# Copyright 2023 Jij Inc.
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
# http://www.apache.org/licenses/LICENSE-2.0
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
from __future__ import annotations
import inspect
from logging import getLogger
import numpy as np
logger = getLogger(__name__)
[docs]
def solver_benchmark(
solver,
time_list,
solutions=[],
args={},
p_r=0.99,
ref_energy=0,
measure_with_energy=False,
time_name="execution_time",
):
"""Calculate 'success probability', 'TTS', 'Residual energy','Standard Error' with computation time
Args:
solver (callable): returns openjij.Response, and solver has arguments 'time' and '**args'
time_list (list):
solutions (list(list(int)), list(int)): true solution or list of solution (if solutions are degenerated).
args (dict): Arguments for solver.
p_r (float): Thereshold probability for time to solutions.
ref_energy (float): The ground (reference to calculate success probability and the residual energy) energy.
measure_with_energy (bool): use a energy as measure for success
Returns:
dict: dictionary which has the following keys:
* **time**: list of compuation time
* **success_prob** list of success probability at each computation time
* **tts**: list of time to solusion at each computation time
* **residual_energy**: list of residual energy at each computation time
* **se_lower_tts**: list of tts's lower standard error at each computation time
* **se_upper_tts**: list of tts's upper standard error at each computation time
* **se_success_prob**: list of success probability's standard error at each computation time
* **se_residual_energy**: list of residual_energy's standard error at each computation time
* **info** (dict): Parameter information for the benchmark
"""
if not measure_with_energy:
if solutions == []:
raise ValueError("need input 'solutions': (list(list))")
logger.info("function " + inspect.currentframe().f_code.co_name + " start")
computation_times = []
success_probabilities = []
tts_list = []
residual_energies = []
se_lower_tts_list = []
se_upper_tts_list = []
se_success_prob_list = []
se_residual_energy_list = []
for time in time_list:
response = solver(time, **args)
comp_time = response.info[time_name]
computation_times.append(comp_time)
ps = success_probability(response, solutions, ref_energy, measure_with_energy)
tts = time_to_solution(ps, comp_time, p_r)
success_probabilities.append(ps)
tts_list.append(tts)
residual_energies.append(residual_energy(response, ref_energy))
se_ps = se_success_probability(
response, solutions, ref_energy, measure_with_energy
)
se_success_prob_list.append(se_ps)
se_lower_tts_list.append(se_lower_tts(tts, ps, comp_time, p_r, se_ps))
se_upper_tts_list.append(se_upper_tts(tts, ps, comp_time, p_r, se_ps))
se_residual_energy_list.append(se_residual_energy(response, ref_energy))
return {
"time": computation_times,
"success_prob": success_probabilities,
"tts": tts_list,
"residual_energy": residual_energies,
"se_lower_tts": se_lower_tts_list,
"se_upper_tts": se_upper_tts_list,
"se_success_prob": se_success_prob_list,
"se_residual_energy": se_residual_energy_list,
"info": {
"tts_threshold_prob": p_r,
"ref_energy": ref_energy,
"measure_with_energy": measure_with_energy,
},
}
[docs]
def residual_energy(response, ref_energy):
"""Calculate redisual energy from measure energy
Args:
response (openjij.Response): response from solver (or sampler).
ref_energy (float): the reference energy (usually use the ground energy)
Returns:
float: Residual energy which is defined as :math:`\\langle E \\rangle - E_0` (:math:`\\langle...\\rangle` represents average, :math:`E_0` is the reference energy (usually use the ground energy)).
"""
return np.mean(response.energies) - ref_energy
[docs]
def se_residual_energy(response, ref_energy):
"""Calculate redisual energy's standard error from measure energy
Args:
response (openjij.Response): response from solver (or sampler).
ref_energy (float): the reference energy (usually use the ground energy)
Returns:
float: redisual energy's standard error from measure energy
"""
return np.std(response.energies, ddof=1)
[docs]
def success_probability(response, solutions, ref_energy=0, measure_with_energy=False):
"""Calculate success probability from openjij.response
Args:
response (openjij.Response): response from solver (or sampler).
solutions (list[int]): true solutions.
Returns:
float: Success probability.
* When measure_with_energy is False, success is defined as getting the same state as solutions.
* When measure_with_energy is True, success is defined as getting a state which energy is below reference energy
"""
if measure_with_energy:
suc_prob = np.count_nonzero(np.array(response.energies) <= ref_energy) / len(
response.energies
)
else:
if isinstance(solutions[0], dict):
sampled_states = response.samples()
suc_prob = np.mean(
[1 if dict(state) in solutions else 0 for state in sampled_states]
)
else:
sampled_states = response.states
suc_prob = np.mean(
[1 if list(state) in solutions else 0 for state in sampled_states]
)
return suc_prob
[docs]
def se_success_probability(
response, solutions, ref_energy=0, measure_with_energy=False
):
"""Calculate success probability's standard error from openjij.response
Args:
response (openjij.Response): response from solver (or sampler).
solutions (list[int]): true solutions.
Returns:
float: Success probability's standard error.
* When measure_with_energy is False, success is defined as getting the same state as solutions.
* When measure_with_energy is True, success is defined as getting a state which energy is below reference energy
"""
if measure_with_energy:
se_suc_prob = np.sqrt(
np.count_nonzero(np.array(response.energies) <= ref_energy)
/ (len(response.energies) - 1)
)
else:
if isinstance(solutions[0], dict):
sampled_states = response.samples()
se_suc_prob = np.std(
[1 if dict(state) in solutions else 0 for state in sampled_states]
)/np.sqrt(len(sampled_states))
else:
sampled_states = response.states
se_suc_prob = np.std(
[1 if list(state) in solutions else 0 for state in sampled_states]
)/np.sqrt(len(sampled_states))
return se_suc_prob
[docs]
def time_to_solution(success_prob, computation_time, p_r):
"""
Args:
success_prob (float): success probability.
computation_time (float):
p_r (float): thereshold probability to calculate time to solution.
Returns:
float: time to solution :math:`\\tau * \\log(1-pr)/\\log(1-ps)` which pr is thereshold probability, ps is success probability and :math:`tau` is computation time.
"""
if success_prob == 1.0:
tts = 0.0
elif success_prob == 0.0:
tts = np.inf
else:
tts = computation_time * np.log(1 - p_r) / np.log(1 - success_prob)
return tts
[docs]
def se_lower_tts(tts, success_prob, computation_time, p_r, se_success_prob):
"""
Args:
success_prob (float): success probability.
computation_time (float):
p_r (float): thereshold probability to calculate time to solution.
Returns:
float: time to solution :math:`\\tau * \\log(1-pr)/\\log(1-ps)` 's standard error which pr is thereshold probability, ps is success probability and :math:`tau` is computation time.
"""
if 1 - (success_prob + se_success_prob) <= 0.0:
tts_low_error = 0.0
elif success_prob == 0.0:
tts_low_error = 0.0
else:
tts_low_error = (
computation_time
* np.log(1 - p_r)
/ np.log(1 - (success_prob + se_success_prob))
)
se_lower_tts = abs(tts_low_error - tts)
return se_lower_tts
[docs]
def se_upper_tts(tts, success_prob, computation_time, p_r, se_success_prob):
"""
Args:
success_prob (float): success probability.
computation_time (float):
p_r (float): thereshold probability to calculate time to solution.
Returens:
float: time to solution :math:`\\tau * \\log(1-pr)/\\log(1-ps)` 's standard error which pr is thereshold probability, ps is success probability and :math:`tau` is computation time.
"""
if success_prob == 1.0:
tts_up_error = 0.0
elif success_prob == 0.0:
tts_up_error = 0.0
else:
tts_up_error = (
computation_time
* np.log(1 - p_r)
/ np.log(1 - (success_prob - se_success_prob))
)
se_upper_tts = abs(tts_up_error - tts)
return se_upper_tts
