Add more nonlinear tests

Author: serenity4

src/analysis/ipoincidence.jl

@@ -109,7 +109,11 @@ function apply_linear_incidence(𝕃, ret::Incidence, caller::Union{CallerMappin
                         end
                         # We'll only be state-dependent if variables from the callee
                         # map to at least one other variable than `j`.
-                        state_dependent |= length(used_caller_variables) - did_use_time > 1
+                        if j == 1 # time
+                            state_dependent |= length(used_caller_variables) > 1
+                        else # state
+                            state_dependent |= length(used_caller_variables) - did_use_time > 1
+                        end
                         # If another state may contain time, we may be time-dependent too.
                         time_dependent |= did_use_time
                     end

test/incidence.jl

@@ -272,6 +272,26 @@ dependencies(row) = sort(rowvals(row) .=> nonzeros(row), by = first)
   incidence = @infer_incidence _muladd2(u₁, u₂, u₁, u₃)
   @test dependencies(incidence.row) == [2 => nonlinear, 3 => linear_state_dependent, 4 => linear_state_dependent]
   @test incidence == incidence"f(u₁, ∝ₛu₂, ∝ₛu₃)"
+
+  incidence = @infer_incidence exp(u₁)
+  @test dependencies(incidence.row) == [2 => nonlinear]
+  @test incidence == incidence"a + f(u₁)"
+
+  incidence = @infer_incidence t * exp(u₁)
+  @test dependencies(incidence.row) == [1 => linear_state_dependent, 2 => nonlinear]
+  @test incidence == incidence"a + f(∝ₛt, u₁)"
+
+  incidence = @infer_incidence u₁ * exp(t)
+  @test dependencies(incidence.row) == [1 => nonlinear, 2 => linear_time_dependent]
+  @test incidence == incidence"a + f(t, ∝ₜu₁)"
+
+  incidence = @infer_incidence u₁ * exp(t + u₂)
+  @test dependencies(incidence.row) == [1 => nonlinear, 2 => linear_time_and_state_dependent, 3 => nonlinear]
+  @test incidence == incidence"a + f(t, ∝ₜₛu₁, u₂)"
+
+  incidence = @infer_incidence atan(u₁, u₂)
+  @test dependencies(incidence.row) == [2 => nonlinear, 3 => nonlinear]
+  @test incidence == incidence"a + f(u₁, u₂)"
 end;
 
 end