From d349260fdb1e2164ab6d182aae48e1134957faf5 Mon Sep 17 00:00:00 2001
From: schillic <schillic@informatik.uni-freiburg.de>
Date: Wed, 23 Jan 2019 20:46:25 +0100
Subject: [PATCH] constraints_list for LinearMap

---
 docs/src/lib/operations.md |  1 +
 src/LinearMap.jl           | 35 ++++++++++++++++++++++++++++++++---
 test/unit_LinearMap.jl     | 19 +++++++++++++++++++
 3 files changed, 52 insertions(+), 3 deletions(-)

diff --git a/docs/src/lib/operations.md b/docs/src/lib/operations.md
index 149c0c99db..949b76ccbc 100644
--- a/docs/src/lib/operations.md
+++ b/docs/src/lib/operations.md
@@ -228,6 +228,7 @@ an_element(::LinearMap{N}) where {N<:Real}
 isbounded(::LinearMap)
 isempty(::LinearMap)
 vertices_list(::LinearMap{N}) where {N<:Real}
+constraints_list(::LinearMap{N, S}) where {N<:Real, S<:Union{AbstractPolytope{N}, HPolyhedron{N}}
 ```
 Inherited from [`LazySet`](@ref):
 * [`norm`](@ref norm(::LazySet, ::Real))
diff --git a/src/LinearMap.jl b/src/LinearMap.jl
index 0b4d156371..30afd81278 100644
--- a/src/LinearMap.jl
+++ b/src/LinearMap.jl
@@ -1,7 +1,8 @@
 import Base: *, ∈, isempty
 
 export LinearMap,
-       an_element
+       an_element,
+       constraints_list
 
 """
     LinearMap{N<:Real, S<:LazySet{N}, NM, MAT<:AbstractMatrix{NM}} <: LazySet{N}
@@ -316,7 +317,7 @@ end
 """
     vertices_list(lm::LinearMap{N})::Vector{Vector{N}} where {N<:Real}
 
-Return the list of vertices of a (polytopic) linear map.
+Return the list of vertices of a (polyhedral) linear map.
 
 ### Input
 
@@ -328,7 +329,7 @@ A list of vertices.
 
 ### Algorithm
 
-We assume that the underlying set `X` is polytopic.
+We assume that the underlying set `X` is polyhedral.
 Then the result is just the linear map applied to the vertices of `X`.
 """
 function vertices_list(lm::LinearMap{N})::Vector{Vector{N}} where {N<:Real}
@@ -349,3 +350,31 @@ function vertices_list(lm::LinearMap{N})::Vector{Vector{N}} where {N<:Real}
 
     return vlist
 end
+
+"""
+    constraints_list(lm::LinearMap{N, S}) where
+        {N<:Real, S<:Union{AbstractPolytope{N}, HPolyhedron{N}}}
+
+Return the list of constraints of a (polyhedral) linear map.
+
+### Input
+
+- `lm` -- linear map
+
+### Output
+
+The list of constraints of the linear map.
+
+### Notes
+
+We assume that the underlying set `X` is polyhedral, i.e., offers a method
+`constraints_list(X)`.
+
+### Algorithm
+
+We fall back to a concrete set representation and apply `linear_map`.
+"""
+function constraints_list(lm::LinearMap{N, S}) where
+        {N<:Real, S<:Union{AbstractPolytope{N}, HPolyhedron{N}}}
+    return constraints_list(linear_map(lm.M, lm.X))
+end
diff --git a/test/unit_LinearMap.jl b/test/unit_LinearMap.jl
index 4002564e12..647a8fc24e 100644
--- a/test/unit_LinearMap.jl
+++ b/test/unit_LinearMap.jl
@@ -1,3 +1,5 @@
+import LazySets.Approximations.BoxDiagDirections
+
 for N in [Float64, Rational{Int}, Float32]
     # π/2 trigonometric rotation
     b = BallInf(N[1, 2], N(1))
@@ -83,4 +85,21 @@ for N in [Float64, Rational{Int}, Float32]
     M = zeros(N, 2, 2)
     vlist = vertices_list(LinearMap(M, b))
     @test vlist == [zeros(N, 2)]
+
+    if test_suite_polyhedra
+        # constraints_list
+        b = BallInf(N[0, 0], N(1))
+        M = N[2 3; 1 2]  # invertible
+        lm1 = LinearMap(M, b)
+        clist = constraints_list(lm1)
+        p1 = HPolygon(clist)
+        M = N[2 3; 0 0]  # not invertible
+        lm2 = LinearMap(M, b)
+        clist = constraints_list(lm2)
+        p2 = HPolygon(clist)
+        for d in BoxDiagDirections{N}(2)
+            @test ρ(d, lm1) ≈ ρ(d, p1)
+            @test ρ(d, lm2) ≈ ρ(d, p2)
+        end
+    end
 end