From 2fca26b3d5d998e0ad71ffc9ae1ec44edf7770f1 Mon Sep 17 00:00:00 2001
From: schillic <schillic@informatik.uni-freiburg.de>
Date: Mon, 27 Jan 2020 17:10:24 +0100
Subject: [PATCH 1/4] tmp

---
 Project.toml            |  1 +
 src/IntervalMatrices.jl |  3 +++
 src/power.jl            | 17 +++++++++++++++++
 3 files changed, 21 insertions(+)
 create mode 100644 src/power.jl

diff --git a/Project.toml b/Project.toml
index a7f2851..278b7c8 100644
--- a/Project.toml
+++ b/Project.toml
@@ -7,6 +7,7 @@ IntervalArithmetic = "d1acc4aa-44c8-5952-acd4-ba5d80a2a253"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
+SymEngine = "123dc426-2d89-5057-bbad-38513e3affd8"
 
 [compat]
 julia = "1"
diff --git a/src/IntervalMatrices.jl b/src/IntervalMatrices.jl
index 36da1eb..04ead67 100644
--- a/src/IntervalMatrices.jl
+++ b/src/IntervalMatrices.jl
@@ -6,6 +6,8 @@ using LinearAlgebra
 import Random
 using Random: AbstractRNG, GLOBAL_RNG, seed!
 
+import SymEngine
+
 using Reexport
 @reexport using IntervalArithmetic
 
@@ -18,6 +20,7 @@ include("matrix.jl")
 # Arithmetic for interval matrices
 # =================================
 include("arithmetic.jl")
+include("power.jl")
 
 # =======================================================
 # Methods to handle the exponential of an interval matrix
diff --git a/src/power.jl b/src/power.jl
new file mode 100644
index 0000000..d61b9b1
--- /dev/null
+++ b/src/power.jl
@@ -0,0 +1,17 @@
+import Base: ^
+
+function ^(M::IntervalMatrix{T}, k::Integer) where {T}
+    n = checksquare(M)
+#     Ms = [SymEngine.symbols("M_$(i)_$(j)") for i in 1:n, j in 1:n]
+    Ms = Matrix{SymEngine.Basic}(undef, n, n)
+    dict = Dict{SymEngine.Basic, T}()
+    for i in 1:n, j in 1:n
+        var = SymEngine.symbols("M_$(i)_$(j)")
+        Ms[i, j] = var
+        dict[var] = M[i, j]
+    end
+    println(Ms)
+    Msᵏ = Ms^k
+    Mᵏ = subs(Msᵏ, dict)
+    return Mᵏ
+end

From ab19da215f8d104aa69af60d3ec35051e8283e7f Mon Sep 17 00:00:00 2001
From: schillic <schillic@informatik.uni-freiburg.de>
Date: Mon, 27 Jan 2020 17:28:30 +0100
Subject: [PATCH 2/4] tmp

---
 src/power.jl | 17 +++++++++++++----
 1 file changed, 13 insertions(+), 4 deletions(-)

diff --git a/src/power.jl b/src/power.jl
index d61b9b1..6c2cc42 100644
--- a/src/power.jl
+++ b/src/power.jl
@@ -2,16 +2,25 @@ import Base: ^
 
 function ^(M::IntervalMatrix{T}, k::Integer) where {T}
     n = checksquare(M)
-#     Ms = [SymEngine.symbols("M_$(i)_$(j)") for i in 1:n, j in 1:n]
+
+    # create symbolic matrix
     Ms = Matrix{SymEngine.Basic}(undef, n, n)
-    dict = Dict{SymEngine.Basic, T}()
+    dict = Dict{SymEngine.Basic, Interval{T}}()
     for i in 1:n, j in 1:n
         var = SymEngine.symbols("M_$(i)_$(j)")
         Ms[i, j] = var
         dict[var] = M[i, j]
     end
-    println(Ms)
+
+    # compute symbolic matrix power
     Msᵏ = Ms^k
-    Mᵏ = subs(Msᵏ, dict)
+
+    # substitute intervals in symbolic result
+    Mᵏ = similar(M)
+    for i in 1:n, j in 1:n
+        println(Msᵏ[i, j])
+        println(dict)
+        Mᵏ[i, j] = SymEngine.subs(Msᵏ[i, j], dict)
+    end
     return Mᵏ
 end

From 0ac80aaf4c11cb53367f20b87dce9c3e9793f80b Mon Sep 17 00:00:00 2001
From: schillic <schillic@informatik.uni-freiburg.de>
Date: Mon, 27 Jan 2020 17:53:12 +0100
Subject: [PATCH 3/4] tmp

---
 src/power.jl | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/src/power.jl b/src/power.jl
index 6c2cc42..5e75871 100644
--- a/src/power.jl
+++ b/src/power.jl
@@ -20,7 +20,8 @@ function ^(M::IntervalMatrix{T}, k::Integer) where {T}
     for i in 1:n, j in 1:n
         println(Msᵏ[i, j])
         println(dict)
-        Mᵏ[i, j] = SymEngine.subs(Msᵏ[i, j], dict)
+        substituted = SymEngine.subs(Msᵏ[i, j], dict)
+        Mᵏ[i, j] = SymEngine.lambdify(substituted)
     end
     return Mᵏ
 end

From 47b88e9ba9f6cf420e8e2f529a2a0d29e8fb8b42 Mon Sep 17 00:00:00 2001
From: schillic <schillic@informatik.uni-freiburg.de>
Date: Mon, 27 Jan 2020 18:04:48 +0100
Subject: [PATCH 4/4] tmp

---
 src/power.jl | 12 ++++++++----
 1 file changed, 8 insertions(+), 4 deletions(-)

diff --git a/src/power.jl b/src/power.jl
index 5e75871..b87953e 100644
--- a/src/power.jl
+++ b/src/power.jl
@@ -6,10 +6,12 @@ function ^(M::IntervalMatrix{T}, k::Integer) where {T}
     # create symbolic matrix
     Ms = Matrix{SymEngine.Basic}(undef, n, n)
     dict = Dict{SymEngine.Basic, Interval{T}}()
+    dict2 = Dict{SymEngine.Basic, T}()
     for i in 1:n, j in 1:n
         var = SymEngine.symbols("M_$(i)_$(j)")
         Ms[i, j] = var
         dict[var] = M[i, j]
+        dict2[var] = mid(M[i, j])
     end
 
     # compute symbolic matrix power
@@ -18,10 +20,12 @@ function ^(M::IntervalMatrix{T}, k::Integer) where {T}
     # substitute intervals in symbolic result
     Mᵏ = similar(M)
     for i in 1:n, j in 1:n
-        println(Msᵏ[i, j])
-        println(dict)
-        substituted = SymEngine.subs(Msᵏ[i, j], dict)
-        Mᵏ[i, j] = SymEngine.lambdify(substituted)
+        expr = Msᵏ[i, j]
+#         for (k, v) in dict
+#             expr = SymEngine.subs(expr, k, mid(v))
+#         end
+        expr = SymEngine.subs(expr, dict2...)
+        Mᵏ[i, j] = SymEngine.lambdify(expr)
     end
     return Mᵏ
 end