Benchmark of chbv.jl implementations

benchs_chbv.md

see PR #16 in Expokit.jl.

data

the different implementations were tested on a fixed set of 8 hermitian negative semidefinite matrices the were randomly generated. the MAT file is available here.

the functions to generate the matrices were:

function test_chbv_real(n::Int, p=0.1)
    D = diagm(-rand(n))
    T = sprandn(n, n, p)
    H = T * D * T'  # random negative semidefinite symmetric matrix
    vec = randn(n)
    return H, vec
end

function test_chbv_complex(n::Int, p=0.1)
    D = diagm(-rand(n))
    T = sprandn(n, n, p) + sprandn(n, n, p)*im
    H = T * D * T.'  # random negative semidefinite hermitian matrix
    vec = randn(n) + randn(n)*im
    return H, vec
end

results with expm

n	p	type	min time (expm)	mem (expm)	allocs (expm)
100	0.2	real	919.252 μs	3.21 MiB	93
1000	0.2	real	536.044 ms	358.60 MiB	103
100	0.2	complex	4.324 ms	6.57 MiB	247
1000	0.2	complex	1.679 s	732.44 MiB	105
100	0.01	real	782.828 μs	2.83 MiB	83
1000	0.01	real	458.346 ms	320.45 MiB	93
100	0.01	complex	3.534 ms	5.96 MiB	87
1000	0.01	complex	1.711 s	671.41 MiB	97

results: preliminary implementation

n	p	type	min time (chbv)	mem (chbv)	allocs (chbv)
100	0.2	real	5.571 ms	6.65 MiB	125
1000	0.2	real	1.368 s	663.82 MiB	125
100	0.2	complex	12.628 ms	13.14 MiB	247
1000	0.2	complex	3.105 s	1.28 GiB	247
100	0.01	real	5.639 ms	6.65 MiB	125
1000	0.01	real	1.283 s	663.82 MiB	125
100	0.01	complex	12.595 ms	13.14 MiB	247
1000	0.01	complex	2.921 s	1.28 GiB	247

results: using inplace sums

n	p	type	min time (chbv)	mem (chbv)	allocs (chbv)
100	0.2	real	4.035 ms	3.32 MiB	95
1000	0.2	real	335.461 ms	328.36 MiB	95
100	0.2	complex	9.532 ms	6.63 MiB	190
1000	0.2	complex	748.766 ms	656.69 MiB	190
100	0.01	real	3.938 ms	3.32 MiB	95
1000	0.01	real	328.811 ms	328.36 MiB	95
100	0.01	complex	9.643 ms	6.63 MiB	190
1000	0.01	complex	799.387 ms	656.69 MiB	190

results: using UnitScaling and merge real parts

n	p	type	min time (chbv)	mem (chbv)	allocs (chbv)
100	0.2	real	6.424 ms	2.17 MiB	85
1000	0.2	real	475.669 ms	213.96 MiB	85
100	0.2	complex	8.035 ms	4.34 MiB	160
1000	0.2	complex	542.883 ms	427.81 MiB	160
100	0.01	real	3.434 ms	2.17 MiB	85
1000	0.01	real	267.228 ms	213.96 MiB	85
100	0.01	complex	7.910 ms	4.34 MiB	160
1000	0.01	complex	557.828 ms	427.81 MiB	160