drgep

Module containing Directed Relation Graph with Error Propagation (DRGEP) reduction method.

pymars.drgep.create_drgep_matrix(state, solution)

Creates DRGEP graph adjacency matrix

Parameters

  • state (tuple) – Tuple of state with temperature, pressure, and species mass fractions

  • solution (cantera.Solution) – Cantera object of the solution being analyzed

Returns

adjacency_matrix – Adjacency matrix based on calculated direct interaction coefficients

Return type

numpy.ndarray

pymars.drgep.get_importance_coeffs(species_names, target_species, matrices)

Calculate importance coefficients for all species

Parameters

  • species_names (list of str) – Species names

  • target_species (list of str) – List of target species

  • matrices (list of numpy.ndarray) – List of adjacency matrices

Returns

importance_coefficients – Maximum coefficients over all sampled states

Return type

dict

pymars.drgep.graph_search_drgep(graph, target_species)

Searches graph to generate a dictionary of the greatest paths to all species from one of the targets.

Parameters

  • graph (networkx.DiGraph) – Graph representing model

  • target_species (list of str) – List of target species to search from

Returns

overall_coefficients – Overall interaction coefficients; maximum over all paths from all targets to each species

Return type

dict

pymars.drgep.mod_dijkstra(G, source, get_weight, pred=None, paths=None, cutoff=None, target=None)

Modified implementation of Dijkstra’s algorithm for DRGEP method.

Multiples values along graph pathways instead of adding and returns a dictionary with nodes as keys and values containing the greatest path to that node. Each edge weight must be <= 1 so that the further they are from the source, the less important they are.

Parameters

  • G (networkx.Graph) – Graph to be considered

  • source (str or int) – Starting node for path

  • get_weight (function) – Function for getting edge weight

  • pred (list, optional) – List of predecessors of a node

  • paths (dict, optional) – Path from the source to a target node.

  • target (str or int, optional) – Ending node for path

  • cutoff (int or float, optional) – Depth to stop the search. Only paths of length <= cutoff are returned.

Returns

  • distance, path (dict) – Returns a tuple of two dictionaries keyed by node. The first dictionary stores distance from the source. The second stores the path from the source to that node.

  • pred, distance (dict) – Returns two dictionaries representing a list of predecessors of a node and the distance to each node.

  • distance (dict) – Dictionary of greatest lengths keyed by target.

pymars.drgep.reduce_drgep(model_file, species_safe, threshold, importance_coeffs, ignition_conditions, sampled_metrics, phase_name='', previous_model=None, num_threads=1, path='')

Given a threshold and DRGEP coefficients, reduce the model and determine the error.

Parameters

  • model_file (str) – Filename for model being reduced

  • species_safe (list of str) – List of species to always be retained

  • threshold (float) – DRG threshold for trimming graph

  • importance_coeffs (dict) – Dictionary with species and their overall interaction coefficients.

  • ignition_conditions (list of InputIgnition) – List of autoignition initial conditions.

  • sampled_metrics (numpy.ndarray) – Global metrics from original model used to evaluate error

  • phase_name (str, optional) – Optional name for phase to load from CTI file (e.g., ‘gas’).

  • previous_model (ReducedModel, optional) – Model produced at previous threshold level; used to avoid repeated work.

  • num_threads (int, optional) – Number of CPU threads to use for performing simulations in parallel. Optional; default = 1, in which the multiprocessing module is not used. If 0, then use the available number of cores minus one. Otherwise, use the specified number of threads.

  • path (str, optional) – Optional path for writing files

Returns

Return reduced model and associated metadata

Return type

ReducedModel

pymars.drgep.run_drgep(model_file, ignition_conditions, psr_conditions, flame_conditions, error_limit, species_targets, species_safe, phase_name='', threshold_upper=None, num_threads=1, path='')

Main function for running DRGEP reduction.

Parameters

  • model_file (str) – Original model file

  • ignition_conditions (list of InputIgnition) – List of autoignition initial conditions.

  • psr_conditions (list of InputPSR) – List of PSR simulation conditions.

  • flame_conditions (list of InputLaminarFlame) – List of laminar flame simulation conditions.

  • error_limit (float) – Maximum allowable error level for reduced model

  • species_targets (list of str) – List of target species names

  • species_safe (list of str) – List of species names to always be retained

  • phase_name (str, optional) – Optional name for phase to load from CTI file (e.g., ‘gas’).

  • threshold_upper (float, optional) – Upper threshold (epsilon^*) to identify limbo species for sensitivity analysis

  • num_threads (int, optional) – Number of CPU threads to use for performing simulations in parallel. Optional; default = 1, in which the multiprocessing module is not used. If 0, then use the available number of cores minus one. Otherwise, use the specified number of threads.

  • path (str, optional) – Optional path for writing files

Returns

Return reduced model and associated metadata

Return type

ReducedModel

pymars.drgep.ss_dijkstra_path_length_modified(G, source, cutoff=None, weight='weight')

Compute the greatest path length via multiplication between source and all other reachable nodes for a weighted graph with all weights <= 1.

Parameters

  • G (networkx.Graph) – Graph to be considered

  • source (node label) – Starting node for path

  • weight (str, optional (default='weight')) – Edge data key corresponding to the edge weight.

  • cutoff (int or float, optional) – Depth to stop the search. Only paths of length <= cutoff are returned.

Returns

length – Dictionary of shortest lengths keyed by target.

Return type

dictionary

Examples

>>> G=networkx.path_graph(5)
>>> length=networkx.ss_dijkstra_path_length_modified(G,0)
>>> length[4]
1
>>> print(length)
{0: 0, 1: 1, 2: 1, 3: 1, 4: 1}

Notes

Edge weight attributes must be numerical and <= 1. Distances are calculated as products of weighted edges traversed. Don’t use a cutoff.

See also

single_source_dijkstra()