#676 - Add _projection method for set - hyperplane lazy intersection #694
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mforets
changed the title
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Apart from the unit test that i'll add now, it is ready from my side. I gave the options Once we have an efficient intersection of zonogon and line (here, they will work by default when a zonotope is given because of the dispatch on |
src/Intersection.jl
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| @@ -308,6 +308,11 @@ or a hyperplane in a given direction. | |||
| * `"line_search"` -- solve the associated univariate optimization problem | |||
| using a line search method (either Brent or the | |||
| Golden Section method) | |||
| * `"projection"` -- evaluate the support function by reducing the problem to | |||
| the 2D intersection of a rank 2 linear transformation of | |||
| the given compat set in the plane generated by the given | |||
src/Intersection.jl
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| the 2D intersection of a rank 2 linear transformation of | ||
| the given compat set in the plane generated by the given | ||
| direction `d` and the hyperplane's normal vector `n`; | ||
| only valid for intersection with a hyperplane |
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Maybe move the last sentence to the top; otherwise the hyperplane in the text is confusing.
src/Intersection.jl
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| - `ℓ` -- direction | ||
| - `X` -- set | ||
| - `H` -- hyperplane |
src/Intersection.jl
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| _projection(ℓ, X, H::Union{Hyperplane{N}, Line{N}}; kwargs...) where {N} | ||
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| Given a compact and convex set ``X`` and a hyperplane ``H = \\{x: n ⋅ x = γ \\}``, | ||
| calculate ... |
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haha sorry. forgot to write the maths
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| The support function of ``X ∩ H`` along direction ``ℓ``. | ||
| """ | ||
| function _projection(ℓ, X, H::Union{Hyperplane{N}, Line{N}}; |
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if u don't mind i would keep ℓ here so that it matches the original algorithm
src/Intersection.jl
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| lazy_2d_intersection=true, | ||
| kwargs...) where {N} | ||
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| options = Dict(kwargs) |
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options is never actually used.
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correct, i have to remove it 👍
| options = Dict(kwargs) | ||
| n = H.a # normal vector to the hyperplane | ||
| γ = H.b # displacement of the hyperplane | ||
| Πnℓ = vcat(n', ℓ') # projection map |
src/Intersection.jl
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| Lγ = Line(x_dir, γ) | ||
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| Snℓ = lazy_linear_map ? LinearMap(Πnℓ, X) : linear_map(Πnℓ, X) |
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In the spirit of above, what about \bigcap<TAB>Sℓ or S\bigcap<TAB>ℓ (resp. d instead of ℓ)?
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nice! we can use the \bigcap notation in the hybrid algorithm too 👍
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I misinterpreted the n as a symbol for intersection 😄
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hmm better if i use Xnℓ since the given set is X
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Thanks for the comments, i've addressed them all. I've also reworked the return statement and added a new keyword argument. The idea is to have more control on how the 2D intersection is performed. |
Codecov Report
@@ Coverage Diff @@
## master #694 +/- ##
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+ Coverage 94.26% 98.42% +4.16%
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Files 51 51
Lines 1674 1271 -403
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- Hits 1578 1251 -327
+ Misses 96 20 -76
Continue to review full report at Codecov.
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Closes #676.