# Source code for adg.diag

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

import numpy
import networkx as nx

[docs]def no_trace(matrices):
"""Select matrices with full 0 diagonal.

Args:
matrices (list): A list of adjacency matrices.

Returns:
(list): The adjacency matrices without non-zero diagonal elements.

>>> 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]]]
>>> no_trace()
Traceback (most recent call last):
File "/usr/lib/python2.7/doctest.py", line 1315, in __run
compileflags, 1) in test.globs
File "<doctest __main__.no_trace[4]>", line 1, in <module>
no_trace()
TypeError: no_trace() takes exactly 1 argument (0 given)

"""
traceless_matrices = []
for matrix in matrices:
test_traceless = True
for ind_i, line in enumerate(matrix):
if line[ind_i] != 0:
test_traceless = False
break
if test_traceless:
traceless_matrices.append(matrix)
return traceless_matrices

[docs]def 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.

Args:
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 = [[[0, 1, 2], [1, 0, 1], [0, 2, 0]], \
[[2, 0, 2], [1, 2, 3], [1, 0, 0]], \
[[0, 1, 3], [2, 0, 8], [2, 1, 0]]]
>>> check_vertex_degree(test_matrices, True, 3, False, 0)
>>> test_matrices
[[[0, 1, 2], [1, 0, 1], [0, 2, 0]], [[2, 0, 2], [1, 2, 3], [1, 0, 0]]]
>>> check_vertex_degree(test_matrices, False, 2, False, 0)
>>> test_matrices
[[[0, 1, 2], [1, 0, 1], [0, 2, 0]]]

"""
authorized_deg = [4]
if three_body_use:
authorized_deg.append(6)
if not canonical_only or vertex_id == 0:
authorized_deg.append(2)
authorized_deg = tuple(authorized_deg)

for i_mat in xrange(len(matrices)-1, -1, -1):
matrix = matrices[i_mat]
vertex_degree = sum(matrix[index][vertex_id] + matrix[vertex_id][index]
for index in xrange(len(matrix[0])))
vertex_degree -= matrix[vertex_id][vertex_id]

if (vertex_id != 0 and vertex_degree not in authorized_deg) \
or (vertex_id == 0 and vertex_degree > 2*nbody_max_observable):
del matrices[i_mat]

[docs]def topologically_distinct_diagrams(diagrams):
"""Return a list of diagrams all topologically distinct.

Args:
diagrams (list): The Diagrams of interest.

Returns:
(list): Topologically unique diagrams.

"""
iso = nx.algorithms.isomorphism
op_nm = iso.categorical_node_match('operator', False)
for i_diag in xrange(len(diagrams)-1, -1, -1):
graph = diagrams[i_diag].graph
diag_io_degrees = diagrams[i_diag].io_degrees
for i_comp_diag in xrange(i_diag+1, len(diagrams), 1):
if diag_io_degrees == diagrams[i_comp_diag].io_degrees:
matcher = iso.DiGraphMatcher(graph,
diagrams[i_comp_diag].graph,
node_match=op_nm)
if matcher.is_isomorphic():
diagrams[i_diag].tags += diagrams[i_comp_diag].tags
if isinstance(diagrams[i_diag],
diagrams[i_diag].perms.update(
diagrams[i_comp_diag].perms)
diagrams[i_diag].perms[diagrams[i_comp_diag].tags[0]] \
= matcher.mapping
del diagrams[i_comp_diag]
break
return diagrams

[docs]def label_vertices(graphs_list, theory_type):
"""Account for different status of vertices in operator diagrams.

Args:
graphs_list (list): The Diagrams of interest.
theory_type (str): The name of the theory of interest.

"""
for graph in graphs_list:
for node in graph:
graph.node[node]['operator'] = False
if theory_type == "BMBPT":
graph.node[0]['operator'] = True

[docs]def feynmf_generator(graph, theory_type, diagram_name):
"""Generate the feynmanmp instructions corresponding to the diagram.

Args:
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.

"""
p_order = graph.number_of_nodes()
diag_size = 20*p_order

theories = ["MBPT", "BMBPT"]
prop_types = ["half_prop", "prop_pm"]
propa = prop_types[theories.index(theory_type)]

fmf_file = open(diagram_name + ".tex", 'w')
fmf_file.write("\\parbox{%ipt}{\\begin{fmffile}{%s}\n" % (diag_size,
diagram_name)
+ "\\begin{fmfgraph*}(%i,%i)\n" % (diag_size, diag_size))

# Define the appropriate line propagator_style
fmf_file.write(propagator_style(propa))

# Set the position of the vertices
fmf_file.write("\\fmftop{v%i}\\fmfbottom{v0}\n" % (p_order-1))
for vert in xrange(p_order-1):
fmf_file.write("\\fmf{phantom}{v%i,v%i}\n" % (vert, (vert+1)))
fmf_file.write(
"\\fmfv{d.shape=square,d.filled=full,d.size=3thick"
if graph.node[vert]['operator']
else "\\fmfv{d.shape=circle,d.filled=full,d.size=3thick")
fmf_file.write("}{v%i}\n" % vert)
fmf_file.write("\\fmfv{d.shape=circle,d.filled=full,d.size=3thick}{v%i}\n"
% (p_order-1))
fmf_file.write("\\fmffreeze\n")

# Loop over all elements of the graph to draw associated propagators
for vert_i in graph:
for vert_j in graph:
props_left_to_draw = graph.number_of_edges(vert_i, vert_j)
# Special config for consecutive vertices
if (props_left_to_draw % 2 == 1) and (abs(vert_i-vert_j) == 1):
fmf_file.write("\\fmf{%s" % propa)
# Check for specific MBPT configuration
if graph.number_of_edges(vert_j, vert_i) == 1:
fmf_file.write(",right=0.5")
fmf_file.write("}{v%i,v%i}\n" % (vert_i, vert_j))
props_left_to_draw -= 1
while props_left_to_draw > 0:
fmf_file.write("\\fmf{%s," % propa)
fmf_file.write("right=" if props_left_to_draw % 2 == 1
else "left=")
if (props_left_to_draw == 6) or (props_left_to_draw == 5):
fmf_file.write("0.9")
elif (props_left_to_draw == 4) or (props_left_to_draw == 3) \
or ((props_left_to_draw == 1) and
(graph.number_of_edges(vert_j, vert_i) == 2)):
fmf_file.write("0.75")
elif (props_left_to_draw == 2) or (props_left_to_draw == 1):
fmf_file.write("0.5" if abs(vert_i-vert_j) == 1 else "0.6")
fmf_file.write("}{v%i,v%i}\n" % (vert_i, vert_j))
props_left_to_draw -= 1
fmf_file.write("\\end{fmfgraph*}\n\\end{fmffile}}\n")
fmf_file.close()

[docs]def propagator_style(prop_type):
"""Return the FeynMF definition for the appropriate propagator type.

Args:
prop_type (str): The type of propagators used in the diagram.

Returns:
(str): The FeynMF definition for the propagator style used.

"""
line_styles = {}

line_styles['prop_pm'] = "\\fmfcmd{style_def prop_pm expr p =\n" \
+ "draw_plain p;\nshrink(.7);\n" \
+ "\tcfill (marrow (p, .25));\n" \
+ "\tcfill (marrow (p, .75))\n" \
+ "endshrink;\nenddef;}\n"

line_styles['half_prop'] = "\\fmfcmd{style_def half_prop expr p =\n" \
+ "draw_plain p;\nshrink(.7);\n" \
+ "\tcfill (marrow (p, .5))\n" \
+ "endshrink;\nenddef;}\n"

return line_styles[prop_type]

[docs]def draw_diagram(directory, result_file, diagram_index, diag_type):
"""Copy the diagram feynmanmp instructions in the result file.

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

"""
diag_file = open(directory+"/Diagrams/%s_%i.tex" % (diag_type,
diagram_index))
diag_file.close()

[docs]def to_skeleton(graph):
"""Return the bare skeleton of a graph, i.e. only non-redundant links.

Args:
graph (NetworkX MultiDiGraph): The graph to be turned into a skeleton.

Returns:
(NetworkX MultiDiGraph): The skeleton of the initial graph.

"""
for vertex_a in graph:
for vertex_b in graph:
while graph.number_of_edges(vertex_a, vertex_b) > 1:
graph.remove_edge(vertex_a, vertex_b)
if len(list(nx.all_simple_paths(graph, vertex_a, vertex_b))) > 1:
while len(nx.shortest_path(graph, vertex_a, vertex_b)) == 2:
graph.remove_edge(vertex_a, vertex_b)
return graph

[docs]def extract_denom(start_graph, subgraph):
"""Extract the appropriate denominator using the subgraph rule.

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

Returns:
(str): The denominator factor for this subgraph.

"""
denomin = r"\epsilon^{" \
+ "".join("%s"
% propa[3]['qp_state']
for propa
in start_graph.out_edges(subgraph, keys=True, data=True)
if not subgraph.has_edge(propa[0], propa[1], propa[2])) \
+ "}_{" \
+ "".join("%s"
% propa[3]['qp_state']
for propa
in start_graph.in_edges(subgraph, keys=True, data=True)
if not subgraph.has_edge(propa[0], propa[1], propa[2])) \
+ "}"
return denomin

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

Args:
directory (str): The path to the output directory.
diagrams (list): All the diagrams.

"""
with open(directory+"/adjacency_matrices.txt", "w") as mat_file:
for idx, diagram in enumerate(diagrams):
mat_file.write("Diagram n: %i\n" % (idx + 1))
mat_file.write("\n")

[docs]class Diagram(object):
"""Describes a diagram with its related properties.

Attributes:
graph (NetworkX MultiDiGraph): The actual graph.
unsorted_degrees (tuple): The degrees of the graph vertices
degrees (tuple): The ascendingly sorted degrees of the graph vertices.
unsort_io_degrees (tuple): The list of in- and out-degrees for each
vertex of the graph, stored in a (in, out) tuple.
io_degrees (tuple): The sorted version of unsort_io_degrees.
max_degree (int): The maximal degree of a vertex in the graph.
tags (list): The tag numbers associated to a diagram.
adjacency_mat (NumPy array): The adjacency matrix of the graph.

"""

def __init__(self, nx_graph):
"""Generate a Diagram object starting from the NetworkX graph.

Args:
nx_graph (NetworkX MultiDiGraph): The graph of interest.

"""
self.graph = nx_graph
self.unsort_degrees = tuple(nx_graph.degree(node) for node in nx_graph)
self.degrees = sorted(self.unsort_degrees)
self.unsort_io_degrees = tuple((nx_graph.in_degree(node),
nx_graph.out_degree(node))
for node in nx_graph)
self.io_degrees = sorted(self.unsort_io_degrees)
self.max_degree = self.degrees[-1]
self.tags = [0]
self.adjacency_mat = nx.to_numpy_matrix(self.graph, dtype=int)

[docs]    def write_graph(self, latex_file, directory, write_time):
"""Write the graph of the diagram to the LaTeX file.

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

"""
latex_file.write('\n\\begin{center}\n')
draw_diagram(directory, latex_file, self.tags[0], 'diag')
latex_file.write('\n\\end{center}\n\n')