

[odow]

Caching is faster, but it's not thaaaat much faster.

This would simplify a lot of the code:

julia> import Xpress_jll

julia> ENV["XPAUTH_PATH"] = "/Users/odow/git/jump-dev/Xpress/xpauth.xpr"
"/Users/odow/git/jump-dev/Xpress/xpauth.xpr"

julia> ENV["XPRESS_JL_LIBRARY"] = Xpress_jll.libxprs
"/Users/odow/.julia/artifacts/de1f33df0ad1d3821c28981f866e70c548b30efd/lib/libxprs.dylib"

julia> using JuMP, Xpress

julia> function build_prob(N)
           model = direct_model(Xpress.Optimizer())
           set_silent(model)
           @variable(model, x[1:N], Bin)
           @constraint(model, rand(N)' * x <= 0.1 * N)
           @objective(model, Max, rand(N)' * x)
           optimize!(model)
           return backend(model)
       end
build_prob (generic function with 1 method)

julia> function get_cached(prob, N)
           solstatusP = Ref{Cint}()
           cache = zeros(Cdouble, N)
           @assert XPRSgetsolution(prob, solstatusP, cache, 0, N - 1) == 0
           return cache
       end
get_cached (generic function with 1 method)

julia> function get_iter(prob, N)
           solstatusP = Ref{Cint}()
           cache = zeros(Cdouble, N)
           cacheP = Ref{Cdouble}()
           for i in 1:N
               @assert XPRSgetsolution(prob, solstatusP, cacheP, i-1, i-1) == 0
               cache[i] = cacheP[]
           end
           return cache
       end
get_iter (generic function with 1 method)

julia> function main(N)
           prob = build_prob(N)
           @time a = get_cached(prob, N)
           @time b = get_iter(prob, N)
           @assert a == b
           return
       end
main (generic function with 1 method)

julia> main(100)
  0.005504 seconds (8.31 k allocations: 402.859 KiB, 99.62% compilation time)
  0.006516 seconds (10.23 k allocations: 527.172 KiB, 97.79% compilation time)

julia> main(100)
  0.000024 seconds (2 allocations: 928 bytes)
  0.000355 seconds (2 allocations: 928 bytes)

julia> main(1000)
  0.000033 seconds (4 allocations: 8.078 KiB)
  0.017494 seconds (4 allocations: 8.078 KiB)

julia> main(10000)
  0.000018 seconds (4 allocations: 96.078 KiB)
  0.001619 seconds (4 allocations: 96.078 KiB)

julia> main(100000)
  0.000025 seconds (4 allocations: 800.078 KiB)
  0.007707 seconds (4 allocations: 800.078 KiB)

julia> main(1000000)
  0.000391 seconds (4 allocations: 7.656 MiB)
  0.079414 seconds (4 allocations: 7.656 MiB)

[odow]

Ugh. GitHub seems to have lost my comment. To briefly summarise what I wrote out longer:

• XPRSgetsolution works for getting a single element of VariablePrimal, but we'd still need the cache for XPRSgetprimalray which doesn't support individual elements.
• The same goes for XPRSgetduals and XPRSgetdualray
• There's also the issue with XPRSgetslacks and ConstraintPrimal; we want f(x) but Xpress returns s where f(x) + s = b. We could do this per constraint but it is a bit annoying
• Reduced costs would work.
• Same with the termination'primal/dual statuses

However, if we're going to half the effort to cache the infeasibility certificates, we may as well just cache the rest of the solution. Moreover, it's what we've been doing for ages and no one seems to complain about it.