SALib.sample.morris.morris module#

SALib.sample.morris.morris.sample(problem: Dict, N: int, num_levels: int = 4, optimal_trajectories: int | None = None, local_optimization: bool = True, seed: int | Generator | None = None) → ndarray[source]#

Generate model inputs using the Method of Morris.

Three variants of Morris’ sampling for elementary effects is supported:

  • Vanilla Morris (see [1]) when optimal_trajectories is None/False and local_optimization is False

  • Optimised trajectories when optimal_trajectories=True using

    Campolongo’s enhancements (see [2]) and optionally Ruano’s enhancement (see [3]) when local_optimization=True

  • Morris with groups when the problem definition specifies groups of parameters

Results from these model inputs are intended to be used with SALib.analyze.morris.analyze().

Notes

Campolongo et al., [2] introduces an optimal trajectories approach which attempts to maximize the parameter space scanned for a given number of trajectories (where optimal_trajectories \(\in {2, ..., N}\)). The approach accomplishes this aim by randomly generating a high number of possible trajectories (500 to 1000 in [2]) and selecting a subset of r trajectories which have the highest spread in parameter space. The r variable in [2] corresponds to the optimal_trajectories parameter here.

Calculating all possible combinations of trajectories can be computationally expensive. The number of factors makes little difference, but the ratio between number of optimal trajectories and the sample size results in an exponentially increasing number of scores that must be computed to find the optimal combination of trajectories. We suggest going no higher than 4 levels from a pool of 100 samples with this “brute force” approach.

Ruano et al., [3] proposed an alternative approach with an iterative process that maximizes the distance between subgroups of generated trajectories, from which the final set of trajectories are selected, again maximizing the distance between each. The approach is not guaranteed to produce the most optimal spread of trajectories, but are at least locally maximized and significantly reduce the time taken to select trajectories. With local_optimization = True (which is default), it is possible to go higher than the previously suggested 4 levels from a pool of 100 samples.

Parameters:

  • problem (dict) – The problem definition

  • N (int) – The number of trajectories to generate

  • num_levels (int, default=4) – The number of grid levels (should be even)

  • optimal_trajectories (int) – The number of optimal trajectories to sample (between 2 and N)

  • local_optimization (bool, default=True) – Flag whether to use local optimization according to Ruano et al. (2012) Speeds up the process tremendously for bigger N and num_levels. If set to False brute force method is used, unless gurobipy is available

  • seed ({None, int, numpy.random.Generator}, optional) – If seed is None the numpy.random.Generator generator is used. If seed is an int, a new Generator instance is used, seeded with seed. If seed is already a Generator instance then that instance is used. Default is None.

Returns:

sample_morris – Array containing the model inputs required for Method of Morris. The resulting matrix has \((G/D+1)*N/T\) rows and \(D\) columns, where \(D\) is the number of parameters, \(G\) is the number of groups (if no groups are selected, the number of parameters). \(T\) is the number of trajectories \(N\), or optimal_trajectories if selected.

Return type:

np.ndarray

References

  1. Morris, M.D., 1991. Factorial Sampling Plans for Preliminary Computational Experiments. Technometrics 33, 161-174. https://doi.org/10.1080/00401706.1991.10484804

  2. Campolongo, F., Cariboni, J., & Saltelli, A. 2007. An effective screening design for sensitivity analysis of large models. Environmental Modelling & Software, 22(10), 1509-1518. https://doi.org/10.1016/j.envsoft.2006.10.004

  3. Ruano, M.V., Ribes, J., Seco, A., Ferrer, J., 2012. An improved sampling strategy based on trajectory design for application of the Morris method to systems with many input factors. Environmental Modelling & Software 37, 103-109. https://doi.org/10.1016/j.envsoft.2012.03.008

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