def lp_track_weights(graph,
connection_weights,
detection_weights,
entry_weight,
verbose=False,
add_gt_hamming=False):
if not graph:
return []
lp = LinearProgram(verbose)
def Var():
v = lp.Var()
lp.add_constraint(0 <= v <= 1)
return v
for d in graph:
d.outgoing = [Var() for n in d.next]
d.exit = Var()
d.entry = Var()
d.present = Var()
for d in graph:
d.incomming = [p.outgoing[p.next.index(d)] for p in d.prev]
connection_weight = 0
for d in graph:
lp.add_constraint(sum(d.outgoing) + d.exit - d.present == 0)
lp.add_constraint(sum(d.incomming) + d.entry - d.present == 0)
connection_weight += sum(connection_weights[i].item() * v
for v, i in zip(d.outgoing, d.weight_index))
if add_gt_hamming:
connection_weight += sum(
hamming_weight(v, gt) for v, gt in zip(d.outgoing, d.gt_next))
detection_weight = sum(d.present * detection_weights[d.index] +
entry_weight * d.entry for d in graph)
if add_gt_hamming:
detection_weight += sum(
hamming_weight(d.present, d.gt_present) +
hamming_weight(d.entry, d.gt_entry) for d in graph)
lp.objective = connection_weight + detection_weight
m = lp.maximize()
tracks = []
for d in graph:
if d.entry.value:
tr = [d]
while not d.exit.value:
d = d.next[max([(v.value, i)
for i, v in enumerate(d.outgoing)])[1]]
tr.append(d)
tracks.append(tr)
return tracks
def test_expr():
lp = LinearProgram()
x, y = lp.Var(), lp.Var()
assert str(x + y) == " 1.00 X1 + 1.00 X2"
assert str(2 * (x + y)) == " 2.00 X1 + 2.00 X2"
assert str(2 * x + 3 * y) == " 2.00 X1 + 3.00 X2"
assert str(0 <= 2 * x) == " 2.00 X1 >= 0.00"
assert str(3 * y <= 7) == " 3.00 X2 <= 7.00"
e = 0 <= 2 * x + 3 * y <= 7
assert str(e) == " 0.00 <= 2.00 X1 + 3.00 X2 <= 7.00"
e = 2 * x + 3 * y
assert str(e <= 7) == " 2.00 X1 + 3.00 X2 <= 7.00"
assert str(0 <= e) == " 2.00 X1 + 3.00 X2 >= 0.00"
assert str(x * 4 == 8) == " 4.00 X1 == 8.00"
assert str(y <= 6) == "X2 <= 6.00"
assert str(2 * x - 3 * y) == " 2.00 X1 + -3.00 X2"
e += 3 * lp.Var()
assert str(e) == " 2.00 X1 + 3.00 X2 + 3.00 X3"
def test_mip1():
lp = LinearProgram()
x, y, z = lp.IntVar(), lp.IntVar(), lp.IntVar()
lp.objective = 10 * x - 6 * y + 4 * z
lp.add_constraint(0 <= x <= 10)
lp.add_constraint(0 <= y <= 10)
lp.add_constraint(0 <= z <= 10)
minval = lp.minimize()
print(minval)
print(x.value, y.value, z.value)
assert minval == -60
assert (x.value, y.value, z.value) == (0, 10, 0)
def test_lp3():
lp = LinearProgram()
x, y, z = lp.Var(), lp.Var(), lp.Var()
lp.objective = 10 * x + 6 * y + 4 * z
lp.add_constraint(x + y + z <= 100)
lp.add_constraint(10 * x + 4 * y + 5 * z <= 600)
lp.add_constraint(2 * x + 2 * y + 6 * z <= 300)
lp.add_constraint(x >= 0)
lp.add_constraint(y >= 0)
lp.add_constraint(z >= 0)
maxval = lp.maximize()
print(maxval)
print(x.value, y.value, z.value)
assert int(maxval) == 733
assert int(x.value) == 33
assert int(y.value) == 66
assert int(z.value) == 0
def test_lp2():
lp = LinearProgram()
x, y, z = lp.Var(), lp.Var(), lp.Var()
lp.objective = 10 * x - 6 * y + 4 * z
lp.add_constraint(x <= 10)
lp.add_constraint(0 <= y)
lp.add_constraint(z <= 10)
maxval = lp.maximize()
print(maxval)
print(x.value, y.value, z.value)
assert maxval == 140
assert (x.value, y.value, z.value) == (10, 0, 10)
def test_mip_zero():
lp = LinearProgram()
x, y, z = lp.IntVar(), lp.IntVar(), lp.IntVar()
lp.objective = 10 * x + 6 * y + 4 * z
lp.add_constraint(0 + x + y + z <= 100)
lp.add_constraint(0 + 10 * x + 4 * y + 5 * z <= 600)
lp.add_constraint(2 * x + 2 * y + 6 * z + 0 <= 300)
lp.add_constraint(x >= 0)
lp.add_constraint(y >= 0)
lp.add_constraint(z >= 0)
maxval = lp.maximize()
print(maxval)
print(x.value, y.value, z.value)
assert maxval == 732.0
assert x.value == 33
assert y.value == 67
assert z.value == 0
def test_isub():
lp = LinearProgram()
x, y = lp.Var(), lp.Var()
lp.objective += 10 * x - 6 * y
lp.add_constraint(x <= 10)
lp.add_constraint(0 <= y)
lp.objective -= 6 * y
z = lp.Var()
lp.add_constraint(z <= 10)
lp.objective += 4 * z
maxval = lp.maximize()
print(maxval)
print(x.value, y.value, z.value)
assert maxval == 140
assert (x.value, y.value, z.value) == (10, 0, 10)