Source code for SALib.sample.ff

"""The sampling implementation of fractional factorial method

This implementation is based on the formulation put forward in
[`Saltelli et al. 2008 <http://www.wiley.com/WileyCDA/WileyTitle/productCd-0470059974.html>`_]

"""

from scipy.linalg import hadamard
import numpy as np
from . import common_args
from ..util import scale_samples, read_param_file


[docs]def find_smallest(num_vars): """Find the smallest exponent of two that is greater than the number of variables Parameters ---------- num_vars : int Number of variables Returns ------- x : int Smallest exponent of two greater than `num_vars` """ for x in range(10): if num_vars <= 2 ** x: return x
[docs]def extend_bounds(problem): """Extends the problem bounds to the nearest power of two Parameters ---------- problem : dict The problem definition """ num_vars = problem['num_vars'] num_ff_vars = 2 ** find_smallest(num_vars) num_dummy_variables = num_ff_vars - num_vars bounds = list(problem['bounds']) names = problem['names'] if num_dummy_variables > 0: bounds.extend([[0, 1] for x in range(num_dummy_variables)]) names.extend(["dummy_" + str(var) for var in range(num_dummy_variables)]) problem['bounds'] = bounds problem['names'] = names problem['num_vars'] = num_ff_vars return problem
[docs]def generate_contrast(problem): """Generates the raw sample from the problem file Parameters ---------- problem : dict The problem definition """ num_vars = problem['num_vars'] # Find the smallest n, such that num_vars < k k = [2 ** n for n in range(16)] k_chosen = 2 ** find_smallest(num_vars) # Generate the fractional factorial contrast contrast = np.vstack([hadamard(k_chosen), -hadamard(k_chosen)]) return contrast
[docs]def sample(problem, seed=None): """Generates model inputs using a fractional factorial sample Returns a NumPy matrix containing the model inputs required for a fractional factorial analysis. The resulting matrix has D columns, where D is smallest power of 2 that is greater than the number of parameters. These model inputs are intended to be used with :func:`SALib.analyze.ff.analyze`. The problem file is padded with a number of dummy variables called ``dummy_0`` required for this procedure. These dummy variables can be used as a check for errors in the analyze procedure. This algorithm is an implementation of that contained in Saltelli et al [`Saltelli et al. 2008 <http://www.wiley.com/WileyCDA/WileyTitle/productCd-0470059974.html>`_] Parameters ---------- problem : dict The problem definition Returns ------- sample : :class:`numpy.array` References ---------- .. [1] Saltelli, A., Ratto, M., Andres, T., Campolongo, F., Cariboni, J., Gatelli, D., Saisana, M., Tarantola, S., 2008. Global Sensitivity Analysis: The Primer. Wiley, West Sussex, U.K. https://dx.doi.org/10.1002/9780470725184 """ if seed: np.random.seed(seed) contrast = generate_contrast(problem) sample = np.array((contrast + 1.) / 2, dtype=float) problem = extend_bounds(problem) sample = scale_samples(sample, problem) return sample
# No additional CLI options cli_parse = None
[docs]def cli_action(args): """Run sampling method Parameters ---------- args : argparse namespace """ problem = read_param_file(args.paramfile) param_values = sample(problem, 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)