Support materializing banded * banded with one ∞ dimension (#32)

* Support materializing banded * banded with one ∞ dimension

* Update runtests.jl

Author: dlfivefifty

src/InfiniteLinearAlgebra.jl

@@ -4,7 +4,7 @@ using BlockArrays, BlockBandedMatrices, BandedMatrices, LazyArrays, LazyBandedMa
 
 import Base: +, -, *, /, \, ^, OneTo, getindex, promote_op, _unsafe_getindex, print_matrix_row, size, axes,
             AbstractMatrix, AbstractArray, Matrix, Array, Vector, AbstractVector, Slice,
-            show, getproperty, copy, map, require_one_based_indexing
+            show, getproperty, copy, map, require_one_based_indexing, similar
 import Base.Broadcast: BroadcastStyle, Broadcasted, broadcasted
 
 import ArrayLayouts: colsupport, rowsupport, triangularlayout, MatLdivVec, triangulardata, TriangularLayout, sublayout, _qr, 

src/banded/infbanded.jl

@@ -349,6 +349,18 @@ end
 
 _default_banded_broadcast(bc::Broadcasted, ::Tuple{<:OneToInf,<:Any}) = copy(Broadcasted{LazyArrayStyle{2}}(bc.f, bc.args))
 
+###
+# Banded * Banded
+###
+
+BandedMatrix{T}(::UndefInitializer, axes::Tuple{OneToInf{Int},OneTo{Int}}, lu::NTuple{2,Integer}) where T = 
+    BandedMatrix{T}(undef, map(length,axes), lu)
+
+similar(M::MulAdd{<:AbstractBandedLayout,<:AbstractBandedLayout}, ::Type{T}, axes::Tuple{OneTo{Int},OneToInf{Int}}) where T =
+    transpose(BandedMatrix{T}(undef, reverse(axes), reverse(bandwidths(M))))
+similar(M::MulAdd{<:AbstractBandedLayout,<:AbstractBandedLayout}, ::Type{T}, axes::Tuple{OneToInf{Int},OneTo{Int}}) where T =
+    BandedMatrix{T}(undef, axes, bandwidths(M))
+
 
 ###
 # BandedFill * BandedFill

test/runtests.jl

@@ -100,6 +100,17 @@ end
         @test A*A isa BandedMatrix
         @test (A^2)[1:10,1:10] == (A*A)[1:10,1:10] == (A[1:100,1:100]^2)[1:10,1:10]
         @test (A^3)[1:10,1:10] == (A*A*A)[1:10,1:10]  == ((A*A)*A)[1:10,1:10]  == (A*(A*A))[1:10,1:10] == (A[1:100,1:100]^3)[1:10,1:10]
+
+        @testset "∞ x finite" begin
+            A = BandedMatrix(1 => 1:∞) + BandedMatrix(-1 => Fill(2,∞))
+            B = _BandedMatrix(randn(3,5), ∞, 1,1)
+
+            @test_broken A*B isa BandedMatrix
+            @test B'A isa Transpose{<:Any,<:BandedMatrix}
+
+            @test_broken (A*B)[1:7,1:5] ≈ A[1:7,1:6] * B[1:6,1:5]
+            @test (B'A)[1:5,1:7] ≈ (B')[1:5,1:6] * A[1:6,1:7]
+        end
     end
 
     @testset "BlockTridiagonal" begin