# Unit Testing in QuantEcon

## Summary

The QuantEcon package uses Nose to manage tests. We adhere to some conventions to facilitate ease of maintenance and management of test cases. The main conventions are as follows:

• Tests live in Python files, which in turn live in quantecon/tests/
• These test files should be prepended with test_ followed by module name (e.g., tests for asset_pricing.py should be found in quantecon/tests/test_asset_pricing.py).
• Test files may contain either traditional Python unittest classes or the simpler deftest_function() style tests made available by Nose.

If you use Nose style test functions, please refer to the test name conventions discussed below so that nose can identify them as tests.

## Test Fundamentals

The basic premise of testing in Python is to write functions that make assertions. An assertion checks a given logical condition. If the condition is met, then the program continues onto the next line. If not, the assertion will trigger an Exception and issue an AssertionError. Here’s a simple example:

def test_equal(a,b):
"""
# Communicate what this Test Does In the DocString #
This tests for equality between two arguments a and b
"""
assert a==b, "Test failed: Arguments are not equal."

Running TestsIf a=2 and b=1 then this test would fail and raise an AssertionError with the the message string after the comma.

Nose parses Python files in the QuantEcon repository and collects all tests (i.e., all functions that satisfy the test naming convention discussed below). It then runs them one by one and provides you with a report of which passed and which failed.

To run the test suite, you need to type nosetests at the command line, or nosetests -v for a more verbose report.

### Test Function Names

Perhaps the easiest way to write basic tests is using Nose test functions. When nose parses the repository looking for tests it will search for the following regular expression: ?:^|[\\b_\\.-])[Tt]est. What this means is that your function name must contain test or Test either at a word boundary after an underscore or hyphen. Examples:

• test_somethinghere
• somethinghere_test
• TestSomethingHere

When naming your test function or class, remember to use PEP8 convention, as reading files that are similarly formated is less tiresome. Also make sure your clearly indicate what part of a module (be it a function or class etc.) that your test suite is testing.

### Assertion Methods

While it’s fine to construct your own logic and messaging using assert statements as above, note that there are also many helpful pre-existing assertion methods available in other packages, such as

These packages are used throughout QuantEcon, so it is safe to retrieved functions and methods from them directly using import statements such as:

from numpy.testing import assert_allclose

Next StepsThis particular function is useful in testing if an array matches a known solution, allowing for a degree of tolerance through the rtol= relative tolerance or atol= absolute tolerance keyword arguments.

To learn more, you can either read on below or browse some of the files in quantecon/tests/ and learn from these examples.

### Example 1: A Basic Test

Now let’s now look at an extended example, concerning a basic test for the mc_compute_startionary function from the mc_tools.py module.

We will use a known matrix and compute it’s stationary distribution.

$$\begin{split}P := \left( \begin{array}{cc} 0.4 & 0.6 \\ 0.2 & 0.8 \end{array} \right)\end{split}$$

We know that the unique stationary distribution should be (0.25, 0.75)

Now let’s write a test case in the file: tests/test_mc_tools.py and have a look at the results.

# Check required infrastructure is imported
import numpy as np
from numpy.testing import assert_array_equal

# Check that the test_mc_tools.py file has imported the relevant function we wish to test: mc_compute_stationary
from quantecon import mc_compute_stationary

def test_mc_compute_stationary_pmatrix():
"""
Test for a Known Solution
Module:     mc_tools.py
Function:   mc_compute_stationary
""""
P = np.array([[0.4,0.6], [0.2,0.8]])
P_known = np.array([0.25, 0.75])
computed = mc_compute_stationary(P)
assert_array_equal(computed, P_known)
---------------------------------------------------------------------------
AssertionError                            Traceback (most recent call last)
#Traceback details are presented here

AssertionError:
Arrays are not equal

(mismatch 50.0%)
x: array([ 0.25,  0.75])
y: array([ 0.25,  0.75])

This test actually fails! Why? This is because computed results and perfect analytical results are often very close but not quite equal. Let’s take a look at what the variable computed looks like in this case (by returning it and having a look using IPython):Running this test returns

In [1]: computed
Out[1]: array([ 0.25,  0.75])
In [2]: computed[0]
Out[2]: 0.24999999999999994
In [3]: computed[1]
Out[3]: 0.75
In [4]: computed == known
Out[4]: array([False,  True], dtype=bool)

Updating the test to make use of assert_allclose will produce the expected result due to the small difference in relative values.As you can see the test results really are the same and numerical exactness in computing the results in this case is an issue. That’s why numpy.testing also has asserts such as assert_allclose where you can set a relative tolerance and absolute tolerance through the keyword arguments rtol= and atol= (default values: rtol=1e-07, atol=0)

# Check required infrastructure is imported
import numpy as np
from numpy.testing import assert_allclose

# Check that the test_mc_tools.py file has imported the relevant function we wish to test: mc_compute_stationary
from quantecon import mc_compute_stationary

def test_mc_compute_stationary_pmatrix():
"""
Test mc_compute_stationary for a Known Solution of Matrix P
Module:     mc_tools.py
Function:   mc_compute_stationary
""""
P = np.array([[0.4,0.6], [0.2,0.8]])
P_known = np.array([0.25, 0.75])
computed = mc_compute_stationary(P)
assert_allclose(computed, P_known)

### Making this test more General

Other considerations to testing include making useful test functions that can generalise. For example, to make this test a bit more usable with a larger set of P Matrices, you may want to update the test function by allowing arguments which might accept a tuple of data and the known solution test_set_1 = (P, know). Now others can also make use of this test if they want to add another (or special case) P Matrix and associated known solution by looping over a list of tuples. A simple update to this test would then look like:

def test_mc_compute_stationary_pmatrix():
testset1 = (np.array([[0.4,0.6], [0.2,0.8]]), np.array([0.25, 0.75]))
check_mc_compute_stationary_pmatrix(testset1)

def check_mc_compute_stationary_pmatrix(testset):
"""
Test mc_compute_stationary for a Known Solution of Matrix P
Module:     mc_tools.py
Function:   mc_compute_stationary

Arguments
---------
[1] test_set    :   tuple(np.array(P), np.array(known_solution))
"""

(P, known) = testset
computed = mc_compute_stationary(P)
assert_allclose(computed, known)

## Example 2: An Extended Example

As a more extended example, we will make use of mc_tools.py and write some tests for the mc_compute_stationary function that requires some setup prior to running a test. This test is constructed from an example written by https://github.com/oyamad/test_mc_compute_stationary and compares three different approaches to demonstrate some benefits to using classes to organise the tests. As you will see in this example one big advantage to using classes is that you can specify setUp and tearDown functions which ensure each test is run in a consistent environment and state.

So let’s setup our test file (assuming it didn’t already exist) which we would call test_mc_tools.py and place it in the tests/ directory:

"""
Tests for mc_tools.py

Functions
---------
mc_compute_stationary
"""

from __future__ import division

import numpy as np
import unittest

# Tests: mc_compute_stationary #
################################

from ..mc_tools import mc_compute_stationary    # An example of using relative references within a package

def KMRMarkovMatrixSequential(N, p, epsilon):
"""
Generate the Markov matrix for the KMR model with *sequential* move

N: number of players
p: level of p-dominance for action 1
= the value of p such that action 1 is the BR for (1-q, q) for any q > p,
where q (1-q, resp.) is the prob that the opponent plays action 1 (0, resp.)
epsilon: mutation probability

References:
"""

P = np.zeros((N+1, N+1), dtype=float)
P[0, 0], P[0, 1] = 1 - epsilon * (1/2), epsilon * (1/2)
for n in range(1, N):
P[n, n-1] = \ (n/N) * (epsilon * (1/2) + (1 - epsilon) * (((n-1)/(N-1) &lt; p) + ((n-1)/(N-1) == p) * (1/2)))
P[n, n+1] = \ ((N-n)/N) * (epsilon * (1/2) + (1 - epsilon) * ((n/(N-1) > p) + (n/(N-1) == p) * (1/2)))
P[n, n] = 1 - P[n, n-1] - P[n, n+1]
P[N, N-1], P[N, N] = epsilon * (1/2), 1 - epsilon * (1/2)
return P


Sometimes Supporting Test Functions may be required for Generating Markov Matrices such as the KMR Model. However more often then not these support functions can be imported from the project. This can make it clearer regarding what is actually acting as input into the test cases.

Note: In production code - there should also be tests for the above function to ensure it is producing expected results given N, p, and epsilon.

### Using unittest.TestCase Framework

unittest.TestCase is a class provided by the python unittest module. By constructing a class instance using inheritance of the TestCase class, we inherit a number of useful methods. However it does specify some conventions that need to be used to make it all work. A test setup method needs to be located in a method called: def setUp(self) and a test teardown methods needs to be located in a method called: deftearDown(self). Specifying these methods ensures a common setup is performed prior to running each test. This relocates code from each test function and reduces the chances of error.

Some benefits to inheriting unittest.TestCase includes the inbuilt support for some assert methods like self.assertEqual() etc.

# Construct a Class
class TestMcComputeStationaryKMRMarkovMatrix(unittest.TestCase):
""""
Test Suite for mc_compute_stationary using KMR Markov Matrix [using unittest.TestCase]
""""

# Starting Values #

N = 27
epsilon = 1e-2
p = 1/3
TOL = 1e-2

def setUp(self):
self.P = KMRMarkovMatrixSequential(self.N, self.p, self.epsilon)
self.v = mc_compute_stationary(self.P)

def test_markov_matrix(self):
for i in range(len(self.P)):
self.assertEqual(sum(self.P[i, :]), 1)

def test_sum_one(self):
self.assertTrue(np.allclose(sum(self.v), 1, atol=self.TOL))

def test_nonnegative(self):
self.assertEqual(np.prod(self.v >= 0-self.TOL), 1)

def test_left_eigen_vec(self):
self.assertTrue(np.allclose(np.dot(self.v, self.P), self.v, atol=self.TOL))

def tearDown(self):
pass

### Using nose test functions

This example can also be written as nose test_ functions. The required setup can be done in a setup_func() and then importing a with_setup decorator from nose.tools. This decorator will then run the setup function before every test is performed. Nose also allows you to specify teardown_ functions as a second argument to with_setup.

from nose.tools import with_setup

N = 27
epsilon = 1e-2
p = 1/3
TOL = 1e-2

def setup_func():
"""
Setup a KMRMarkovMatrix and Compute Stationary Values
"""

global P                                            # Not Usually Recommended
P = KMRMarkovMatrixSequential(N, p, epsilon)
global v                                            # Not Usually Recommended
v = mc_compute_stationary(P)

@with_setup(setup_func)
def test_markov_matrix():
for i in range(len(P)):
assert sum(P[i, :]) == 1, "sum(P[i,:]) %s != 1" % sum(P[i, :])

@with_setup(setup_func)
def test_sum_one():
assert np.allclose(sum(v), 1, atol=TOL) == True, "np.allclose(sum(v), 1, atol=%s) != True" % TOL

@with_setup(setup_func)
def test_nonnegative():
assert np.prod(v >= 0-TOL) == 1, "np.prod(v >= 0-TOL) %s != 1" % np.prod(v >= 0-TOL)

@with_setup(setup_func)
def test_left_eigen_vec():
assert np.allclose(np.dot(v, P), v, atol=TOL) == True, "np.allclose(np.dot(v, P), v, atol=%s) != True" % TOL

### Using nose class based structures

Nose can also parse classes. As discussed in the unittest section in more complex test suites classes are useful for bringing structure to the code. While it is not a requirement to use unittest.TestCase in QuantEcon if you do choose to write tests in a class structure it can be helpful for cross readership to adopt the standard setUp() and tearDown() methods as used in unittest.TestCase. The main benefit of using Class structures is to collect your tests into one logical space and allow easy parameter passing without resorting to global variables etc.

class TestMcComputeStationaryKMRMarkovMatrix():
"""
Test Suite for mc_compute_stationary using KMR Markov Matrix [suitable for nose]
"""
# Starting Values #

N = 27
epsilon = 1e-2
p = 1/3
TOL = 1e-2

def setUp(self):
"""
Setup a KMRMarkovMatrix and Compute Stationary Values
"""
self.P = KMRMarkovMatrixSequential(self.N, self.p, self.epsilon)
self.v = mc_compute_stationary(self.P)

def test_markov_matrix(self):
for i in range(len(self.P)):
assert sum(self.P[i, :]) == 1, "sum(P[i,:]) %s != 1" % sum(self.P[i, :])

def test_sum_one(self):
assert np.allclose(sum(self.v), 1, atol=self.TOL) == True, "np.allclose(sum(v), 1, atol=%s) != True" % self.TOL

def test_nonnegative(self):
assert np.prod(self.v >= 0-self.TOL) == 1, "np.prod(v >= 0-TOL) %s != 1" % np.prod(self.v >= 0-self.TOL)

def test_left_eigen_vec(self):
assert np.allclose(np.dot(self.v, self.P), self.v, atol=self.TOL) == True, "np.allclose(np.dot(v, P), v, atol=%s) != True" % self.TOL