def is_formula_equal(expected, given, samples, cs=True, tolerance=0.01):
try:
variables = samples.split('@')[0].split(',')
sranges = zip(*map(lambda x: map(float, x.split(",")),
samples.split('@')[1].split('#')[0].split(':')))
ranges = dict(zip(variables, sranges))
except Exception as err:
raise Exception("is_formula_eq: failed to evaluate samples expression '%s', err=%s" % (samples, str(err)))
try:
numsamples = int(samples.split('@')[1].split('#')[1])
except Exception as err:
raise Exception("is_formula_eq: failed to evaluate samples expression '%s', bad specification of number of samples, err=%s" % (samples, str(err)))
if not len(variables)==len(sranges):
raise Exception("is_formula_eq: bad samples expression '%s', # variables = %s, but # ranges = %s" % (samples, len(variables), len(sranges)))
for i in range(numsamples):
vvariables = {}
for var in ranges:
value = random.uniform(*ranges[var])
vvariables[str(var)] = value
try:
instructor_result = evaluator(vvariables, dict(), expected, case_sensitive=cs)
except Exception as err:
raise Exception("is_formula_eq: failed to evaluate expected instructor result, formula='%s', vvariables=%s, err=%s" % (expected, vvariables, str(err)))
try:
student_result = evaluator(vvariables, dict(), given, case_sensitive=cs)
except Exception as err:
raise Exception("is_formula_eq: failed to evaluate student result entry, formula='%s', vvariables=%s, err=%s" % (given, vvariables, str(err)))
if abs(instructor_result-student_result) > tolerance:
return False
return True
def test_complex_expression(self):
"""
Calculate combinations of operators and default functions
"""
self.assertAlmostEqual(
calc.evaluator({}, {}, "(2^2+1.0)/sqrt(5e0)*5-1"),
10.180,
delta=1e-3
)
self.assertAlmostEqual(
calc.evaluator({}, {}, "1+1/(1+1/(1+1/(1+1)))"),
1.6,
delta=1e-3
)
self.assertAlmostEqual(
calc.evaluator({}, {}, "10||sin(7+5)"),
-0.567, delta=0.01
)
self.assertAlmostEqual(
calc.evaluator({}, {}, "sin(e)"),
0.41, delta=0.01
)
self.assertAlmostEqual(
calc.evaluator({}, {}, "e^(j*pi)"),
-1, delta=1e-5
)
def test_parallel_resistors_with_zero(self):
"""
Check the behavior of the || operator with 0
"""
self.assertTrue(numpy.isnan(calc.evaluator({}, {}, '0||1')))
self.assertTrue(numpy.isnan(calc.evaluator({}, {}, '0.0||1')))
self.assertTrue(numpy.isnan(calc.evaluator({'x': 0.0}, {}, 'x||1')))
def test_period(self):
"""
The string '.' should not evaluate to anything.
"""
with self.assertRaises(ParseException):
calc.evaluator({}, {}, '.')
with self.assertRaises(ParseException):
calc.evaluator({}, {}, '1+.')
def test_mismatched_parens(self):
"""
Check to see if the evaluator catches mismatched parens
"""
with self.assertRaisesRegexp(calc.UnmatchedParenthesis, 'opened but never closed'):
calc.evaluator({}, {}, "(1+2")
with self.assertRaisesRegexp(calc.UnmatchedParenthesis, 'no matching opening parenthesis'):
calc.evaluator({}, {}, "(1+2))")
def compare_with_tolerance(student_complex, instructor_complex, tolerance=default_tolerance, relative_tolerance=False):
"""
Compare student_complex to instructor_complex with maximum tolerance tolerance.
- student_complex : student result (float complex number)
- instructor_complex : instructor result (float complex number)
- tolerance : float, or string (representing a float or a percentage)
- relative_tolerance: bool, to explicitly use passed tolerance as relative
Note: when a tolerance is a percentage (i.e. '10%'), it will compute that
percentage of the instructor result and yield a number.
If relative_tolerance is set to False, it will use that value and the
instructor result to define the bounds of valid student result:
instructor_complex = 10, tolerance = '10%' will give [9.0, 11.0].
If relative_tolerance is set to True, it will use that value and both
instructor result and student result to define the bounds of valid student
result:
instructor_complex = 10, student_complex = 20, tolerance = '10%' will give
[8.0, 12.0].
This is typically used internally to compare float, with a
default_tolerance = '0.001%'.
Default tolerance of 1e-3% is added to compare two floats for
near-equality (to handle machine representation errors).
Default tolerance is relative, as the acceptable difference between two
floats depends on the magnitude of the floats.
(http://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/)
Examples:
In [183]: 0.000016 - 1.6*10**-5
Out[183]: -3.3881317890172014e-21
In [212]: 1.9e24 - 1.9*10**24
Out[212]: 268435456.0
"""
if isinstance(tolerance, str):
if tolerance == default_tolerance:
relative_tolerance = True
if tolerance.endswith('%'):
tolerance = evaluator(dict(), dict(), tolerance[:-1]) * 0.01
if not relative_tolerance:
tolerance = tolerance * abs(instructor_complex)
else:
tolerance = evaluator(dict(), dict(), tolerance)
if relative_tolerance:
tolerance = tolerance * max(abs(student_complex), abs(instructor_complex))
if isinf(student_complex) or isinf(instructor_complex):
# If an input is infinite, we can end up with `abs(student_complex-instructor_complex)` and
# `tolerance` both equal to infinity. Then, below we would have
# `inf <= inf` which is a fail. Instead, compare directly.
return student_complex == instructor_complex
else:
# v1 and v2 are, in general, complex numbers:
# there are some notes about backward compatibility issue: see responsetypes.get_staff_ans()).
return abs(student_complex - instructor_complex) <= tolerance
def test_function_case_sensitivity(self):
"""
Test the case sensitivity of functions
"""
functions = {'f': lambda x: x,
'F': lambda x: x + 1}
# Test case insensitive evaluation
# Both evaulations should call the same function
self.assertEqual(calc.evaluator({}, functions, 'f(6)'),
calc.evaluator({}, functions, 'F(6)'))
# Test case sensitive evaluation
self.assertNotEqual(calc.evaluator({}, functions, 'f(6)', cs=True),
calc.evaluator({}, functions, 'F(6)', cs=True))
def test_simple_funcs(self):
"""
Subsitution of custom functions
"""
variables = {'x': 4.712}
functions = {'id': lambda x: x}
self.assertEqual(calc.evaluator({}, functions, 'id(2.81)'), 2.81)
self.assertEqual(calc.evaluator({}, functions, 'id(2.81)'), 2.81)
self.assertEqual(calc.evaluator(variables, functions, 'id(x)'), 4.712)
functions.update({'f': numpy.sin})
self.assertAlmostEqual(calc.evaluator(variables, functions, 'f(x)'),
-1, delta=1e-3)
def test_parallel_resistors(self):
"""
Test the parallel resistor operator ||
The formula is given by
a || b || c ...
= 1 / (1/a + 1/b + 1/c + ...)
It is the resistance of a parallel circuit of resistors with resistance
a, b, c, etc&. See if this evaulates correctly.
"""
self.assertEqual(calc.evaluator({}, {}, '1||1'), 0.5)
self.assertEqual(calc.evaluator({}, {}, '1||1||2'), 0.4)
self.assertEqual(calc.evaluator({}, {}, "j||1"), 0.5 + 0.5j)
def test_variable_case_sensitivity(self):
"""
Test the case sensitivity flag and corresponding behavior
"""
self.assertEqual(
calc.evaluator({'R1': 2.0, 'R3': 4.0}, {}, "r1*r3"),
8.0)
variables = {'t': 1.0}
self.assertEqual(calc.evaluator(variables, {}, "t"), 1.0)
self.assertEqual(calc.evaluator(variables, {}, "T"), 1.0)
self.assertEqual(calc.evaluator(variables, {}, "t", cs=True), 1.0)
# Recall 'T' is a default constant, with value 298.15
self.assertAlmostEqual(calc.evaluator(variables, {}, "T", cs=True),
298, delta=0.2)
def test_constants(self):
"""
Test the default constants provided in calc.py
which are: j (complex number), e, pi, k, c, T, q
"""
# Of the form ('expr', python value, tolerance (or None for exact))
default_variables = [
('i', 1j, None),
('j', 1j, None),
('e', 2.7183, 1e-4),
('pi', 3.1416, 1e-4),
('k', 1.3806488e-23, 1e-26), # Boltzmann constant (Joules/Kelvin)
('c', 2.998e8, 1e5), # Light Speed in (m/s)
('T', 298.15, 0.01), # 0 deg C = T Kelvin
('q', 1.602176565e-19, 1e-22) # Fund. Charge (Coulombs)
]
for (variable, value, tolerance) in default_variables:
fail_msg = "Failed on constant '{0}', not within bounds".format(
variable
)
result = calc.evaluator({}, {}, variable)
if tolerance is None:
self.assertEqual(value, result, msg=fail_msg)
else:
self.assertAlmostEqual(
value, result,
delta=tolerance, msg=fail_msg
)
def test_constants(self):
"""
Test the default constants provided in calc.py
which are: j (complex number), e, pi
"""
# Of the form ('expr', python value, tolerance (or None for exact))
default_variables = [
('i', 1j, None),
('j', 1j, None),
('e', 2.7183, 1e-4),
('pi', 3.1416, 1e-4),
]
for (variable, value, tolerance) in default_variables:
fail_msg = "Failed on constant '{0}', not within bounds".format(
variable
)
result = calc.evaluator({}, {}, variable)
if tolerance is None:
self.assertEqual(value, result, msg=fail_msg)
else:
self.assertAlmostEqual(
value, result,
delta=tolerance, msg=fail_msg
)
def test_trailing_period(self):
"""
Test that things like '4.' will be 4 and not throw an error
"""
try:
self.assertEqual(4.0, calc.evaluator({}, {}, '4.'))
except ParseException:
self.fail("'4.' is a valid input, but threw an exception")
def _evaluate_row(self, index, row):
# funcs_dict is used as a required positional argument in the formularesponse grader calc.evaluator. However, it is never used for anything.
funcs_dict = {}
if row['submission']==self.metadata['empty_encoding']:
raise EmptySubmissionException
else:
for sample_index, vars_dict in enumerate(self.metadata['vars_dict_list']):
self.data.loc[index,'eval.'+str(sample_index) ] = calc.evaluator(vars_dict, funcs_dict, row['submission'],case_sensitive=self.metadata['case_sensitive'])
return
def test_function_case_sensitive(self):
"""
Test case sensitive evaluation
Incorrectly capitilized should fail
Also, it should pick the correct version of a function.
"""
with self.assertRaisesRegexp(calc.UndefinedVariable, 'SiN'):
calc.evaluator({}, {}, 'SiN(6)', case_sensitive=True)
# With case sensitive turned on, it should pick the right function
functions = {'f': lambda x: x, 'F': lambda x: x + 1}
self.assertEqual(
6, calc.evaluator({}, functions, 'f(6)', case_sensitive=True)
)
self.assertEqual(
7, calc.evaluator({}, functions, 'F(6)', case_sensitive=True)
)
def is_formula_equal(expected, given, samples, cs=True, tolerance=0.01):
variables = samples.split('@')[0].split(',')
numsamples = int(samples.split('@')[1].split('#')[1])
sranges = zip(*map(lambda x: map(float, x.split(",")),
samples.split('@')[1].split('#')[0].split(':')))
ranges = dict(zip(variables, sranges))
for i in range(numsamples):
vvariables = {}
for var in ranges:
value = random.uniform(*ranges[var])
vvariables[str(var)] = value
try:
instructor_result = evaluator(vvariables, dict(), expected, case_sensitive=cs)
student_result = evaluator(vvariables, dict(), given, case_sensitive=cs)
except Exception as err:
raise Exception("is_formula_eq: vvariables=%s, err=%s" % (vvariables, str(err)))
if abs(instructor_result-student_result) > tolerance:
return False
return True
def test_variable_case_sensitivity(self):
"""
Test the case sensitivity flag and corresponding behavior
"""
self.assertEqual(
calc.evaluator({'R1': 2.0, 'R3': 4.0}, {}, "r1*r3"),
8.0
)
variables = {'E': 1.0}
self.assertEqual(
calc.evaluator(variables, {}, "E", case_sensitive=True),
1.0
)
# Recall 'e' is a default constant, with value 2.718
self.assertAlmostEqual(
calc.evaluator(variables, {}, "e", case_sensitive=True),
2.718, delta=0.02
)
def calculate(request):
""" Calculator in footer of every page. """
equation = request.GET["equation"]
try:
result = calc.evaluator({}, {}, equation)
except:
event = {"error": map(str, sys.exc_info()), "equation": equation}
track.views.server_track(request, "error:calc", event, page="calc")
return HttpResponse(json.dumps({"result": "Invalid syntax"}))
return HttpResponse(json.dumps({"result": str(result)}))
def hint_mag(answer_ids, student_answers, new_cmap, old_cmap, anum=0, sign=False):
global expected
try:
aid = answer_ids[0]
except Exception as err:
raise Exception(
"cannot get answer_ids[%d], answer_ids=%s, new_cmap=%s, err=%s" % (anum, answer_ids, new_cmap, err)
)
ans = student_answers[aid]
try:
ans = float(ans)
except Exception as err:
try:
ans = evaluator({}, {}, ans)
except Exception as err:
hint = '<font color="red">Cannot evaluate your answer</font>'
new_cmap.set_hint_and_mode(aid, hint, "always")
return
try:
if type(expected) == list:
expect = expected[anum]
else:
expect = expected
except Exception as err:
raise Exception("expected answer not evaluated, expected=%s, anum=%s, err=%s" % (expected, anum, str(err)))
# if expect is a dict, then generate hints by range in addition to
extra_hints = []
hint = ""
if type(expect) == dict:
expect_dict = expect
expect = expect_dict["val"]
extra_hints = expect_dict.get("extra_hints", [])
if new_cmap.is_correct(aid):
# if correct, make sure answer is close, else direct student to look at solution
if not is_tight(ans, expect, 0.01):
hint = '<font color="green">Your answer is accepted as correct, but more than 1% from the expected. Please check the solutions, and use the expected answer in any further calculations.</font>'
else:
hint = is_close(ans, expect)
if not hint and sign:
hint = is_sign_correct(ans, expect)
for eh in extra_hints:
range = eh.get("range", "")
if range:
if in_range(ans, range):
hint += " " + eh["hint"]
if hint:
new_cmap.set_hint_and_mode(aid, hint, "always")
def calculate(request):
''' Calculator in footer of every page. '''
equation = request.GET['equation']
try:
result = calc.evaluator({}, {}, equation)
except:
event = {'error': map(str, sys.exc_info()),
'equation': equation}
track.views.server_track(request, 'error:calc', event, page='calc')
return HttpResponse(json.dumps({'result': 'Invalid syntax'}))
return HttpResponse(json.dumps({'result': str(result)}))
def test_function_case_insensitive(self):
"""
Test case insensitive evaluation
Normal functions with some capitals should be fine
"""
self.assertAlmostEqual(-0.28,
calc.evaluator({}, {},
'SiN(6)',
case_sensitive=False),
delta=1e-3)
def test_variable_case_sensitivity(self):
"""
Test the case sensitivity flag and corresponding behavior
"""
self.assertEqual(calc.evaluator({
'R1': 2.0,
'R3': 4.0
}, {}, "r1*r3"), 8.0)
variables = {'t': 1.0}
self.assertEqual(calc.evaluator(variables, {}, "t"), 1.0)
self.assertEqual(calc.evaluator(variables, {}, "T"), 1.0)
self.assertEqual(
calc.evaluator(variables, {}, "t", case_sensitive=True), 1.0)
# Recall 'T' is a default constant, with value 298.15
self.assertAlmostEqual(calc.evaluator(variables, {},
"T",
case_sensitive=True),
298,
delta=0.2)
def test_exponential_answer(self):
"""
Test for correct interpretation of scientific notation
"""
answer = 50
correct_responses = [
"50", "50.0", "5e1", "5e+1", "50e0", "50.0e0", "500e-1"
]
incorrect_responses = ["", "3.9", "4.1", "0", "5.01e1"]
for input_str in correct_responses:
result = calc.evaluator({}, {}, input_str)
fail_msg = "Expected '{0}' to equal {1}".format(input_str, answer)
self.assertEqual(answer, result, msg=fail_msg)
for input_str in incorrect_responses:
result = calc.evaluator({}, {}, input_str)
fail_msg = "Expected '{0}' to not equal {1}".format(
input_str, answer)
self.assertNotEqual(answer, result, msg=fail_msg)
def calculate(request):
''' Calculator in footer of every page. '''
equation = request.GET['equation']
try:
result = calc.evaluator({}, {}, equation)
except:
event = {'error': map(str, sys.exc_info()),
'equation': equation}
track.views.server_track(request, 'error:calc', event, page='calc')
return HttpResponse(json.dumps({'result': 'Invalid syntax'}))
return HttpResponse(json.dumps({'result': str(result)}))
def test_exponential_answer(self):
"""
Test for correct interpretation of scientific notation
"""
answer = 50
correct_responses = ["50", "50.0", "5e1", "5e+1",
"50e0", "50.0e0", "500e-1"]
incorrect_responses = ["", "3.9", "4.1", "0", "5.01e1"]
for input_str in correct_responses:
result = calc.evaluator({}, {}, input_str)
fail_msg = "Expected '{0}' to equal {1}".format(
input_str, answer)
self.assertEqual(answer, result, msg=fail_msg)
for input_str in incorrect_responses:
result = calc.evaluator({}, {}, input_str)
fail_msg = "Expected '{0}' to not equal {1}".format(
input_str, answer)
self.assertNotEqual(answer, result, msg=fail_msg)
def test_function_case_insensitive(self):
"""
Test case insensitive evaluation
Normal functions with some capitals should be fine
"""
self.assertAlmostEqual(
-0.28,
calc.evaluator({}, {}, 'SiN(6)', case_sensitive=False),
delta=1e-3
)
def test_complex_expression(self):
"""
Calculate combinations of operators and default functions
"""
self.assertAlmostEqual(calc.evaluator({}, {},
"(2^2+1.0)/sqrt(5e0)*5-1"),
10.180,
delta=1e-3)
self.assertAlmostEqual(calc.evaluator({}, {}, "1+1/(1+1/(1+1/(1+1)))"),
1.6,
delta=1e-3)
self.assertAlmostEqual(calc.evaluator({}, {}, "10||sin(7+5)"),
-0.567,
delta=0.01)
self.assertAlmostEqual(calc.evaluator({}, {}, "sin(e)"),
0.41,
delta=0.01)
self.assertAlmostEqual(calc.evaluator({}, {}, "e^(j*pi)"),
-1,
delta=1e-5)
def test_explicit_sci_notation(self):
"""
Expressions like 1.6*10^-3 (not 1.6e-3) it should evaluate.
"""
self.assertEqual(
calc.evaluator({}, {}, "-1.6*10^-3"),
-0.0016
)
self.assertEqual(
calc.evaluator({}, {}, "-1.6*10^(-3)"),
-0.0016
)
self.assertEqual(
calc.evaluator({}, {}, "-1.6*10^3"),
-1600
)
self.assertEqual(
calc.evaluator({}, {}, "-1.6*10^(3)"),
-1600
)
def test_explicit_sci_notation(self):
"""
Expressions like 1.6*10^-3 (not 1.6e-3) it should evaluate.
"""
self.assertEqual(
calc.evaluator({}, {}, "-1.6*10^-3"),
-0.0016
)
self.assertEqual(
calc.evaluator({}, {}, "-1.6*10^(-3)"),
-0.0016
)
self.assertEqual(
calc.evaluator({}, {}, "-1.6*10^3"),
-1600
)
self.assertEqual(
calc.evaluator({}, {}, "-1.6*10^(3)"),
-1600
)
def hint_mag(answer_ids, student_answers, new_cmap, old_cmap, anum=0, sign=False):
global expected
try:
aid = answer_ids[0]
except Exception as err:
raise Exception('cannot get answer_ids[%d], answer_ids=%s, new_cmap=%s, err=%s' % (anum, answer_ids, new_cmap, err))
ans = student_answers[aid]
try:
ans = float(ans)
except Exception as err:
try:
ans = evaluator({},{}, ans)
except Exception as err:
hint = '<font color="red">Cannot evaluate your answer</font>'
new_cmap.set_hint_and_mode(aid, hint, 'always')
return
try:
if type(expected)==list:
expect = expected[anum]
else:
expect = expected
except Exception as err:
raise Exception('expected answer not evaluated, expected=%s, anum=%s, err=%s' % (expected, anum, str(err)))
# if expect is a dict, then generate hints by range in addition to
extra_hints = []
hint = ''
if type(expect)==dict:
expect_dict = expect
expect = expect_dict['val']
extra_hints = expect_dict.get('extra_hints', [])
if new_cmap.is_correct(aid):
# if correct, make sure answer is close, else direct student to look at solution
if not is_tight(ans, expect, 0.01):
hint = '<font color="green">Your answer is accepted as correct, but more than 1% from the expected. Please check the solutions, and use the expected answer in any further calculations.</font>'
else:
hint = is_close(ans, expect)
if not hint and sign:
hint = is_sign_correct(ans, expect)
for eh in extra_hints:
range = eh.get('range','')
if range:
if in_range(ans, range):
hint += ' ' + eh['hint']
if hint:
new_cmap.set_hint_and_mode(aid, hint, 'always')
def test_undefined_vars(self):
"""
Check to see if the evaluator catches undefined variables
"""
variables = {'R1': 2.0, 'R3': 4.0}
with self.assertRaisesRegexp(calc.UndefinedVariable, r'QWSEKO'):
calc.evaluator({}, {}, "5+7*QWSEKO")
with self.assertRaisesRegexp(calc.UndefinedVariable, r'r2'):
calc.evaluator({'r1': 5}, {}, "r1+r2")
with self.assertRaisesRegexp(calc.UndefinedVariable, r'r1, r3'):
calc.evaluator(variables, {}, "r1*r3", case_sensitive=True)
with self.assertRaisesRegexp(calc.UndefinedVariable, r'did you forget to use \*'):
calc.evaluator(variables, {}, "R1(R3 + 1)")
def compare_with_tolerance(complex1, complex2, tolerance=default_tolerance, relative_tolerance=False):
"""
Compare complex1 to complex2 with maximum tolerance tol.
If tolerance is type string, then it is counted as relative if it ends in %; otherwise, it is absolute.
- complex1 : student result (float complex number)
- complex2 : instructor result (float complex number)
- tolerance : string representing a number or float
- relative_tolerance: bool, used when`tolerance` is float to explicitly use passed tolerance as relative.
Default tolerance of 1e-3% is added to compare two floats for
near-equality (to handle machine representation errors).
Default tolerance is relative, as the acceptable difference between two
floats depends on the magnitude of the floats.
(http://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/)
Examples:
In [183]: 0.000016 - 1.6*10**-5
Out[183]: -3.3881317890172014e-21
In [212]: 1.9e24 - 1.9*10**24
Out[212]: 268435456.0
"""
if relative_tolerance:
tolerance = tolerance * max(abs(complex1), abs(complex2))
elif tolerance.endswith('%'):
tolerance = evaluator(dict(), dict(), tolerance[:-1]) * 0.01
tolerance = tolerance * max(abs(complex1), abs(complex2))
else:
tolerance = evaluator(dict(), dict(), tolerance)
if isinf(complex1) or isinf(complex2):
# If an input is infinite, we can end up with `abs(complex1-complex2)` and
# `tolerance` both equal to infinity. Then, below we would have
# `inf <= inf` which is a fail. Instead, compare directly.
return complex1 == complex2
else:
# v1 and v2 are, in general, complex numbers:
# there are some notes about backward compatibility issue: see responsetypes.get_staff_ans()).
return abs(complex1 - complex2) <= tolerance
def test_undefined_vars(self):
"""
Check to see if the evaluator catches undefined variables
"""
variables = {'R1': 2.0, 'R3': 4.0}
with self.assertRaisesRegexp(calc.UndefinedVariable, r'QWSEKO'):
calc.evaluator({}, {}, "5+7*QWSEKO")
with self.assertRaisesRegexp(calc.UndefinedVariable, r'r2'):
calc.evaluator({'r1': 5}, {}, "r1+r2")
with self.assertRaisesRegexp(calc.UndefinedVariable, r'r1, r3'):
calc.evaluator(variables, {}, "r1*r3", case_sensitive=True)
with self.assertRaisesRegexp(calc.UndefinedVariable,
r'did you forget to use \*'):
calc.evaluator(variables, {}, "R1(R3 + 1)")
def test_operator_sanity(self):
"""
Test for simple things like '5+2' and '5/2'
"""
var1 = 5.0
var2 = 2.0
operators = [('+', 7), ('-', 3), ('*', 10), ('/', 2.5), ('^', 25)]
for (operator, answer) in operators:
input_str = "{0} {1} {2}".format(var1, operator, var2)
result = calc.evaluator({}, {}, input_str)
fail_msg = "Failed on operator '{0}': '{1}' was not {2}".format(
operator, input_str, answer)
self.assertEqual(answer, result, msg=fail_msg)
def compare_with_tolerance(v1, v2, tol):
''' Compare v1 to v2 with maximum tolerance tol
tol is relative if it ends in %; otherwise, it is absolute
- v1 : student result (number)
- v2 : instructor result (number)
- tol : tolerance (string representing a number)
'''
relative = tol.endswith('%')
if relative:
tolerance_rel = evaluator(dict(), dict(), tol[:-1]) * 0.01
tolerance = tolerance_rel * max(abs(v1), abs(v2))
else:
tolerance = evaluator(dict(), dict(), tol)
if isinf(v1) or isinf(v2):
# If an input is infinite, we can end up with `abs(v1-v2)` and
# `tolerance` both equal to infinity. Then, below we would have
# `inf <= inf` which is a fail. Instead, compare directly.
return v1 == v2
else:
return abs(v1 - v2) <= tolerance
def test_operator_sanity(self):
"""
Test for simple things like '5+2' and '5/2'
"""
var1 = 5.0
var2 = 2.0
operators = [('+', 7), ('-', 3), ('*', 10), ('/', 2.5), ('^', 25)]
for (operator, answer) in operators:
input_str = "{0} {1} {2}".format(var1, operator, var2)
result = calc.evaluator({}, {}, input_str)
fail_msg = "Failed on operator '{0}': '{1}' was not {2}".format(
operator, input_str, answer)
self.assertEqual(answer, result, msg=fail_msg)
def assert_function_values(self, fname, ins, outs, tolerance=1e-3):
"""
Helper function to test many values at once
Test the accuracy of evaluator's use of the function given by fname
Specifically, the equality of `fname(ins[i])` against outs[i].
This is used later to test a whole bunch of f(x) = y at a time
"""
for (arg, val) in zip(ins, outs):
input_str = "{0}({1})".format(fname, arg)
result = calc.evaluator({}, {}, input_str)
fail_msg = "Failed on function {0}: '{1}' was not {2}".format(
fname, input_str, val)
self.assertAlmostEqual(val, result, delta=tolerance, msg=fail_msg)
def test_trig_functions(self):
"""
Test the trig functions provided in calc.py
which are: sin, cos, tan, arccos, arcsin, arctan
"""
angles = ['-pi/4', '0', 'pi/6', 'pi/5', '5*pi/4', '9*pi/4', '1 + j']
sin_values = [-0.707, 0, 0.5, 0.588, -0.707, 0.707, 1.298 + 0.635j]
cos_values = [0.707, 1, 0.866, 0.809, -0.707, 0.707, 0.834 - 0.989j]
tan_values = [-1, 0, 0.577, 0.727, 1, 1, 0.272 + 1.084j]
# Cannot test tan(pi/2) b/c pi/2 is a float and not precise...
self.assert_function_values('sin', angles, sin_values)
self.assert_function_values('cos', angles, cos_values)
self.assert_function_values('tan', angles, tan_values)
# Include those where the real part is between -pi/2 and pi/2
arcsin_inputs = ['-0.707', '0', '0.5', '0.588', '1.298 + 0.635*j']
arcsin_angles = [-0.785, 0, 0.524, 0.629, 1 + 1j]
self.assert_function_values('arcsin', arcsin_inputs, arcsin_angles)
# Rather than a complex number, numpy.arcsin gives nan
self.assertTrue(numpy.isnan(calc.evaluator({}, {}, 'arcsin(-1.1)')))
self.assertTrue(numpy.isnan(calc.evaluator({}, {}, 'arcsin(1.1)')))
# Include those where the real part is between 0 and pi
arccos_inputs = ['1', '0.866', '0.809', '0.834-0.989*j']
arccos_angles = [0, 0.524, 0.628, 1 + 1j]
self.assert_function_values('arccos', arccos_inputs, arccos_angles)
self.assertTrue(numpy.isnan(calc.evaluator({}, {}, 'arccos(-1.1)')))
self.assertTrue(numpy.isnan(calc.evaluator({}, {}, 'arccos(1.1)')))
# Has the same range as arcsin
arctan_inputs = ['-1', '0', '0.577', '0.727', '0.272 + 1.084*j']
arctan_angles = arcsin_angles
self.assert_function_values('arctan', arctan_inputs, arctan_angles)
def assert_function_values(self, fname, ins, outs, tolerance=1e-3):
"""
Helper function to test many values at once
Test the accuracy of evaluator's use of the function given by fname
Specifically, the equality of `fname(ins[i])` against outs[i].
This is used later to test a whole bunch of f(x) = y at a time
"""
for (arg, val) in zip(ins, outs):
input_str = "{0}({1})".format(fname, arg)
result = calc.evaluator({}, {}, input_str)
fail_msg = "Failed on function {0}: '{1}' was not {2}".format(
fname, input_str, val)
self.assertAlmostEqual(val, result, delta=tolerance, msg=fail_msg)
def test_trig_functions(self):
"""
Test the trig functions provided in calc.py
which are: sin, cos, tan, arccos, arcsin, arctan
"""
angles = ['-pi/4', '0', 'pi/6', 'pi/5', '5*pi/4', '9*pi/4', '1 + j']
sin_values = [-0.707, 0, 0.5, 0.588, -0.707, 0.707, 1.298 + 0.635j]
cos_values = [0.707, 1, 0.866, 0.809, -0.707, 0.707, 0.834 - 0.989j]
tan_values = [-1, 0, 0.577, 0.727, 1, 1, 0.272 + 1.084j]
# Cannot test tan(pi/2) b/c pi/2 is a float and not precise...
self.assert_function_values('sin', angles, sin_values)
self.assert_function_values('cos', angles, cos_values)
self.assert_function_values('tan', angles, tan_values)
# Include those where the real part is between -pi/2 and pi/2
arcsin_inputs = ['-0.707', '0', '0.5', '0.588', '1.298 + 0.635*j']
arcsin_angles = [-0.785, 0, 0.524, 0.629, 1 + 1j]
self.assert_function_values('arcsin', arcsin_inputs, arcsin_angles)
# Rather than a complex number, numpy.arcsin gives nan
self.assertTrue(numpy.isnan(calc.evaluator({}, {}, 'arcsin(-1.1)')))
self.assertTrue(numpy.isnan(calc.evaluator({}, {}, 'arcsin(1.1)')))
# Include those where the real part is between 0 and pi
arccos_inputs = ['1', '0.866', '0.809', '0.834-0.989*j']
arccos_angles = [0, 0.524, 0.628, 1 + 1j]
self.assert_function_values('arccos', arccos_inputs, arccos_angles)
self.assertTrue(numpy.isnan(calc.evaluator({}, {}, 'arccos(-1.1)')))
self.assertTrue(numpy.isnan(calc.evaluator({}, {}, 'arccos(1.1)')))
# Has the same range as arcsin
arctan_inputs = ['-1', '0', '0.577', '0.727', '0.272 + 1.084*j']
arctan_angles = arcsin_angles
self.assert_function_values('arctan', arctan_inputs, arctan_angles)
def compare_with_tolerance(v1, v2, tol=default_tolerance):
'''
Compare v1 to v2 with maximum tolerance tol.
tol is relative if it ends in %; otherwise, it is absolute
- v1 : student result (float complex number)
- v2 : instructor result (float complex number)
- tol : tolerance (string representing a number)
Default tolerance of 1e-3% is added to compare two floats for near-equality
(to handle machine representation errors).
It is relative, as the acceptable difference between two floats depends on the magnitude of the floats.
(http://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/)
Examples:
In [183]: 0.000016 - 1.6*10**-5
Out[183]: -3.3881317890172014e-21
In [212]: 1.9e24 - 1.9*10**24
Out[212]: 268435456.0
'''
relative = tol.endswith('%')
if relative:
tolerance_rel = evaluator(dict(), dict(), tol[:-1]) * 0.01
tolerance = tolerance_rel * max(abs(v1), abs(v2))
else:
tolerance = evaluator(dict(), dict(), tol)
if isinf(v1) or isinf(v2):
# If an input is infinite, we can end up with `abs(v1-v2)` and
# `tolerance` both equal to infinity. Then, below we would have
# `inf <= inf` which is a fail. Instead, compare directly.
return v1 == v2
else:
# v1 and v2 are, in general, complex numbers:
# there are some notes about backward compatibility issue: see responsetypes.get_staff_ans()).
return abs(v1 - v2) <= tolerance
def test_raises_zero_division_err(self):
"""
Ensure division by zero gives an error
"""
with self.assertRaises(ZeroDivisionError):
calc.evaluator({}, {}, '1/0')
with self.assertRaises(ZeroDivisionError):
calc.evaluator({}, {}, '1/0.0')
with self.assertRaises(ZeroDivisionError):
calc.evaluator({'x': 0.0}, {}, '1/x')
def test_si_suffix(self):
"""
Test calc.py's unique functionality of interpreting si 'suffixes'.
For instance '%' stand for 1/100th so '1%' should be 0.01
"""
test_mapping = [('4.2%', 0.042)]
for (expr, answer) in test_mapping:
tolerance = answer * 1e-6 # Make rel. tolerance, because of floats
fail_msg = "Failure in testing suffix '{0}': '{1}' was not {2}"
fail_msg = fail_msg.format(expr[-1], expr, answer)
self.assertAlmostEqual(calc.evaluator({}, {}, expr),
answer,
delta=tolerance,
msg=fail_msg)
def test_number_input(self):
"""
Test different kinds of float inputs
See also
test_trailing_period (slightly different)
test_exponential_answer
test_si_suffix
"""
easy_eval = lambda x: calc.evaluator({}, {}, x)
self.assertEqual(easy_eval("13"), 13)
self.assertEqual(easy_eval("3.14"), 3.14)
self.assertEqual(easy_eval(".618033989"), 0.618033989)
self.assertEqual(easy_eval("-13"), -13)
self.assertEqual(easy_eval("-3.14"), -3.14)
self.assertEqual(easy_eval("-.618033989"), -0.618033989)
def test_si_suffix(self):
"""
Test calc.py's unique functionality of interpreting si 'suffixes'.
For instance 'k' stand for 'kilo-' so '1k' should be 1,000
"""
test_mapping = [('4.2%', 0.042), ('2.25k', 2250), ('8.3M', 8300000),
('9.9G', 9.9e9), ('1.2T', 1.2e12), ('7.4c', 0.074),
('5.4m', 0.0054), ('8.7u', 0.0000087),
('5.6n', 5.6e-9), ('4.2p', 4.2e-12)]
for (expr, answer) in test_mapping:
tolerance = answer * 1e-6 # Make rel. tolerance, because of floats
fail_msg = "Failure in testing suffix '{0}': '{1}' was not {2}"
fail_msg = fail_msg.format(expr[-1], expr, answer)
self.assertAlmostEqual(calc.evaluator({}, {}, expr),
answer,
delta=tolerance,
msg=fail_msg)
def compare_with_tolerance(student_complex, instructor_complex, tolerance=default_tolerance, relative_tolerance=False):
"""
Compare student_complex to instructor_complex with maximum tolerance tolerance.
- student_complex : student result (float complex number)
- instructor_complex : instructor result (float complex number)
- tolerance : float, or string (representing a float or a percentage)
- relative_tolerance: bool, to explicitly use passed tolerance as relative
Note: when a tolerance is a percentage (i.e. '10%'), it will compute that
percentage of the instructor result and yield a number.
If relative_tolerance is set to False, it will use that value and the
instructor result to define the bounds of valid student result:
instructor_complex = 10, tolerance = '10%' will give [9.0, 11.0].
If relative_tolerance is set to True, it will use that value and both
instructor result and student result to define the bounds of valid student
result:
instructor_complex = 10, student_complex = 20, tolerance = '10%' will give
[8.0, 12.0].
This is typically used internally to compare float, with a
default_tolerance = '0.001%'.
Default tolerance of 1e-3% is added to compare two floats for
near-equality (to handle machine representation errors).
Default tolerance is relative, as the acceptable difference between two
floats depends on the magnitude of the floats.
(http://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/)
Examples:
In [183]: 0.000016 - 1.6*10**-5
Out[183]: -3.3881317890172014e-21
In [212]: 1.9e24 - 1.9*10**24
Out[212]: 268435456.0
"""
if isinstance(tolerance, str):
if tolerance == default_tolerance:
relative_tolerance = True
if tolerance.endswith('%'):
tolerance = evaluator(dict(), dict(), tolerance[:-1]) * 0.01
if not relative_tolerance:
tolerance = tolerance * abs(instructor_complex)
else:
tolerance = evaluator(dict(), dict(), tolerance)
if relative_tolerance:
tolerance = tolerance * max(abs(student_complex), abs(instructor_complex))
if isinf(student_complex) or isinf(instructor_complex):
# If an input is infinite, we can end up with `abs(student_complex-instructor_complex)` and
# `tolerance` both equal to infinity. Then, below we would have
# `inf <= inf` which is a fail. Instead, compare directly.
return student_complex == instructor_complex
# because student_complex and instructor_complex are not necessarily
# complex here, we enforce it here:
student_complex = complex(student_complex)
instructor_complex = complex(instructor_complex)
# if both the instructor and student input are real,
# compare them as Decimals to avoid rounding errors
if not (instructor_complex.imag or student_complex.imag):
# if either of these are not a number, short circuit and return False
if isnan(instructor_complex.real) or isnan(student_complex.real):
return False
student_decimal = Decimal(str(student_complex.real))
instructor_decimal = Decimal(str(instructor_complex.real))
tolerance_decimal = Decimal(str(tolerance))
return abs(student_decimal - instructor_decimal) <= tolerance_decimal
else:
# v1 and v2 are, in general, complex numbers:
# there are some notes about backward compatibility issue: see responsetypes.get_staff_ans()).
return abs(student_complex - instructor_complex) <= tolerance
def compare_with_tolerance(student_complex,
instructor_complex,
tolerance=default_tolerance,
relative_tolerance=False):
"""
Compare student_complex to instructor_complex with maximum tolerance tolerance.
- student_complex : student result (float complex number)
- instructor_complex : instructor result (float complex number)
- tolerance : float, or string (representing a float or a percentage)
- relative_tolerance: bool, to explicitly use passed tolerance as relative
Note: when a tolerance is a percentage (i.e. '10%'), it will compute that
percentage of the instructor result and yield a number.
If relative_tolerance is set to False, it will use that value and the
instructor result to define the bounds of valid student result:
instructor_complex = 10, tolerance = '10%' will give [9.0, 11.0].
If relative_tolerance is set to True, it will use that value and both
instructor result and student result to define the bounds of valid student
result:
instructor_complex = 10, student_complex = 20, tolerance = '10%' will give
[8.0, 12.0].
This is typically used internally to compare float, with a
default_tolerance = '0.001%'.
Default tolerance of 1e-3% is added to compare two floats for
near-equality (to handle machine representation errors).
Default tolerance is relative, as the acceptable difference between two
floats depends on the magnitude of the floats.
(http://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/)
Examples:
In [183]: 0.000016 - 1.6*10**-5
Out[183]: -3.3881317890172014e-21
In [212]: 1.9e24 - 1.9*10**24
Out[212]: 268435456.0
"""
if isinstance(tolerance, str):
if tolerance == default_tolerance:
relative_tolerance = True
if tolerance.endswith('%'):
tolerance = evaluator(dict(), dict(), tolerance[:-1]) * 0.01
if not relative_tolerance:
tolerance = tolerance * abs(instructor_complex)
else:
tolerance = evaluator(dict(), dict(), tolerance)
if relative_tolerance:
tolerance = tolerance * max(abs(student_complex),
abs(instructor_complex))
if isinf(student_complex) or isinf(instructor_complex):
# If an input is infinite, we can end up with `abs(student_complex-instructor_complex)` and
# `tolerance` both equal to infinity. Then, below we would have
# `inf <= inf` which is a fail. Instead, compare directly.
return student_complex == instructor_complex
else:
# v1 and v2 are, in general, complex numbers:
# there are some notes about backward compatibility issue: see responsetypes.get_staff_ans()).
decimal_places = None
# count the "decimal_places" for "student_complex". e.g, for
# "student_complex" value "152.3667" the "decimal_places" will be
# 4 as there are 4 digits "3667" after decimal
if isinstance(student_complex, float):
decimal_places = Decimal(
str(student_complex)).as_tuple().exponent * -1 # pylint: disable=E1103
abs_value = abs(student_complex - instructor_complex)
# decimal_places could be NaN in some cases
if decimal_places and isinstance(decimal_places, int):
# abs_value contains 17 digits exponent value so
# round it up to "decimal_places"
abs_value = round(abs_value, decimal_places)
return abs_value <= tolerance
def test_trailing_period(self):
"""
Test that things like '4.' will be 4 and not throw an error
"""
self.assertEqual(4.0, calc.evaluator({}, {}, '4.'))
def easy_eval(x):
return calc.evaluator({}, {}, x)
def test_simple_vars(self):
"""
Substitution of variables into simple equations
"""
variables = {
'x': 9.72,
'y': 7.91,
'loooooong': 6.4,
"f_0'": 2.0,
"T_{ijk}^{123}''": 5.2
}
# Should not change value of constant
# even with different numbers of variables...
self.assertEqual(calc.evaluator({'x': 9.72}, {}, '13'), 13)
self.assertEqual(calc.evaluator({'x': 9.72, 'y': 7.91}, {}, '13'), 13)
self.assertEqual(calc.evaluator(variables, {}, '13'), 13)
# Easy evaluation
self.assertEqual(calc.evaluator(variables, {}, 'x'), 9.72)
self.assertEqual(calc.evaluator(variables, {}, 'y'), 7.91)
self.assertEqual(calc.evaluator(variables, {}, 'loooooong'), 6.4)
self.assertEqual(calc.evaluator(variables, {}, "f_0'"), 2.0)
self.assertEqual(calc.evaluator(variables, {}, "T_{ijk}^{123}''"), 5.2)
# Test a simple equation
self.assertAlmostEqual(
calc.evaluator(variables, {}, '3*x-y'),
21.25,
delta=0.01 # = 3 * 9.72 - 7.91
)
self.assertAlmostEqual(calc.evaluator(variables, {}, 'x*y'),
76.89,
delta=0.01)
self.assertEqual(calc.evaluator({'x': 9.72, 'y': 7.91}, {}, "13"), 13)
self.assertEqual(calc.evaluator(variables, {}, "13"), 13)
self.assertEqual(
calc.evaluator(
{
'a': 2.2997471478310274,
'k': 9,
'm': 8,
'x': 0.6600949841121
}, {}, "5"), 5)
def test_calc(self):
variables = {'R1': 2.0, 'R3': 4.0}
functions = {'sin': numpy.sin, 'cos': numpy.cos}
self.assertTrue(abs(calc.evaluator(variables, functions, "10000||sin(7+5)+0.5356")) < 0.01)
self.assertEqual(calc.evaluator({'R1': 2.0, 'R3': 4.0}, {}, "13"), 13)
self.assertEqual(calc.evaluator(variables, functions, "13"), 13)
self.assertEqual(calc.evaluator({'a': 2.2997471478310274, 'k': 9, 'm': 8, 'x': 0.66009498411213041}, {}, "5"), 5)
self.assertEqual(calc.evaluator({}, {}, "-1"), -1)
self.assertEqual(calc.evaluator({}, {}, "-0.33"), -.33)
self.assertEqual(calc.evaluator({}, {}, "-.33"), -.33)
self.assertEqual(calc.evaluator(variables, functions, "R1*R3"), 8.0)
self.assertTrue(abs(calc.evaluator(variables, functions, "sin(e)-0.41")) < 0.01)
self.assertTrue(abs(calc.evaluator(variables, functions, "k*T/q-0.025")) < 0.001)
self.assertTrue(abs(calc.evaluator(variables, functions, "e^(j*pi)") + 1) < 0.00001)
self.assertTrue(abs(calc.evaluator(variables, functions, "j||1") - 0.5 - 0.5j) < 0.00001)
variables['t'] = 1.0
# Use self.assertAlmostEqual here...
self.assertTrue(abs(calc.evaluator(variables, functions, "t") - 1.0) < 0.00001)
self.assertTrue(abs(calc.evaluator(variables, functions, "T") - 1.0) < 0.00001)
self.assertTrue(abs(calc.evaluator(variables, functions, "t", cs=True) - 1.0) < 0.00001)
self.assertTrue(abs(calc.evaluator(variables, functions, "T", cs=True) - 298) < 0.2)
# Use self.assertRaises here...
exception_happened = False
try:
calc.evaluator({}, {}, "5+7 QWSEKO")
except:
exception_happened = True
self.assertTrue(exception_happened)
try:
calc.evaluator({'r1': 5}, {}, "r1+r2")
except calc.UndefinedVariable:
pass
self.assertEqual(calc.evaluator(variables, functions, "r1*r3"), 8.0)
exception_happened = False
try:
calc.evaluator(variables, functions, "r1*r3", cs=True)
except:
exception_happened = True
self.assertTrue(exception_happened)