def eval_product(parse_result):
"""
Multiply/divide inputs appropriately
Arguments:
parse_result: A list of numbers to combine, separated by "*" and "/"
[a, "*", b, "/", c] = a*b/c
Has some extra logic to avoid ambiguous vector triple products.
See https://github.com/mitodl/mitx-grading-library/issues/108
Usage
=====
>>> MathExpression.eval_product([2,"*",3,"/",4])
1.5
>>> try:
... MathExpression.eval_product([2,"*",3,"+",4])
... except CalcError as error:
... print(error)
Unexpected symbol + in eval_product
"""
double_vector_mult_has_occured = False
triple_vector_mult_error = CalcError(
"Multiplying three or more vectors is ambiguous. "
"Please place parentheses around vector multiplications.")
result = parse_result[0]
data = parse_result[1:]
while data:
op = data.pop(0)
value = data.pop(0)
if op == '/':
# Don't use in-place ops, it conflicts with numpy version 1.16
# 'same-type' casting
result = result / value
elif op == '*':
if is_vector(value):
if double_vector_mult_has_occured:
raise triple_vector_mult_error
elif is_vector(result):
double_vector_mult_has_occured = True
result = result * value
else:
raise CalcError(
"Unexpected symbol {} in eval_product".format(op))
# Need to cast np numerics as builtins here (in addition to during
# eval_node) because the result is changing shape
result = cast_np_numeric_as_builtin(result)
return result
def vector_phase_comparer(comparer_params_eval, student_eval, utils):
"""
Check that student input equals a given input (to within tolerance), up to
an overall phase factor.
comparer_params: [target_vector]
Usage
=====
>>> from mitxgraders import MatrixGrader
>>> grader = MatrixGrader(
... answers={
... 'comparer_params': [
... '[1, exp(-i*phi)]',
... ],
... 'comparer': vector_phase_comparer
... },
... variables=['phi'],
... )
>>> grader(None, '[1, exp(-i*phi)]')['ok']
True
>>> grader(None, '[exp(i*phi/2), exp(-i*phi/2)]')['ok']
True
>>> grader(None, '[i, exp(i*(pi/2 - phi))]')['ok']
True
>>> grader(None, '[1, exp(+i*phi)]')['ok']
False
>>> grader(None, '[2, 2*exp(-i*phi)]')['ok']
False
The comparer_params should be list with a single vector:
>>> grader = MatrixGrader(
... answers={
... 'comparer_params': [
... '[1, 1, 0]',
... '[0, 1, 1]'
... ],
... 'comparer': vector_phase_comparer
... },
... )
>>> try:
... grader(None, '[1, 2, 3]') # doctest: +ELLIPSIS
... except StudentFacingError as error:
... print(error)
Problem Configuration Error: ...to a single vector.
"""
# Validate that author comparer_params evaluate to a single vector
if not len(comparer_params_eval) == 1 and is_vector(comparer_params_eval[0]):
raise StudentFacingError('Problem Configuration Error: comparer_params '
'should be a list of strings that evaluate to a single vector.')
# We'll check that student input is in the span as target vector and that
# it has the same magnitude
in_span = vector_span_comparer(comparer_params_eval, student_eval, utils)
expected_mag = np.linalg.norm(comparer_params_eval[0])
student_mag = np.linalg.norm(student_eval)
same_magnitude = utils.within_tolerance(expected_mag, student_mag)
return in_span and same_magnitude