Merge pull request #1442 from JuliaReach/schillic/1364

#1364 - Concrete linear map of a translation
JuliaReach · Jun 14, 2019 · 894fda3 · 894fda3
2 parents d9da4d4 + 0fd6c1e
commit 894fda3
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Showing 3 changed files with 37 additions and 4 deletions.
diff --git a/docs/src/lib/operations.md b/docs/src/lib/operations.md
@@ -349,6 +349,7 @@ an_element(::Translation)
 isempty(::Translation)
 constraints_list(::Translation{N}, ::Val{true}) where {N<:Real}
 LinearMap(::AbstractMatrix{N}, ::Translation{N}) where {N<:Real}
+linear_map(M::AbstractMatrix{N}, tr::Translation{N}) where {N<:Real}
 ∈(::AbstractVector{N}, ::Translation{N}) where {N<:Real}
 ```
 

diff --git a/src/Translation.jl b/src/Translation.jl
@@ -2,7 +2,8 @@ import Base: isempty
 
 export Translation,
        an_element,
-       constraints_list
+       constraints_list,
+       linear_map
 
 """
     Translation{N<:Real, VN<:AbstractVector{N}, S<:LazySet{N}} <: LazySet{N}
@@ -364,3 +365,29 @@ This implementation relies on the set membership function for the wrapped set
 function ∈(x::AbstractVector{N}, tr::Translation{N})::Bool where {N<:Real}
     return ∈(x - tr.v, tr.X)
 end
+
+"""
+    linear_map(M::AbstractMatrix{N}, tr::Translation{N}) where {N<:Real}
+
+Concrete linear map of a polyhedron in constraint representation.
+
+### Input
+
+- `M`  -- matrix
+- `tr` -- translation of a convex set
+
+### Output
+
+A concrete set corresponding to the linear map.
+The type of the result depends on the type of the set wrapped by `tr`.
+
+### Algorithm
+
+We compute `translate(linear_map(M, tr.X), M * tr.v)`.
+"""
+function linear_map(M::AbstractMatrix{N}, tr::Translation{N}) where {N<:Real}
+    @assert dim(tr) == size(M, 2) "a linear map of size $(size(M)) cannot be " *
+        "applied to a set of dimension $(dim(tr))"
+
+    return translate(linear_map(M, tr.X), M * tr.v)
+end
diff --git a/test/unit_Translation.jl b/test/unit_Translation.jl
@@ -1,9 +1,8 @@
 for N in [Float64, Rational{Int}, Float32]
-
     # ==================================
     # Constructor and interface methods
     # ==================================
- 
+
     B = BallInf(zeros(N, 3), N(1))
     v = N[1, 0, 0] # translation along dimension 1
     tr = Translation(B, v)
@@ -15,7 +14,7 @@ for N in [Float64, Rational{Int}, Float32]
 
     # dimension check
     @test_throws AssertionError Translation(B, N[0, 0])
-    
+
     @test dim(tr) == 3
 
     # support vector
@@ -42,6 +41,12 @@ for N in [Float64, Rational{Int}, Float32]
     B = Ball2(zeros(N, 2), N(1))
     @test center(B) ∈ B ⊕ zeros(N, 2)
 
+    # concrete linear map
+    B = BallInf(ones(N, 2), N(1))
+    tr = B ⊕ N[1, 0]
+    clm = linear_map(N[1 2; 0 1], tr)
+    @test ispermutation(vertices_list(clm), [N[5, 2], [1, 0], [3, 0], [7, 2]])
+
     # ==================================
     # Type-specific methods
     # ==================================