update the tests

Author: shashi

test/global_PDE.jl

@@ -0,0 +1,62 @@
+using FiniteDiff, LinearAlgebra, Test
+using SparsityDetection, SparseArrays
+
+# Define the constants for the PDE
+const α₂ = 1.0
+const α₃ = 1.0
+const β₁ = 1.0
+const β₂ = 1.0
+const β₃ = 1.0
+const r₁ = 1.0
+const r₂ = 1.0
+const D = 100.0
+const γ₁ = 0.1
+const γ₂ = 0.1
+const γ₃ = 0.1
+const N = 8
+const X = reshape([i for i in 1:N for j in 1:N],N,N)
+const Y = reshape([j for i in 1:N for j in 1:N],N,N)
+const α₁ = 1.0.*(X.>=4*N/5)
+
+const Mx = Tridiagonal([1.0 for i in 1:N-1],[-2.0 for i in 1:N],[1.0 for i in 1:N-1])
+const My = copy(Mx)
+Mx[2,1] = 2.0
+Mx[end-1,end] = 2.0
+My[1,2] = 2.0
+My[end,end-1] = 2.0
+
+# Define the initial condition as normal arrays
+u0 = zeros(N,N,3)
+
+const MyA = zeros(N,N);
+const AMx = zeros(N,N);
+const DA = zeros(N,N);
+# Define the discretized PDE as an ODE function
+function f(du,u,p,t)
+   A = @view  u[:,:,1]
+   B = @view  u[:,:,2]
+   C = @view  u[:,:,3]
+  dA = @view du[:,:,1]
+  dB = @view du[:,:,2]
+  dC = @view du[:,:,3]
+  mul!(MyA,My,A)
+  mul!(AMx,A,Mx)
+  @. DA = D*(MyA + AMx)
+  @. dA = DA + α₁ - β₁*A - r₁*A*B + r₂*C
+  @. dB = α₂ - β₂*B - r₁*A*B + r₂*C
+  @. dC = α₃ - β₃*C + r₁*A*B - r₂*C
+end
+
+input = rand(N,N,3)
+output = similar(input)
+sparsity_pattern = jacobian_sparsity(f,output,input,nothing,0.0)
+jac_sparsity = Float64.(sparse(sparsity_pattern))
+
+function testf2(u)
+	_u = reshape(u,size(input)...)
+	du = similar(_u)
+	f(du,_u,nothing,0.0)
+	vec(du)
+end
+findifjac = FiniteDiff.finite_difference_jacobian(testf2,input)
+@test all((abs.(findifjac) .> 0) .== (jac_sparsity .> 0))

test/hessian.jl

@@ -36,7 +36,7 @@ Term(i...) = TermCombination(Set([Dict(j=>1 for j in i)]))
 # copy
 @test hesstesttag(x->copy(x)[1], [1,2]) == Term(1)
 @test hesstesttag(x->x[:][1], [1,2]) == Term(1)
-#@test hesstesttag(x->x[1:1][1], [1,2]) == Term(1)
+@test hesstesttag(x->x[1:1][1], [1,2]) == Term(1)
 
 # tests `iterate`
 function mysum(x)

test/runtests.jl

@@ -1,8 +1,10 @@
 include("common.jl")
 
 @testset "Jacobian Sparsity" begin include("jacobian.jl") end
-@testset "Hessian sparsity" begin include("hessian.jl") end
 @testset "Paraboloid example" begin include("paraboloid.jl") end
+@testset "PDE with globals" begin include("global_PDE.jl") end
+
+@testset "Hessian sparsity" begin include("hessian.jl") end
 
 @testset "Exploration" begin include("ifsandbuts.jl") end
 @testset "Examples" begin include("examples.jl") end