From 87ef0a6c3d93d1415163078a04076ee6d3ebc990 Mon Sep 17 00:00:00 2001
From: lucaferranti <lucaa.ferranti@gmail.com>
Date: Sat, 6 Aug 2022 20:02:58 +0300
Subject: [PATCH 1/2] add merge ID

---
 docs/src/lib/sets/SparsePolynomialZonotope.md |  1 +
 src/Sets/SparsePolynomialZonotope.jl          | 39 ++++++++++++++++++-
 test/Sets/SparsePolynomialZonotope.jl         | 17 ++++++++
 3 files changed, 56 insertions(+), 1 deletion(-)

diff --git a/docs/src/lib/sets/SparsePolynomialZonotope.md b/docs/src/lib/sets/SparsePolynomialZonotope.md
index 4dd9360364..050f33dca5 100644
--- a/docs/src/lib/sets/SparsePolynomialZonotope.md
+++ b/docs/src/lib/sets/SparsePolynomialZonotope.md
@@ -13,6 +13,7 @@ independent_genmat(::SparsePolynomialZonotope)
 expmat(::SparsePolynomialZonotope)
 indexvector(P::SparsePolynomialZonotope)
 uniqueID(::Int)
+mergeID(::SparsePolynomialZonotope, ::SparsePolynomialZonotope)
 dim(::SparsePolynomialZonotope)
 ndependentgens(::SparsePolynomialZonotope)
 nindependentgens(::SparsePolynomialZonotope)
diff --git a/src/Sets/SparsePolynomialZonotope.jl b/src/Sets/SparsePolynomialZonotope.jl
index f2cc9941e1..eaa15e5634 100644
--- a/src/Sets/SparsePolynomialZonotope.jl
+++ b/src/Sets/SparsePolynomialZonotope.jl
@@ -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
 
 """
@@ -207,6 +207,43 @@ 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
+
+### 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)
+    @show idx_new
+    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)
+    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)
 
diff --git a/test/Sets/SparsePolynomialZonotope.jl b/test/Sets/SparsePolynomialZonotope.jl
index 649f73b633..66fdbd0535 100644
--- a/test/Sets/SparsePolynomialZonotope.jl
+++ b/test/Sets/SparsePolynomialZonotope.jl
@@ -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]

From 1d4ae3b38d1107e83dc918b112db6550fd802a59 Mon Sep 17 00:00:00 2001
From: Luca Ferranti <49938764+lucaferranti@users.noreply.github.com>
Date: Mon, 8 Aug 2022 10:06:43 +0300
Subject: [PATCH 2/2] Update src/Sets/SparsePolynomialZonotope.jl

---
 src/Sets/SparsePolynomialZonotope.jl | 1 -
 1 file changed, 1 deletion(-)

diff --git a/src/Sets/SparsePolynomialZonotope.jl b/src/Sets/SparsePolynomialZonotope.jl
index eaa15e5634..cf7aeb7070 100644
--- a/src/Sets/SparsePolynomialZonotope.jl
+++ b/src/Sets/SparsePolynomialZonotope.jl
@@ -231,7 +231,6 @@ function mergeID(P1::SparsePolynomialZonotope, P2::SparsePolynomialZonotope)
 
     H = setdiff(idx2, idx1)
     idx_new = vcat(idx1, H)
-    @show idx_new
     E1 = vcat(expmat(P1), zeros(Int, length(H), ndependentgens(P1)))
     E2 = zeros(Int, length(idx1) + length(H), ndependentgens(P2))
     E2_old = expmat(P2)