add irregular grid test

Author: fgerick

test/generic_operator_validation.jl

@@ -1,30 +1,66 @@
-using DiffEqOperators
-
-n = 100
-x=0.0:0.005:2π
-xprime = x[2:(end-1)]
-dx=diff(x)
-y = exp.(π*x)
-y_im = exp.(π*im*x)
-yim_ = y_im[2:(end-1)]
+using DiffEqOperators, SparseArrays, LinearAlgebra
+
+x = 0.0:0.01:π
+x_ = x[2:end-1]
+dx = diff(x)
+y = sin.(2x)
 y_ = y[2:(end-1)]
+dy = [2cos.(2x_),-4sin.(2x_),-8cos.(2x_),16y_,32cos.(2x_)]
+
+
+
+# test concretization against regular grid operator
+for dor in 1:4, aor in 2:2:6
+    Dr = CenteredDifference(dor,aor,dx[1],length(x)-2)
+    Dir = CenteredDifference(dor,aor,dx,length(x)-2)
+
+    @test sparse(Dr)≈sparse(Dir)
+    @test Array(Dr)≈Array(Dir)
 
-@test_broken for dor in 1:6, aor in 1:6
+end
+
+# test irregular grid operator with regular grid
+for dor in 1:4, aor in 2:6
 
-    D1 = CenteredDifference(dor,aor,dx,length(x))
+    D1 = CenteredDifference(dor,aor,dx,length(x)-2)
 
     #take derivative
     yprime1 = D1*y
 
     #test result
-    @test_broken yprime1 ≈ (π^dor)*y_ # test operator with known derivative of exp(kx)
+    @test yprime1 ≈ dy[dor] atol = 10.0^(1-aor)#2test operator with known derivative of exp(kx)
+
+    #TODO: implement specific tests for the left and right boundary regions, waiting until after update
+end
 
-    #take derivatives
-    y_imprime1 = D1*y_im
+
+# test irregular grid
+
+x = sin.(0.0:0.05:π)
+x = cumsum(x)
+x = x/x[end]*π
+x_ = x[2:end-1]
+dx = diff(x)
+y  = sin.(2x)
+y_ = y[2:(end-1)]
+dy = [2cos.(2x_), -4sin.(2x_), -8cos.(2x_), 16y_, 32cos.(2x_)]
+
+for dor in 1:4, aor in 4:10
+
+    D1 = CenteredDifference(dor,aor,dx,length(x)-2)
+
+    #take derivative
+    yprime1 = D1*y
 
     #test result
-    @test_broken y_imprime1 ≈ ((pi*im)^dor)*yim_ # test operator with known derivative of exp(jkx)
+    tol = 2*10.0^(2-aor)*maximum(dx)^(2-dor)
+    # error estimate is fairly difficult for high order derivatives and small dx.
+
+    # err = norm(yprime1.-dy[dor])
+    # @show err
+    # @show tol
 
+    @test yprime1 ≈ dy[dor] atol = tol #2test operator with known derivative of exp(kx)
 
     #TODO: implement specific tests for the left and right boundary regions, waiting until after update
 end