add weaklaplacian (#165)

* add weaklaplacian

* add test

Author: dlfivefifty

Project.toml

@@ -1,6 +1,6 @@
 name = "ContinuumArrays"
 uuid = "7ae1f121-cc2c-504b-ac30-9b923412ae5c"
-version = "0.16.2"
+version = "0.16.3"
 
 [deps]
 AbstractFFTs = "621f4979-c628-5d54-868e-fcf4e3e8185c"

src/bases/bases.jl

@@ -637,13 +637,18 @@ end
 grammatrix(A) = grammatrix_layout(MemoryLayout(A), A)
 grammatrix_layout(_, A) = error("Not implemented")
 
+
 function grammatrix_layout(::MappedBasisLayouts, P)
     Q = demap(P)
     kr = basismap(P)
     @assert kr isa AbstractAffineQuasiVector
     grammatrix(Q)/kr.A
 end
 
+weaklaplacian(A) = weaklaplacian_layout(MemoryLayout(A), A)
+weaklaplacian_layout(_, A) = weaklaplacian_axis(axes(A,1), A)
+weaklaplacian_axis(::Inclusion{<:Number}, A) = -(diff(A)'diff(A))
+
 function copy(M::Mul{<:AdjointMappedBasisLayouts, <:MappedBasisLayouts})
     A = M.A'
     kr = basismap(A)

test/test_splines.jl

@@ -1,7 +1,7 @@
 using ContinuumArrays, LinearAlgebra, Base64, FillArrays, QuasiArrays, BandedMatrices, Test
 using QuasiArrays: ApplyQuasiArray, ApplyStyle, MemoryLayout, mul, MulQuasiMatrix, Vec
 import LazyArrays: MulStyle, LdivStyle, arguments, applied, apply
-import ContinuumArrays: basis, AdjointBasisLayout, ExpansionLayout, BasisLayout, SubBasisLayout, AdjointMappedBasisLayouts, MappedBasisLayout, plan_grid_transform
+import ContinuumArrays: basis, AdjointBasisLayout, ExpansionLayout, BasisLayout, SubBasisLayout, AdjointMappedBasisLayouts, MappedBasisLayout, plan_grid_transform, weaklaplacian
 
 @testset "Splines" begin
     @testset "HeavisideSpline" begin
@@ -241,6 +241,8 @@ import ContinuumArrays: basis, AdjointBasisLayout, ExpansionLayout, BasisLayout,
         @test A isa BandedMatrix
         @test A == (D*L)'*(D*L) == [1.0 -1 0; -1.0 2.0 -1.0; 0.0 -1.0 1.0]
         @test bandwidths(A) == (1,1)
+
+        @test weaklaplacian(L) == -A
     end
 
     @testset "Views" begin