Alfonso matlab code comparison

[chriscoey]

running Alfonso 75cba5f with default options against the following Alfonso.m Matlab code with (the same) default options:

seed = 2017;
tol = 1e-06;
results = random_lp(500, 1000, tol, seed);
seed = 2017;
tol = 1e-06;
intParams = ChebInterval(5); 
results = polyEnv(intParams, 2, 5, tol, seed);
tol = 1e-06;
intParams = FeketeCube(6, 2); 
results = polyOpt(intParams, 'butcher', tol);
intParams = FeketeCube(4, 4); 
results = polyOpt(intParams, 'caprasse', tol);
intParams = FeketeCube(4, 3);
results = polyOpt(intParams, 'lotka-volterra', tol);
intParams = PaduaSquare(7); 
results = polyOpt(intParams, 'motzkin', tol);
intParams = FeketeCube(3, 4); 
results = polyOpt(intParams, 'reaction-diffusion', tol);
intParams = PaduaSquare(8);
results = polyOpt(intParams, 'robinson', tol);

primal and dual objectives for the Julia code and Matlab code match. the iteration counts (very similar) and timings (in seconds) are:

test	iters	Matlab	75cba5f	c9f1eb5	133b422
dense lp	65	5.8	4.1	2.03	1.25
envelope	30	0.085	0.043	0.020	x
butcher	32/30	0.63	0.41	0.357	0.136
caprasse	31/30	1.38	1.87	1.80	0.530
lotka-volt	31/30	0.47	0.38	0.37	0.104
motzkin	41/42	0.35	0.24	x	0.054
reac-diff	29/30	0.32	0.23	0.19	0.075
robinson	29	0.34	0.23	0.17	0.034

[blegat]

Looks good, so Alfonso.jl is faster in all examples ! What do you mean by 32/30 does it mean 32 in Matlab and 30 in Julia ?

[chriscoey]

The Julia code was slower on Caprasse only. Yes 32/30 means 32 on Matlab and 30 on Alfonso. There shouldn't be a difference at this point as the algorithms (modulo some linear algebra) are currently the same (this will change), so it comes down to different numerical procedures in Matlab vs Julia.

[chriscoey]

the LP might be faster after https://github.com/JuliaLang/julia/pull/29296 is merged. but we are currently using views so maybe not - it's worth investigating.

[chriscoey]

things are pretty tough to compare now since the package has diverged significantly. if anyone is very interested we can try to compare again.