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IPM/HSD: use logical slicing instead of elementwise multiplication
We now do basically this for a logical vector l: `dot(a[l], b[l])`, instead of `dot(a .* l, b .* l) as before. This is as suggested here: #122 (comment) Helps with the performance of the BigFloat arithmetic. A Julia script and a Unix shell script were used to conduct an experiment for assesing the impact of this commit and the previous commit on performance. The scripts and the resulting CSV file follow. The benchmark experiment is conducted and the CSV created by removing sources of system load on a computer and running the shell script four times: once with the `init` command and three times with the `run` command, each time checking out a different commit in the Tulip git repo. Unix (Bourne) shell script: ```sh set -u command=$1 julia_opts='-O3 --min-optlevel=3 --heap-size-hint=5G --depwarn=error --warn-overwrite=yes' script=tulip_benchmark.jl case "$command" in init_csv) printf '%s,%s,%s,%s\n' 'Tulip version' estimator 'measurement type' value ;; run) tulip_version=$2 $PATH_TO_JULIA_BIN $julia_opts "$script" "$tulip_version" ;; *) printf '%s\n' error 2>&1 exit 1 ;; esac ``` Julia script: ```julia const benchmark_seconds = 500 const polynomial_degree = 20 setprecision(BigFloat, 12 * 2^7) using BenchmarkTools import FindMinimaxPolynomial, # v0.2.3 Tulip, MathOptInterface const FMP = FindMinimaxPolynomial const MMX = FMP.Minimax const PPTI = FMP.PolynomialPassingThroughIntervals const NE = FMP.NumericalErrorTypes const to_poly = FMP.ToSparsePolynomial.to_sparse_polynomial const mmx = MMX.minimax_polynomial const error_type_relative = NE.RelativeError() const MOI = MathOptInterface const itv_max_err = FMP.ApproximateInfinityNorm.interval_max_err function make_lp() lp = Tulip.Optimizer{BigFloat}() # Remove iteration limit just in case MOI.set(lp, MOI.RawOptimizerAttribute("IPM_IterationsLimit"), 2000) # Disable presolve, speeds things up #MOI.set(lp, MOI.RawOptimizerAttribute("Presolve_Level"), 0) lp end const itv = (-big"2.0"^-3, big"45.0") odd_monomials(n::Int) = 1:2:n sind_mmx(n::Int) = mmx( make_lp, sind, (itv,), odd_monomials(n), # Small factor to have less variance in the results initial_perturb_factor = 1//(2^20), # We're benchmarking LP, so disable other stuff worst_segments_density = 5, worst_segments_breadth_limit = 2, worst_segments_depth_ratio = 1/2, # Exit right after the first step exit_condition = true, ) function report(estimator; benchmark, benchmark_name) b = estimator(benchmark) println("$benchmark_name,$estimator,time,$(b.time)") println("$benchmark_name,$estimator,gctime,$(b.gctime)") println("$benchmark_name,$estimator,memory,$(b.memory)") println("$benchmark_name,$estimator,allocs,$(b.allocs)") end function report(;benchmark, benchmark_name) for quantile in (minimum, median, maximum) report( quantile, benchmark = benchmark, benchmark_name = benchmark_name, ) end end report( benchmark = (@benchmark sind_mmx(polynomial_degree) seconds=benchmark_seconds), benchmark_name = first(ARGS), ) ``` CSV results: ```csv Tulip version,estimator,measurement type,value v0.9.5,minimum,time,2.63759609e8 v0.9.5,minimum,gctime,3.4505713e7 v0.9.5,minimum,memory,495299296 v0.9.5,minimum,allocs,3629874 v0.9.5,median,time,4.2594161e8 v0.9.5,median,gctime,1.3250321e8 v0.9.5,median,memory,495299296 v0.9.5,median,allocs,3629874 v0.9.5,maximum,time,4.55935021e8 v0.9.5,maximum,gctime,1.40426286e8 v0.9.5,maximum,memory,495299296 v0.9.5,maximum,allocs,3629874 MutableArithmetics for IPM/HSD,minimum,time,2.57993117e8 MutableArithmetics for IPM/HSD,minimum,gctime,2.9403466e7 MutableArithmetics for IPM/HSD,minimum,memory,442052896 MutableArithmetics for IPM/HSD,minimum,allocs,3238720 MutableArithmetics for IPM/HSD,median,time,4.22323273e8 MutableArithmetics for IPM/HSD,median,gctime,1.282365305e8 MutableArithmetics for IPM/HSD,median,memory,442052896 MutableArithmetics for IPM/HSD,median,allocs,3238720 MutableArithmetics for IPM/HSD,maximum,time,4.56330849e8 MutableArithmetics for IPM/HSD,maximum,gctime,1.57061172e8 MutableArithmetics for IPM/HSD,maximum,memory,442052896 MutableArithmetics for IPM/HSD,maximum,allocs,3238720 IPM/HSD: use logical slicing ...,minimum,time,2.40996648e8 IPM/HSD: use logical slicing ...,minimum,gctime,2.5335783e7 IPM/HSD: use logical slicing ...,minimum,memory,386588512 IPM/HSD: use logical slicing ...,minimum,allocs,2833356 IPM/HSD: use logical slicing ...,median,time,3.76039574e8 IPM/HSD: use logical slicing ...,median,gctime,1.06930941e8 IPM/HSD: use logical slicing ...,median,memory,386588512 IPM/HSD: use logical slicing ...,median,allocs,2833356 IPM/HSD: use logical slicing ...,maximum,time,4.00347376e8 IPM/HSD: use logical slicing ...,maximum,gctime,1.27260987e8 IPM/HSD: use logical slicing ...,maximum,memory,386588512 IPM/HSD: use logical slicing ...,maximum,allocs,2833356 ``` Fixes #122
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