Fix 3-arg dot for 1x1 structured matrices (#46473)

(cherry picked from commit c3d5009)

Author: dkarrasch

stdlib/LinearAlgebra/src/bidiag.jl

@@ -702,14 +702,15 @@ function dot(x::AbstractVector, B::Bidiagonal, y::AbstractVector)
     require_one_based_indexing(x, y)
     nx, ny = length(x), length(y)
     (nx == size(B, 1) == ny) || throw(DimensionMismatch())
-    if iszero(nx)
-        return dot(zero(eltype(x)), zero(eltype(B)), zero(eltype(y)))
+    if nx ≤ 1
+        nx == 0 && return dot(zero(eltype(x)), zero(eltype(B)), zero(eltype(y)))
+        return dot(x[1], B.dv[1], y[1])
     end
     ev, dv = B.ev, B.dv
-    if B.uplo == 'U'
+    @inbounds if B.uplo == 'U'
         x₀ = x[1]
         r = dot(x[1], dv[1], y[1])
-        @inbounds for j in 2:nx-1
+        for j in 2:nx-1
             x₋, x₀ = x₀, x[j]
             r += dot(adjoint(ev[j-1])*x₋ + adjoint(dv[j])*x₀, y[j])
         end
@@ -719,7 +720,7 @@ function dot(x::AbstractVector, B::Bidiagonal, y::AbstractVector)
         x₀ = x[1]
         x₊ = x[2]
         r = dot(adjoint(dv[1])*x₀ + adjoint(ev[1])*x₊, y[1])
-        @inbounds for j in 2:nx-1
+        for j in 2:nx-1
             x₀, x₊ = x₊, x[j+1]
             r += dot(adjoint(dv[j])*x₀ + adjoint(ev[j])*x₊, y[j])
         end

stdlib/LinearAlgebra/src/tridiag.jl

@@ -256,21 +256,24 @@ end
 function dot(x::AbstractVector, S::SymTridiagonal, y::AbstractVector)
     require_one_based_indexing(x, y)
     nx, ny = length(x), length(y)
-    (nx == size(S, 1) == ny) || throw(DimensionMismatch())
-    if iszero(nx)
-        return dot(zero(eltype(x)), zero(eltype(S)), zero(eltype(y)))
+    (nx == size(S, 1) == ny) || throw(DimensionMismatch("dot"))
+    if nx ≤ 1
+        nx == 0 && return dot(zero(eltype(x)), zero(eltype(S)), zero(eltype(y)))
+        return dot(x[1], S.dv[1], y[1])
     end
     dv, ev = S.dv, S.ev
-    x₀ = x[1]
-    x₊ = x[2]
-    sub = transpose(ev[1])
-    r = dot(adjoint(dv[1])*x₀ + adjoint(sub)*x₊, y[1])
-    @inbounds for j in 2:nx-1
-        x₋, x₀, x₊ = x₀, x₊, x[j+1]
-        sup, sub = transpose(sub), transpose(ev[j])
-        r += dot(adjoint(sup)*x₋ + adjoint(dv[j])*x₀ + adjoint(sub)*x₊, y[j])
-    end
-    r += dot(adjoint(transpose(sub))*x₀ + adjoint(dv[nx])*x₊, y[nx])
+    @inbounds begin
+        x₀ = x[1]
+        x₊ = x[2]
+        sub = transpose(ev[1])
+        r = dot(adjoint(dv[1])*x₀ + adjoint(sub)*x₊, y[1])
+        for j in 2:nx-1
+            x₋, x₀, x₊ = x₀, x₊, x[j+1]
+            sup, sub = transpose(sub), transpose(ev[j])
+            r += dot(adjoint(sup)*x₋ + adjoint(dv[j])*x₀ + adjoint(sub)*x₊, y[j])
+        end
+        r += dot(adjoint(transpose(sub))*x₀ + adjoint(dv[nx])*x₊, y[nx])
+    end
     return r
 end
 
@@ -841,18 +844,21 @@ function dot(x::AbstractVector, A::Tridiagonal, y::AbstractVector)
     require_one_based_indexing(x, y)
     nx, ny = length(x), length(y)
     (nx == size(A, 1) == ny) || throw(DimensionMismatch())
-    if iszero(nx)
-        return dot(zero(eltype(x)), zero(eltype(A)), zero(eltype(y)))
-    end
-    x₀ = x[1]
-    x₊ = x[2]
-    dl, d, du = A.dl, A.d, A.du
-    r = dot(adjoint(d[1])*x₀ + adjoint(dl[1])*x₊, y[1])
-    @inbounds for j in 2:nx-1
-        x₋, x₀, x₊ = x₀, x₊, x[j+1]
-        r += dot(adjoint(du[j-1])*x₋ + adjoint(d[j])*x₀ + adjoint(dl[j])*x₊, y[j])
-    end
-    r += dot(adjoint(du[nx-1])*x₀ + adjoint(d[nx])*x₊, y[nx])
+    if nx ≤ 1
+        nx == 0 && return dot(zero(eltype(x)), zero(eltype(A)), zero(eltype(y)))
+        return dot(x[1], A.d[1], y[1])
+    end
+    @inbounds begin
+        x₀ = x[1]
+        x₊ = x[2]
+        dl, d, du = A.dl, A.d, A.du
+        r = dot(adjoint(d[1])*x₀ + adjoint(dl[1])*x₊, y[1])
+        for j in 2:nx-1
+            x₋, x₀, x₊ = x₀, x₊, x[j+1]
+            r += dot(adjoint(du[j-1])*x₋ + adjoint(d[j])*x₀ + adjoint(dl[j])*x₊, y[j])
+        end
+        r += dot(adjoint(du[nx-1])*x₀ + adjoint(d[nx])*x₊, y[nx])
+    end
     return r
 end
 

stdlib/LinearAlgebra/test/bidiag.jl

@@ -623,22 +623,22 @@ end
 end
 
 @testset "generalized dot" begin
-    for elty in (Float64, ComplexF64)
-        dv = randn(elty, 5)
-        ev = randn(elty, 4)
-        x = randn(elty, 5)
-        y = randn(elty, 5)
+    for elty in (Float64, ComplexF64), n in (5, 1)
+        dv = randn(elty, n)
+        ev = randn(elty, n-1)
+        x = randn(elty, n)
+        y = randn(elty, n)
         for uplo in (:U, :L)
             B = Bidiagonal(dv, ev, uplo)
-            @test dot(x, B, y) ≈ dot(B'x, y) ≈ dot(x, Matrix(B), y)
+            @test dot(x, B, y) ≈ dot(B'x, y) ≈ dot(x, B*y) ≈ dot(x, Matrix(B), y)
         end
         dv = Vector{elty}(undef, 0)
         ev = Vector{elty}(undef, 0)
         x = Vector{elty}(undef, 0)
         y = Vector{elty}(undef, 0)
         for uplo in (:U, :L)
             B = Bidiagonal(dv, ev, uplo)
-            @test dot(x, B, y) ≈ dot(zero(elty), zero(elty), zero(elty))
+            @test dot(x, B, y) === zero(elty)
         end
     end
 end

stdlib/LinearAlgebra/test/tridiag.jl

@@ -434,7 +434,11 @@ end
         @testset "generalized dot" begin
             x = fill(convert(elty, 1), n)
             y = fill(convert(elty, 1), n)
-            @test dot(x, A, y) ≈ dot(A'x, y)
+            @test dot(x, A, y) ≈ dot(A'x, y) ≈ dot(x, A*y)
+            @test dot([1], SymTridiagonal([1], Int[]), [1]) == 1
+            @test dot([1], Tridiagonal(Int[], [1], Int[]), [1]) == 1
+            @test dot(Int[], SymTridiagonal(Int[], Int[]), Int[]) === 0
+            @test dot(Int[], Tridiagonal(Int[], Int[], Int[]), Int[]) === 0
         end
     end
 end