SALib.test_functions.lake_problem module#

SALib.test_functions.lake_problem.evaluate(values: ndarray, nvars: int = 100, seed=101)[source]#

Evaluate the Lake Problem with an array of parameter values.

Parameters:

  • values (np.ndarray,) – model inputs in the (column) order of a, q, b, mean, stdev, delta, alpha

  • nvars (int,) – number of decision variables to simulate (default: 100)

Returns:

np.ndarray

Return type:

max_P, utility, inertia, reliability

SALib.test_functions.lake_problem.evaluate_lake(values: ndarray, seed=101) → ndarray[source]#

Evaluate the Lake Problem with an array of parameter values.

References

[1]

Hadka, D., Herman, J., Reed, P., Keller, K., (2015). “An open source framework for many-objective robust decision making.” Environmental Modelling & Software 74, 114–129. doi:10.1016/j.envsoft.2015.07.014

[2]

Singh, R., Reed, P., Keller, K., (2015). “Many-objective robust decision making for managing an ecosystem with a deeply uncertain threshold response.” Ecology and Society 20. doi:10.5751/ES-07687-200312

Parameters:

values (np.ndarray,) –

model inputs in the (column) order of a, q, b, mean, stdev

where * a is rate of anthropogenic pollution * q is exponent controlling recycling rate * b is decay rate for phosphorus * mean and * stdev set the log normal distribution of eps, see [2]

Return type:

np.ndarray, of Phosphorus pollution over time t

SALib.test_functions.lake_problem.lake_problem(X: float | array, a: float | array = 0.1, q: float | array = 2.0, b: float | array = 0.42, eps: float | array = 0.02) → float[source]#

Lake Problem as given in Hadka et al., (2015) and Kwakkel (2017) modified for use as a test function.

The mean and stdev parameters control the log normal distribution of natural inflows (epsilon in [1] and [2]).

References

[1]

Hadka, D., Herman, J., Reed, P., Keller, K., (2015). “An open source framework for many-objective robust decision making.” Environmental Modelling & Software 74, 114-129. doi:10.1016/j.envsoft.2015.07.014

[2]

Kwakkel, J.H, (2017). “The Exploratory Modeling Workbench: An open source toolkit for exploratory modeling, scenario discovery, and (multi-objective) robust decision making.” Environmental Modelling & Software 96, 239-250. doi:10.1016/j.envsoft.2017.06.054

[3]

Singh, R., Reed, P., Keller, K., (2015). “Many-objective robust decision making for managing an ecosystem with a deeply uncertain threshold response.” Ecology and Society 20. doi:10.5751/ES-07687-200312

Parameters:

  • X (float or np.ndarray) – normalized concentration of Phosphorus at point in time

  • a (float or np.ndarray) – rate of anthropogenic pollution (0.0 to 0.1)

  • q (float or np.ndarray) – exponent controlling recycling rate (2.0 to 4.5).

  • b (float or np.ndarray) – decay rate for phosphorus (0.1 to 0.45, where default 0.42 is irreversible, as described in [1])

  • eps (float or np.ndarray) – natural inflows of phosphorus (pollution), see [3]

Return type:

float, phosphorus pollution for a point in time