Use sparsity in B for Triangular * B and Triangular \ B (#38)

* Use sparsity in B for Triangular * B and Triangular \ B

* Update Project.toml

Author: dlfivefifty

Project.toml

@@ -1,7 +1,7 @@
 name = "ArrayLayouts"
 uuid = "4c555306-a7a7-4459-81d9-ec55ddd5c99a"
 authors = ["Sheehan Olver <[email protected]>"]
-version = "0.4.4"
+version = "0.4.5"
 
 [deps]
 FillArrays = "1a297f60-69ca-5386-bcde-b61e274b549b"

src/mul.jl

@@ -252,3 +252,4 @@ dot(a, b) = materialize(Dot(a, b))
 # We go to generic fallback as layout-arrays are structured
 dot(x, A, y) = dot(x, mul(A, y))
 LinearAlgebra.dot(x::AbstractVector, A::LayoutMatrix, y::AbstractVector) = dot(x, A, y)
+LinearAlgebra.dot(x::AbstractVector, A::Symmetric{<:Real,<:LayoutMatrix}, y::AbstractVector) = dot(x, A, y)

src/triangular.jl

@@ -29,10 +29,11 @@ function materialize!(M::Lmul{<:TriangularLayout{'U','N'}})
         throw(DimensionMismatch("right hand side B needs first dimension of size $(size(A,1)), has size $m"))
     end
     Adata = triangulardata(A)
-    for j = 1:n
-        for i = 1:m
+    for j = rowsupport(B)
+        cs = colsupport(B,j)
+        for i = cs
             Bij = Adata[i,i]*B[i,j]
-            for k = (i + 1:m) ∩ rowsupport(Adata,i)
+            for k = (i + 1:m) ∩ cs ∩ rowsupport(Adata,i)
                 Bij += Adata[i,k]*B[k,j]
             end
             B[i,j] = Bij
@@ -48,10 +49,11 @@ function materialize!(M::Lmul{<:TriangularLayout{'U','U'}})
         throw(DimensionMismatch("right hand side B needs first dimension of size $(size(A,1)), has size $m"))
     end
     Adata = triangulardata(A)
-    for j = 1:n
-        for i = 1:m
+    for j = rowsupport(B)
+        cs = colsupport(B,j)
+        for i = cs
             Bij = B[i,j]
-            for k = (i + 1:m) ∩ rowsupport(Adata,i)
+            for k = (i + 1:m) ∩ cs ∩ rowsupport(Adata,i)
                 Bij += Adata[i,k]*B[k,j]
             end
             B[i,j] = Bij