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)