#!/usr/bin/env python
# coding=utf8
import numpy as np
from scipy.signal import periodogram
from scipy.stats import norm
from . import common_args
from ..util import read_param_file, ResultDict
[docs]def analyze(problem, X, Y, M=10, num_resamples=100, conf_level=0.95, print_to_console=False, seed=None):
"""Performs the Random Balanced Design - Fourier Amplitude Sensitivity Test
(RBD-FAST) on model outputs.
Returns a dictionary with keys 'S1', where each entry is a list of
size D (the number of parameters) containing the indices in the same order
as the parameter file.
Compatible with
---------------
* all samplers
Parameters
----------
problem : dict
The problem definition
X : numpy.array
A NumPy array containing the model inputs
Y : numpy.array
A NumPy array containing the model outputs
M : int
The interference parameter, i.e., the number of harmonics to sum in
the Fourier series decomposition (default 10)
print_to_console : bool
Print results directly to console (default False)
References
----------
.. [1] S. Tarantola, D. Gatelli and T. Mara (2006) "Random Balance Designs
for the Estimation of First Order Global Sensitivity Indices",
Reliability Engineering and System Safety, 91:6, 717-727
.. [2] Elmar Plischke (2010) "An effective algorithm for computing global
sensitivity indices (EASI) Reliability Engineering & System Safety",
95:4, 354-360. doi:10.1016/j.ress.2009.11.005
.. [3] Jean-Yves Tissot, Clémentine Prieur (2012) "Bias correction for the
estimation of sensitivity indices based on random balance designs.",
Reliability Engineering and System Safety, Elsevier, 107, 205-213.
doi:10.1016/j.ress.2012.06.010
.. [4] Jeanne Goffart, Mickael Rabouille & Nathan Mendes (2015)
"Uncertainty and sensitivity analysis applied to hygrothermal
simulation of a brick building in a hot and humid climate",
Journal of Building Performance Simulation.
doi:10.1080/19401493.2015.1112430
Examples
--------
>>> X = latin.sample(problem, 1000)
>>> Y = Ishigami.evaluate(X)
>>> Si = rbd_fast.analyze(problem, X, Y, print_to_console=False)
"""
if seed:
np.random.seed(seed)
D = problem['num_vars']
N = Y.size
# Calculate and Output the First Order Value
Si = ResultDict((k, [None] * D) for k in ['S1', 'S1_conf'])
Si['names'] = problem['names']
for i in range(D):
S1 = compute_first_order(permute_outputs(X[:, i], Y), M)
S1 = unskew_S1(S1, M, N)
Si['S1'][i] = S1
Si['S1_conf'][i] = bootstrap(X[:, i], Y, M, num_resamples, conf_level)
if print_to_console:
print(Si.to_df())
return Si
[docs]def permute_outputs(X, Y):
"""
Permute the output according to one of the inputs as in [_2]
References
----------
.. [2] Elmar Plischke (2010) "An effective algorithm for computing global
sensitivity indices (EASI) Reliability Engineering & System Safety",
95:4, 354-360. doi:10.1016/j.ress.2009.11.005
"""
permutation_index = np.argsort(X)
permutation_index = np.concatenate([permutation_index[::2],
permutation_index[1::2][::-1]])
return Y[permutation_index]
[docs]def compute_first_order(permuted_outputs, M):
_, Pxx = periodogram(permuted_outputs)
V = np.sum(Pxx[1:])
D1 = np.sum(Pxx[1: M + 1])
return D1 / V
[docs]def unskew_S1(S1, M, N):
"""
Unskew the sensivity indice
(Jean-Yves Tissot, Clémentine Prieur (2012) "Bias correction for the
estimation of sensitivity indices based on random balance designs.",
Reliability Engineering and System Safety, Elsevier, 107, 205-213.
doi:10.1016/j.ress.2012.06.010)
"""
lamb = (2 * M) / N
return S1 - lamb / (1 - lamb) * (1 - S1)
[docs]def bootstrap(X_d, Y, M, resamples, conf_level):
# Use half of available data each time
T_data = X_d.shape[0]
n_size = int(T_data * 0.5)
res = np.zeros(resamples)
for i in range(resamples):
sample_idx = np.random.choice(T_data, replace=True, size=n_size)
X_rs, Y_rs = X_d[sample_idx], Y[sample_idx]
S1 = compute_first_order(permute_outputs(X_rs, Y_rs), M)
S1 = unskew_S1(S1, M, Y_rs.size)
res[i] = S1
return norm.ppf(0.5 + conf_level / 2.0) * res.std(ddof=1)
[docs]def cli_parse(parser):
parser.add_argument('-X', '--model-input-file',
type=str, required=True, help='Model input file')
parser.add_argument('-M', '--M', type=int, required=False,
default=10,
help='Inference parameter')
parser.add_argument('-r', '--resamples', type=int, required=False,
default=100,
help='Number of bootstrap resamples for Sobol '
'confidence intervals')
return parser
[docs]def cli_action(args):
problem = read_param_file(args.paramfile)
X = np.loadtxt(args.model_input_file,
delimiter=args.delimiter)
Y = np.loadtxt(args.model_output_file,
delimiter=args.delimiter,
usecols=(args.column,))
analyze(problem, X, Y, M=args.M, num_resamples=args.resamples, print_to_console=True, seed=args.seed)
if __name__ == "__main__":
common_args.run_cli(cli_parse, cli_action)