Minor memory optimization for Zernike jacobi matrices (#122)

* Remove unnecessary stored 0s due to symmetry

* adapt size test for smaller data

* increase coverage

Author: TSGut

src/disk.jl

@@ -224,11 +224,7 @@ function zernikejacobibandsX(Z::Zernike)
     du = sqrt.( (dufirst .+ dueven .+ duodd ) ./ quotient)
     dl = sqrt.( (dleven .+ dlodd .+ dlspecial)  ./ quotient)
 
-    return BlockHcat(
-        BlockBroadcastArray(hcat, du, Zeros((axes(n,1),)), dl),
-        Zeros((axes(n,1),Base.OneTo(3))),
-        Zeros((axes(n,1),Base.OneTo(3)))                  
-        )
+    return BlockBroadcastArray(hcat, du, Zeros((axes(n,1),)), dl)
 end
 
 function zernikejacobibandsY(Z::Zernike)
@@ -264,12 +260,8 @@ function zernikejacobibandsY(Z::Zernike)
     dl = (-1) .* (nodd .* kodd .+ neven .* keven) .* Vcat(0 , d)
     du = (-1) .* (nodd .* keven .+ neven .* kodd) .* d[2:end]
 
-    # zero blocks for banded blockarray structure
-    z = Zeros((axes(n,1),))
-    z5 = Zeros((axes(n,1),Base.OneTo(5)))
-
     # generate and return bands
-    return dat = BlockHcat(BlockBroadcastArray(hcat, dl, z, d, z, du), z5, z5)  
+    return dat = BlockBroadcastArray(hcat, dl, Zeros((axes(n,1),)), d, Zeros((axes(n,1),)), du)
 end
 
 function getindex(b::ZernikeJacobimatrixBandsX{T},i,j) where T
@@ -282,15 +274,15 @@ end
 function jacobimatrix(::Val{1}, Z::Zernike{T}) where T
     if iszero(Z.a)
         dat = ZernikeJacobimatrixBandsX{T}(Z)
-        return Symmetric(BlockBandedMatrices._BandedBlockBandedMatrix(dat', axes(dat,1), (1,1), (1,1)))
+        return Symmetric(BlockBandedMatrices._BandedBlockBandedMatrix(dat', axes(dat,1), (-1,1), (1,1)))
     else
         error("Implement for non-zero first basis parameter.")
     end
 end
 function jacobimatrix(::Val{2}, Z::Zernike{T}) where T
     if iszero(Z.a)
         dat = ZernikeJacobimatrixBandsY{T}(Z)
-        return Symmetric(BlockBandedMatrices._BandedBlockBandedMatrix(dat', axes(dat,1), (1,1), (2,2)))
+        return Symmetric(BlockBandedMatrices._BandedBlockBandedMatrix(dat', axes(dat,1), (-1,1), (2,2)))
     else
         error("Implement for non-zero first basis parameter.")
     end

test/test_disk.jl

@@ -103,8 +103,12 @@ import ForwardDiff: hessian
         yf = Z \ (y.*sin.(x.*y) .+ y .* x.^2 .- y.^2)
         @test Y[Block.(1:20),Block.(1:20)]*f[Block.(1:20)] ≈ yf[Block.(1:20)]
         # data size tests
-        @test size((X.data).data) == (9, ℵ₀)
-        @test size((Y.data).data) == (15, ℵ₀)
+        @test size((X.data).data) == (3, ℵ₀)
+        @test size((Y.data).data) == (5, ℵ₀)
+            
+        # for now, reject non-zero first parameter options
+        @test_throws ErrorException("Implement for non-zero first basis parameter.") jacobimatrix(Val(1),Zernike(1,1))  
+        @test_throws ErrorException("Implement for non-zero first basis parameter.") jacobimatrix(Val(2),Zernike(1,1))
     end
 
     @testset "Transform" begin