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"""Tools for visualization of time-series data.
Depends on matplotlib. Some functions depend also on networkx
"""
from __future__ import print_function
# If you are running nosetests right now, you might want to use 'agg' as a backend:
import sys
# Then do all the rest of it:
import numpy as np
from scipy import fftpack
import matplotlib as mpl
from matplotlib import pyplot as plt
import matplotlib.ticker as ticker
import matplotlib.colors as colors
from mpl_toolkits.axes_grid1 import make_axes_locatable
from nitime import timeseries as ts
import nitime.utils as tsu
from nitime.utils import threshold_arr, minmax_norm, rescale_arr
import nitime.analysis as nta
# Matplotlib 1.3 has a bug in it, so if that's what you have, we'll replace it
# for you with a fixed version of that module:
import matplotlib
if matplotlib.__version__[:3] == '1.3' or matplotlib.__version__[:3] == '1.4':
import nitime._mpl_units as mpl_units
import matplotlib.axis as ax
ax.munits = mpl_units
from nitime.utils import triu_indices
#Some visualization functions require networkx. Import that if possible:
try:
import networkx as nx
#If not, throw an error and get on with business:
except ImportError:
e_s = "Networkx is not available. Some visualization tools might not work"
e_s += "\n To download networkx: http://networkx.lanl.gov/"
print(e_s)
class NetworkxNotInstalled(object):
def __getattribute__(self, x):
raise ImportError(e_s)
nx = NetworkxNotInstalled()
def plot_tseries(time_series, fig=None, axis=0,
xticks=None, xunits=None, yticks=None, yunits=None,
xlabel=None, ylabel=None, yerror=None, error_alpha=0.1,
time_unit=None, **kwargs):
"""plot a timeseries object
Arguments
---------
time_series: a nitime time-series object
fig: a figure handle, opens a new figure if None
subplot: an axis number (if there are several in the figure to be opened),
defaults to 0.
xticks: optional, list, specificies what values to put xticks on. Defaults
to the matlplotlib-generated.
yticks: optional, list, specificies what values to put xticks on. Defaults
to the matlplotlib-generated.
xlabel: optional, list, specificies what labels to put on xticks
ylabel: optional, list, specificies what labels to put on yticks
yerror: optional, UniformTimeSeries with the same sampling_rate and number
of samples and channels as time_series, the error will be displayed as a
shading above and below the plotted time-series
"""
if fig is None:
fig = plt.figure()
if not fig.get_axes():
ax = fig.add_subplot(1, 1, 1)
else:
ax = fig.get_axes()[axis]
#Make sure that time displays on the x axis with the units you want:
#If you want to change the time-unit on the visualization from that used to
#represent the time-series:
if time_unit is not None:
tu = time_unit
conv_fac = ts.time_unit_conversion[time_unit]
#Otherwise, get the information from your input:
else:
tu = time_series.time_unit
conv_fac = time_series.time._conversion_factor
this_time = time_series.time / float(conv_fac)
ax.plot(this_time, time_series.data.T, **kwargs)
if xlabel is None:
ax.set_xlabel('Time (%s)' % tu)
else:
ax.set_xlabel(xlabel)
if ylabel is not None:
ax.set_ylabel(ylabel)
if yerror is not None:
if len(yerror.data.shape) == 1:
this_e = yerror.data[np.newaxis, :]
else:
this_e = yerror.data
delta = this_e
e_u = time_series.data + delta
e_d = time_series.data - delta
for i in range(e_u.shape[0]):
ax.fill_between(this_time, e_d[i], e_u[i], alpha=error_alpha)
return fig
def matshow_tseries(time_series, fig=None, axis=0, xtick_n=5, time_unit=None,
xlabel=None, ylabel=None):
"""Creates an image of the time-series, ordered according to the first
dimension of the time-series object
Parameters
----------
time_series: a nitime time-series object
fig: a figure handle, opens a new figure if None
axis: an axis number (if there are several in the figure to be opened),
defaults to 0.
xtick_n: int, optional, sets the number of ticks to be placed on the x axis
"""
if fig is None:
fig = plt.figure()
if not fig.get_axes():
ax = fig.add_subplot(1, 1, 1)
else:
ax = fig.get_axes()[axis]
#Make sure that time displays on the x axis with the units you want:
#If you want to change the time-unit on the visualization from that used to
#represent the time-series:
if time_unit is not None:
tu = time_unit
conv_fac = ts.time_unit_conversion[time_unit]
#Otherwise, get the information from your input:
else:
tu = time_series.time_unit
conv_fac = time_series.time._conversion_factor
this_time = time_series.time / float(conv_fac)
ax.matshow(time_series.data)
ax.set_xticks(list(range(len(this_time)))[::len(this_time) / xtick_n])
ax.set_xticklabels(this_time[::len(this_time) / xtick_n])
if xlabel is None:
ax.set_xlabel('Time (%s)' % tu)
else:
ax.set_xlabel(xlabel)
if ylabel is not None:
ax.set_ylabel(ylabel)
return fig
## Helper functions for matshow_roi and for drawgraph_roi, in order to get the
## right cmap for the colorbar:
##Currently not used at all - should they be removed?
def rgb_to_dict(value, cmap):
return dict(zip(('red', 'green', 'blue', 'alpha'), cmap(value)))
def subcolormap(xmin, xmax, cmap):
'''Returns the part of cmap between xmin, xmax, scaled to 0,1.'''
assert xmin < xmax
assert xmax <= 1
cd = cmap._segmentdata.copy()
colornames = ('red', 'green', 'blue')
rgbmin, rgbmax = rgb_to_dict(xmin, cmap), rgb_to_dict(xmax, cmap)
for k in cd:
tmp = [x for x in cd[k] if x[0] >= xmin and x[0] <= xmax]
if tmp == [] or tmp[0][0] > xmin:
tmp = [(xmin, rgbmin[k], rgbmin[k])] + tmp
if tmp == [] or tmp[-1][0] < xmax:
tmp = tmp + [(xmax, rgbmax[k], rgbmax[k])]
#now scale all this to (0,1)
square = list(zip(*tmp))
xbreaks = [(x - xmin) / (xmax - xmin) for x in square[0]]
square[0] = xbreaks
tmp = list(zip(*square))
cd[k] = tmp
return colors.LinearSegmentedColormap('local', cd, N=256)
def drawmatrix_channels(in_m, channel_names=None, fig=None, x_tick_rot=0,
size=None, cmap=plt.cm.RdBu_r, colorbar=True,
color_anchor=None, title=None):
r"""Creates a lower-triangle of the matrix of an nxn set of values. This is
the typical format to show a symmetrical bivariate quantity (such as
correlation or coherence between two different ROIs).
Parameters
----------
in_m: nxn array with values of relationships between two sets of rois or
channels
channel_names (optional): list of strings with the labels to be applied to
the channels in the input. Defaults to '0','1','2', etc.
fig (optional): a matplotlib figure
cmap (optional): a matplotlib colormap to be used for displaying the values
of the connections on the graph
title (optional): string to title the figure (can be like '$\alpha$')
color_anchor (optional): determine the mapping from values to colormap
if None, min and max of colormap correspond to min and max of in_m
if 0, min and max of colormap correspond to max of abs(in_m)
if (a,b), min and max of colormap correspond to (a,b)
Returns
-------
fig: a figure object
"""
N = in_m.shape[0]
ind = np.arange(N) # the evenly spaced plot indices
def channel_formatter(x, pos=None):
thisind = np.clip(int(x), 0, N - 1)
return channel_names[thisind]
if fig is None:
fig = plt.figure()
if size is not None:
fig.set_figwidth(size[0])
fig.set_figheight(size[1])
w = fig.get_figwidth()
h = fig.get_figheight()
ax_im = fig.add_subplot(1, 1, 1)
# If you want to draw the colorbar:
if colorbar:
divider = make_axes_locatable(ax_im)
ax_cb = divider.new_vertical(size="10%", pad=0.1, pack_start=True)
fig.add_axes(ax_cb)
# Make a copy of the input, so that you don't make changes to the original
# data provided
m = in_m.copy()
# Null the upper triangle, so that you don't get the redundant and the
# diagonal values:
idx_null = triu_indices(m.shape[0])
m[idx_null] = np.nan
# Extract the minimum and maximum values for scaling of the
# colormap/colorbar:
max_val = np.nanmax(m)
min_val = np.nanmin(m)
if color_anchor is None:
color_min = min_val
color_max = max_val
elif color_anchor == 0:
bound = max(abs(max_val), abs(min_val))
color_min = -bound
color_max = bound
else:
color_min = color_anchor[0]
color_max = color_anchor[1]
# The call to imshow produces the matrix plot:
im = ax_im.imshow(m, origin='upper', interpolation='nearest',
vmin=color_min, vmax=color_max, cmap=cmap)
# Formatting:
ax = ax_im
ax.grid(True)
# Label each of the cells with the row and the column:
if channel_names is not None:
for i in range(0, m.shape[0]):
if i < (m.shape[0] - 1):
ax.text(i - 0.3, i, channel_names[i], rotation=x_tick_rot)
if i > 0:
ax.text(-1, i + 0.3, channel_names[i],
horizontalalignment='right')
ax.set_axis_off()
ax.set_xticks(np.arange(N))
ax.xaxis.set_major_formatter(ticker.FuncFormatter(channel_formatter))
fig.autofmt_xdate(rotation=x_tick_rot)
ax.set_yticks(np.arange(N))
ax.set_yticklabels(channel_names)
ax.set_ybound([-0.5, N - 0.5])
ax.set_xbound([-0.5, N - 1.5])
# Make the tick-marks invisible:
for line in ax.xaxis.get_ticklines():
line.set_markeredgewidth(0)
for line in ax.yaxis.get_ticklines():
line.set_markeredgewidth(0)
ax.set_axis_off()
if title is not None:
ax.set_title(title)
# The following produces the colorbar and sets the ticks
if colorbar:
# Set the ticks - if 0 is in the interval of values, set that, as well
# as the maximal and minimal values:
if min_val < 0:
ticks = [color_min, min_val, 0, max_val, color_max]
# Otherwise - only set the minimal and maximal value:
else:
ticks = [color_min, min_val, max_val, color_max]
# This makes the colorbar:
cb = fig.colorbar(im, cax=ax_cb, orientation='horizontal',
cmap=cmap,
norm=im.norm,
boundaries=np.linspace(color_min, color_max, 256),
ticks=ticks,
format='%.2f')
# Set the current figure active axis to be the top-one, which is the one
# most likely to be operated on by users later on
fig.sca(ax)
return fig
def drawgraph_channels(in_m, channel_names=None, cmap=plt.cm.RdBu_r,
node_shapes=None, node_colors=None,
title=None, layout=None, threshold=None):
"""Draw a graph based on the matrix specified in in_m. Wrapper to
draw_graph.
Parameters
----------
in_m: nxn array with values of relationships between two sets of channels
or channels
channel_names (optional): list of strings with the labels to be applied to
the channels in the input. Defaults to '0','1','2', etc.
cmap (optional): a matplotlib colormap to be used for displaying the values
of the connections on the graph
node_shapes: defaults to circle
node_colors: defaults to white,
title: str
Sets a title for the figure.
layout, defaults to nx.circular_layout
Returns
-------
fig: a figure object
Notes
-----
The layout of the graph is done using functions from networkx
(http://networkx.lanl.gov), which is a dependency of this function
"""
nnodes = in_m.shape[0]
if channel_names is None:
node_labels = None # [None]*nnodes
else:
node_labels = list(channel_names)
if node_shapes is None:
node_shapes = ['o'] * nnodes
if node_colors is None:
node_colors = ['w'] * nnodes
# Make a copy, avoiding making changes to the original data:
m = in_m.copy()
# Set the diagonal values to the minimal value of the matrix, so that the
# vrange doesn't always get stretched to 1:
m[np.arange(nnodes), np.arange(nnodes)] = min(np.nanmin(m), -np.nanmax(m))
range_setter = max(abs(np.nanmin(m)), abs(np.nanmax(m)))
vrange = [-range_setter, range_setter]
if threshold is None:
#If there happens to be an off-diagnoal edge in the adjacency matrix
#which is just as small as the minimum, we don't want to drop that one:
eps = 10 ** -10
G = mkgraph(m, threshold=vrange[0] - eps, threshold2=None)
else:
G = mkgraph(m, threshold=threshold[0], threshold2=threshold[1])
fig = draw_graph(G,
node_colors=node_colors,
node_shapes=node_shapes,
node_scale=2,
labels=node_labels,
edge_cmap=cmap,
colorbar=True,
vrange=vrange,
title=title,
stretch_factor=1,
edge_alpha=False,
layout=layout
)
return fig
def plot_xcorr(xc, ij, fig=None, line_labels=None, xticks=None, yticks=None,
xlabel=None, ylabel=None):
""" Visualize the cross-correlation function"""
if fig is None:
fig = plt.figure()
if not fig.get_axes():
ax = fig.add_subplot(1, 1, 1)
else:
ax = fig.get_axes()[0]
if line_labels is not None:
#Reverse the order, so that pop() works:
line_labels.reverse()
this_labels = line_labels
#Use the ij input as the labels:
else:
this_labels = [str(this) for this in ij].reverse()
#Make sure that time displays on the x axis with the units you want:
conv_fac = xc.time._conversion_factor
this_time = xc.time / float(conv_fac)
for (i, j) in ij:
if this_labels is not None:
#Use pop() to get the first one and remove it:
ax.plot(this_time, xc.data[i, j].squeeze(),
label=this_labels.pop())
else:
ax.plot(this_time, xc.data[i, j].squeeze())
ax.set_xlabel('Time(sec)')
ax.set_ylabel('Correlation(normalized)')
if xlabel is None:
#Make sure that time displays on the x axis with the units you want:
conv_fac = xc.time._conversion_factor
time_label = xc.time / float(conv_fac)
ax.set_xlabel('Time (%s)' % xc.time_unit)
else:
time_label = xlabel
ax.set_xlabel(xlabel)
if line_labels is not None:
plt.legend()
if ylabel is None:
ax.set_ylabel('Correlation')
else:
ax.set_ylabel(ylabel)
return fig
#-----------------------------------------------------------------------------
# Functions from brainx:
#-----------------------------------------------------------------------------
def draw_matrix(mat, th1=None, th2=None, clim=None, cmap=None):
"""Draw a matrix, optionally thresholding it.
"""
if th1 is not None:
m2 = tsu.thresholded_arr(mat, th1, th2)
else:
m2 = mat
ax = plt.matshow(m2, cmap=cmap)
if clim is not None:
ax.set_clim(*clim)
plt.colorbar()
return ax
def draw_arrows(G, pos, edgelist=None, ax=None, edge_color='k', alpha=1.0,
width=1):
"""Draw arrows on a set of edges"""
if ax is None:
ax = plt.gca()
if edgelist is None:
edgelist = G.edges()
if not edgelist or len(edgelist) == 0: # no edges!
return
# set edge positions
edge_pos = np.asarray([(pos[e[0]], pos[e[1]]) for e in edgelist])
arrow_colors = (colors.colorConverter.to_rgba('k', alpha), )
a_pos = []
# Radius of the nodes in world coordinates
radius = 0.5
head_length = 0.31
overhang = 0.1
#ipvars('edge_pos') # dbg
for src, dst in edge_pos:
dd = dst - src
nd = np.linalg.norm(dd)
if nd == 0: # source and target at same position
continue
s = 1.0 - radius / nd
dd *= s
x1, y1 = src
dx, dy = dd
ax.arrow(x1, y1,
dx, dy,
lw=width, width=width,
head_length=head_length,
fc=edge_color, ec='none',
alpha=alpha, overhang=overhang)
def draw_graph(G,
labels=None,
node_colors=None,
node_shapes=None,
node_scale=1.0,
edge_style='solid',
edge_cmap=None,
colorbar=False,
vrange=None,
layout=None,
title=None,
font_family='sans-serif',
font_size=9,
stretch_factor=1.0,
edge_alpha=True,
fig_size=None):
"""Draw a weighted graph with options to visualize link weights.
The resulting diagram uses the rank of each node as its size, and the
weight of each link (after discarding thresholded values, see below) as the
link opacity.
It maps edge weight to color as well as line opacity and thickness,
allowing the color part to be hardcoded over a value range (to permit valid
cross-figure comparisons for different graphs, so the same color
corresponds to the same link weight even if each graph has a different
range of weights). The nodes sizes are proportional to their degree,
computed as the sum of the weights of all their links. The layout defaults
to circular, but any nx layout function can be passed in, as well as a
statically precomputed layout.
Parameters
----------
G : weighted graph
The values must be of the form (v1,v2), with all v2 in [0,1]. v1 are
used for colors, v2 for thickness/opacity.
labels : list or dict, optional.
An indexable object that maps nodes to strings. If not given, the
string form of each node is used as a label. If False, no labels are
drawn.
node_colors : list or dict, optional.
An indexable object that maps nodes to valid matplotlib color specs. See
matplotlib's plot() function for details.
node_shapes : list or dict, optional.
An indexable object that maps nodes to valid matplotlib shape specs. See
matplotlib's scatter() function for details. If not given, circles are
used.
node_scale : float, optional
A scale factor to globally stretch or shrink all nodes symbols by.
edge_style : string, optional
Line style for the edges, defaults to 'solid'.
edge_cmap : matplotlib colormap, optional.
A callable that returns valid color specs, like matplotlib colormaps.
If not given, edges are colored black.
colorbar : bool
If true, automatically add a colorbar showing the mapping of graph weight
values to colors.
vrange : pair of floats
If given, this indicates the total range of values that the weights can
in principle occupy, and is used to set the lower/upper range of the
colormap. This allows you to set the range of multiple different figures
to the same values, even if each individual graph has range variations,
so that visual color comparisons across figures are valid.
layout : function or layout dict, optional
A NetworkX-like layout function or the result of a precomputed layout for
the given graph. NetworkX produces layouts as dicts keyed by nodes and
with (x,y) pairs of coordinates as values, any function that produces
this kind of output is acceptable. Defaults to nx.circular_layout.
title : string, optional.
If given, title to put on the main plot.
font_family : string, optional.
Font family used for the node labels and title.
font_size : int, optional.
Font size used for the node labels and title.
stretch_factor : float, optional
A global scaling factor to make the graph larger (or smaller if <1).
This can be used to separate the nodes if they start overlapping.
edge_alpha: bool, optional
Whether to weight the transparency of each edge by a factor equivalent to
its relative weight
fig_size: list of height by width, the size of the figure (in
inches). Defaults to [6,6]
Returns
-------
fig
The matplotlib figure object with the plot.
"""
if fig_size is None:
figsize = [6, 6]
scaler = figsize[0] / 6.
# For the size of the node symbols
node_size_base = 1000 * scaler
node_min_size = 200 * scaler
default_node_shape = 'o'
# Default colors if none given
default_node_color = 'r'
default_edge_color = 'k'
# Max edge width
max_width = 13 * scaler
min_width = 2 * scaler
font_family = 'sans-serif'
# We'll use the nodes a lot, let's make a numpy array of them
nodes = np.array(sorted(G.nodes()))
nnod = len(nodes)
# Build a 'weighted degree' array obtained by adding the (absolute value)
# of the weights for all edges pointing to each node:
amat = nx.adj_matrix(G).A # get a normal array out of it
degarr = abs(amat).sum(0) # weights are sums across rows
# Map the degree to the 0-1 range so we can use it for sizing the nodes.
try:
odegree = rescale_arr(degarr, 0, 1)
# Make an array of node sizes based on node degree
node_sizes = odegree * node_size_base + node_min_size
except ZeroDivisionError:
# All nodes same size
node_sizes = np.empty(nnod, float)
node_sizes.fill(0.5 * node_size_base + node_min_size)
# Adjust node size list. We square the scale factor because in mpl, node
# sizes represent area, not linear size, but it's more intuitive for the
# user to think of linear factors (the overall figure scale factor is also
# linear).
node_sizes *= node_scale ** 2
# Set default node properties
if node_colors is None:
node_colors = [default_node_color] * nnod
if node_shapes is None:
node_shapes = [default_node_shape] * nnod
# Set default edge colormap
if edge_cmap is None:
# Make an object with the colormap API, that maps all input values to
# the default color (with proper alhpa)
edge_cmap = (lambda val, alpha:
colors.colorConverter.to_rgba(default_edge_color, alpha))
# if vrange is None, we set the color range from the values, else the user
# can specify it
# e[2] is edge value: edges_iter returns (i,j,data)
gvals = np.array([e[2]['weight'] for e in G.edges(data=True)])
gvmin, gvmax = gvals.min(), gvals.max()
gvrange = gvmax - gvmin
if vrange is None:
vrange = gvmin, gvmax
# Now, construct the normalization for the colormap
cnorm = mpl.colors.Normalize(vmin=vrange[0], vmax=vrange[1])
# Create the actual plot where the graph will be displayed
figsize = np.array(figsize, float)
figsize *= stretch_factor
fig = plt.figure(figsize=figsize)
ax_graph = fig.add_subplot(1, 1, 1)
fig.sca(ax_graph)
if layout is None:
layout = nx.circular_layout
# Compute positions for all nodes - nx has several algorithms
if callable(layout):
pos = layout(G)
else:
# The user can also provide a precomputed layout
pos = layout
# Draw nodes
for nod in nodes:
nx.draw_networkx_nodes(G,
pos,
nodelist=[nod],
node_color=node_colors[nod],
node_shape=node_shapes[nod],
node_size=node_sizes[nod],
edgecolors='k')
# Draw edges
if not isinstance(G, nx.DiGraph):
# Undirected graph, simple lines for edges
# We need the size of the value range to properly scale colors
vsize = vrange[1] - vrange[0]
gvals_normalized = G.metadata['vals_norm']
for (u, v, y) in G.edges(data=True):
# The graph value is the weight, and the normalized values are in
# [0,1], used for thickness/transparency
alpha = gvals_normalized[u, v]
# Scale the color choice to the specified vrange, so that
ecol = (y['weight'] - vrange[0]) / vsize
#print 'u,v:',u,v,'y:',y,'ecol:',ecol # dbg
if edge_alpha:
fade = alpha
else:
fade = 1.0
edge_color = [tuple(edge_cmap(ecol, fade))]
#dbg:
#print u,v,y
nx.draw_networkx_edges(G,
pos,
edgelist=[(u, v)],
width=min_width + alpha * max_width,
edge_color=edge_color,
style=edge_style)
else:
# Directed graph, use arrows.
# XXX - this is currently broken.
raise NotImplementedError("arrow drawing currently broken")
## for (u,v,x) in G.edges(data=True):
## y,w = x
## draw_arrows(G,pos,edgelist=[(u,v)],
## edge_color=[w],
## alpha=w,
## edge_cmap=edge_cmap,
## width=w*max_width)
# Draw labels. If not given, we use the string form of the nodes. If
# labels is False, no labels are drawn.
if labels is None:
labels = map(str, nodes)
if labels:
lab_idx = list(range(len(labels)))
labels_dict = dict(zip(lab_idx, labels))
nx.draw_networkx_labels(G,
pos,
labels_dict,
font_size=font_size,
font_family=font_family)
if title:
plt.title(title, fontsize=font_size)
# Turn off x and y axes labels in pylab
plt.xticks([])
plt.yticks([])
# Add a colorbar if requested
if colorbar:
divider = make_axes_locatable(ax_graph)
ax_cb = divider.new_vertical(size="20%", pad=0.2, pack_start=True)
fig.add_axes(ax_cb)
cb = mpl.colorbar.ColorbarBase(ax_cb,
cmap=edge_cmap,
norm=cnorm,
#boundaries = np.linspace(min((gvmin,0)),
# max((gvmax,0)),
# 256),
orientation='horizontal',
format='%.2f')
# Always return the MPL figure object so the user can further manipulate it
return fig
def lab2node(labels, labels_dict):
return [labels_dict[ll] for ll in labels]
def mkgraph(cmat, threshold=0.0, threshold2=None):
"""Make a weighted graph object out of an adjacency matrix.
The values in the original matrix cmat can be thresholded out. If only one
threshold is given, all values below that are omitted when creating edges.
If two thresholds are given, then values in the th2-th1 range are
omitted. This allows for the easy creation of weighted graphs with
positive and negative values where a range of weights around 0 is omitted.
Parameters
----------
cmat : 2-d square array
Adjacency matrix.
threshold : float
First threshold.
threshold2 : float
Second threshold.
Returns
-------
G : a NetworkX weighted graph object, to which a dictionary called
G.metadata is appended. This dict contains the original adjacency matrix
cmat, the two thresholds, and the weights
"""
# Input sanity check
nrow, ncol = cmat.shape
if nrow != ncol:
raise ValueError("Adjacency matrix must be square")
row_idx, col_idx, vals = threshold_arr(cmat, threshold, threshold2)
# Also make the full thresholded array available in the metadata
cmat_th = np.empty_like(cmat)
if threshold2 is None:
cmat_th.fill(threshold)
else:
cmat_th.fill(-np.inf)
cmat_th[row_idx, col_idx] = vals
# Next, make a normalized copy of the values. For the 2-threshold case, we
# use 'folding' normalization
if threshold2 is None:
vals_norm = minmax_norm(vals)
else:
vals_norm = minmax_norm(vals, 'folding', [threshold, threshold2])
# Now make the actual graph
G = nx.Graph(weighted=True)
G.add_nodes_from(list(range(nrow)))
# To keep the weights of the graph to simple values, we store the
# normalize ones in a separate dict that we'll stuff into the graph
# metadata.
normed_values = {}
for i, j, val, nval in zip(row_idx, col_idx, vals, vals_norm):
if i == j:
# no self-loops
continue
G.add_edge(i, j, weight=val)
normed_values[i, j] = nval
# Write a metadata dict into the graph and save the threshold info there
G.metadata = dict(threshold1=threshold,
threshold2=threshold2,
cmat_raw=cmat,
cmat_th=cmat_th,
vals_norm=normed_values,
)
return G
def plot_snr(tseries, lb=0, ub=None, fig=None):
"""
Show the coherence, snr and information of an SNRAnalyzer
Parameters
----------
tseries: nitime TimeSeries object
Multi-trial data in response to one stimulus/protocol with the dims:
(n_channels,n_repetitions,time)
lb,ub: float
Lower and upper bounds on the frequency range over which to
calculate (default to [0,Nyquist]).
Returns
-------
A tuple containing:
fig: a matplotlib figure object
This figure displays:
1. Coherence
2. SNR
3. Information
"""
if fig is None:
fig = plt.figure()
ax_spectra = fig.add_subplot(1, 2, 1)
ax_snr_info = fig.add_subplot(1, 2, 2)
A = []
info = []
s_n_r = []
coh = []
noise_spectra = []
signal_spectra = []
#If you only have one channel, make sure that everything still works by
#adding an axis
if len(tseries.data.shape) < 3:
this = tseries.data[np.newaxis, :, :]
else:
this = tseries.data
for i in range(this.shape[0]):
A.append(nta.SNRAnalyzer(ts.TimeSeries(this[i],
sampling_rate=tseries.sampling_rate)))
info.append(A[-1].mt_information)
s_n_r.append(A[-1].mt_snr)
coh.append(A[-1].mt_coherence)
noise_spectra.append(A[-1].mt_noise_psd)
signal_spectra.append(A[-1].mt_signal_psd)
freqs = A[-1].mt_frequencies
lb_idx, ub_idx = tsu.get_bounds(freqs, lb, ub)
freqs = freqs[lb_idx:ub_idx]
coh_mean = np.mean(coh, 0)
snr_mean = np.mean(s_n_r, 0)
info_mean = np.mean(info, 0)
n_spec_mean = np.mean(noise_spectra, 0)
s_spec_mean = np.mean(signal_spectra, 0)
ax_spectra.plot(freqs, np.log(s_spec_mean[lb_idx:ub_idx]), label='Signal')
ax_spectra.plot(freqs, np.log(n_spec_mean[lb_idx:ub_idx]), label='Noise')
ax_spectra.set_xlabel('Frequency (Hz)')
ax_spectra.set_ylabel('Spectral power (dB)')
ax_snr_info.plot(freqs, snr_mean[lb_idx:ub_idx], label='SNR')
ax_snr_info.plot(np.nan, np.nan, 'r', label='Info')
ax_snr_info.set_ylabel('SNR')
ax_snr_info.set_xlabel('Frequency (Hz)')
ax_info = ax_snr_info.twinx()
ax_info.plot(freqs, np.cumsum(info_mean[lb_idx:ub_idx]), 'r')
ax_info.set_ylabel('Cumulative information rate (bits/sec)')
return fig
def plot_snr_diff(tseries1, tseries2, lb=0, ub=None, fig=None,
ts_names=['1', '2'],
bandwidth=None, adaptive=False, low_bias=True):
"""
Show distributions of differences between two time-series in the
amount of snr (freq band by freq band) and information. For example,
for comparing two stimulus conditions
Parameters
----------
tseries1, tseries2 : nitime TimeSeries objects
These are the time-series to compare, with each of them having the
dims: (n_channels, n_reps, time), where n_channels1 = n_channels2
lb,ub: float
Lower and upper bounds on the frequency range over which to
calculate the information rate (default to [0,Nyquist]).
fig: matplotlib figure object
If you want to do this on already existing figure. Otherwise, a new
figure object will be generated.
ts_names: list of str
Labels for the two inputs, to be used in plotting (defaults to
['1','2'])
bandwidth, adaptive, low_bias: See :func:`nta.SNRAnalyzer` for details
Returns
-------
A tuple containing:
fig: a matplotlib figure object
This figure displays:
1. The histogram of the information differences between the two
time-series
2. The frequency-dependent SNR for the two time-series
info1, info2: float arrays
The frequency-dependent information rates (in bits/sec)
s_n_r1, s_n_r2: float arrays
The frequncy-dependent signal-to-noise ratios
"""
if fig is None:
fig = plt.figure()
ax_scatter = fig.add_subplot(1, 2, 1)
ax_snr = fig.add_subplot(1, 2, 2)
SNR1 = []
s_n_r1 = []
info1 = []
SNR2 = []
info2 = []
s_n_r2 = []
#If you only have one channel, make sure that everything still works by
#adding an axis
if len(tseries1.data.shape) < 3:
this1 = tseries1.data[np.newaxis, :, :]
this2 = tseries2.data[np.newaxis, :, :]
else:
this1 = tseries1.data
this2 = tseries2.data
for i in range(this1.shape[0]):
SNR1.append(nta.SNRAnalyzer(ts.TimeSeries(this1[i],
sampling_rate=tseries1.sampling_rate),
bandwidth=bandwidth,
adaptive=adaptive,
low_bias=low_bias))
info1.append(SNR1[-1].mt_information)
s_n_r1.append(SNR1[-1].mt_snr)
SNR2.append(nta.SNRAnalyzer(ts.TimeSeries(this2[i],
sampling_rate=tseries2.sampling_rate),
bandwidth=bandwidth,
adaptive=adaptive,
low_bias=low_bias))
info2.append(SNR2[-1].mt_information)
s_n_r2.append(SNR2[-1].mt_snr)
freqs = SNR1[-1].mt_frequencies
lb_idx, ub_idx = tsu.get_bounds(freqs, lb, ub)
freqs = freqs[lb_idx:ub_idx]
info1 = np.array(info1)
info_sum1 = np.sum(info1[:, lb_idx:ub_idx], -1)
info2 = np.array(info2)
info_sum2 = np.sum(info2[:, lb_idx:ub_idx], -1)
ax_scatter.scatter(info_sum1, info_sum2)
ax_scatter.errorbar(np.mean(info_sum1), np.mean(info_sum2),
yerr=np.std(info_sum2),
xerr=np.std(info_sum1))
plot_min = min(min(info_sum1), min(info_sum2))
plot_max = max(max(info_sum1), max(info_sum2))
ax_scatter.plot([plot_min, plot_max], [plot_min, plot_max], 'k--')
ax_scatter.set_xlabel('Information %s (bits/sec)' % ts_names[0])
ax_scatter.set_ylabel('Information %s (bits/sec)' % ts_names[1])
snr_mean1 = np.mean(s_n_r1, 0)
snr_mean2 = np.mean(s_n_r2, 0)
ax_snr.plot(freqs, snr_mean1[lb_idx:ub_idx], label=ts_names[0])
ax_snr.plot(freqs, snr_mean2[lb_idx:ub_idx], label=ts_names[1])
ax_snr.legend()
ax_snr.set_xlabel('Frequency (Hz)')
ax_snr.set_ylabel('SNR')
return fig, info1, info2, s_n_r1, s_n_r2
def plot_corr_diff(tseries1, tseries2, fig=None,
ts_names=['1', '2']):
"""
Show the differences in *Fischer-transformed* snr correlations for two
time-series
Parameters
----------
tseries1, tseries2 : nitime TimeSeries objects
These are the time-series to compare, with each of them having the
dims: (n_channels, n_reps, time), where n_channels1 = n_channels2
lb,ub: float
Lower and upper bounds on the frequency range over which to
calculate the information rate (default to [0,Nyquist]).
fig: matplotlib figure object
If you want to do this on already existing figure. Otherwise, a new
figure object will be generated.
ts_names: list of str
Labels for the two inputs, to be used in plotting (defaults to
['1','2'])
bandwidth, adaptive, low_bias: See :func:`SNRAnalyzer` for details
Returns
-------
fig: a matplotlib figure object
"""
if fig is None:
fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)
SNR1 = []
SNR2 = []
corr1 = []
corr2 = []
corr_e1 = []
corr_e2 = []
for i in range(tseries1.shape[0]):
SNR1.append(nta.SNRAnalyzer(ts.TimeSeries(tseries1.data[i],
sampling_rate=tseries1.sampling_rate)))
corr1.append(np.arctanh(np.abs(SNR1[-1].correlation[0])))
corr_e1.append(SNR1[-1].correlation[1])
SNR2.append(nta.SNRAnalyzer(ts.TimeSeries(tseries2.data[i],
sampling_rate=tseries2.sampling_rate)))
corr2.append(np.arctanh(np.abs(SNR2[-1].correlation[0])))
corr_e2.append(SNR1[-1].correlation[1])
ax.scatter(np.array(corr1), np.array(corr2))
ax.errorbar(np.mean(corr1), np.mean(corr2),
yerr=np.std(corr2),
xerr=np.std(corr1))
plot_min = min(min(corr1), min(corr2))
plot_max = max(max(corr1), max(corr2))
ax.plot([plot_min, plot_max], [plot_min, plot_max], 'k--')
ax.set_xlabel('Correlation (Fischer Z) %s' % ts_names[0])
ax.set_ylabel('Correlation (Fischer Z) %s' % ts_names[1])
return fig, corr1, corr2
def winspect(win, f, name=None):
"""
Inspect a window by showing it and its spectrum
Utility file used in building the documentation
"""
npts = len(win)
ax1, ax2 = f.add_subplot(1, 2, 1), f.add_subplot(1, 2, 2)
ax1.plot(win)
ax1.set_xlabel('Time')
ax1.set_ylabel('Window amplitude')
ax1.set_ylim(-0.1, 1.1)
ax1.set_xlim(0, npts)
wf = fftpack.fft(win)
ax1.set_xticks(np.arange(npts / 8., npts, npts / 8.))
toplot = np.abs(fftpack.fftshift(wf).real)
toplot /= np.max(toplot)
toplot = np.log(toplot)
ax2.plot(toplot, label=name)
ax2.set_xlim(0, npts)
ax2.set_xticks(np.arange(npts / 8., npts, npts / 8.))
ax2.set_xticklabels(np.arange((-1 / 2. + 1 / 8.), 1 / 2., 1 / 8.))
ax2.set_xlabel('Relative frequency')
ax2.set_ylabel('Relative attenuation (log scale)')
ax2.grid()
ax2.legend(loc=4)
f.set_size_inches([10, 6])
def plot_spectral_estimate(f, sdf, sdf_ests, limits=None, elabels=()):
"""
Plot an estimate of a spectral transform against the ground truth.
Utility file used in building the documentation
"""
fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)
ax_limits = (sdf.min() - 2*np.abs(sdf.min()),
sdf.max() + 1.25*np.abs(sdf.max()))
ax.plot(f, sdf, 'c', label='True S(f)')
if not elabels:
elabels = ('',) * len(sdf_ests)
colors = 'bgkmy'
for e, l, c in zip(sdf_ests, elabels, colors):
ax.plot(f, e, color=c, linewidth=2, label=l)
if limits is not None:
ax.fill_between(f, limits[0], y2=limits[1], color=(1, 0, 0, .3),
alpha=0.5)
ax.set_ylim(ax_limits)
ax.legend()
return fig
# Patch in a fix to networkx's draw_networkx_nodes
# This function is broken in version 1.11, and the fix is a one-line change:
# and is the addition of the `**kwds` into the call to `ax.scatter` below.
# Without this addition, `scatter` defaults to plot the points with the edge
# color set to be the same as the face color, which caused our issue #153
def draw_networkx_nodes(G, pos,
nodelist=None,
node_size=300,
node_color='r',
node_shape='o',
alpha=1.0,
cmap=None,
vmin=None,
vmax=None,
ax=None,
linewidths=None,
label=None,
**kwds):
"""Draw the nodes of the graph G.
This draws only the nodes of the graph G.
Parameters
----------
G : graph
A networkx graph
pos : dictionary
A dictionary with nodes as keys and positions as values.
Positions should be sequences of length 2.
ax : Matplotlib Axes object, optional
Draw the graph in the specified Matplotlib axes.
nodelist : list, optional
Draw only specified nodes (default G.nodes())
node_size : scalar or array
Size of nodes (default=300). If an array is specified it must be the
same length as nodelist.
node_color : color string, or array of floats
Node color. Can be a single color format string (default='r'),
or a sequence of colors with the same length as nodelist.
If numeric values are specified they will be mapped to
colors using the cmap and vmin,vmax parameters. See
matplotlib.scatter for more details.
node_shape : string
The shape of the node. Specification is as matplotlib.scatter
marker, one of 'so^>v<dph8' (default='o').
alpha : float
The node transparency (default=1.0)
cmap : Matplotlib colormap
Colormap for mapping intensities of nodes (default=None)
vmin,vmax : floats
Minimum and maximum for node colormap scaling (default=None)
linewidths : [None | scalar | sequence]
Line width of symbol border (default =1.0)
label : [None| string]
Label for legend
Returns
-------
matplotlib.collections.PathCollection
`PathCollection` of the nodes.
Examples
--------
>>> G=nx.dodecahedral_graph()
>>> nodes=nx.draw_networkx_nodes(G,pos=nx.spring_layout(G))
Also see the NetworkX drawing examples at
http://networkx.github.io/documentation/latest/gallery.html
See Also
--------
draw()
draw_networkx()
draw_networkx_edges()
draw_networkx_labels()
draw_networkx_edge_labels()
"""
try:
import matplotlib.pyplot as plt
import numpy
except ImportError:
raise ImportError("Matplotlib required for draw()")
except RuntimeError:
print("Matplotlib unable to open display")
raise
if ax is None:
ax = plt.gca()
if nodelist is None:
nodelist = G.nodes()
if not nodelist or len(nodelist) == 0: # empty nodelist, no drawing
return None
try:
xy = numpy.asarray([pos[v] for v in nodelist])
except KeyError as e:
raise nx.NetworkXError('Node %s has no position.'%e)
except ValueError:
raise nx.NetworkXError('Bad value in node positions.')
node_collection = ax.scatter(xy[:, 0], xy[:, 1],
s=node_size,
c=node_color,
marker=node_shape,
cmap=cmap,
vmin=vmin,
vmax=vmax,
alpha=alpha,
linewidths=linewidths,
label=label,
**kwds)
node_collection.set_zorder(2)
return node_collection
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