BMBPT Diagram¶
Routines and class for Bogoliubov MBPT diagrams.

class
adg.bmbpt.
BmbptFeynmanDiagram
(nx_graph, tag_num)[source]¶ Bases:
adg.diag.Diagram
Describes a BMBPT Feynman diagram with its related properties.

two_or_three_body
¶ The 2 or 3body characted of the vertices.
Type: int

time_tag
¶ The tag number associated to the diagram’s associated TSD.
Type: int

tsd_is_tree
¶ The tree or nontree character of the associated TSD.
Type: bool

feynman_exp
¶ The Feynman expression associated to the diagram.
Type: str

diag_exp
¶ The Goldstone expression associated to the diagram.
Type: str

vert_exp
¶ The expression associated to the vertices.
Type: list

hf_type
¶ The HartreeFock, nonHartreeFock or HartreeFock for the energy operator only character of the graph.
Type: str

unique_id
¶ A unique number associated to the diagram.
Type: int

vertex_exchange_sym_factor
¶ Lazyinitialized symmetry factor associated to the vertex exchange, stored to avoid being computed several times.
Type: int

attribute_expressions
(time_diag)[source]¶ Attribute the correct Feynman and Goldstone expressions.
Parameters: time_diag (TimeStructureDiagram) – The associated TSD.

degrees
¶

diag_exp

equivalent_permutations
()[source]¶ Return the permutations generating equivalent diagrams.
Returns: Vertices permutations as dictionnaries. Return type: (list)

extract_integral
()[source]¶ Return the integral part of the Feynman expression of the diag.
Returns: The integral part of its Feynman expression. Return type: (str)

extract_numerator
()[source]¶ Return the numerator associated to a BMBPT graph.
Returns: The numerator of the graph. Return type: (str)

feynman_exp

graph
¶

has_crossing_sign
()[source]¶ Return True for a minus sign associated with crossing propagators.
Use the fact that all lines propagate upwards and the canonical representation of the diagrams and vertices.
Returns:  Encode for the sign factor associated with crossing
 propagators.
Return type: (bool)

has_sign_factor
()[source]¶ Return True if a sign factor is associated to the diagram.
Wrapper allowing for easy refactoring of expression code.
Returns: The presence of a sign factor. Return type: (boolean)

hf_type

io_degrees
¶

max_degree
¶

multiplicity_symmetry_factor
()[source]¶ Return the symmetry factor associated with propagators multiplicity.
Returns: The symmetry factor associated with equivalent lines. Return type: (str)

symmetry_factor
()[source]¶ Return the overall symmetry factor of the diagram.
Returns: The combination of all symmetry factors. Return type: (str)

time_tag

time_tree_denominator
(time_graph)[source]¶ Return the denominator for a timetree graph.
Parameters: time_graph (NetworkX MultiDiGraph) – Its associated timestructure graph. Returns: The denominator of the graph. Return type: (str)

tsd_is_tree

two_or_three_body

unique_id

unsort_degrees
¶

unsort_io_degrees
¶

vert_exp

vertex_exchange_sym_factor
Return the symmetry factor associated with vertex exchange.
Returns: The symmetry factor for vertex exchange. Return type: (int)

vertex_expression
(vertex)[source]¶ Return the expression associated to a given vertex.
Parameters: vertex (int) – The vertex of interest in the graph. Returns: The LaTeX expression associated to the vertex. Return type: (str)

write_diag_exps
(latex_file, norder)[source]¶ Write the expressions associated to a diagram in the LaTeX file.
Parameters:  latex_file (file) – The LaTeX outputfile of the program.
 norder (int) – The order in BMBPT formalism.

write_graph
(latex_file, directory, write_time)[source]¶ Write the BMBPT graph and its associated TSD to the LaTeX file.
Parameters:  latex_file (file) – The LaTeX output file of the program.
 directory (str) – The path to the result folder.
 write_time (bool) –
True
if we want informations on the associated TSDs.

write_section
(result, commands, section_flags)[source]¶ Write section and subsections for BMBPT result file.
Parameters:  result (file) – The LaTeX output file of the program.
 commands (dict) – The flags associated with run management.
 section_flags (dict) – UniqueIDs of diags starting each section.

write_tsd_info
(diagrams_time, latex_file)[source]¶ Write info related to the BMBPT associated TSD to the LaTeX file.
Parameters:  diagrams_time (list) – The associated TSDs.
 latex_file (file) – The LaTeX output file of the program.

write_vertices_values
(latex_file, mapping)[source]¶ Write the qp energies associated to each vertex of the diag.
Parameters:  latex_file (file) – The LaTeX output file of the program.
 mapping (dict) – A mapping between the vertices in the diagram and the vertices in its euivalent TSD, since permutations between vertices are possible.


adg.bmbpt.
check_topologically_equivalent
(matrices, max_vertex)[source]¶ Exclude matrices that would spawn topologically equivalent graphs.
Parameters:  matrices (list) – Adjacency matrices to be checked.
 max_vertex (int) – The maximum vertex which have been filled.
Returns: The topologically unique matrices.
Return type: (list)
>>> import numpy >>> mats = [numpy.array([[0, 2, 0, 0], [2, 0, 0, 1], [0, 0, 0, 0], [0, 0, 0, 0]]), numpy.array([[0, 0, 2, 0], [0, 0, 0, 0], [2, 0, 0, 1], [0, 0, 0, 0]])] >>> >>> mats = check_topologically_equivalent(mats, 2) >>> mats # doctest: +NORMALIZE_WHITESPACE [array([[0, 2, 0, 0], [2, 0, 0, 1], [0, 0, 0, 0], [0, 0, 0, 0]])] >>> >>> mats = check_topologically_equivalent([], 2) >>> mats # doctest: +NORMALIZE_WHITESPACE []

adg.bmbpt.
check_unconnected_spawn
(matrices, max_filled_vertex)[source]¶ Exclude some matrices that would spawn unconnected diagrams.
Do several permutations among the rows and columns corresponding to already filled vertices, and check if one obtains a blockdiagonal organisation, where the offdiagonals blocks connecting the alreadyfilled and yetunfilled parts of the matrix would be empty. In that case, remove the matrix.
Parameters:  matrices (list) – The adjacency matrices to be checked.
 max_filled_vertex (int) – The furthest vertex until which the matrices have been filled.
>>> import numpy >>> mats = [numpy.array([[0, 2, 0], [2, 0, 0], [0, 0, 0]]), numpy.array([[0, 2, 1], [2, 0, 1], [0, 0, 0]])] >>> >>> check_unconnected_spawn(mats, 1) >>> mats # doctest: +NORMALIZE_WHITESPACE [array([[0, 2, 1], [2, 0, 1], [0, 0, 0]])]

adg.bmbpt.
diagrams_generation
(p_order, three_body_use, nbody_obs, canonical)[source]¶ Generate diagrams for BMBPT from bottom up.
Parameters:  p_order (int) – The BMBPT perturbative order of the studied diagrams.
 three_body_use (bool) – Flag for the use of threebody forces.
 nbody_obs (int) – Nbody character of the obervable of interest.
 canonical (bool) –
True
if one draws only canonical diagrams.
Returns: NumPy arrays encoding the adjacency matrices of the graphs.
Return type: (list)
>>> diags = diagrams_generation(1, False, 2, False) >>> len(diags) 2 >>> any(np.array_equal([[0, 4], [0, 0]], diag) for diag in diags) True >>> any(np.array_equal([[0, 2], [0, 0]], diag) for diag in diags) True >>> diags = diagrams_generation(1, True, 3, False) >>> len(diags) 3 >>> any(np.array_equal([[0, 6], [0, 0]], diag) for diag in diags) True >>> any(np.array_equal([[0, 4], [0, 0]], diag) for diag in diags) True >>> any(np.array_equal([[0, 2], [0, 0]], diag) for diag in diags) True >>> diags = diagrams_generation(2, False, 2, True) >>> len(diags) 2 >>> any(np.array_equal([[0, 2, 2], [0, 0, 2], [0, 0, 0]], d) for d in diags) True >>> any(np.array_equal([[0, 1, 1], [0, 0, 3], [0, 0, 0]], d) for d in diags) True

adg.bmbpt.
order_and_remove_topologically_equiv
(matrices, max_vertex)[source]¶ Order the matrices in sublist and remove topologically equivalent ones.
Parameters:  matrices (list) – The adjacency matrices to be checked.
 max_vertex (int) – The maximum vertex which has been filled.
Returns: The ordered topologically unique matrices.
Return type: (list)

adg.bmbpt.
order_diagrams
(diagrams)[source]¶ Order the BMBPT diagrams and return number of diags for each type.
Parameters: diagrams (list) – Possibly redundant BmbptFeynmanDiagrams. Returns:  First element is the list of topologically unique, ordered
 diagrams. Second element is a dict with the number of diagrams for each major type. Third element is a dict with the identifiers of diagrams starting each output file section.
Return type: (tuple)

adg.bmbpt.
produce_expressions
(diagrams, diagrams_time)[source]¶ Produce and store the expressions associated to the BMBPT diagrams.
Parameters:  diagrams (list) – The list of all BmbptFeynmanDiagrams.
 diagrams_time (list) – Their associates TSDs.