Classroom exercise: energy calculation

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.

%matplotlib inline
import numpy as np
from matplotlib import pyplot as plt

density = np.array([0, 0, 3, 5, 8, 4, 2, 1])
fig, ax = plt.subplots()
ax.bar(np.arange(len(density)) - 0.5, density)
ax.xrange = [-0.5, len(density) - 0.5]
ax.set_ylabel("Particle count $n_i$")
ax.set_xlabel("Position $i$")
Text(0.5, 0, 'Position $i$')
../_images/05_03_energy_example_1_1.png

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:

%%bash
rm -rf diffusion
mkdir diffusion
touch diffusion/__init__.py

Windows: You will need to run the following instead

%%cmd
rmdir /s diffusion
mkdir diffusion
type nul > diffusion/__init__.py

NB. If you are using the Windows command prompt, you will also have to replace all subsequent %%bash directives with %%cmd

  • Implementation file: diffusion_model.py

%%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
Writing diffusion/model.py
  • Testing file: test_diffusion_model.py

%%writefile diffusion/test_model.py
from .model import energy


def test_energy():
    pass
    # Test something
Writing diffusion/test_model.py

Invoke the tests:

%%bash
cd diffusion
pytest
============================= test session starts ==============================
platform linux -- Python 3.8.13, pytest-7.1.2, pluggy-1.0.0
rootdir: /home/runner/work/rse-course/rse-course/module05_testing_your_code/diffusion
plugins: cov-3.0.0, anyio-3.6.1
collected 1 item

test_model.py .                                                          [100%]

============================== 1 passed in 0.02s ===============================

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 the spirit of test-driven development let’s first consider our tests.

%%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
Overwriting diffusion/test_model.py

Now let’s write an implementation that passes the tests.

%%writefile diffusion/model.py
"""Simplistic 1-dimensional diffusion model."""
from numpy import array, any, sum


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
    """

    # 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))
Overwriting diffusion/model.py
%%bash
cd diffusion
pytest
============================= test session starts ==============================
platform linux -- Python 3.8.13, pytest-7.1.2, pluggy-1.0.0
rootdir: /home/runner/work/rse-course/rse-course/module05_testing_your_code/diffusion
plugins: cov-3.0.0, anyio-3.6.1
collected 6 items

test_model.py ......                                                     [100%]

============================== 6 passed in 0.12s ===============================

Coverage

With pytest, you can use the “pytest-cov” plugin to measure test coverage

%%bash
cd diffusion
pytest --cov
============================= test session starts ==============================
platform linux -- Python 3.8.13, pytest-7.1.2, pluggy-1.0.0
rootdir: /home/runner/work/rse-course/rse-course/module05_testing_your_code/diffusion
plugins: cov-3.0.0, anyio-3.6.1
collected 6 items

test_model.py ......                                                     [100%]

---------- coverage: platform linux, python 3.8.13-final-0 -----------
Name            Stmts   Miss  Cover
-----------------------------------
__init__.py         0      0   100%
model.py           10      0   100%
test_model.py      33      0   100%
-----------------------------------
TOTAL              43      0   100%


============================== 6 passed in 0.18s ===============================

Or an html report:

%%bash
#%%cmd (windows)
cd diffusion
pytest --cov --cov-report html
============================= test session starts ==============================
platform linux -- Python 3.8.13, pytest-7.1.2, pluggy-1.0.0
rootdir: /home/runner/work/rse-course/rse-course/module05_testing_your_code/diffusion
plugins: cov-3.0.0, anyio-3.6.1
collected 6 items

test_model.py ......                                                     [100%]

---------- coverage: platform linux, python 3.8.13-final-0 -----------
Coverage HTML written to dir htmlcov


============================== 6 passed in 0.20s ===============================

The HTML coverage results will be in diffusion/htmlcov/index.html