def test_readPopulationAgeStructured_fails_missing_header():
with tempfile.NamedTemporaryFile(mode="w+", delete=False) as fp:
rows = ["S08000015,Female,12,2,3,5", "S08000015,Male,20,7,11,13"]
fp.write("\n".join(rows))
fp.flush()
with pytest.raises(ValueError):
loaders.readPopulationAgeStructured(fp.name)
def test_readPopulationAgeStructured_fails_inconsistent_data():
with tempfile.NamedTemporaryFile(mode="w+", delete=False) as fp:
rows = [
"Health_Board,Sex,Total_across_age,Young,Medium,Old",
"S08000015,Female,12,2,3,5",
"S08000015,Male,20,7,11,13",
]
fp.write("\n".join(rows))
fp.flush()
with pytest.raises(ValueError):
loaders.readPopulationAgeStructured(fp.name)
def test_readPopulationAgeStructured_bad_total(total):
df = pd.DataFrame([
{
"Health_Board": "S08000015",
"Sex": "Female",
"Age": "[17,70)",
"Total": total
},
])
with pytest.raises(ValueError):
loaders.readPopulationAgeStructured(df)
def test_readPopulationAgeStructured_single_row():
with tempfile.NamedTemporaryFile(mode="w+", delete=False) as fp:
rows = ["Health_Board,Sex,Total_across_age,Young,Medium,Old", "S08000015,Female,10,2,3,5"]
fp.write("\n".join(rows))
fp.flush()
population = loaders.readPopulationAgeStructured(fp.name)
assert population["S08000015"]["Female"] == {"y": 2, "m": 3, "o": 5, "All_Ages": 10}
assert population["S08000015"]["All_Sex"]["y"] == 2
assert population["S08000015"]["All_Sex"]["m"] == 3
assert population["S08000015"]["All_Sex"]["o"] == 5
assert population["S08000015"]["All_Sex"]["All_Ages"] == 10
def test_readPopulationAgeStructured_sums_all_ages():
with tempfile.NamedTemporaryFile(mode="w+", delete=False) as fp:
rows = [
"Health_Board,Sex,Total_across_age,Young,Medium,Old",
"S08000015,Female,10,2,3,5",
"S08000015,Male,31,7,11,13",
]
fp.write("\n".join(rows))
fp.flush()
population = loaders.readPopulationAgeStructured(fp.name)
assert population["S08000015"]["All_Sex"]["y"] == 2 + 7
assert population["S08000015"]["All_Sex"]["m"] == 3 + 11
assert population["S08000015"]["All_Sex"]["o"] == 5 + 13
assert population["S08000015"]["All_Sex"]["All_Ages"] == 10 + 31
def test_readPopulationAgeStructured_aggregate_ages():
df = pd.DataFrame([
{
"Health_Board": "S08000015",
"Sex": "Female",
"Age": "[17,70)",
"Total": 100
},
{
"Health_Board": "S08000015",
"Sex": "Male",
"Age": "[17,70)",
"Total": 100
},
])
population = loaders.readPopulationAgeStructured(df)
assert population == {"S08000015": {"[17,70)": 200}}
def test_basicSimulationInternalAgeStructure_invariants(
age_transitions,
demographics,
commute_moves,
compartment_names,
age_infection_matrix,
num_infected,
generic_infection,
seed,
):
age_to_trans = np.setUpParametersAges(
loaders.readParametersAgeStructured(age_transitions))
population = loaders.readPopulationAgeStructured(demographics)
graph = loaders.genGraphFromContactFile(commute_moves)
states = np.setupInternalPopulations(graph, compartment_names,
list(age_to_trans.keys()), population)
old_graph = copy.deepcopy(graph)
old_age_to_trans = copy.deepcopy(age_to_trans)
initial_population = sum(_count_people_per_region(
states[0])) + num_infected
np.basicSimulationInternalAgeStructure(
rand=random.Random(seed),
graph=graph,
numInfected=num_infected,
timeHorizon=50,
genericInfection=generic_infection,
ageInfectionMatrix=age_infection_matrix,
diseaseProgressionProbs=age_to_trans,
dictOfStates=states,
)
# population remains constant
assert all([
sum(_count_people_per_region(state)) == pytest.approx(
initial_population) for state in states.values()
])
# the graph is unchanged
assert nx.is_isomorphic(old_graph, graph)
# infection matrix is unchanged
assert age_to_trans == old_age_to_trans
def test_readPopulationAgeStructured(data_api):
population = loaders.readPopulationAgeStructured(
data_api.read_table("human/population"))
expected = {
"S08000015": {
"[0,17)": 65307,
"[17,70)": 245680,
"70+": 58683
},
"S08000016": {
"[0,17)": 20237,
"[17,70)": 75008,
"70+": 20025
},
"S08000017": {
"[0,17)": 24842,
"[17,70)": 96899,
"70+": 27049
},
"S08000019": {
"[0,17)": 55873,
"[17,70)": 209221,
"70+": 40976
},
"S08000020": {
"[0,17)": 105607,
"[17,70)": 404810,
"70+": 74133
},
"S08000022": {
"[0,17)": 55711,
"[17,70)": 214008,
"70+": 52081
},
"S08000024": {
"[0,17)": 159238,
"[17,70)": 635249,
"70+": 103283
},
"S08000025": {
"[0,17)": 3773,
"[17,70)": 14707,
"70+": 3710
},
"S08000026": {
"[0,17)": 4448,
"[17,70)": 15374,
"70+": 3168
},
"S08000028": {
"[0,17)": 4586,
"[17,70)": 17367,
"70+": 4877
},
"S08000029": {
"[0,17)": 68150,
"[17,70)": 250133,
"70+": 53627
},
"S08000030": {
"[0,17)": 71822,
"[17,70)": 280547,
"70+": 63711
},
"S08000031": {
"[0,17)": 208091,
"[17,70)": 829574,
"70+": 137315
},
"S08000032": {
"[0,17)": 125287,
"[17,70)": 450850,
"70+": 83063
},
}
assert population == expected
def test_readPopulationAgeStructured(demographics):
population = loaders.readPopulationAgeStructured(demographics)
expected = {
"S08000015": {
"Female": {"y": 31950, "m": 127574, "o": 32930, "All_Ages": 192454},
"Male": {"y": 33357, "m": 118106, "o": 25753, "All_Ages": 177216},
"All_Sex": {"y": 65307, "m": 245680, "o": 58683, "All_Ages": 369670},
},
"S08000016": {
"Female": {"y": 9957, "m": 38363, "o": 10961, "All_Ages": 59281},
"Male": {"y": 10280, "m": 36645, "o": 9064, "All_Ages": 55989},
"All_Sex": {"y": 20237, "m": 75008, "o": 20025, "All_Ages": 115270},
},
"S08000017": {
"Female": {"y": 12176, "m": 49559, "o": 14734, "All_Ages": 76469},
"Male": {"y": 12666, "m": 47340, "o": 12315, "All_Ages": 72321},
"All_Sex": {"y": 24842, "m": 96899, "o": 27049, "All_Ages": 148790},
},
"S08000019": {
"Female": {"y": 27102, "m": 106902, "o": 22899, "All_Ages": 156903},
"Male": {"y": 28771, "m": 102319, "o": 18077, "All_Ages": 149167},
"All_Sex": {"y": 55873, "m": 209221, "o": 40976, "All_Ages": 306070},
},
"S08000020": {
"Female": {"y": 51441, "m": 201015, "o": 41366, "All_Ages": 293822},
"Male": {"y": 54166, "m": 203795, "o": 32767, "All_Ages": 290728},
"All_Sex": {"y": 105607, "m": 404810, "o": 74133, "All_Ages": 584550},
},
"S08000022": {
"Female": {"y": 27187, "m": 107483, "o": 28823, "All_Ages": 163493},
"Male": {"y": 28524, "m": 106525, "o": 23258, "All_Ages": 158307},
"All_Sex": {"y": 55711, "m": 214008, "o": 52081, "All_Ages": 321800},
},
"S08000024": {
"Female": {"y": 77589, "m": 324258, "o": 58984, "All_Ages": 460831},
"Male": {"y": 81649, "m": 310991, "o": 44299, "All_Ages": 436939},
"All_Sex": {"y": 159238, "m": 635249, "o": 103283, "All_Ages": 897770},
},
"S08000025": {
"Female": {"y": 1847, "m": 7315, "o": 1989, "All_Ages": 11151},
"Male": {"y": 1926, "m": 7392, "o": 1721, "All_Ages": 11039},
"All_Sex": {"y": 3773, "m": 14707, "o": 3710, "All_Ages": 22190},
},
"S08000026": {
"Female": {"y": 2112, "m": 7493, "o": 1672, "All_Ages": 11277},
"Male": {"y": 2336, "m": 7881, "o": 1496, "All_Ages": 11713},
"All_Sex": {"y": 4448, "m": 15374, "o": 3168, "All_Ages": 22990},
},
"S08000028": {
"Female": {"y": 2204, "m": 8636, "o": 2743, "All_Ages": 13583},
"Male": {"y": 2382, "m": 8731, "o": 2134, "All_Ages": 13247},
"All_Sex": {"y": 4586, "m": 17367, "o": 4877, "All_Ages": 26830},
},
"S08000029": {
"Female": {"y": 33155, "m": 128255, "o": 29880, "All_Ages": 191290},
"Male": {"y": 34995, "m": 121878, "o": 23747, "All_Ages": 180620},
"All_Sex": {"y": 68150, "m": 250133, "o": 53627, "All_Ages": 371910},
},
"S08000030": {
"Female": {"y": 35016, "m": 142530, "o": 35848, "All_Ages": 213394},
"Male": {"y": 36806, "m": 138017, "o": 27863, "All_Ages": 202686},
"All_Sex": {"y": 71822, "m": 280547, "o": 63711, "All_Ages": 416080},
},
"S08000031": {
"Female": {"y": 101619, "m": 423135, "o": 80469, "All_Ages": 605223},
"Male": {"y": 106472, "m": 406439, "o": 56846, "All_Ages": 569757},
"All_Sex": {"y": 208091, "m": 829574, "o": 137315, "All_Ages": 1174980},
},
"S08000032": {
"Female": {"y": 61191, "m": 231416, "o": 47571, "All_Ages": 340178},
"Male": {"y": 64096, "m": 219434, "o": 35492, "All_Ages": 319022},
"All_Sex": {"y": 125287, "m": 450850, "o": 83063, "All_Ages": 659200},
},
}
assert population == expected
def test_readPopulationAgeStructured_no_rows():
with tempfile.NamedTemporaryFile(mode="w+", delete=False) as fp:
rows = ["Health_Board,Sex,Total_across_age,Young,Medium,Old"]
fp.write("\n".join(rows))
fp.flush()
assert loaders.readPopulationAgeStructured(fp.name) == {}
def test_readPopulationAgeStructured_invalid_file():
with pytest.raises(IOError):
loaders.readPopulationAgeStructured("")
def test_readPopulationAgeStructured_empty_file():
with tempfile.NamedTemporaryFile(mode="w+", delete=False) as fp:
with pytest.raises(ValueError):
assert loaders.readPopulationAgeStructured(fp.name) == {}
def createNetworkOfPopulation(
compartment_transition_table: pd.DataFrame,
population_table: pd.DataFrame,
commutes_table: pd.DataFrame,
mixing_matrix_table: pd.DataFrame,
infectious_states: pd.DataFrame,
infection_prob: pd.DataFrame,
initial_infections: pd.DataFrame,
trials: pd.DataFrame,
movement_multipliers_table: pd.DataFrame = None,
stochastic_mode: pd.DataFrame = None,
random_seed: pd.DataFrame = None) -> NetworkOfPopulation:
"""Create the network of the population, loading data from files.
:param compartment_transition_table: pd.Dataframe specifying the transition rates between infected compartments.
:param population_table: pd.Dataframe with the population size in each region by gender and age.
:param commutes_table: pd.Dataframe with the movements between regions.
:param mixing_matrix_table: pd.Dataframe with the age infection matrix.
:param movement_multipliers_table: pd.Dataframe with the movement multipliers. This may be None, in
which case no multipliers are applied to the movements.
:param infectious_states: States that are considered infectious
:param infection_prob: Probability that a given contact will result in an infection
:param initial_infections: Initial infections of the population at time 0
:param trials: Number of trials for the model
:param stochastic_mode: Use stochastic mode for the model
:param random_seed: Random number generator seed used for stochastic mode
:return: The constructed network
"""
infection_prob = loaders.readInfectionProbability(infection_prob)
infectious_states = loaders.readInfectiousStates(infectious_states)
initial_infections = loaders.readInitialInfections(initial_infections)
trials = loaders.readTrials(trials)
stochastic_mode = loaders.readStochasticMode(stochastic_mode)
random_seed = loaders.readRandomSeed(random_seed)
# diseases progression matrix
progression = loaders.readCompartmentRatesByAge(
compartment_transition_table)
# population census data
population = loaders.readPopulationAgeStructured(population_table)
# Check some requirements for this particular model to work with the progression matrix
all_states = set()
for states in progression.values():
assert SUSCEPTIBLE_STATE not in states, "progression from susceptible state is not allowed"
for state, nextStates in states.items():
for nextState in nextStates:
all_states.add(state)
all_states.add(nextState)
assert state == nextState or nextState != EXPOSED_STATE, \
"progression into exposed state is not allowed other than in self reference"
assert (set(infectious_states) - all_states) == set(), \
f"mismatched infectious states and states {infectious_states} {set(progression.keys())}"
# people movement's graph
graph = loaders.genGraphFromContactFile(commutes_table)
# movement multipliers (dampening or heightening)
if movement_multipliers_table is not None:
movementMultipliers = loaders.readMovementMultipliers(
movement_multipliers_table)
else:
movementMultipliers: Dict[int, loaders.Multiplier] = {}
# age-based infection matrix
mixingMatrix = loaders.MixingMatrix(mixing_matrix_table)
agesInInfectionMatrix = set(mixingMatrix)
for age in mixingMatrix:
assert agesInInfectionMatrix == set(
mixingMatrix[age]), "infection matrix columns/rows mismatch"
# Checks across datasets
assert agesInInfectionMatrix == set(
progression.keys()), "infection matrix and progression ages mismatch"
assert agesInInfectionMatrix == {age for region in population.values() for age in region}, \
"infection matrix and population ages mismatch"
assert set(graph.nodes()) == set(
population.keys()), "regions mismatch between graph and population"
state0: Dict[str, Dict[Tuple[str, str], float]] = {}
for node in list(graph.nodes()):
region = state0.setdefault(node, {})
for age, compartments in progression.items():
region[(age, SUSCEPTIBLE_STATE)] = population[node][age]
for compartment in compartments:
region[(age, compartment)] = 0
logger.info("Nodes: %s, Ages: %s, States: %s", len(state0),
agesInInfectionMatrix, all_states)
return NetworkOfPopulation(progression=progression,
graph=graph,
initialState=state0,
mixingMatrix=mixingMatrix,
movementMultipliers=movementMultipliers,
infectiousStates=infectious_states,
infectionProb=infection_prob,
initialInfections=initial_infections,
trials=trials,
stochastic=stochastic_mode,
randomState=np.random.default_rng(random_seed))
def createNetworkOfPopulation(
compartment_transition_table: pd.DataFrame,
population_table: pd.DataFrame,
commutes_table: pd.DataFrame,
mixing_matrix_table: pd.DataFrame,
infectious_states: pd.DataFrame,
infection_prob: pd.DataFrame,
initial_infections: pd.DataFrame,
trials: pd.DataFrame,
start_end_date: pd.DataFrame,
movement_multipliers_table: pd.DataFrame = None,
stochastic_mode: pd.DataFrame = None,
) -> Tuple[NetworkOfPopulation, List[standard_api.Issue]]:
"""Create the network of the population, loading data from files.
:param compartment_transition_table: pd.Dataframe specifying the transition rates between infected compartments.
:param population_table: pd.Dataframe with the population size in each region by gender and age.
:param commutes_table: pd.Dataframe with the movements between regions.
:param mixing_matrix_table: pd.Dataframe with the age infection matrix.
:param infectious_states: States that are considered infectious
:param infection_prob: Probability that a given contact will result in an infection
:param initial_infections: Initial infections of the population at time 0
:param trials: Number of trials for the model
:param start_end_date: Starting and ending dates of the model
:param movement_multipliers_table: pd.Dataframe with the movement multipliers. This may be None, in
which case no multipliers are applied to the movements.
:param stochastic_mode: Use stochastic mode for the model
:return: A tuple with the constructed network and a list of any issues found. Although it may look convenient,
storing this list inside of NetworkOfPopulation is not a good idea, as that may give the functions that
receive it the false impression they can just append new issues there
"""
issues: List[standard_api.Issue] = []
infection_prob = loaders.readInfectionProbability(infection_prob)
infectious_states = loaders.readInfectiousStates(infectious_states)
initial_infections = loaders.readInitialInfections(initial_infections)
trials = loaders.readTrials(trials)
start_date, end_date = loaders.readStartEndDate(start_end_date)
stochastic_mode = loaders.readStochasticMode(stochastic_mode)
# diseases progression matrix
progression = loaders.readCompartmentRatesByAge(
compartment_transition_table)
# population census data
population = loaders.readPopulationAgeStructured(population_table)
# Check some requirements for this particular model to work with the progression matrix
all_states = set()
for states in progression.values():
assert SUSCEPTIBLE_STATE not in states, "progression from susceptible state is not allowed"
for state, nextStates in states.items():
for nextState in nextStates:
all_states.add(state)
all_states.add(nextState)
assert state == nextState or nextState != EXPOSED_STATE, \
"progression into exposed state is not allowed other than in self reference"
assert (set(infectious_states) - all_states) == set(), \
f"mismatched infectious states and states {infectious_states} {all_states}"
# people movement's graph
graph = loaders.genGraphFromContactFile(commutes_table)
# movement multipliers (dampening or heightening)
if movement_multipliers_table is not None:
movementMultipliers = loaders.readMovementMultipliers(
movement_multipliers_table)
else:
movementMultipliers = {}
# age-based infection matrix
mixingMatrix = loaders.MixingMatrix(mixing_matrix_table)
agesInInfectionMatrix = set(mixingMatrix)
for age in mixingMatrix:
assert agesInInfectionMatrix == set(
mixingMatrix[age]), "infection matrix columns/rows mismatch"
# Checks across datasets
assert agesInInfectionMatrix == set(
progression.keys()), "infection matrix and progression ages mismatch"
assert agesInInfectionMatrix == {age for region in population.values() for age in region}, \
"infection matrix and population ages mismatch"
disconnected_nodes = set(population.keys()) - set(graph.nodes())
if disconnected_nodes:
log_issue(
logger,
f"These nodes have no contacts in the current network: {','.join(disconnected_nodes)}",
IssueSeverity.MEDIUM,
issues,
)
state0: Dict[str, Dict[Tuple[str, str], float]] = {}
for node in list(graph.nodes()):
region = state0.setdefault(node, {})
for age, compartments in progression.items():
if node not in population:
log_issue(
logger,
f"Node {node} is not in the population table, assuming population of 0 for all ages",
IssueSeverity.MEDIUM,
issues,
)
pop = 0.0
else:
pop = population[node][age]
region[(age, SUSCEPTIBLE_STATE)] = pop
for compartment in compartments:
region[(age, compartment)] = 0
logger.info("Nodes: %s, Ages: %s, States: %s", len(state0),
agesInInfectionMatrix, all_states)
nop = NetworkOfPopulation(
progression=progression,
graph=graph,
initialState=state0,
mixingMatrix=mixingMatrix,
movementMultipliers=movementMultipliers,
infectiousStates=infectious_states,
infectionProb=infection_prob,
initialInfections=initial_infections,
trials=trials,
startDate=start_date,
endDate=end_date,
stochastic=stochastic_mode,
)
return (nop, issues)
def test_basic_simulation(age_transitions, demographics, commute_moves,
compartment_names, age_infection_matrix):
age_to_trans = np.setUpParametersAges(
loaders.readParametersAgeStructured(age_transitions))
population = loaders.readPopulationAgeStructured(demographics)
graph = loaders.genGraphFromContactFile(commute_moves)
states = np.setupInternalPopulations(graph, compartment_names,
list(age_to_trans.keys()), population)
result = np.basicSimulationInternalAgeStructure(
rand=random.Random(1),
graph=graph,
numInfected=10,
timeHorizon=200,
genericInfection=0.1,
ageInfectionMatrix=age_infection_matrix,
diseaseProgressionProbs=age_to_trans,
dictOfStates=states,
)
expected = [
0,
4.27,
5.959639,
7.495598979703686,
9.31292448442533,
11.550960285080539,
14.32076069530553,
17.750346856443436,
21.996595859880493,
27.253215606191763,
33.75958029276324,
41.81147883471944,
51.77434261313086,
64.09953959129047,
79.34443722167374,
98.19708895391234,
121.5065842268399,
150.32032333168627,
185.92974139403356,
229.92631464707316,
284.27004075722795,
351.3729944719362,
434.2010173334121,
536.3970957055917,
662.4304939975676,
817.7762023518806,
1009.1296689642635,
1244.6620222362512,
1534.3209088397605,
1890.1814875375615,
2326.8507704591293,
2861.926080186407,
3516.5045468063877,
4315.734994514654,
5289.3961276280115,
6472.475902589639,
7905.717433786824,
9636.08906655341,
11717.13446074682,
14209.16871256282,
17179.315999723975,
20701.439040274323,
24856.09052908778,
29730.707243910434,
35420.33217223618,
42029.128554931965,
49672.773024855385,
58481.44396269627,
68602.60309097261,
80202.27853153124,
93463.37789059673,
108579.96624726593,
125747.53880875603,
145150.90161910592,
166952.82966413427,
191287.47020551964,
218261.74745540041,
247965.3261465324,
280485.2367071461,
315916.38015373435,
354356.14564567205,
395872.69490304653,
440443.1364258809,
487868.5388265991,
537684.1860953799,
589091.5046792259,
640938.9095905811,
691769.9762481726,
739939.1843065555,
783772.9904113912,
821736.8679191938,
852567.1996643285,
875343.2246963251,
889499.9704796937,
894803.485637448,
891314.7525319818,
879359.4394061461,
859505.977536541,
832543.5198251844,
799448.8236543302,
761336.2708291251,
719393.6436135583,
674812.7866198674,
628726.0228195366,
582156.5631853839,
535986.5646189475,
490942.3244969345,
447593.5332414354,
406362.5717409869,
367540.01510870096,
331303.2145504978,
297735.6728639047,
266845.6949524783,
238583.40447859198,
212855.66475276518,
189538.74944848128,
168488.80761225612,
149550.28647197766,
132562.53827530914,
117364.86191178164,
103800.22980549172,
91717.93520231653,
80975.37134265121,
71439.12677319416,
62985.553271939556,
55500.93643588842,
48881.374979513224,
43032.45371205615,
37868.777124977256,
33313.415413891256,
29297.302334462536,
25758.61423633403,
22642.151601387908,
19898.738109895345,
17484.64737342592,
15361.063743396788,
13493.580801682876,
11851.739073032668,
10408.603009095552,
9140.37625068078,
8026.053473547509,
7047.106679898116,
6187.203546762776,
5431.955332005772,
4768.691828813375,
4186.260919647075,
3674.8503875840925,
3225.8297793633656,
2831.6102674926847,
2485.5206191429197,
2181.697540636489,
1914.9888235502897,
1680.8678687529227,
1475.3583061787265,
1294.9675597411838,
1136.6283280441162,
997.6470624276589,
875.6586246476982,
768.5863975872606,
674.6072044116167,
592.1204651473781,
519.721085459352,
456.1756310875024,
400.40139364220994,
351.44799986096695,
308.4812575877343,
270.76896818966605,
237.66846737351318,
208.61568486118352,
183.11553854396615,
160.73350093111426,
141.08819527652577,
123.8448960080496,
108.70982326635439,
95.42513472402354,
83.76452961376395,
73.52939023666997,
64.54539531517312,
56.65954754922215,
49.73756475976603,
43.66159017682611,
38.328182852791116,
33.64655394541582,
29.537018798984292,
25.929638426375362,
22.763027221103627,
19.98330656117008,
17.54318645356159,
15.401159551545785,
13.520793793496033,
11.870111594347737,
10.42104499749586,
9.148957491085977,
8.032224330272163,
7.051864205475331,
6.191215972979529,
5.435654933281273,
4.7723438175693484,
4.1900142350687,
3.678774853837169,
3.2299430438278187,
2.835897111408885,
2.4899466059017845,
2.186218487054244,
1.9195572129748524,
1.6854370455381997,
1.4798850786813753,
1.29941367791204,
1.1409611798590402,
1.001839841559402,
0.8796901527963475,
0.772440733292397,
0.6782731317724259,
0.5955909274692558,
0.5229926079757407,
0.45924776170425224,
0.40327617969564616,
0.35412951108933594,
0.3109751600700831,
0.2730821502880063,
]
assert result == pytest.approx(expected)