Generic Diagram

Routines and class for all types of diagrams, inherited by others.

class adg.diag.Diagram(nx_graph)

Bases: object

Describes a diagram with its related properties.

graph

The actual graph.

Type:NetworkX MultiDiGraph

unsorted_degrees

The degrees of the graph vertices

Type:tuple

degrees

The ascendingly sorted degrees of the graph vertices.

Type:tuple

unsort_io_degrees

The list of in- and out-degrees for each vertex of the graph, stored in a (in, out) tuple.

Type:tuple

io_degrees

The sorted version of unsort_io_degrees.

Type:tuple

max_degree

The maximal degree of a vertex in the graph.

Type:int

tags

The tag numbers associated to a diagram.

Type:list

degrees

graph

io_degrees

max_degree

tags

unsort_degrees

unsort_io_degrees

write_graph(latex_file, directory, write_time)

Write the graph of the diagram to the LaTeX file.

Parameters:

• latex_file (file) – The LaTeX ouput file of the program.
• directory (str) – Path to the result folder.
• write_time (bool) – (Here to emulate polymorphism).

adg.diag.bimsrg_diagram_internals(graph, fmf_file, prop_type)

Write to file the vertices and propagators of BIMSRG diagrams.

Parameters:

• graph (NetworkX MultiDiGraph) – The graph to be drawn.
• fmf_file (file) – The FeymanMF file to be written to.
• prop_type (str) – The FeymanMF type for drawing the propagators.

adg.diag.check_vertex_degree(matrices, three_body_use, nbody_max_observable, canonical_only, vertex_id)

Check the degree of a specific vertex in a set of matrices.

Parameters:

• matrices (list) – Adjacency matrices.
• three_body_use (bool) – True if one uses three-body forces.
• nbody_max_observable (int) – Maximum body number for the observable.
• canonical_only (bool) – True if one draws only canonical diagrams.
• vertex_id (int) – The position of the studied vertex.

>>> test_matrices = [numpy.array([[0, 1, 2], [1, 0, 1], [0, 2, 0]]),         numpy.array([[2, 0, 2], [1, 2, 3], [1, 0, 0]]),         numpy.array([[0, 1, 3], [2, 0, 8], [2, 1, 0]])]
>>> check_vertex_degree(test_matrices, True, 3, False, 0)
>>> test_matrices #doctest: +NORMALIZE_WHITESPACE
[array([[0, 1, 2], [1, 0, 1], [0, 2, 0]]),
 array([[2, 0, 2], [1, 2, 3], [1, 0, 0]])]
>>> check_vertex_degree(test_matrices, False, 2, False, 0)
>>> test_matrices #doctest: +NORMALIZE_WHITESPACE
[array([[0, 1, 2], [1, 0, 1], [0, 2, 0]])]

adg.diag.create_checkable_diagram(pbmbpt_graph)

Return a graph with anomalous props going both ways for topo check.

Parameters:pbmbpt_graph (NetworkX MultiDiGraph) – The graph to be copied. Returns:Graph with double the anomalous props. Return type:(NetworkX MultiDiGraph)

adg.diag.draw_diagram(directory, result_file, diagram_index, diag_type)

Copy the diagram feynmanmp instructions in the result file.

Parameters:

• directory (str) – The path to the output folder.
• result_file (file) – The LaTeX ouput file of the program.
• diagram_index (str) – The number associated to the diagram.
• diag_type (str) – The type of diagram used here.

adg.diag.extract_denom(start_graph, subgraph)

Extract the appropriate denominator using the subgraph rule.

Parameters:

• start_graph (NetworkX MultiDiGraph) – The studied graph.
• subgraph (NetworkX MultiDiGraph) – The subgraph used for this particular denominator factor.

Returns:

The denominator factor for this subgraph.

Return type:

(str)

adg.diag.feynmf_generator(graph, theory_type, diagram_name)

Generate the feynmanmp instructions corresponding to the diagram.

Parameters:

• graph (NetworkX MultiDiGraph) – The graph of interest.
• theory_type (str) – The name of the theory of interest.
• diagram_name (str) – The name of the studied diagram.

adg.diag.label_vertices(graphs_list, theory_type, switch_flag)

Account for different status of vertices in operator diagrams.

Parameters:

• graphs_list (list) – The Diagrams of interest.
• theory_type (str) – The name of the theory of interest.
• switch_flag (int) – When to switch A and B operators for BIMSRG.

adg.diag.no_trace(matrices)

Select matrices with full 0 diagonal.

Parameters:matrices (list) – A list of adjacency matrices. Returns:The adjacency matrices without non-zero diagonal elements. Return type:(list)

>>> test_matrices = [[[0, 1, 2], [2, 0, 1], [5, 2, 0]],     [[2, 2, 2], [1, 2, 3], [0, 0, 0]],     [[0, 1, 3], [2, 0, 8], [2, 1, 0]]]
>>> no_trace(test_matrices)
[[[0, 1, 2], [2, 0, 1], [5, 2, 0]], [[0, 1, 3], [2, 0, 8], [2, 1, 0]]]

adg.diag.print_adj_matrices(directory, diagrams)

Print a computer-readable file with the diagrams’ adjacency matrices.

Parameters:

• directory (str) – The path to the output directory.
• diagrams (list) – All the diagrams.

adg.diag.prop_directions(vert_distance, nb_props)

Return a list of possible propagators directions.

Parameters:

• vert_distance (int) – Distance between the two connected vertices.
• nb_props (int) – Number of propagators to be drawn.

Returns:

Propagators directions stored as strings.

Return type:

(list)

adg.diag.propagator_style(prop_type)

Return the FeynMF definition for the appropriate propagator type.

Parameters:prop_type (str) – The type of propagators used in the diagram. Returns:The FeynMF definition for the propagator style used. Return type:(str)

adg.diag.self_contractions(graph)

Return the instructions for drawing the graph’s self-contractions.

Parameters:graph (NetworkX MultiDiGraph) – The graph being drawn. Returns:FeynMF instructions for drawing the self-contractions. Return type:(str)

adg.diag.to_skeleton(graph)

Return the bare skeleton of a graph, i.e. only non-redundant links.

Parameters:graph (NetworkX MultiDiGraph) – The graph to be turned into a skeleton. Returns:The skeleton of the initial graph. Return type:(NetworkX MultiDiGraph)

adg.diag.topologically_distinct_diagrams(diagrams)

Return a list of diagrams all topologically distinct.

Parameters:diagrams (list) – The Diagrams of interest. Returns:Topologically unique diagrams. Return type:(list)

adg.diag.update_permutations(comp_graph_perms, comp_graph_tag, mapping)

Update permutations associated to the BMBPT diags for a shared TSD.

Parameters:

• comp_graph_perms (dict) – Permutations to be updated.
• comp_graph_tag (int) – The tag associated to the TSD configuration.
• mapping (dict) – permutations to go from previous ref TSD to new one.

adg.diag.vertex_positions(graph, order)

Return the positions of the graph’s vertices.

Parameters:

• graph (NetworkX MultiDiGraph) – The graph of interest.
• order (int) – The perturbative order of the graph.

Returns:

The FeynMP instructions for positioning the vertices.

Return type:

(str)