Issue with alias_elimination

[tshort]

I suspect there's an issue with alias_elimination in the following example. The reduced set of equations doesn't seem right.

using ModelingToolkit

@parameters t
const D = Differential(t)
@variables v47(t) v57(t) v66(t) v25(t) i74(t) i75(t) i64(t) i71(t) v1(t) v2(t)

eq = [
 v47 ~ v1
 v47 ~ sin(376.99111843077515t)
 v57 ~ v1 - v2
 v57 ~ 10.0i64
 v66 ~ v2
 v66 ~ 5.0i74
 v25 ~ v2
 i75 ~ 0.005 * D(v25)
 0 ~ i74 + i75 - i64
 0 ~ i64 + i71]


sys0 = ODESystem(eq, t)
sys = initialize_system_structure(alias_elimination(sys0))

The equations look right for sys0:

julia> equations(sys0)
10-element Array{Equation,1}:
 v47(t) ~ v1(t)
 v47(t) ~ sin(376.99111843077515t)
 v57(t) ~ v1(t) - v2(t)
 v57(t) ~ 10.0i64(t)
 v66(t) ~ v2(t)
 v66(t) ~ 5.0i74(t)
 v25(t) ~ v2(t)
 i75(t) ~ 0.005Differential(t)(v25(t))
 0 ~ i74(t) + i75(t) - i64(t)
 0 ~ i64(t) + i71(t)

But, after alias_elimination, the system becomes disconnected. In the following equations, v47 is only used in the first equation.

julia> equations(sys)
4-element Array{Equation,1}:
 0 ~ sin(376.99111843077515t) - v47(t)
 0 ~ 5i74(t) - v2(t)
 0 ~ v2(t) - v25(t)
 0 ~ 0.005Differential(t)(v25(t))

To test for a modeling error, I got a version of this to work in TinyModia. (That doesn't fully rule out user error here.)

[ChrisRackauckas]

Does structural_simplify work?

[tshort]

No. After structural_simplify, I'm left with one equation: 0 ~ 0.005Differential(t)(v25(t)). Then, after digging deeper, it seemed like the problem was in alias_elimination.

[ChrisRackauckas]

Is the only issue that it didn't move the derivative over?

[tshort]

No. The main issue is that the sin term is disconnected from the rest of the equations. There's no more driving term, so the answers are all zeros.

[YingboMa]

Yeah, this looks like a real bug.

[tshort]

Here's what TinyModia comes up with after it's alias reduction:

Perform alias elimination and remove singularities

    Variables that have been eliminated:
       6: v66 = v25
      11: i71 = -i64
       4: v2 = v25
       2: v1 = v47

    Remaining transformed linear Integer equations:
       9: 0 = -i74 - i75 + i64
       3: 0 = v57 - v47 + v25

States:
   1: v25
Unknowns after alias reduction:
   1: v47
   2: v57
   3: i64
   4: i74
   5: i75
   6: der(v25)
Equations after alias reduction:
   1: v47 = sin((376.99111843077515time) * u"1/s")
   2: 0 = (v57 + -1v47) + v25
   3: v57 = 10.0i64
   4: v25 = 5.0i74
   5: i75 = 0.005 * der(v25)
   6: 0 = (-1i74 + -1i75) + i64
  The DAE is structurally nonsingular.