from __future__ import division
from __future__ import print_function
from scipy.stats import norm
import numpy as np
from . import common_args
from ..util import read_param_file, ResultDict
[docs]def analyze(problem, X, Y, num_resamples=100,
conf_level=0.95, print_to_console=False, seed=None):
"""Calculates Derivative-based Global Sensitivity Measure on model outputs.
Returns a dictionary with keys 'vi', 'vi_std', 'dgsm', and 'dgsm_conf',
where each entry is a list of size D (the number of parameters) containing
the indices in the same order as the parameter file.
Parameters
----------
problem : dict
The problem definition
X : numpy.matrix
The NumPy matrix containing the model inputs
Y : numpy.array
The NumPy array containing the model outputs
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)
References
----------
.. [1] Sobol, I. M. and S. Kucherenko (2009). "Derivative based global
sensitivity measures and their link with global sensitivity
indices." Mathematics and Computers in Simulation, 79(10):3009-3017,
doi:10.1016/j.matcom.2009.01.023.
"""
if seed:
np.random.seed(seed)
D = problem['num_vars']
Y_size = Y.size
if Y_size % (D + 1) == 0:
N = int(Y_size / (D + 1))
else:
raise RuntimeError("Incorrect number of samples in model output file.")
if not 0 < conf_level < 1:
raise RuntimeError("Confidence level must be between 0-1.")
dims = (N, D)
base = np.empty(N)
X_base = np.empty(dims)
perturbed = np.empty(dims)
X_perturbed = np.empty(dims)
step = D + 1
base = Y[0:Y_size:step]
X_base = X[0:Y_size:step, :]
# First order (+conf.) and Total order (+conf.)
keys = ('vi', 'vi_std', 'dgsm', 'dgsm_conf')
S = ResultDict((k, np.empty(D)) for k in keys)
S['names'] = problem['names']
if print_to_console:
print("Parameter %s %s %s %s" % keys)
bounds = problem['bounds']
for j in range(D):
perturbed[:, j] = Y[(j + 1):Y_size:step]
X_perturbed[:, j] = X[(j + 1):Y_size:step, j]
diff = X_perturbed[:, j] - X_base[:, j]
perturbed_j = perturbed[:, j]
S['vi'][j], S['vi_std'][j] = calc_vi_stats(base,
perturbed_j,
diff)
S['dgsm'][j], S['dgsm_conf'][j] = calc_dgsm(base,
perturbed_j,
diff,
bounds[j],
num_resamples,
conf_level)
if print_to_console:
print("%s %f %f %f %f" % (
S['names'][j], S['vi'][j], S['vi_std'][j], S['dgsm'][j], S['dgsm_conf'][j]))
return S
[docs]def calc_vi_stats(base, perturbed, x_delta):
"""Calculate v_i mean and std.
v_i sensitivity measure following Sobol and Kucherenko (2009)
For comparison, Morris mu* < sqrt(v_i)
Same as calc_vi_mean but returns standard deviation as well.
"""
dfdx = ((perturbed - base) / x_delta)**2
return np.mean(dfdx), np.std(dfdx)
[docs]def calc_vi_mean(base, perturbed, x_delta):
"""Calculate v_i mean.
Same as calc_vi_stats but only returns the mean.
"""
dfdx = ((perturbed - base) / x_delta)**2
return dfdx.mean()
[docs]def calc_dgsm(base, perturbed, x_delta, bounds, num_resamples, conf_level):
"""v_i sensitivity measure following Sobol and Kucherenko (2009).
For comparison, total order S_tot <= dgsm
"""
D = np.var(base)
vi = calc_vi_mean(base, perturbed, x_delta)
dgsm = vi * (bounds[1] - bounds[0])**2 / (D * np.pi**2)
len_base = len(base)
s = np.empty(num_resamples)
r = np.random.randint(len_base, size=(num_resamples, len_base))
for i in range(num_resamples):
r_i = r[i]
s[i] = calc_vi_mean(base[r_i], perturbed[r_i], x_delta[r_i])
return dgsm, norm.ppf(0.5 + conf_level / 2.0) * s.std(ddof=1)
[docs]def cli_parse(parser):
parser.add_argument('-X', '--model-input-file', type=str,
required=True, default=None,
help='Model input file')
parser.add_argument('-r', '--resamples', type=int, required=False,
default=1000,
help='Number of bootstrap resamples for Sobol \
confidence intervals')
return parser
[docs]def cli_action(args):
problem = read_param_file(args.paramfile)
Y = np.loadtxt(args.model_output_file,
delimiter=args.delimiter, usecols=(args.column,))
X = np.loadtxt(args.model_input_file, delimiter=args.delimiter, ndmin=2)
if len(X.shape) == 1:
X = X.reshape((len(X), 1))
analyze(problem, X, Y, num_resamples=args.resamples, print_to_console=True,
seed=args.seed)
if __name__ == "__main__":
common_args.run_cli(cli_parse, cli_action)