Fix reduce_order for SPZ of smaller order

src/Sets/SparsePolynomialZonotope.jl

@@ -413,23 +413,29 @@ This method implements the algorithm described in Proposition 3.1.39 of [1].
 """
 function reduce_order(P::SparsePolynomialZonotope, r::Real,
                       method::AbstractReductionMethod=GIR05())
-    @assert r ≥ 1
+    @assert r ≥ 1 "cannot reduce below order 1 (got $r)"
+
+    if order(P) <= r
+        return P
+    end
+
     n = dim(P)
     h = ngens_dep(P)
     q = ngens_indep(P)
 
+    a = min(h + q, ceil(Int, h + q - n * (r - 1)))
+    @assert a > 0  # holds because `r > order(P)`
+
     c = center(P)
     G = genmat_dep(P)
     GI = genmat_indep(P)
     E = expmat(P)
     idx = indexvector(P)
 
-    a = max(0, min(h + q, ceil(Int, h + q - n * (r - 1))))
     Gbar = hcat(G, GI)
     norms = [norm(g) for g in eachcol(Gbar)]
     th = sort(norms)[a]
 
-    # TODO: case a = 0
     # TODO is constructing an array of booleans the most efficient way?
     K = [norms[i] ≤ th for i in 1:h]
     Kbar = .!K

test/Sets/SparsePolynomialZonotope.jl

@@ -158,4 +158,9 @@ let
 
     @test expmat(Pred) == [1 0 1 2; 0 1 1 0]
     @test indexvector(Pred) == [1, 2]
+
+    @test order(P) == 4
+    for r in 4:8
+        @test reduce_order(P, r) == P
+    end
 end