From 69da0632e77e764b1660b4b920f8d3ef04823ec5 Mon Sep 17 00:00:00 2001
From: Tianyi Pu <912396513@qq.com>
Date: Sat, 25 Mar 2023 23:03:43 +0000
Subject: [PATCH 01/11] add unary and number broadcast; add `_all`

---
 src/ToeplitzMatrices.jl |  7 ++++---
 src/special.jl          | 10 ++++------
 src/toeplitz.jl         |  7 ++++---
 3 files changed, 12 insertions(+), 12 deletions(-)

diff --git a/src/ToeplitzMatrices.jl b/src/ToeplitzMatrices.jl
index 687cd4f..b4abf44 100644
--- a/src/ToeplitzMatrices.jl
+++ b/src/ToeplitzMatrices.jl
@@ -2,8 +2,9 @@ module ToeplitzMatrices
 # import StatsBase: levinson!, levinson
 import DSP: conv
 
-import Base: adjoint, convert, transpose, size, getindex, similar, copy, getproperty, inv, sqrt, copyto!, reverse, conj, zero, fill!, checkbounds, real, imag, isfinite, DimsInteger, iszero
+import Base: adjoint, convert, transpose, size, getindex, similar, copy, getproperty, inv, sqrt, copyto!, reverse, conj, zero, fill!, checkbounds, real, isfinite, DimsInteger, _all
 import Base: ==, +, -, *, \
+import Base.Broadcast: broadcasted, DefaultMatrixStyle
 import LinearAlgebra: Cholesky, Factorization
 import LinearAlgebra: ldiv!, factorize, lmul!, pinv, eigvals, cholesky!, cholesky, tril!, triu!, checksquare, rmul!, dot, mul!, tril, triu
 import LinearAlgebra: UpperTriangular, LowerTriangular, Symmetric, Adjoint
@@ -16,7 +17,7 @@ export durbin, trench, levinson
 include("iterativeLinearSolvers.jl")
 
 # Abstract
-abstract type AbstractToeplitz{T<:Number} <: AbstractMatrix{T} end
+abstract type AbstractToeplitz{T} <: AbstractMatrix{T} end
 
 size(A::AbstractToeplitz) = (length(A.vc),length(A.vr))
 @inline _vr(A::AbstractToeplitz) = A.vr
@@ -28,7 +29,7 @@ AbstractArray{T}(A::AbstractToeplitz) where T = AbstractToeplitz{T}(A)
 convert(::Type{AbstractToeplitz{T}}, A::AbstractToeplitz) where T = AbstractToeplitz{T}(A)
 
 isconcrete(A::AbstractToeplitz) = isconcretetype(typeof(A.vc)) && isconcretetype(typeof(A.vr))
-iszero(A::AbstractToeplitz) = iszero(A.vc) && iszero(A.vr)
+_all(f, A::AbstractToeplitz, ::Colon) = _all(f, A.vc, :) && _all(f, A.vr, :)
 
 """
     ToeplitzFactorization
diff --git a/src/special.jl b/src/special.jl
index 6e271c8..e78c2e7 100644
--- a/src/special.jl
+++ b/src/special.jl
@@ -14,9 +14,10 @@ for TYPE in (:SymmetricToeplitz, :Circulant, :LowerTriangularToeplitz, :UpperTri
 
         size(A::$TYPE) = (length(A.v),length(A.v))
         
+        broadcasted(::DefaultMatrixStyle, f, A::$TYPE) = $TYPE(f.(A.v))
+        broadcasted(::DefaultMatrixStyle, f, x::Number, A::$TYPE) = $TYPE(f.(x, A.v))
+        broadcasted(::DefaultMatrixStyle, f, A::$TYPE, x::Number) = $TYPE(f.(A.v, x))
         adjoint(A::$TYPE) = transpose(conj(A))
-        (*)(scalar::Number, C::$TYPE) = $TYPE(scalar * C.v)
-        (*)(C::$TYPE, scalar::Number) = $TYPE(C.v * scalar)
         (==)(A::$TYPE,B::$TYPE) = A.v==B.v
         function zero!(A::$TYPE)
             if isconcrete(A)
@@ -40,12 +41,9 @@ for TYPE in (:SymmetricToeplitz, :Circulant, :LowerTriangularToeplitz, :UpperTri
             A
         end
     end
-    for fun in (:zero, :conj, :copy, :-, :real, :imag)
+    for fun in (:zero, :copy)
         @eval $fun(A::$TYPE) = $TYPE($fun(A.v))
     end
-    for fun in (:iszero,)
-        @eval $fun(A::$TYPE) = $fun(A.v)
-    end
     for op in (:+, :-)
         @eval $op(A::$TYPE,B::$TYPE) = $TYPE($op(A.v,B.v))
     end
diff --git a/src/toeplitz.jl b/src/toeplitz.jl
index 5bb97fd..5eb2cd8 100644
--- a/src/toeplitz.jl
+++ b/src/toeplitz.jl
@@ -53,6 +53,9 @@ Base.@propagate_inbounds function getindex(A::AbstractToeplitz, i::Integer, j::I
     end
 end
 
+broadcasted(::DefaultMatrixStyle, f, A::AbstractToeplitz) = Toeplitz(f.(A.vc), f.(A.vr))
+broadcasted(::DefaultMatrixStyle, f, x::Number, A::AbstractToeplitz) = Toeplitz(f.(x, A.vc), f.(x, A.vr))
+
 checknonaliased(A::Toeplitz) = Base.mightalias(A.vc, A.vr) && throw(ArgumentError("Cannot modify Toeplitz matrices in place with aliased data"))
 
 function tril!(A::Toeplitz, k::Integer=0)
@@ -110,7 +113,7 @@ function similar(A::AbstractToeplitz, T::Type, dims::Dims{2})
     vr[1]=vc[1]
     Toeplitz{T}(vc,vr)
 end
-for fun in (:zero, :conj, :copy, :-, :real, :imag)
+for fun in (:zero, :copy)
     @eval $fun(A::AbstractToeplitz)=Toeplitz($fun(A.vc),$fun(A.vr))
 end
 for op in (:+, :-)
@@ -129,8 +132,6 @@ function fill!(A::Toeplitz, x::Number)
     fill!(A.vr,x)
     A
 end
-(*)(scalar::Number, C::AbstractToeplitz) = Toeplitz(scalar * C.vc, scalar * C.vr)
-(*)(C::AbstractToeplitz,scalar::Number) = Toeplitz(C.vc * scalar, C.vr * scalar)
 
 function lmul!(x::Number, A::Toeplitz)
     checknonaliased(A)

From 5a619d5f86964b95246ff6f9fe7ac4e20e27a8f0 Mon Sep 17 00:00:00 2001
From: Tianyi Pu <912396513@qq.com>
Date: Sun, 26 Mar 2023 11:22:19 +0100
Subject: [PATCH 02/11] Update toeplitz.jl

---
 src/toeplitz.jl | 24 +++++++++++++++++-------
 1 file changed, 17 insertions(+), 7 deletions(-)

diff --git a/src/toeplitz.jl b/src/toeplitz.jl
index 5eb2cd8..5536e2b 100644
--- a/src/toeplitz.jl
+++ b/src/toeplitz.jl
@@ -9,7 +9,7 @@ struct Toeplitz{T, VC<:AbstractVector{T}, VR<:AbstractVector{T}} <: AbstractToep
     vr::VR
 
     function Toeplitz{T, VC, VR}(vc::VC, vr::VR) where {T, VC<:AbstractVector{T}, VR<:AbstractVector{T}}
-        if first(vc) != first(vr)
+        if !isequal(first(vc), first(vr))
             error("First element of the vectors must be the same")
         end
         return new{T,VC,VR}(vc, vr)
@@ -42,6 +42,22 @@ AbstractToeplitz{T}(A::Toeplitz) where T = Toeplitz{T}(A)
 convert(::Type{Toeplitz{T}}, A::AbstractToeplitz) where {T} = Toeplitz{T}(A)
 convert(::Type{Toeplitz}, A::AbstractToeplitz) = Toeplitz(A)
 
+# Dims for disambiguity
+for DIM in (:DimsInteger, :Dims)
+    @eval function similar(::Type{Toeplitz{T, VC, VR}}, dims::$DIM{2}) where {T, VC, VR}
+        vc = similar(VC, dims[1])
+        vr = similar(VR, dims[2])
+        vr[1] = vc[1]
+        Toeplitz(vc, vr)
+    end
+    @eval function similar(A::AbstractToeplitz, T::Type = eltype(A), dims::$DIM{2} = size(A))
+        vc = similar(A.vc, T, dims[1])
+        vr = similar(A.vr, T, dims[2])
+        vr[1] = vc[1]
+        Toeplitz{T}(vc, vr)
+    end
+end
+
 # Retrieve an entry
 Base.@propagate_inbounds function getindex(A::AbstractToeplitz, i::Integer, j::Integer)
     @boundscheck checkbounds(A,i,j)
@@ -107,12 +123,6 @@ end
 
 adjoint(A::AbstractToeplitz) = transpose(conj(A))
 transpose(A::AbstractToeplitz) = Toeplitz(A.vr, A.vc)
-function similar(A::AbstractToeplitz, T::Type, dims::Dims{2})
-    vc=similar(A.vc, T, dims[1])
-    vr=similar(A.vr, T, dims[2])
-    vr[1]=vc[1]
-    Toeplitz{T}(vc,vr)
-end
 for fun in (:zero, :copy)
     @eval $fun(A::AbstractToeplitz)=Toeplitz($fun(A.vc),$fun(A.vr))
 end

From 34e56a56c40a9dc09fb8457516805bd7747ee21b Mon Sep 17 00:00:00 2001
From: Tianyi Pu <912396513@qq.com>
Date: Sun, 26 Mar 2023 11:30:49 +0100
Subject: [PATCH 03/11] Update toeplitz.jl

---
 src/toeplitz.jl | 1 +
 1 file changed, 1 insertion(+)

diff --git a/src/toeplitz.jl b/src/toeplitz.jl
index 5536e2b..ffc7e46 100644
--- a/src/toeplitz.jl
+++ b/src/toeplitz.jl
@@ -71,6 +71,7 @@ end
 
 broadcasted(::DefaultMatrixStyle, f, A::AbstractToeplitz) = Toeplitz(f.(A.vc), f.(A.vr))
 broadcasted(::DefaultMatrixStyle, f, x::Number, A::AbstractToeplitz) = Toeplitz(f.(x, A.vc), f.(x, A.vr))
+broadcasted(::DefaultMatrixStyle, f, A::AbstractToeplitz, x::Number) = Toeplitz(f.(A.vc, x), f.(A.vr, x))
 
 checknonaliased(A::Toeplitz) = Base.mightalias(A.vc, A.vr) && throw(ArgumentError("Cannot modify Toeplitz matrices in place with aliased data"))
 

From 797625c12b9ae1d4cf8e014059d3289230bdfe67 Mon Sep 17 00:00:00 2001
From: Tianyi Pu <912396513@qq.com>
Date: Sun, 26 Mar 2023 11:42:50 +0100
Subject: [PATCH 04/11] Update runtests.jl

---
 test/runtests.jl | 1 +
 1 file changed, 1 insertion(+)

diff --git a/test/runtests.jl b/test/runtests.jl
index df1b49f..bfebdef 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -362,6 +362,7 @@ end
         T=copy(TA)
     end
     @test fill!(Toeplitz(zeros(2,2)),1) == ones(2,2)
+    @test isa(similar(Toeplitz{Int, Vector{Int}, Vector{Int}}, 5, 3), Toeplitz)
 
     @testset "aliasing" begin
         v = [1,2,3]

From e9e57f38e3ea2decf3c2e5ba398990387779dd69 Mon Sep 17 00:00:00 2001
From: Tianyi Pu <912396513@qq.com>
Date: Sun, 26 Mar 2023 12:12:09 +0100
Subject: [PATCH 05/11] add a case where broadcast breaks

---
 test/runtests.jl | 11 +++++++++++
 1 file changed, 11 insertions(+)

diff --git a/test/runtests.jl b/test/runtests.jl
index bfebdef..e68eb38 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -378,6 +378,17 @@ end
     end
 end
 
+@testset "Broadcast" begin
+    A = rand(ComplexF64, 3, 3)
+    T = Toeplitz(A)
+    S = Symmetric(T)
+    C = Circulant(T)
+    U = UpperTriangular(T)
+    L = LowerTriangular(T)
+
+    @test U .+ 1 == Matrix(U) .+ 1
+end
+
 @testset "Circulant mathematics" begin
     C1 = Circulant(rand(5))
     C2 = Circulant(rand(5))

From 51900b6f9a92980f46e2bde2dc68f9371e9cd1a8 Mon Sep 17 00:00:00 2001
From: Tianyi Pu <912396513@qq.com>
Date: Sun, 26 Mar 2023 13:44:12 +0100
Subject: [PATCH 06/11] fixes and more tests

---
 README.md        | 11 ++++-------
 src/special.jl   | 19 ++++++++++++++++++-
 src/toeplitz.jl  |  9 ++++++---
 test/runtests.jl |  8 +++++++-
 4 files changed, 35 insertions(+), 12 deletions(-)

diff --git a/README.md b/README.md
index 8915c56..b2b9ce3 100644
--- a/README.md
+++ b/README.md
@@ -78,10 +78,7 @@ The `reverse` can transform between Hankel and Toeplitz. It is used to achieve f
 |copy|✓|✓|✓|✓|✓|✓|
 |similar|✓|✓|✓|✓|✓|✓|
 |zero|✓|✓|✓|✓|✓|✓|
-|real|✓|✓|✓|✓|✓|✓|
-|imag|✓|✓|✓|✓|✓|✓|
 |fill!|✓|✗|✗|✗|✗|✓|
-|conj|✓|✓|✓|✓|✓|✓|
 |transpose|✓|✓|✓|✓|✓|✓|
 |adjoint|✓|✓|✓|✓|✓|✓|
 |tril!|✓|✗|✗|✓|✓|✗|
@@ -90,19 +87,19 @@ The `reverse` can transform between Hankel and Toeplitz. It is used to achieve f
 |triu|✓|✓|✓|✓|✓|✗|
 |+|✓|✓|✓|✓|✓|✓|
 |-|✓|✓|✓|✓|✓|✓|
-|scalar<br>mult|✓|✓|✓|✓|✓|✓|
 |==|✓|✓|✓|✓|✓|✓|
 |issymmetric|||||||
 |istriu|||||||
 |istril|||||||
-|iszero|✓|✓|✓|✓|✓||
 |isone|||||||
 |copyto!|✓|✓|✓|✓|✓|✓|
 |reverse|✓|✓|✓|✓|✓|✓|
-|broadcast|||||||
+|\_all|✓|✓|✓|✓|✓||
+|unary broadcast|✓|✓|✓|✓|✓||
+|number broadcast|✓|✓|✓|✓|✓||
 |broadcast!|||||||
 
-Note that scalar multiplication, `conj`, `+` and `-` could be removed once `broadcast` is implemented.
+Note that `+` and `-` could be removed once binary `broadcast` is implemented.
 
 `reverse(Hankel)` returns a `Toeplitz`, while `reverse(AbstractToeplitz)` returns a `Hankel`.
 
diff --git a/src/special.jl b/src/special.jl
index e78c2e7..a8a31c2 100644
--- a/src/special.jl
+++ b/src/special.jl
@@ -51,7 +51,8 @@ for TYPE in (:SymmetricToeplitz, :Circulant, :LowerTriangularToeplitz, :UpperTri
         @eval $TYPE(v::$TY) = $TYPE{eltype(v)}(v)
     end
 end
-TriangularToeplitz{T}=Union{UpperTriangularToeplitz{T},LowerTriangularToeplitz{T}}
+SymToeplitzOrCirc{T} = Union{SymmetricToeplitz{T}, Circulant{T}}
+TriangularToeplitz{T} = Union{UpperTriangularToeplitz{T}, LowerTriangularToeplitz{T}}
 
 # vc and vr
 function getproperty(A::SymmetricToeplitz, s::Symbol)
@@ -102,6 +103,22 @@ transpose(A::Circulant) = Circulant(A.vr)
 transpose(A::LowerTriangularToeplitz) = UpperTriangularToeplitz(A.v)
 transpose(A::UpperTriangularToeplitz) = LowerTriangularToeplitz(A.v)
 
+# _all
+_all(f, A::SymToeplitzOrCirc, ::Colon) = _all(f, A.v, :)
+_all(f, A::TriangularToeplitz, ::Colon) = f(zero(eltype(A))) && _all(f, A.v, :)
+
+# broadcast
+for TYPE in (:SymmetricToeplitz, :Circulant)
+    @eval broadcasted(::DefaultMatrixStyle, f, A::$TYPE) = $TYPE(f.(A.v))
+    @eval broadcasted(::DefaultMatrixStyle, f, x::Number, A::$TYPE) = $TYPE(f.(x, A.v))
+    @eval broadcasted(::DefaultMatrixStyle, f, A::$TYPE, x::Number) = $TYPE(f.(A.v, x))
+end
+for TYPE in (:UpperTriangularToeplitz, :LowerTriangularToeplitz)
+    @eval broadcasted(::DefaultMatrixStyle, f, A::$TYPE) = iszero(f(zero(eltype(A)))) ? $TYPE(f.(A.v)) : _toep_broadcast(f, A)
+    @eval broadcasted(::DefaultMatrixStyle, f, x::Number, A::$TYPE) = iszero(f(x, zero(eltype(A)))) ? $TYPE(f.(x, A.v)) : _toep_broadcast(f, x, A)
+    @eval broadcasted(::DefaultMatrixStyle, f, A::$TYPE, x::Number) = iszero(f(zero(eltype(A)), x)) ? $TYPE(f.(A.v, x)) : _toep_broadcast(f, A, x)
+end
+
 # getindex
 Base.@propagate_inbounds function getindex(A::SymmetricToeplitz, i::Integer, j::Integer)
     @boundscheck checkbounds(A,i,j)
diff --git a/src/toeplitz.jl b/src/toeplitz.jl
index ffc7e46..d86938a 100644
--- a/src/toeplitz.jl
+++ b/src/toeplitz.jl
@@ -69,9 +69,12 @@ Base.@propagate_inbounds function getindex(A::AbstractToeplitz, i::Integer, j::I
     end
 end
 
-broadcasted(::DefaultMatrixStyle, f, A::AbstractToeplitz) = Toeplitz(f.(A.vc), f.(A.vr))
-broadcasted(::DefaultMatrixStyle, f, x::Number, A::AbstractToeplitz) = Toeplitz(f.(x, A.vc), f.(x, A.vr))
-broadcasted(::DefaultMatrixStyle, f, A::AbstractToeplitz, x::Number) = Toeplitz(f.(A.vc, x), f.(A.vr, x))
+broadcasted(::DefaultMatrixStyle, f, A::AbstractToeplitz) = _toep_broadcast(f, A)
+broadcasted(::DefaultMatrixStyle, f, x::Number, A::AbstractToeplitz) = _toep_broadcast(f, x, A)
+broadcasted(::DefaultMatrixStyle, f, A::AbstractToeplitz, x::Number) = _toep_broadcast(f, A, x)
+_toep_broadcast(f, A::AbstractToeplitz) = Toeplitz(f.(A.vc), f.(A.vr))
+_toep_broadcast(f, x::Number, A::AbstractToeplitz) = Toeplitz(f.(x, A.vc), f.(x, A.vr))
+_toep_broadcast(f, A::AbstractToeplitz, x::Number) = Toeplitz(f.(A.vc, x), f.(A.vr, x))
 
 checknonaliased(A::Toeplitz) = Base.mightalias(A.vc, A.vr) && throw(ArgumentError("Cannot modify Toeplitz matrices in place with aliased data"))
 
diff --git a/test/runtests.jl b/test/runtests.jl
index e68eb38..ad1c99f 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -386,7 +386,13 @@ end
     U = UpperTriangular(T)
     L = LowerTriangular(T)
 
-    @test U .+ 1 == Matrix(U) .+ 1
+    for M in (T, S, C, U, L)
+        @testset "$(typeof(M))" begin
+            @test M .+ 1 == Matrix(M) .+ 1
+            @test exp.(M) == exp.(Matrix(M))
+            @test isa(M .* 2, typeof(M))
+        end
+    end
 end
 
 @testset "Circulant mathematics" begin

From 652caaef8deb9b5443277f7e6121e3ca9fbf282c Mon Sep 17 00:00:00 2001
From: Tianyi Pu <912396513@qq.com>
Date: Sun, 26 Mar 2023 13:58:29 +0100
Subject: [PATCH 07/11] fix

---
 src/special.jl | 3 ---
 1 file changed, 3 deletions(-)

diff --git a/src/special.jl b/src/special.jl
index a8a31c2..15f323e 100644
--- a/src/special.jl
+++ b/src/special.jl
@@ -14,9 +14,6 @@ for TYPE in (:SymmetricToeplitz, :Circulant, :LowerTriangularToeplitz, :UpperTri
 
         size(A::$TYPE) = (length(A.v),length(A.v))
         
-        broadcasted(::DefaultMatrixStyle, f, A::$TYPE) = $TYPE(f.(A.v))
-        broadcasted(::DefaultMatrixStyle, f, x::Number, A::$TYPE) = $TYPE(f.(x, A.v))
-        broadcasted(::DefaultMatrixStyle, f, A::$TYPE, x::Number) = $TYPE(f.(A.v, x))
         adjoint(A::$TYPE) = transpose(conj(A))
         (==)(A::$TYPE,B::$TYPE) = A.v==B.v
         function zero!(A::$TYPE)

From 3f3fb59e0237992a20cb050ddf231c82fe7b79a2 Mon Sep 17 00:00:00 2001
From: Tianyi Pu <912396513@qq.com>
Date: Mon, 27 Mar 2023 17:54:54 +0100
Subject: [PATCH 08/11] hankel

---
 README.md     | 6 +++---
 src/hankel.jl | 8 +++++---
 2 files changed, 8 insertions(+), 6 deletions(-)

diff --git a/README.md b/README.md
index b2b9ce3..f0212cb 100644
--- a/README.md
+++ b/README.md
@@ -94,9 +94,9 @@ The `reverse` can transform between Hankel and Toeplitz. It is used to achieve f
 |isone|||||||
 |copyto!|✓|✓|✓|✓|✓|✓|
 |reverse|✓|✓|✓|✓|✓|✓|
-|\_all|✓|✓|✓|✓|✓||
-|unary broadcast|✓|✓|✓|✓|✓||
-|number broadcast|✓|✓|✓|✓|✓||
+|\_all|✓|✓|✓|✓|✓|✓|
+|unary broadcast|✓|✓|✓|✓|✓|✓|
+|number broadcast|✓|✓|✓|✓|✓|✓|
 |broadcast!|||||||
 
 Note that `+` and `-` could be removed once binary `broadcast` is implemented.
diff --git a/src/hankel.jl b/src/hankel.jl
index 6d12ee4..dd8685c 100644
--- a/src/hankel.jl
+++ b/src/hankel.jl
@@ -59,6 +59,10 @@ end
 convert(::Type{AbstractArray{T}}, A::Hankel) where {T<:Number} = convert(Hankel{T}, A)
 convert(::Type{AbstractMatrix{T}}, A::Hankel) where {T<:Number} = convert(Hankel{T}, A)
 convert(::Type{Hankel{T}}, A::Hankel) where {T<:Number} = Hankel{T}(convert(AbstractVector{T}, A.v), size(A))
+broadcasted(::DefaultMatrixStyle, f, A::Hankel) = Hankel(f.(A.v), A.size)
+broadcasted(::DefaultMatrixStyle, f, x::Number, A::Hankel) = Hankel(f.(x, A.v), A.size)
+broadcasted(::DefaultMatrixStyle, f, A::Hankel, x::Number) = Hankel(f.(A.v, x), A.size)
+_all(f, A::Hankel, ::Colon) = _all(f, A.v, :)
 
 # Size
 size(H::Hankel) = H.size
@@ -70,7 +74,7 @@ Base.@propagate_inbounds function getindex(A::Hankel, i::Integer, j::Integer)
 end
 similar(A::Hankel, T::Type, dims::DimsInteger{2}) = Hankel{T}(similar(A.v, T, dims[1]+dims[2]-true), dims)
 similar(A::Hankel, T::Type, dims::Tuple{Int64,Int64}) = Hankel{T}(similar(A.v, T, dims[1]+dims[2]-true), dims) # for ambiguity with `similar(a::AbstractArray, ::Type{T}, dims::Tuple{Vararg{Int64, N}}) where {T, N}` in Base
-for fun in (:zero, :conj, :copy, :-, :similar, :real, :imag)
+for fun in (:zero, :copy, :similar)
     @eval $fun(A::Hankel) = Hankel($fun(A.v), size(A))
 end
 for op in (:+, :-)
@@ -100,8 +104,6 @@ end
 transpose(A::Hankel) = Hankel(A.v, reverse(size(A)))
 adjoint(A::Hankel) = transpose(conj(A))
 (==)(A::Hankel, B::Hankel) = A.v == B.v && size(A) == size(B)
-(*)(scalar::Number, C::Hankel) = Hankel(scalar * C.v, size(C))
-(*)(C::Hankel,scalar::Number) = Hankel(C.v * scalar, size(C))
 
 isconcrete(A::Hankel) = isconcretetype(A.v)
 

From 5da10122f1186463e376200acbe5eb7231d2271d Mon Sep 17 00:00:00 2001
From: Tianyi Pu <912396513@qq.com>
Date: Mon, 27 Mar 2023 18:19:16 +0100
Subject: [PATCH 09/11] Update hankel.jl

---
 src/hankel.jl | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/src/hankel.jl b/src/hankel.jl
index dd8685c..42db9ed 100644
--- a/src/hankel.jl
+++ b/src/hankel.jl
@@ -72,9 +72,9 @@ Base.@propagate_inbounds function getindex(A::Hankel, i::Integer, j::Integer)
     @boundscheck checkbounds(A, i, j)
     return A.v[i+j-1]
 end
-similar(A::Hankel, T::Type, dims::DimsInteger{2}) = Hankel{T}(similar(A.v, T, dims[1]+dims[2]-true), dims)
-similar(A::Hankel, T::Type, dims::Tuple{Int64,Int64}) = Hankel{T}(similar(A.v, T, dims[1]+dims[2]-true), dims) # for ambiguity with `similar(a::AbstractArray, ::Type{T}, dims::Tuple{Vararg{Int64, N}}) where {T, N}` in Base
-for fun in (:zero, :copy, :similar)
+similar(A::Hankel, T::Type = eltype(A), dims::DimsInteger{2} = size(A)) = Hankel{T}(similar(A.v, T, dims[1]+dims[2]-true), dims)
+similar(A::Hankel, T::Type = eltype(A), dims::Tuple{Int64,Int64} = size(A)) = Hankel{T}(similar(A.v, T, dims[1]+dims[2]-true), dims) # for ambiguity with `similar(a::AbstractArray, ::Type{T}, dims::Tuple{Vararg{Int64, N}}) where {T, N}` in Base
+for fun in (:zero, :copy)
     @eval $fun(A::Hankel) = Hankel($fun(A.v), size(A))
 end
 for op in (:+, :-)

From 343ace00625be75b0b0df2b813cbdd628c0d875d Mon Sep 17 00:00:00 2001
From: Tianyi Pu <912396513@qq.com>
Date: Mon, 27 Mar 2023 22:11:33 +0100
Subject: [PATCH 10/11] `_all` to `all`

---
 src/ToeplitzMatrices.jl | 4 ++--
 src/hankel.jl           | 2 +-
 src/special.jl          | 4 ++--
 3 files changed, 5 insertions(+), 5 deletions(-)

diff --git a/src/ToeplitzMatrices.jl b/src/ToeplitzMatrices.jl
index b4abf44..d939dd8 100644
--- a/src/ToeplitzMatrices.jl
+++ b/src/ToeplitzMatrices.jl
@@ -2,7 +2,7 @@ module ToeplitzMatrices
 # import StatsBase: levinson!, levinson
 import DSP: conv
 
-import Base: adjoint, convert, transpose, size, getindex, similar, copy, getproperty, inv, sqrt, copyto!, reverse, conj, zero, fill!, checkbounds, real, isfinite, DimsInteger, _all
+import Base: adjoint, convert, transpose, size, getindex, similar, copy, getproperty, inv, sqrt, copyto!, reverse, conj, zero, fill!, checkbounds, real, isfinite, DimsInteger, all
 import Base: ==, +, -, *, \
 import Base.Broadcast: broadcasted, DefaultMatrixStyle
 import LinearAlgebra: Cholesky, Factorization
@@ -29,7 +29,7 @@ AbstractArray{T}(A::AbstractToeplitz) where T = AbstractToeplitz{T}(A)
 convert(::Type{AbstractToeplitz{T}}, A::AbstractToeplitz) where T = AbstractToeplitz{T}(A)
 
 isconcrete(A::AbstractToeplitz) = isconcretetype(typeof(A.vc)) && isconcretetype(typeof(A.vr))
-_all(f, A::AbstractToeplitz, ::Colon) = _all(f, A.vc, :) && _all(f, A.vr, :)
+all(f, A::AbstractToeplitz, ::Colon) = all(f, A.vc, :) && all(f, A.vr, :)
 
 """
     ToeplitzFactorization
diff --git a/src/hankel.jl b/src/hankel.jl
index 42db9ed..5a2b4fb 100644
--- a/src/hankel.jl
+++ b/src/hankel.jl
@@ -62,7 +62,7 @@ convert(::Type{Hankel{T}}, A::Hankel) where {T<:Number} = Hankel{T}(convert(Abst
 broadcasted(::DefaultMatrixStyle, f, A::Hankel) = Hankel(f.(A.v), A.size)
 broadcasted(::DefaultMatrixStyle, f, x::Number, A::Hankel) = Hankel(f.(x, A.v), A.size)
 broadcasted(::DefaultMatrixStyle, f, A::Hankel, x::Number) = Hankel(f.(A.v, x), A.size)
-_all(f, A::Hankel, ::Colon) = _all(f, A.v, :)
+all(f, A::Hankel, ::Colon) = all(f, A.v, :)
 
 # Size
 size(H::Hankel) = H.size
diff --git a/src/special.jl b/src/special.jl
index 15f323e..2948b5e 100644
--- a/src/special.jl
+++ b/src/special.jl
@@ -101,8 +101,8 @@ transpose(A::LowerTriangularToeplitz) = UpperTriangularToeplitz(A.v)
 transpose(A::UpperTriangularToeplitz) = LowerTriangularToeplitz(A.v)
 
 # _all
-_all(f, A::SymToeplitzOrCirc, ::Colon) = _all(f, A.v, :)
-_all(f, A::TriangularToeplitz, ::Colon) = f(zero(eltype(A))) && _all(f, A.v, :)
+all(f, A::SymToeplitzOrCirc, ::Colon) = all(f, A.v, :)
+all(f, A::TriangularToeplitz, ::Colon) = f(zero(eltype(A))) && all(f, A.v, :)
 
 # broadcast
 for TYPE in (:SymmetricToeplitz, :Circulant)

From 4ed4ab0fd3b41dc24076d00623af0dab87568d25 Mon Sep 17 00:00:00 2001
From: Tianyi Pu <912396513@qq.com>
Date: Tue, 14 Nov 2023 10:44:35 +0000
Subject: [PATCH 11/11] resolve conflict and add mapreduce for + and max

---
 src/ToeplitzMatrices.jl |  7 ++++++-
 src/toeplitz.jl         | 16 ----------------
 test/runtests.jl        |  1 -
 3 files changed, 6 insertions(+), 18 deletions(-)

diff --git a/src/ToeplitzMatrices.jl b/src/ToeplitzMatrices.jl
index a30d440..fd5730b 100644
--- a/src/ToeplitzMatrices.jl
+++ b/src/ToeplitzMatrices.jl
@@ -1,7 +1,8 @@
 module ToeplitzMatrices
 import DSP: conv
 
-import Base: adjoint, convert, transpose, size, getindex, similar, copy, getproperty, inv, sqrt, copyto!, reverse, conj, zero, fill!, checkbounds, real, imag, isfinite, DimsInteger, iszero
+import Base: convert, size, getindex, similar, copy, getproperty, copyto!, reverse, zero, fill!, checkbounds, isfinite, DimsInteger, iszero
+import Base: all, adjoint, transpose, real, imag, inv, sqrt, conj
 import Base: parent
 import Base: ==, +, -, *, \
 import Base: AbstractMatrix
@@ -47,6 +48,10 @@ AbstractArray{T}(A::AbstractToeplitz) where T = AbstractToeplitz{T}(A)
 convert(::Type{AbstractToeplitz{T}}, A::AbstractToeplitz) where T = AbstractToeplitz{T}(A)
 
 isconcrete(A::AbstractToeplitz) = isconcretetype(typeof(A.vc)) && isconcretetype(typeof(A.vr))
+
+for op in (:+, :max)
+    @eval mapreduce(f, ::typeof($op), A::AbstractToeplitz) = mapreduce(identity, $op, [mapreduce(f, $op, diag(A, k)) for k in -size(A,1)+1:size(A,2)-1])
+end
 all(f, A::AbstractToeplitz, ::Colon) = all(f, A.vc, :) && all(f, A.vr, :)
 iszero(A::AbstractToeplitz) = iszero(A.vc) && iszero(A.vr)
 function diag(A::AbstractToeplitz, k::Integer=0)
diff --git a/src/toeplitz.jl b/src/toeplitz.jl
index b89f2ea..ca3216f 100644
--- a/src/toeplitz.jl
+++ b/src/toeplitz.jl
@@ -43,22 +43,6 @@ AbstractToeplitz{T}(A::Toeplitz) where T = Toeplitz{T}(A)
 convert(::Type{Toeplitz{T}}, A::AbstractToeplitz) where {T} = Toeplitz{T}(A)
 convert(::Type{Toeplitz}, A::AbstractToeplitz) = Toeplitz(A)
 
-# Dims for disambiguity
-for DIM in (:DimsInteger, :Dims)
-    @eval function similar(::Type{Toeplitz{T, VC, VR}}, dims::$DIM{2}) where {T, VC, VR}
-        vc = similar(VC, dims[1])
-        vr = similar(VR, dims[2])
-        vr[1] = vc[1]
-        Toeplitz(vc, vr)
-    end
-    @eval function similar(A::AbstractToeplitz, T::Type = eltype(A), dims::$DIM{2} = size(A))
-        vc = similar(A.vc, T, dims[1])
-        vr = similar(A.vr, T, dims[2])
-        vr[1] = vc[1]
-        Toeplitz{T}(vc, vr)
-    end
-end
-
 # Retrieve an entry
 Base.@propagate_inbounds function getindex(A::AbstractToeplitz, i::Integer, j::Integer)
     @boundscheck checkbounds(A,i,j)
diff --git a/test/runtests.jl b/test/runtests.jl
index 3a907dc..c1f0c55 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -377,7 +377,6 @@ end
         T=copy(TA)
     end
     @test fill!(Toeplitz(zeros(2,2)),1) == ones(2,2)
-    @test isa(similar(Toeplitz{Int, Vector{Int}, Vector{Int}}, 5, 3), Toeplitz)
 	
 	@testset "diag" begin
 		H = Hankel(1:11, 4, 8)