def reduce_order_interaction():
# A function f defined over binary variables represented as a
# vector stored in decimal order
#
# f(x4, x3, x2, x1) = a
# + b * x1
# + c * x2
# + d * x3
# + e * x4
# + g * x1 * x2
# + h * x1 * x3
# + i * x1 * x4
# + j * x2 * x3
# + k * x2 * x4
# + l * x3 * x4
# + m * x1 * x2 * x3
# + n * x1 * x2 * x4
# + o * x1 * x3 * x4
# + p * x2 * x3 * x4
# + q * x1 * x2 * x3 * x4
#
# f(0000) means when x4 = 0, x3 = 0, x2 = 0, x1 = 0, so f(0000) = a
# f(0001) means when x4 = 0, x3 = 0, x2 = 0, x1 = 1, so f(0001) = a + b
# f(0010) means when x4 = 0, x3 = 0, x2 = 1, x1 = 0, so f(0010) = a + c
# etc.
f = [0, -3, 0, 2, 1, -4, 0, 5, 1, 2, 0, 2, 1, 0, -3, -1]
# new_terms means terms after using ancillary variables
# vars_rep means ancillary variables
(Q, new_terms, vars_rep) = make_quadratic(f)
print "Q: ", Q
print "new_terms: ", new_terms
print "vars_rep: ", vars_rep
# f = x1 * x2
# + x3 * x4
terms = [[1, 2], [3, 4]]
(new_terms, vars_rep) = reduce_degree(terms)
print "new_terms: ", new_terms
print "vars_rep", vars_rep
# f = x2 * x3 * x4 * x5 * x8
# + x3 * x6 * x8
# + x1 * x6 * x7 * x8
# + x2 * x3 * x5 * x6 * x7
# + x1 * x3 * x6
# + x1 * x6 * x8 * x10 * x12
terms = [[2, 3, 4, 5, 8], [3, 6, 8], [1, 6, 7, 8], [2, 3, 5, 6, 7],
[1, 3, 6], [1, 6, 8, 10, 12]]
(new_terms, vars_rep) = reduce_degree(terms)
print "new_terms: ", new_terms
print "vars_rep", vars_rep
def test(f):
q, new_terms, mapping = make_quadratic(f)
assert q_vals(q, int(math.log(len(f), 2))) == f
assert all(len(t) <= 2 for t in new_terms)
def test_trivial():
assert make_quadratic([0]) == ({}, [], [])
def test_bad_f_zero():
with pytest.raises(ValueError):
make_quadratic([1])
def test_bad_f_size():
with pytest.raises(ValueError):
make_quadratic([])
with pytest.raises(ValueError):
make_quadratic([0, 1, 1])