# discretize.Tests.OrderTest¶

class discretize.Tests.OrderTest(methodName='runTest')[source]

Bases: unittest.case.TestCase

OrderTest is a base class for testing convergence orders with respect to mesh sizes of integral/differential operators.

Mathematical Problem:

Given are an operator A and its discretization A[h]. For a given test function f and h –> 0 we compare:

$error(h) = \| A[h](f) - A(f) \|_{\infty}$

Note that you can provide any norm.

Test is passed when estimated rate order of convergence is at least within the specified tolerance of the estimated rate supplied by the user.

Minimal example for a curl operator:

class TestCURL(OrderTest):
name = "Curl"

def getError(self):
# For given Mesh, generate A[h], f and A(f) and return norm of error.

fun  = lambda x: np.cos(x)  # i (cos(y)) + j (cos(z)) + k (cos(x))
sol = lambda x: np.sin(x)  # i (sin(z)) + j (sin(x)) + k (sin(y))

Ex = fun(self.M.gridEx[:, 1])
Ey = fun(self.M.gridEy[:, 2])
Ez = fun(self.M.gridEz[:, 0])
f = np.concatenate((Ex, Ey, Ez))

Fx = sol(self.M.gridFx[:, 2])
Fy = sol(self.M.gridFy[:, 0])
Fz = sol(self.M.gridFz[:, 1])
Af = np.concatenate((Fx, Fy, Fz))

# Generate DIV matrix
Ah = self.M.edgeCurl

curlE = Ah*E
err = np.linalg.norm((Ah*f -Af), np.inf)
return err

def test_order(self):
# runs the test
self.orderTest()


Methods

 __call__(self, \*args, \*\*kwds) Call self as a function. addCleanup(self, function, \*args, \*\*kwargs) Add a function, with arguments, to be called when the test is completed. addTypeEqualityFunc(self, typeobj, function) Add a type specific assertEqual style function to compare a type. assertAlmostEqual(self, first, second[, …]) Fail if the two objects are unequal as determined by their difference rounded to the given number of decimal places (default 7) and comparing to zero, or by comparing that the difference between the two objects is more than the given delta. assertCountEqual(self, first, second[, msg]) An unordered sequence comparison asserting that the same elements, regardless of order. assertDictContainsSubset(self, subset, …) Checks whether dictionary is a superset of subset. assertEqual(self, first, second[, msg]) Fail if the two objects are unequal as determined by the ‘==’ operator. assertFalse(self, expr[, msg]) Check that the expression is false. assertGreater(self, a, b[, msg]) Just like self.assertTrue(a > b), but with a nicer default message. assertGreaterEqual(self, a, b[, msg]) Just like self.assertTrue(a >= b), but with a nicer default message. assertIn(self, member, container[, msg]) Just like self.assertTrue(a in b), but with a nicer default message. assertIs(self, expr1, expr2[, msg]) Just like self.assertTrue(a is b), but with a nicer default message. assertIsInstance(self, obj, cls[, msg]) Same as self.assertTrue(isinstance(obj, cls)), with a nicer default message. assertIsNone(self, obj[, msg]) Same as self.assertTrue(obj is None), with a nicer default message. assertIsNot(self, expr1, expr2[, msg]) Just like self.assertTrue(a is not b), but with a nicer default message. assertIsNotNone(self, obj[, msg]) Included for symmetry with assertIsNone. assertLess(self, a, b[, msg]) Just like self.assertTrue(a < b), but with a nicer default message. assertLessEqual(self, a, b[, msg]) Just like self.assertTrue(a <= b), but with a nicer default message. assertListEqual(self, list1, list2[, msg]) A list-specific equality assertion. assertLogs(self[, logger, level]) Fail unless a log message of level level or higher is emitted on logger_name or its children. assertMultiLineEqual(self, first, second[, msg]) Assert that two multi-line strings are equal. assertNotAlmostEqual(self, first, second[, …]) Fail if the two objects are equal as determined by their difference rounded to the given number of decimal places (default 7) and comparing to zero, or by comparing that the difference between the two objects is less than the given delta. assertNotEqual(self, first, second[, msg]) Fail if the two objects are equal as determined by the ‘!=’ operator. assertNotIn(self, member, container[, msg]) Just like self.assertTrue(a not in b), but with a nicer default message. assertNotIsInstance(self, obj, cls[, msg]) Included for symmetry with assertIsInstance. assertNotRegex(self, text, unexpected_regex) Fail the test if the text matches the regular expression. assertRaises(self, expected_exception, …) Fail unless an exception of class expected_exception is raised by the callable when invoked with specified positional and keyword arguments. assertRaisesRegex(self, expected_exception, …) Asserts that the message in a raised exception matches a regex. assertRegex(self, text, expected_regex[, msg]) Fail the test unless the text matches the regular expression. assertSequenceEqual(self, seq1, seq2[, msg, …]) An equality assertion for ordered sequences (like lists and tuples). assertSetEqual(self, set1, set2[, msg]) A set-specific equality assertion. assertTrue(self, expr[, msg]) Check that the expression is true. assertTupleEqual(self, tuple1, tuple2[, msg]) A tuple-specific equality assertion. assertWarns(self, expected_warning, \*args, …) Fail unless a warning of class warnClass is triggered by the callable when invoked with specified positional and keyword arguments. assertWarnsRegex(self, expected_warning, …) Asserts that the message in a triggered warning matches a regexp. debug(self) Run the test without collecting errors in a TestResult doCleanups(self) Execute all cleanup functions. fail(self[, msg]) Fail immediately, with the given message. failureException alias of builtins.AssertionError getError(self) For given h, generate A[h], f and A(f) and return norm of error. orderTest(self) For number of cells specified in meshSizes setup mesh, call getError and prints mesh size, error, ratio between current and previous error, and estimated order of convergence. setUp(self) Hook method for setting up the test fixture before exercising it. setUpClass() Hook method for setting up class fixture before running tests in the class. shortDescription(self) Returns a one-line description of the test, or None if no description has been provided. skipTest(self, reason) Skip this test. subTest(self[, msg]) Return a context manager that will return the enclosed block of code in a subtest identified by the optional message and keyword parameters. tearDown(self) Hook method for deconstructing the test fixture after testing it. tearDownClass() Hook method for deconstructing the class fixture after running all tests in the class.
 assertAlmostEquals assertDictEqual assertEquals assertNotAlmostEquals assertNotEquals assertNotRegexpMatches assertRaisesRegexp assertRegexpMatches assert_ countTestCases defaultTestResult failIf failIfAlmostEqual failIfEqual failUnless failUnlessAlmostEqual failUnlessEqual failUnlessRaises id run setupMesh

## Attributes¶

OrderTest.expectedOrders = 2.0
OrderTest.longMessage = True
OrderTest.maxDiff = 640
OrderTest.meshDimension = 3
OrderTest.meshSizes = [4, 8, 16, 32]
OrderTest.meshTypes = ['uniformTensorMesh']
OrderTest.name = 'Order Test'
OrderTest.tolerance = 0.85

## Methods¶

OrderTest.addCleanup(self, function, *args, **kwargs)

Add a function, with arguments, to be called when the test is completed. Functions added are called on a LIFO basis and are called after tearDown on test failure or success.

Cleanup items are called even if setUp fails (unlike tearDown).

OrderTest.addTypeEqualityFunc(self, typeobj, function)

Add a type specific assertEqual style function to compare a type.

This method is for use by TestCase subclasses that need to register their own type equality functions to provide nicer error messages.

Parameters: typeobj – The data type to call this function on when both values are of the same type in assertEqual(). function – The callable taking two arguments and an optional msg= argument that raises self.failureException with a useful error message when the two arguments are not equal.
OrderTest.assertAlmostEqual(self, first, second, places=None, msg=None, delta=None)

Fail if the two objects are unequal as determined by their difference rounded to the given number of decimal places (default 7) and comparing to zero, or by comparing that the difference between the two objects is more than the given delta.

Note that decimal places (from zero) are usually not the same as significant digits (measured from the most significant digit).

If the two objects compare equal then they will automatically compare almost equal.

OrderTest.assertAlmostEquals(*args, **kwargs)
OrderTest.assertCountEqual(self, first, second, msg=None)

An unordered sequence comparison asserting that the same elements, regardless of order. If the same element occurs more than once, it verifies that the elements occur the same number of times.

self.assertEqual(Counter(list(first)),
Counter(list(second)))
Example:
• [0, 1, 1] and [1, 0, 1] compare equal.
• [0, 0, 1] and [0, 1] compare unequal.
OrderTest.assertDictContainsSubset(self, subset, dictionary, msg=None)

Checks whether dictionary is a superset of subset.

OrderTest.assertDictEqual(self, d1, d2, msg=None)
OrderTest.assertEqual(self, first, second, msg=None)

Fail if the two objects are unequal as determined by the ‘==’ operator.

OrderTest.assertEquals(*args, **kwargs)
OrderTest.assertFalse(self, expr, msg=None)

Check that the expression is false.

OrderTest.assertGreater(self, a, b, msg=None)

Just like self.assertTrue(a > b), but with a nicer default message.

OrderTest.assertGreaterEqual(self, a, b, msg=None)

Just like self.assertTrue(a >= b), but with a nicer default message.

OrderTest.assertIn(self, member, container, msg=None)

Just like self.assertTrue(a in b), but with a nicer default message.

OrderTest.assertIs(self, expr1, expr2, msg=None)

Just like self.assertTrue(a is b), but with a nicer default message.

OrderTest.assertIsInstance(self, obj, cls, msg=None)

Same as self.assertTrue(isinstance(obj, cls)), with a nicer default message.

OrderTest.assertIsNone(self, obj, msg=None)

Same as self.assertTrue(obj is None), with a nicer default message.

OrderTest.assertIsNot(self, expr1, expr2, msg=None)

Just like self.assertTrue(a is not b), but with a nicer default message.

OrderTest.assertIsNotNone(self, obj, msg=None)

Included for symmetry with assertIsNone.

OrderTest.assertLess(self, a, b, msg=None)

Just like self.assertTrue(a < b), but with a nicer default message.

OrderTest.assertLessEqual(self, a, b, msg=None)

Just like self.assertTrue(a <= b), but with a nicer default message.

OrderTest.assertListEqual(self, list1, list2, msg=None)

A list-specific equality assertion.

Parameters: list1 – The first list to compare. list2 – The second list to compare. msg – Optional message to use on failure instead of a list of differences.
OrderTest.assertLogs(self, logger=None, level=None)

Fail unless a log message of level level or higher is emitted on logger_name or its children. If omitted, level defaults to INFO and logger defaults to the root logger.

This method must be used as a context manager, and will yield a recording object with two attributes: output and records. At the end of the context manager, the output attribute will be a list of the matching formatted log messages and the records attribute will be a list of the corresponding LogRecord objects.

Example:

with self.assertLogs('foo', level='INFO') as cm:
logging.getLogger('foo').info('first message')
logging.getLogger('foo.bar').error('second message')
self.assertEqual(cm.output, ['INFO:foo:first message',
'ERROR:foo.bar:second message'])

OrderTest.assertMultiLineEqual(self, first, second, msg=None)

Assert that two multi-line strings are equal.

OrderTest.assertNotAlmostEqual(self, first, second, places=None, msg=None, delta=None)

Fail if the two objects are equal as determined by their difference rounded to the given number of decimal places (default 7) and comparing to zero, or by comparing that the difference between the two objects is less than the given delta.

Note that decimal places (from zero) are usually not the same as significant digits (measured from the most significant digit).

Objects that are equal automatically fail.

OrderTest.assertNotAlmostEquals(*args, **kwargs)
OrderTest.assertNotEqual(self, first, second, msg=None)

Fail if the two objects are equal as determined by the ‘!=’ operator.

OrderTest.assertNotEquals(*args, **kwargs)
OrderTest.assertNotIn(self, member, container, msg=None)

Just like self.assertTrue(a not in b), but with a nicer default message.

OrderTest.assertNotIsInstance(self, obj, cls, msg=None)

Included for symmetry with assertIsInstance.

OrderTest.assertNotRegex(self, text, unexpected_regex, msg=None)

Fail the test if the text matches the regular expression.

OrderTest.assertNotRegexpMatches(*args, **kwargs)
OrderTest.assertRaises(self, expected_exception, *args, **kwargs)

Fail unless an exception of class expected_exception is raised by the callable when invoked with specified positional and keyword arguments. If a different type of exception is raised, it will not be caught, and the test case will be deemed to have suffered an error, exactly as for an unexpected exception.

If called with the callable and arguments omitted, will return a context object used like this:

with self.assertRaises(SomeException):
do_something()


An optional keyword argument ‘msg’ can be provided when assertRaises is used as a context object.

The context manager keeps a reference to the exception as the ‘exception’ attribute. This allows you to inspect the exception after the assertion:

with self.assertRaises(SomeException) as cm:
do_something()
the_exception = cm.exception
self.assertEqual(the_exception.error_code, 3)

OrderTest.assertRaisesRegex(self, expected_exception, expected_regex, *args, **kwargs)

Asserts that the message in a raised exception matches a regex.

Parameters: expected_exception – Exception class expected to be raised. expected_regex – Regex (re.Pattern object or string) expected to be found in error message. args – Function to be called and extra positional args. kwargs – Extra kwargs. msg – Optional message used in case of failure. Can only be used when assertRaisesRegex is used as a context manager.
OrderTest.assertRaisesRegexp(*args, **kwargs)
OrderTest.assertRegex(self, text, expected_regex, msg=None)

Fail the test unless the text matches the regular expression.

OrderTest.assertRegexpMatches(*args, **kwargs)
OrderTest.assertSequenceEqual(self, seq1, seq2, msg=None, seq_type=None)

An equality assertion for ordered sequences (like lists and tuples).

For the purposes of this function, a valid ordered sequence type is one which can be indexed, has a length, and has an equality operator.

Parameters: seq1 – The first sequence to compare. seq2 – The second sequence to compare. seq_type – The expected datatype of the sequences, or None if no datatype should be enforced. msg – Optional message to use on failure instead of a list of differences.
OrderTest.assertSetEqual(self, set1, set2, msg=None)

A set-specific equality assertion.

Parameters: set1 – The first set to compare. set2 – The second set to compare. msg – Optional message to use on failure instead of a list of differences.

assertSetEqual uses ducktyping to support different types of sets, and is optimized for sets specifically (parameters must support a difference method).

OrderTest.assertTrue(self, expr, msg=None)

Check that the expression is true.

OrderTest.assertTupleEqual(self, tuple1, tuple2, msg=None)

A tuple-specific equality assertion.

Parameters: tuple1 – The first tuple to compare. tuple2 – The second tuple to compare. msg – Optional message to use on failure instead of a list of differences.
OrderTest.assertWarns(self, expected_warning, *args, **kwargs)

Fail unless a warning of class warnClass is triggered by the callable when invoked with specified positional and keyword arguments. If a different type of warning is triggered, it will not be handled: depending on the other warning filtering rules in effect, it might be silenced, printed out, or raised as an exception.

If called with the callable and arguments omitted, will return a context object used like this:

with self.assertWarns(SomeWarning):
do_something()


An optional keyword argument ‘msg’ can be provided when assertWarns is used as a context object.

The context manager keeps a reference to the first matching warning as the ‘warning’ attribute; similarly, the ‘filename’ and ‘lineno’ attributes give you information about the line of Python code from which the warning was triggered. This allows you to inspect the warning after the assertion:

with self.assertWarns(SomeWarning) as cm:
do_something()
the_warning = cm.warning
self.assertEqual(the_warning.some_attribute, 147)

OrderTest.assertWarnsRegex(self, expected_warning, expected_regex, *args, **kwargs)

Asserts that the message in a triggered warning matches a regexp. Basic functioning is similar to assertWarns() with the addition that only warnings whose messages also match the regular expression are considered successful matches.

Parameters: expected_warning – Warning class expected to be triggered. expected_regex – Regex (re.Pattern object or string) expected to be found in error message. args – Function to be called and extra positional args. kwargs – Extra kwargs. msg – Optional message used in case of failure. Can only be used when assertWarnsRegex is used as a context manager.
OrderTest.assert_(*args, **kwargs)
OrderTest.countTestCases(self)
OrderTest.debug(self)

Run the test without collecting errors in a TestResult

OrderTest.defaultTestResult(self)
OrderTest.doCleanups(self)

Execute all cleanup functions. Normally called for you after tearDown.

OrderTest.fail(self, msg=None)

Fail immediately, with the given message.

OrderTest.failIf(*args, **kwargs)
OrderTest.failIfAlmostEqual(*args, **kwargs)
OrderTest.failIfEqual(*args, **kwargs)
OrderTest.failUnless(*args, **kwargs)
OrderTest.failUnlessAlmostEqual(*args, **kwargs)
OrderTest.failUnlessEqual(*args, **kwargs)
OrderTest.failUnlessRaises(*args, **kwargs)
OrderTest.getError(self)[source]

For given h, generate A[h], f and A(f) and return norm of error.

OrderTest.id(self)
OrderTest.orderTest(self)[source]

For number of cells specified in meshSizes setup mesh, call getError and prints mesh size, error, ratio between current and previous error, and estimated order of convergence.

OrderTest.run(self, result=None)
OrderTest.setUp(self)

Hook method for setting up the test fixture before exercising it.

classmethod OrderTest.setUpClass()

Hook method for setting up class fixture before running tests in the class.

OrderTest.setupMesh(self, nC)[source]
OrderTest.shortDescription(self)

Returns a one-line description of the test, or None if no description has been provided.

The default implementation of this method returns the first line of the specified test method’s docstring.

OrderTest.skipTest(self, reason)

Skip this test.

OrderTest.subTest(self, msg=<object object at 0x7f346084ec10>, **params)

Return a context manager that will return the enclosed block of code in a subtest identified by the optional message and keyword parameters. A failure in the subtest marks the test case as failed but resumes execution at the end of the enclosed block, allowing further test code to be executed.

OrderTest.tearDown(self)

Hook method for deconstructing the test fixture after testing it.

classmethod OrderTest.tearDownClass()

Hook method for deconstructing the class fixture after running all tests in the class.