Added @materialize convenience DSL

src/LazyArrays.jl

@@ -60,10 +60,11 @@ end
 
 export Mul, Applied, MulArray, MulVector, MulMatrix, InvMatrix, PInvMatrix,
         Hcat, Vcat, Kron, BroadcastArray, BroadcastMatrix, BroadcastVector, cache, Ldiv, Inv, PInv, Diff, Cumsum,
-        applied, materialize, materialize!, ApplyArray, ApplyMatrix, ApplyVector, apply, ⋆, @~, LazyArray
+        applied, materialize, materialize!, @materialize, ApplyArray, ApplyMatrix, ApplyVector, apply, ⋆, @~, LazyArray
 
 
 include("lazyapplying.jl")
+include("materialize_dsl.jl")
 include("lazybroadcasting.jl")
 include("linalg/linalg.jl")
 include("cache.jl")

src/materialize_dsl.jl

@@ -0,0 +1,124 @@
+# For unparametrized destination types
+generate_copyto!_signature(dest, dest_type::Symbol, Msig) =
+    :(Base.copyto!($(dest)::$(dest_type), applied_obj::$(Msig)))
+
+# For parametrized destination types
+function generate_copyto!_signature(dest, dest_type::Expr, Msig)
+    dest_type.head == :curly ||
+        throw(ArgumentError("Invalid destination specification $(dest)::$(dest_type)"))
+    :(Base.copyto!($(dest)::$(dest_type), applied_obj::$(Msig)) where {$(dest_type.args[2:end]...)})
+end
+
+function generate_copyto!(body, factor_names, Msig)
+    body.head == :(->) ||
+        throw(ArgumentError("Invalid copyto! specification"))
+    body.args[1].head == :(::) ||
+        throw(ArgumentError("Invalid destination specification $(body.args[1])"))
+    (dest,dest_type) = body.args[1].args
+    copyto!_signature = generate_copyto!_signature(dest, dest_type, Msig)
+    f_body = quote
+        axes($dest) == axes(applied_obj) || throw(DimensionMismatch("axes must be same"))
+        $(factor_names) = applied_obj.args
+        $(body.args[2].args...)
+        $(dest)
+    end
+    Expr(:function, copyto!_signature, f_body)
+end
+
+"""
+    @materialize function op(args...)
+
+This macro simplifies the setup of a few functions necessary for the
+materialization of [`Applied`](@ref) objects:
+
+- `ApplyStyle`, used to ensure dispatch of the applied object to the
+  routines below
+
+- `copyto!(dest::DestType, applied_obj::Applied{...,op})` performs the
+  actual materialization of `applied_obj` into the destination object
+  which has been generated by
+
+- `similar` which usually returns a suitable matrix
+
+- `materialize` which makes use of the above functions
+
+# Example
+
+```julia
+@materialize function *(Ac::MyAdjointBasis,
+                        O::MyOperator,
+                        B::MyBasis)
+    MyApplyStyle # An instance of this type will be returned by ApplyStyle
+    T -> begin # generates similar
+        A = parent(Ac)
+        parent(A) == parent(B) ||
+            throw(ArgumentError("Incompatible bases"))
+
+        # There may be different matrices best representing different
+        # situations:
+        if ...
+            Diagonal(Vector{T}(undef, size(B,1)))
+        else
+            Tridiagonal(Vector{T}(undef, size(B,1)-1),
+                        Vector{T}(undef, size(B,1)),
+                        Vector{T}(undef, size(B,1)-1))
+        end
+    end
+    dest::Diagonal{T} -> begin # generate copyto!(dest::Diagonal{T}, ...) where T
+        dest.diag .= 1
+    end
+    dest::Tridiagonal{T} -> begin # generate copyto!(dest::Tridiagonal{T}, ...) where T
+        dest.dl .= -2
+        dest.ev .= 1
+        dest.du .= 3
+    end
+end
+```
+"""
+macro materialize(expr)
+    expr.head == :function || expr.head == :(=) || error("Must start with a function")
+    @assert expr.args[1].head == :call
+    op = expr.args[1].args[1]
+
+    bodies = filter(e -> !(e isa LineNumberNode), expr.args[2].args)
+    length(bodies) < 3 &&
+        throw(ArgumentError("At least three blocks required (ApplyStyle, similar, and at least one copyto!)"))
+
+    factor_types = :(<:Tuple{})
+    factor_names = :(())
+    apply_style = first(bodies)
+    apply_style_fun = :(LazyArrays.ApplyStyle(::typeof($op)) = $(apply_style)())
+
+    # Generate Applied signature
+    for arg in expr.args[1].args[2:end]
+        arg isa Expr && arg.head == :(::) ||
+            throw(ArgumentError("Invalid argument specification $(arg)"))
+        arg_name, arg_typ = arg.args
+        push!(factor_types.args[1].args, :(<:$(arg_typ)))
+        push!(factor_names.args, arg_name)
+        push!(apply_style_fun.args[1].args, :(::Type{<:$(arg_typ)}))
+    end
+    Msig = :(LazyArrays.Applied{$(apply_style), typeof($op), $(factor_types)})
+
+    sim_body = bodies[2]
+    sim_body.head == :(->) ||
+        throw(ArgumentError("Invalid similar specification"))
+    T = first(sim_body.args)
+
+    copytos! = map(body -> generate_copyto!(body, factor_names, Msig), bodies[3:end])
+
+    f = quote
+        $(apply_style_fun)
+
+        function Base.similar(applied_obj::$Msig, ::Type{$T}=eltype(applied_obj)) where $T
+            $(factor_names) = applied_obj.args
+            $(sim_body.args[2])
+        end
+
+        $(copytos!...)
+
+        LazyArrays.materialize(applied_obj::$Msig) =
+            copyto!(similar(applied_obj, eltype(applied_obj)), applied_obj)
+    end
+    esc(f)
+end

test/materialize_dsl.jl

@@ -0,0 +1,59 @@
+struct MyOperator{T}
+    n::Int
+    kind::Symbol
+end
+
+Base.axes(O::MyOperator) = (Base.OneTo(O.n),Base.OneTo(O.n))
+Base.axes(O::MyOperator,i) = axes(O)[i]
+Base.size(O::MyOperator) = (O.n,O.n)
+Base.eltype(::MyOperator{T}) where T = T
+
+struct MyApplyStyle <: ApplyStyle end
+
+@materialize function *(Ac::Adjoint{<:Any,<:AbstractMatrix},
+                        O::MyOperator,
+                        B::AbstractMatrix)
+    MyApplyStyle
+    T -> begin
+        A = parent(Ac)
+
+        if O.kind == :diagonal
+            Diagonal(Vector{T}(undef, O.n))
+        else
+            Tridiagonal(Vector{T}(undef, O.n-1),
+                        Vector{T}(undef, O.n),
+                        Vector{T}(undef, O.n-1))
+        end
+    end
+    dest::Diagonal{T} -> begin
+        dest.diag .= 1
+    end
+    dest::Tridiagonal{T} -> begin
+        dest.dl .= -2
+        dest.d .= 1
+        dest.du .= 3
+    end
+end
+
+@testset "Materialize DSL" begin
+    o = ones(10)
+    M = ones(10,10)
+    D = MyOperator{Float64}(10, :diagonal)
+    T = MyOperator{ComplexF64}(10, :tridiagonal)
+
+    @test LazyArrays.ApplyStyle(*, typeof(M'), typeof(D), typeof(M)) == MyApplyStyle()
+    @test LazyArrays.ApplyStyle(*, typeof(M'), typeof(T), typeof(M)) == MyApplyStyle()
+
+    d = apply(*, M', D, M)
+    @test d isa Diagonal{Float64}
+    @test all(d.diag .== 1)
+
+    t = apply(*, M', T, M)
+    @test t isa Tridiagonal
+    @test all(t.dl .== -2)
+    @test all(t.d .== 1)
+    @test all(t.du .== 3)
+
+    M̃ = ones(11,11)
+    @test_throws DimensionMismatch apply(*, M̃', D, M̃)
+end

test/runtests.jl

@@ -1,6 +1,7 @@
 using Test, LinearAlgebra, LazyArrays, StaticArrays, FillArrays, ArrayLayouts
 import LazyArrays: CachedArray, colsupport, rowsupport, LazyArrayStyle, broadcasted,
-            PaddedLayout, ApplyLayout, BroadcastLayout, AddArray, LazyLayout
+    PaddedLayout, ApplyLayout, BroadcastLayout, AddArray, LazyLayout,
+    ApplyStyle
 
 @testset "Lazy MemoryLayout" begin
     @testset "ApplyArray" begin
@@ -25,6 +26,7 @@ import LazyArrays: CachedArray, colsupport, rowsupport, LazyArrayStyle, broadcas
     end
 end
 include("applytests.jl")
+include("materialize_dsl.jl")
 include("multests.jl")
 include("ldivtests.jl")
 include("addtests.jl")
@@ -341,4 +343,4 @@ end
     @test exp.(transpose(v)) isa BroadcastMatrix
     @test exp.(M') isa BroadcastMatrix
     @test exp.(transpose(M)) isa BroadcastMatrix
-end
+end