From bfd53e0a25ef3cb26b40a63b2c7e479f971f8f2f Mon Sep 17 00:00:00 2001
From: Arun <sanganalarun@gmail.com>
Date: Fri, 25 Jun 2021 00:28:40 +0530
Subject: [PATCH 01/23] Float 16 factors

---
 stdlib/LinearAlgebra/src/cholesky.jl  | 6 ++++++
 stdlib/LinearAlgebra/src/eigen.jl     | 7 +++++++
 stdlib/LinearAlgebra/src/svd.jl       | 6 ++++++
 stdlib/LinearAlgebra/test/cholesky.jl | 9 +++++++++
 stdlib/LinearAlgebra/test/eigen.jl    | 8 ++++++++
 stdlib/LinearAlgebra/test/svd.jl      | 9 +++++++++
 6 files changed, 45 insertions(+)

diff --git a/stdlib/LinearAlgebra/src/cholesky.jl b/stdlib/LinearAlgebra/src/cholesky.jl
index 6e381243faf43..76a6f50a124ce 100644
--- a/stdlib/LinearAlgebra/src/cholesky.jl
+++ b/stdlib/LinearAlgebra/src/cholesky.jl
@@ -388,6 +388,12 @@ true
 cholesky(A::Union{StridedMatrix,RealHermSymComplexHerm{<:Real,<:StridedMatrix}},
     ::Val{false}=Val(false); check::Bool = true) = cholesky!(cholcopy(A); check = check)
 
+function cholesky(A::Union{StridedMatrix{T},RealHermSymComplexHerm{<:T,<:StridedMatrix}}, ::Val{false}=Val(false); check::Bool = true) where T<:Float16
+    X = cholesky!(cholcopy(A); check = check)
+    Xnew = convert(AbstractMatrix{T}, X.factors)
+    Cholesky{T, typeof(Xnew)}(Xnew, X.uplo, X.info)
+end
+
 
 ## With pivoting
 """
diff --git a/stdlib/LinearAlgebra/src/eigen.jl b/stdlib/LinearAlgebra/src/eigen.jl
index 3341a2a9bc744..c54b5597540b1 100644
--- a/stdlib/LinearAlgebra/src/eigen.jl
+++ b/stdlib/LinearAlgebra/src/eigen.jl
@@ -275,6 +275,13 @@ function eigen(A::AbstractMatrix{T}; permute::Bool=true, scale::Bool=true, sortb
     isdiag(AA) && return eigen(Diagonal(AA); permute=permute, scale=scale, sortby=sortby)
     return eigen!(AA; permute=permute, scale=scale, sortby=sortby, jvl=jvl, jvr=jvr, jce=jce, jcv=jcv)
 end
+function eigen(A::AbstractMatrix{T}; permute::Bool=true, scale::Bool=true, sortby::Union{Function,Nothing}=eigsortby) where T<:Float16
+    AA = copy_oftype(A, eigtype(T))
+    isdiag(AA) && return eigen(Diagonal(AA); permute=permute, scale=scale, sortby=sortby)
+    A = eigen!(AA; permute=permute, scale=scale, sortby=sortby)
+    Eigen(convert(Vector{Float16}, A.values),
+          convert(AbstractArray{Float16}, A.vectors))
+end
 eigen(x::Number) = Eigen([x], fill(one(x), 1, 1))
 
 """
diff --git a/stdlib/LinearAlgebra/src/svd.jl b/stdlib/LinearAlgebra/src/svd.jl
index dca1cfaaf1e73..cf8c272a894ea 100644
--- a/stdlib/LinearAlgebra/src/svd.jl
+++ b/stdlib/LinearAlgebra/src/svd.jl
@@ -175,6 +175,12 @@ true
 function svd(A::StridedVecOrMat{T}; full::Bool = false, alg::Algorithm = default_svd_alg(A)) where {T}
     svd!(copy_oftype(A, eigtype(T)), full = full, alg = alg)
 end
+function svd(A::StridedVecOrMat{T}; full::Bool = false, alg::Algorithm = default_svd_alg(A)) where {T<:Float16}
+    A=svd!(copy_oftype(A, eigtype(T)), full = full, alg = alg)
+    SVD(convert(AbstractArray{Float16}, A.U),
+        convert(Vector{Float16}, A.S),
+        convert(AbstractArray{Float16}, A.Vt))
+end
 function svd(x::Number; full::Bool = false, alg::Algorithm = default_svd_alg(x))
     SVD(x == 0 ? fill(one(x), 1, 1) : fill(x/abs(x), 1, 1), [abs(x)], fill(one(x), 1, 1))
 end
diff --git a/stdlib/LinearAlgebra/test/cholesky.jl b/stdlib/LinearAlgebra/test/cholesky.jl
index 83aed94de9e35..6ba635593433c 100644
--- a/stdlib/LinearAlgebra/test/cholesky.jl
+++ b/stdlib/LinearAlgebra/test/cholesky.jl
@@ -483,4 +483,13 @@ end
     @test F\b == F'\b
 end
 
+@testset "Float16" begin
+    A = Float16[4. 12. -16.; 12. 37. -43.; -16. -43. 98.]
+    B = cholesky(A)
+    @test B isa Cholesky{Float16, Matrix{Float16}}
+    @test B.U isa UpperTriangular{Float16, Matrix{Float16}}
+    @test B.L isa LowerTriangular{Float16, Matrix{Float16}}
+    @test B.UL isa UpperTriangular{Float16, Matrix{Float16}}
+end
+
 end # module TestCholesky
diff --git a/stdlib/LinearAlgebra/test/eigen.jl b/stdlib/LinearAlgebra/test/eigen.jl
index 6ac0dc6852df9..339d108e1de7e 100644
--- a/stdlib/LinearAlgebra/test/eigen.jl
+++ b/stdlib/LinearAlgebra/test/eigen.jl
@@ -177,4 +177,12 @@ end
     @test isequal(eigen(A), eigen(A))
 end
 
+@testset "Float16" begin
+    A = Float16[4. 12. -16.; 12. 37. -43.; -16. -43. 98.]
+    B = eigen(A)
+    @test B isa Eigen{Float16, Float16, Matrix{Float16}, Vector{Float16}, Vector{Float16}}
+    @test B.values isa Vector{Float16}
+    @test B.vectors isa Matrix{Float16}
+end
+
 end # module TestEigen
diff --git a/stdlib/LinearAlgebra/test/svd.jl b/stdlib/LinearAlgebra/test/svd.jl
index e9361f65a1bca..820509b7aae70 100644
--- a/stdlib/LinearAlgebra/test/svd.jl
+++ b/stdlib/LinearAlgebra/test/svd.jl
@@ -248,4 +248,13 @@ end
     end
 end
 
+@testset "Float16" begin
+    A = Float16[4. 12. -16.; 12. 37. -43.; -16. -43. 98.]
+    B = svd(A)
+    @test B isa SVD{Float16, Float16, Matrix{Float16}}
+    @test B.U isa Matrix{Float16}
+    @test B.Vt isa Matrix{Float16}
+    @test B.S isa Vector{Float16}
+end
+
 end # module TestSVD

From 6ce856108500c230c1509e8dbe361ad375e0ceca Mon Sep 17 00:00:00 2001
From: Arun sanganal <74652697+ArunSanganal@users.noreply.github.com>
Date: Fri, 25 Jun 2021 15:03:36 +0530
Subject: [PATCH 02/23] Update stdlib/LinearAlgebra/src/eigen.jl

Co-authored-by: Daniel Karrasch <daniel.karrasch@posteo.de>
---
 stdlib/LinearAlgebra/src/eigen.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/stdlib/LinearAlgebra/src/eigen.jl b/stdlib/LinearAlgebra/src/eigen.jl
index c54b5597540b1..8dd42ccea30d8 100644
--- a/stdlib/LinearAlgebra/src/eigen.jl
+++ b/stdlib/LinearAlgebra/src/eigen.jl
@@ -275,8 +275,8 @@ function eigen(A::AbstractMatrix{T}; permute::Bool=true, scale::Bool=true, sortb
     isdiag(AA) && return eigen(Diagonal(AA); permute=permute, scale=scale, sortby=sortby)
     return eigen!(AA; permute=permute, scale=scale, sortby=sortby, jvl=jvl, jvr=jvr, jce=jce, jcv=jcv)
 end
-function eigen(A::AbstractMatrix{T}; permute::Bool=true, scale::Bool=true, sortby::Union{Function,Nothing}=eigsortby) where T<:Float16
-    AA = copy_oftype(A, eigtype(T))
+function eigen(A::AbstractMatrix{Float16}; permute::Bool=true, scale::Bool=true, sortby::Union{Function,Nothing}=eigsortby)
+    AA = copy_oftype(A, eigtype(Float16))
     isdiag(AA) && return eigen(Diagonal(AA); permute=permute, scale=scale, sortby=sortby)
     A = eigen!(AA; permute=permute, scale=scale, sortby=sortby)
     Eigen(convert(Vector{Float16}, A.values),

From 2a5acfa52b18284ad486382cd28a8f108b50e76d Mon Sep 17 00:00:00 2001
From: Arun sanganal <74652697+ArunSanganal@users.noreply.github.com>
Date: Fri, 25 Jun 2021 15:11:32 +0530
Subject: [PATCH 03/23] Update stdlib/LinearAlgebra/src/cholesky.jl

Co-authored-by: Daniel Karrasch <daniel.karrasch@posteo.de>
---
 stdlib/LinearAlgebra/src/cholesky.jl | 5 ++---
 1 file changed, 2 insertions(+), 3 deletions(-)

diff --git a/stdlib/LinearAlgebra/src/cholesky.jl b/stdlib/LinearAlgebra/src/cholesky.jl
index 76a6f50a124ce..2ad2135da5d9c 100644
--- a/stdlib/LinearAlgebra/src/cholesky.jl
+++ b/stdlib/LinearAlgebra/src/cholesky.jl
@@ -388,10 +388,9 @@ true
 cholesky(A::Union{StridedMatrix,RealHermSymComplexHerm{<:Real,<:StridedMatrix}},
     ::Val{false}=Val(false); check::Bool = true) = cholesky!(cholcopy(A); check = check)
 
-function cholesky(A::Union{StridedMatrix{T},RealHermSymComplexHerm{<:T,<:StridedMatrix}}, ::Val{false}=Val(false); check::Bool = true) where T<:Float16
+function cholesky(A::Union{StridedMatrix{Float16},RealHermSymComplexHerm{Float16,<:StridedMatrix}}, ::Val{false}=Val(false); check::Bool = true)
     X = cholesky!(cholcopy(A); check = check)
-    Xnew = convert(AbstractMatrix{T}, X.factors)
-    Cholesky{T, typeof(Xnew)}(Xnew, X.uplo, X.info)
+    return Cholesky{Float16}(X)
 end
 
 

From 226e098cdd8ea5c75a6c03c4c765638aca15744a Mon Sep 17 00:00:00 2001
From: Arun <sanganalarun@gmail.com>
Date: Fri, 25 Jun 2021 15:53:48 +0530
Subject: [PATCH 04/23] Update eigen.jl

---
 stdlib/LinearAlgebra/src/eigen.jl | 15 ++++++++++-----
 1 file changed, 10 insertions(+), 5 deletions(-)

diff --git a/stdlib/LinearAlgebra/src/eigen.jl b/stdlib/LinearAlgebra/src/eigen.jl
index c54b5597540b1..4178e844bc482 100644
--- a/stdlib/LinearAlgebra/src/eigen.jl
+++ b/stdlib/LinearAlgebra/src/eigen.jl
@@ -275,13 +275,18 @@ function eigen(A::AbstractMatrix{T}; permute::Bool=true, scale::Bool=true, sortb
     isdiag(AA) && return eigen(Diagonal(AA); permute=permute, scale=scale, sortby=sortby)
     return eigen!(AA; permute=permute, scale=scale, sortby=sortby, jvl=jvl, jvr=jvr, jce=jce, jcv=jcv)
 end
-function eigen(A::AbstractMatrix{T}; permute::Bool=true, scale::Bool=true, sortby::Union{Function,Nothing}=eigsortby) where T<:Float16
-    AA = copy_oftype(A, eigtype(T))
+function eigen(A::AbstractMatrix{Float16}; permute::Bool=true, scale::Bool=true, sortby::Union{Function,Nothing}=eigsortby)
+    AA = copy_oftype(A, eigtype(Float16))
     isdiag(AA) && return eigen(Diagonal(AA); permute=permute, scale=scale, sortby=sortby)
     A = eigen!(AA; permute=permute, scale=scale, sortby=sortby)
-    Eigen(convert(Vector{Float16}, A.values),
-          convert(AbstractArray{Float16}, A.vectors))
-end
+    if isreal(A.values) == false
+        Eigen(convert(Vector{Complex{Float16}}, A.values),
+            convert(AbstractArray{Complex{Float16}}, A.vectors))
+    else
+        Eigen(convert(Vector{Float16}, A.values),
+            convert(AbstractArray{Float16}, A.vectors))
+    end
+end 
 eigen(x::Number) = Eigen([x], fill(one(x), 1, 1))
 
 """

From 0bb1904f6c4ca61ae27ec3d60d70f27b1b656995 Mon Sep 17 00:00:00 2001
From: Arun sanganal <74652697+ArunSanganal@users.noreply.github.com>
Date: Fri, 25 Jun 2021 16:05:12 +0530
Subject: [PATCH 05/23] Update eigen.jl

---
 stdlib/LinearAlgebra/src/eigen.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/stdlib/LinearAlgebra/src/eigen.jl b/stdlib/LinearAlgebra/src/eigen.jl
index 4178e844bc482..a5d40bb9c535f 100644
--- a/stdlib/LinearAlgebra/src/eigen.jl
+++ b/stdlib/LinearAlgebra/src/eigen.jl
@@ -286,7 +286,7 @@ function eigen(A::AbstractMatrix{Float16}; permute::Bool=true, scale::Bool=true,
         Eigen(convert(Vector{Float16}, A.values),
             convert(AbstractArray{Float16}, A.vectors))
     end
-end 
+end
 eigen(x::Number) = Eigen([x], fill(one(x), 1, 1))
 
 """

From 7f41e64c30de1215ab5502681bd1895a282c08f8 Mon Sep 17 00:00:00 2001
From: Arun <sanganalarun@gmail.com>
Date: Fri, 25 Jun 2021 16:07:47 +0530
Subject: [PATCH 06/23] Update svd.jl

---
 stdlib/LinearAlgebra/src/svd.jl | 6 ++----
 1 file changed, 2 insertions(+), 4 deletions(-)

diff --git a/stdlib/LinearAlgebra/src/svd.jl b/stdlib/LinearAlgebra/src/svd.jl
index cf8c272a894ea..b7a87e1d6bb21 100644
--- a/stdlib/LinearAlgebra/src/svd.jl
+++ b/stdlib/LinearAlgebra/src/svd.jl
@@ -175,11 +175,9 @@ true
 function svd(A::StridedVecOrMat{T}; full::Bool = false, alg::Algorithm = default_svd_alg(A)) where {T}
     svd!(copy_oftype(A, eigtype(T)), full = full, alg = alg)
 end
-function svd(A::StridedVecOrMat{T}; full::Bool = false, alg::Algorithm = default_svd_alg(A)) where {T<:Float16}
+function svd(A::StridedVecOrMat{T}; full::Bool = false, alg::Algorithm = default_svd_alg(A)) where {T <: Union{Float16,Complex{Float16}}
     A=svd!(copy_oftype(A, eigtype(T)), full = full, alg = alg)
-    SVD(convert(AbstractArray{Float16}, A.U),
-        convert(Vector{Float16}, A.S),
-        convert(AbstractArray{Float16}, A.Vt))
+    return SVD{T}(A)
 end
 function svd(x::Number; full::Bool = false, alg::Algorithm = default_svd_alg(x))
     SVD(x == 0 ? fill(one(x), 1, 1) : fill(x/abs(x), 1, 1), [abs(x)], fill(one(x), 1, 1))

From 5f3bf76b6a7406bfb37875b79823e7797c859a66 Mon Sep 17 00:00:00 2001
From: Arun sanganal <74652697+ArunSanganal@users.noreply.github.com>
Date: Fri, 25 Jun 2021 16:17:00 +0530
Subject: [PATCH 07/23] Update stdlib/LinearAlgebra/src/eigen.jl

Co-authored-by: Daniel Karrasch <daniel.karrasch@posteo.de>
---
 stdlib/LinearAlgebra/src/eigen.jl | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/stdlib/LinearAlgebra/src/eigen.jl b/stdlib/LinearAlgebra/src/eigen.jl
index a5d40bb9c535f..4941e8449d04f 100644
--- a/stdlib/LinearAlgebra/src/eigen.jl
+++ b/stdlib/LinearAlgebra/src/eigen.jl
@@ -279,12 +279,12 @@ function eigen(A::AbstractMatrix{Float16}; permute::Bool=true, scale::Bool=true,
     AA = copy_oftype(A, eigtype(Float16))
     isdiag(AA) && return eigen(Diagonal(AA); permute=permute, scale=scale, sortby=sortby)
     A = eigen!(AA; permute=permute, scale=scale, sortby=sortby)
-    if isreal(A.values) == false
-        Eigen(convert(Vector{Complex{Float16}}, A.values),
-            convert(AbstractArray{Complex{Float16}}, A.vectors))
-    else
+    if isreal(A.values)
         Eigen(convert(Vector{Float16}, A.values),
             convert(AbstractArray{Float16}, A.vectors))
+    else
+        Eigen(convert(Vector{Complex{Float16}}, A.values),
+            convert(AbstractArray{Complex{Float16}}, A.vectors))
     end
 end
 eigen(x::Number) = Eigen([x], fill(one(x), 1, 1))

From 1ffd9c7c8efd4e6e6320874a05f54a085f375efe Mon Sep 17 00:00:00 2001
From: Arun sanganal <74652697+ArunSanganal@users.noreply.github.com>
Date: Fri, 25 Jun 2021 16:17:14 +0530
Subject: [PATCH 08/23] Update stdlib/LinearAlgebra/src/svd.jl

Co-authored-by: Daniel Karrasch <daniel.karrasch@posteo.de>
---
 stdlib/LinearAlgebra/src/svd.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/stdlib/LinearAlgebra/src/svd.jl b/stdlib/LinearAlgebra/src/svd.jl
index b7a87e1d6bb21..cd21b46d33f45 100644
--- a/stdlib/LinearAlgebra/src/svd.jl
+++ b/stdlib/LinearAlgebra/src/svd.jl
@@ -176,7 +176,7 @@ function svd(A::StridedVecOrMat{T}; full::Bool = false, alg::Algorithm = default
     svd!(copy_oftype(A, eigtype(T)), full = full, alg = alg)
 end
 function svd(A::StridedVecOrMat{T}; full::Bool = false, alg::Algorithm = default_svd_alg(A)) where {T <: Union{Float16,Complex{Float16}}
-    A=svd!(copy_oftype(A, eigtype(T)), full = full, alg = alg)
+    A = svd!(copy_oftype(A, eigtype(T)), full = full, alg = alg)
     return SVD{T}(A)
 end
 function svd(x::Number; full::Bool = false, alg::Algorithm = default_svd_alg(x))

From 641c408996682063fe0b67765a33fd39b00c5832 Mon Sep 17 00:00:00 2001
From: Arun sanganal <74652697+ArunSanganal@users.noreply.github.com>
Date: Fri, 25 Jun 2021 16:44:25 +0530
Subject: [PATCH 09/23] Update eigen.jl

---
 stdlib/LinearAlgebra/src/eigen.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/stdlib/LinearAlgebra/src/eigen.jl b/stdlib/LinearAlgebra/src/eigen.jl
index 4941e8449d04f..1b293cf707694 100644
--- a/stdlib/LinearAlgebra/src/eigen.jl
+++ b/stdlib/LinearAlgebra/src/eigen.jl
@@ -275,7 +275,7 @@ function eigen(A::AbstractMatrix{T}; permute::Bool=true, scale::Bool=true, sortb
     isdiag(AA) && return eigen(Diagonal(AA); permute=permute, scale=scale, sortby=sortby)
     return eigen!(AA; permute=permute, scale=scale, sortby=sortby, jvl=jvl, jvr=jvr, jce=jce, jcv=jcv)
 end
-function eigen(A::AbstractMatrix{Float16}; permute::Bool=true, scale::Bool=true, sortby::Union{Function,Nothing}=eigsortby)
+function eigen(A::AbstractMatrix{Union{Float16,Complex{Float16}}}; permute::Bool=true, scale::Bool=true, sortby::Union{Function,Nothing}=eigsortby)
     AA = copy_oftype(A, eigtype(Float16))
     isdiag(AA) && return eigen(Diagonal(AA); permute=permute, scale=scale, sortby=sortby)
     A = eigen!(AA; permute=permute, scale=scale, sortby=sortby)

From d721eac8e67837655a74d10d6c080d5120f2881f Mon Sep 17 00:00:00 2001
From: Arun sanganal <74652697+ArunSanganal@users.noreply.github.com>
Date: Fri, 25 Jun 2021 17:09:14 +0530
Subject: [PATCH 10/23] Update stdlib/LinearAlgebra/src/svd.jl

Co-authored-by: Daniel Karrasch <daniel.karrasch@posteo.de>
---
 stdlib/LinearAlgebra/src/svd.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/stdlib/LinearAlgebra/src/svd.jl b/stdlib/LinearAlgebra/src/svd.jl
index cd21b46d33f45..bee4c8451c0a6 100644
--- a/stdlib/LinearAlgebra/src/svd.jl
+++ b/stdlib/LinearAlgebra/src/svd.jl
@@ -175,7 +175,7 @@ true
 function svd(A::StridedVecOrMat{T}; full::Bool = false, alg::Algorithm = default_svd_alg(A)) where {T}
     svd!(copy_oftype(A, eigtype(T)), full = full, alg = alg)
 end
-function svd(A::StridedVecOrMat{T}; full::Bool = false, alg::Algorithm = default_svd_alg(A)) where {T <: Union{Float16,Complex{Float16}}
+function svd(A::StridedVecOrMat{T}; full::Bool = false, alg::Algorithm = default_svd_alg(A)) where {T <: Union{Float16,Complex{Float16}}}
     A = svd!(copy_oftype(A, eigtype(T)), full = full, alg = alg)
     return SVD{T}(A)
 end

From fd459bbebbcaa61f0dc06f3957cc1f4feb3740bd Mon Sep 17 00:00:00 2001
From: Arun <sanganalarun@gmail.com>
Date: Fri, 25 Jun 2021 18:10:34 +0530
Subject: [PATCH 11/23] Update eigen.jl

---
 stdlib/LinearAlgebra/src/eigen.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/stdlib/LinearAlgebra/src/eigen.jl b/stdlib/LinearAlgebra/src/eigen.jl
index 1b293cf707694..64376c99db968 100644
--- a/stdlib/LinearAlgebra/src/eigen.jl
+++ b/stdlib/LinearAlgebra/src/eigen.jl
@@ -275,8 +275,8 @@ function eigen(A::AbstractMatrix{T}; permute::Bool=true, scale::Bool=true, sortb
     isdiag(AA) && return eigen(Diagonal(AA); permute=permute, scale=scale, sortby=sortby)
     return eigen!(AA; permute=permute, scale=scale, sortby=sortby, jvl=jvl, jvr=jvr, jce=jce, jcv=jcv)
 end
-function eigen(A::AbstractMatrix{Union{Float16,Complex{Float16}}}; permute::Bool=true, scale::Bool=true, sortby::Union{Function,Nothing}=eigsortby)
-    AA = copy_oftype(A, eigtype(Float16))
+function eigen(A::AbstractMatrix{T}; permute::Bool=true, scale::Bool=true, sortby::Union{Function,Nothing}=eigsortby) where {T <: Union{Float16,Complex{Float16}}}
+    AA = copy_oftype(A, eigtype(T))
     isdiag(AA) && return eigen(Diagonal(AA); permute=permute, scale=scale, sortby=sortby)
     A = eigen!(AA; permute=permute, scale=scale, sortby=sortby)
     if isreal(A.values)

From 973b22acb821b021fc68c53bfe4c1e1541743046 Mon Sep 17 00:00:00 2001
From: Arun <sanganalarun@gmail.com>
Date: Fri, 25 Jun 2021 18:17:58 +0530
Subject: [PATCH 12/23] Update eigen.jl

---
 stdlib/LinearAlgebra/test/eigen.jl | 10 ++++++++++
 1 file changed, 10 insertions(+)

diff --git a/stdlib/LinearAlgebra/test/eigen.jl b/stdlib/LinearAlgebra/test/eigen.jl
index 339d108e1de7e..29d7e04713321 100644
--- a/stdlib/LinearAlgebra/test/eigen.jl
+++ b/stdlib/LinearAlgebra/test/eigen.jl
@@ -180,9 +180,19 @@ end
 @testset "Float16" begin
     A = Float16[4. 12. -16.; 12. 37. -43.; -16. -43. 98.]
     B = eigen(A)
+    C = Float16[3 -2; 4 -1]
+    D = eigen(C)
+    E = complex(C)
+    F = eigen(E)
     @test B isa Eigen{Float16, Float16, Matrix{Float16}, Vector{Float16}, Vector{Float16}}
     @test B.values isa Vector{Float16}
     @test B.vectors isa Matrix{Float16}
+    @test D isa Eigen{ComplexF16, ComplexF16, Matrix{ComplexF16}, Vector{ComplexF16}, Vector{Float16}}
+    @test D.values isa Vector{ComplexF16}
+    @test D.vectors isa Matrix{ComplexF16}
+    @test F isa Eigen{ComplexF16, ComplexF16, Matrix{ComplexF16}, Vector{ComplexF16}, Vector{Float16}}
+    @test F.values isa Vector{ComplexF16}
+    @test F.vectors isa Matrix{ComplexF16}
 end
 
 end # module TestEigen

From 85169ed3808484cb229fa8679a458d87aa2760bf Mon Sep 17 00:00:00 2001
From: Arun <sanganalarun@gmail.com>
Date: Sat, 26 Jun 2021 07:30:38 +0530
Subject: [PATCH 13/23] Update eigen.jl

---
 stdlib/LinearAlgebra/test/eigen.jl | 9 +++++++++
 1 file changed, 9 insertions(+)

diff --git a/stdlib/LinearAlgebra/test/eigen.jl b/stdlib/LinearAlgebra/test/eigen.jl
index 29d7e04713321..8a8d39a940c07 100644
--- a/stdlib/LinearAlgebra/test/eigen.jl
+++ b/stdlib/LinearAlgebra/test/eigen.jl
@@ -187,12 +187,21 @@ end
     @test B isa Eigen{Float16, Float16, Matrix{Float16}, Vector{Float16}, Vector{Float16}}
     @test B.values isa Vector{Float16}
     @test B.vectors isa Matrix{Float16}
+    @test B.rcondv isa Vector{Float16}
+    @test B.rconde isa Vector{Float16}
+    @test B.vectorsl isa Matrix{Float16}
     @test D isa Eigen{ComplexF16, ComplexF16, Matrix{ComplexF16}, Vector{ComplexF16}, Vector{Float16}}
     @test D.values isa Vector{ComplexF16}
     @test D.vectors isa Matrix{ComplexF16}
+    @test D.rcondv isa Vector{Float16}
+    @test D.rconde isa Vector{Float16}
+    @test D.vectorsl isa Matrix{ComplexF16}
     @test F isa Eigen{ComplexF16, ComplexF16, Matrix{ComplexF16}, Vector{ComplexF16}, Vector{Float16}}
     @test F.values isa Vector{ComplexF16}
     @test F.vectors isa Matrix{ComplexF16}
+    @test F.rcondv isa Vector{Float16}
+    @test F.rconde isa Vector{Float16}
+    @test F.vectorsl isa Matrix{ComplexF16}
 end
 
 end # module TestEigen

From 27ea310e2a37f6e33916167ec32aec4b8cb656c6 Mon Sep 17 00:00:00 2001
From: Arun sanganal <74652697+ArunSanganal@users.noreply.github.com>
Date: Sat, 26 Jun 2021 17:27:31 +0530
Subject: [PATCH 14/23] Update eigen.jl

---
 stdlib/LinearAlgebra/test/eigen.jl | 9 ---------
 1 file changed, 9 deletions(-)

diff --git a/stdlib/LinearAlgebra/test/eigen.jl b/stdlib/LinearAlgebra/test/eigen.jl
index 8a8d39a940c07..29d7e04713321 100644
--- a/stdlib/LinearAlgebra/test/eigen.jl
+++ b/stdlib/LinearAlgebra/test/eigen.jl
@@ -187,21 +187,12 @@ end
     @test B isa Eigen{Float16, Float16, Matrix{Float16}, Vector{Float16}, Vector{Float16}}
     @test B.values isa Vector{Float16}
     @test B.vectors isa Matrix{Float16}
-    @test B.rcondv isa Vector{Float16}
-    @test B.rconde isa Vector{Float16}
-    @test B.vectorsl isa Matrix{Float16}
     @test D isa Eigen{ComplexF16, ComplexF16, Matrix{ComplexF16}, Vector{ComplexF16}, Vector{Float16}}
     @test D.values isa Vector{ComplexF16}
     @test D.vectors isa Matrix{ComplexF16}
-    @test D.rcondv isa Vector{Float16}
-    @test D.rconde isa Vector{Float16}
-    @test D.vectorsl isa Matrix{ComplexF16}
     @test F isa Eigen{ComplexF16, ComplexF16, Matrix{ComplexF16}, Vector{ComplexF16}, Vector{Float16}}
     @test F.values isa Vector{ComplexF16}
     @test F.vectors isa Matrix{ComplexF16}
-    @test F.rcondv isa Vector{Float16}
-    @test F.rconde isa Vector{Float16}
-    @test F.vectorsl isa Matrix{ComplexF16}
 end
 
 end # module TestEigen

From a9951a7c7119c1b647915a4fe1fd4c59b62cc13f Mon Sep 17 00:00:00 2001
From: Arun <sanganalarun@gmail.com>
Date: Sat, 26 Jun 2021 20:17:10 +0530
Subject: [PATCH 15/23] Added type converter for Eigen.

---
 stdlib/LinearAlgebra/src/eigen.jl | 7 +++++++
 1 file changed, 7 insertions(+)

diff --git a/stdlib/LinearAlgebra/src/eigen.jl b/stdlib/LinearAlgebra/src/eigen.jl
index 64376c99db968..cdde4ce5811d5 100644
--- a/stdlib/LinearAlgebra/src/eigen.jl
+++ b/stdlib/LinearAlgebra/src/eigen.jl
@@ -57,6 +57,13 @@ struct Eigen{T,V,S<:AbstractMatrix,U<:AbstractVector,R<:AbstractVector} <: Facto
     Eigen{T,V,S,U,R}(values::AbstractVector{V}, vectors::AbstractMatrix{T}, vectorsl::AbstractMatrix{T}, unitary::Bool, rconde::R, rcondv::R) where {T,V,S,U,R} =
         new(values, vectors, vectorsl, unitary, rconde, rcondv)
 end
+Eigen{T}(F::Eigen) where {T} = Eigen(
+           convert(AbstractVector{T}, F.values),
+           convert(AbstractMatrix{T}, F.vectors),
+           convert(AbstractMatrix{T}, F.vectorsl),
+           F.unitary::Bool,
+           convert(AbstractVector{T}, F.rconde),
+           convert(AbstractVector{T}, F.rcondv))
 Eigen(values::AbstractVector{V}, vectors::AbstractMatrix{T}, vectorsl=vectors, uni=true, rce=zeros(real(T),0), rcv=zeros(real(T), 0)) where {T,V} =
     Eigen{T,V,typeof(vectors),typeof(values),typeof(rce)}(values, vectors, vectorsl, uni, rce, rcv)
 

From ff71500bd54fc548bf5bdba312cff1a89f0a8763 Mon Sep 17 00:00:00 2001
From: Arun sanganal <74652697+ArunSanganal@users.noreply.github.com>
Date: Sat, 26 Jun 2021 20:54:35 +0530
Subject: [PATCH 16/23] Update eigen.jl

---
 stdlib/LinearAlgebra/src/eigen.jl | 7 -------
 1 file changed, 7 deletions(-)

diff --git a/stdlib/LinearAlgebra/src/eigen.jl b/stdlib/LinearAlgebra/src/eigen.jl
index cdde4ce5811d5..64376c99db968 100644
--- a/stdlib/LinearAlgebra/src/eigen.jl
+++ b/stdlib/LinearAlgebra/src/eigen.jl
@@ -57,13 +57,6 @@ struct Eigen{T,V,S<:AbstractMatrix,U<:AbstractVector,R<:AbstractVector} <: Facto
     Eigen{T,V,S,U,R}(values::AbstractVector{V}, vectors::AbstractMatrix{T}, vectorsl::AbstractMatrix{T}, unitary::Bool, rconde::R, rcondv::R) where {T,V,S,U,R} =
         new(values, vectors, vectorsl, unitary, rconde, rcondv)
 end
-Eigen{T}(F::Eigen) where {T} = Eigen(
-           convert(AbstractVector{T}, F.values),
-           convert(AbstractMatrix{T}, F.vectors),
-           convert(AbstractMatrix{T}, F.vectorsl),
-           F.unitary::Bool,
-           convert(AbstractVector{T}, F.rconde),
-           convert(AbstractVector{T}, F.rcondv))
 Eigen(values::AbstractVector{V}, vectors::AbstractMatrix{T}, vectorsl=vectors, uni=true, rce=zeros(real(T),0), rcv=zeros(real(T), 0)) where {T,V} =
     Eigen{T,V,typeof(vectors),typeof(values),typeof(rce)}(values, vectors, vectorsl, uni, rce, rcv)
 

From 9924e716bad6ebdb2ac6e3752b5af3fb82fbb2d8 Mon Sep 17 00:00:00 2001
From: Arun sanganal <74652697+ArunSanganal@users.noreply.github.com>
Date: Sat, 26 Jun 2021 20:54:48 +0530
Subject: [PATCH 17/23] Update stdlib/LinearAlgebra/src/eigen.jl

Co-authored-by: Daniel Karrasch <daniel.karrasch@posteo.de>
---
 stdlib/LinearAlgebra/src/eigen.jl | 11 ++++-------
 1 file changed, 4 insertions(+), 7 deletions(-)

diff --git a/stdlib/LinearAlgebra/src/eigen.jl b/stdlib/LinearAlgebra/src/eigen.jl
index 64376c99db968..6f6dcbfd2979a 100644
--- a/stdlib/LinearAlgebra/src/eigen.jl
+++ b/stdlib/LinearAlgebra/src/eigen.jl
@@ -279,13 +279,10 @@ function eigen(A::AbstractMatrix{T}; permute::Bool=true, scale::Bool=true, sortb
     AA = copy_oftype(A, eigtype(T))
     isdiag(AA) && return eigen(Diagonal(AA); permute=permute, scale=scale, sortby=sortby)
     A = eigen!(AA; permute=permute, scale=scale, sortby=sortby)
-    if isreal(A.values)
-        Eigen(convert(Vector{Float16}, A.values),
-            convert(AbstractArray{Float16}, A.vectors))
-    else
-        Eigen(convert(Vector{Complex{Float16}}, A.values),
-            convert(AbstractArray{Complex{Float16}}, A.vectors))
-    end
+    values = convert(AbstractVector{isreal(A.values) ? Float16 : Complex{Float16}}, A.values)
+    vectors = convert(AbstractMatrix{isreal(A.vectors) ? Float16 : Complex{Float16}}, A.vectors)
+    vectorsl = convert(AbstractMatrix{isreal(A.vectorsl) ? Float16 : Complex{Float16}}, A.vectorsl)
+    return Eigen(values, vectors, vectorsl, A.unitary, A.rconde, A.rcondv)
 end
 eigen(x::Number) = Eigen([x], fill(one(x), 1, 1))
 

From 3ca6c902074f8b5544da20e9d931ce065c0f90c9 Mon Sep 17 00:00:00 2001
From: Arun sanganal <74652697+ArunSanganal@users.noreply.github.com>
Date: Sat, 26 Jun 2021 22:39:35 +0530
Subject: [PATCH 18/23] Update stdlib/LinearAlgebra/src/eigen.jl

Co-authored-by: Daniel Karrasch <daniel.karrasch@posteo.de>
---
 stdlib/LinearAlgebra/src/eigen.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/stdlib/LinearAlgebra/src/eigen.jl b/stdlib/LinearAlgebra/src/eigen.jl
index 6f6dcbfd2979a..997ddb74a96f6 100644
--- a/stdlib/LinearAlgebra/src/eigen.jl
+++ b/stdlib/LinearAlgebra/src/eigen.jl
@@ -281,7 +281,7 @@ function eigen(A::AbstractMatrix{T}; permute::Bool=true, scale::Bool=true, sortb
     A = eigen!(AA; permute=permute, scale=scale, sortby=sortby)
     values = convert(AbstractVector{isreal(A.values) ? Float16 : Complex{Float16}}, A.values)
     vectors = convert(AbstractMatrix{isreal(A.vectors) ? Float16 : Complex{Float16}}, A.vectors)
-    vectorsl = convert(AbstractMatrix{isreal(A.vectorsl) ? Float16 : Complex{Float16}}, A.vectorsl)
+    vectorsl = convert(AbstractMatrix{isreal(A.vectors) ? Float16 : Complex{Float16}}, A.vectorsl)
     return Eigen(values, vectors, vectorsl, A.unitary, A.rconde, A.rcondv)
 end
 eigen(x::Number) = Eigen([x], fill(one(x), 1, 1))

From 63fcccf982e429e7d7e899fb2992ab1de1b7ed3c Mon Sep 17 00:00:00 2001
From: Arun <sanganalarun@gmail.com>
Date: Sat, 26 Jun 2021 23:39:26 +0530
Subject: [PATCH 19/23] updates

---
 stdlib/LinearAlgebra/src/eigen.jl     |  4 +++-
 stdlib/LinearAlgebra/test/cholesky.jl |  4 ++++
 stdlib/LinearAlgebra/test/eigen.jl    | 15 +++++++++++++++
 stdlib/LinearAlgebra/test/svd.jl      |  4 ++++
 4 files changed, 26 insertions(+), 1 deletion(-)

diff --git a/stdlib/LinearAlgebra/src/eigen.jl b/stdlib/LinearAlgebra/src/eigen.jl
index 997ddb74a96f6..069ac6bca83ae 100644
--- a/stdlib/LinearAlgebra/src/eigen.jl
+++ b/stdlib/LinearAlgebra/src/eigen.jl
@@ -282,7 +282,9 @@ function eigen(A::AbstractMatrix{T}; permute::Bool=true, scale::Bool=true, sortb
     values = convert(AbstractVector{isreal(A.values) ? Float16 : Complex{Float16}}, A.values)
     vectors = convert(AbstractMatrix{isreal(A.vectors) ? Float16 : Complex{Float16}}, A.vectors)
     vectorsl = convert(AbstractMatrix{isreal(A.vectors) ? Float16 : Complex{Float16}}, A.vectorsl)
-    return Eigen(values, vectors, vectorsl, A.unitary, A.rconde, A.rcondv)
+    rconde = convert(Vector{isreal(A.rconde) ? Float16 : Complex{Float16}}, A.rconde)
+    rcondv = convert(Vector{isreal(A.rcondv) ? Float16 : Complex{Float16}}, A.rcondv)
+    return Eigen(values, vectors, vectorsl, A.unitary, rconde, rcondv)
 end
 eigen(x::Number) = Eigen([x], fill(one(x), 1, 1))
 
diff --git a/stdlib/LinearAlgebra/test/cholesky.jl b/stdlib/LinearAlgebra/test/cholesky.jl
index 6ba635593433c..53a18c4a62186 100644
--- a/stdlib/LinearAlgebra/test/cholesky.jl
+++ b/stdlib/LinearAlgebra/test/cholesky.jl
@@ -486,10 +486,14 @@ end
 @testset "Float16" begin
     A = Float16[4. 12. -16.; 12. 37. -43.; -16. -43. 98.]
     B = cholesky(A)
+    B32 = cholesky(Float32.(A))
     @test B isa Cholesky{Float16, Matrix{Float16}}
     @test B.U isa UpperTriangular{Float16, Matrix{Float16}}
     @test B.L isa LowerTriangular{Float16, Matrix{Float16}}
     @test B.UL isa UpperTriangular{Float16, Matrix{Float16}}
+    @test B.U ≈ B32.U
+    @test B.L ≈ B32.L
+    @test B.UL ≈ B32.UL
 end
 
 end # module TestCholesky
diff --git a/stdlib/LinearAlgebra/test/eigen.jl b/stdlib/LinearAlgebra/test/eigen.jl
index 29d7e04713321..927160b724bce 100644
--- a/stdlib/LinearAlgebra/test/eigen.jl
+++ b/stdlib/LinearAlgebra/test/eigen.jl
@@ -180,19 +180,34 @@ end
 @testset "Float16" begin
     A = Float16[4. 12. -16.; 12. 37. -43.; -16. -43. 98.]
     B = eigen(A)
+    B32 = eigen(Float32.(A))
     C = Float16[3 -2; 4 -1]
     D = eigen(C)
+    D32 = eigen(Float32.(C))
     E = complex(C)
     F = eigen(E)
+    F32 = eigen(Float32.(E))
     @test B isa Eigen{Float16, Float16, Matrix{Float16}, Vector{Float16}, Vector{Float16}}
     @test B.values isa Vector{Float16}
     @test B.vectors isa Matrix{Float16}
+    @test B.vectorsl is Matrix{Float16}
+    @test B.values ≈ B32.values
+    @test B.vectors ≈ B32.vectors
+    @test B.vectorsl ≈ B32.vectorsl
     @test D isa Eigen{ComplexF16, ComplexF16, Matrix{ComplexF16}, Vector{ComplexF16}, Vector{Float16}}
     @test D.values isa Vector{ComplexF16}
     @test D.vectors isa Matrix{ComplexF16}
+    @test D.vectorsl isa Matrix{ComplexF16}
+    @test D.values ≈ D32.values
+    @test D.vectors ≈ D32.vectors
+    @test D.vectorsl ≈ D32.vectorsl
     @test F isa Eigen{ComplexF16, ComplexF16, Matrix{ComplexF16}, Vector{ComplexF16}, Vector{Float16}}
     @test F.values isa Vector{ComplexF16}
     @test F.vectors isa Matrix{ComplexF16}
+    @test F.vectorsl isa Matrix{ComplexF16}
+    @test F.values ≈ F32.values
+    @test F.vectors ≈ F32.vectors
+    @test F.vectorsl ≈ F32.vectorsl
 end
 
 end # module TestEigen
diff --git a/stdlib/LinearAlgebra/test/svd.jl b/stdlib/LinearAlgebra/test/svd.jl
index 820509b7aae70..8bd3edadc911d 100644
--- a/stdlib/LinearAlgebra/test/svd.jl
+++ b/stdlib/LinearAlgebra/test/svd.jl
@@ -251,10 +251,14 @@ end
 @testset "Float16" begin
     A = Float16[4. 12. -16.; 12. 37. -43.; -16. -43. 98.]
     B = svd(A)
+    B32 = svd(Float32.(A))
     @test B isa SVD{Float16, Float16, Matrix{Float16}}
     @test B.U isa Matrix{Float16}
     @test B.Vt isa Matrix{Float16}
     @test B.S isa Vector{Float16}
+    @test B.U ≈ B32.U
+    @test B.Vt ≈ B32.Vt
+    @test B.S ≈ B32.S
 end
 
 end # module TestSVD

From 7be61147f1e6d059619da72c663c2b09911700d4 Mon Sep 17 00:00:00 2001
From: Arun sanganal <74652697+ArunSanganal@users.noreply.github.com>
Date: Sun, 27 Jun 2021 01:06:52 +0530
Subject: [PATCH 20/23] Update eigen.jl

---
 stdlib/LinearAlgebra/test/eigen.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/stdlib/LinearAlgebra/test/eigen.jl b/stdlib/LinearAlgebra/test/eigen.jl
index 927160b724bce..a8129532321a0 100644
--- a/stdlib/LinearAlgebra/test/eigen.jl
+++ b/stdlib/LinearAlgebra/test/eigen.jl
@@ -190,7 +190,7 @@ end
     @test B isa Eigen{Float16, Float16, Matrix{Float16}, Vector{Float16}, Vector{Float16}}
     @test B.values isa Vector{Float16}
     @test B.vectors isa Matrix{Float16}
-    @test B.vectorsl is Matrix{Float16}
+    @test B.vectorsl isa Matrix{Float16}
     @test B.values ≈ B32.values
     @test B.vectors ≈ B32.vectors
     @test B.vectorsl ≈ B32.vectorsl

From 5a58bfadc4aebfae109c360f1469eda37160bfb2 Mon Sep 17 00:00:00 2001
From: Arun sanganal <74652697+ArunSanganal@users.noreply.github.com>
Date: Sun, 27 Jun 2021 01:09:31 +0530
Subject: [PATCH 21/23] Update eigen.jl

---
 stdlib/LinearAlgebra/src/eigen.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/stdlib/LinearAlgebra/src/eigen.jl b/stdlib/LinearAlgebra/src/eigen.jl
index 069ac6bca83ae..aa58c055231a1 100644
--- a/stdlib/LinearAlgebra/src/eigen.jl
+++ b/stdlib/LinearAlgebra/src/eigen.jl
@@ -282,8 +282,8 @@ function eigen(A::AbstractMatrix{T}; permute::Bool=true, scale::Bool=true, sortb
     values = convert(AbstractVector{isreal(A.values) ? Float16 : Complex{Float16}}, A.values)
     vectors = convert(AbstractMatrix{isreal(A.vectors) ? Float16 : Complex{Float16}}, A.vectors)
     vectorsl = convert(AbstractMatrix{isreal(A.vectors) ? Float16 : Complex{Float16}}, A.vectorsl)
-    rconde = convert(Vector{isreal(A.rconde) ? Float16 : Complex{Float16}}, A.rconde)
-    rcondv = convert(Vector{isreal(A.rcondv) ? Float16 : Complex{Float16}}, A.rcondv)
+    rconde = convert(Vector{Float16}, A.rconde)
+    rcondv = convert(Vector{Float16}, A.rcondv)
     return Eigen(values, vectors, vectorsl, A.unitary, rconde, rcondv)
 end
 eigen(x::Number) = Eigen([x], fill(one(x), 1, 1))

From e303b10c172935633053e5ad78022b63adddbea5 Mon Sep 17 00:00:00 2001
From: Arun sanganal <74652697+ArunSanganal@users.noreply.github.com>
Date: Sun, 27 Jun 2021 08:38:20 +0530
Subject: [PATCH 22/23] Update eigen.jl

---
 stdlib/LinearAlgebra/test/eigen.jl | 5 ++---
 1 file changed, 2 insertions(+), 3 deletions(-)

diff --git a/stdlib/LinearAlgebra/test/eigen.jl b/stdlib/LinearAlgebra/test/eigen.jl
index a8129532321a0..e87fc9cec1832 100644
--- a/stdlib/LinearAlgebra/test/eigen.jl
+++ b/stdlib/LinearAlgebra/test/eigen.jl
@@ -184,9 +184,8 @@ end
     C = Float16[3 -2; 4 -1]
     D = eigen(C)
     D32 = eigen(Float32.(C))
-    E = complex(C)
-    F = eigen(E)
-    F32 = eigen(Float32.(E))
+    F = eigen(complex(C))
+    F32 = eigen(complex(Float32.(C)))
     @test B isa Eigen{Float16, Float16, Matrix{Float16}, Vector{Float16}, Vector{Float16}}
     @test B.values isa Vector{Float16}
     @test B.vectors isa Matrix{Float16}

From 31d40195a9109340755e6b30167b51c30a841d4e Mon Sep 17 00:00:00 2001
From: Arun sanganal <74652697+ArunSanganal@users.noreply.github.com>
Date: Mon, 28 Jun 2021 07:45:25 +0530
Subject: [PATCH 23/23] Update stdlib/LinearAlgebra/src/eigen.jl

Co-authored-by: Fredrik Bagge Carlson <baggepinnen@gmail.com>
---
 stdlib/LinearAlgebra/src/eigen.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/stdlib/LinearAlgebra/src/eigen.jl b/stdlib/LinearAlgebra/src/eigen.jl
index aa58c055231a1..27207541b3d5a 100644
--- a/stdlib/LinearAlgebra/src/eigen.jl
+++ b/stdlib/LinearAlgebra/src/eigen.jl
@@ -278,7 +278,7 @@ end
 function eigen(A::AbstractMatrix{T}; permute::Bool=true, scale::Bool=true, sortby::Union{Function,Nothing}=eigsortby) where {T <: Union{Float16,Complex{Float16}}}
     AA = copy_oftype(A, eigtype(T))
     isdiag(AA) && return eigen(Diagonal(AA); permute=permute, scale=scale, sortby=sortby)
-    A = eigen!(AA; permute=permute, scale=scale, sortby=sortby)
+    A = eigen!(AA; permute, scale, sortby)
     values = convert(AbstractVector{isreal(A.values) ? Float16 : Complex{Float16}}, A.values)
     vectors = convert(AbstractMatrix{isreal(A.vectors) ? Float16 : Complex{Float16}}, A.vectors)
     vectorsl = convert(AbstractMatrix{isreal(A.vectors) ? Float16 : Complex{Float16}}, A.vectorsl)