From dae8a58c075034ef786dfd752fe7b317cae12150 Mon Sep 17 00:00:00 2001
From: Felix Gerick <felixgerick@gmail.com>
Date: Tue, 28 Jul 2020 11:45:26 +0200
Subject: [PATCH 1/7] start support for arbitrary precision numbers

---
 .travis.yml            |  4 ++--
 Manifest.toml          | 19 +++++++++++++++++--
 Project.toml           |  3 ++-
 src/expansion.jl       | 13 ++++++-------
 test/collect_eigen.jl  |  4 ++--
 test/runtests.jl       | 21 +++++++++++----------
 test/schur_to_eigen.jl |  9 +++++----
 7 files changed, 45 insertions(+), 28 deletions(-)

diff --git a/.travis.yml b/.travis.yml
index e906751..524ba4a 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -2,10 +2,10 @@ language: julia
 os:
     - linux
 julia:
-    - 0.7
+    - 1.4
 notifications:
     email: false
 after_success:
   - julia -e 'using Pkg; Pkg.add(["Documenter", "Coverage"])'
   - julia -e 'using Pkg, Coverage, ArnoldiMethod; cd(joinpath(dirname(pathof(ArnoldiMethod)), "..")); Codecov.submit(process_folder())'
-  - julia -e 'using Pkg, ArnoldiMethod; cd(joinpath(dirname(pathof(ArnoldiMethod)), "..")); include(joinpath("docs", "make.jl"))'
\ No newline at end of file
+  - julia -e 'using Pkg, ArnoldiMethod; cd(joinpath(dirname(pathof(ArnoldiMethod)), "..")); include(joinpath("docs", "make.jl"))'
diff --git a/Manifest.toml b/Manifest.toml
index 62232aa..cf271e1 100644
--- a/Manifest.toml
+++ b/Manifest.toml
@@ -1,12 +1,20 @@
+# This file is machine-generated - editing it directly is not advised
+
 [[Base64]]
 uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
 
 [[Distributed]]
-deps = ["LinearAlgebra", "Random", "Serialization", "Sockets"]
+deps = ["Random", "Serialization", "Sockets"]
 uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"
 
+[[GenericSchur]]
+deps = ["LinearAlgebra", "Printf"]
+git-tree-sha1 = "43b4dc5648028be2c6e96201aa3653903bd1af21"
+uuid = "c145ed77-6b09-5dd9-b285-bf645a82121e"
+version = "0.4.0"
+
 [[InteractiveUtils]]
-deps = ["LinearAlgebra", "Markdown"]
+deps = ["Markdown"]
 uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
 
 [[Libdl]]
@@ -23,6 +31,10 @@ uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"
 deps = ["Base64"]
 uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"
 
+[[Printf]]
+deps = ["Unicode"]
+uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"
+
 [[Random]]
 deps = ["Serialization"]
 uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
@@ -50,3 +62,6 @@ uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 [[Test]]
 deps = ["Distributed", "InteractiveUtils", "Logging", "Random"]
 uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+
+[[Unicode]]
+uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"
diff --git a/Project.toml b/Project.toml
index e6ab300..e2f1dfc 100644
--- a/Project.toml
+++ b/Project.toml
@@ -9,8 +9,9 @@ Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 
 [extras]
+GenericSchur = "c145ed77-6b09-5dd9-b285-bf645a82121e"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["Test", "SparseArrays"]
+test = ["Test", "SparseArrays","GenericSchur"]
diff --git a/src/expansion.jl b/src/expansion.jl
index 02afd37..cd7baea 100644
--- a/src/expansion.jl
+++ b/src/expansion.jl
@@ -1,6 +1,5 @@
 using Random
 using LinearAlgebra
-using LinearAlgebra.BLAS: gemv!
 
 """
     reinitialize!(a::Arnoldi, j::Int = 0) → a
@@ -32,7 +31,7 @@ function reinitialize!(arnoldi::Arnoldi{T}, j::Int = 0) where {T}
 
     # Orthogonalize: h = Vprev' * v, v ← v - Vprev * Vprev' * v = v - Vprev * h
     h = Vprev' * v
-    gemv!('N', -one(T), Vprev, h, one(T), v)
+    mul!(v,Vprev,h,-one(T),one(T))
 
     # Norm after orthogonalization
     wnorm = norm(v)
@@ -41,7 +40,7 @@ function reinitialize!(arnoldi::Arnoldi{T}, j::Int = 0) where {T}
     if wnorm < η * rnorm
         rnorm = wnorm
         mul!(h, Vprev', v)
-        gemv!('N', -one(T), Vprev, h, one(T), v)
+        mul!(v,Vprev,h,-one(T),one(T))
         wnorm = norm(v)
     end
 
@@ -79,7 +78,7 @@ function orthogonalize!(arnoldi::Arnoldi{T}, j::Integer) where {T}
 
     # Orthogonalize: h = Vprev' * v, v ← v - Vprev * Vprev' * v = v - Vprev * h
     mul!(h, Vprev', v)
-    gemv!('N', -one(T), Vprev, h, one(T), v)
+    mul!(v,Vprev,h,-one(T),one(T))
 
     # Norm after orthogonalization
     wnorm = norm(v)
@@ -88,7 +87,7 @@ function orthogonalize!(arnoldi::Arnoldi{T}, j::Integer) where {T}
     if wnorm < η * rnorm
         rnorm = wnorm
         correction = Vprev' * v
-        gemv!('N', -one(T), Vprev, correction, one(T), v)
+        mul!(v,Vprev,correction,-one(T),one(T))
         h .+= correction
         wnorm = norm(v)
     end
@@ -112,7 +111,7 @@ Perform Arnoldi from `from` to `to`.
 """
 function iterate_arnoldi!(A, arnoldi::Arnoldi{T}, range::UnitRange{Int}) where {T}
     V, H = arnoldi.V, arnoldi.H
-    
+
     for j = range
         # Generate a new column of the Krylov subspace
         mul!(view(V, :, j+1), A, view(V, :,j))
@@ -127,4 +126,4 @@ function iterate_arnoldi!(A, arnoldi::Arnoldi{T}, range::UnitRange{Int}) where {
     end
 
     return arnoldi
-end
\ No newline at end of file
+end
diff --git a/test/collect_eigen.jl b/test/collect_eigen.jl
index 28ce0c7..384ebbb 100644
--- a/test/collect_eigen.jl
+++ b/test/collect_eigen.jl
@@ -38,7 +38,7 @@ rot(θ) = [cos(θ) sin(θ); -sin(θ) cos(θ)]
     R = triu(rand(n, n))
     R[1:2,1:2] .= rot(1.0) + I
     R[10:11,10:11] .= rot(1.2) + 2I
-    
+
     # Compute exact eigenvectors according to LAPACK
     λs, xs = eigen(R)
 
@@ -63,4 +63,4 @@ end
         θs = copy_eigenvalues!(rand(ComplexF64, length(range)), R, range)
         @test sort!(λs, by = reim) ≈ sort!(θs, by = reim)
     end
-end
\ No newline at end of file
+end
diff --git a/test/runtests.jl b/test/runtests.jl
index 53b2723..143a882 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -2,16 +2,17 @@ using Test
 using LinearAlgebra
 using SparseArrays
 using Random
+using GenericSchur
 
-include("expansion.jl")
-include("givens_rotation.jl")
-include("ordering.jl")
-
-include("schurfact.jl")
-include("sylvester.jl")
-include("sort_schur.jl")
-include("collect_eigen.jl")
-
-include("partial_schur.jl")
+# include("expansion.jl")
+# include("givens_rotation.jl")
+# include("ordering.jl")
+# #
+# include("schurfact.jl")
+# include("sylvester.jl")
+# include("sort_schur.jl")
+# # include("collect_eigen.jl")
+#
+# include("partial_schur.jl")
 # include("locked_restart.jl")
 include("schur_to_eigen.jl")
diff --git a/test/schur_to_eigen.jl b/test/schur_to_eigen.jl
index 7fd56c1..d2e5b95 100644
--- a/test/schur_to_eigen.jl
+++ b/test/schur_to_eigen.jl
@@ -2,11 +2,12 @@ using Test
 using LinearAlgebra, SparseArrays
 using ArnoldiMethod: partialschur, partialeigen
 using Random
+using GenericSchur
 
-@testset "Schur to eigen $T take $i" for T in (Float64,ComplexF64), i in 1:10
+@testset "Schur to eigen $T take $i" for T in (Float64,ComplexF64,BigFloat,Complex{BigFloat}), i in 1:10
     Random.seed!(i)
-    A = spdiagm(0 => 1:100) + sprand(100, 100, 0.01)
-    ε = 1e-7
+    A = spdiagm(0 => 1:100) + sprand(T,100, 100, 0.01)
+    ε = sqrt(eps(real(T)))
     minim, maxim = 10, 20
 
     decomp, history = partialschur(A, nev=minim, tol=ε, restarts=200)
@@ -18,4 +19,4 @@ using Random
     for i = 1 : minim
         @test norm(A * vecs[:,i] - vecs[:,i] * vals[i]) < ε * abs(vals[i])
     end
-end
\ No newline at end of file
+end

From 9000fdf1691cb2872d9054a68b0926e07ef7fa47 Mon Sep 17 00:00:00 2001
From: fgerick <felixgerick@gmail.com>
Date: Wed, 17 Feb 2021 13:56:15 +0100
Subject: [PATCH 2/7] bigfloat with tests

---
 src/schursort.jl        |  14 ++-
 test/collect_eigen.jl   |  54 ++++----
 test/expansion.jl       |  64 +++++-----
 test/givens_rotation.jl |   8 +-
 test/partial_schur.jl   |  21 ++--
 test/runtests.jl        |  20 +--
 test/schurfact.jl       | 187 ++++++++++++++--------------
 test/sort_schur.jl      | 269 +++++++++++++++++++++-------------------
 8 files changed, 339 insertions(+), 298 deletions(-)

diff --git a/src/schursort.jl b/src/schursort.jl
index 6c9eb8d..dfd57ad 100644
--- a/src/schursort.jl
+++ b/src/schursort.jl
@@ -74,9 +74,13 @@ Computes the LU factorization of A using complete pivoting.
 """
 function lu(A::SMatrix{N,N,T}, ::Type{CompletePivoting}) where {N,T}
     # A, p and q should allocate, but escape analysis will eliminate this!
-    A = MMatrix(A)
-    p = @MVector fill(N, N)
+    if isbitstype(T)
+        A = MMatrix(A)
+    else
+        A = SizedMatrix(A)
+    end
     q = @MVector fill(N, N)
+    p = @MVector fill(N, N)
     singular = false
 
     # Maybe I should consider doing this recursively.
@@ -132,7 +136,11 @@ function lu(A::SMatrix{N,N,T}, ::Type{CompletePivoting}) where {N,T}
 end
 
 function (\)(LU::CompletelyPivotedLU{T,N}, b::SVector{N}) where {T,N}
-    x = MVector(b)
+    if isbitstype(T)
+        x = MVector(b)
+    else
+        x = SizedVector(b)
+    end
 
     # x ← L \ (P * b)
     for i = OneTo(N)
diff --git a/test/collect_eigen.jl b/test/collect_eigen.jl
index 384ebbb..abb69c6 100644
--- a/test/collect_eigen.jl
+++ b/test/collect_eigen.jl
@@ -7,13 +7,17 @@ using LinearAlgebra
     n = 20
 
     # Exactly upper triangular matrix R
-    for T in (Float64, ComplexF64)
+    for T in (Float64, ComplexF64, BigFloat, Complex{BigFloat})
 
         # Upper triangular matrix
         R = triu(rand(T, n, n))
 
         # Compute exact eigenvectors according to LAPACK
-        λs, xs = eigen(R)
+        if VERSION >= v"1.2.0-DEV.275"
+            λs, xs = eigen(R, sortby=nothing)
+        else
+            λs, xs = eigen(R)
+        end
 
         # Allocate a complex-valued eigenvector
         x = zeros(complex(T), n)
@@ -34,33 +38,41 @@ rot(θ) = [cos(θ) sin(θ); -sin(θ) cos(θ)]
 
 @testset "Eigenvectors quasi-upper triangular matrix" begin
     # Real arithmetic with conjugate eigvals -- quasi-upper triangular R
-    n = 20
-    R = triu(rand(n, n))
-    R[1:2,1:2] .= rot(1.0) + I
-    R[10:11,10:11] .= rot(1.2) + 2I
+    for T in (Float64, BigFloat)
+        n = 20
+        R = triu(rand(T, n, n))
+        R[1:2,1:2] .= rot(one(T)) + I
+        R[10:11,10:11] .= rot(T(6//5)) + 2I
 
-    # Compute exact eigenvectors according to LAPACK
-    λs, xs = eigen(R)
+        # Compute exact eigenvectors according to LAPACK
+        if VERSION >= v"1.2.0-DEV.275"
+            λs, xs = eigen(R, sortby=nothing)
+        else
+            λs, xs = eigen(R)
+        end
 
-    # Allocate a complex-valued eigenvector
-    x = zeros(ComplexF64, n)
+        # Allocate a complex-valued eigenvector
+        x = zeros(Complex{T}, n)
 
-    for i = 1:n
-        fill!(x, 0.0)
-        collect_eigen!(x, R, i)
+        for i = 1:n
+            fill!(x, 0)
+            collect_eigen!(x, R, i)
 
-        @test norm(x) ≈ 1
-        @test abs.(x) ≈ abs.(xs[:, i])
+            @test norm(x) ≈ 1
+            @test abs.(x) ≈ abs.(xs[:, i])
+        end
     end
 end
 
 @testset "Extract partial" begin
     n = 20
-    R = triu(rand(n, n))
-    R[1:2,1:2] .= rot(1.0) + I
-    for range = (1:3, 1:4)
-        λs = eigvals(R[range, range])
-        θs = copy_eigenvalues!(rand(ComplexF64, length(range)), R, range)
-        @test sort!(λs, by = reim) ≈ sort!(θs, by = reim)
+    for T in (Float64, BigFloat)
+        R = triu(rand(T,n, n))
+        R[1:2,1:2] .= rot(1.0) + I
+        for range = (1:3, 1:4)
+            λs = eigvals(R[range, range])
+            θs = copy_eigenvalues!(rand(Complex{T}, length(range)), R, range)
+            @test sort!(λs, by = reim) ≈ sort!(θs, by = reim)
+        end
     end
 end
diff --git a/test/expansion.jl b/test/expansion.jl
index 3c016e5..d2d3947 100644
--- a/test/expansion.jl
+++ b/test/expansion.jl
@@ -12,38 +12,42 @@ end
 @testset "Arnoldi Factorization" begin
     n = 10
     max = 6
-    A = sprand(n, n, .1) + I
-
-    arnoldi = Arnoldi{Float64}(n, max)
-    reinitialize!(arnoldi)
-    V, H = arnoldi.V, arnoldi.H
-
-    # Do a few iterations
-    iterate_arnoldi!(A, arnoldi, 1:3)
-    @test A * V[:,1:3] ≈ V[:,1:4] * H[1:4,1:3]
-    @test norm(V[:,1:4]' * V[:,1:4] - I) < 1e-10
-
-    # Do the rest of the iterations.
-    iterate_arnoldi!(A, arnoldi, 4:max)
-    @test A * V[:,1:max] ≈ V * H
-    @test norm(V' * V - I) < 1e-10
+    for T in (Float64, BigFloat)
+        A = sprand(T, n, n, .1) + I
+
+        arnoldi = Arnoldi{T}(n, max)
+        reinitialize!(arnoldi)
+        V, H = arnoldi.V, arnoldi.H
+
+        # Do a few iterations
+        iterate_arnoldi!(A, arnoldi, 1:3)
+        @test A * V[:,1:3] ≈ V[:,1:4] * H[1:4,1:3]
+        @test norm(V[:,1:4]' * V[:,1:4] - I) < sqrt(eps(T))/100
+
+        # Do the rest of the iterations.
+        iterate_arnoldi!(A, arnoldi, 4:max)
+        @test A * V[:,1:max] ≈ V * H
+        @test norm(V' * V - I) < sqrt(eps(T))/100
+    end
 end
 
 @testset "Invariant subspace" begin
     # Generate a block-diagonal matrix A
-    A = [rand(4,4)  zeros(4,4); 
-         zeros(4,4) rand(4,4)]
-
-    # and an initial vector [1; 0; ... 0]
-    vh = Arnoldi{Float64}(8, 5)
-    V, H = vh.V, vh.H
-    V[:,1] .= 0.0
-    V[1,1] = 1.0
-
-    # Then {v, Av, A²v, A³v}
-    # is an invariant subspace
-    iterate_arnoldi!(A, vh, 1:5)
-
-    @test norm(V' * V - I) < 1e-10
-    @test iszero(H[5, 4])
+    for T in (Float64, BigFloat)
+        A = [rand(T,4,4)  zeros(T,4,4); 
+            zeros(T,4,4) rand(T,4,4)]
+
+        # and an initial vector [1; 0; ... 0]
+        vh = Arnoldi{T}(8, 5)
+        V, H = vh.V, vh.H
+        V[:,1] .= zero(T)
+        V[1,1] = one(T)
+
+        # Then {v, Av, A²v, A³v}
+        # is an invariant subspace
+        iterate_arnoldi!(A, vh, 1:5)
+
+        @test norm(V' * V - I) < sqrt(eps(T))/100
+        @test iszero(H[5, 4])
+    end
 end
\ No newline at end of file
diff --git a/test/givens_rotation.jl b/test/givens_rotation.jl
index 42457a1..1e445d0 100644
--- a/test/givens_rotation.jl
+++ b/test/givens_rotation.jl
@@ -6,7 +6,7 @@ using ArnoldiMethod: Hessenberg, Rotation2, Rotation3
 
 @testset "Givens rotation" begin
     @testset "Single rotation" begin
-        @testset "lmul!" for T in (Float64, ComplexF64)
+        @testset "lmul!" for T in (Float64, ComplexF64, BigFloat, Complex{BigFloat})
             A = rand(T, 6, 5)
 
             G = Rotation2(rand(real(T)), rand(T), 2)
@@ -16,7 +16,7 @@ using ArnoldiMethod: Hessenberg, Rotation2, Rotation3
             @test G_mat * A ≈ lmul!(G, copy(A))
         end
 
-        @testset "rmul!" for T in (Float64, ComplexF64)
+        @testset "rmul!" for T in (Float64, ComplexF64, BigFloat, Complex{BigFloat})
             A = rand(T, 10, 5)
 
             G = Rotation2(rand(real(T)), rand(T), 2)
@@ -28,7 +28,7 @@ using ArnoldiMethod: Hessenberg, Rotation2, Rotation3
     end
 
     @testset "Double rotation" begin
-        @testset "lmul!" for T in (Float64, ComplexF64)
+        @testset "lmul!" for T in (Float64, ComplexF64, BigFloat, Complex{BigFloat})
             A = rand(T, 6, 5)
 
             G = Rotation3(rand(real(T)), rand(T), rand(real(T)), rand(T), 2)
@@ -38,7 +38,7 @@ using ArnoldiMethod: Hessenberg, Rotation2, Rotation3
             @test G_mat * A ≈ lmul!(G, copy(A))
         end
 
-        @testset "rmul!" for T in (Float64, ComplexF64)
+        @testset "rmul!" for T in (Float64, ComplexF64, BigFloat, Complex{BigFloat})
             A = rand(T, 10, 5)
 
             G = Rotation3(rand(real(T)), rand(T), rand(real(T)), rand(T), 2)
diff --git a/test/partial_schur.jl b/test/partial_schur.jl
index 265cdc7..cb53ced 100644
--- a/test/partial_schur.jl
+++ b/test/partial_schur.jl
@@ -10,19 +10,20 @@ using LinearAlgebra
     # the stopping criterion works for these zero eigenvalues, we don't take
     # into account that it finds the complete eigenspace of the 0 eigenvalue.
     # (we have too few basis vectors for it anyways)
+    for T in (Float64, ComplexF64, BigFloat, Complex{BigFloat})
+        A = rand(T,10, 3)
 
-    A = rand(10, 3)
+        # Rank 3 matrix.
+        B = A * A' 
 
-    # Rank 3 matrix.
-    B = A * A' 
+        schur, history = partialschur(B, nev = 5, mindim = 5, maxdim = 7, tol = eps())
 
-    schur, history = partialschur(B, nev = 5, mindim = 5, maxdim = 7, tol = eps())
-
-    @test history.converged
-    @test history.mvproducts == 7
-    @test norm(schur.Q'schur.Q - I) < 100eps()
-    @test norm(B * schur.Q - schur.Q * schur.R) < 100eps()
-    @test norm(diag(schur.R)[4:5]) < 100eps()
+        @test history.converged
+        @test history.mvproducts == 7
+        @test norm(schur.Q'schur.Q - I) < 100eps(real(T))
+        @test norm(B * schur.Q - schur.Q * schur.R) < 100eps(real(T))
+        @test norm(diag(schur.R)[4:5]) < 100eps(real(T))
+    end
 end
 
 @testset "Right number type" begin
diff --git a/test/runtests.jl b/test/runtests.jl
index 143a882..2718a01 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -4,15 +4,15 @@ using SparseArrays
 using Random
 using GenericSchur
 
-# include("expansion.jl")
-# include("givens_rotation.jl")
-# include("ordering.jl")
-# #
-# include("schurfact.jl")
-# include("sylvester.jl")
-# include("sort_schur.jl")
-# # include("collect_eigen.jl")
-#
-# include("partial_schur.jl")
+include("expansion.jl")
+include("givens_rotation.jl")
+include("ordering.jl")
+
+include("schurfact.jl")
+include("sylvester.jl")
+include("sort_schur.jl")
+include("collect_eigen.jl")
+
+include("partial_schur.jl")
 # include("locked_restart.jl")
 include("schur_to_eigen.jl")
diff --git a/test/schurfact.jl b/test/schurfact.jl
index 7933c3c..c62e319 100644
--- a/test/schurfact.jl
+++ b/test/schurfact.jl
@@ -8,106 +8,108 @@ using ArnoldiMethod: eigenvalues, local_schurfact!, is_offdiagonal_small,
 include("utils.jl")
 
 @testset "Schur factorization" begin
-    let
-        # 2-by-2 matrix with distinct eigenvalues while H[2,1] != 0
-        H = [1.0 2.0; 3.0 4.0]
-        H′ = copy(H)
-        Q = Matrix{Float64}(I, 2, 2)
-        
-        @test local_schurfact!(H′, 1, 2, Q, eps(), 2)
-        @test norm(H * Q - Q * H′) < 10eps()
-        @test sort!(eigenvalues(H′), by=realimag) ≈ sort!(eigvals(H′), by=realimag)
-        @test sort!(eigenvalues(H′), by=realimag) ≈ sort!(eigvals(H), by=realimag)
-        @test iszero(H′[2,1])
-    end
-
-    let
-        # 2-by-2 matrix with distinct eigenvalues while H[2,1] = 0
-        H = [1.0 2.0; 0.0 4.0]
-        H′ = copy(H)
-        Q = Matrix{Float64}(I, 2, 2)
-        
-        @test local_schurfact!(H′, 1, 2, Q, eps(), 2)
-        @test norm(H * Q - Q * H′) < 10eps()
-        @test sort!(eigenvalues(H′), by=realimag) ≈ sort!(eigvals(H′), by=realimag)
-        @test sort!(eigenvalues(H′), by=realimag) ≈ sort!(eigvals(H), by=realimag)
-        @test iszero(H′[2,1])
-    end
-
-    let
-        # 2-by-2 matrix with conjugate eigenvalues
-        H = [1.0 4.0; -5.0 3.0]
-        H′ = copy(H)
-        Q = Matrix{Float64}(I, 2, 2)
-        
-        @test local_schurfact!(H′, 1, 2, Q, eps(), 2)
-        @test norm(H * Q - Q * H′) < 10eps()
-        @test sort!(eigenvalues(H′), by=realimag) ≈ sort!(eigvals(H′), by=realimag)
-        @test sort!(eigenvalues(H′), by=realimag) ≈ sort!(eigvals(H), by=realimag)
-    end
-    
-    # Larger real matrix.
-
-    let
-        n = 10
-        # Transforming a 1+i by n-i block of the matrix H into upper triangular form
-        for i = 0 : 4
-            Q = Matrix{Float64}(I, n, n)
-            H = triu(randn(Float64, n, n))
-            H[1+i:n-i,1+i:n-i] = normal_hessenberg_matrix(Float64, i+1:n-i)
+    for T in (Float64, BigFloat)
+        let
+            # 2-by-2 matrix with distinct eigenvalues while H[2,1] != 0
+            H = [one(T) 2one(T); 3one(T) 4one(T)]
             H′ = copy(H)
+            Q = Matrix{T}(I, 2, 2)
+            
+            @test local_schurfact!(H′, 1, 2, Q, eps(T), 2)
+            @test norm(H * Q - Q * H′) < 10eps(T)
+            @test sort!(eigenvalues(H′), by=realimag) ≈ sort!(eigvals(H′), by=realimag)
+            @test sort!(eigenvalues(H′), by=realimag) ≈ sort!(eigvals(H), by=realimag)
+            @test iszero(H′[2,1])
+        end
 
-            # Test that the procedure has converged
-            @test local_schurfact!(H′, 1+i, n-i, Q)
-
-            for j = 1+i:n-i-1
-                t = H′[j,j] + H′[j+1,j+1]
-                d = H′[j,j] * H′[j+1,j+1] - H′[j+1,j] * H′[j,j+1]
-
-                # Test if subdiagonal is small. If not, check if conjugate eigenvalues.
-                @test is_offdiagonal_small(H′, j) || t^2 < 4d
-            end
-
-            # Test that the elements below the subdiagonal are 0
-            @test is_hessenberg(H′)
-
-            # Test that the partial Schur decomposition relation holds
-            @test norm(H * Q - Q * H′) < 1000eps()
+        let
+            # 2-by-2 matrix with distinct eigenvalues while H[2,1] = 0
+            H = [one(T) 2one(T); zero(T) 4one(T)]
+            H′ = copy(H)
+            Q = Matrix{T}(I, 2, 2)
             
-            # Test that the eigenvalues of H are the same before and after transformation
-            @test sort!(eigvals(H), by=realimag) ≈ sort!(eigvals(H′), by=realimag)
+            @test local_schurfact!(H′, 1, 2, Q, eps(T), 2)
+            @test norm(H * Q - Q * H′) < 10eps(T)
+            @test sort!(eigenvalues(H′), by=realimag) ≈ sort!(eigvals(H′), by=realimag)
+            @test sort!(eigenvalues(H′), by=realimag) ≈ sort!(eigvals(H), by=realimag)
+            @test iszero(H′[2,1])
         end
 
-    end
+        let
+            # 2-by-2 matrix with conjugate eigenvalues
+            H = [1one(T) 4one(T); -5one(T) 3one(T)]
+            H′ = copy(H)
+            Q = Matrix{T}(I, 2, 2)
+            
+            @test local_schurfact!(H′, 1, 2, Q, eps(T), 2)
+            @test norm(H * Q - Q * H′) < 10eps(T)
+            @test sort!(eigenvalues(H′), by=realimag) ≈ sort!(eigvals(H′), by=realimag)
+            @test sort!(eigenvalues(H′), by=realimag) ≈ sort!(eigvals(H), by=realimag)
+        end
+    end 
+        # Larger real matrix.
+    for T in (Float64,) #randn(BigFloat,n,n) does not yet exist https://github.com/JuliaLang/julia/pull/35111
+        let
+            n = 10
+            # Transforming a 1+i by n-i block of the matrix H into upper triangular form
+            for i = 0 : 4
+                Q = Matrix{T}(I, n, n)
+                H = triu(randn(T, n, n))
+                H[1+i:n-i,1+i:n-i] = normal_hessenberg_matrix(T, i+1:n-i)
+                H′ = copy(H)
+
+                # Test that the procedure has converged
+                @test local_schurfact!(H′, 1+i, n-i, Q)
+
+                for j = 1+i:n-i-1
+                    t = H′[j,j] + H′[j+1,j+1]
+                    d = H′[j,j] * H′[j+1,j+1] - H′[j+1,j] * H′[j,j+1]
+
+                    # Test if subdiagonal is small. If not, check if conjugate eigenvalues.
+                    @test is_offdiagonal_small(H′, j) || t^2 < 4d
+                end
+
+                # Test that the elements below the subdiagonal are 0
+                @test is_hessenberg(H′)
+
+                # Test that the partial Schur decomposition relation holds
+                @test norm(H * Q - Q * H′) < 1000eps(T)
+                
+                # Test that the eigenvalues of H are the same before and after transformation
+                @test sort!(eigvals(H), by=realimag) ≈ sort!(eigvals(H′), by=realimag)
+            end
+        end
+    
 
 
     # COMPLEX ARITHMETIC
 
-    let
-        n = 10
-        # Transforming a 1+i by 10-i block of the matrix H into upper triangular form
-        for i = 0 : 4
-            Q = Matrix{ComplexF64}(I, n, n)
-            H = triu(randn(ComplexF64, n, n))
-            H[i+1:n-i,i+1:n-i] = normal_hessenberg_matrix(ComplexF64, (i+1:n-i) .* (1 + im))
-            H′ = copy(H)
-
-            # Test that the procedure has converged
-            @test local_schurfact!(H′, 1+i, n-i, Q)
-
-            # Test if subdiagonal is small. 
-            for j = 1+i:n-i-1
-                @test iszero(H′[j+1,j])
+        let
+            n = 10
+            # Transforming a 1+i by 10-i block of the matrix H into upper triangular form
+            for i = 0 : 4
+                Q = Matrix{Complex{T}}(I, n, n)
+                H = triu(randn(Complex{T}, n, n))
+                H[i+1:n-i,i+1:n-i] = normal_hessenberg_matrix(Complex{T}, (i+1:n-i) .* (1 + im))
+                H′ = copy(H)
+
+                # Test that the procedure has converged
+                @test local_schurfact!(H′, 1+i, n-i, Q)
+
+                # Test if subdiagonal is small. 
+                for j = 1+i:n-i-1
+                    @test iszero(H′[j+1,j])
+                end
+
+                # Test that the elements below the subdiagonal are 0
+                @test is_hessenberg(H′)
+
+                # Test that the partial Schur decomposition relation holds
+                @test norm(H * Q - Q * H′) < 1000eps(T)
+                
+                # Test that the eigenvalues of H are the same before and after transformation
+                @test sort!(eigvals(H), by=realimag) ≈ sort!(eigvals(H′), by=realimag)
             end
-
-            # Test that the elements below the subdiagonal are 0
-            @test is_hessenberg(H′)
-
-            # Test that the partial Schur decomposition relation holds
-            @test norm(H * Q - Q * H′) < 1000eps()
-            
-            # Test that the eigenvalues of H are the same before and after transformation
-            @test sort!(eigvals(H), by=realimag) ≈ sort!(eigvals(H′), by=realimag)
         end
     end
 end
@@ -119,6 +121,7 @@ end
     mat(ε) = [2   0    0  ;
               5ε  1-ε  2ε ;
               0   3ε   1+ε]
-
-    @test local_schurfact!(mat(eps()))
+    for T in (Float64,BigFloat)
+        @test local_schurfact!(mat(eps(T)))
+    end
 end
\ No newline at end of file
diff --git a/test/sort_schur.jl b/test/sort_schur.jl
index de13f01..11c3f61 100644
--- a/test/sort_schur.jl
+++ b/test/sort_schur.jl
@@ -6,7 +6,7 @@ using ArnoldiMethod: swap11!, swap12!, swap21!, swap22!, rotate_right!, eigenval
 
 # These tests are only necessary in real arithmetic, but why not do complex for completeness
 
-@testset "Reordering the Schur form 1 ↔ 1 ($T)" for T in (Float64, ComplexF64) 
+@testset "Reordering the Schur form 1 ↔ 1 ($T)" for T in (Float64, ComplexF64, BigFloat, Complex{BigFloat}) 
     Q1 = Matrix{T}(I, 2, 2)
     R1 = triu(rand(T, 2, 2))
     Q2 = copy(Q1)
@@ -19,7 +19,7 @@ using ArnoldiMethod: swap11!, swap12!, swap21!, swap22!, rotate_right!, eigenval
     @test R1 * Q2 ≈ Q2 * R2
 end
 
-@testset "Reordering the Schur form 1 ↔ 2 ($T)" for T in (Float64, ComplexF64) 
+@testset "Reordering the Schur form 1 ↔ 2 ($T)" for T in (Float64, ComplexF64, BigFloat, Complex{BigFloat})  
     # x x x
     # . x x
     # . x x
@@ -39,7 +39,7 @@ end
     @test R1 * Q2 ≈ Q2 * R2
 end
 
-@testset "Reordering the Schur form 2 ↔ 1 ($T)" for T in (Float64, ComplexF64)
+@testset "Reordering the Schur form 2 ↔ 1 ($T)" for T in (Float64, ComplexF64, BigFloat, Complex{BigFloat}) 
     # x x x
     # x x x
     # . . x
@@ -59,7 +59,7 @@ end
     @test R1 * Q2 ≈ Q2 * R2
 end
 
-@testset "Reordering the Schur form 2 ↔ 2 ($T)" for T in (Float64, ComplexF64)
+@testset "Reordering the Schur form 2 ↔ 2 ($T)" for T in (Float64, ComplexF64, BigFloat, Complex{BigFloat}) 
     # x x x x
     # x x x x
     # . . x x
@@ -84,129 +84,136 @@ end
 end
 
 @testset "Rotation right with single eigenvalues" begin
-    # 10 × 10 quasi upper triangular matrix with 2 × 2 block on R[4:5,4:5]
-    R = triu(rand(10, 10))
-    Q = Matrix(1.0I, 10, 10)
-    R[4,5] = -2.0; R[5,4] = 2.0
+    for T in (Float64, ComplexF64, BigFloat, Complex{BigFloat}) 
+        # 10 × 10 quasi upper triangular matrix with 2 × 2 block on R[4:5,4:5]
+        R = triu(rand(T, 10, 10))
+        Q = Matrix(one(T)*I, 10, 10)
+        R[4,5] = -2*one(T); R[5,4] = 2*one(T)
 
-    λ_before = eigenvalues(R)
+        λ_before = eigenvalues(R)
 
-    # Rotate the last block right before the first one.
-    R_after = copy(R)
-    rotate_right!(R_after, 1, 10, Q)
-    λ_after = eigenvalues(R_after)
+        # Rotate the last block right before the first one.
+        R_after = copy(R)
+        rotate_right!(R_after, 1, 10, Q)
+        λ_after = eigenvalues(R_after)
 
-    # Test whether Q is more or less a similarity transform
-    @test opnorm(R - Q * R_after * Q', 1) < 10eps() * opnorm(R, 1)
+        # Test whether Q is more or less a similarity transform
+        @test opnorm(R - Q * R_after * Q', 1) < 10eps(real(T)) * opnorm(R, 1)
 
-    # Test orthonormality of Q
-    @test norm(Q'Q - I) < 10eps()
+        # Test orthonormality of Q
+        @test norm(Q'Q - I) < 10eps(real(T))
 
-    # Middle guys have been rotated
-    for (i, j) = zip(1:10, circshift(1:10, -1))
-        @test λ_before[i] ≈ λ_after[j]
+        # Middle guys have been rotated
+        for (i, j) = zip(1:10, circshift(1:10, -1))
+            @test λ_before[i] ≈ λ_after[j]
+        end
     end
 end
 
 @testset "Rotation right with two conjugate pairs" begin
-    # 10 × 10 quasi upper triangular matrix with 2 × 2 blocks on R[2:3,2:3] and R[6:7,6:7]
-    R = triu(rand(10, 10))
-    Q = Matrix(1.0I, 10, 10)
-    R[3,2] = -2.0; R[2,3] = 2.0
-    R[7,6] = 3.0; R[6,7] = -2.0
+    for T in (Float64, ComplexF64, BigFloat, Complex{BigFloat}) 
+        # 10 × 10 quasi upper triangular matrix with 2 × 2 blocks on R[2:3,2:3] and R[6:7,6:7]
+        R = triu(rand(T, 10, 10))
+        Q = Matrix(one(T)*I, 10, 10)
+        R[3,2] = -2*one(T); R[2,3] = 2*one(T)
+        R[7,6] = 3*one(T); R[6,7] = -2*one(T)
 
-    λ_before = eigenvalues(R)
+        λ_before = eigenvalues(R)
 
-    # Rotate the last block right before the first one.
-    R_after = copy(R)
-    rotate_right!(R_after, 3, 6, Q)
+        # Rotate the last block right before the first one.
+        R_after = copy(R)
+        rotate_right!(R_after, 3, 6, Q)
 
-    λ_after = eigenvalues(R_after)
+        λ_after = eigenvalues(R_after)
 
-    # Test whether Q is more or less a similarity transform
-    @test opnorm(R - Q * R_after * Q', 1) < 10eps() * opnorm(R, 1)
+        # Test whether Q is more or less a similarity transform
+        @test opnorm(R - Q * R_after * Q', 1) < 10eps(real(T)) * opnorm(R, 1)
 
-    # Test orthonormality of Q
-    @test norm(Q'Q - I) < 10eps()
+        # Test orthonormality of Q
+        @test norm(Q'Q - I) < 10eps(real(T))
 
-    # First eigenvalue should be exactly equal
-    @test λ_before[1] == λ_after[1]
+        # First eigenvalue should be exactly equal
+        @test λ_before[1] == λ_after[1]
 
-    # Middle guys have been rotated
-    for (i, j) = zip(2:7, circshift(2:7, -2))
-        @test λ_before[i] ≈ λ_after[j]
-    end
+        # Middle guys have been rotated
+        for (i, j) = zip(2:7, circshift(2:7, -2))
+            @test λ_before[i] ≈ λ_after[j]
+        end
 
-    # Last eigenvalues should be exactly equal
-    @test λ_before[8:10] == λ_after[8:10]
+        # Last eigenvalues should be exactly equal
+        @test λ_before[8:10] == λ_after[8:10]
+    end
 end
 
 @testset "Rotation right with one 2 × 2 block on the right" begin
-    # 10 × 10 quasi upper triangular matrix with 2 × 2 block on R[6:7,6:7]
-    R = triu(rand(10, 10))
-    Q = Matrix(1.0I, 10, 10)
-    R[6,7] = -2.0; R[7,6] = 2.0
+    for T in (Float64, ComplexF64, BigFloat, Complex{BigFloat}) 
+        # 10 × 10 quasi upper triangular matrix with 2 × 2 block on R[6:7,6:7]
+        R = triu(rand(T,10, 10))
+        Q = Matrix(one(T)*I, 10, 10)
+        R[6,7] = -2*one(T); R[7,6] = 2*one(T)
 
-    λ_before = eigenvalues(R)
+        λ_before = eigenvalues(R)
 
-    # Rotate the last block right before the first one.
-    R_after = copy(R)
-    rotate_right!(R_after, 2, 6, Q)
-    λ_after = eigenvalues(R_after)
+        # Rotate the last block right before the first one.
+        R_after = copy(R)
+        rotate_right!(R_after, 2, 6, Q)
+        λ_after = eigenvalues(R_after)
 
-    # Test whether Q is more or less a similarity transform
-    @test opnorm(R - Q * R_after * Q', 1) < 10eps() * opnorm(R, 1)
+        # Test whether Q is more or less a similarity transform
+        @test opnorm(R - Q * R_after * Q', 1) < 10eps(real(T)) * opnorm(R, 1)
 
-    # Test orthonormality of Q
-    @test norm(Q'Q - I) < 10eps()
+        # Test orthonormality of Q
+        @test norm(Q'Q - I) < 10eps(real(T))
 
-    # First eigenvalue should be exactly equal
-    @test λ_before[1] == λ_after[1]
+        # First eigenvalue should be exactly equal
+        @test λ_before[1] == λ_after[1]
 
-    # Middle guys have been rotated
-    for (i, j) = zip(2:7, circshift(2:7, -2))
-        @test λ_before[i] ≈ λ_after[j]
-    end
+        # Middle guys have been rotated
+        for (i, j) = zip(2:7, circshift(2:7, -2))
+            @test λ_before[i] ≈ λ_after[j]
+        end
 
-    # Last eigenvalues should be exactly equal
-    for i = 8:10
-        @test λ_before[i] == λ_after[i]
+        # Last eigenvalues should be exactly equal
+        for i = 8:10
+            @test λ_before[i] == λ_after[i]
+        end
     end
 
 end
 
 @testset "Rotation right with one 2 × 2 block on the left" begin
-    # 10 × 10 quasi upper triangular matrix with 2 × 2 block on R[2:3,2:3]
-    R = triu(rand(10, 10))
-    Q = Matrix(1.0I, 10, 10)
-    R[2,3] = -2.0; R[2,3] = 2.0
+    for T in (Float64, ComplexF64, BigFloat, Complex{BigFloat}) 
+        # 10 × 10 quasi upper triangular matrix with 2 × 2 block on R[2:3,2:3]
+        R = triu(rand(T, 10, 10))
+        Q = Matrix(one(T)*I, 10, 10)
+        R[2,3] = -2*one(T); R[2,3] = 2*one(T)
 
-    λ_before = eigenvalues(R)
+        λ_before = eigenvalues(R)
 
-    # Rotate the last block right before the first one.
-    R_after = copy(R)
-    rotate_right!(R_after, 2, 6, Q)
-    λ_after = eigenvalues(R_after)
+        # Rotate the last block right before the first one.
+        R_after = copy(R)
+        rotate_right!(R_after, 2, 6, Q)
+        λ_after = eigenvalues(R_after)
 
-    # Test whether Q is more or less a similarity transform
-    @test opnorm(R - Q * R_after * Q', 1) < 10eps() * opnorm(R, 1)
+        # Test whether Q is more or less a similarity transform
+        @test opnorm(R - Q * R_after * Q', 1) < 10eps(real(T)) * opnorm(R, 1)
 
-    # Test orthonormality of Q
-    @test opnorm(Q'Q - I, 1) < 10 * eps()
+        # Test orthonormality of Q
+        @test opnorm(Q'Q - I, 1) < 10 * eps(real(T))
 
-    # First eigenvalue should be exactly equal
-    @test λ_before[1] == λ_after[1]
+        # First eigenvalue should be exactly equal
+        @test λ_before[1] == λ_after[1]
 
-    # Middle guys have been rotated
-    for (i, j) = zip(2:6, circshift(2:6, -1))
-        @test λ_before[i] ≈ λ_after[j]
-    end
+        # Middle guys have been rotated
+        for (i, j) = zip(2:6, circshift(2:6, -1))
+            @test λ_before[i] ≈ λ_after[j]
+        end
 
-    # Last eigenvalues should be exactly equal
-    for i = 7:10
-        @test λ_before[i] == λ_after[i]
+        # Last eigenvalues should be exactly equal
+        for i = 7:10
+            @test λ_before[i] == λ_after[i]
+        end
     end
-
 end
 
 # Stewart's example in Bai & Demmel's article
@@ -215,55 +222,61 @@ end
 # Sorensen's implicit restart and convoluted locking + purging strategies that were 
 # necessary exactly because of this.
 @testset "Stewart's example" begin
-    A(τ) = [7.0010 -87.0000  39.4000τ  22.2000τ;
-            5.0000   7.0010 -12.2000τ  36.0000τ;
-            0.0000   0.0000   7.0100  -11.7567 ;
-            0.0000   0.0000   37.0000    7.0100 ]
+    A(τ) = [7+1//1000 -87  (39+2//5)*τ  (22+2//5)*τ;
+            5   7+1//1000 -(12+2//5)*τ  36τ;
+            0   0   7+1//100  -7567//10000 ;
+            0   0   37    7+1//100 ]
     
-    for τ in (1, 10, 100)
-        B = A(τ)
-
-        # Eigenvalues do not depend on τ, but we just compute them here for ease.
-        λs_before = eigenvalues(B)
-        swap22!(B, 1)
-        λs_after = eigenvalues(B)
-
-        # Test swapping is approximately equal
-        @test abs(λs_before[1]) ≈ abs(λs_after[3])
-        @test abs(λs_before[3]) ≈ abs(λs_after[1])
+    for T in (Float64, BigFloat)
+        for τ in (1, 10, 100)
+            B = A(τ*one(T))
+
+            # Eigenvalues do not depend on τ, but we just compute them here for ease.
+            λs_before = eigenvalues(B)
+            swap22!(B, 1)
+            λs_after = eigenvalues(B)
+
+            # Test swapping is approximately equal
+            @test abs(λs_before[1]) ≈ abs(λs_after[3])
+            @test abs(λs_before[3]) ≈ abs(λs_after[1])
+        end
     end
 end
 
 # Example taken from Bai & Demmel
 @testset "Small eigenvalue separation" begin
     # This should result in a very ill-conditioned Sylvester equation.
-    A = [ 1.00 -100.0   400.000 -1000.000;
-          0.01    1.0  1200.000   -10.000;
-          0.00    0.0     1.0+eps()    -0.010;
-          0.00    0.0   100.000     1.0+eps()]
-
-    A′ = copy(A)
-    Q = Matrix(1.0I, 4, 4)
-    λs_before = eigenvalues(A)
-    swap22!(A′, 1, Q)
-    λs_after = eigenvalues(A)
-    @test abs(λs_before[1]) ≈ abs(λs_after[3])
-    @test abs(λs_before[3]) ≈ abs(λs_after[1])
-    @test opnorm(I - Q'Q, 1) < 10eps() # we should be able to get rid of this prefactor?
-    @test opnorm(A * Q - Q * A′, 1) < opnorm(A, 1) * eps()
+    for T in (Float64, BigFloat)
+        A = [ 1 -100   400 -1000;
+            1//100    1  1200   -10;
+            0    0     1+eps(T)    -1//100;
+            0    0   100     1+eps(T)]
+
+        A′ = copy(A)
+        Q = Matrix(one(T)*I, 4, 4)
+        λs_before = eigenvalues(A)
+        swap22!(A′, 1, Q)
+        λs_after = eigenvalues(A)
+        @test abs(λs_before[1]) ≈ abs(λs_after[3])
+        @test abs(λs_before[3]) ≈ abs(λs_after[1])
+        @test opnorm(I - Q'Q, 1) < 10eps(T) # we should be able to get rid of this prefactor?
+        @test opnorm(A * Q - Q * A′, 1) < opnorm(A, 1) * eps(T)
+    end
 end
 
 @testset "Identical eigenvalues should not blow up" begin
-    A = [1.0 2.0 3.0 4.0;
-         0.0 1.0 5.0 6.0;
-         0.0 0.0 1.0 7.0;
-         0.0 0.0 0.0 1.0]
-         
-    A′ = copy(A)
-    swap22!(A′, 1)
-    @test A == A′
-    swap12!(A′, 1)
-    @test A == A′
-    swap21!(A′, 1)
-    @test A == A′
+    for T in (Float64, BigFloat)
+        A = T[1 2 3 4;
+             0 1 5 6;
+             0 0 1 7;
+             0 0 0 1]
+            
+        A′ = copy(A)
+        swap22!(A′, 1)
+        @test A == A′
+        swap12!(A′, 1)
+        @test A == A′
+        swap21!(A′, 1)
+        @test A == A′
+    end
 end
\ No newline at end of file

From 2644c2abc20e39907008ed6423dacd0da4745cb6 Mon Sep 17 00:00:00 2001
From: fgerick <felixgerick@gmail.com>
Date: Wed, 17 Feb 2021 14:02:44 +0100
Subject: [PATCH 3/7] change ci to 1.5

---
 .travis.yml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.travis.yml b/.travis.yml
index 524ba4a..d01acbf 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -2,7 +2,7 @@ language: julia
 os:
     - linux
 julia:
-    - 1.4
+    - 1.5
 notifications:
     email: false
 after_success:

From 0b9facb7a7bdba119126c33746f03f34a07a7642 Mon Sep 17 00:00:00 2001
From: fgerick <felixgerick@gmail.com>
Date: Wed, 17 Feb 2021 14:09:58 +0100
Subject: [PATCH 4/7] up staticarrays

---
 Manifest.toml | 44 +++-----------------------------------------
 Project.toml  |  2 +-
 2 files changed, 4 insertions(+), 42 deletions(-)

diff --git a/Manifest.toml b/Manifest.toml
index cf271e1..3bfe1c7 100644
--- a/Manifest.toml
+++ b/Manifest.toml
@@ -1,22 +1,5 @@
 # This file is machine-generated - editing it directly is not advised
 
-[[Base64]]
-uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
-
-[[Distributed]]
-deps = ["Random", "Serialization", "Sockets"]
-uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"
-
-[[GenericSchur]]
-deps = ["LinearAlgebra", "Printf"]
-git-tree-sha1 = "43b4dc5648028be2c6e96201aa3653903bd1af21"
-uuid = "c145ed77-6b09-5dd9-b285-bf645a82121e"
-version = "0.4.0"
-
-[[InteractiveUtils]]
-deps = ["Markdown"]
-uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
-
 [[Libdl]]
 uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"
 
@@ -24,17 +7,6 @@ uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"
 deps = ["Libdl"]
 uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 
-[[Logging]]
-uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"
-
-[[Markdown]]
-deps = ["Base64"]
-uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"
-
-[[Printf]]
-deps = ["Unicode"]
-uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"
-
 [[Random]]
 deps = ["Serialization"]
 uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
@@ -42,26 +14,16 @@ uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 [[Serialization]]
 uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
 
-[[Sockets]]
-uuid = "6462fe0b-24de-5631-8697-dd941f90decc"
-
 [[SparseArrays]]
 deps = ["LinearAlgebra", "Random"]
 uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 
 [[StaticArrays]]
-deps = ["InteractiveUtils", "LinearAlgebra", "Random", "Statistics", "Test"]
-git-tree-sha1 = "d432c79bef174a830304f8601427a4357dfdbfb7"
+deps = ["LinearAlgebra", "Random", "Statistics"]
+git-tree-sha1 = "9da72ed50e94dbff92036da395275ed114e04d49"
 uuid = "90137ffa-7385-5640-81b9-e52037218182"
-version = "0.8.3"
+version = "1.0.1"
 
 [[Statistics]]
 deps = ["LinearAlgebra", "SparseArrays"]
 uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
-
-[[Test]]
-deps = ["Distributed", "InteractiveUtils", "Logging", "Random"]
-uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
-
-[[Unicode]]
-uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"
diff --git a/Project.toml b/Project.toml
index 8429926..f774bf1 100644
--- a/Project.toml
+++ b/Project.toml
@@ -18,4 +18,4 @@ SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["Test", "SparseArrays","GenericSchur"]
+test = ["Test", "SparseArrays", "GenericSchur"]

From b35ec4c6bd6d5f051677362b5d2b8ead73f036be Mon Sep 17 00:00:00 2001
From: Harmen Stoppels <harmenstoppels@gmail.com>
Date: Thu, 18 Feb 2021 16:42:51 +0100
Subject: [PATCH 5/7] Ignore and remove Manifest.toml

---
 .gitignore    |  3 ++-
 Manifest.toml | 29 -----------------------------
 2 files changed, 2 insertions(+), 30 deletions(-)
 delete mode 100644 Manifest.toml

diff --git a/.gitignore b/.gitignore
index 8f1d8ff..62913ba 100644
--- a/.gitignore
+++ b/.gitignore
@@ -1,2 +1,3 @@
 .DS_Store
-docs/build
\ No newline at end of file
+docs/build
+Manifest.toml
\ No newline at end of file
diff --git a/Manifest.toml b/Manifest.toml
deleted file mode 100644
index 3bfe1c7..0000000
--- a/Manifest.toml
+++ /dev/null
@@ -1,29 +0,0 @@
-# This file is machine-generated - editing it directly is not advised
-
-[[Libdl]]
-uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"
-
-[[LinearAlgebra]]
-deps = ["Libdl"]
-uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
-
-[[Random]]
-deps = ["Serialization"]
-uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
-
-[[Serialization]]
-uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
-
-[[SparseArrays]]
-deps = ["LinearAlgebra", "Random"]
-uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
-
-[[StaticArrays]]
-deps = ["LinearAlgebra", "Random", "Statistics"]
-git-tree-sha1 = "9da72ed50e94dbff92036da395275ed114e04d49"
-uuid = "90137ffa-7385-5640-81b9-e52037218182"
-version = "1.0.1"
-
-[[Statistics]]
-deps = ["LinearAlgebra", "SparseArrays"]
-uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"

From ea01824b87fb5179641e4d3f2422755e0c57fc5c Mon Sep 17 00:00:00 2001
From: Harmen Stoppels <harmenstoppels@gmail.com>
Date: Thu, 18 Feb 2021 18:01:24 +0100
Subject: [PATCH 6/7] Fix CI

---
 .github/workflows/ci.yaml |  2 +-
 .travis.yml               | 11 -----------
 2 files changed, 1 insertion(+), 12 deletions(-)
 delete mode 100644 .travis.yml

diff --git a/.github/workflows/ci.yaml b/.github/workflows/ci.yaml
index ee18dd8..4a2bcea 100644
--- a/.github/workflows/ci.yaml
+++ b/.github/workflows/ci.yaml
@@ -14,7 +14,7 @@ jobs:
       fail-fast: false
       matrix:
         version:
-          - "1.0"
+          - "1.3"
           - "1"
           - "nightly"
         os:
diff --git a/.travis.yml b/.travis.yml
deleted file mode 100644
index d01acbf..0000000
--- a/.travis.yml
+++ /dev/null
@@ -1,11 +0,0 @@
-language: julia
-os:
-    - linux
-julia:
-    - 1.5
-notifications:
-    email: false
-after_success:
-  - julia -e 'using Pkg; Pkg.add(["Documenter", "Coverage"])'
-  - julia -e 'using Pkg, Coverage, ArnoldiMethod; cd(joinpath(dirname(pathof(ArnoldiMethod)), "..")); Codecov.submit(process_folder())'
-  - julia -e 'using Pkg, ArnoldiMethod; cd(joinpath(dirname(pathof(ArnoldiMethod)), "..")); include(joinpath("docs", "make.jl"))'

From ad110a4792cf227fafebcc085a69519f705051b1 Mon Sep 17 00:00:00 2001
From: Harmen Stoppels <harmenstoppels@gmail.com>
Date: Thu, 18 Feb 2021 18:12:54 +0100
Subject: [PATCH 7/7] Bump version

---
 Project.toml | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Project.toml b/Project.toml
index f774bf1..3c5a97d 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "ArnoldiMethod"
 uuid = "ec485272-7323-5ecc-a04f-4719b315124d"
 author = ["Harmen Stoppels <me@harmenstoppels.nl>", "Lauri Nyman"]
-version = "0.1.0"
+version = "0.2.0"
 
 [deps]
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
@@ -10,7 +10,7 @@ StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 
 [compat]
 StaticArrays = "0.8, 0.9, 0.10, 0.11, 0.12, 1.0"
-julia = "1"
+julia = "1.3"
 
 [extras]
 GenericSchur = "c145ed77-6b09-5dd9-b285-bf645a82121e"