github.com/SALib/SALib @v1.5.2

SALib: Advanced options

Parameter files

In the parameter file, lines beginning with # will be treated as comments and ignored.

# name lower_bound upper_bound
P1 0.0 1.0
P2 0.0 5.0
P3 0.0 5.0
...etc.

Parameter files can also be comma-delimited if your parameter names or group names contain spaces. This should be detected automatically.

Command-line interface

Generate samples (the -p flag is the parameter file)

salib sample saltelli \
     -n 1024 \
     -p ./src/SALib/test_functions/params/Ishigami.txt \
     -o model_input.txt

Run the model this will usually be a user-defined model, maybe even in another language. Just save the outputs.

Run the analysis

salib analyze sobol \
     -p ./src/SALib/test_functions/params/Ishigami.txt \
     -Y model_output.txt \
     -c 0

This will print indices and confidence intervals to the command line. You can redirect to a file using the > operator.

Parallel indices calculation (Sobol method only)

Si = sobol.analyze(problem, Y, calc_second_order=True, conf_level=0.95,
                   print_to_console=False, parallel=True, n_processors=4)

Other methods include Morris, FAST, Delta-MIM, and DGSM. For an explanation of all command line options for each method, see the examples here.

Groups of variables (Sobol and Morris methods only)

It is sometimes useful to perform sensitivity analysis on groups of input variables to reduce the number of model runs required, when variables belong to the same component of a model, or there is some reason to believe that they should behave similarly.

Groups can be specified in two ways for the Sobol and Morris methods. First, as a fourth column in the parameter file:

# name lower_bound upper_bound group_name
P1 0.0 1.0 Group_1
P2 0.0 5.0 Group_2
P3 0.0 5.0 Group_2
...etc.

Or in the problem dictionary:

problem = {
  'groups': ['Group_1', 'Group_2', 'Group_2'],
  'names': ['x1', 'x2', 'x3'],
  'num_vars': 3,
  'bounds': [[-3.14, 3.14], [-3.14, 3.14], [-3.14, 3.14]]
}

groups is a list of strings specifying the group name to which each variable belongs. The rest of the code stays the same:

param_values = saltelli.sample(problem, 1024)
Y = Ishigami.evaluate(param_values)
Si = sobol.analyze(problem, Y, print_to_console=True)

But the output is printed by group:

Group S1 S1_conf ST ST_conf
Group_1 0.307834 0.066424 0.559577 0.082978
Group_2 0.444052 0.080255 0.667258 0.060871

Group_1 Group_2 S2 S2_conf
Group_1 Group_2 0.242964 0.124229

The output can then be converted to a Pandas DataFrame for further analysis.

total_Si, first_Si, second_Si = Si.to_df()

Generating alternate distributions

In the Quick Start we generate a uniform sample of parameter space.

from SALib.sample import saltelli
from SALib.analyze import sobol
from SALib.test_functions import Ishigami
import numpy as np

problem = {
     'num_vars': 3,
     'names': ['x1', 'x2', 'x3'],
     'bounds': [[-3.14159265359, 3.14159265359],
               [-3.14159265359, 3.14159265359],
               [-3.14159265359, 3.14159265359]]
}

param_values = saltelli.sample(problem, 1024)

SALib is also capable of generating alternate sampling distributions by specifying a dist entry in the problem specification.

As implied in the basic example, a uniform distribution is the default.

When an entry for dist is not 'unif', the bounds entry does not indicate parameter bounds but sample-specific metadata.

bounds definitions for available distributions:

• unif: uniform distribution e.g. :code:[-np.pi, np.pi] defines the lower and upper bounds

• triang: triangular with lower and upper bounds, as well as location of peak The location of peak is in percentage of width e.g. :code:[1.0, 3.0, 0.5] indicates 1.0 to 3.0 with a peak at 2.0

  A soon-to-be deprecated two-value format assumes the lower bound to be 0 e.g. :code:[3, 0.5] assumes 0 to 3, with a peak at 1.5 * norm: normal distribution with mean and standard deviation * lognorm: lognormal with ln-space mean and standard deviation

An example specification is shown below:

problem = {
     'names': ['x1', 'x2', 'x3'],
     'num_vars': 3,
     'bounds': [[-np.pi, np.pi], [1.0, 0.2], [3, 0.5]],
     'groups': ['G1', 'G2', 'G1'],
     'dists': ['unif', 'lognorm', 'triang']
}