Make strides into a generic trait

Returns `nothing` for non-strided arrays, otherwise gives the
give strides in memory. Useful as an extensible trait in generic
contexts, and simpler to overload for cases of "wrapped" arrays where
"stridedness" can be deferred to the parent rather than a complex
(and inextensible) method signature.

base/abstractarray.jl

@@ -311,7 +311,9 @@ last(a) = a[end]
 """
     strides(A)
 
-Return a tuple of the memory strides in each dimension.
+Return a tuple of the memory strides in each dimension, for an `AbstractArray` with a
+strided memory layout. For arrays with a non-strided layout (such as sparse arrays), return
+`nothing`.
 
 # Examples
 ```jldoctest
@@ -321,7 +323,7 @@ julia> strides(A)
 (1, 3, 12)
 ```
 """
-function strides end
+strides(::AbstractArray) = nothing
 
 """
     stride(A, k::Integer)
@@ -339,7 +341,14 @@ julia> stride(A,3)
 12
 ```
 """
-stride(A::AbstractArray, k::Integer) = strides(A)[k]
+function stride(A::AbstractArray, k::Integer)
+    str = strides(A)
+    if str === nothing
+        return nothing
+    else
+        return str[k]
+    end
+end
 
 @inline size_to_strides(s, d, sz...) = (s, size_to_strides(s * d, sz...)...)
 size_to_strides(s, d) = (s,)

base/permuteddimsarray.jl

@@ -60,7 +60,11 @@ Base.pointer(A::PermutedDimsArray, i::Integer) = throw(ArgumentError("pointer(A,
 
 function Base.strides(A::PermutedDimsArray{T,N,perm}) where {T,N,perm}
     s = strides(parent(A))
-    ntuple(d->s[perm[d]], Val(N))
+    if s === nothing
+        return nothing
+    else
+        return ntuple(d->s[perm[d]], Val(N))
+    end
 end
 
 @inline function Base.getindex(A::PermutedDimsArray{T,N,perm,iperm}, I::Vararg{Int,N}) where {T,N,perm,iperm}

stdlib/LinearAlgebra/src/adjtrans.jl

@@ -155,6 +155,25 @@ vec(v::TransposeAbsVec) = parent(v)
 cmp(A::AdjOrTransAbsVec, B::AdjOrTransAbsVec) = cmp(parent(A), parent(B))
 isless(A::AdjOrTransAbsVec, B::AdjOrTransAbsVec) = isless(parent(A), parent(B))
 
+# provide strides, but only for eltypes that are directly stored in memory (i.e. unaffected
+# by recursive `adjoint` and `transpose`, being `Real` and `Number` respectively)
+function Base.strides(a::Union{Adjoint{<:Real, <:AbstractVector}, Transpose{<:Number, <:AbstractVector}})
+    str = strides(a.parent)
+    if str === nothing
+        return nothing
+    else
+        return (1, str[1])
+    end
+end
+function Base.strides(a::Union{Adjoint{<:Real, <:AbstractMatrix}, Transpose{<:Number, <:AbstractMatrix}})
+    str = strides(a.parent)
+    if str === nothing
+        return nothing
+    else
+        return (str[2], str[1])
+    end
+end
+
 ### concatenation
 # preserve Adjoint/Transpose wrapper around vectors
 # to retain the associated semantics post-concatenation