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Remove redundant generators in zonotope overapproximations #3446

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merged 4 commits into from
Mar 18, 2024
Merged

Remove redundant generators in zonotope overapproximations #3446

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5aa76f2
remove redundant generators in SPZ overapproximation
schillic Feb 26, 2024
7d2a57b
remove redundant generators in TM overapproximation (rename kwarg)
schillic Feb 26, 2024
7f1719f
fix test (check for equivalence, not equality)
schillic Feb 26, 2024
460a141
fix doctest
schillic Feb 26, 2024
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36 changes: 19 additions & 17 deletions src/Approximations/overapproximate_zonotope.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -303,7 +303,9 @@ A zonotope.
"""
function overapproximate(P::SparsePolynomialZonotope, ::Type{<:Zonotope})
cnew, Gnew = _zonotope_overapprox(center(P), genmat_dep(P), expmat(P))
return Zonotope(cnew, hcat(Gnew, genmat_indep(P)))
Z = Zonotope(cnew, hcat(Gnew, genmat_indep(P)))
Zred = remove_redundant_generators(Z)
return Zred
end

"""
Expand Down Expand Up @@ -380,7 +382,7 @@ function load_taylormodels_overapproximation()

"""
overapproximate(vTM::Vector{TaylorModel1{T, S}}, ::Type{<:Zonotope};
[remove_zero_generators]::Bool=true
[remove_redundant_generators]::Bool=true
[normalize]::Bool=true) where {T, S}

Overapproximate a Taylor model in one variable with a zonotope.
Expand All @@ -389,8 +391,8 @@ function load_taylormodels_overapproximation()

- `vTM` -- vector of `TaylorModel1`
- `Zonotope` -- target set type
- `remove_zero_generators` -- (optional; default: `true`) flag to remove zero
generators of the resulting zonotope
- `remove_redundant_generators` -- (optional; default: `true`) flag to remove
redundant generators of the resulting zonotope
- `normalize` -- (optional; default: `true`) flag to skip the normalization of
the Taylor models

Expand Down Expand Up @@ -527,16 +529,16 @@ function load_taylormodels_overapproximation()
normalization onto the symmetric intervals ``[-1, 1]``.
"""
function overapproximate(vTM::Vector{TaylorModel1{T,S}}, ::Type{<:Zonotope};
remove_zero_generators::Bool=true,
remove_redundant_generators::Bool=true,
normalize::Bool=true) where {T,S}
return _overapproximate_vTM_zonotope(vTM, 1, T;
remove_zero_generators=remove_zero_generators,
remove_redundant_generators=remove_redundant_generators,
normalize=normalize)
end

"""
overapproximate(vTM::Vector{TaylorModelN{N, T, S}}, ::Type{<:Zonotope};
[remove_zero_generators]::Bool=true
[remove_redundant_generators]::Bool=true
[normalize]::Bool=true) where {N, T, S}


Expand All @@ -546,8 +548,8 @@ function load_taylormodels_overapproximation()

- `vTM` -- vector of `TaylorModelN`
- `Zonotope` -- target set type
- `remove_zero_generators` -- (optional; default: `true`) flag to remove zero
generators of the resulting zonotope
- `remove_redundant_generators` -- (optional; default: `true`) flag to remove
redundant generators of the resulting zonotope
- `normalize` -- (optional; default: `true`) flag to skip the normalization of
the Taylor models

Expand Down Expand Up @@ -604,26 +606,26 @@ function load_taylormodels_overapproximation()
124.0

julia> Matrix(genmat(Z))
2×4 Matrix{Float64}:
0.0 -1.0 5.0 0.0
1.5 0.0 0.0 123.0
2×2 Matrix{Float64}:
0.0 -6.0
124.5 0.0
```

### Algorithm

We refer to the algorithm description for the univariate case.
"""
function overapproximate(vTM::Vector{TaylorModelN{N,T,S}}, ::Type{<:Zonotope};
remove_zero_generators::Bool=true,
remove_redundant_generators::Bool=true,
normalize::Bool=true) where {N,T,S}
n = N # number of variables is get_numvars() in TaylorSeries
return _overapproximate_vTM_zonotope(vTM, n, T;
remove_zero_generators=remove_zero_generators,
remove_redundant_generators=remove_redundant_generators,
normalize=normalize)
end

function _overapproximate_vTM_zonotope(vTM, n, N;
remove_zero_generators::Bool=true,
remove_redundant_generators::Bool=true,
normalize::Bool=true)
m = length(vTM)

Expand Down Expand Up @@ -656,8 +658,8 @@ function load_taylormodels_overapproximation()
end

Z = Zonotope(c, G)
if remove_zero_generators
Z = LazySets.remove_zero_generators(Z)
if remove_redundant_generators
Z = LazySets.remove_redundant_generators(Z)
end
return Z
end
Expand Down
4 changes: 1 addition & 3 deletions test/Sets/SparsePolynomialZonotope.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -87,9 +87,7 @@ for N in [Float64, Float32, Rational{Int}]
S = SparsePolynomialZonotope(N[-0.5, -0.5], N[1.0 1 1 1; 1 0 -1 1], zeros(N, 2, 0),
[1 0 1 2; 0 1 1 0])
Z = overapproximate(S, Zonotope)

@test center(Z) == N[0, 0]
@test genmat(Z) == N[1 1 1 0.5; 1 0 -1 0.5]
@test isequivalent(Z, Zonotope(N[0, 0], N[1.5 1 1; 1.5 0 -1]))

PZ = SparsePolynomialZonotope(N[-1, 2], N[1 2 0 2; 0 1 2 -1], N[1 0; 2 0], [1 0 1 2; 0 0 0 1])
PZreduced = remove_redundant_generators(PZ)
Expand Down
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