Fix initialization of accumulators in _generic_matmatmul! (#27123)

Remove some redundant methods related to multiplication of Adjoint/Transpose

Expand multi-line functions to multiple lines instead of using one-line
syntax with ;s

Author: andreasnoack

stdlib/LinearAlgebra/src/adjtrans.jl

@@ -204,13 +204,16 @@ end
 *(u::AdjointAbsVec, v::AdjointAbsVec) = throw(MethodError(*, (u, v)))
 *(u::TransposeAbsVec, v::TransposeAbsVec) = throw(MethodError(*, (u, v)))
 
-# Adjoint/Transpose-vector * matrix
-*(u::AdjointAbsVec, A::AbstractMatrix) = adjoint(adjoint(A) * u.parent)
-*(u::TransposeAbsVec, A::AbstractMatrix) = transpose(transpose(A) * u.parent)
-# Adjoint/Transpose-vector * Adjoint/Transpose-matrix
-*(u::AdjointAbsVec, A::Adjoint{<:Any,<:AbstractMatrix}) = adjoint(A.parent * u.parent)
-*(u::TransposeAbsVec, A::Transpose{<:Any,<:AbstractMatrix}) = transpose(A.parent * u.parent)
-
+# AdjOrTransAbsVec{<:Any,<:AdjOrTransAbsVec} is a lazy conj vectors
+# We need to expand the combinations to avoid ambiguities
+(*)(u::TransposeAbsVec, v::AdjointAbsVec{<:Any,<:TransposeAbsVec}) =
+    sum(uu*vv for (uu, vv) in zip(u, v))
+(*)(u::AdjointAbsVec,   v::AdjointAbsVec{<:Any,<:TransposeAbsVec}) =
+    sum(uu*vv for (uu, vv) in zip(u, v))
+(*)(u::TransposeAbsVec, v::TransposeAbsVec{<:Any,<:AdjointAbsVec}) =
+    sum(uu*vv for (uu, vv) in zip(u, v))
+(*)(u::AdjointAbsVec,   v::TransposeAbsVec{<:Any,<:AdjointAbsVec}) =
+    sum(uu*vv for (uu, vv) in zip(u, v))
 
 ## pseudoinversion
 pinv(v::AdjointAbsVec, tol::Real = 0) = pinv(v.parent, tol).parent
@@ -226,16 +229,3 @@ pinv(v::TransposeAbsVec, tol::Real = 0) = pinv(conj(v.parent)).parent
 /(u::TransposeAbsVec, A::AbstractMatrix) = transpose(transpose(A) \ u.parent)
 /(u::AdjointAbsVec, A::Transpose{<:Any,<:AbstractMatrix}) = adjoint(conj(A.parent) \ u.parent) # technically should be adjoint(copy(adjoint(copy(A))) \ u.parent)
 /(u::TransposeAbsVec, A::Adjoint{<:Any,<:AbstractMatrix}) = transpose(conj(A.parent) \ u.parent) # technically should be transpose(copy(transpose(copy(A))) \ u.parent)
-
-# dismabiguation methods
-*(A::AdjointAbsVec, B::Transpose{<:Any,<:AbstractMatrix}) = A * copy(B)
-*(A::TransposeAbsVec, B::Adjoint{<:Any,<:AbstractMatrix}) = A * copy(B)
-*(A::Transpose{<:Any,<:AbstractMatrix}, B::Adjoint{<:Any,<:AbstractMatrix}) = copy(A) * B
-*(A::Adjoint{<:Any,<:AbstractMatrix}, B::Transpose{<:Any,<:AbstractMatrix}) = A * copy(B)
-# Adj/Trans-vector * Trans/Adj-vector, shouldn't exist, here for ambiguity resolution? TODO: test removal
-*(A::Adjoint{<:Any,<:AbstractVector}, B::Transpose{<:Any,<:AbstractVector}) = throw(MethodError(*, (A, B)))
-*(A::Transpose{<:Any,<:AbstractVector}, B::Adjoint{<:Any,<:AbstractVector}) = throw(MethodError(*, (A, B)))
-# Adj/Trans-matrix * Trans/Adj-vector, shouldn't exist, here for ambiguity resolution? TODO: test removal
-*(A::Adjoint{<:Any,<:AbstractMatrix}, B::Adjoint{<:Any,<:AbstractVector}) = throw(MethodError(*, (A, B)))
-*(A::Adjoint{<:Any,<:AbstractMatrix}, B::Transpose{<:Any,<:AbstractVector}) = throw(MethodError(*, (A, B)))
-*(A::Transpose{<:Any,<:AbstractMatrix}, B::Adjoint{<:Any,<:AbstractVector}) = throw(MethodError(*, (A, B)))