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Classroom exercise: energy calculation¶
Diffusion model in 1D¶
Description: A one-dimensional diffusion model. (Could be a gas of particles, or a bunch of crowded people in a corridor, or animals in a valley habitat...)
- Agents are on a 1d axis
- Agents do not want to be where there are other agents
- This is represented as an 'energy': the higher the energy, the more unhappy the agents.
Implementation:
- Given a vector $n$ of positive integers, and of arbitrary length
- Compute the energy, $E(n) = \sum_i n_i(n_i - 1)$
- Later, we will have the likelyhood of an agent moving depend on the change in energy.
In [1]:
import numpy as np
from matplotlib import pyplot as plt
%matplotlib inline
density = np.array([0, 0, 3, 5, 8, 4, 2, 1])
fig, ax = plt.subplots()
ax.bar(np.arange(len(density)), density)
ax.xrange=[-0.5, len(density)-0.5]
ax.set_ylabel("Particle count $n_i$")
ax.set_xlabel("Position $i$")
Out[1]:
Here, the total energy due to position 2 is $3 (3-1)=6$, and due to column 7 is $1 (1-1)=0$. We need to sum these to get the total energy.
Starting point¶
Create a Python module:
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%%bash
mkdir -p diffusion
touch diffusion/__init__.py
- Implementation file: diffusion_model.py
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%%writefile diffusion/model.py
def energy(density, coeff=1.0):
"""
Energy associated with the diffusion model
Parameters
----------
density: array of positive integers
Number of particles at each position i in the array
coeff: float
Diffusion coefficient.
"""
# implementation goes here
- Testing file: test_diffusion_model.py
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%%writefile diffusion/test_model.py
from .model import energy
def test_energy():
""" Optional description for reporting """
# Test something
Invoke the tests:
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%%bash
cd diffusion
pytest
Now, write your code (in model.py), and tests (in test_model.py), testing as you do.
Solution¶
Don't look until after you've tried!
In [6]:
%%writefile diffusion/model.py
""" Simplistic 1-dimensional diffusion model """
def energy(density):
"""
Energy associated with the diffusion model
:Parameters:
density: array of positive integers
Number of particles at each position i in the array/geometry
"""
from numpy import array, any, sum
# Make sure input is an numpy array
density = array(density)
# ...of the right kind (integer). Unless it is zero length,
# in which case type does not matter.
if density.dtype.kind != 'i' and len(density) > 0:
raise TypeError("Density should be a array of *integers*.")
# and the right values (positive or null)
if any(density < 0):
raise ValueError("Density should be an array of *positive* integers.")
if density.ndim != 1:
raise ValueError("Density should be an a *1-dimensional*" +
"array of positive integers.")
return sum(density * (density - 1))
In [7]:
%%writefile diffusion/test_model.py
""" Unit tests for a diffusion model """
from pytest import raises
from .model import energy
def test_energy_fails_on_non_integer_density():
with raises(TypeError) as exception:
energy([1.0, 2, 3])
def test_energy_fails_on_negative_density():
with raises(ValueError) as exception: energy(
[-1, 2, 3])
def test_energy_fails_ndimensional_density():
with raises(ValueError) as exception: energy(
[[1, 2, 3], [3, 4, 5]])
def test_zero_energy_cases():
# Zero energy at zero density
densities = [ [], [0], [0, 0, 0] ]
for density in densities:
assert energy(density) == 0
def test_derivative():
from numpy.random import randint
# Loop over vectors of different sizes (but not empty)
for vector_size in randint(1, 1000, size=30):
# Create random density of size N
density = randint(50, size=vector_size)
# will do derivative at this index
element_index = randint(vector_size)
# modified densities
density_plus_one = density.copy()
density_plus_one[element_index] += 1
# Compute and check result
# d(n^2-1)/dn = 2n
expected = (2.0 * density[element_index]
if density[element_index] > 0
else 0 )
actual = energy(density_plus_one) - energy(density)
assert expected == actual
def test_derivative_no_self_energy():
""" If particle is alone, then its participation to energy is zero """
from numpy import array
density = array([1, 0, 1, 10, 15, 0])
density_plus_one = density.copy()
density[1] += 1
expected = 0
actual = energy(density_plus_one) - energy(density)
assert expected == actual
In [8]:
%%bash
cd diffusion
pytest
Coverage¶
With py.test, you can use the "pytest-cov" plugin to measure test coverage
In [9]:
%%bash
cd diffusion
pytest --cov="diffusion"
Or an html report:
In [10]:
%%bash
cd diffusion
pytest --cov="diffusion" --cov-report html
Look at the coverage results
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