From cd5d84289db9465dafc8153595b2b6e6cf9b8887 Mon Sep 17 00:00:00 2001
From: schillic <git@christianschilling.net>
Date: Fri, 16 Dec 2022 19:24:10 +0100
Subject: [PATCH 1/2] fix rand of HParallelotope

---
 src/Sets/HParallelotope.jl | 16 ++++++++++++++++
 1 file changed, 16 insertions(+)

diff --git a/src/Sets/HParallelotope.jl b/src/Sets/HParallelotope.jl
index 82a2c198d3..d42c38f13f 100644
--- a/src/Sets/HParallelotope.jl
+++ b/src/Sets/HParallelotope.jl
@@ -344,6 +344,15 @@ A random parallelotope.
 ### Notes
 
 All numbers are normally distributed with mean 0 and standard deviation 1.
+
+Technically there is a chance that the resulting set represents an unbounded
+set, but this case has not been observed in practice.
+
+### Algorithm
+
+The directions matrix and offset vector are created randomly. On average there
+is a good chance that this resulting set is empty. We then modify the offset to
+ensure non-emptiness.
 """
 function rand(::Type{HParallelotope};
               N::Type{<:Real}=Float64,
@@ -353,6 +362,13 @@ function rand(::Type{HParallelotope};
     rng = reseed(rng, seed)
     D = randn(rng, N, dim, dim)
     offset = randn(rng, N, 2 * dim)
+
+    # make sure that the set is not empty:
+    # `offset[i] >= -offset[i-dim]` for all `i ∈ dim+1:2*dim`
+    @inbounds for i in dim+1:2*dim
+        offset[i] = -offset[i-dim] + abs(offset[i])
+    end
+
     return HParallelotope(D, offset)
 end
 

From 7b2f35b3b13b4f3d47f48d4042ad01bee65e873c Mon Sep 17 00:00:00 2001
From: schillic <git@christianschilling.net>
Date: Sun, 19 Feb 2023 23:08:33 +0100
Subject: [PATCH 2/2] let rand of HParallelotope return bounded set

---
 src/Sets/HParallelotope.jl | 32 +++++++++++++++++++++-----------
 1 file changed, 21 insertions(+), 11 deletions(-)

diff --git a/src/Sets/HParallelotope.jl b/src/Sets/HParallelotope.jl
index d42c38f13f..9d48acefba 100644
--- a/src/Sets/HParallelotope.jl
+++ b/src/Sets/HParallelotope.jl
@@ -345,14 +345,14 @@ A random parallelotope.
 
 All numbers are normally distributed with mean 0 and standard deviation 1.
 
-Technically there is a chance that the resulting set represents an unbounded
-set, but this case has not been observed in practice.
-
 ### Algorithm
 
 The directions matrix and offset vector are created randomly. On average there
 is a good chance that this resulting set is empty. We then modify the offset to
 ensure non-emptiness.
+
+There is a chance that the resulting set represents an unbounded set. This
+implementation checks for that case and then samples a new set.
 """
 function rand(::Type{HParallelotope};
               N::Type{<:Real}=Float64,
@@ -360,16 +360,26 @@ function rand(::Type{HParallelotope};
               rng::AbstractRNG=GLOBAL_RNG,
               seed::Union{Int, Nothing}=nothing)
     rng = reseed(rng, seed)
-    D = randn(rng, N, dim, dim)
-    offset = randn(rng, N, 2 * dim)
 
-    # make sure that the set is not empty:
-    # `offset[i] >= -offset[i-dim]` for all `i ∈ dim+1:2*dim`
-    @inbounds for i in dim+1:2*dim
-        offset[i] = -offset[i-dim] + abs(offset[i])
-    end
+    while true
+        D = randn(rng, N, dim, dim)
+        offset = randn(rng, N, 2 * dim)
 
-    return HParallelotope(D, offset)
+        # make sure that the set is not empty:
+        # `offset[i] >= -offset[i-dim]` for all `i ∈ dim+1:2*dim`
+        @inbounds for i in dim+1:2*dim
+            offset[i] = -offset[i-dim] + abs(offset[i])
+        end
+
+        P = HParallelotope(D, offset)
+
+        # convert to polyhedron to check boundedness
+        Q = HPolyhedron(vcat(P.directions, -P.directions), P.offset)
+        if isbounded(Q)
+            return P
+        end
+        # set is unbounded; sample a new set in the next iteration
+    end
 end
 
 """