Disallow Bool indices in structured matrix indexing (#54475)

Currently,
```julia
julia> B = Bidiagonal(1:3, 1:2, :U)
3×3 Bidiagonal{Int64, UnitRange{Int64}}:
 1  1  ⋅
 ⋅  2  2
 ⋅  ⋅  3

julia> B[3, true]
0

julia> Matrix(B)[3, true]
ERROR: ArgumentError: invalid index: true of type Bool
```
This PR changes the behavior to
```julia
julia> B[3, true]
ERROR: ArgumentError: invalid index: true of type Bool
```

stdlib/LinearAlgebra/src/bidiag.jl

@@ -156,7 +156,7 @@ end
     end
 end
 
-@inline function getindex(A::Bidiagonal{T}, i::Integer, j::Integer) where T
+@inline function getindex(A::Bidiagonal{T}, i::Int, j::Int) where T
     @boundscheck checkbounds(A, i, j)
     if i == j
         return @inbounds A.dv[i]

stdlib/LinearAlgebra/src/hessenberg.jl

@@ -87,7 +87,7 @@ end
 Base.isassigned(H::UpperHessenberg, i::Int, j::Int) =
     i <= j+1 ? isassigned(H.data, i, j) : true
 
-Base.@propagate_inbounds getindex(H::UpperHessenberg{T}, i::Integer, j::Integer) where {T} =
+Base.@propagate_inbounds getindex(H::UpperHessenberg{T}, i::Int, j::Int) where {T} =
     i <= j+1 ? convert(T, H.data[i,j]) : zero(T)
 
 Base.@propagate_inbounds function setindex!(A::UpperHessenberg, x, i::Integer, j::Integer)

stdlib/LinearAlgebra/src/symmetric.jl

@@ -233,7 +233,7 @@ axes(A::HermOrSym) = axes(A.data)
     end
 end
 
-@inline function getindex(A::Symmetric, i::Integer, j::Integer)
+@inline function getindex(A::Symmetric, i::Int, j::Int)
     @boundscheck checkbounds(A, i, j)
     @inbounds if i == j
         return symmetric(A.data[i, j], sym_uplo(A.uplo))::symmetric_type(eltype(A.data))
@@ -243,7 +243,7 @@ end
         return transpose(A.data[j, i])
     end
 end
-@inline function getindex(A::Hermitian, i::Integer, j::Integer)
+@inline function getindex(A::Hermitian, i::Int, j::Int)
     @boundscheck checkbounds(A, i, j)
     @inbounds if i == j
         return hermitian(A.data[i, j], sym_uplo(A.uplo))::hermitian_type(eltype(A.data))

stdlib/LinearAlgebra/src/triangular.jl

@@ -269,13 +269,13 @@ Base.isstored(A::UnitUpperTriangular, i::Int, j::Int) =
 Base.isstored(A::UpperTriangular, i::Int, j::Int) =
     i <= j ? Base.isstored(A.data, i, j) : false
 
-@propagate_inbounds getindex(A::UnitLowerTriangular{T}, i::Integer, j::Integer) where {T} =
+@propagate_inbounds getindex(A::UnitLowerTriangular{T}, i::Int, j::Int) where {T} =
     i > j ? A.data[i,j] : ifelse(i == j, oneunit(T), zero(T))
-@propagate_inbounds getindex(A::LowerTriangular, i::Integer, j::Integer) =
+@propagate_inbounds getindex(A::LowerTriangular, i::Int, j::Int) =
     i >= j ? A.data[i,j] : _zero(A.data,j,i)
-@propagate_inbounds getindex(A::UnitUpperTriangular{T}, i::Integer, j::Integer) where {T} =
+@propagate_inbounds getindex(A::UnitUpperTriangular{T}, i::Int, j::Int) where {T} =
     i < j ? A.data[i,j] : ifelse(i == j, oneunit(T), zero(T))
-@propagate_inbounds getindex(A::UpperTriangular, i::Integer, j::Integer) =
+@propagate_inbounds getindex(A::UpperTriangular, i::Int, j::Int) =
     i <= j ? A.data[i,j] : _zero(A.data,j,i)
 
 @propagate_inbounds function setindex!(A::UpperTriangular, x, i::Integer, j::Integer)

stdlib/LinearAlgebra/src/tridiag.jl

@@ -445,7 +445,7 @@ end
     end
 end
 
-@inline function getindex(A::SymTridiagonal{T}, i::Integer, j::Integer) where T
+@inline function getindex(A::SymTridiagonal{T}, i::Int, j::Int) where T
     @boundscheck checkbounds(A, i, j)
     if i == j
         return symmetric((@inbounds A.dv[i]), :U)::symmetric_type(eltype(A.dv))
@@ -680,7 +680,7 @@ end
     end
 end
 
-@inline function getindex(A::Tridiagonal{T}, i::Integer, j::Integer) where T
+@inline function getindex(A::Tridiagonal{T}, i::Int, j::Int) where T
     @boundscheck checkbounds(A, i, j)
     if i == j
         return @inbounds A.d[i]

stdlib/LinearAlgebra/test/bidiag.jl

@@ -911,4 +911,11 @@ end
     @test M == B
 end
 
+@testset "getindex with Integers" begin
+    dv, ev = 1:4, 1:3
+    B = Bidiagonal(dv, ev, :U)
+    @test_throws "invalid index" B[3, true]
+    @test B[1,2] == B[Int8(1),UInt16(2)] == B[big(1), Int16(2)]
+end
+
 end # module TestBidiagonal

stdlib/LinearAlgebra/test/hessenberg.jl

@@ -258,5 +258,11 @@ end
     @test copyto!(B, A) == A2
 end
 
+@testset "getindex with Integers" begin
+    M = reshape(1:9, 3, 3)
+    S = UpperHessenberg(M)
+    @test_throws "invalid index" S[3, true]
+    @test S[1,2] == S[Int8(1),UInt16(2)] == S[big(1), Int16(2)]
+end
 
 end # module TestHessenberg

stdlib/LinearAlgebra/test/symmetric.jl

@@ -1062,4 +1062,13 @@ end
     end
 end
 
+@testset "getindex with Integers" begin
+    M = reshape(1:4,2,2)
+    for ST in (Symmetric, Hermitian)
+        S = ST(M)
+        @test_throws "invalid index" S[true, true]
+        @test S[1,2] == S[Int8(1),UInt16(2)] == S[big(1), Int16(2)]
+    end
+end
+
 end # module TestSymmetric

stdlib/LinearAlgebra/test/triangular.jl

@@ -1070,4 +1070,18 @@ end
     end
 end
 
+@testset "getindex with Integers" begin
+    M = reshape(1:4,2,2)
+    for Ttype in (UpperTriangular, UnitUpperTriangular)
+        T = Ttype(M)
+        @test_throws "invalid index" T[2, true]
+        @test T[1,2] == T[Int8(1),UInt16(2)] == T[big(1), Int16(2)]
+    end
+    for Ttype in (LowerTriangular, UnitLowerTriangular)
+        T = Ttype(M)
+        @test_throws "invalid index" T[true, 2]
+        @test T[2,1] == T[Int8(2),UInt16(1)] == T[big(2), Int16(1)]
+    end
+end
+
 end # module TestTriangular

stdlib/LinearAlgebra/test/tridiag.jl

@@ -859,4 +859,12 @@ end
     @test axes(B) === (ax, ax)
 end
 
+@testset "getindex with Integers" begin
+    dv, ev = 1:4, 1:3
+    for S in (Tridiagonal(ev, dv, ev), SymTridiagonal(dv, ev))
+        @test_throws "invalid index" S[3, true]
+        @test S[1,2] == S[Int8(1),UInt16(2)] == S[big(1), Int16(2)]
+    end
+end
+
 end # module TestTridiagonal