def _RBS_DIG(self, contaminated_set):
""" Binary splitting algorithm.
Input: contaminated set
Output: - single contaminated item in input set
- list of items declared healthy
"""
healthy_set = [[], []]
while len(contaminated_set[0]) >> 1:
test_group = aux._split_groups(contaminated_set)
if aux._make_test(test_group[0][1], self.success_rate_test,
self.false_posivite_rate_test, self.prob_sick,
self.tests_repetitions,
self.test_result_decision_strategy) == 1:
contaminated_set = test_group[0]
else:
contaminated_set = test_group[1]
for i in range(2):
for item in test_group[0][i]:
healthy_set[i] += [item]
self.number_of_tests += self.tests_repetitions
# single sick individual returned
if contaminated_set == [[], []]:
return None, healthy_set
else:
return [contaminated_set[0][0],
contaminated_set[1][0]], healthy_set
def two_stage_testing_time_dependent(self, num_simultaneous_tests,
test_duration, group_size):
# number of tests which can be performed at once
self.num_simultaneous_tests = num_simultaneous_tests
# duration of one test [h]
self.test_duration = test_duration
self.number_groupwise_tests = np.ones(
int(np.ceil(self.sample_size / group_size)))
# initialize active groups
self.active_groups = []
self.confirmed_sick_individuals = []
# this is for indexing the individuals
self.continuousIndex = 0
for i in range(self.num_simultaneous_tests):
self.get_next_group_from_data(group_size)
while (len(self.active_groups) > 0):
# Caution: new groups are added to active_groups every time a group is positively tested
# However, we can only process the ones that existed at the beginning of this loop iteration
for i in range(
min(len(self.active_groups), self.num_simultaneous_tests)):
testgroup = self.active_groups[0]
self.active_groups = self.active_groups[1:]
testresult = aux._make_test(testgroup[1],
self.success_rate_test,
self.false_posivite_rate_test,
self.prob_sick,
self.tests_repetitions,
self.test_result_decision_strategy)
self.number_of_tests += self.tests_repetitions
if testresult == 1:
if len(testgroup[1]) == 1:
self.sick_individuals.append(testgroup[0][0])
else:
# If a group is tested positive all its individuals are tested positive.
# We consider this two consecutive tests.
self.number_groupwise_tests[int(
np.floor(testgroup[0][0] / group_size))] = 2
for j in range(len(testgroup[1])):
self.active_groups += [[[testgroup[0][j]],
[testgroup[1][j]]]]
if len(self.active_groups) < self.num_simultaneous_tests:
# groups have been fully processed. Add next group from data
for i in range(self.num_simultaneous_tests -
len(self.active_groups)):
self.get_next_group_from_data(group_size)
#self.total_time += self.test_duration
self.total_time = self.number_of_tests * self.test_duration * self.tests_repetitions / self.num_simultaneous_tests
self.update_sick_lists_and_success_rate()
def individual_testing_time_dependent(self,
num_simultaneous_tests,
test_duration,
group_size=1):
self.num_simultaneous_tests = num_simultaneous_tests
self.test_duration = test_duration
if group_size == 1:
self.number_groupwise_tests = np.ones(self.sample_size)
# initialize active groups
self.active_groups = []
self.confirmed_sick_individuals = []
# this is for indexing the individuals
self.continuousIndex = 0
for i in range(self.num_simultaneous_tests):
self.get_next_group_from_data(group_size)
while (len(self.active_groups) > 0):
# Caution: binary_splitting_step adds new groups to active_groups every time it is
# called. However, we can only process the ones that existed at the beginning of this
# loop iteration
self.number_of_rounds += 1
for i in range(
min(len(self.active_groups), self.num_simultaneous_tests)):
testgroup = self.active_groups[0]
self.active_groups = self.active_groups[1:]
testresult = aux._make_test(testgroup[1],
self.success_rate_test,
self.false_posivite_rate_test,
self.prob_sick,
self.tests_repetitions,
self.test_result_decision_strategy)
self.number_of_tests += self.tests_repetitions
if testresult == 1:
for individual in testgroup[0]:
self.sick_individuals.append(individual)
if len(self.active_groups) < self.num_simultaneous_tests:
# groups have been fully processed. Add next group from data
for i in range(self.num_simultaneous_tests -
len(self.active_groups)):
self.get_next_group_from_data(group_size)
#self.total_time += self.test_duration * self.tests_repetitions
self.total_time = self.number_of_tests * self.test_duration * self.tests_repetitions / self.num_simultaneous_tests
self.update_sick_lists_and_success_rate()
def binary_splitting_step(self, testgroup):
self.number_of_rounds += 1
# instantiate test results
result_test = [0, 0]
# split in left and right branch
for i in range(2):
if len(testgroup[i][0]) != 0:
result_test[i] += aux._make_test(
testgroup[i][1], self.success_rate_test,
self.false_posivite_rate_test, self.prob_sick,
self.tests_repetitions, self.test_result_decision_strategy)
# Adjust the counter for the number of tests
self.number_of_tests += self.tests_repetitions
# Determine the outcome of the finding
if result_test[i] == 1:
if len(testgroup[i][1]) == 1:
self.sick_individuals.append(testgroup[i][0][0])
else:
self.active_groups += [testgroup[i]]
def purim_time_dependent(self, num_simultaneous_tests, test_duration,
group_size):
'''
Purim matrix based testing algorithm as in
Fargion, Benjamin Isac, et al.
"Purim: a rapid method with reduced cost for massive detection of CoVid-19."
arXiv preprint arXiv:2003.11975 (2020).
'''
self.num_simultaneous_tests = num_simultaneous_tests
self.test_duration = test_duration
# initialize active groups
self.active_groups = []
self.confirmed_sick_individuals = []
# this is for indexing the individuals
self.continuousIndex = 0
# by definition the sequential depth of purim is always two (right?)
self.number_groupwise_tests = np.ones(
int(np.ceil(self.sample_size / (group_size**2)))) * 2
for i in range(self.num_simultaneous_tests):
self.get_next_group_from_data(group_size**2)
while (len(self.active_groups) > 0):
self.number_of_rounds += 1
for i in range(
min(len(self.active_groups), self.num_simultaneous_tests)):
testgroup = self.active_groups[0]
self.active_groups = self.active_groups[1:]
nearest_square = round(np.sqrt(len(testgroup[1])))**2
diff = nearest_square - len(testgroup[1])
if len(testgroup[1]) <= 4:
# if the number of people in a group is 2 or less, do individual testing
for j in range(len(testgroup[1])):
result = aux._make_test(
[testgroup[1][j]], self.success_rate_test,
self.false_posivite_rate_test, self.prob_sick,
self.tests_repetitions,
self.test_result_decision_strategy)
self.number_of_tests += self.tests_repetitions
if result == 1:
self.sick_individuals += [testgroup[0][j]]
elif int(diff) < 0:
# write into nearest_square+1 x nearest_square+1 array
testarray = np.ones(
int(nearest_square + 2 * np.sqrt(nearest_square) + 1))
for l in range(len(testgroup[1])):
testarray[l] = testgroup[1][l]
testarray = testarray.reshape(
(int(np.sqrt(nearest_square) + 1),
int(np.sqrt(nearest_square) + 1)))
testarray_index = np.ones(
int(nearest_square + 2 * np.sqrt(nearest_square) + 1))
for l in range(len(testgroup[0])):
testarray_index[l] = testgroup[0][l]
# testarray_index = np.append(np.asarray(testgroup[0]),np.ones(int(-diff)+1))
testarray_index = testarray_index.reshape(
(int(np.sqrt(nearest_square) + 1),
int(np.sqrt(nearest_square) + 1)))
columns = []
rows = []
for k in range(int(np.sqrt(nearest_square) + 1)):
result = aux._make_test(
testarray[k, :], self.success_rate_test,
self.false_posivite_rate_test, self.prob_sick,
self.tests_repetitions,
self.test_result_decision_strategy)
self.number_of_tests += self.tests_repetitions
if result == 1:
columns += [k]
for j in range(int(np.sqrt(nearest_square) + 1)):
result = aux._make_test(
testarray[:, j], self.success_rate_test,
self.false_posivite_rate_test, self.prob_sick,
self.tests_repetitions,
self.test_result_decision_strategy)
self.number_of_tests += self.tests_repetitions
if result == 1:
rows += [j]
for k in columns:
for j in rows:
result = aux._make_test(
[testarray[k, j]], self.success_rate_test,
self.false_posivite_rate_test, self.prob_sick,
self.tests_repetitions,
self.test_result_decision_strategy)
self.number_of_tests += self.tests_repetitions
if result == 1:
self.sick_individuals += [
int(testarray_index[k, j])
]
else:
testarray = np.ones(int(nearest_square))
for l in range(len(testgroup[1])):
testarray[l] = testgroup[1][l]
testarray = testarray.reshape(
(int(np.sqrt(nearest_square)),
int(np.sqrt(nearest_square))))
testarray_index = np.ones(int(nearest_square))
for l in range(len(testgroup[0])):
testarray_index[l] = testgroup[0][l]
# testarray_index = np.append(np.asarray(testgroup[0]),np.ones(int(diff)))
testarray_index = testarray_index.reshape(
(int(np.sqrt(nearest_square)),
int(np.sqrt(nearest_square))))
columns = []
rows = []
for k in range(int(np.sqrt(nearest_square))):
result = aux._make_test(
testarray[k, :], self.success_rate_test,
self.false_posivite_rate_test, self.prob_sick,
self.tests_repetitions,
self.test_result_decision_strategy)
self.number_of_tests += self.tests_repetitions
if result == 1:
columns += [k]
for j in range(int(np.sqrt(nearest_square))):
result = aux._make_test(
testarray[:, j], self.success_rate_test,
self.false_posivite_rate_test, self.prob_sick,
self.tests_repetitions,
self.test_result_decision_strategy)
self.number_of_tests += self.tests_repetitions
if result == 1:
rows += [j]
for k in columns:
for j in rows:
result = aux._make_test(
[testarray[k, j]], self.success_rate_test,
self.false_posivite_rate_test, self.prob_sick,
self.tests_repetitions,
self.test_result_decision_strategy)
self.number_of_tests += self.tests_repetitions
if result == 1:
self.sick_individuals += [
int(testarray_index[k, j])
]
if len(self.active_groups) < self.num_simultaneous_tests:
# groups have been fully processed. Add next group from data
for i in range(self.num_simultaneous_tests -
len(self.active_groups)):
self.get_next_group_from_data(group_size**2)
# simplified time measure, because individual time tracking is a bit complicated for RBS
self.total_time = self.number_of_tests * self.test_duration / self.num_simultaneous_tests
self.update_sick_lists_and_success_rate()
def binary_splitting_time_dependent(self, num_simultaneous_tests,
test_duration, group_size):
# in contrast to 'binary_splitting' this does not start with one huge group of all individuals
# but with as many groups as tests are available, each group a reasonable size
# when there are less groups than simultaneously processable tests new groups are added to
# active_groups
# number of tests which can be performed at once
self.num_simultaneous_tests = num_simultaneous_tests
# duration of one test [h]
self.test_duration = test_duration
self.number_groupwise_tests = np.ones(
int(np.ceil(self.sample_size / group_size)))
# initialize active groups
self.active_groups = []
self.confirmed_sick_individuals = []
# this is for indexing the individuals
self.continuousIndex = 0
for i in range(self.num_simultaneous_tests):
self.get_next_group_from_data(group_size)
while (len(self.active_groups) > 0):
# Caution: binary_splitting_step adds new groups to active_groups every time it is
# called. However, we can only process the ones that existed at the beginning of this
# loop iteration
self.number_of_rounds += 1
# print('---')
for i in range(
min(len(self.active_groups), self.num_simultaneous_tests)):
testgroup = self.active_groups[0]
self.active_groups = self.active_groups[1:]
testresult = aux._make_test(testgroup[1],
self.success_rate_test,
self.false_posivite_rate_test,
self.prob_sick,
self.tests_repetitions,
self.test_result_decision_strategy)
self.number_of_tests += self.tests_repetitions
if testresult == 1:
# when a group of initial size is tested positive a tree of depth
# log2(groupsize)+1 will be created. Otherwise only default depth 1
if len(testgroup[1]) == group_size:
self.number_groupwise_tests[int(
np.floor(testgroup[0][0] / group_size))] = np.ceil(
np.log2(group_size)) + 1
# if only one individual in group
if len(testgroup[1]) == 1:
self.sick_individuals.append(testgroup[0][0])
else:
new_groups = aux._split_groups(testgroup)
self.active_groups.append(new_groups[0])
self.active_groups.append(new_groups[1])
if len(self.active_groups) < self.num_simultaneous_tests:
# groups have been fully processed. Add next group from data
for i in range(self.num_simultaneous_tests -
len(self.active_groups)):
self.get_next_group_from_data(group_size)
#self.total_time += self.test_duration * self.tests_repetitions
self.total_time = self.number_of_tests * self.test_duration * self.tests_repetitions / self.num_simultaneous_tests
self.update_sick_lists_and_success_rate()
def sobel_main(self, num_simultaneous_tests, test_duration, maxGroupsize):
'''
The algorithm R1 from (Sobel, Groll 1959)
Sobel, Milton, and Phyllis A. Groll.
"Group testing to eliminate efficiently all defectives in a binomial sample."
Bell System Technical Journal 38.5 (1959): 1179-1252.
'''
self.num_simultaneous_tests = num_simultaneous_tests
self.test_duration = test_duration
self.continuousIndex = 0
self.maxGroupsize = maxGroupsize
# counter for the number of tests which are performed on one initial group of
# maxGroupsize in total
self.number_groupwise_tests = np.zeros(
int(np.ceil(self.sample_size / maxGroupsize)))
self.G, self.x = self.sobel_computeGx(1 - self.prob_sick, maxGroupsize)
# initialize active groups
self.active_groups = []
self.confirmed_sick_individuals = []
# this is for indexing the individuals
while (len(self.rawdata) > 0):
# initial groups have maximal size
# TODO: inefficient way of getting groups
self.get_next_group_from_data(maxGroupsize)
binomial_set = self.active_groups[0]
self.active_groups = self.active_groups[1:]
# size of current defective group
sobel_m = 0
# size of current other group
sobel_n = maxGroupsize
testgroup = [[], []]
defective_set = [[], []]
while (sobel_m != 0 or sobel_n != 0):
# TODO This was causing errors. Is it ok to break if both are empty (because there
# is nothing else to do), or is this a symptomatic error and the groups should never
# be empty !?
if len(binomial_set[0]) == 0 and len(defective_set[0]) == 0:
break
k = self.x[(sobel_m, sobel_n)]
(mSuccess,
nSuccess), (mFailure,
nFailure) = self.sobel_step(sobel_m, sobel_n)
if sobel_m == 0:
# H-situation
# take k individuals from binomial set into testgroup
testgroup = [binomial_set[0][:k], binomial_set[1][:k]]
binomial_set = [binomial_set[0][k:], binomial_set[1][k:]]
testresult = aux._make_test(
testgroup[1], self.success_rate_test,
self.false_posivite_rate_test, self.prob_sick,
self.tests_repetitions,
self.test_result_decision_strategy)
self.number_of_tests += self.tests_repetitions
self.number_groupwise_tests[int(
np.floor(testgroup[0][0] / self.maxGroupsize))] += 1
if testresult == 1:
# infected
if len(testgroup[0]) == 1:
# print("single infected index {} identified".format(testgroup[0][0]))
self.sick_individuals.append(testgroup[0][0])
testgroup = [[], []]
else:
defective_set = testgroup # TODO make a copy here!?
elif testresult == 0:
# clean
testgroup = [[], []]
if len(defective_set[0]) == 1:
# print("identified index {} by conlusion".format(defective_set[0][0]))
self.sick_individuals.append(defective_set[0][0])
defective_set = [[], []]
elif sobel_m > 0:
# G situation
# take k individuals from defective set into testgroup
testgroup = [defective_set[0][:k], defective_set[1][:k]]
defective_set = [
defective_set[0][k:], defective_set[1][k:]
]
testresult = aux._make_test(
testgroup[1], self.success_rate_test,
self.false_posivite_rate_test, self.prob_sick,
self.tests_repetitions,
self.test_result_decision_strategy)
self.number_of_tests += self.tests_repetitions
self.number_groupwise_tests[int(
np.floor(testgroup[0][0] / self.maxGroupsize))] += 1
if testresult == 1:
# pinfected
if len(testgroup[0]) == 1:
# print("single infected index {} identified".format(testgroup[0][0]))
self.sick_individuals.append(testgroup[0][0])
testgroup = [[], []]
binomial_set = [
binomial_set[0] + defective_set[0],
binomial_set[1] + defective_set[1]
]
defective_set = testgroup
elif testresult == 0:
# clean
testgroup = [[], []]
if len(defective_set[0]) == 1:
# print("identified index {} by conlusion".format(defective_set[0][0]))
self.sick_individuals.append(defective_set[0][0])
defective_set = [[], []]
if testresult == 1:
sobel_m = mFailure
sobel_n = nFailure
elif testresult == 0:
sobel_m = mSuccess
sobel_n = nSuccess
# simplified time measure, because individual time tracking is a bit complicated
self.total_time = self.number_of_tests * self.test_duration * self.tests_repetitions / self.num_simultaneous_tests
self.update_sick_lists_and_success_rate()
def RBS_time_step(self):
for i in range(
min(len(self.active_groups), self.num_simultaneous_tests)):
# remove empty lists
self.active_groups = [x for x in self.active_groups if any(x)]
if not any(self.active_groups):
# if self.active_groups is empty
return
testgroup = self.active_groups[0]
self.active_groups = self.active_groups[1:]
if len(testgroup[0]) == 1:
if not self.indicator:
self.number_of_tests += self.tests_repetitions
self.number_groupwise_tests[int(
np.floor(testgroup[0][0] / self.group_size))] += 1
if aux._make_test(testgroup[1], self.success_rate_test,
self.false_posivite_rate_test,
self.prob_sick, self.tests_repetitions,
self.test_result_decision_strategy) == 1:
self.sick_individuals.append(testgroup[0][0])
return
else:
self.sick_individuals.append(testgroup[0][0])
return
# else:
# fix for empty groups ?
elif len(testgroup[0]) != 0:
if not self.indicator:
testresult = aux._make_test(
testgroup[1], self.success_rate_test,
self.false_posivite_rate_test, self.prob_sick,
self.tests_repetitions,
self.test_result_decision_strategy)
self.number_of_tests += self.tests_repetitions
# TODO ACTIVATE
#self.number_groupwise_tests[int(np.floor(testgroup[0][0] / self.group_size))] += 1
else:
testresult = 1
if testresult == 1:
testgroup = aux._split_groups(testgroup)
# instantiate test results
result_test = [0, 0]
# split in left and right branch
for i in range(2):
result_test[i] += aux._make_test(
testgroup[i][1], self.success_rate_test,
self.false_posivite_rate_test, self.prob_sick,
self.tests_repetitions,
self.test_result_decision_strategy)
self.number_of_tests += self.tests_repetitions
# TODO ACTIVATE
#self.number_groupwise_tests[int(np.floor(testgroup[i][0][0] / self.group_size))] += 1
# Determine the outcome of the finding
if result_test[0] == 0 and result_test[1] == 1:
sick_ind, healthy_ind = self._RBS_DIG(testgroup[1])
# remove healthy individuals found by DIG from testgroup
for i in range(2):
for item in healthy_ind[i]:
testgroup[1][i].remove(item)
if sick_ind is not None:
# add found infected individual
self.sick_individuals += [sick_ind[0]]
# remove found sick individual from testgroup
testgroup[1][0].remove(sick_ind[0])
testgroup[1][1].remove(sick_ind[1])
# update active groups
self.active_groups += [testgroup[1]]
else:
# update active groups
self.active_groups += [testgroup[1]]
self.indicator = False
return
elif result_test[0] == 1 and result_test[1] == 0:
sick_ind, healthy_ind = self._RBS_DIG(testgroup[0])
# remove healthy individuals found by DIG from testgroup
for i in range(2):
for item in healthy_ind[i]:
testgroup[0][i].remove(item)
if sick_ind is not None:
# add found sick individual
self.sick_individuals += [sick_ind[0]]
# remove found sick individual from testgroup
testgroup[0][0].remove(sick_ind[0])
testgroup[0][1].remove(sick_ind[1])
# update active groups
self.active_groups += [testgroup[0]]
else:
# update active groups
self.active_groups += [testgroup[0]]
self.indicator = False
return
elif result_test[0] == 1 and result_test[1] == 1:
self.active_groups += testgroup
self.indicator = True
return
else:
return