def test_FF_with_NAN():
'''
Test if ff.analyze raise a ValueError when nan are passed in the Y values
'''
problem, model_results, param_values = setup_samples()
# Should raise a ValueError type of error
with pytest.raises(ValueError):
ff.analyze(problem, param_values, model_results)
def test_ff_to_df():
params = ['x1', 'x2', 'x3']
main_index = params + ['dummy_0']
problem = {
'num_vars':
3,
'names':
params,
'groups':
None,
'bounds': [[-3.14159265359, 3.14159265359],
[-3.14159265359, 3.14159265359],
[-3.14159265359, 3.14159265359]]
}
X = ff_sample.sample(problem)
Y = X[:, 0] + (0.1 * X[:, 1]) + ((1.2 * X[:, 2]) * (0.2 + X[:, 0]))
Si = ff.analyze(problem, X, Y, second_order=True, print_to_console=False)
main_effect, inter_effect = Si.to_df()
assert isinstance(main_effect, pd.DataFrame), \
"FF ME: Expected DataFrame, got {}".format(type(main_effect))
assert isinstance(main_effect, pd.DataFrame), \
"FF IE: Expected DataFrame, got {}".format(type(inter_effect))
assert set(main_effect.index) == set(main_index), \
"Incorrect index in Main Effect DataFrame"
inter_index = set([('x1', 'x2'), ('x1', 'x3'), ('x2', 'x3'),
('x1', 'dummy_0'), ('x2', 'dummy_0'),
('x3', 'dummy_0')])
assert set(inter_effect.index) == inter_index, \
"Incorrect index in Interaction Effect DataFrame"
def test_ff_to_df():
params = ['x1', 'x2', 'x3']
main_index = params + ['dummy_0']
problem = {
'num_vars': 3,
'names': params,
'groups': None,
'bounds': [[-3.14159265359, 3.14159265359],
[-3.14159265359, 3.14159265359],
[-3.14159265359, 3.14159265359]]
}
X = ff_sample.sample(problem)
Y = X[:, 0] + (0.1 * X[:, 1]) + ((1.2 * X[:, 2]) * (0.2 + X[:, 0]))
Si = ff.analyze(problem, X, Y, second_order=True, print_to_console=False)
main_effect, inter_effect = Si.to_df()
assert isinstance(main_effect, pd.DataFrame), \
"FF ME: Expected DataFrame, got {}".format(type(main_effect))
assert isinstance(main_effect, pd.DataFrame), \
"FF IE: Expected DataFrame, got {}".format(type(inter_effect))
assert set(main_effect.index) == set(main_index), \
"Incorrect index in Main Effect DataFrame"
inter_index = set([('x1', 'x2'),
('x1', 'x3'),
('x2', 'x3'),
('x1', 'dummy_0'),
('x2', 'dummy_0'),
('x3', 'dummy_0')])
assert set(inter_effect.index) == inter_index, \
"Incorrect index in Interaction Effect DataFrame"
def test_interactions_from_saltelli():
'''
'''
problem = {
'bounds': np.repeat([-1, 1], 12).reshape(2, 12).T,
'num_vars': 12,
'names': ["x" + str(x + 1) for x in range(12)]
}
X = sample(problem)
Y = np.array([
10, -2, 4, -8, 2, 6, -4, 0, 2, 6, -4, 0, 10, -2, 4, -8, -2, -6, 4, 0,
-10, 2, -4, 8, -10, 2, -4, 8, -2, -6, 4, 0
])
Si = analyze(problem, X, Y, second_order=True)
actual = Si['IE']
expected = [
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 4.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0
]
assert_equal(actual, expected)
def test_ff_example():
'''
'''
problem = {
'bounds': np.repeat([-1, 1], 12).reshape(2, 12).T,
'num_vars': 12,
'names': ["x" + str(x + 1) for x in range(12)]
}
X = sample(problem)
Y = X[:, 0] + 2 * X[:, 1] + 3 * X[:, 2] + 4 * X[:, 6] * X[:, 11]
expected = np.array([
10, -2, 4, -8, 2, 6, -4, 0, 2, 6, -4, 0, 10, -2, 4, -8, -2, -6, 4, 0,
-10, 2, -4, 8, -10, 2, -4, 8, -2, -6, 4, 0
])
assert_equal(Y, expected)
Si = analyze(problem, X, Y)
expected = np.array([1, 2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
dtype=np.float)
assert_equal(expected, Si['ME'])
def analyze_ff(self):
# Fractional Factorial
return ff.analyze(self.sa_problem,
self.samples_x,
self.samples_y,
second_order=True,
print_to_console=self.options["print_to_console"])
def _analizar(símismo, vec_res, muestra, ops):
if símismo.método == 'sobol':
return sobol.analyze(problem=símismo.problema, Y=vec_res, **ops)
elif símismo.método == 'fast':
return fast.analyze(problem=símismo.problema, Y=vec_res, **ops)
elif símismo.método == 'morris':
return morris_anlz.analyze(problem=símismo.problema, X=muestra, Y=vec_res, **ops)
elif símismo.método == 'dmim':
return delta.analyze(problem=símismo.problema, X=muestra, Y=vec_res, **ops)
elif símismo.método == 'dgsm':
return dgsm.analyze(problem=símismo.problema, X=muestra, Y=vec_res, **ops)
elif símismo.método == 'ff':
return ff_anlz.analyze(problem=símismo.problema, X=muestra, Y=vec_res, **ops)
else:
raise ValueError('Método de análisis de sensibilidad "{}" no reconocido.'.format(símismo.método))
def test_ff_analyze():
'''
'''
problem = {
'bounds': [[0., 2.5], [0., 1.], [0., 1.], [0., 1.]],
'num_vars': 4,
'names': ['x1', 'x2', 'x3', 'x4']
}
X = np.array([[1, 1, 1, 1], [1, 0, 1, 0], [1, 1, 0, 0], [1, 0, 0, 1],
[0, 0, 0, 0], [0, 1, 0, 1], [0, 0, 1, 1], [0, 1, 1, 0]],
dtype=np.float)
Y = np.array([1.5, 1, 1.5, 1, 2, 2.5, 2, 2.5], dtype=np.float)
actual = analyze(problem, X, Y)
expected = {
'ME': np.array([-0.5, 0.25, 0., 0.]),
'names': ['x1', 'x2', 'x3', 'x4']
}
assert_equal(actual, expected)
def sa(model, response, policy={}, method="sobol", nsamples=1000, **kwargs):
if len(model.uncertainties) == 0:
raise ValueError("no uncertainties defined in model")
problem = {
'num_vars': len(model.uncertainties),
'names': model.uncertainties.keys(),
'bounds': [[0.0, 1.0] for u in model.uncertainties],
'groups': kwargs.get("groups", None)
}
# estimate the argument N passed to the sampler that produces the requested
# number of samples
N = _predict_N(method, nsamples, problem["num_vars"], kwargs)
# generate the samples
if method == "sobol":
samples = saltelli.sample(problem, N,
**_cleanup_kwargs(saltelli.sample, kwargs))
elif method == "morris":
samples = morris_sampler.sample(
problem, N, **_cleanup_kwargs(morris_sampler.sample, kwargs))
elif method == "fast":
samples = fast_sampler.sample(
problem, N, **_cleanup_kwargs(fast_sampler.sample, kwargs))
elif method == "ff":
samples = ff_sampler.sample(
problem, **_cleanup_kwargs(ff_sampler.sample, kwargs))
elif method == "dgsm":
samples = finite_diff.sample(
problem, N, **_cleanup_kwargs(finite_diff.sample, kwargs))
elif method == "delta":
if "samples" in kwargs:
samples = kwargs["samples"]
else:
samples = latin.sample(problem, N,
**_cleanup_kwargs(latin.sample, kwargs))
# convert from samples in [0, 1] to uncertainty domain
for i, u in enumerate(model.uncertainties):
samples[:, i] = u.ppf(samples[:, i])
# run the model and collect the responses
responses = np.empty(samples.shape[0])
for i in range(samples.shape[0]):
sample = {k: v for k, v in zip(model.uncertainties.keys(), samples[i])}
responses[i] = evaluate(model, overwrite(sample, policy))[response]
# run the sensitivity analysis method
if method == "sobol":
result = sobol.analyze(problem, responses,
**_cleanup_kwargs(sobol.analyze, kwargs))
elif method == "morris":
result = morris_analyzer.analyze(
problem, samples, responses,
**_cleanup_kwargs(morris_analyzer.analyze, kwargs))
elif method == "fast":
result = fast.analyze(problem, responses,
**_cleanup_kwargs(fast.analyze, kwargs))
elif method == "ff":
result = ff_analyzer.analyze(
problem, samples, responses,
**_cleanup_kwargs(ff_analyzer.analyze, kwargs))
elif method == "dgsm":
result = dgsm.analyze(problem, samples, responses,
**_cleanup_kwargs(dgsm.analyze, kwargs))
elif method == "delta":
result = delta.analyze(problem, samples, responses,
**_cleanup_kwargs(delta.analyze, kwargs))
# convert the SALib results into a form allowing pretty printing and
# lookups using the parameter name
pretty_result = SAResult(
list(result["names"] if "names" in result else problem["names"]))
if "S1" in result:
pretty_result["S1"] = {
k: float(v)
for k, v in zip(problem["names"], result["S1"])
}
if "S1_conf" in result:
pretty_result["S1_conf"] = {
k: float(v)
for k, v in zip(problem["names"], result["S1_conf"])
}
if "ST" in result:
pretty_result["ST"] = {
k: float(v)
for k, v in zip(problem["names"], result["ST"])
}
if "ST_conf" in result:
pretty_result["ST_conf"] = {
k: float(v)
for k, v in zip(problem["names"], result["ST_conf"])
}
if "S2" in result:
pretty_result["S2"] = _S2_to_dict(result["S2"], problem)
if "S2_conf" in result:
pretty_result["S2_conf"] = _S2_to_dict(result["S2_conf"], problem)
if "delta" in result:
pretty_result["delta"] = {
k: float(v)
for k, v in zip(problem["names"], result["delta"])
}
if "delta_conf" in result:
pretty_result["delta_conf"] = {
k: float(v)
for k, v in zip(problem["names"], result["delta_conf"])
}
if "vi" in result:
pretty_result["vi"] = {
k: float(v)
for k, v in zip(problem["names"], result["vi"])
}
if "vi_std" in result:
pretty_result["vi_std"] = {
k: float(v)
for k, v in zip(problem["names"], result["vi_std"])
}
if "dgsm" in result:
pretty_result["dgsm"] = {
k: float(v)
for k, v in zip(problem["names"], result["dgsm"])
}
if "dgsm_conf" in result:
pretty_result["dgsm_conf"] = {
k: float(v)
for k, v in zip(problem["names"], result["dgsm_conf"])
}
if "mu" in result:
pretty_result["mu"] = {
k: float(v)
for k, v in zip(result["names"], result["mu"])
}
if "mu_star" in result:
pretty_result["mu_star"] = {
k: float(v)
for k, v in zip(result["names"], result["mu_star"])
}
if "mu_star_conf" in result:
pretty_result["mu_star_conf"] = {
k: float(v)
for k, v in zip(result["names"], result["mu_star_conf"])
}
if "sigma" in result:
pretty_result["sigma"] = {
k: float(v)
for k, v in zip(result["names"], result["sigma"])
}
return pretty_result
def sa(model, response, policy={}, method="sobol", nsamples=1000, **kwargs):
if len(model.uncertainties) == 0:
raise ValueError("no uncertainties defined in model")
problem = { 'num_vars' : len(model.uncertainties),
'names' : model.uncertainties.keys(),
'bounds' : [[0.0, 1.0] for u in model.uncertainties],
'groups' : kwargs.get("groups", None) }
# estimate the argument N passed to the sampler that produces the requested
# number of samples
N = _predict_N(method, nsamples, problem["num_vars"], kwargs)
# generate the samples
if method == "sobol":
samples = saltelli.sample(problem, N, **_cleanup_kwargs(saltelli.sample, kwargs))
elif method == "morris":
samples = morris_sampler.sample(problem, N, **_cleanup_kwargs(morris_sampler.sample, kwargs))
elif method == "fast":
samples = fast_sampler.sample(problem, N, **_cleanup_kwargs(fast_sampler.sample, kwargs))
elif method == "ff":
samples = ff_sampler.sample(problem, **_cleanup_kwargs(ff_sampler.sample, kwargs))
elif method == "dgsm":
samples = finite_diff.sample(problem, N, **_cleanup_kwargs(finite_diff.sample, kwargs))
elif method == "delta":
if "samples" in kwargs:
samples = kwargs["samples"]
else:
samples = latin.sample(problem, N, **_cleanup_kwargs(latin.sample, kwargs))
# convert from samples in [0, 1] to uncertainty domain
for i, u in enumerate(model.uncertainties):
samples[:,i] = u.ppf(samples[:,i])
# run the model and collect the responses
responses = np.empty(samples.shape[0])
for i in range(samples.shape[0]):
sample = {k : v for k, v in zip(model.uncertainties.keys(), samples[i])}
responses[i] = evaluate(model, overwrite(sample, policy))[response]
# run the sensitivity analysis method
if method == "sobol":
result = sobol.analyze(problem, responses, **_cleanup_kwargs(sobol.analyze, kwargs))
elif method == "morris":
result = morris_analyzer.analyze(problem, samples, responses, **_cleanup_kwargs(morris_analyzer.analyze, kwargs))
elif method == "fast":
result = fast.analyze(problem, responses, **_cleanup_kwargs(fast.analyze, kwargs))
elif method == "ff":
result = ff_analyzer.analyze(problem, samples, responses, **_cleanup_kwargs(ff_analyzer.analyze, kwargs))
elif method == "dgsm":
result = dgsm.analyze(problem, samples, responses, **_cleanup_kwargs(dgsm.analyze, kwargs))
elif method == "delta":
result = delta.analyze(problem, samples, responses, **_cleanup_kwargs(delta.analyze, kwargs))
# convert the SALib results into a form allowing pretty printing and
# lookups using the parameter name
pretty_result = SAResult(result["names"] if "names" in result else problem["names"])
if "S1" in result:
pretty_result["S1"] = {k : float(v) for k, v in zip(problem["names"], result["S1"])}
if "S1_conf" in result:
pretty_result["S1_conf"] = {k : float(v) for k, v in zip(problem["names"], result["S1_conf"])}
if "ST" in result:
pretty_result["ST"] = {k : float(v) for k, v in zip(problem["names"], result["ST"])}
if "ST_conf" in result:
pretty_result["ST_conf"] = {k : float(v) for k, v in zip(problem["names"], result["ST_conf"])}
if "S2" in result:
pretty_result["S2"] = _S2_to_dict(result["S2"], problem)
if "S2_conf" in result:
pretty_result["S2_conf"] = _S2_to_dict(result["S2_conf"], problem)
if "delta" in result:
pretty_result["delta"] = {k : float(v) for k, v in zip(problem["names"], result["delta"])}
if "delta_conf" in result:
pretty_result["delta_conf"] = {k : float(v) for k, v in zip(problem["names"], result["delta_conf"])}
if "vi" in result:
pretty_result["vi"] = {k : float(v) for k, v in zip(problem["names"], result["vi"])}
if "vi_std" in result:
pretty_result["vi_std"] = {k : float(v) for k, v in zip(problem["names"], result["vi_std"])}
if "dgsm" in result:
pretty_result["dgsm"] = {k : float(v) for k, v in zip(problem["names"], result["dgsm"])}
if "dgsm_conf" in result:
pretty_result["dgsm_conf"] = {k : float(v) for k, v in zip(problem["names"], result["dgsm_conf"])}
if "mu" in result:
pretty_result["mu"] = {k : float(v) for k, v in zip(result["names"], result["mu"])}
if "mu_star" in result:
pretty_result["mu_star"] = {k : float(v) for k, v in zip(result["names"], result["mu_star"])}
if "mu_star_conf" in result:
pretty_result["mu_star_conf"] = {k : float(v) for k, v in zip(result["names"], result["mu_star_conf"])}
if "sigma" in result:
pretty_result["sigma"] = {k : float(v) for k, v in zip(result["names"], result["sigma"])}
return pretty_result
from SALib.sample.ff import sample
from SALib.test_functions import Ishigami
from SALib.util import read_param_file
sys.path.append('../..')
# Read the parameter range file and generate samples
problem = read_param_file('../../SALib/test_functions/params/Ishigami.txt')
# or define manually without a parameter file:
# problem = {
# 'num_vars': 3,
# 'names': ['x1', 'x2', 'x3'],
# 'groups': None,
# 'bounds': [[-3.14159265359, 3.14159265359],
# [-3.14159265359, 3.14159265359],
# [-3.14159265359, 3.14159265359]]
# }
# Generate samples
X = sample(problem)
# Run the "model" -- this will happen offline for external models
Y = X[:, 0] + (0.1 * X[:, 1]) + ((1.2 * X[:, 2]) * (0.2 + X[:, 0]))
# Perform the sensitivity analysis using the model output
# Specify which column of the output file to analyze (zero-indexed)
analyze(problem, X, Y, second_order=True, print_to_console=True)
# Returns a dictionary with keys 'ME' (main effect) and 'IE' (interaction effect)
# The techniques bulks out the number of parameters with dummy parameters to the
# nearest 2**n. Any results involving dummy parameters should be treated with
# a sceptical eye.
from SALib.analyze.ff import analyze
from SALib.sample.ff import sample
from SALib.util import read_param_file
sys.path.append('../..')
# Read the parameter range file and generate samples
problem = read_param_file('../../src/SALib/test_functions/params/Ishigami.txt')
# or define manually without a parameter file:
# problem = {
# 'num_vars': 3,
# 'names': ['x1', 'x2', 'x3'],
# 'groups': None,
# 'bounds': [[-3.14159265359, 3.14159265359],
# [-3.14159265359, 3.14159265359],
# [-3.14159265359, 3.14159265359]]
# }
# Generate samples
X = sample(problem)
# Run the "model" -- this will happen offline for external models
Y = X[:, 0] + (0.1 * X[:, 1]) + ((1.2 * X[:, 2]) * (0.2 + X[:, 0]))
# Perform the sensitivity analysis using the model output
analyze(problem, X, Y, second_order=True, print_to_console=True)
# Returns a dictionary with keys 'ME' (main effect) and 'IE' (interaction effect)
# The techniques bulks out the number of parameters with dummy parameters to the
# nearest 2**n. Any results involving dummy parameters should be treated with
# a sceptical eye.
def run(self,
input_ids=None,
output_ids=None,
method=None,
calc_second_order=None,
conf_level=None,
**kwargs):
self._update_parameters(method, calc_second_order, conf_level)
self.other_parameters = kwargs
if input_ids is None:
input_ids = range(self.n_inputs)
self.problem = {
"num_vars": len(input_ids),
"names": np.array(self.input_names)[input_ids].tolist(),
"bounds": np.array(self.input_bounds)[input_ids].tolist()
}
if output_ids is None:
output_ids = range(self.n_outputs)
n_outputs = len(output_ids)
if self.method.lower() == "sobol":
self.logger.warning(
"'sobol' method requires 'saltelli' sampling scheme!")
# Additional keyword parameters and their defaults:
# calc_second_order (bool): Calculate second-order sensitivities (default True)
# num_resamples (int): The number of resamples used to compute the confidence intervals (default 1000)
# conf_level (float): The confidence interval level (default 0.95)
# print_to_console (bool): Print results directly to console (default False)
# parallel: False,
# n_processors: None
self.analyzer = lambda output: sobol.analyze(
self.problem,
output,
calc_second_order=self.calc_second_order,
conf_level=self.conf_level,
num_resamples=self.other_parameters.get("num_resamples", 1000),
parallel=self.other_parameters.get("parallel", False),
n_processors=self.other_parameters.get("n_processors", None),
print_to_console=self.other_parameters.get(
"print_to_console", False))
elif np.in1d(self.method.lower(), ["latin", "delta"]):
self.logger.warning(
"'latin' sampling scheme is recommended for 'delta' method!")
# Additional keyword parameters and their defaults:
# num_resamples (int): The number of resamples used to compute the confidence intervals (default 1000)
# conf_level (float): The confidence interval level (default 0.95)
# print_to_console (bool): Print results directly to console (default False)
self.analyzer = lambda output: delta.analyze(
self.problem,
self.input_samples[:, input_ids],
output,
conf_level=self.conf_level,
num_resamples=self.other_parameters.get("num_resamples", 1000),
print_to_console=self.other_parameters.get(
"print_to_console", False))
elif np.in1d(self.method.lower(), ["fast", "fast_sampler"]):
self.logger.warning(
"'fast' method requires 'fast_sampler' sampling scheme!")
# Additional keyword parameters and their defaults:
# M (int): The interference parameter,
# i.e., the number of harmonics to sum in the Fourier series decomposition (default 4)
# print_to_console (bool): Print results directly to console (default False)
self.analyzer = lambda output: fast.analyze(
self.problem,
output,
M=self.other_parameters.get("M", 4),
print_to_console=self.other_parameters.get(
"print_to_console", False))
elif np.in1d(self.method.lower(), ["ff", "fractional_factorial"]):
# Additional keyword parameters and their defaults:
# second_order (bool, default=False): Include interaction effects
# print_to_console (bool, default=False): Print results directly to console
self.logger.warning(
"'fractional_factorial' method requires 'fractional_factorial' sampling scheme!"
)
self.analyzer = lambda output: ff.analyze(
self.problem,
self.input_samples[:, input_ids],
output,
calc_second_order=self.calc_second_order,
conf_level=self.conf_level,
num_resamples=self.other_parameters.get("num_resamples", 1000),
print_to_console=self.other_parameters.get(
"print_to_console", False))
elif self.method.lower().lower() == "morris":
self.logger.warning(
"'morris' method requires 'morris' sampling scheme!")
# Additional keyword parameters and their defaults:
# num_resamples (int): The number of resamples used to compute the confidence intervals (default 1000)
# conf_level (float): The confidence interval level (default 0.95)
# print_to_console (bool): Print results directly to console (default False)
# grid_jump (int): The grid jump size, must be identical to the value passed to
# SALib.sample.morris.sample() (default 2)
# num_levels (int): The number of grid levels, must be identical to the value passed to
# SALib.sample.morris (default 4)
self.analyzer = lambda output: morris.analyze(
self.problem,
self.input_samples[:, input_ids],
output,
conf_level=self.conf_level,
grid_jump=self.other_parameters.get("grid_jump", 2),
num_levels=self.other_parameters.get("num_levels", 4),
num_resamples=self.other_parameters.get("num_resamples", 1000),
print_to_console=self.other_parameters.get(
"print_to_console", False))
elif self.method.lower() == "dgsm":
# num_resamples (int): The number of resamples used to compute the confidence intervals (default 1000)
# conf_level (float): The confidence interval level (default 0.95)
# print_to_console (bool): Print results directly to console (default False)
self.analyzer = lambda output: dgsm.analyze(
self.problem,
self.input_samples[:, input_ids],
output,
conf_level=self.conf_level,
num_resamples=self.other_parameters.get("num_resamples", 1000),
print_to_console=self.other_parameters.get(
"print_to_console", False))
else:
raise_value_error("Method " + str(self.method) +
" is not one of the available methods " +
str(METHODS) + " !")
output_names = []
results = []
for io in output_ids:
output_names.append(self.output_names[io])
results.append(self.analyzer(self.output_values[:, io]))
# TODO: Adjust list_of_dicts_to_dicts_of_ndarrays to handle ndarray concatenation
results = list_of_dicts_to_dicts_of_ndarrays(results)
results.update({"output_names": output_names})
return results
