Fix whitespace

examples/blocktridiagonal.jl

@@ -1,8 +1,7 @@
 using InfiniteLinearAlgebra, BlockBandedMatrices, BandedMatrices, BlockArrays, InfiniteArrays, FillArrays, LazyArrays, Test
 
-A = BlockTridiagonal(Vcat([fill(1.0,2,1),Matrix(1.0I,2,2),Matrix(1.0I,2,2),Matrix(1.0I,2,2)],Fill(Matrix(1.0I,2,2), ∞)), 
-                       Vcat([zeros(1,1)], Fill(zeros(2,2), ∞)), 
+A = BlockTridiagonal(Vcat([fill(1.0,2,1),Matrix(1.0I,2,2),Matrix(1.0I,2,2),Matrix(1.0I,2,2)],Fill(Matrix(1.0I,2,2), ∞)),
+                       Vcat([zeros(1,1)], Fill(zeros(2,2), ∞)),
                        Vcat([fill(1.0,1,2),Matrix(1.0I,2,2)], Fill(Matrix(1.0I,2,2), ∞)))
 
 
-

examples/intervalarithmetic.jl

@@ -1,2 +1,2 @@
 using InfiniteLinearAlgebra
-import IntervalArithmetic
+import IntervalArithmetic

examples/jacobi.jl

@@ -17,7 +17,7 @@ ql(Δ - λ*I).L[1,1]
 end
 
 λ2 = Interval(m,λ.hi)
-ql(Δ - λ1.hi*I).L[1,1] 
+ql(Δ - λ1.hi*I).L[1,1]
 
 
 ql(Δ - Interval(4.2)I).L[1,1]
@@ -41,7 +41,7 @@ Z,A,B = 0.5,-4.0,0.5
 
 A = 4
 rig_qltail(-2,10,B)
-    
+
 d,e = d2,e2
 
 rig_qltail(Z,A,B,d,e)
@@ -106,4 +106,4 @@ X[2,:] .= (zero(T), X[1,1], X[1,2]);
 X[1,:] .= (Z,A,B);
 QL = _qlfactUnblocked!(X)
 
-X, QL.τ[end]      
+X, QL.τ[end]

examples/periodicschrodinger.jl

@@ -3,8 +3,8 @@ using InfiniteLinearAlgebra, Plots
 # Consider a rank-1 perturbation of periodic semi-infinite Schrödinger (Jacobi) operator.
 # We can construct it as a block matrix as follows:
 
-A = BlockTridiagonal(Vcat([[0. 1.; 0. 0.]],Fill([0. 1.; 0. 0.], ∞)), 
-                       Vcat([[-1. 1.; 1. 1.]], Fill([-1. 1.; 1. 1.], ∞)), 
+A = BlockTridiagonal(Vcat([[0. 1.; 0. 0.]],Fill([0. 1.; 0. 0.], ∞)),
+                       Vcat([[-1. 1.; 1. 1.]], Fill([-1. 1.; 1. 1.], ∞)),
                        Vcat([[0. 0.; 1. 0.]], Fill([0. 0.; 1. 0.], ∞)))
 
 A[1,1] = 2 # perturbation
@@ -16,7 +16,7 @@ n = 100; scatter(eigvals(A[1:n,1:n]), zeros(n); label="finite-section")
 # In any case, we can also calculate the spectrum using ∞-QL:
 xx = [-0.95:0.05:0.95; 2.25:0.125/4:4.0]
 plot!(xx, (x -> ql(A-x*I).L[1,1]).(xx); label="L[1,1]")
-xx = 
+xx =
 plot!(xx, (x -> ql(A-x*I).L[1,1]).(xx))
 
 

examples/perttoeplitz.jl

@@ -23,11 +23,11 @@ A = BandedMatrix(-2 => Vcat([1], Fill(1,∞)),  0 => Vcat(a, Fill(0,∞)), 1 =>
 x,y = range(-2,2; length=200),range(-2,2;length=200)
     z = abs.(ℓ.(x' .+ y.*im))
     contour(x,y,z; nlevels=50, title="z^2 + 1/(4z)")
-    scatter!(eigvals(Matrix(A[1:100,1:100]')); label="A' finite section")     
+    scatter!(eigvals(Matrix(A[1:100,1:100]')); label="A' finite section")
     scatter!(eigvals(Matrix(A[1:100,1:100])); label="A finite section")
 
 x = range(-2,2,length=1_000)
-    plot(x, abs.(ℓ.(x.+eps()im)); label="abs(L[1,1])")    
+    plot(x, abs.(ℓ.(x.+eps()im)); label="abs(L[1,1])")
 
 a = [-0.1,0.2,0.3]
 A = BandedMatrix(-2 => Vcat([1], Fill(1,∞)),  0 => Vcat(a, Fill(0,∞)), 1 => Vcat([1/4], Fill(1/4,∞)))

examples/toeplitz.jl

@@ -12,9 +12,9 @@ using InfiniteLinearAlgebra, BandedMatrices, PyPlot
 ###
 
 function ℓ11(A,λ; kwds...)
-    try 
-        abs(ql(A-λ*I; kwds...).L[1,1]) 
-    catch DomainError 
+    try
+        abs(ql(A-λ*I; kwds...).L[1,1])
+    catch DomainError
         -1.0
     end
 end
@@ -64,7 +64,7 @@ clf(); qlplot(A; branch=findsecond, x=range(-2,3; length=100), y=range(-2.5,2.5;
 clf(); qlplot(transpose(A); x=range(-2,3; length=100), y=range(-2.5,2.5;length=100)); symbolplot(A; color=:black); title("Limacon, transpose")
 
 
-### 
+###
 # bull-head
 ###
 
@@ -95,7 +95,7 @@ clf(); qlplot(transpose(A); branch=branch(2), x=range(-2,2; length=100), y=range
 # Whale
 ###
 
-A = BandedMatrix(-4 => Fill(im,∞), -3 => Fill(4,∞), -2 => Fill(3+im,∞), -1 => Fill(10,∞), 
+A = BandedMatrix(-4 => Fill(im,∞), -3 => Fill(4,∞), -2 => Fill(3+im,∞), -1 => Fill(10,∞),
                     1 => Fill(1,∞), 2 => Fill(im,∞), 3 => Fill(-(3+2im),∞), 4=>Fill(-1,∞))
 
 clf(); qlplot(A; x=range(-15,20; length=100), y=range(-20,20;length=100)); symbolplot(A; color=:black); title("Whale")

src/InfiniteLinearAlgebra.jl

@@ -8,7 +8,7 @@ import Base: +, -, *, /, \, ^, OneTo, getindex, promote_op, _unsafe_getindex, si
             show, getproperty, copy, copyto!, map, require_one_based_indexing, similar, inv
 import Base.Broadcast: BroadcastStyle, Broadcasted, broadcasted
 
-import ArrayLayouts: colsupport, rowsupport, triangularlayout, MatLdivVec, triangulardata, TriangularLayout, TridiagonalLayout, 
+import ArrayLayouts: colsupport, rowsupport, triangularlayout, MatLdivVec, triangulardata, TriangularLayout, TridiagonalLayout,
                         sublayout, _qr, __qr, MatLmulVec, MatLmulMat, AbstractQLayout, materialize!, diagonaldata, subdiagonaldata, supdiagonaldata,
                         _bidiag_forwardsub!, mulreduce, RangeCumsum, _factorize, transposelayout, ldiv!, lmul!, mul, CNoPivot
 import BandedMatrices: BandedMatrix, _BandedMatrix, AbstractBandedMatrix, bandeddata, bandwidths, BandedColumns, bandedcolumns,
@@ -46,7 +46,7 @@ else
     import Base: oneto, unitrange
 end
 
-if VERSION ≥ v"1.7-"
+if VERSION ≥ v"1.7-"
     LinearAlgebra._cut_B(x::AbstractVector, r::InfUnitRange) = x
     LinearAlgebra._cut_B(X::AbstractMatrix, r::InfUnitRange) = X
 end

src/banded/hessenbergq.jl

@@ -43,7 +43,7 @@ function show(io::IO, mime::MIME{Symbol("text/plain")}, F::QLHessenberg)
     show(io, mime, F.L)
 end
 
-@inline function getL(F::QLHessenberg, _) 
+@inline function getL(F::QLHessenberg, _)
     m, n = size(F)
     tril!(getfield(F, :factors)[end-min(m,n)+1:end, 1:n], max(n-m,0))
 end
@@ -78,7 +78,7 @@ for Typ in (:UpperHessenbergQ, :LowerHessenbergQ)
             end
         end
 
-        $Typ(q::AbstractVector{<:AbstractMatrix{T}}) where T = 
+        $Typ(q::AbstractVector{<:AbstractMatrix{T}}) where T =
             $Typ{T,typeof(q)}(q)
     end
 end
@@ -111,7 +111,7 @@ function materialize!(L::MatLmulVec{<:HessenbergQLayout{'L'}})
         v = view(x, n:n+1)
         mul!(t, Q.q[n], v)
         v .= t
-        n > nz && norm(t) ≤ 10floatmin(real(T)) && return x
+        n > nz && norm(t) ≤ 10floatmin(real(T)) && return x
     end
     x
 end

src/banded/infbanded.jl

@@ -23,7 +23,7 @@ function _inf_banded_sub_materialize(::BandedColumns, V)
     b = parentindices(V)[1].b
     data = bandeddata(A)
     l,u = bandwidths(A)
-    if -l ≤ b ≤ u
+    if -l ≤ b ≤ u
         data[u+1-b, max(1,b+1):end]
     else
         Zeros{eltype(V)}(∞) # Not type stable
@@ -86,7 +86,7 @@ function BandedMatrix{T}(kv::Tuple{Vararg{Pair{<:Integer,<:Vcat{<:Any,1,<:Tuple{
     m,n = mn
     @assert isinf(n)
     l,u = lu
-    M = mapreduce(x -> length(x.second.args[1]) + max(0,x.first), max, kv) # number of data rows
+    M = mapreduce(x -> length(x.second.args[1]) + max(0,x.first), max, kv) # number of data rows
     data = zeros(T, u+l+1, M)
     t = zeros(T, u+l+1)
     for (k,v) in kv
@@ -110,30 +110,30 @@ function BandedMatrix(Ac::Adjoint{T,<:InfToeplitz}) where T
     A = parent(Ac)
     l,u = bandwidths(A)
     a = A.data.args[1]
-    _BandedMatrix(reverse(conj(a)) * Ones{T}(1,∞), ℵ₀, u, l)
+    _BandedMatrix(reverse(conj(a)) * Ones{T}(1,∞), ℵ₀, u, l)
 end
 
 function BandedMatrix(Ac::Transpose{T,<:InfToeplitz}) where T
     A = parent(Ac)
     l,u = bandwidths(A)
     a = A.data.args[1]
-    _BandedMatrix(reverse(a) * Ones{T}(1,∞), ℵ₀, u, l)
+    _BandedMatrix(reverse(a) * Ones{T}(1,∞), ℵ₀, u, l)
 end
 
 function BandedMatrix(Ac::Adjoint{T,<:PertToeplitz}) where T
     A = parent(Ac)
     l,u = bandwidths(A)
     a,b = A.data.args
     Ac_fd = BandedMatrix(_BandedMatrix(Hcat(a, b[:,1:l+1]), size(a,2)+l, l, u)')
-    _BandedMatrix(Hcat(Ac_fd.data, reverse(conj(b.args[1])) * Ones{T}(1,∞)), ℵ₀, u, l)
+    _BandedMatrix(Hcat(Ac_fd.data, reverse(conj(b.args[1])) * Ones{T}(1,∞)), ℵ₀, u, l)
 end
 
 function BandedMatrix(Ac::Transpose{T,<:PertToeplitz}) where T
     A = parent(Ac)
     l,u = bandwidths(A)
     a,b = A.data.args
     Ac_fd = BandedMatrix(transpose(_BandedMatrix(Hcat(a, b[:,1:l+1]), size(a,2)+l, l, u)))
-    _BandedMatrix(Hcat(Ac_fd.data, reverse(b.args[1]) * Ones{T}(1,∞)), ℵ₀, u, l)
+    _BandedMatrix(Hcat(Ac_fd.data, reverse(b.args[1]) * Ones{T}(1,∞)), ℵ₀, u, l)
 end
 
 
@@ -231,7 +231,7 @@ end
 function BandedMatrix(A::PertToeplitz{T}, (l,u)::Tuple{Int,Int}) where T
     @assert A.u == u # Not implemented
     a, b = A.data.args
-    t = b.args[1] # topelitz part
+    t = b.args[1] # topelitz part
     t_pad = vcat(t,Zeros(l-A.l))
     data = Hcat([vcat(a,Zeros{T}(l-A.l,size(a,2))) repeat(t_pad,1,l)], t_pad * Ones{T}(1,∞))
     _BandedMatrix(data, ℵ₀, l, u)
@@ -509,7 +509,7 @@ copyto!(dest::AbstractArray, L::Ldiv{BidiagonalToeplitzLayout,Lay}) where Lay =
 
 # copy for AdjOrTrans
 copy(A::Adjoint{T,<:BandedMatrix{T,<:Any,OneToInf{Int}}}) where T = copy(parent(A))'
-copy(A::Transpose{T,<:BandedMatrix{T,<:Any,OneToInf{Int}}}) where T = transpose(copy(parent(A))) 
+copy(A::Transpose{T,<:BandedMatrix{T,<:Any,OneToInf{Int}}}) where T = transpose(copy(parent(A)))
 
 
 ##

src/banded/infqltoeplitz.jl

@@ -191,4 +191,4 @@ ql(A::InfToeplitz; kwds...) = _inf_ql(A; kwds...)
 ql(A::PertToeplitz; kwds...) = _inf_ql(A; kwds...)
 
 ql(A::Adjoint{<:Any,<:InfToeplitz}) = ql(BandedMatrix(A))
-ql(A::Adjoint{<:Any,<:PertToeplitz}) = ql(BandedMatrix(A))
+ql(A::Adjoint{<:Any,<:PertToeplitz}) = ql(BandedMatrix(A))

src/blockbanded/infblocktridiagonal.jl

@@ -86,4 +86,4 @@ function BlockBandedMatrix(A::BlockTriPertToeplitz{T}, (l,u)::NTuple{2,Int}) whe
     B = _BlockSkylineMatrix(Vcat(data,tl), BlockSkylineSizes(A, (l,u)))
 end
 
-BlockBandedMatrix(A::BlockTriPertToeplitz) = BlockBandedMatrix(A, blockbandwidths(A))
+BlockBandedMatrix(A::BlockTriPertToeplitz) = BlockBandedMatrix(A, blockbandwidths(A))

src/infcholesky.jl

@@ -18,7 +18,7 @@ MemoryLayout(::Type{AdaptiveCholeskyFactors{T,DM,M}}) where {T,DM,M} = AdaptiveL
 
 
 function partialcholesky!(F::AdaptiveCholeskyFactors{T,<:BandedMatrix}, n::Int) where T
-    if n > F.ncols 
+    if n > F.ncols
         _,u = bandwidths(F.data.array)
         resizedata!(F.data,n+u,n+u);
         ncols = F.ncols
@@ -106,4 +106,4 @@ function ldiv!(R::UpperTriangular{<:Any,<:AdaptiveCholeskyFactors}, B::CachedVec
     partialcholesky!(parent(R), n)
     ldiv!(UpperTriangular(view(parent(R).data.data,oneto(n),oneto(n))), view(B.data,oneto(n)))
     B
-end
+end

src/infconv.jl

@@ -38,11 +38,11 @@ end
 
 
 function conv(r::InfRanges, x::AbstractVector)
-    length(x) ≠ 1 && throw(ArgumentError("conv(::$(typeof(r)), ::$(typeof(x))) not implemented"))
+    length(x) ≠ 1 && throw(ArgumentError("conv(::$(typeof(r)), ::$(typeof(x))) not implemented"))
     first(x)*r
 end
 function conv(x::AbstractVector, r::InfRanges)
-    length(x) ≠ 1 && throw(ArgumentError("conv(::$(typeof(r)), ::$(typeof(x))) not implemented"))
+    length(x) ≠ 1 && throw(ArgumentError("conv(::$(typeof(r)), ::$(typeof(x))) not implemented"))
     first(x)*r
 end
 

src/infql.jl

@@ -26,8 +26,8 @@ function tailiterate!(X::AbstractMatrix{T}) where T
     c,a,b = X[1,:]
     h = zero(T)
     for _=1:10_000_000
-        QL = ql!(X)     
-        if h == X[1,3] 
+        QL = ql!(X)
+        if h == X[1,3]
             return QL
         end
         h = X[1,3]
@@ -52,17 +52,17 @@ function qltail(Z::Number, A::Number, B::Number)
 
     e = sqrt(n^2 - abs2(B))
     d = σ*e*Z/n
- 
+
     ql!([Z A B; 0 d e])
 end
 
 
 ql_hessenberg(A::InfBandedMatrix{T}; kwds...) where T = ql_hessenberg!(BandedMatrix(A, (bandwidth(A,1)+bandwidth(A,2),bandwidth(A,2))); kwds...)
 
-toeptail(B::BandedMatrix{T}) where T = 
+toeptail(B::BandedMatrix{T}) where T =
     _BandedMatrix(B.data.args[end].args[1][1:end-B.u]*Ones{T}(1,∞), size(B,1), B.l-B.u, B.u)
 
-# asymptotics of A[:,j:end] as j -> ∞  
+# asymptotics of A[:,j:end] as j -> ∞
 rightasymptotics(d::Hcat) = last(d.args)
 rightasymptotics(d::Vcat) = Vcat(rightasymptotics.(d.args)...)
 rightasymptotics(d) = d
@@ -81,12 +81,12 @@ function ql_hessenberg!(B::InfBandedMatrix{TT}; kwds...) where TT
     B̃[end,end] = L∞[1,1]
     B̃[end:end,end-l+1:end-1] = adjoint(Q∞)[1:1,1:l-1]*T[l:2(l-1),1:l-1]
     F = ql!(B̃)
-    
-    # fill in data with L∞
+
+    # fill in data with L∞
     B̃ = _BandedMatrix(B̃.data, size(data,2)+l, l,u)
     B̃[size(data,2)+1:end,end-l+1:end] = adjoint(Q∞)[2:l+1,1:l+1] * T[l:2l,1:l]
 
-    
+
     # combine finite and infinite data
     H = Hcat(B̃.data, rightasymptotics(F∞.factors.data))
     QLHessenberg(_BandedMatrix(H, ℵ₀, l, 1), Vcat( LowerHessenbergQ(F.Q).q, F∞.q))
@@ -103,7 +103,7 @@ nzzeros(A::AbstractArray, k) = size(A,k)
 nzzeros(::Zeros, k) = 0
 nzzeros(B::Vcat, k) = sum(size.(B.args[1:end-1],k))
 nzzeros(B::CachedArray, k) = max(B.datasize[k], nzzeros(B.array,k))
-function nzzeros(B::AbstractMatrix, k) 
+function nzzeros(B::AbstractMatrix, k)
     l,u = bandwidths(B)
     k == 1 ? size(B,2) + l : size(B,1) + u
 end
@@ -176,7 +176,7 @@ end
 function _lmul_cache(A::AbstractMatrix{T}, x::AbstractVector{S}) where {T,S}
     TS = promote_op(matprod, T, S)
     lmul!(A, cache(convert(AbstractVector{TS},x)))
-end    
+end
 
 (*)(A::QLPackedQ{T,<:InfBandedMatrix}, x::AbstractVector) where {T} = _lmul_cache(A, x)
 (*)(A::Adjoint{T,<:QLPackedQ{T,<:InfBandedMatrix}}, x::AbstractVector) where {T} = _lmul_cache(A, x)
@@ -190,7 +190,7 @@ function blocktailiterate(c,a,b, d=c, e=a)
         X = [c a b; z d e]
         F = ql!(X)
         d̃,ẽ = F.L[1:2,1:2], F.L[1:2,3:4]
-        
+
         d̃,ẽ = QLPackedQ(F.factors[1:2,3:4],F.τ[1:2])*d̃,QLPackedQ(F.factors[1:2,3:4],F.τ[1:2])*ẽ  # undo last rotation
         if ≈(d̃, d; atol=1E-10) && ≈(ẽ, e; atol=1E-10)
             X[1:2,1:2] = d̃; X[1:2,3:4] = ẽ
@@ -211,7 +211,7 @@ function _blocktripert_ql(A, d, e)
     c,a,b = A[Block(N+1,N)],A[Block(N,N)],A[Block(N-1,N)]
     P,τ = blocktailiterate(c,a,b,d,e)
     B = BlockBandedMatrix(A,(2,1))
-    
+
 
     BB = _BlockBandedMatrix(B.data.args[1], (fill(2,N+2), fill(2,N)), (2,1))
     BB[Block(N),Block.(N-1:N)] .= P[Block(1), Block.(1:2)]
@@ -290,7 +290,7 @@ function materialize!(M::MatLdivVec{<:TriangularLayout{'L','N',BandedColumns{Per
     @inbounds for j in 1:n
         iszero(data[j,j]) && throw(SingularException(j))
         bj = b[j] = data[j,j] \ b[j]
-        allzero = j > nz && iszero(bj)
+        allzero = j > nz && iszero(bj)
         for i in (j+1:n) ∩ colsupport(data,j)
             b[i] -= data[i,j] * bj
             allzero = allzero && iszero(b[i])
@@ -316,7 +316,7 @@ function _ql(::SymTridiagonalLayout, ::NTuple{2,OneToInf{Int}}, A, args...; kwds
     T = eltype(A)
     d,d∞ = _data_tail(A.dv)
     ev,ev∞ = _data_tail(A.ev)
-    
+
     m = max(length(d), length(ev)+1)
     dat = zeros(T, 3, m)
     dat[1,2:1+length(ev)] .= ev
@@ -338,7 +338,7 @@ function _ql(::TridiagonalLayout, ::NTuple{2,OneToInf{Int}}, A, args...; kwds...
     d,d∞ = _data_tail(A.d)
     dl,dl∞ = _data_tail(A.dl)
     du,du∞ = _data_tail(A.du)
-    
+
     m = max(length(d), length(du)+1, length(dl))
     dat = zeros(T, 3, m)
     dat[1,2:1+length(du)] .= du