#!/usr/bin/env python
#-*- coding:utf-8 -*-
#
# This file is part of the NNGT project to generate and analyze
# neuronal networks and their activity.
# Copyright (C) 2015-2017 Tanguy Fardet
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
import numpy as np
from matplotlib.patches import FancyArrowPatch, ArrowStyle, FancyArrow, Circle
from matplotlib.patches import Arc, RegularPolygon
from matplotlib.collections import PatchCollection
from matplotlib.colors import ListedColormap, Normalize, cnames, ColorConverter
from mpl_toolkits.axes_grid1 import make_axes_locatable
import nngt
from nngt.lib import POS, nonstring_container
from nngt.analysis import num_wcc
from .custom_plt import palette, format_exponent
'''
Network plotting
================
Implemented
-----------
Simple representation for spatial graphs, random distribution if non-spatial.
Support for edge-size (according to betweenness or synaptic weight).
Objectives
----------
Implement the spring-block minimization.
If edges have varying size, plot only those that are visible (size > min)
'''
__all__ = ["draw_network"]
# ------- #
# Drawing #
# ------- #
[docs]def draw_network(network, nsize="total-degree", ncolor="group", nshape="o",
nborder_color="k", nborder_width=0.5, esize=1., ecolor="k",
ealpha=0.5, max_nsize=5., max_esize=2., curved_edges=False,
threshold=0.5, decimate=None, spatial=True,
restrict_sources=None, restrict_targets=None,
show_environment=True, fast=False, size=(600,600), xlims=None,
ylims=None, dpi=75, axis=None, colorbar=False, show=False,
**kwargs):
'''
Draw a given graph/network.
Parameters
----------
network : :class:`~nngt.Graph` or subclass
The graph/network to plot.
nsize : float, array of float or string, optional (default: "total-degree")
Size of the nodes as a percentage of the canvas length. Otherwise, it
can be a string that correlates the size to a node attribute among
"in/out/total-degree", or "betweenness".
ncolor : float, array of floats or string, optional (default: 0.5)
Color of the nodes; if a float in [0, 1], position of the color in the
current palette, otherwise a string that correlates the color to a node
attribute among "in/out/total-degree", "betweenness" or "group".
nshape : char or array of chars, optional (default: "o")
Shape of the nodes (see `Matplotlib markers <http://matplotlib.org/api/
markers_api.html?highlight=marker#module-matplotlib.markers>`_).
nborder_color : char, float or array, optional (default: "k")
Color of the node's border using predefined `Matplotlib colors
<http://matplotlib.org/api/colors_api.html?highlight=color
#module-matplotlib.colors>`_).
or floats in [0, 1] defining the position in the palette.
nborder_width : float or array of floats, optional (default: 0.5)
Width of the border in percent of canvas size.
esize : float, str, or array of floats, optional (default: 0.5)
Width of the edges in percent of canvas length. Available string values
are "betweenness" and "weight".
ecolor : str, char, float or array, optional (default: "k")
Edge color. If ecolor="groups", edges color will depend on the source
and target groups, i.e. only edges from and toward same groups will
have the same color.
max_esize : float, optional (default: 5.)
If a custom property is entered as `esize`, this normalizes the edge
width between 0. and `max_esize`.
decimate : int, optional (default: keep all connections)
Plot only one connection every `decimate`. Use -1 to hide all edges.
spatial : bool, optional (default: True)
If True, use the neurons' positions to draw them.
restrict_sources : str or list, optional (default: all)
Only draw edges starting from a restricted set of source nodes.
restrict_targets : str or list, optional (default: all)
Only draw edges ending on a restricted set of target nodes.
show_environment : bool, optional (default: True)
Plot the environment if the graph is spatial.
fast : bool, optional (default: False)
Use a faster algorithm to plot the edges. This method leads to less
pretty plots and zooming on the graph will make the edges start or
ending in places that will differ more or less strongly from the actual
node positions.
size : tuple of ints, optional (default: (600,600))
(width, height) tuple for the canvas size (in px).
dpi : int, optional (default: 75)
Resolution (dot per inch).
colorbar : bool, optional (default: False)
Whether to display a colorbar for the node colors or not.
show : bool, optional (default: True)
Display the plot immediately.
'''
from matplotlib.cm import get_cmap
from mpl_toolkits.axes_grid1 import make_axes_locatable
import matplotlib.pyplot as plt
# figure and axes
size_inches = (size[0]/float(dpi), size[1]/float(dpi))
if axis is None:
fig = plt.figure(facecolor='white', figsize=size_inches, dpi=dpi)
axis = fig.add_subplot(111, frameon=0, aspect=1)
axis.set_axis_off()
pos, layout = None, None
# restrict sources and targets
if nonstring_container(restrict_sources):
if isinstance(restrict_sources[0], str):
assert network.is_network(), \
"`restrict_sources` canbe string only for Network."
sources = []
for name in restrict_sources:
sources.extend(network.population[name].ids)
restrict_sources = sources
elif isinstance(restrict_sources, str):
assert network.is_network(), \
"`restrict_sources` canbe string only for Network."
restrict_sources = network.population[restrict_sources].ids
if nonstring_container(restrict_targets):
if isinstance(restrict_targets[0], str):
assert network.is_network(), \
"`restrict_targets` canbe string only for Network."
targets = []
for name in restrict_targets:
targets.extend(network.population[name].ids)
restrict_targets = targets
elif isinstance(restrict_targets, str):
assert network.is_network(), \
"`restrict_sources` canbe string only for Network."
restrict_targets = network.population[restrict_targets].ids
# get nodes and edges
n = network.node_nb()
adj_mat = network.adjacency_matrix(weights=None)
if restrict_sources is not None:
adj_mat = adj_mat[restrict_sources, :]
if restrict_targets is not None:
adj_mat = adj_mat[:, restrict_targets]
e = adj_mat.nnz
# compute properties
decimate = 1 if decimate is None else decimate
if isinstance(nsize, str):
if e:
nsize = _node_size(network, nsize)
nsize *= max_nsize
else:
nsize = np.ones(n, dtype=float)
elif isinstance(nsize, (float, int, np.number)):
nsize = np.repeat(nsize, n)
nsize *= 0.01 * size[0]
if isinstance(esize, str) and e:
# @todo check why this "if" is here
if isinstance(ecolor, str):
raise RuntimeError("Cannot use esize='{}' ".format(esize) +\
"and ecolor='{}'.".format(ecolor))
esize = _edge_size(network, esize)
esize *= max_esize
esize[esize < threshold] = 0.
#~ elif isinstance(esize, float):
#~ esize = np.repeat(esize, e)
esize *= 0.005 * size[0] # border on each side (so 0.5 %)
# node color information
ncmap = get_cmap(kwargs.get("node_cmap", palette()))
node_color, nticks, ntickslabels, nlabel = _node_color(network, ncolor)
if nonstring_container(ncolor):
assert len(ncolor) == network.node_nb(), "For color arrays, one " +\
"color per node is required."
ncolor = "custom"
c = node_color
if not nonstring_container(nborder_color):
nborder_color = np.repeat(nborder_color, n)
# check edge color
group_based = False
if isinstance(ecolor, float):
ecolor = np.repeat(ecolor, e)
elif ecolor == "groups" or ecolor == "group":
if not network.is_network():
raise TypeError(
"The graph must be a Network to use `ecolor='groups'`.")
group_based = True
ecolor = {}
for i, src in enumerate(network.population):
if network.population[src].ids:
idx1 = network.population[src].ids[0]
for j, tgt in enumerate(network.population):
if network.population[tgt].ids:
idx2 = network.population[tgt].ids[0]
if src == tgt:
ecolor[(src, tgt)] = node_color[idx1]
else:
ecolor[(src, tgt)] = \
np.abs(0.8*node_color[idx1]
- 0.2*node_color[idx2])
# draw
pos = np.zeros((n, 2))
if spatial and network.is_spatial():
if show_environment:
nngt.geometry.plot.plot_shape(network.shape, axis=axis, show=False)
pos = network.get_positions()
else:
pos[:, 0] = size[0]*(np.random.uniform(size=n)-0.5)
pos[:, 1] = size[1]*(np.random.uniform(size=n)-0.5)
# make nodes
nodes = []
if nonstring_container(c):
# make the colorbar for the nodes
cmap = ncmap
if colorbar:
clist = np.unique(c, axis=0) if ncolor == "group" else None
cnorm = None
if ncolor.startswith("group"):
cmap = _discrete_cmap(len(nticks), ncmap, clist=clist)
cnorm = Normalize(nticks[0]-0.5, nticks[-1] + 0.5)
else:
cnorm = Normalize(np.min(c), np.max(c))
sm = plt.cm.ScalarMappable(cmap=cmap, norm=cnorm)
c = cnorm(c)
if ncolor.startswith("group"):
sm.set_array(nticks)
else:
sm.set_array(c)
plt.subplots_adjust(right=0.95)
divider = make_axes_locatable(axis)
cax = divider.append_axes("right", size="5%", pad=0.05)
if ncolor.startswith("group"):
cb = plt.colorbar(sm, ticks=nticks, cax=cax, shrink=0.8)
cb.set_ticklabels(ntickslabels)
if nlabel:
cb.set_label(nlabel)
else:
cb = plt.colorbar(sm, cax=cax, shrink=0.8)
else:
cmin, cmax = np.min(c), np.max(c)
if cmin != cmax:
c = (c - cmin)/(cmax - cmin)
c = cmap(c)
else:
if not isinstance(c, str):
minc = np.min(node_color)
c = ncmap((node_color - minc)/(np.max(node_color) - minc))
c = np.array([c for _ in range(n)])
if kwargs.get("simple_nodes", False):
axis.scatter(pos[:, 0], pos[:, 1], c=c, s=0.5*np.array(nsize))
if network.is_network():
for group in network.population.values():
idx = group.ids
for i, fc in zip(idx, c[idx]):
nodes.append(
Circle(pos[i], 0.5*nsize[i], fc=fc, ec=nborder_color[i]))
else:
for i, ci in enumerate(c):
nodes.append(
Circle(pos[i], 0.5*nsize[i], fc=ci, ec=nborder_color[i]))
nodes = PatchCollection(nodes, match_original=True)
nodes.set_zorder(2)
axis.add_collection(nodes)
if not show_environment or not spatial or not network.is_spatial():
_set_ax_lim(axis, pos[:, 0], pos[:, 1], xlims, ylims)
# use quiver to draw the edges
if e and decimate != -1:
adj_mat = network.adjacency_matrix(weights=None)
avg_size = np.average(nsize)
arr_style = ArrowStyle.Simple(head_length=0.15*avg_size,
head_width=0.1*avg_size,
tail_width=0.05*avg_size)
arrows = []
if group_based:
for src_name, src_group in network.population.items():
for tgt_name, tgt_group in network.population.items():
s_ids = src_group.ids
if restrict_sources is not None:
s_ids = list(set(restrict_sources).intersection(s_ids))
t_ids = tgt_group.ids
if restrict_targets is not None:
t_ids = list(set(restrict_targets).intersection(t_ids))
if t_ids and s_ids:
s_min, s_max = np.min(s_ids), np.max(s_ids) + 1
t_min, t_max = np.min(t_ids), np.max(t_ids) + 1
edges = np.array(
adj_mat[s_min:s_max, t_min:t_max].nonzero(),
dtype=int)
edges[0, :] += s_min
edges[1, :] += t_min
if nonstring_container(esize):
keep = (esize > 0)
edges = edges[:, keep]
esize = esize[keep]
if decimate > 1:
edges = edges[:, ::decimate]
if nonstring_container(esize):
esize = esize[::decimate]
# plot
ec = palette(ecolor[(src_name, tgt_name)])
if fast:
dl = 0.5*np.max(nsize)
arrow_x = pos[edges[1], 0] - pos[edges[0], 0]
arrow_x -= np.sign(arrow_x) * dl
arrow_y = pos[edges[1], 1] - pos[edges[0], 1]
arrow_x -= np.sign(arrow_y) * dl
axis.quiver(
pos[edges[0], 0], pos[edges[0], 1], arrow_x,
arrow_y, scale_units='xy', angles='xy',
scale=1, alpha=0.5, width=1.5e-3,
linewidths=0.5*esize, edgecolors=ec, zorder=1)
else:
for s, t in zip(edges[0], edges[1]):
xs, ys = pos[s, 0], pos[s, 1]
xt, yt = pos[t, 0], pos[t, 1]
dl = 0.5*nsize[t]
dx = xt-xs
dx -= np.sign(dx) * dl
dy = yt-ys
dy -= np.sign(dy) * dl
if curved_edges:
arrow = FancyArrowPatch(
posA=(xs, ys), posB=(xt, yt),
arrowstyle=arr_style,
connectionstyle='arc3,rad=0.1',
alpha=ealpha, fc=ec, lw=0.5)
axis.add_patch(arrow)
else:
arrows.append(FancyArrow(
xs, ys, dx, dy, width=0.3*avg_size,
head_length=0.7*avg_size,
head_width=0.7*avg_size,
length_includes_head=True,
alpha=ealpha, fc=ec, lw=0.5))
else:
edges = np.array(adj_mat.nonzero(), dtype=int)
s_min, s_max, t_min, t_max = 0, n, 0, n
if restrict_sources is not None:
s_min = np.min(restrict_sources)
s_max = np.min(np.max(restrict_sources) + 1, n)
if restrict_targets is not None:
t_min = np.min(restrict_targets)
t_max = np.min(np.max(restrict_targets) + 1, n)
edges = np.array(
adj_mat[s_min:s_max, t_min:t_max].nonzero(), dtype=int)
edges[0, :] += s_min
edges[1, :] += t_min
# keep only large edges
if nonstring_container(esize):
keep = (esize > 0)
edges = edges[:, keep]
if nonstring_container(ecolor):
ecolor = ecolor[keep]
esize = esize[keep]
if decimate > 1:
edges = edges[:, ::decimate]
if nonstring_container(esize):
esize = esize[::decimate]
if nonstring_container(ecolor):
ecolor = ecolor[::decimate]
if isinstance(ecolor, str):
ecolor = [ecolor for i in range(0, e, decimate)]
if fast:
dl = 0.5*np.max(nsize)
arrow_x = pos[edges[1], 0] - pos[edges[0], 0]
arrow_x -= np.sign(arrow_x) * dl
arrow_y = pos[edges[1], 1] - pos[edges[0], 1]
arrow_x -= np.sign(arrow_y) * dl
axis.quiver(pos[edges[0], 0], pos[edges[0], 1], arrow_x,
arrow_y, scale_units='xy', angles='xy', scale=1,
alpha=0.5, width=1.5e-3, linewidths=0.5*esize,
edgecolors=ecolor, zorder=1)
else:
for i, (s, t) in enumerate(zip(edges[0], edges[1])):
xs, ys = pos[s, 0], pos[s, 1]
xt, yt = pos[t, 0], pos[t, 1]
if curved_edges:
arrow = FancyArrowPatch(
posA=(xs, ys), posB=(xt, yt), arrowstyle=arr_style,
connectionstyle='arc3,rad=0.1',
alpha=ealpha, fc=ecolor[i], lw=0.5)
axis.add_patch(arrow)
else:
dl = 0.5*nsize[t]
dx = xt-xs
dx -= np.sign(dx) * dl
dy = yt-ys
dy -= np.sign(dy) * dl
arrows.append(FancyArrow(
xs, ys, dx, dy, width=0.3*avg_size,
head_length=0.7*avg_size, head_width=0.7*avg_size,
length_includes_head=True, alpha=ealpha,
fc=ecolor[i], lw=0.5))
if not fast:
arrows = PatchCollection(arrows, match_original=True)
arrows.set_zorder(1)
axis.add_collection(arrows)
if kwargs.get('tight', True):
plt.tight_layout()
plt.subplots_adjust(
hspace=0., wspace=0., left=0., right=0.95 if colorbar else 1.,
top=1., bottom=0.)
if show:
plt.show()
#-----------------------------------------------------------------------------#
# Tools
#------------------------
#
def _set_ax_lim(ax, xdata, ydata, xlims, ylims):
if xlims is not None:
ax.set_xlim(*xlims)
else:
x_min, x_max = np.min(xdata), np.max(xdata)
width = x_max - x_min
ax.set_xlim(x_min - 0.05*width, x_max + 0.05*width)
if ylims is not None:
ax.set_ylim(*ylims)
else:
y_min, y_max = np.min(ydata), np.max(ydata)
height = y_max - y_min
ax.set_ylim(y_min - 0.05*height, y_max + 0.05*height)
def _node_size(network, nsize):
size = np.ones(network.node_nb(), dtype=float)
if "degree" in nsize:
deg_type = nsize[:nsize.index("-")]
size = network.get_degrees(deg_type).astype(float)
if np.isclose(size.min(), 0):
size[np.isclose(size, 0)] = 0.5
if size.max() > 15*size.min():
size = np.power(size, 0.4)
elif nsize == "betweenness":
betw = network.betweenness_list("node").astype(float)
if num_wcc(network) == 1:
size *= betw
if size.max() > 15*size.min():
min_size = size[size!=0].min()
size[size == 0.] = min_size
size = np.log(size)
if size.min()<0:
size -= 1.1*size.min()
elif nsize == "clustering":
size *= nngt.analysis.local_clustering(network)
elif nsize in nngt.analyze_graph:
size *= nngt.analyze_graph[nsize](network)
size /= size.max()
return size.astype(float)
def _edge_size(network, esize):
size = np.repeat(1., network.edge_nb())
if esize == "betweenness":
size = network.betweenness_list("edge")
if esize == "weight":
size = network.get_weights()
size /= size.max()
return size
def _node_color(network, ncolor):
'''
Return an array of colors, a set of ticks, and a label for the colorbar
of the nodes (if necessary).
'''
color = ncolor
nticks = None
ntickslabels = None
nlabel = ""
if isinstance(ncolor, np.float):
color = np.repeat(ncolor, network.node_nb())
elif isinstance(ncolor, str):
if ncolor == "group" or ncolor == "groups":
color = np.zeros(network.node_nb())
if hasattr(network, "population"):
l = len(network.population)
c = np.linspace(0, 1, l)
for i, group in enumerate(network.population.values()):
color[group.ids] = c[i]
nlabel = "Neuron groups"
nticks = list(range(len(network.population)))
ntickslabels = [s.replace("_", " ") for s in network.population.keys()]
else:
values = None
if "degree" in ncolor:
dtype = ncolor[:ncolor.find("-")]
values = network.get_degrees(dtype)
elif ncolor == "betweenness":
values = network.get_betweenness("node")
elif ncolor in network.nodes_attributes:
values = network.get_node_attributes(name=ncolor)
elif ncolor == "clustering" :
values = nngt.analysis.local_clustering(network)
elif ncolor in nngt.analyze_graph:
values = nngt.analyze_graph[ncolor](network)
elif ncolor not in cnames and ncolor not in ColorConverter.colors:
raise RuntimeError("Invalid `ncolor`: {}.".format(ncolor))
if values is not None:
vmin, vmax = np.min(values), np.max(values)
#~ color = (values - vmin) / (vmax - vmin)
color = values
nlabel = "Node " + ncolor.replace("_", " ")
setval = set(values)
if len(setval) <= 10:
nticks = list(setval)
nticks.sort()
ntickslabels = nticks
else:
nticks = np.linspace(vmin, vmax, 10)
ntickslabels = nticks
else:
nlabel = "Custom node colors"
uniques = np.unique(ncolor, axis=0)
if len(uniques) <= 10:
nticks = uniques
else:
nticks = np.linspace(np.min(ncolor), np.max(ncolor), 10)
ntickslabels = nticks
return color, nticks, ntickslabels, nlabel
def _discrete_cmap(N, base_cmap=None, clist=None):
'''
Create an N-bin discrete colormap from the specified input map
Parameters
----------
N : number of values
base_cmap : str, None, or cmap object
clist : list of colors
# Modified from Jake VanderPlas
# License: BSD-style
'''
import matplotlib.pyplot as plt
# Note that if base_cmap is a string or None, you can simply do
# return plt.cm.get_cmap(base_cmap, N)
# The following works for string, None, or a colormap instance:
base = plt.cm.get_cmap(base_cmap, N)
color_list = base(np.linspace(0, 1, N)) if clist is None else clist
cmap_name = base.name + str(N)
try:
return base.from_list(cmap_name, color_list, N)
except:
return ListedColormap(color_list, cmap_name, N=N)
def _custom_arrows(sources, targets, angle):
'''
Create a curved arrow between `source` and `target` as the combination of
the arc of a circle and a triangle.
The initial and final angle $\alpha$ between the source-target line and
the arrow is linked to the radius of the circle, $r$ and the distance $d$
between the points:
.. math:: r = \frac{d}{2 \cdot \tan(\alpha)}
The beginning and the end of the arc are given through initial and final
angles, respectively $\theta_1$ and $\theta_2$, which are given with
respect to the y-axis; This leads to $\alpha = 0.5(\theta_1 - \theta_2)$.
'''
# compute the distances between the points
pass
#~ # compute the radius and the position of the center of the circle
#~ #========Line
#~ arc = Arc([centX,centY],radius,radius,angle=angle_,
#~ theta1=0,theta2=theta2_,capstyle='round',linestyle='-',lw=10,color=color_)
#~ ax.add_patch(arc)
#~ #========Create the arrow head
#~ endX=centX+(radius/2)*np.cos(rad(theta2_+angle_)) #Do trig to determine end position
#~ endY=centY+(radius/2)*np.sin(rad(theta2_+angle_))
#~ ax.add_patch( #Create triangle as arrow head
#~ RegularPolygon(
#~ (endX, endY), # (x,y)
#~ 3, # number of vertices
#~ radius/9, # radius
#~ rad(angle_+theta2_), # orientation
#~ color=color_
#~ )
#~ )
