Added dual prices for the probability simplex and the unit simplex #15
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partially resolves Issue #7 |
| @@ -13,11 +13,11 @@ const grad(x) = 2 * (x-xp) | |||
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| function cf(x,xp) | |||
| return LinearAlgebra.norm(x-xp)^2 | |||
| return @. LinearAlgebra.norm(x-xp)^2 | |||
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Not sure the broadcast will be needed here, x and xp should have the same dimensions right?
x - xp works for vectors x and xp, it will only error if one of them is a scalar
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good point - saves half the memory though 126MB vs. 63
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Ok curious, well let's leave it as-is then
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i am not sure yet that i understand where the grossly different allocations come from with and without broadcasting. see numbers below
| function cgrad(x,xp) | ||
| return 2 * (x-xp) | ||
| function cgrad(x,xp) | ||
| return @. 2 * (x-xp) |
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same here: they basically halve the memory allocs when you broadcast:
without broadcast:
Size of single vector (Float64): 0.762939453125 MB
─────────────────────────────────────────────────────────────────────────────
Time Allocations
────────────────────── ───────────────────────
caching 100 points 100 1.65s 95.6% 16.5ms 7.68GiB 95.4% 78.6MiB
lmo 100 21.1ms 1.22% 211μs 0.00B 0.00% 0.00B
update (blas) 100 18.3ms 1.06% 183μs 153MiB 1.85% 1.53MiB
grad 100 15.6ms 0.90% 156μs 153MiB 1.85% 1.53MiB
f 100 12.5ms 0.72% 125μs 76.3MiB 0.93% 781KiB
update (memory) 100 6.46ms 0.37% 64.6μs 0.00B 0.00% 0.00B
dual gap 100 2.11ms 0.12% 21.1μs 0.00B 0.00% 0.00B
─────────────────────────────────────────────────────────────────────────────
with broadcasting
Size of single vector (Float64): 0.762939453125 MB
─────────────────────────────────────────────────────────────────────────────
Time Allocations
────────────────────── ───────────────────────
Tot / % measured: 2.08s / 89.4% 8.57GiB / 92.2%
Section ncalls time %tot avg alloc %tot avg
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caching 100 points 100 1.79s 96.4% 17.9ms 7.60GiB 96.2% 77.8MiB
lmo 100 20.1ms 1.08% 201μs 0.00B 0.00% 0.00B
update (blas) 100 19.6ms 1.05% 196μs 153MiB 1.89% 1.53MiB
f 100 9.52ms 0.51% 95.2μs 76.3MiB 0.94% 781KiB
grad 100 9.19ms 0.50% 91.9μs 76.3MiB 0.94% 781KiB
update (memory) 100 6.46ms 0.35% 64.6μs 0.00B 0.00% 0.00B
dual gap 100 2.01ms 0.11% 20.1μs 0.00B 0.00% 0.00B
─────────────────────────────────────────────────────────────────────────────
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done for the gradient here as example
currently the rationelle is to pass both the objective (i.e., the direction) as well as the primal optimal point from a previous LP call to compute the dual solutions. This is because the primal solution is not unique and we want primal-dual pairs!