def solve_dp(self, items, total_charge_diff, pos_total_charge, max_sum,
blowup):
solutionTime = -perf_counter()
# lower and upper capacity limits
upper = round(blowup * (pos_total_charge + total_charge_diff))
lower = max(0, round(blowup * (pos_total_charge - total_charge_diff)))
# check if feasible solutions may exist
reachable = round(blowup * max_sum)
if upper < 0 or lower > reachable:
# sum of min weights over all sets is larger than the upper bound
# or sum of max weights over all sets is smaller than the lower bound
raise AssignmentError('Could not solve DP problem. Please retry'
' with a SimpleCharger')
# init DP and traceback tables
dp = [0] + [-float('inf')] * upper
tb = [[] for _ in range(upper + 1)]
# DP
# iterate over all sets
for items_l in items:
# iterate over all capacities
for d in range(upper, -1, -1):
try:
# find max. profit with capacity i over all items j in set k
idx, dp[d] = max(((item[0], dp[d - item[1]] + item[2])
for item in items_l if d - item[1] >= 0),
key=lambda x: x[1])
# copy old traceback indices and add new index to traceback
if dp[d] >= 0:
tb[d] = tb[d - items_l[idx][1]] + [idx]
except ValueError:
dp[d] = -float('inf')
# find max profit
max_pos, max_val = max(enumerate(dp[lower:upper + 1]),
key=lambda x: x[1])
solutionTime += perf_counter()
if max_val == -float('inf'):
raise AssignmentError('Could not solve DP problem. Please retry'
' with a SimpleCharger')
solution = tb[lower + max_pos]
return solution, solutionTime
def solve_dp_c(self, charge_dists, total_charge, total_charge_diff):
import charge.c.dp as dp
num_sets = len(charge_dists)
num_items = sum(
len(charges) for (_, (charges, _)) in charge_dists.items())
weights = dp.new_doublea(num_items)
profits = dp.new_doublea(num_items)
sets = dp.new_ushorta(num_sets)
solution = dp.new_ushorta(num_sets)
offset = 0
pos_total = total_charge
for k, (atom, (charges,
frequencies)) in enumerate(charge_dists.items()):
dp.ushorta_setitem(sets, k, len(charges))
for i, (charge, frequency) in enumerate(zip(charges, frequencies)):
dp.doublea_setitem(weights, offset + i, charge)
dp.doublea_setitem(profits, offset + i, frequency)
pos_total -= min(charges)
offset += len(charges)
solutionTime = -perf_counter()
profit = dp.solve_dp(weights, profits, sets, num_items, num_sets,
self.__rounding_digits, total_charge,
total_charge_diff, solution)
solutionTime += perf_counter()
dp_solution = list()
if profit >= 0:
for k in range(num_sets):
i = dp.ushorta_getitem(solution, k)
dp_solution.append((k, i))
dp.delete_doublea(weights)
dp.delete_doublea(profits)
dp.delete_ushorta(sets)
dp.delete_ushorta(solution)
if profit < 0:
raise AssignmentError('Could not solve DP problem. Please retry'
' with a SimpleCharger')
return dp_solution, solutionTime, num_items, (pos_total +
total_charge_diff)
def _handle_error(self, no_vals: List[Atom], shells: List[int]) -> None:
"""Raises an AssignmentError if no_vals is not empty.
Args:
no_vals: List of atoms for which no charges could be found.
shells: List of tried shell sizes.
Raises:
AssignmentError: If no_vals is not empty.
"""
if len(no_vals) > 0:
err = 'Could not find charges for atoms {0}.'.format(', '.join(
map(str, no_vals)))
if not 0 in shells:
err += ' Please retry with a smaller "shell" parameter.'
raise AssignmentError(err)
def solve_dp_c(
self, charge_dists: Dict[Atom, Tuple[ChargeList, WeightList, str]],
total_charge: float, total_charge_diff: float
) -> Tuple[List[Tuple[int, int]], float, int, float]:
"""Solves the knapsack problem with dynamic programming implemented in C.
Args:
charge_dists: Charge distributions for the atoms, obtained \
by a Collector.
total_charge: The total charge of the molecule.
total_charge_diff: Maximum allowed deviation from the total charge
Returns:
Tuple of solution, solution time, the number of items and the scaled capacity.
"""
import charge.c.dp as dp
num_sets = len(charge_dists)
num_items = sum(
len(charges) for (_, (charges, _, _)) in charge_dists.items())
weights = dp.new_doublea(num_items)
profits = dp.new_doublea(num_items)
sets = dp.new_ushorta(num_sets)
solution = dp.new_ushorta(num_sets)
offset = 0
pos_total = total_charge
for k, (atom, (charges, frequencies,
_)) in enumerate(charge_dists.items()):
dp.ushorta_setitem(sets, k, len(charges))
for i, (charge, frequency) in enumerate(zip(charges, frequencies)):
dp.doublea_setitem(weights, offset + i, charge)
dp.doublea_setitem(profits, offset + i, frequency)
pos_total -= min(charges)
offset += len(charges)
solutionTime = -perf_counter()
profit = dp.solve_dp(weights, profits, sets, num_items, num_sets,
self._rounding_digits, total_charge,
total_charge_diff, solution)
solutionTime += perf_counter()
dp_solution = list()
if profit >= 0:
for k in range(num_sets):
i = dp.ushorta_getitem(solution, k)
dp_solution.append((k, i))
dp.delete_doublea(weights)
dp.delete_doublea(profits)
dp.delete_ushorta(sets)
dp.delete_ushorta(solution)
if profit < 0:
raise AssignmentError(
'Could not solve DP problem. Please retry with a SimpleCharger'
)
return dp_solution, solutionTime, num_items, (pos_total +
total_charge_diff)
def solve_dp(items: List[List[Tuple[int, int,
float]]], total_charge_diff: float,
pos_total_charge: float, max_sum: float, blowup: int):
"""Solves the knapsack problem with dynamic programming implemented in Python.
Args:
items: Knapsack items.
total_charge_diff: Maximum allowed deviation from the total charge.
pos_total_charge: Transformed total charge.
max_sum: Sum of all maximal charges per item class.
blowup: Blowup factor.
Returns:
Tuple of solution and solution time.
"""
solutionTime = -perf_counter()
# lower and upper capacity limits
upper = round(blowup * (pos_total_charge + total_charge_diff))
lower = max(0, round(blowup * (pos_total_charge - total_charge_diff)))
# check if feasible solutions may exist
reachable = round(blowup * max_sum)
if upper < 0 or lower > reachable:
# sum of min weights over all sets is larger than the upper bound
# or sum of max weights over all sets is smaller than the lower bound
raise AssignmentError(
'Could not solve DP problem. Please retry with a SimpleCharger'
)
# init DP and traceback tables
dp = [0] + [-float('inf')] * upper
tb = [[] for _ in range(upper + 1)]
# DP
# iterate over all sets
for items_l in items:
# iterate over all capacities
for d in range(upper, -1, -1):
try:
# find max. profit with capacity i over all items j in set k
idx, dp[d] = max(((item[0], dp[d - item[1]] + item[2])
for item in items_l if d - item[1] >= 0),
key=lambda x: x[1])
# copy old traceback indices and add new index to traceback
if dp[d] >= 0:
tb[d] = tb[d - items_l[idx][1]] + [idx]
except ValueError:
dp[d] = -float('inf')
# find max profit
max_pos, max_val = max(enumerate(dp[lower:upper + 1]),
key=lambda x: x[1])
solutionTime += perf_counter()
if max_val == -float('inf'):
raise AssignmentError(
'Could not solve DP problem. Please retry with a SimpleCharger'
)
solution = tb[lower + max_pos]
return solution, solutionTime
def solve_partial_charges(
self,
graph: nx.Graph,
charge_dists: Dict[Atom, Tuple[ChargeList, WeightList, str]],
total_charge: int,
total_charge_diff: float = DEFAULT_TOTAL_CHARGE_DIFF,
**kwargs) -> None:
"""Assign charges to the atoms in a graph.
Modify a graph by adding additional attributes describing the \
atoms' charges and scores. In particular, each atom will get \
a 'partial_charge' attribute with the partial charge, and a \
'score' attribute giving a degree of certainty for that charge.
This solver formulates a relaxed version of the \
epsilon-Equivalence-Multiple Choice Knapsack Problem as an \
Linear Programming problem and then uses a generic LP solver \
from the pulp library to produce optimised charges.
Atoms with isomorphic neighborhoods are considered equal and we \
assign the same charge to all atoms in an equivalence class.
Args:
graph: The molecule graph to solve charges for.
charge_dists: Charge distributions for the atoms, obtained \
by a Collector, plus the atom's canonical key.
total_charge: The total charge of the molecule.
total_charge_diff: Maximum allowed deviation from the total charge
"""
atom_idx = dict()
idx = list()
# weights = partial charges
weights = dict()
# profits = frequencies
profits = dict()
pos_total = total_charge
for k, (atom, (charges, frequencies,
_)) in enumerate(charge_dists.items()):
atom_idx[k] = atom
idx.append(list(zip(itertools.repeat(k), range(len(charges)))))
weights[k] = charges
profits[k] = frequencies
pos_total -= min(charges)
x = LpVariable.dicts('x',
itertools.chain.from_iterable(idx),
lowBound=0,
upBound=1)
charging_problem = LpProblem("Atomic Charging Problem", LpMaximize)
# maximize profits
charging_problem += sum([
profits[k][i] * x[(k, i)]
for k, i in itertools.chain.from_iterable(idx)
])
# select exactly one item per set
for indices in idx:
charging_problem += sum([x[(k, i)] for k, i in indices]) == 1
# total charge difference
charging_problem +=\
sum([weights[k][i] * x[(k, i)] for k, i in itertools.chain.from_iterable(idx)]) - total_charge\
<= total_charge_diff
charging_problem +=\
sum([weights[k][i] * x[(k, i)] for k, i in itertools.chain.from_iterable(idx)]) - total_charge\
>= -total_charge_diff
# identical neighborhood charge conditions
neighborhoodclasses = self.compute_atom_neighborhood_classes(
atom_idx, charge_dists)
for neighborhood_class in neighborhoodclasses:
i = neighborhood_class[0]
for j in neighborhood_class[1::]:
for (_, k) in idx[i]:
charging_problem += x[(i, k)] - x[(
j, k
)] == 0 # weight k from atom i is selected as partial charge <=> weight k of atom j is selected as partial charge
solutionTime = -perf_counter()
try:
charging_problem.solve(solver=self._solver)
except:
raise AssignmentError(
'Could not solve ILP problem. Please retry with a SimpleCharger'
)
solutionTime += perf_counter()
if not charging_problem.status == LpStatusOptimal:
raise AssignmentError(
'Could not solve ILP problem. Please retry with a SimpleCharger'
)
solution = []
profit = 0
charge = 0
for k, i in itertools.chain.from_iterable(idx):
if x[(k, i)].value() != 0.0:
if 'partial_charge' in graph.nodes[
atom_idx[k]] and 'score' in graph.nodes[atom_idx[k]]:
graph.nodes[atom_idx[k]][
'partial_charge'] += weights[k][i] * x[(k, i)].value()
graph.nodes[atom_idx[k]]['score'] += profits[k][i] * x[
(k, i)].value()
else:
graph.nodes[atom_idx[k]][
'partial_charge'] = weights[k][i] * x[(k, i)].value()
graph.nodes[atom_idx[k]]['score'] = profits[k][i] * x[
(k, i)].value()
solution.append(i)
for node in graph.nodes:
profit += graph.nodes[node]['score']
charge += graph.nodes[node]['partial_charge']
graph.graph['total_charge'] = round(charge, self._rounding_digits)
graph.graph['score'] = profit
graph.graph['time'] = solutionTime
graph.graph['items'] = len(x)
graph.graph['scaled_capacity'] = pos_total + total_charge_diff
graph.graph['neighborhoods'] = [[atom_idx[k] for k in i]
for i in neighborhoodclasses]
def solve_partial_charges(
self,
graph: nx.Graph,
charge_dists: Dict[Atom, Tuple[ChargeList, WeightList, str]],
total_charge: int,
total_charge_diff: float = DEFAULT_TOTAL_CHARGE_DIFF,
**kwargs) -> None:
"""Assign charges to the atoms in a graph.
Modify a graph by adding additional attributes describing the \
atoms' charges and scores. In particular, each atom will get \
a 'partial_charge' attribute with the partial charge, and a \
'score' attribute giving a degree of certainty for that charge.
This solver formulates the epsilon-Multiple Choice Knapsack \
Problem as an Integer Linear Programming problem and then uses \
a generic ILP solver from the pulp library to produce optimised \
charges.
Args:
graph: The molecule graph to solve charges for.
charge_dists: Charge distributions for the atoms, obtained \
by a Collector, plus the atom's canonical key.
total_charge: The total charge of the molecule
total_charge_diff: Maximum allowed deviation from the total charge
"""
atom_idx = dict()
idx = list()
# weights = partial charges
weights = dict()
# profits = frequencies
profits = dict()
pos_total = total_charge
for k, (atom, (charges, frequencies,
_)) in enumerate(charge_dists.items()):
atom_idx[k] = atom
idx.append(list(zip(itertools.repeat(k), range(len(charges)))))
weights[k] = charges
profits[k] = frequencies
pos_total -= min(charges)
x = LpVariable.dicts('x',
itertools.chain.from_iterable(idx),
lowBound=0,
upBound=1,
cat=LpInteger)
charging_problem = LpProblem("Atomic Charging Problem", LpMaximize)
# maximize profits
charging_problem += sum([
profits[k][i] * x[(k, i)]
for k, i in itertools.chain.from_iterable(idx)
])
# select exactly one item per set
for indices in idx:
charging_problem += sum([x[(k, i)] for k, i in indices]) == 1
# total charge difference
charging_problem +=\
sum([weights[k][i] * x[(k, i)] for k, i in itertools.chain.from_iterable(idx)]) - total_charge\
<= total_charge_diff
charging_problem +=\
sum([weights[k][i] * x[(k, i)] for k, i in itertools.chain.from_iterable(idx)]) - total_charge\
>= -total_charge_diff
solutionTime = -perf_counter()
try:
charging_problem.solve(solver=self._solver)
except:
raise AssignmentError(
'Could not solve ILP problem. Please retry with a SimpleCharger'
)
solutionTime += perf_counter()
if not charging_problem.status == LpStatusOptimal:
raise AssignmentError(
'Could not solve ILP problem. Please retry with a SimpleCharger'
)
solution = []
profit = 0
charge = 0
for k, i in itertools.chain.from_iterable(idx):
if x[(k, i)].value() == 1.0:
graph.nodes[atom_idx[k]]['partial_charge'] = weights[k][i]
graph.nodes[atom_idx[k]]['score'] = profits[k][i]
solution.append(i)
profit += profits[k][i]
charge += graph.nodes[atom_idx[k]]['partial_charge']
graph.graph['total_charge'] = round(charge, self._rounding_digits)
graph.graph['score'] = profit
graph.graph['time'] = solutionTime
graph.graph['items'] = len(x)
graph.graph['scaled_capacity'] = pos_total + total_charge_diff
def solve_partial_charges(
self,
graph: nx.Graph,
charge_dists: Dict[Atom, Tuple[ChargeList, WeightList]],
total_charge: int,
keydict: Dict[Atom, str] = None,
total_charge_diff: float = DEFAULT_TOTAL_CHARGE_DIFF,
**kwargs) -> None:
"""Assign charges to the atoms in a graph.
Modify a graph by adding additional attributes describing the \
atoms' charges and scores. In particular, each atom will get \
a 'partial_charge' attribute with the partial charge, and a \
'score' attribute giving a degree of certainty for that charge.
This solver uses Dynamic Programming to solve the \
epsilon-Multiple Choice Knapsack Problem. This is the Python \
version of the algorithm, see CDPSolver for a faster \
implementation.
Args:
graph: The molecule graph to solve charges for.
charge_dists: Charge distributions for the atoms, obtained \
by a Collector.
total_charge: The total charge of the molecule.
total_charge_diff: Maximum allowed deviation from the total charge
"""
blowup = 10**self.__rounding_digits
deflate = 10**(-self.__rounding_digits)
atom_idx = dict()
idx = list()
# item = (index, weight, profit)
items = list()
# min weights
w_min = dict()
solutionTime = -perf_counter()
# transform weights to non-negative integers
pos_total_charge = total_charge
max_sum = 0
for k, (atom, (charges,
frequencies)) in enumerate(charge_dists.items()):
atom_idx[k] = atom
idx.append(zip(itertools.repeat(k), range(len(charges))))
w_min[k] = min(charges)
max_sum += max(charges) - w_min[k]
items.append(
list(
zip(range(len(charges)), [
round(blowup * (charge - w_min[k]))
for charge in charges
], frequencies)))
pos_total_charge -= w_min[k]
# lower and upper capacity limits
upper = round(blowup * (pos_total_charge + total_charge_diff))
lower = max(0, round(blowup * (pos_total_charge - total_charge_diff)))
# check if feasible solutions may exist
reachable = round(blowup * max_sum)
if upper < 0 or lower > reachable:
# sum of min weights over all sets is larger than the upper bound
# or sum of max weights over all sets is smaller than the lower bound
raise AssignmentError('Could not solve DP problem. Please retry'
' with a SimpleCharger')
# init DP and traceback tables
dp = [0] + [-float('inf')] * upper
tb = [[] for _ in range(upper + 1)]
# DP
# iterate over all sets
for items_l in items:
# iterate over all capacities
for d in range(upper, -1, -1):
try:
# find max. profit with capacity i over all items j in set k
idx, dp[d] = max(((item[0], dp[d - item[1]] + item[2])
for item in items_l if d - item[1] >= 0),
key=lambda x: x[1])
# copy old traceback indices and add new index to traceback
if dp[d] >= 0:
tb[d] = tb[d - items_l[idx][1]] + [idx]
except ValueError:
dp[d] = -float('inf')
# find max profit
max_pos, max_val = max(enumerate(dp[lower:upper + 1]),
key=lambda x: x[1])
solutionTime += perf_counter()
if max_val == -float('inf'):
raise AssignmentError('Could not solve DP problem. Please retry'
' with a SimpleCharger')
solution = tb[lower + max_pos]
charge = 0
score = 0
for i, j in enumerate(solution):
graph.node[atom_idx[i]]['partial_charge'] = charge_dists[
atom_idx[i]][0][j]
graph.node[atom_idx[i]]['score'] = charge_dists[atom_idx[i]][1][j]
charge += graph.node[atom_idx[i]]['partial_charge']
score += graph.node[atom_idx[i]]['score']
graph.graph['total_charge'] = round(charge, self.__rounding_digits)
graph.graph['score'] = score
graph.graph['time'] = solutionTime
graph.graph['items'] = sum(len(i) for i in items)
graph.graph['scaled_capacity'] = pos_total_charge + total_charge_diff
