def test_summation():
grader = SumGrader(answers={
'lower': '0',
'upper': '1',
'summand': 'x',
'summation_variable': 'x'
},
input_positions={'summand': 1})
# Here we bypass the class entirely to just test the summation capabilities.
def summand(x):
return x
assert 6 == grader.perform_summation(summand, lower=1, upper=3, even_odd=0)
assert 9 == grader.perform_summation(summand, lower=1, upper=5, even_odd=1)
assert 6 == grader.perform_summation(summand, lower=1, upper=5, even_odd=2)
assert 1e3 * (1e3 + 1) / 2 == grader.perform_summation(summand,
lower=1,
upper=float('inf'),
even_odd=0)
def summand(x):
return x**2
assert 14 == grader.perform_summation(summand,
lower=1,
upper=3,
even_odd=0)
def test_convergence():
# Test that we get convergence to well-known functions
# Here we bypass the class entirely to just test the summation capabilities.
grader = SumGrader(answers={
'lower': '0',
'upper': '1',
'summand': 'x',
'summation_variable': 'x'
},
input_positions={'summand': 1})
x = 0.1
def exp_summand(n):
value, _ = evaluator('x^n/fact(n)', {'n': n, 'x': x})
return value
result = grader.perform_summation(exp_summand,
lower=0,
upper=float('inf'),
even_odd=0,
infty_val=100)
expect = np.exp(x)
assert abs(result - expect) < 1e-14
def sin_summand(n):
value, _ = evaluator('(-1)^((n-1)/2)*x^n/fact(n)', {'n': n, 'x': x})
return value
result = grader.perform_summation(sin_summand,
lower=0,
upper=float('inf'),
even_odd=1,
infty_val=100)
expect = np.sin(x)
assert abs(result - expect) < 1e-14
def cos_summand(n):
value, _ = evaluator('(-1)^(n/2)*x^n/fact(n)', {'n': n, 'x': x})
return value
result = grader.perform_summation(cos_summand,
lower=0,
upper=float('inf'),
even_odd=2,
infty_val=100)
expect = np.cos(x)
assert abs(result - expect) < 1e-14