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My2Ddist.py
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import pylab
import numpy
from numpy import argwhere, zeros, hstack, append
import matplotlib.patches
from mpl_toolkits.axes_grid1 import make_axes_locatable
import scipy.stats
import matplotlib as mpl
def fracs_inside_contours(x, y, contours):
"""
Calculate the fraction of points x,y inside each contour level.
"""
fracs = []
xy = numpy.vstack([x,y]).transpose()
for (icollection, collection) in enumerate(contours.collections):
path = collection.get_paths()[0]
frac = float(sum(path.contains_points(xy)))/len(x)
fracs.append(frac)
return fracs
def frac_label_contours(x, y, contours, format='%.2f'):
"""
Label contours according to the fraction of points x,y inside.
"""
fracs = fracs_inside_contours(x,y,contours)
levels = contours.levels
labels = {}
for (level, frac) in zip(levels, fracs):
labels[level] = format % frac
contours.clabel(fmt=labels)
def contour_enclosing(x, y, fractions, xgrid, ygrid, zvals,
axes, nstart = 200,
*args, **kwargs):
"""
Plot contours encompassing specified fractions of points x,y.
"""
# Generate a large set of contours initially.
contours = axes.contour(xgrid, ygrid, zvals, nstart,extend='both')
# Set up fracs and levs for interpolation.
levs = contours.levels
fracs = numpy.array(fracs_inside_contours(x,y,contours))
sortinds = numpy.argsort(fracs)
levs = levs[sortinds]
fracs = fracs[sortinds]
# Find the levels that give the specified fractions.
levels = scipy.interp(fractions, fracs, levs)
# Remove the old contours from the graph.
for coll in contours.collections:
coll.remove()
# Reset the contours
contours.__init__(axes, xgrid, ygrid, zvals, levels, *args, **kwargs)
return contours
def invert_boxcox(z,lam):
return (1+z*lam)**(1.0/lam)
def plot2Ddist(variables,axeslist=None,maxvalues=None,histbinslist=[100, 100],
labels=[r'$l$',r'$\sigma_f$'],scaleview=True,plotscatter=True,
plothists=True,plotcontours=True,contourNGrid=200,bcx=True,
contourFractions=[0.68, 0.95],labelcontours=True):
"""
Plot contours of 2D distribution with marginal histograms:
Input:
variables = 2d array with samples
axes = optional pass axes to add plots to
maxvalues = values of hypers that maximise marginal posterior
histbinlist = number of bins to use for the histogram
labels = optional x and y axis labels
scaleview = optional argument determines whether to set the axes limits according to the plotted data
plotscatter, plothists, plotcontours = optional bool whether to plot the scatter, marginal histograms, and contours
contourNGrid = int number of grid points to evaluate kde on
contourFractions = optional % levels for contours
labelcontours = bool whether to label the contours with the fraction of points enclosed
"""
### Set up figures and axes. ###
if axeslist is None:
fig1 = pylab.figure(figsize=(8,8))
fig1.set_label('traces')
ax1 = pylab.gca()
divider = make_axes_locatable(ax1)
ax2 = divider.append_axes("top", 1.5, pad=0.0, sharex=ax1)
ax3 = divider.append_axes("right", 1.5, pad=0.0, sharey=ax1)
for tl in (ax2.get_xticklabels() + ax2.get_yticklabels() + ax3.get_xticklabels() + ax3.get_yticklabels()):
tl.set_visible(False)
axeslist = (ax1, ax2, ax3)
else:
ax1, ax2, ax3 = axeslist
#Do box-cox transform on data
if bcx:
x, mx = scipy.stats.boxcox(variables[0])
y, my = scipy.stats.boxcox(variables[1])
else:
x = variables[0]
y = variables[1]
### Plot the variables. ###
# Plot 2D scatter of variables.
if plotscatter:
ax1.plot(x, y,ls='',marker=',',color='r',alpha=0.15)
#Here we use kde to plot contours, might be better to use smoothing splines
if plotcontours:
style = {'linewidths':2.0, 'alpha':0.75,'zorder':10,'color':'k'}
gkde = scipy.stats.gaussian_kde([x,y])
xgrid, ygrid = numpy.mgrid[min(x):max(x):contourNGrid * 1j,min(y):max(y):contourNGrid * 1j]
zvals = numpy.array(gkde.evaluate([xgrid.flatten(),ygrid.flatten()])).reshape(xgrid.shape)
contours = contour_enclosing(x, y, contourFractions,xgrid, ygrid, zvals,ax1, **style)
# Plot marginal histograms.
if plothists:
style = {'histtype':'step', 'normed':True, 'color':'k'}
ax2.hist(x, histbinslist[0], **style)
ax3.hist(y, histbinslist[1], orientation='horizontal', **style)
# Plot lines to indicate max values.
if maxvalues is not None:
ax1.axvline(x=maxvalues[0], ls=':', c='k')
ax1.axhline(y=maxvalues[1], ls=':', c='k')
ax2.axvline(x=maxvalues[0], ls=':', c='k')
ax3.axhline(y=maxvalues[1], ls=':', c='k')
if scaleview:
ax2.relim()
ax3.relim()
ax1.relim()
ax2.autoscale_view(tight=True)
ax3.autoscale_view(tight=True)
ax1.autoscale_view(tight=True)
ax2.set_ylim(bottom=0)
ax3.set_xlim(left=0)
#Set labels
ax1.set_xlabel(labels[0],fontsize=35)
ax1.set_ylabel(labels[1],fontsize=35)
if plotcontours and labelcontours:
frac_label_contours(x, y, contours)
return fig1
def plot2Ddist2(x,y,ax1,contourNGrid=200,contourFractions=[0.68, 0.95],mode1='x',mode2='y',colour='blue',alp=0.5):
"""
Plot contours of 2D distribution
"""
# Plot 2D scatter of variables.
#ax1.plot(x, y,ls='',marker=',',color='r',alpha=0.15)
#Here we use kde to plot contours, might be better to use smoothing splines
style = {'linewidths':1.0, 'alpha':0.0,'zorder':10,'color':'k'}
gkde = scipy.stats.gaussian_kde([x,y])
# bw = gkde.covariance_factor()
# gkde = scipy.stats.gaussian_kde([x,y],bw_method=bw/10.0)
xgrid, ygrid = numpy.mgrid[min(x):max(x):contourNGrid * 1j,min(y):max(y):contourNGrid * 1j]
zvals = numpy.array(gkde.evaluate([xgrid.flatten(),ygrid.flatten()])).reshape(xgrid.shape)
contours = contour_enclosing(x, y, contourFractions,xgrid, ygrid, zvals,ax1, **style)
p1 = contours.collections[1].get_paths()[0]
v1 = p1.vertices
p2 = contours.collections[0].get_paths()[0]
v2 = p2.vertices
if (mode1 == 'fill'):
t1 = v1[-1,0]
v10 = v1[:,0]
q1 = argwhere(v10 < t1)
l1 = q1.size
v10app = v10[q1]
z1 = zeros([l1,1])
v11app = hstack((z1,v10app))
v1 = append(v1,v11app,axis=0)
if (mode2=='fill'):
t2 = v2[-1,0]
v20 = v2[:,0]
q2 = argwhere(v20 < t2)
l2 = q2.size
v20app = v20[q2]
z2 = zeros([l2,1])
v21app = hstack((z2,v20app))
v2 = append(v2,v21app,axis=0)
ax1.fill(v1[:,0],v1[:,1],colour,alpha=alp)
#ax1.fill(v2[:,0],v2[:,1],colour,alpha=0.5)
#Label the contours
#frac_label_contours(x, y, contours)
#ax1.fill()
# ax1.relim()
#ax1.autoscale_view(True,True,True)
return contours