import math
import numpy as np
from . import common_args
from ..util import scale_samples, read_param_file
[docs]
def sample(problem, N, M=4, seed=None):
"""Generate model inputs for extended Fourier Amplitude Sensitivity Test.
Returns a NumPy matrix containing the model inputs required by the extended
Fourier Amplitude sensitivity test. The resulting matrix contains N * D
rows and D columns, where D is the number of parameters.
The samples generated are intended to be used by
:func:`SALib.analyze.fast.analyze`.
Parameters
----------
problem : dict
The problem definition
N : int
The number of samples to generate
M : int
The interference parameter, i.e., the number of harmonics to sum in the
Fourier series decomposition (default 4)
seed : int
Seed to generate a random number
References
----------
1. Cukier, R.I., Fortuin, C.M., Shuler, K.E., Petschek, A.G.,
Schaibly, J.H., 1973.
Study of the sensitivity of coupled reaction systems to
uncertainties in rate coefficients. I theory.
Journal of Chemical Physics 59, 3873-3878.
https://doi.org/10.1063/1.1680571
2. Saltelli, A., S. Tarantola, and K. P.-S. Chan (1999).
A Quantitative Model-Independent Method for Global Sensitivity Analysis
of Model Output.
Technometrics, 41(1):39-56,
doi:10.1080/00401706.1999.10485594.
"""
if seed:
np.random.seed(seed)
if N <= 4 * M**2:
raise ValueError(
"""
Sample size N > 4M^2 is required. M=4 by default."""
)
D = problem["num_vars"]
omega = np.zeros([D])
omega[0] = math.floor((N - 1) / (2 * M))
m = math.floor(omega[0] / (2 * M))
if m >= (D - 1):
omega[1:] = np.floor(np.linspace(1, m, D - 1))
else:
omega[1:] = np.arange(D - 1) % m + 1
# Discretization of the frequency space, s
s = (2 * math.pi / N) * np.arange(N)
# Transformation to get points in the X space
X = np.zeros([N * D, D])
omega2 = np.zeros([D])
for i in range(D):
omega2[i] = omega[0]
idx = list(range(i)) + list(range(i + 1, D))
omega2[idx] = omega[1:]
z = range(i * N, (i + 1) * N)
# random phase shift on [0, 2pi) following Saltelli et al.
# Technometrics 1999
phi = 2 * math.pi * np.random.rand()
for j in range(D):
g = 0.5 + (1 / math.pi) * np.arcsin(np.sin(omega2[j] * s + phi))
X[z, j] = g
X = scale_samples(X, problem)
return X
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def cli_parse(parser):
"""Add method specific options to CLI parser.
Parameters
----------
parser : argparse object
Returns
-------
Updated argparse object
"""
parser.add_argument(
"-M",
"--m-coef",
type=int,
required=False,
default=4,
help="M coefficient, default 4",
dest="M",
)
return parser
[docs]
def cli_action(args):
"""Run sampling method
Parameters
----------
args : argparse namespace
"""
problem = read_param_file(args.paramfile)
param_values = sample(problem, N=args.samples, M=args.M, seed=args.seed)
np.savetxt(
args.output,
param_values,
delimiter=args.delimiter,
fmt="%." + str(args.precision) + "e",
)
if __name__ == "__main__":
common_args.run_cli(cli_parse, cli_action)
