Source code for SALib.analyze.dgsm

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. Compatible with --------------- * `finite_diff` 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'] 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.to_df()) 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)