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add mergeID #3027

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add mergeID #3027

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add merge ID
lucaferranti Aug 6, 2022
1d4ae3b
Update src/Sets/SparsePolynomialZonotope.jl
lucaferranti Aug 8, 2022
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1 change: 1 addition & 0 deletions docs/src/lib/sets/SparsePolynomialZonotope.md
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Expand Up @@ -13,6 +13,7 @@ independent_genmat(::SparsePolynomialZonotope)
expmat(::SparsePolynomialZonotope)
indexvector(P::SparsePolynomialZonotope)
uniqueID(::Int)
mergeID(::SparsePolynomialZonotope, ::SparsePolynomialZonotope)
dim(::SparsePolynomialZonotope)
ndependentgens(::SparsePolynomialZonotope)
nindependentgens(::SparsePolynomialZonotope)
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38 changes: 37 additions & 1 deletion src/Sets/SparsePolynomialZonotope.jl
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@@ -1,5 +1,5 @@
export SparsePolynomialZonotope, expmat, nparams, ndependentgens, nindependentgens,
dependent_genmat, independent_genmat, indexvector, exact_sum, ⊞,
dependent_genmat, independent_genmat, indexvector, mergeID, exact_sum, ⊞,
linear_map, quadratic_map, remove_redundant_generators

"""
Expand Down Expand Up @@ -207,6 +207,42 @@ indexvector(P::SPZ) = P.idx
Returns a collection of n unique identifiers (intergers 1, …, n).
"""
uniqueID(n::Int) = 1:n

"""
mergeID(P1::SparsePolynomialZonotope, P2::SparsePolynomialZonotope)

Returns two polynomial zonotopes equivalent to the correspondent input but with the same
index vector.

### Input

- `P1` -- sparse polynomial zonotope
- `P2` -- sprase polynomial zonotope
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### Output

two polynomial zonotopes with the same index vector
"""
function mergeID(P1::SparsePolynomialZonotope, P2::SparsePolynomialZonotope)

idx1 = indexvector(P1)
idx2 = indexvector(P2)
idx1 == idx2 && return (P1, P2)

H = setdiff(idx2, idx1)
idx_new = vcat(idx1, H)
Comment on lines +232 to +233
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I am not sure this is correct. It seems non-symmetric. Does the test still work in the other order?

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I think it's symmetric up to permutation. That is the merged zonotopes will have the same parameters, but these will not necessarily ordered by index (i.e. the index vector is not ordered). If one also sorted the index vector, then it would be symmetric I think

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at least looking at the algorithm description on page 35 of Niklas' thesis, the algorithm doesn't seem to be symmetric (because it doesn't fix the order)

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So when you do mergeID(PZ2, PZ1) in the test case, you get the IDs [2, 4, 1, 3]. Is this acceptable or should the indices be sorted?

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based on today's conversation, should we normalize the order?

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@lucaferranti lucaferranti Aug 8, 2022 •
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if in functions that require the same idvector (quadratic map, exact sum) you so something like

indexvector(PZ1) == indexvector(PZ2) || (PZ1, PZ2 = mergeID(PZ1, PZ2)

I think even without normalizing the order it would be correct, because calling mergeID would not change PZ1, PZ2 as setdiff(idx2, idx1) would be empty on the other hand, I don't see harm in normalizing the order either

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I would not be surprised if some operations assume the same order after mergeID. So I would sort.

E1 = vcat(expmat(P1), zeros(Int, length(H), ndependentgens(P1)))
E2 = zeros(Int, length(idx1) + length(H), ndependentgens(P2))
E2_old = expmat(P2)
@inbounds for (i, idx) in enumerate(idx_new)
j = findfirst(isequal(idx), idx2)
!isnothing(j) && (E2[i, :] .= E2_old[j, :])
end
P1_new = SparsePolynomialZonotope(center(P1), dependent_genmat(P1), independent_genmat(P1), E1, idx_new)
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P2_new = SparsePolynomialZonotope(center(P2), dependent_genmat(P2), independent_genmat(P2), E2, idx_new)
return (P1_new, P2_new)
end

"""
linear_map(M::AbstractMatrix, P::SparsePolynomialZonotope)

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17 changes: 17 additions & 0 deletions test/Sets/SparsePolynomialZonotope.jl
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Expand Up @@ -53,3 +53,20 @@ for Z in [rand(Zonotope), rand(Hyperrectangle)]
@test isempty(independent_genmat(ZS))
@test expmat(ZS) == I
end

E1 = [1 2 3; 4 5 6;7 8 9]
E2 = [1 2 0;1 1 1]
PZ1 = SparsePolynomialZonotope(rand(2), rand(2, 3), rand(2, 2), E1, 1:3)
PZ2 = SparsePolynomialZonotope(rand(2), rand(2, 3), rand(2, 2), E2, [2, 4])

mPZ1, mPZ2 = mergeID(PZ1, PZ2)
@test indexvector(mPZ1) == [1, 2, 3, 4]
@test indexvector(mPZ2) == [1, 2, 3, 4]

for f in (:center, :dependent_genmat, :independent_genmat)
@eval @test $f(mPZ1) == $f(PZ1)
@eval @test $f(mPZ2) == $f(PZ2)
end

@test expmat(mPZ1) == [1 2 3;4 5 6;7 8 9;0 0 0]
@test expmat(mPZ2) == [0 0 0;1 2 0;0 0 0;1 1 1]