def test_instructor_vars():
"""Ensures that instructor variables are not available to students"""
grader = FormulaGrader(
answers='sin(x)/cos(x)',
variables=['x', 's', 'c'],
numbered_vars=['y'],
sample_from={
'x': [-3.14159, 3.14159],
's': DependentSampler(depends=["x"], formula="sin(x)"),
'c': DependentSampler(depends=["x"], formula="cos(x)")
},
instructor_vars=['x', 'pi', 'y_{0}',
'nothere'] # nothere will be ignored
)
assert grader(None, 's/c')['ok']
assert not grader(None, 'y_{1}')['ok']
with raises(UndefinedVariable,
match="'x' not permitted in answer as a variable"):
grader(None, 'tan(x)')
with raises(UndefinedVariable,
match="'pi' not permitted in answer as a variable"):
grader(None, 'pi')
with raises(UndefinedVariable,
match=r"'y_\{0\}' not permitted in answer as a variable"):
grader(None, 'y_{0}')
def test_overriding_constant_with_dependent_sampling():
symbols = ['a', 'b', 'c']
samples = 1
sample_from = {
'a': RealInterval([10, 10]),
'b': DependentSampler(depends=["a"], formula="a+1"),
'c': DependentSampler(depends=["b"], formula="b+1")
}
funcs, suffs = {}, {}
consts = {'unity': 1, 'b': 3.14}
result = gen_symbols_samples(symbols, samples, sample_from, funcs, suffs, consts)[0]
a, b, c = [result[sym] for sym in 'abc']
assert a == 10
assert b == 11
assert c == 12
def test_dependent_sampler_infers_dependence():
sampler = DependentSampler(formula="a+1")
assert sampler.config['depends'] == ['a']
sampler = DependentSampler(formula="x^2+y^2+sin(c)")
assert set(sampler.config['depends']) == set(['x', 'y', 'c'])
# Test that 'depends' is now ignored
symbols = ["x", "y"]
samples = 1
sample_from = {
'x': DependentSampler(depends=["y"], formula="1"),
'y': DependentSampler(depends=["x"], formula="1")
}
funcs, suffs, consts = {}, {}, {}
# This does NOT raise an error; the depends entry is ignored
gen_symbols_samples(symbols, samples, sample_from, funcs, suffs, consts)
def test_dependent_sampler():
"""Tests the DependentSampler class"""
# Test basic usage and multiple samples
result = gen_symbols_samples(
["a", "b"], 2, {
'a': IntegerRange([1, 1]),
'b': DependentSampler(depends=["a"], formula="a+1")
})
assert result == [{"a": 1, "b": 2.0}, {"a": 1, "b": 2.0}]
result = gen_symbols_samples(
["a", "b", "c", "d"], 1, {
'a': RealInterval([1, 1]),
'd': DependentSampler(depends=["c"], formula="c+1"),
'c': DependentSampler(depends=["b"], formula="b+1"),
'b': DependentSampler(depends=["a"], formula="a+1")
})[0]
assert result["b"] == 2 and result["c"] == 3 and result["d"] == 4
result = gen_symbols_samples(
["x", "y", "z", "r"], 1, {
'x':
RealInterval([-5, 5]),
'y':
RealInterval([-5, 5]),
'z':
RealInterval([-5, 5]),
'r':
DependentSampler(depends=["x", "y", "z"],
formula="sqrt(x^2+y^2+z^2)")
})[0]
assert result["x"]**2 + result["y"]**2 + result["z"]**2 == approx(
result["r"]**2)
with raises(ConfigError,
match="Circularly dependent DependentSamplers detected: x, y"):
gen_symbols_samples(
["x", "y"], 1, {
'x': DependentSampler(depends=["y"], formula="1"),
'y': DependentSampler(depends=["x"], formula="1")
})
with raises(ConfigError,
match=r"Formula error in dependent sampling formula: 1\+\(2"):
gen_symbols_samples(
["x"], 1, {'x': DependentSampler(depends=[], formula="1+(2")})
with raises(Exception,
match="DependentSampler must be invoked with compute_sample."):
DependentSampler(depends=[], formula="1").gen_sample()
def test_dependentsampler():
# Ensure that dependentsampler can make use of user-defined functions
grader = FormulaGrader(
answers='y',
variables=['x', 'y'],
user_functions={'f': lambda x: x**2},
sample_from={'y': DependentSampler(depends=["x"], formula="f(x)")})
assert grader(None, 'y')['ok']
assert grader(None, 'x^2')['ok']
def test_docs():
"""Make sure that the documentation examples work"""
# Generate random real numbers between 3 and 7
sampler = RealInterval(start=3, stop=7)
# This is equivalent to
sampler = RealInterval([3, 7])
# The default is [1, 5]
sampler = RealInterval()
# Generate random integers between 3 and 7 inclusive
sampler = IntegerRange(start=3, stop=7)
# This is equivalent to
sampler = IntegerRange([3, 7])
# The default is [1, 5]
sampler = IntegerRange()
# Select random numbers from (1, 3, 5, 7, 9)
sampler = DiscreteSet((1, 3, 5, 7, 9))
# Always select 3.5
sampler = DiscreteSet(3.5)
# Select random complex numbers from 0 to 1 + i
sampler = ComplexRectangle(re=[0, 1], im=[0, 1])
# The default is re=[1, 3], im=[1, 3]
sampler = ComplexRectangle()
# Select random complex numbers from inside the unit circle
sampler = ComplexSector(modulus=[0, 1], argument=[-np.pi, np.pi])
# The default is modulus=[1, 3], argument=[0, pi/2]
sampler = ComplexSector()
# Test dependent sampling
sampler = DependentSampler(depends=["x", "y", "z"],
formula="sqrt(x^2+y^2+z^2)")
# Select either sin or cos randomly
functionsampler = SpecificFunctions([np.cos, np.sin])
# Always select a single lambda function
functionsampler = SpecificFunctions(lambda x: x * x)
# Generate a random function
functionsampler = RandomFunction(center=1, amplitude=2)
# The default is center=0, amplitude=10
functionsampler = RandomFunction()
# Generate a random sinusoid
functionsampler = RandomFunction(num_terms=1)
# Generate a function that takes in two values and outputs a 3D vector
functionsampler = RandomFunction(input_dim=2, output_dim=3)
def test_dependent_sampler():
"""Tests the DependentSampler class"""
# Test basic usage and multiple samples
symbols = ["a", "b"]
samples = 2
sample_from = {
'a': IntegerRange([1, 1]),
'b': DependentSampler(depends=["a"], formula="a+1")
}
funcs, suffs, consts = {}, {}, {}
result = gen_symbols_samples(symbols, samples, sample_from, funcs, suffs, consts)
assert result == [{"a": 1, "b": 2.0}, {"a": 1, "b": 2.0}]
symbols = ["a", "b", "c", "d"]
samples = 1
sample_from = {
'a': RealInterval([1, 1]),
'd': DependentSampler(depends=["c"], formula="c+1"),
'c': DependentSampler(depends=["b"], formula="b+1"),
'b': DependentSampler(depends=["a"], formula="a+1")
}
funcs, suffs, consts = {}, {}, {}
result = gen_symbols_samples(symbols, samples, sample_from, funcs, suffs, consts)[0]
assert result["b"] == 2 and result["c"] == 3 and result["d"] == 4
symbols = ["x", "y", "z", "r"]
samples = 1
sample_from = {
'x': RealInterval([-5, 5]),
'y': RealInterval([-5, 5]),
'z': RealInterval([-5, 5]),
'r': DependentSampler(depends=["x", "y", "z"], formula="sqrt(x^2+y^2+z^2 + unity)")
}
funcs = {'sqrt': lambda x: x**0.5}
consts = {'unity': 1}
suffs = {}
result = gen_symbols_samples(symbols, samples, sample_from, funcs, suffs, consts)[0]
assert result["x"]**2 + result["y"]**2 + result["z"]**2 + 1 == approx(result["r"]**2)
symbols = ["x", "y"]
samples = 1
sample_from = {
'x': DependentSampler(depends=["y"], formula="y"),
'y': DependentSampler(depends=["x"], formula="x")
}
funcs, suffs, consts = {}, {}, {}
with raises(ConfigError, match="Circularly dependent DependentSamplers detected: x, y"):
gen_symbols_samples(symbols, samples, sample_from, funcs, suffs, consts)
with raises(ConfigError, match=r"Formula error in dependent sampling formula: 1\+\(2"):
DependentSampler(formula="1+(2")
symbols = ["x"]
samples = 1
sample_from = {'x': DependentSampler(formula="min(j, i)")}
with raises(ConfigError, match=r"Formula error in dependent sampling formula: min\(j, i\)"):
gen_symbols_samples(symbols, samples, sample_from, funcs, suffs, {'i': 1j, 'j': 1j})
with raises(ConfigError, match=r"DependentSamplers depend on undefined quantities: i, j"):
gen_symbols_samples(symbols, samples, sample_from, funcs, suffs, consts)
with raises(Exception, match="DependentSampler must be invoked with compute_sample."):
DependentSampler(depends=[], formula="1").gen_sample()