# Problems interpolating a UserExpression and plotting it

**URL:** <https://fenicsproject.discourse.group/t/problems-interpolating-a-userexpression-and-plotting-it/1303>\
**Category:** Uncategorized\
**Created:** [August 12, 2019, 7:52am UTC](https://fenicsproject.discourse.group/t/problems-interpolating-a-userexpression-and-plotting-it/1303 "2019-08-12T07:52:58Z")\
**Posts on this page:** 4\
**Page:** 1

<div class="post-metadata">

**Author:** ![Yannik](https://avatars.discourse-cdn.com/v4/letter/y/5fc32e/32.png) [@Yannik](https://fenicsproject.discourse.group/u/Yannik)\
**Post date:** [August 12, 2019, 7:52am UTC](https://fenicsproject.discourse.group/t/problems-interpolating-a-userexpression-and-plotting-it/1303/1 "2019-08-12T07:52:58Z")

</div>

Hi everyone,

I’m using macOS Mojave (10.14.6), miniconda, and FEniCS 2018 with Python. I want to define have an expression/function e: \mathbb{R}^2 \rightarrow \mathbb{R} which is defined as such that f(x, y) = 1 for x \leq 0.2, f(x, y) = 2 for x \geq 0.8, f(x, y) = 3 for y \geq 0.9 and 0 else. So I thought that this

```
from fenics import *
N = 16
mesh = UnitSquareMesh(N, N)
V = FunctionSpace(mesh, 'P', 1)

class MyExpression(UserExpression):
  def eval(self, value, x):
    if x[0] <= 0.2:
        value[0] = 1
    elif x[0] >= 0.8:
        value[0] = 2
    elif x[1] >= 0.9:
        value[0] = 3
    else:
        value[0] = 0

  def value_shape(self):
    return (1,)

e = MyExpression(degree = 2)
Ie = interpolate(e, V)

```

should work. But I get the error

```
RuntimeError: 

*** -------------------------------------------------------------------------
*** DOLFIN encountered an error. If you are not able to resolve this issue
*** using the information listed below, you can ask for help at
***
*** fenics-support@googlegroups.com
***
*** Remember to include the error message listed below and, if possible,
*** include a *minimal* running example to reproduce the error.
***
*** -------------------------------------------------------------------------
*** Error: Unable to interpolate function into function space.
*** Reason: Rank of function (1) does not match rank of function space (0).
*** Where: This error was encountered inside FunctionSpace.cpp.
*** Process: 0
*** 
*** DOLFIN version: 2018.1.0
*** Git changeset:  
*** -------------------------------------------------------------------------

```

I do not know what the reason wants me to tell. Projecting does also not work. Could there be a problem with if/else test in my expression? Thanks for help.

---

<div class="post-metadata">

**Author:** ![Yannik](https://avatars.discourse-cdn.com/v4/letter/y/5fc32e/32.png) [@Yannik](https://fenicsproject.discourse.group/u/Yannik)\
**Post date:** [August 12, 2019, 1:38pm UTC](https://fenicsproject.discourse.group/t/problems-interpolating-a-userexpression-and-plotting-it/1303/2 "2019-08-12T13:38:52Z")

</div>

If I omit

```
  def value_shape(self):
    return (1,)

```

then I get the warning:  
`WARNING: user expression has not supplied value_shape method or an element. Assuming scalar element.`  
Could someone explain this to me?

---

<div class="post-metadata">

**Author:** ![kamensky](https://avatars.discourse-cdn.com/v4/letter/k/e95f7d/32.png) [@kamensky](https://fenicsproject.discourse.group/u/kamensky)\
**Post date:** [August 12, 2019, 2:05pm UTC](https://fenicsproject.discourse.group/t/problems-interpolating-a-userexpression-and-plotting-it/1303/3 "2019-08-12T14:05:57Z")

</div>

UFL distinguishes between a scalar, and a vector of rank 1 and dimension 1. You can get rid of the warning with

```python
  def value_shape(self):
    #return (1,)
    return ()

```

---

<div class="post-metadata">

**Author:** ![Yannik](https://avatars.discourse-cdn.com/v4/letter/y/5fc32e/32.png) [@Yannik](https://fenicsproject.discourse.group/u/Yannik)\
**Post date:** [August 13, 2019, 5:37am UTC](https://fenicsproject.discourse.group/t/problems-interpolating-a-userexpression-and-plotting-it/1303/4 "2019-08-13T05:37:35Z")

</div>

Thank you very much.