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debug needsPackage "NumericalAlgebraicGeometry"
NAGtrace 0
load (currentFileDirectory|"benchmarks.m2")
-- BENCHMARK SYSTEMS: ---------------------------------------------------------
systems = {
-- random system in n variables of degree d
(n = 5; d = 4; setRandomSeed 0; -- #sols=1024, M2:1/4/5, B:20/18, P:20/18; (old... M2:4, H:11, B:51, P:63)
T = (randomSystem(n,d,CC))_*; (S,solsS) = totalDegreeStartSystem T; (T,S,solsS)),
(n = 5; d = 5; setRandomSeed 0; -- #sols=3125, M2:8/37/43, B:159/153, P:136/206; (old... M2:30, H:78, B:402, P:550)
T = (randomSystem(n,d,CC))_*; (S,solsS) = totalDegreeStartSystem T; (T,S,solsS)),
-- katsura
(T = (katsuraBench 11)_*; -- #sols=1024, M2:2/3/3, B:12/13, P:14/52; (old... M2:4, H:7, B:15, P:37)
(S,solsS) = totalDegreeStartSystem T; (T,S,solsS)),
(T = (katsuraBench 12)_*, -- #sols=2048, M2:5/7/8, B:43/46, P:37/182; (old... M2:11, H:19, B:37, P:102) -- PHCpack loses some sols in solveSystem
(S,solsS) = totalDegreeStartSystem T; (T,S,solsS)),
-- random generalized eigenvalue problem
(setRandomSeed 0; randomGeneralizedEigenvalueProblem 35) -- #sols=35, M2:2/10/???, B:136/???, P:47: (old... M2:3, B:40, P:323)
-- PHCpack thinks 4 solutions are singular
-- M2 goes to precision=100 (with multiprecision)
};
software = {
M2engine,
BERTINI,
PHCPACK
-- , HOM4PS2
};
timeSystemSoftware = (system,soft) -> (
(T,S,solsS) = system;
<< "---------------------------------------------------------" << endl;
<< "---------- COMPUTING with " << soft << "-----------------" << endl;
<< "---------------------------------------------------------" << endl;
soft=>sortSolutions if soft===HOM4PS2 then elapsedTime solveSystem(T,Software=>soft)/point
else (
print "track";
elapsedTime print tally (status \ track(S,T,solsS,gamma=>1+ii,Software=>soft)) ;
if soft===M2engine then (
print "trackHomotopy";
elapsedTime print tally (status \ trackHomotopy(segmentHomotopy(polySystem S,polySystem T, gamma=>1+ii), solsS,EndZoneFactor=>0))
);
print "solveSystem";
s := elapsedTime solveSystem(T,Software=>soft);
print tally (status \ s);
s
)
)
end -----------------------------------------------------------------------------------
restart
load "NumericalAlgebraicGeometry/showcase.m2"
sols = new HashTable from apply(drop(systems,-1), system->(
(system,soft) => apply(software, soft->timeSystemSoftware(system,soft))
))
---------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------
system = first systems;
--...
system = last systems;
soft = M2engine
soft = BERTINI
soft = PHCPACK
timeSystemSoftware(system,soft)
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