Test Robin BC with complex function values

Author: AndiMD

test/robin_complex.jl

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+include("src/DiffEqOperators.jl")
+using .DiffEqOperators
+using LinearAlgebra, Random, Test
+
+# Generate random parameters
+# Generate random parameters
+al = rand(ComplexF64,5)
+bl = rand(ComplexF64,5)
+cl = rand(ComplexF64,5)
+dx = rand(Float64,5)
+ar = rand(ComplexF64,5)
+br = rand(ComplexF64,5)
+cr = rand(ComplexF64,5)
+
+# Construct 5 arbitrary RobinBC operators for each parameter set
+for i in 1:5
+	
+	Q = RobinBC((al[i], bl[i], cl[i]), (ar[i], br[i], cr[i]), dx[i])
+
+	Q_L, Q_b = Array(Q,5i)
+
+	#Check that Q_L is is correctly computed
+	@test Q_L[2:5i+1,1:5i] ≈ Array(I, 5i, 5i)
+	@test Q_L[1,:] ≈ [1 / (1-al[i]*dx[i]/bl[i]); zeros(5i-1)]
+	@test Q_L[5i+2,:] ≈ [zeros(5i-1); 1 / (1+ar[i]*dx[i]/br[i])]
+
+	#Check that Q_b is computed correctly
+	@test Q_b ≈ [cl[i]/(al[i]-bl[i]/dx[i]); zeros(5i); cr[i]/(ar[i]+br[i]/dx[i])]
+
+	# Construct the extended operator and check that it correctly extends u to a (5i+2)
+	# vector, along with encoding boundary condition information.
+	u = rand(ComplexF64,5i)
+
+	Qextended = Q*u
+	CorrectQextended = [(cl[i]-(bl[i]/dx[i])*u[1])/(al[i]-bl[i]/dx[i]); u; (cr[i]+ (br[i]/dx[i])*u[5i])/(ar[i]+br[i]/dx[i])]
+	@test length(Qextended) ≈ 5i+2
+
+	# Check concretization
+	@test Array(Qextended) ≈ CorrectQextended # 	Q.a_l ⋅ u[1:length(Q.a_l)] + Q.b_l, 		Q.a_r ⋅ u[(end-length(Q.a_r)+1):end] + Q.b_r
+
+	# Check that Q_L and Q_b correctly compute BoundaryPaddedVector
+	@test Q_L*u + Q_b ≈ CorrectQextended
+
+	@test [Qextended[1]; Qextended.u; Qextended[5i+2]] ≈ CorrectQextended
+	
+end