def construct_diagram():
pool = Pool()
pool.int_var("x", "y")
b = Builder(pool)
bounds = b.test("x", ">=", 0) & b.test("x", "<=", 8) & b.test("y", ">=", 1) & b.test("y", "<=", 10)
return bounds * b.ite(b.test("x", ">=", "y"), b.terminal("2*x + 3*y"), b.terminal("3*x + 2*y"))
def test_printing(self):
import json
encoded = Pool.to_json(self.diagram.pool)
representation = json.loads(encoded)
reconstructed = Pool.from_json(encoded)
re_encoded = Pool.to_json(reconstructed)
new_representation = json.loads(re_encoded)
self.assertEquals(representation, new_representation)
def test_printing(self):
import json
encoded = Pool.to_json(self.diagram.pool)
representation = json.loads(encoded)
reconstructed = Pool.from_json(encoded)
re_encoded = Pool.to_json(reconstructed)
new_representation = json.loads(re_encoded)
self.assertEquals(representation, new_representation)
def test_inversion(self):
pool = Pool()
build = Builder(pool)
build.vars("bool", "a", "b")
build.vars("int", "x")
test1 = build.test("a")
test2 = build.test("b")
test3 = build.test("x", "<=", 5)
node3 = build.ite(test3, 1, 0)
diagram = build.ite(test1, build.ite(test2, node3, 1), node3)
self.assertTrue(is_ordered(diagram))
def inversion1(root_id):
minus_one = pool.terminal("-1")
return pool.apply(Multiplication, pool.apply(Summation, root_id, minus_one), minus_one)
def transform(terminal_node, d):
if terminal_node.expression == 1:
return d.pool.zero_id
elif terminal_node.expression == 0:
return d.pool.one_id
else:
raise RuntimeError("Could not invert value {}".format(terminal_node.expression))
def inversion2(root_id):
to_invert = pool.diagram(root_id)
profile = WalkingProfile(diagram)
return leaf_transform.transform_leaves(transform, to_invert)
iterations = 1000
timer = Timer(precision=6)
timer.start("Legacy inversion")
for _ in range(iterations):
inversion1(diagram.root_id)
time_legacy = timer.stop()
inverted1 = pool.diagram(inversion1(diagram.root_id))
timer.start("New inversion")
for _ in range(iterations):
inversion2(diagram.root_id)
time_new = timer.stop()
inverted2 = pool.diagram(inversion2(diagram.root_id))
for a in [True, False]:
for b in [True, False]:
for x in range(10):
assignment = {"a": a, "b": b, "x": x}
self.assertNotEqual(diagram.evaluate(assignment), inverted1.evaluate(assignment))
self.assertNotEqual(diagram.evaluate(assignment), inverted2.evaluate(assignment))
self.assertTrue(time_legacy > time_new, "New inversion ({}) not faster than legacy implementation ({})"
.format(time_new, time_legacy))
def test_not(self):
pool = Pool()
pool.int_var("x")
dd_true = Diagram(pool, pool.bool_test(LinearTest("x", ">=")))
dd_false = Diagram(pool, pool.invert(dd_true.root_node.node_id))
for i in range(-5, 6):
assignment = {"x": i}
self.assertEqual((dd_true.evaluate(assignment) + 1) % 2, dd_false.evaluate(assignment))
def test_summation_one_var(self):
pool = Pool()
pool.add_var("x", "int")
pool.add_var("y", "int")
b = Builder(pool)
bounds = b.test("x", ">=", 0) & b.test("x", "<=", 10)
d = b.ite(bounds, b.terminal("x"), b.terminal(0))
d_const = Diagram(pool, SummationWalker(d, "x").walk())
self.assertEqual(55, d_const.evaluate({}))
def construct_diagram():
pool = Pool(empty=True)
pool.int_var("x")
x = pool.terminal("x")
zero = pool.terminal("0")
test1 = pool.internal(LinearTest("x - 5", "<="), x, zero)
test2 = pool.internal(LinearTest("x + 1", ">="), test1, zero)
test3 = pool.internal(LinearTest("x + 2", "<="), x, test2)
root = pool.internal(LinearTest("x", ">="), test1, test3)
return Diagram(pool, root)
def construct_diagram():
pool = Pool(empty=True)
pool.int_var("x")
x = pool.terminal("x")
zero = pool.terminal("0")
test1 = pool.internal(LinearTest("x - 5", "<="), x, zero)
test2 = pool.internal(LinearTest("x + 1", ">="), test1, zero)
test3 = pool.internal(LinearTest("x + 2", "<="), x, test2)
root = pool.internal(LinearTest("x", ">="), test1, test3)
return Diagram(pool, root)
def get_looping_diagram():
pool = Pool()
pool.int_var("x")
test = LinearTest("x", "<=", "2")
zero = pool.terminal(0)
one = pool.terminal(1)
node1 = pool.internal(test, one, zero)
node2 = pool.internal(test, node1, zero)
diagram = pool.diagram(node2)
return diagram
def setUp(self):
pool = Pool()
pool.int_var("x")
pool.int_var("y")
pool.int_var("z")
b = Builder(pool)
self.diagrams = []
d = b.ite(b.test("x", "<=", "y"), b.terminal(1), b.test("x", "<=", 2))
self.diagrams.append(({"x", "y"}, d))
d = b.terminal("x * 2 * y + 5 * z")
self.diagrams.append(({"x", "y", "z"}, d))
d = b.ite(b.test("x", "<", "y"), b.terminal("z"), b.terminal("z * y"))
self.diagrams.append(({"x", "y", "z"}, d))
def setUp(self):
pool = Pool()
pool.int_var("x")
lb = Diagram(pool, pool.bool_test(LinearTest("x - 1", ">=")))
ub = Diagram(pool, pool.bool_test(LinearTest("x - 10", "<=")))
test = Diagram(pool, pool.bool_test(LinearTest("x - 5", "<=")))
term_one = Diagram(pool, pool.terminal("x + 2"))
term_two = Diagram(pool, pool.terminal("7 - 2 * (x - 5)"))
b1 = lb & ub & test * term_one
b2 = lb & ub & ~test * term_two
self.diagram = b1 + b2
def setUp(self):
pool = Pool()
pool.int_var("x")
lb = Diagram(pool, pool.bool_test(LinearTest("x - 1", ">=")))
ub = Diagram(pool, pool.bool_test(LinearTest("x - 10", "<=")))
test = Diagram(pool, pool.bool_test(LinearTest("x - 5", "<=")))
redundant_test = Diagram(pool, pool.bool_test(LinearTest("x - 6", "<=")))
term_one = Diagram(pool, pool.terminal("x + 2"))
term_two = Diagram(pool, pool.terminal("7 - 2 * (x - 5)"))
b1 = (lb & ub & test & redundant_test) * term_one
b2 = (lb & ub & ~test & redundant_test) * term_two
self.diagram = b1 + b2
self.exporter = Exporter(os.path.join(os.path.dirname(os.path.realpath(__file__)), "visual"), "reduce")
def build_diagram_2():
b = Builder(Pool())
b.ints("r", "c")
lb, ub = 1, 10
bounds = b.limit("r", lb, ub) & b.limit("c", lb, ub)
t1 = b.ite(b.test("r", "<=", 0), 2, 4)
t2 = b.ite(b.test("c", ">=", 11), 3, 5)
return bounds * (t1 + t2)
def test_summation_two_var_test(self):
pool = Pool()
pool.add_var("x", "int")
pool.add_var("y", "int")
b = Builder(pool)
bounds = b.test("x", ">=", 0) & b.test("x", "<=", 1)
bounds &= b.test("y", ">=", 1) & b.test("y", "<=", 3)
two = b.test("x", ">=", "y")
d = b.ite(bounds, b.ite(two, b.terminal("x"), b.terminal("10")), b.terminal(0))
summed = Diagram(pool, SummationWalker(d, "x").walk())
d_const = summed.reduce(["y"])
for y in range(-20, 20):
s = 0
for x in range(-20, 20):
s += d.evaluate({"x": x, "y": y})
self.assertEqual(s, d_const.evaluate({"y": y}))
def test_multiplication(self):
pool = Pool()
pool.int_var("x")
two = pool.terminal("2")
x = pool.terminal("x")
test1 = pool.bool_test(LinearTest("x", ">="))
test2 = pool.apply(Multiplication, pool.bool_test(LinearTest("x - 5", "<=")), x)
product = pool.apply(Multiplication, test1, test2)
result = Diagram(pool, pool.apply(Multiplication, product, two))
for i in range(0, 10):
evaluated = result.evaluate({"x": i})
if 0 <= i <= 5:
self.assertEqual(2 * i, evaluated)
else:
self.assertEqual(0, evaluated)
def build_diagram_1():
b = Builder(Pool())
b.ints("r", "c")
lb = 1
ub = 10
bounds = b.limit("r", lb, ub) & b.limit("c", lb, ub)
diagonal = b.test("r", "<=", "c") & b.test("r", ">=", "c")
block_1 = b.test("r", ">", lb + (ub - lb) / 2) & b.test("c", "<=", lb + (ub - lb) / 2)
block_2 = b.test("r", "<=", lb + (ub - lb) / 2) & b.test("c", ">", lb + (ub - lb) / 2)
return bounds * (diagonal * b.exp(6) + (block_1 | block_2))
def setUp(self):
pool_file = "data/test_evaluate_1.txt"
root_id = 1663
with open(pool_file, "r") as stream:
json_input = stream.readline()
exported_pool = Pool.from_json(json_input)
self.diagram1 = exported_pool.diagram(root_id)
self.vars1 = [('r_f0', 0, 1658), ('r_f1', 0, 964), ('c_f0', 0, 1658), ('c_f1', 0, 964)]
def test_invert_terminal(self):
pool = Pool()
self.assertEquals(pool.zero_id, pool.invert(pool.one_id))
self.assertEquals(pool.one_id, pool.invert(pool.zero_id))
try:
pool.invert(pool.terminal(2))
self.assertTrue(False)
except RuntimeError:
self.assertTrue(True)
def setUp(self):
pool_file = "data/test_evaluate_1.txt"
root_id = 1663
with open(pool_file, "r") as stream:
json_input = stream.readline()
exported_pool = Pool.from_json(json_input)
self.diagram1 = exported_pool.diagram(root_id)
self.vars1 = [('r_f0', 0, 1658), ('r_f1', 0, 964), ('c_f0', 0, 1658),
('c_f1', 0, 964)]
def setUp(self):
pool = Pool()
pool.int_var("x")
lb = Diagram(pool, pool.bool_test(LinearTest("x - 1", ">=")))
ub = Diagram(pool, pool.bool_test(LinearTest("x - 10", "<=")))
test = Diagram(pool, pool.bool_test(LinearTest("x - 5", "<=")))
term_one = Diagram(pool, pool.terminal("x + 2"))
term_two = Diagram(pool, pool.terminal("7 - 2 * (x - 5)"))
b1 = lb & ub & test * term_one
b2 = lb & ub & ~test * term_two
self.diagram = b1 + b2
def test_invert_terminal(self):
pool = Pool()
self.assertEquals(pool.zero_id, pool.invert(pool.one_id))
self.assertEquals(pool.one_id, pool.invert(pool.zero_id))
try:
pool.invert(pool.terminal(2))
self.assertTrue(False)
except RuntimeError:
self.assertTrue(True)
def test_not(self):
pool = Pool()
pool.int_var("x")
dd_true = Diagram(pool, pool.bool_test(LinearTest("x", ">=")))
dd_false = Diagram(pool, pool.invert(dd_true.root_node.node_id))
for i in range(-5, 6):
assignment = {"x": i}
self.assertEqual((dd_true.evaluate(assignment) + 1) % 2,
dd_false.evaluate(assignment))
def setUp(self):
pool = Pool()
self.builder = Builder(pool)
self.builder.ints("x", "y")
b = self.builder
limits = b.limit("x", 0, 20) & b.limit("y", 0, 20)
rect1 = b.limit("x", 0, 10) & b.limit("y", 0, 10)
rect2 = b.limit("x", 5, 20) & b.limit("y", 10, 20)
self.diagram = rect1 * b.terminal("5") \
+ rect2 * b.terminal("x + 2") \
+ ~(rect1 | rect2) & limits * b.terminal("1")
self.exporter = Exporter(
os.path.join(os.path.dirname(os.path.realpath(__file__)),
"visual"), "transform")
def setUp(self):
pool = Pool()
pool.int_var("x")
pool.int_var("y")
pool.int_var("z")
b = Builder(pool)
self.diagrams = []
d = b.ite(b.test("x", "<=", "y"), b.terminal(1), b.test("x", "<=", 2))
self.diagrams.append(({"x", "y"}, d))
d = b.terminal("x * 2 * y + 5 * z")
self.diagrams.append(({"x", "y", "z"}, d))
d = b.ite(b.test("x", "<", "y"), b.terminal("z"), b.terminal("z * y"))
self.diagrams.append(({"x", "y", "z"}, d))
def build_example1():
# http://www.math.cornell.edu/~mec/Winter2009/RalucaRemus/Lecture3/lecture3.html
pool = Pool()
build = Builder(pool)
variables = [("i", 1, 4)]
for var in variables:
name = var[0]
build.ints("r_{}".format(name), "c_{}".format(name), name)
limits = build.limit("r_i", 1, 4) & build.limit("c_i", 1, 4)
column1 = (build.limit("c_i", 1, 1)
& build.limit("r_i", 2, 4)) * build.exp("1/3")
column2 = (build.limit("c_i", 2, 2)
& build.limit("r_i", 3, 4)) * build.exp("1/2")
column3 = (build.limit("c_i", 3, 3)
& build.limit("r_i", 1, 1)) * build.exp("1")
column4 = (build.limit("c_i", 4, 4) &
(build.limit("r_i", 1, 1)
| build.limit("r_i", 3, 3))) * build.exp("1/2")
diagram = limits * (column1 + column2 + column3 + column4)
return diagram, variables
def test_leaf_transform_simple_test(self):
pool = Pool()
pool.int_var("x")
test1 = pool.bool_test(LinearTest("x", ">="))
leaf_transform.transform_leaves(lambda t, d: d.pool.terminal(2),
pool.diagram(test1))
from __future__ import print_function
import itertools
from png import Writer
from pyxadd.build import Builder
from pyxadd.diagram import Pool, Diagram
from pyxadd.matrix.matrix import assignments
from pyxadd.reduce import SmtReduce, LinearReduction
from pyxadd.view import export
pool = Pool()
pool.add_var("x", "int")
pool.add_var("xs", "int")
pool.add_var("y", "int")
pool.add_var("ys", "int")
b = Builder(pool)
# TODO needs control over interleaving
class RedGreenBlueDiagrams(object):
def __init__(self, red, green, blue):
self.diagrams = (red, green, blue)
@staticmethod
def all(diagram):
return RedGreenBlueDiagrams(diagram, diagram, diagram)
def _binary(self, op, other):
if isinstance(other, RedGreenBlueDiagrams):
def test_leaf_transform_leaf_node(self):
pool = Pool()
diagram = pool.diagram(pool.one_id)
leaf_transform.transform_leaves(lambda t, d: d.pool.terminal(2), diagram)
def test_leaf_transform_simple_test(self):
pool = Pool()
pool.int_var("x")
test1 = pool.bool_test(LinearTest("x", ">="))
leaf_transform.transform_leaves(lambda t, d: d.pool.terminal(2), pool.diagram(test1))
from __future__ import print_function
import itertools
from png import Writer
from pyxadd.build import Builder
from pyxadd.diagram import Pool, Diagram
from pyxadd.matrix.matrix import assignments
from pyxadd.reduce import SmtReduce, LinearReduction
from pyxadd.view import export
pool = Pool()
pool.add_var("x", "int")
pool.add_var("xs", "int")
pool.add_var("y", "int")
pool.add_var("ys", "int")
b = Builder(pool)
# TODO needs control over interleaving
class RedGreenBlueDiagrams(object):
def __init__(self, red, green, blue):
self.diagrams = (red, green, blue)
@staticmethod
def all(diagram):
return RedGreenBlueDiagrams(diagram, diagram, diagram)
def _binary(self, op, other):
if isinstance(other, RedGreenBlueDiagrams):
def test_leaf_walking_leaf_node(self):
pool = Pool()
diagram = pool.diagram(pool.one_id)
walk.walk_leaves(lambda p, n: True, diagram)
def setUp(self):
pool = Pool()
pool.int_var("x")
self.test1 = pool.bool_test(LinearTest("x", ">="))
self.test2 = pool.bool_test(LinearTest("x + 2", ">"))
self.test3 = pool.bool_test(LinearTest("x + 1", "<="))
self.test4 = pool.bool_test(LinearTest("x - 5", "<="))
self.x = pool.terminal("x")
p1 = pool.apply(Multiplication, self.test1, self.test4)
p2 = pool.apply(Multiplication, pool.invert(self.test1), self.test2)
p3 = pool.apply(
Multiplication,
pool.apply(
Multiplication,
pool.apply(Multiplication, pool.invert(self.test1),
pool.invert(self.test2)), self.test3), self.test4)
result = pool.apply(Summation, pool.apply(Summation, p1, p2), p3)
result = pool.apply(Multiplication, result, self.x)
self.diagram = Diagram(pool, result)
def test_leaf_transform_leaf_node(self):
pool = Pool()
diagram = pool.diagram(pool.one_id)
leaf_transform.transform_leaves(lambda t, d: d.pool.terminal(2),
diagram)
def test_leaf_walking_leaf_node(self):
pool = Pool()
diagram = pool.diagram(pool.one_id)
walk.walk_leaves(lambda p, n: True, diagram)
def setUp(self):
pool = Pool()
pool.int_var("x")
self.test1 = pool.bool_test(LinearTest("x", ">="))
self.test2 = pool.bool_test(LinearTest("x + 2", ">"))
self.test3 = pool.bool_test(LinearTest("x + 1", "<="))
self.test4 = pool.bool_test(LinearTest("x - 5", "<="))
self.x = pool.terminal("x")
p1 = pool.apply(Multiplication, self.test1, self.test4)
p2 = pool.apply(Multiplication, pool.invert(self.test1), self.test2)
p3 = pool.apply(Multiplication, pool.apply(Multiplication, pool.apply(Multiplication,
pool.invert(self.test1),
pool.invert(self.test2)),
self.test3),
self.test4)
result = pool.apply(Summation, pool.apply(Summation, p1, p2), p3)
result = pool.apply(Multiplication, result, self.x)
self.diagram = Diagram(pool, result)
from pyxadd.build import Builder
from pyxadd.diagram import Pool
from pyxadd.view import export
pool = Pool()
b = Builder(pool)
b.ints("r", "c")
xadd_1 = b.terminal("5 + r * c")
export(xadd_1, "visual/examples/xadd_1.dot")
xadd_2 = b.limit("r", 1, 2) & b.limit("c", 1, 2) * xadd_1
export(xadd_2, "visual/examples/xadd_2.dot")
def test_inversion(self):
pool = Pool()
build = Builder(pool)
build.vars("bool", "a", "b")
build.vars("int", "x")
test1 = build.test("a")
test2 = build.test("b")
test3 = build.test("x", "<=", 5)
node3 = build.ite(test3, 1, 0)
diagram = build.ite(test1, build.ite(test2, node3, 1), node3)
self.assertTrue(is_ordered(diagram))
def inversion1(root_id):
minus_one = pool.terminal("-1")
return pool.apply(Multiplication,
pool.apply(Summation, root_id, minus_one),
minus_one)
def transform(terminal_node, d):
if terminal_node.expression == 1:
return d.pool.zero_id
elif terminal_node.expression == 0:
return d.pool.one_id
else:
raise RuntimeError("Could not invert value {}".format(
terminal_node.expression))
def inversion2(root_id):
to_invert = pool.diagram(root_id)
profile = WalkingProfile(diagram)
return leaf_transform.transform_leaves(transform, to_invert)
iterations = 1000
timer = Timer(precision=6)
timer.start("Legacy inversion")
for _ in range(iterations):
inversion1(diagram.root_id)
time_legacy = timer.stop()
inverted1 = pool.diagram(inversion1(diagram.root_id))
timer.start("New inversion")
for _ in range(iterations):
inversion2(diagram.root_id)
time_new = timer.stop()
inverted2 = pool.diagram(inversion2(diagram.root_id))
for a in [True, False]:
for b in [True, False]:
for x in range(10):
assignment = {"a": a, "b": b, "x": x}
self.assertNotEqual(diagram.evaluate(assignment),
inverted1.evaluate(assignment))
self.assertNotEqual(diagram.evaluate(assignment),
inverted2.evaluate(assignment))
self.assertTrue(
time_legacy > time_new,
"New inversion ({}) not faster than legacy implementation ({})".
format(time_new, time_legacy))
def __init__(self, pool=None):
if pool is None:
pool = Pool()
assert isinstance(pool, Pool)
self._pool = pool
def test_multiplication(self):
pool = Pool()
pool.int_var("x")
two = pool.terminal("2")
x = pool.terminal("x")
test1 = pool.bool_test(LinearTest("x", ">="))
test2 = pool.apply(Multiplication,
pool.bool_test(LinearTest("x - 5", "<=")), x)
product = pool.apply(Multiplication, test1, test2)
result = Diagram(pool, pool.apply(Multiplication, product, two))
for i in range(0, 10):
evaluated = result.evaluate({"x": i})
if 0 <= i <= 5:
self.assertEqual(2 * i, evaluated)
else:
self.assertEqual(0, evaluated)
def build_diagram1():
pool = Pool()
b = Builder(pool)
b.ints("x")
return b.ite(b.test("x", "<=", 3),
b.ite(b.test("x", "<=", 2), b.exp(1), b.exp("2*x")), b.exp(1))
def test_multiplication(self):
pool = Pool()
pool.int_var("x1", "x2")
x_two = Diagram(pool, pool.terminal("x2"))
two = Diagram(pool, pool.terminal("2"))
three = Diagram(pool, pool.terminal("3"))
four = Diagram(pool, pool.terminal("4"))
test11 = Diagram(pool, pool.bool_test(LinearTest("x1", ">=")))
test12 = Diagram(pool, pool.bool_test(LinearTest("x1 - 1", "<=")))
test13 = Diagram(pool, pool.bool_test(LinearTest("x1 - 3", ">")))
test21 = Diagram(pool, pool.bool_test(LinearTest("x2", ">=")))
test22 = Diagram(pool, pool.bool_test(LinearTest("x2", ">")))
test23 = Diagram(pool, pool.bool_test(LinearTest("x2 - 1", ">")))
test24 = Diagram(pool, pool.bool_test(LinearTest("x2 - 2", ">")))
x_twos = test12 * ~test23 * x_two
twos = test12 * test23 * two
threes = ~test12 * ~test22 * three
fours = ~test12 * test22 * four
unlimited = x_twos + twos + threes + fours
restricted = unlimited * test11 * ~test13 * test21 * ~test24
vector = test21 * ~test24 * Diagram(pool, pool.terminal("x2 + 1"))
result = Diagram(pool, matrix_multiply(pool, restricted.root_node.node_id, vector.root_node.node_id, ["x2"]))
for x1 in range(0, 4):
self.assertEqual(8 if x1 < 2 else 23, result.evaluate({"x1": x1}))
def get_unordered_diagram():
pool = Pool()
pool.int_var("x")
test1 = LinearTest("x", "<=", "2")
test2 = LinearTest("x", "<=", "3")
zero = pool.terminal(0)
one = pool.terminal(1)
pool.internal(test1, one, zero)
pool.internal(test2, one, zero)
# test2 => test1 => 1
node1 = pool.internal(test1, one, zero)
node2 = pool.internal(test2, node1, zero)
diagram = pool.diagram(node2)
return diagram