From 61d6384636a4fdfdd56d41ead2c3c7bd5e970702 Mon Sep 17 00:00:00 2001
From: ExpandingMan <savastio@protonmail.com>
Date: Tue, 23 Oct 2018 13:10:29 -0400
Subject: [PATCH 1/6] added missing matrix exponentiation methods
---
base/mathconstants.jl | 1 +
1 file changed, 1 insertion(+)
diff --git a/base/mathconstants.jl b/base/mathconstants.jl
index a3d1be99becbb..721a429f1cbda 100644
--- a/base/mathconstants.jl
+++ b/base/mathconstants.jl
@@ -89,6 +89,7 @@ catalan
# loop over types to prevent ambiguities for ^(::Number, x)
for T in (AbstractIrrational, Rational, Integer, Number, Complex)
Base.:^(::Irrational{:ℯ}, x::T) = exp(x)
+ Base.:^(::Irrational{:ℯ}, x::AbstractMatrix{T}) = exp(x)
end
Base.literal_pow(::typeof(^), ::Irrational{:ℯ}, ::Val{p}) where {p} = exp(p)
From 9881db3885fc3ddfc1003674f7f45d0312da4735 Mon Sep 17 00:00:00 2001
From: ExpandingMan <savastio@protonmail.com>
Date: Tue, 23 Oct 2018 13:22:36 -0400
Subject: [PATCH 2/6] added some tests
---
test/math.jl | 5 +++++
1 file changed, 5 insertions(+)
diff --git a/test/math.jl b/test/math.jl
index 85b81b6f17e84..eba799d03876c 100644
--- a/test/math.jl
+++ b/test/math.jl
@@ -40,6 +40,11 @@ end
@test ℯ^2 == exp(2)
@test ℯ^2.4 == exp(2.4)
@test ℯ^(2//3) == exp(2//3)
+ @test ℯ^(fill(2, (4,4))) == exp(fill(2, (4,4)))
+ @test ℯ^(fill(2.4, (4,4))) == exp(fill(2.4, (4,4)))
+ # currently missing `exp` methods for matrices of Rational and Irrational
+ # @test ℯ^(fill(π, (4,4))) == exp(fill(π, (4,4)))
+ # @test ℯ^(fill(2//3, (4,4))) == exp(fill(2//3, (4,4)))
@test Float16(3.0) < pi
@test pi < Float16(4.0)
From 0c483a8e0cf6e208b74bde48f6cc866239a4d46e Mon Sep 17 00:00:00 2001
From: ExpandingMan <savastio@protonmail.com>
Date: Tue, 23 Oct 2018 15:29:59 -0400
Subject: [PATCH 3/6] moved new methods to LinearAlgebra
---
base/mathconstants.jl | 1 -
stdlib/LinearAlgebra/src/LinearAlgebra.jl | 3 +++
stdlib/LinearAlgebra/test/dense.jl | 4 ++++
test/math.jl | 5 -----
4 files changed, 7 insertions(+), 6 deletions(-)
diff --git a/base/mathconstants.jl b/base/mathconstants.jl
index 721a429f1cbda..a3d1be99becbb 100644
--- a/base/mathconstants.jl
+++ b/base/mathconstants.jl
@@ -89,7 +89,6 @@ catalan
# loop over types to prevent ambiguities for ^(::Number, x)
for T in (AbstractIrrational, Rational, Integer, Number, Complex)
Base.:^(::Irrational{:ℯ}, x::T) = exp(x)
- Base.:^(::Irrational{:ℯ}, x::AbstractMatrix{T}) = exp(x)
end
Base.literal_pow(::typeof(^), ::Irrational{:ℯ}, ::Val{p}) where {p} = exp(p)
diff --git a/stdlib/LinearAlgebra/src/LinearAlgebra.jl b/stdlib/LinearAlgebra/src/LinearAlgebra.jl
index c58f98dd83f31..029a649ac958c 100644
--- a/stdlib/LinearAlgebra/src/LinearAlgebra.jl
+++ b/stdlib/LinearAlgebra/src/LinearAlgebra.jl
@@ -340,6 +340,9 @@ rdiv!(A, B)
copy_oftype(A::AbstractArray{T}, ::Type{T}) where {T} = copy(A)
copy_oftype(A::AbstractArray{T,N}, ::Type{S}) where {T,N,S} = convert(AbstractArray{S,N}, A)
+# matrix exponentials for ℯ
+Base.:^(::Irrational{:ℯ}, A::AbstractMatrix) = exp(A)
+
include("adjtrans.jl")
include("transpose.jl")
diff --git a/stdlib/LinearAlgebra/test/dense.jl b/stdlib/LinearAlgebra/test/dense.jl
index ae935b6337b59..b9ca0bc7f4e08 100644
--- a/stdlib/LinearAlgebra/test/dense.jl
+++ b/stdlib/LinearAlgebra/test/dense.jl
@@ -401,6 +401,10 @@ end
[4.000000000000000 -1.414213562373094 -1.414213562373095
-1.414213562373095 4.999999999999996 -0.000000000000000
0 -0.000000000000002 3.000000000000000])
+
+ # alias using ℯ, should be exact
+ @test ℯ^(fill(2, (4,4))) == exp(fill(2, (4,4)))
+ @test ℯ^(fill(2.4, (4,4))) == exp(fill(2.4, (4,4)))
end
@testset "Additional tests for $elty" for elty in (Float64, Complex{Float64})
diff --git a/test/math.jl b/test/math.jl
index eba799d03876c..85b81b6f17e84 100644
--- a/test/math.jl
+++ b/test/math.jl
@@ -40,11 +40,6 @@ end
@test ℯ^2 == exp(2)
@test ℯ^2.4 == exp(2.4)
@test ℯ^(2//3) == exp(2//3)
- @test ℯ^(fill(2, (4,4))) == exp(fill(2, (4,4)))
- @test ℯ^(fill(2.4, (4,4))) == exp(fill(2.4, (4,4)))
- # currently missing `exp` methods for matrices of Rational and Irrational
- # @test ℯ^(fill(π, (4,4))) == exp(fill(π, (4,4)))
- # @test ℯ^(fill(2//3, (4,4))) == exp(fill(2//3, (4,4)))
@test Float16(3.0) < pi
@test pi < Float16(4.0)
From 72266ad9bbb306b7be1d5deaf43b8c95468bc7e3 Mon Sep 17 00:00:00 2001
From: ExpandingMan <savastio@protonmail.com>
Date: Wed, 24 Oct 2018 09:58:15 -0400
Subject: [PATCH 4/6] added general method and cleaned up tests
---
stdlib/LinearAlgebra/src/LinearAlgebra.jl | 4 +++-
stdlib/LinearAlgebra/test/dense.jl | 11 +++++++----
2 files changed, 10 insertions(+), 5 deletions(-)
diff --git a/stdlib/LinearAlgebra/src/LinearAlgebra.jl b/stdlib/LinearAlgebra/src/LinearAlgebra.jl
index 029a649ac958c..4e939ee339af8 100644
--- a/stdlib/LinearAlgebra/src/LinearAlgebra.jl
+++ b/stdlib/LinearAlgebra/src/LinearAlgebra.jl
@@ -340,7 +340,9 @@ rdiv!(A, B)
copy_oftype(A::AbstractArray{T}, ::Type{T}) where {T} = copy(A)
copy_oftype(A::AbstractArray{T,N}, ::Type{S}) where {T,N,S} = convert(AbstractArray{S,N}, A)
-# matrix exponentials for ℯ
+# matrix exponentials
+Base.:^(b::Number, A::AbstractMatrix) = exp(log(b)*A)
+# method for ℯ to explicitly elide the log(b) multiplication
Base.:^(::Irrational{:ℯ}, A::AbstractMatrix) = exp(A)
include("adjtrans.jl")
diff --git a/stdlib/LinearAlgebra/test/dense.jl b/stdlib/LinearAlgebra/test/dense.jl
index b9ca0bc7f4e08..32b217b6fdc53 100644
--- a/stdlib/LinearAlgebra/test/dense.jl
+++ b/stdlib/LinearAlgebra/test/dense.jl
@@ -401,10 +401,6 @@ end
[4.000000000000000 -1.414213562373094 -1.414213562373095
-1.414213562373095 4.999999999999996 -0.000000000000000
0 -0.000000000000002 3.000000000000000])
-
- # alias using ℯ, should be exact
- @test ℯ^(fill(2, (4,4))) == exp(fill(2, (4,4)))
- @test ℯ^(fill(2.4, (4,4))) == exp(fill(2.4, (4,4)))
end
@testset "Additional tests for $elty" for elty in (Float64, Complex{Float64})
@@ -432,6 +428,13 @@ end
end
end
+ @testset "^ tests" for elty in (Float32, Float64, ComplexF32, ComplexF64, Int32, Int64)
+ # should all be exact as the lhs functions are simple aliases
+ @test ℯ^(fill(elty(2), (4,4))) == exp(fill(elty(2), (4,4)))
+ @test 2^(fill(elty(2), (4,4))) == exp(log(2)*fill(elty(2), (4,4)))
+ @test 2.0^(fill(elty(2), (4,4))) == exp(log(2.0)*fill(elty(2), (4,4)))
+ end
+
A8 = 100 * [-1+1im 0 0 1e-8; 0 1 0 0; 0 0 1 0; 0 0 0 1]
@test exp(log(A8)) ≈ A8
end
From 9def8c73a7bc2e6ea9e6943c86d683f1e6ad7ce8 Mon Sep 17 00:00:00 2001
From: ExpandingMan <savastio@protonmail.com>
Date: Wed, 24 Oct 2018 10:30:36 -0400
Subject: [PATCH 5/6] moved methods
---
stdlib/LinearAlgebra/src/LinearAlgebra.jl | 5 -----
stdlib/LinearAlgebra/src/dense.jl | 4 ++++
2 files changed, 4 insertions(+), 5 deletions(-)
diff --git a/stdlib/LinearAlgebra/src/LinearAlgebra.jl b/stdlib/LinearAlgebra/src/LinearAlgebra.jl
index 4e939ee339af8..c58f98dd83f31 100644
--- a/stdlib/LinearAlgebra/src/LinearAlgebra.jl
+++ b/stdlib/LinearAlgebra/src/LinearAlgebra.jl
@@ -340,11 +340,6 @@ rdiv!(A, B)
copy_oftype(A::AbstractArray{T}, ::Type{T}) where {T} = copy(A)
copy_oftype(A::AbstractArray{T,N}, ::Type{S}) where {T,N,S} = convert(AbstractArray{S,N}, A)
-# matrix exponentials
-Base.:^(b::Number, A::AbstractMatrix) = exp(log(b)*A)
-# method for ℯ to explicitly elide the log(b) multiplication
-Base.:^(::Irrational{:ℯ}, A::AbstractMatrix) = exp(A)
-
include("adjtrans.jl")
include("transpose.jl")
diff --git a/stdlib/LinearAlgebra/src/dense.jl b/stdlib/LinearAlgebra/src/dense.jl
index 81a50391b91ce..d3fd085e6a473 100644
--- a/stdlib/LinearAlgebra/src/dense.jl
+++ b/stdlib/LinearAlgebra/src/dense.jl
@@ -489,6 +489,10 @@ julia> exp(A)
exp(A::StridedMatrix{<:BlasFloat}) = exp!(copy(A))
exp(A::StridedMatrix{<:Union{Integer,Complex{<:Integer}}}) = exp!(float.(A))
+Base.:^(b::Number, A::AbstractMatrix) = exp(log(b)*A)
+# method for ℯ to explicitly elide the log(b) multiplication
+Base.:^(::Irrational{:ℯ}, A::AbstractMatrix) = exp(A)
+
## Destructive matrix exponential using algorithm from Higham, 2008,
## "Functions of Matrices: Theory and Computation", SIAM
function exp!(A::StridedMatrix{T}) where T<:BlasFloat
From 6b9f486161ca0ddf6caed5d735d81a9bd8017929 Mon Sep 17 00:00:00 2001
From: ExpandingMan <ExpandingMan@users.noreply.github.com>
Date: Mon, 29 Oct 2018 18:49:07 -0400
Subject: [PATCH 6/6] eliminate spurious allocation
---
stdlib/LinearAlgebra/src/dense.jl | 2 +-
1 file changed, 1 insertion(+), 1 deletion(-)
diff --git a/stdlib/LinearAlgebra/src/dense.jl b/stdlib/LinearAlgebra/src/dense.jl
index d3fd085e6a473..e83164c01216a 100644
--- a/stdlib/LinearAlgebra/src/dense.jl
+++ b/stdlib/LinearAlgebra/src/dense.jl
@@ -489,7 +489,7 @@ julia> exp(A)
exp(A::StridedMatrix{<:BlasFloat}) = exp!(copy(A))
exp(A::StridedMatrix{<:Union{Integer,Complex{<:Integer}}}) = exp!(float.(A))
-Base.:^(b::Number, A::AbstractMatrix) = exp(log(b)*A)
+Base.:^(b::Number, A::AbstractMatrix) = exp!(log(b)*A)
# method for ℯ to explicitly elide the log(b) multiplication
Base.:^(::Irrational{:ℯ}, A::AbstractMatrix) = exp(A)