matflow.subset_simulation.subset_simulation#

Module containing functions to run a subset simulation on a simple toy model, used as a validation of the MatFlow implementation.

Functions

`cumsum_transformation_adjoint`	Adjoint (transpose-Jacobian action) for transformation = lambda x: np.cumsum(x, axis=-1).
`dist_to_str`	Return a string representation of a distribution.
`estimate_cov`	Estimate the coefficient of variation at a given conditional level of the subset simulation.
`generate_coarse_subchain`
`generate_next_level_samples`	Generate one conditional Subset Simulation level using MMH.
`generate_next_level_samples_ACS`	Generate one conditional level using adaptive conditional sampling (aka adaptive subset infinity).
`generate_next_level_samples_CS`	Generate one conditional level using conditional sampling (aka subset infinity).
`generate_next_level_samples_DA`	Generate one conditional level using fixed-subchain RST.
`generate_next_level_samples_DA_single_inner`	Delayed-acceptance modified Metropolis algorithm for subset simulation.
`generate_next_state`	Proposal must be a symmetric distribution centred on zero.
`generate_next_state_ACS`
`generate_next_state_CS`
`get_approx_pf_random_walk`
`get_approx_y_star_random_walk`
`get_stats`
`get_toy_model_results_from_matflow_workflows`	param root_path: A directory containing only (zipped) workflows that are toy-model subset
`get_y_star`
`get_y_star_max_system`	Analytic failure threshold for a 'weakest-link' (series-system) toy model: the system response is the maximum over dimension iid standard normal components, so P(max(X) <= y) = Phi(y)**dimension, giving an exact threshold for a target failure probability.
`log_surrogate_weight`	Note temperature should be of a similar order of magnitude to g_coarse and threshold.
`make_voxel_grouping`	Partition dimension fine grid points into contiguous blocks of block_size (the last block may be smaller), representing a coarser mesh voxelisation.
`model`
`plot_cov_dist`
`plot_cov_estimates`
`plot_many_pf_num_samples`
`plot_many_pf_num_samples_from_files`
`plot_pf_dist`
`plot_pf_num_samples`
`run_convergence`	Run a convergence test on the toy model subset simulation, for either number of samples per level, N, or number of repeats, R.
`run_repeats`
`sample_direct_MC`
`subset_simulation`	Estimate failure probability using Subset Simulation.
`system_analysis_toy_model`	x is within the failure domain if the return is greater than zero.
`voxel_block_average`	Coarse-grain x (..., dimension) by averaging within each block defined by group_idx, broadcasting each block's mean back over its fine positions (so fine and coarse fields live in the same space).
`weakest_link_coarse_gradient_xt`	Analytic gradient of weakest_link_performance_coarse (i.e.
`weakest_link_performance_coarse`	'Coarse mesh' weakest-link performance: as weakest_link_performance_fine, but evaluated on a block-averaged (coarser-voxelised) version of the field.
`weakest_link_performance_fine`	'Fine mesh' weakest-link performance: the system fails if the peak local response (max over all dimension fine grid points) exceeds y_star -- e.g.