def example_3():
"""
Question ID: 1
In the diagram at the right, circle O has a radius of 5, and CE = 2.
Diameter AC is perpendicular to chord BD at E.
What is the length of BD?
:return:
"""
vh = VariableHandler()
A = vh.point('A')
B = vh.point('B')
C = vh.point('C')
D = vh.point('D')
E = vh.point('E')
O = vh.point('O')
CE = vh.line(C, E)
AC = vh.line(A, C)
BD = vh.line(B, D)
cO = vh.circle(O)
p1 = vh.apply('RadiusOf', cO) == 5 # Equals(RadiusOf(cO), 5))
p2 = vh.apply('LengthOf', CE) == 2 # Equals(LengthOf(CE), 2)
p3 = vh.apply('IsDiameterLineOf', AC, cO)
p4 = vh.apply('IsChordOf', BD, cO)
p5 = vh.apply('Perpendicular', AC, BD)
p6 = vh.apply('PointLiesOnLine', E,
AC) # AC intersects BD at E is broken down into two atoms
p7 = vh.apply('PointLiesOnLine', E, BD)
ps = [p1, p2, p3, p4, p5, p6, p7]
ns = NumericSolver(ps, vh)
ans = vh.apply('LengthOf', BD)
if ns.is_sat():
print ns.evaluate(ans), 8 # 8 is the answer
else:
print "Given information is not satisfiable."
def example_2():
"""
AB is tangent to circle O, AO = BO = 1 and AB = sqrt(2). What is the radius of circle O?
:return:
"""
vh = VariableHandler()
O = vh.point('O')
A = vh.point('A')
B = vh.point('B')
AO = vh.line(A, O)
BO = vh.line(B, O)
AB = vh.line(A, B)
# vh.circle() with one argument assumes the radius is an unknown value (i.e. variable).
# if you want to define radius, just give it two arguments, e.g. vh.circle(O, r)
cO = vh.circle(O)
a = vh.apply('LengthOf', AO)
b = vh.apply('LengthOf', BO)
o = vh.apply('LengthOf', AB)
p1 = a == 1
p2 = b == 1
p3 = o == np.sqrt(2)
p4 = vh.apply('Tangent', AB, cO)
ns = NumericSolver([p1, p2, p3, p4], vh)
ans = vh.apply('RadiusOf', cO)
if ns.is_sat():
print ns.evaluate(ans), 1 / np.sqrt(2) # the latter is the true answer
else:
print("Given information is not satisfiable.")
def test_solving():
pk = 973
questions = geoserver_interface.download_questions(pk)
question = questions.values()[0]
label_data = geoserver_interface.download_labels(pk)[pk]
diagram = open_image(question.diagram_path)
graph_parse = diagram_to_graph_parse(diagram)
match_parse = parse_match_from_known_labels(graph_parse, label_data)
AB = v('AB', 'line')
AC = v('AC', 'line')
BC = v('BC', 'line')
ED = v('ED', 'line')
AE = v('AE', 'line')
E = v('E', 'point')
D = v('D', 'point')
x = v('x', 'number')
p1 = f('LengthOf', AB) == f('LengthOf', AC)
p2 = f('IsMidpointOf', E, AB)
p3 = f('IsMidpointOf', D, AC)
p4 = f('LengthOf', AE) == x
p5 = f('LengthOf', ED) == 4
qn = f('LengthOf', BC)
confident_atoms = parse_confident_formulas(graph_parse)
text_atoms = ground_formula_nodes(match_parse, [p1, p2, p3, p4, p5])
atoms = confident_atoms + text_atoms
grounded_qn = ground_formula_nodes(match_parse, [qn])[0]
ns = NumericSolver(atoms)
print ns.evaluate(grounded_qn)
def example_2():
"""
AB is tangent to circle O, AO = BO = 1 and AB = sqrt(2). What is the radius of circle O?
:return:
"""
vh = VariableHandler()
O = vh.point('O')
A = vh.point('A')
B = vh.point('B')
AO = vh.line(A, O)
BO = vh.line(B, O)
AB = vh.line(A, B)
# vh.circle() with one argument assumes the radius is an unknown value (i.e. variable).
# if you want to define radius, just give it two arguments, e.g. vh.circle(O, r)
cO = vh.circle(O)
a = vh.apply('LengthOf', AO)
b = vh.apply('LengthOf', BO)
o = vh.apply('LengthOf', AB)
p1 = a == 1
p2 = b == 1
p3 = o == np.sqrt(2)
p4 = vh.apply('Tangent', AB, cO)
ns = NumericSolver([p1, p2, p3, p4], vh)
ans = vh.apply('RadiusOf', cO)
if ns.is_sat():
print ns.evaluate(ans), 1/np.sqrt(2) # the latter is the true answer
else:
print("Given information is not satisfiable.")
def example_3():
"""
Question ID: 1
In the diagram at the right, circle O has a radius of 5, and CE = 2.
Diameter AC is perpendicular to chord BD at E.
What is the length of BD?
:return:
"""
vh = VariableHandler()
A = vh.point('A')
B = vh.point('B')
C = vh.point('C')
D = vh.point('D')
E = vh.point('E')
O = vh.point('O')
CE = vh.line(C, E)
AC = vh.line(A, C)
BD = vh.line(B, D)
cO = vh.circle(O)
p1 = vh.apply('RadiusOf', cO) == 5 # Equals(RadiusOf(cO), 5))
p2 = vh.apply('LengthOf', CE) == 2 # Equals(LengthOf(CE), 2)
p3 = vh.apply('IsDiameterLineOf', AC, cO)
p4 = vh.apply('IsChordOf', BD, cO)
p5 = vh.apply('Perpendicular', AC, BD)
p6 = vh.apply('PointLiesOnLine', E, AC) # AC intersects BD at E is broken down into two atoms
p7 = vh.apply('PointLiesOnLine', E, BD)
ps = [p1, p2, p3, p4, p5, p6, p7]
ns = NumericSolver(ps, vh)
ans = vh.apply('LengthOf', BD)
if ns.is_sat():
print ns.evaluate(ans), 8 # 8 is the answer
else:
print "Given information is not satisfiable."
def example_1():
"""
AB perpendicular to BC, AB = x, and BC = 4. Is CA = sqrt(x^2+16) a correct answer?
:return:
"""
vh = VariableHandler()
x = vh.number('x')
A = vh.point('A')
B = vh.point('B')
C = vh.point('C')
AB = vh.line(A, B)
BC = vh.line(B, C)
CA = vh.line(C, A)
c = vh.apply('LengthOf', AB)
a = vh.apply('LengthOf', BC)
b = vh.apply('LengthOf', CA)
p1 = a == 4
p2 = c == x
p3 = vh.apply('Perpendicular', AB, BC)
q1 = b == (16 + x**2)**0.5
q2 = b == x**2
ns = NumericSolver([p1, p2, p3], vh)
print(ns.find_assignment(q1)) # find_assignment simply analyzes whether the query relation can be satisfied
print(ns.query_invar(q1)) # query_invar analyzes whether the query relation must hold true
print(ns.find_assignment(q2)) # this is satisfiable; there exists x that satisfies q2.
print(ns.query_invar(q2)) # this is False because q2 is not true for all possible x.
def test_solving():
pk = 973
questions = geoserver_interface.download_questions(pk)
question = questions.values()[0]
label_data = geoserver_interface.download_labels(pk)[pk]
diagram = open_image(question.diagram_path)
graph_parse = diagram_to_graph_parse(diagram)
match_parse = parse_match_from_known_labels(graph_parse, label_data)
AB = v('AB', 'line')
AC = v('AC', 'line')
BC = v('BC', 'line')
ED = v('ED', 'line')
AE = v('AE', 'line')
E = v('E', 'point')
D = v('D', 'point')
x = v('x', 'number')
p1 = f('LengthOf', AB) == f('LengthOf', AC)
p2 = f('IsMidpointOf', E, AB)
p3 = f('IsMidpointOf', D, AC)
p4 = f('LengthOf', AE) == x
p5 = f('LengthOf', ED) == 4
qn = f('LengthOf', BC)
confident_atoms = parse_confident_formulas(graph_parse)
text_atoms = ground_formula_nodes(match_parse, [p1, p2, p3, p4, p5])
atoms = confident_atoms + text_atoms
grounded_qn = ground_formula_nodes(match_parse, [qn])[0]
ns = NumericSolver(atoms)
print ns.evaluate(grounded_qn)
def example_1():
"""
AB perpendicular to BC, AB = x, and BC = 4. Is CA = sqrt(x^2+16) a correct answer?
:return:
"""
vh = VariableHandler()
x = vh.number('x')
A = vh.point('A')
B = vh.point('B')
C = vh.point('C')
AB = vh.line(A, B)
BC = vh.line(B, C)
CA = vh.line(C, A)
c = vh.apply('LengthOf', AB)
a = vh.apply('LengthOf', BC)
b = vh.apply('LengthOf', CA)
p1 = a == 4
p2 = c == x
p3 = vh.apply('Perpendicular', AB, BC)
q1 = b == (16 + x**2)**0.5
q2 = b == x**2
ns = NumericSolver([p1, p2, p3], vh)
print(
ns.find_assignment(q1)
) # find_assignment simply analyzes whether the query relation can be satisfied
print(ns.query_invar(q1)
) # query_invar analyzes whether the query relation must hold true
print(ns.find_assignment(q2)
) # this is satisfiable; there exists x that satisfies q2.
print(ns.query_invar(q2)
) # this is False because q2 is not true for all possible x.
def example_0():
"""
AB = x, BC = 3, CA = 4. Is an answer x=5, x=8 possible?
:return:
"""
vh = VariableHandler()
x = vh.number('x')
A = vh.point('A')
B = vh.point('B')
C = vh.point('C')
AB = vh.line(A, B)
BC = vh.line(B, C)
CA = vh.line(C, A)
c = vh.apply('LengthOf', AB)
a = vh.apply('LengthOf', BC)
b = vh.apply('LengthOf', CA)
p1 = a == 3
p2 = b == 4
p3 = c == x
q1 = x == 8
q2 = x == 5
ns = NumericSolver([p1, p2, p3], vh)
print(ns.find_assignment(q1))
print(ns.find_assignment(q2))
def example_0():
"""
AB = x, BC = 3, CA = 4. Is an answer x=5, x=8 possible?
:return:
"""
vh = VariableHandler()
x = vh.number('x')
A = vh.point('A')
B = vh.point('B')
C = vh.point('C')
AB = vh.line(A, B)
BC = vh.line(B, C)
CA = vh.line(C, A)
c = vh.apply('LengthOf', AB)
a = vh.apply('LengthOf', BC)
b = vh.apply('LengthOf', CA)
p1 = a == 3
p2 = b == 4
p3 = c == x
q1 = x == 8
q2 = x == 5
ns = NumericSolver([p1, p2, p3], vh)
print(ns.find_assignment(q1))
print(ns.find_assignment(q2))
def solve(given_formulas, choice_formulas=None, assignment=None):
"""
:param list true_formulas:
:param dict choice_formulas:
:return:
"""
start_time = time.time()
out = {}
#1. Find query formula in true formulas
true_formulas = []
query_formula = None
for formula in given_formulas:
assert isinstance(formula, FormulaNode)
if formula.has_signature("What") or formula.has_signature(
"Which") or formula.has_signature("Find"):
if query_formula is not None:
logging.warning("More than one query formula.")
query_formula = formula
else:
true_formulas.append(formula)
if query_formula is None:
raise Exception("No query formula.")
elif query_formula.has_signature("What"):
if choice_formulas is None:
ns = NumericSolver(given_formulas, assignment=assignment)
ns.solve()
out = ns.assignment['What']
else:
ns = NumericSolver(given_formulas, assignment=assignment)
ns.solve()
for key, choice_formula in choice_formulas.iteritems():
equal_formula = FormulaNode(
signatures['Equals'],
[ns.assignment['What'], choice_formula])
out[key] = ns.evaluate(equal_formula)
"""
ns = NumericSolver(true_formulas)
ns.solve()
for key, choice_formula in choice_formulas.iteritems():
# print query_formula.children[1], ns.evaluate(query_formula.children[1])
# print choice_formula, ns.evaluate(choice_formula)
tester = lambda node: isinstance(node, FormulaNode) and node.signature.id == "What"
getter = lambda node: choice_formula
replaced_formula = query_formula.replace_node(tester, getter)
# print replaced_formula
out[key] = ns.evaluate(replaced_formula)
"""
# display_entities(ns)
elif query_formula.has_signature("Find"):
ns = NumericSolver(true_formulas, assignment=assignment)
ns.solve()
# display_entities(ns)
if choice_formulas is None:
# No choice given; need to find the answer!
out = ns.evaluate(query_formula.children[0])
else:
for key, choice_formula in choice_formulas.iteritems():
replaced_formula = FormulaNode(
signatures['Equals'],
[query_formula.children[0], choice_formula])
out[key] = ns.evaluate(replaced_formula)
# display_entities(ns)
elif query_formula.has_signature("Which"):
ns = NumericSolver(true_formulas, assignment=assignment)
ns.solve()
for key, choice_formula in choice_formulas.iteritems():
# print query_formula.children[1], ns.evaluate(query_formula.children[1])
# print choice_formula, ns.evaluate(choice_formula)
tester = lambda node: node.signature.id == "Which"
getter = lambda node: choice_formula
replaced_formula = query_formula.replace_node(tester, getter)
out[key] = ns.evaluate(replaced_formula)
# this won't be executed!
elif query_formula.has_signature("Which"):
tester = lambda node: isinstance(node, FormulaNode
) and node.signature.id == "Which"
for choice, choice_formula in choice_formulas.iteritems():
getter = lambda node: choice_formula
replaced_formula = query_formula.replace_node(tester, getter)
all_formulas = true_formulas + [replaced_formula]
ns = NumericSolver(all_formulas)
out[choice] = ns.evaluate(replaced_formula)
print out[choice]
#display_entities(ns)
else:
raise Exception()
end_time = time.time()
delta_time = end_time - start_time
print "%.2f seconds" % delta_time
return out
def solve(given_formulas, choice_formulas=None, assignment=None):
"""
:param list true_formulas:
:param dict choice_formulas:
:return:
"""
start_time = time.time()
out = {}
#1. Find query formula in true formulas
true_formulas = []
query_formula = None
for formula in given_formulas:
assert isinstance(formula, FormulaNode)
if formula.has_signature("What") or formula.has_signature("Which") or formula.has_signature("Find"):
if query_formula is not None:
logging.warning("More than one query formula.")
query_formula = formula
else:
true_formulas.append(formula)
if query_formula is None:
raise Exception("No query formula.")
elif query_formula.has_signature("What"):
if choice_formulas is None:
ns = NumericSolver(given_formulas, assignment=assignment)
ns.solve()
out = ns.assignment['What']
else:
ns = NumericSolver(given_formulas, assignment=assignment)
ns.solve()
for key, choice_formula in choice_formulas.iteritems():
equal_formula = FormulaNode(signatures['Equals'], [ns.assignment['What'], choice_formula])
out[key] = ns.evaluate(equal_formula)
"""
ns = NumericSolver(true_formulas)
ns.solve()
for key, choice_formula in choice_formulas.iteritems():
# print query_formula.children[1], ns.evaluate(query_formula.children[1])
# print choice_formula, ns.evaluate(choice_formula)
tester = lambda node: isinstance(node, FormulaNode) and node.signature.id == "What"
getter = lambda node: choice_formula
replaced_formula = query_formula.replace_node(tester, getter)
# print replaced_formula
out[key] = ns.evaluate(replaced_formula)
"""
# display_entities(ns)
elif query_formula.has_signature("Find"):
ns = NumericSolver(true_formulas, assignment=assignment)
ns.solve()
# display_entities(ns)
if choice_formulas is None:
# No choice given; need to find the answer!
out = ns.evaluate(query_formula.children[0])
else:
for key, choice_formula in choice_formulas.iteritems():
replaced_formula = FormulaNode(signatures['Equals'], [query_formula.children[0], choice_formula])
out[key] = ns.evaluate(replaced_formula)
# display_entities(ns)
elif query_formula.has_signature("Which"):
ns = NumericSolver(true_formulas, assignment=assignment)
ns.solve()
for key, choice_formula in choice_formulas.iteritems():
# print query_formula.children[1], ns.evaluate(query_formula.children[1])
# print choice_formula, ns.evaluate(choice_formula)
tester = lambda node: node.signature.id == "Which"
getter = lambda node: choice_formula
replaced_formula = query_formula.replace_node(tester, getter)
out[key] = ns.evaluate(replaced_formula)
# this won't be executed!
elif query_formula.has_signature("Which"):
tester = lambda node: isinstance(node, FormulaNode) and node.signature.id == "Which"
for choice, choice_formula in choice_formulas.iteritems():
getter = lambda node: choice_formula
replaced_formula = query_formula.replace_node(tester, getter)
all_formulas = true_formulas + [replaced_formula]
ns = NumericSolver(all_formulas)
out[choice] = ns.evaluate(replaced_formula)
print out[choice]
#display_entities(ns)
else:
raise Exception()
end_time = time.time()
delta_time = end_time - start_time
print "%.2f seconds" % delta_time
return out