my equation is :

-(u_xx + u_yy + u_zz) = f(r)

where `r = sqrt(x**2 + y**2 + z**2)`

and

f(r) = 1 for r < 0.5

f(r) = 0 for r > 0.5

I have tried:

```
class Poisson(PDE):
name = "Poisson"
def __init__(self):
# coordinates
x, y, z = Symbol("x"), Symbol("y"), Symbol("z")
rr = Symbol("w")
# make input variables
input_variables = {"x": x, "y": y, "z": z}
# make u function
u = Function("u")(*input_variables)
# source term is $f = \left\{ \begin{array}{ll}
# 1 & \text{if } r < 0.5\\
# 0 & \text{if } r > 0.5
# \end{array} \right. \text{. }$
r = (x ** 2 + y ** 2 + z ** 2) ** 0.5
f = Piecewise((Number(1), rr < Number(0.5)), (Number(0), rr > Number(0.5)))
# set equations
self.equations = {}
self.equations["poisson_u"] = - (u.diff(x, 2) + u.diff(y, 2) + u.diff(z, 2)) - f.subs(rr,r)
```

but failed:

```
could not unroll graph!
This is probably because you are asking to compute a value that is not an output of any node
####################################
invar: [x, y, z, sdf, area]
requested var: [poisson_u]
computable var: [x, y, z, sdf, area, u]
####################################
Nodes in graph:
node: Sympy Node: poisson_u
evaluate: SympyToTorch
inputs: [Piecewise]
derivatives: [u__x__x, u__y__y, u__z__z]
outputs: [poisson_u]
optimize: False
node: Arch Node: poisson_network
evaluate: FullyConnectedArch
inputs: [x, y, z]
derivatives: []
outputs: [u]
optimize: True
####################################
```

I have searched the keyword piecewise on the examples but found nothing helpful.

I am a very beginner so I dont know if there is some method to write such a source term.

Thank you very much.