# Define random values through expression

**URL:** <https://fenicsproject.discourse.group/t/define-random-values-through-expression/1448>\
**Category:** Uncategorized\
**Created:** [September 2, 2019, 4:41am UTC](https://fenicsproject.discourse.group/t/define-random-values-through-expression/1448 "2019-09-02T04:41:29Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![hasanmdmehedi](https://avatars.discourse-cdn.com/v4/letter/h/3ab097/32.png) [@hasanmdmehedi](https://fenicsproject.discourse.group/u/hasanmdmehedi)\
**Post date:** [September 2, 2019, 4:41am UTC](https://fenicsproject.discourse.group/t/define-random-values-through-expression/1448/1 "2019-09-02T04:41:30Z")

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Dear Fenics users,

I want to define some random values in each nodes through expression. Here is my code but it didn’t work:

import numpy as np  
from dolfin import \*  
from fenics import \*

#Define mesh  
N=2;  
mesh = BoxMesh(Point(0, 0, 0), Point(1, 1, 1), N, N, N)

#Define mixed space  
P2 = VectorElement(“Lagrange”, mesh.ufl\_cell(), 1)  
P1 = FiniteElement(“Lagrange”, mesh.ufl\_cell(), 1)  
TH = P2 \* P1  
W = FunctionSpace(mesh, TH)  
gdim = mesh.geometry().dim()  
I = Identity(W.mesh().geometry().dim())  
Z = FunctionSpace(mesh, ‘CG’, 1)  
w = Function(W)  
(u, p) = split(w)  
#Determine number of nodes and denoting them  
dof2vt = dof\_to\_vertex\_map(Z)  
coords = mesh.coordinates()  
coords = coords[dof2vt]  
length\_of\_nodes = coords.shape[0]

mu = 0.5 # a constant  
#Generating random values in each nodes  
ran\_mu = np.random.rand(1,length\_of\_nodes)  
print(“random mu :”, ran\_mu)

#Defining the constant value in expression  
mu\_expr=Expression(“mu”,mu=mu, degree=1)  
mu\_in\_vert=interpolate(mu\_expr, Z)  
print("mu in each nodes : ", mu\_in\_vert.vector().get\_local())

#Now I want to define the random values (ran\_mu) through expression  
ran\_mu\_expr=Expression(“ran\_mu”,ran\_mu=ran\_mu, degree=4)  
ran\_mu\_in\_vert=interpolate(ran\_mu\_expr, Z)

Many thanks in advance for your help.

Regards,  
Mehedi

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**Author:** ![MiroK](https://yyz2.discourse-cdn.com/free1/user_avatar/fenicsproject.discourse.group/mirok/32/33_2.png) [@MiroK](https://fenicsproject.discourse.group/u/MiroK)\
**Post date:** [September 2, 2019, 9:53am UTC](https://fenicsproject.discourse.group/t/define-random-values-through-expression/1448/2 "2019-09-02T09:53:52Z")

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Hi, `f=Expression(“g”, g=g, degree=1)` should be thought of as defining f such that `f(x)=g(x)`. In `ran_mu_expr=Expression(“ran_mu”,ran_mu=ran_mu, degree=4)` you seem to make an assumption that `Expression` will do the lookup in `ran_mu` array to assign the coefficient value appropriately. That is not the case. Consider instead

```python
from dolfin import *
import numpy as np

class RandomScalar(UserExpression):
    def eval(self, value, x):
        value[:] = np.random.rand()
    def value_shape(self, ):
        return ()

    
def fill_random0(f):
    f.assign(interpolate(RandomScalar(degree=1), f.function_space()))
    return f

def fill_random1(f):
    f.vector().set_local(np.random.rand(f.vector().local_size()))
    return f
# To illustrate speed difference
for n in (64, 128, 256):
    mesh = UnitSquareMesh(n, n)
    V = FunctionSpace(mesh, 'CG', 1)
    f = Function(V)
    print('n=%d' % n)
    for fill in (fill_random0, fill_random1):
        t = Timer()
        fill(f)
        print('\t', t.stop())

# Expression using function
mesh = UnitSquareMesh(n, n)
V = FunctionSpace(mesh, 'CG', 1)

f = Function(V)
# Randomize
f = fill_random1(f)

f_expr = Expression('f', f=f, degree=1)
print(sqrt(abs(assemble(inner(f-f_expr, f-f_expr)*dx))))

```

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<div class="post-metadata">

**Author:** ![hasanmdmehedi](https://avatars.discourse-cdn.com/v4/letter/h/3ab097/32.png) [@hasanmdmehedi](https://fenicsproject.discourse.group/u/hasanmdmehedi)\
**Post date:** [September 2, 2019, 4:21pm UTC](https://fenicsproject.discourse.group/t/define-random-values-through-expression/1448/3 "2019-09-02T16:21:58Z")

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Thank you for your reply. Now, it is working.