"""
MCMC plotting methods.
"""
from __future__ import division, print_function
__all__ = ['plot_all', 'plot_corr', 'plot_corrmatrix',
'plot_trace', 'plot_logp', 'format_vars']
import math
import numpy as np
from numpy import arange, squeeze, linspace, meshgrid, vstack, inf
from scipy.stats import gaussian_kde
from . import corrplot
from . import varplot
from .formatnum import format_value
from .stats import var_stats, format_vars, save_vars
[docs]
def plot_all(state, portion=1.0, figfile=None):
# Print/save uncertainty report before loading pylab or creating plots
draw = state.draw(portion=portion)
all_vstats = var_stats(draw)
print(format_vars(all_vstats))
print("\nStatistics and plots based on {nsamp:d} samples "
"({psamp:.1%} of total samples drawn)".format( \
nsamp=len(draw.points), psamp=portion))
if figfile is not None:
save_vars(all_vstats, figfile+"-err.json")
from pylab import figure, savefig, suptitle, rcParams
figext = '.'+rcParams.get('savefig.format', 'png')
# Use finer binning with more samples. For 1% bin variation p,
# points per bin k = (100/p)**2 = 10000, and nbins = N // k.
nbins = max(min(draw.points.shape[0]//10000, 400), 30)
# histograms
figure(figsize=varplot.var_plot_size(len(all_vstats)))
varplot.plot_vars(draw, all_vstats, nbins=nbins)
if state.title:
suptitle(state.title, x=0, y=1, va='top', ha='left')
if figfile is not None:
savefig(figfile+"-vars"+figext)
# parameter traces
figure()
plot_traces(state, portion=portion)
suptitle("Parameter history" + (" for " + state.title if state.title else ""))
if figfile is not None:
savefig(figfile+"-trace"+figext)
# Acceptance rate
if False:
figure()
plot_acceptance_rate(state, portion=portion)
if figfile is not None:
savefig(figfile+"-acceptance"+figext)
# convergence plot
figure()
plot_logp(state, portion=portion)
if state.title:
suptitle(state.title)
if figfile is not None:
savefig(figfile+"-logp"+figext)
# correlation plot
if draw.num_vars <= 25:
figure()
plot_corrmatrix(draw, nbins=nbins)
if state.title:
suptitle(state.title)
if figfile is not None:
savefig(figfile+"-corr"+figext)
# parallel coordinates plot
if draw.num_vars > 1:
from . import parcoord
figure()
parcoord.plot(draw, control_var=0)
if state.title:
suptitle(state.title)
if figfile is not None:
savefig(figfile+"-parcor"+figext)
[docs]
def plot_corrmatrix(draw, nbins=50):
c = corrplot.Corr2d(draw.points.T, bins=nbins, labels=draw.labels)
c.plot()
#print "Correlation matrix\n",c.R()
class KDE1D(gaussian_kde):
covariance_factor = lambda self: 2*self.silverman_factor()
class KDE2D(gaussian_kde):
covariance_factor = gaussian_kde.silverman_factor
def __init__(self, dataset):
gaussian_kde.__init__(self, dataset.T)
def evalxy(self, x, y):
grid_x, grid_y = meshgrid(x, y)
dxy = self.evaluate(vstack([grid_x.flatten(), grid_y.flatten()]))
return dxy.reshape(grid_x.shape)
__call__ = evalxy
[docs]
def plot_corr(draw, vars=(0, 1)):
from pylab import axes, setp, MaxNLocator
_, _ = vars # Make sure vars is length 2
labels = [draw.labels[v] for v in vars]
values = [draw.points[:, v] for v in vars]
# Form kernel density estimates of the parameters
xmin, xmax = min(values[0]), max(values[0])
density_x = KDE1D(values[0])
x = linspace(xmin, xmax, 100)
px = density_x(x)
density_y = KDE1D(values[1])
ymin, ymax = min(values[1]), max(values[1])
y = linspace(ymin, ymax, 100)
py = density_y(y)
nbins = 50
ax_data = axes([0.1, 0.1, 0.63, 0.63]) # x,y,w,h
#density_xy = KDE2D(values[vars])
#dxy = density_xy(x,y)*points.shape[0]
#ax_data.pcolorfast(x,y,dxy,cmap=cm.gist_earth_r) #@UndefinedVariable
ax_data.plot(values[0], values[1], 'k.', markersize=1)
ax_data.set_xlabel(labels[0])
ax_data.set_ylabel(labels[1])
ax_hist_x = axes([0.1, 0.75, 0.63, 0.2], sharex=ax_data)
ax_hist_x.hist(values[0], nbins, orientation='vertical', density=1)
ax_hist_x.plot(x, px, 'k-')
ax_hist_x.yaxis.set_major_locator(MaxNLocator(4, prune="both"))
setp(ax_hist_x.get_xticklabels(), visible=False,)
ax_hist_y = axes([0.75, 0.1, 0.2, 0.63], sharey=ax_data)
ax_hist_y.hist(values[1], nbins, orientation='horizontal', density=1)
ax_hist_y.plot(py, y, 'k-')
ax_hist_y.xaxis.set_major_locator(MaxNLocator(4, prune="both"))
setp(ax_hist_y.get_yticklabels(), visible=False)
def plot_traces(state, vars=None, portion=None):
from pylab import subplot, clf, subplots_adjust
if vars is None:
vars = list(range(min(state.Nvar, 6)))
clf()
nw, nh = tile_axes(len(vars))
subplots_adjust(hspace=0.0)
for k, var in enumerate(vars):
subplot(nw, nh, k+1)
plot_trace(state, var, portion)
[docs]
def plot_trace(state, var=0, portion=None):
from pylab import plot, title, xlabel, ylabel
draw, points, _ = state.chains()
label = state.labels[var]
start = int((1-portion)*len(draw)) if portion else 0
genid = arange(state.generation-len(draw)+start, state.generation)+1
plot(genid*state.thinning,
squeeze(points[start:, state._good_chains, var]))
xlabel('Generation number')
ylabel(label)
[docs]
def plot_logp(state, portion=None):
from pylab import axes, title
from scipy.stats import chi2, kstest
from matplotlib.ticker import NullFormatter
# Plot log likelihoods
draw, logp = state.logp()
start = int((1-portion)*len(draw)) if portion else 0
genid = arange(state.generation-len(draw)+start, state.generation)+1
width, height, margin, delta = 0.7, 0.75, 0.1, 0.01
trace = axes([margin, 0.1, width, height])
trace.plot(genid, logp[start:], ',', markersize=1)
trace.set_xlabel('Generation number')
trace.set_ylabel('Log likelihood at x[k]')
title('Log Likelihood History')
# Plot log likelihood trend line
from bumps.wsolve import wpolyfit
from .formatnum import format_uncertainty
x = np.arange(start, logp.shape[0]) + state.generation - state.Ngen + 1
y = np.mean(logp[start:], axis=1)
dy = np.std(logp[start:], axis=1, ddof=1)
p = wpolyfit(x, y, dy=dy, degree=1)
px, dpx = p.ci(x, 1.)
trace.plot(x, px, 'k-', x, px + dpx, 'k-.', x, px - dpx, 'k-.')
trace.text(x[0], y[0], "slope="+format_uncertainty(p.coeff[0], p.std[0]),
va='top', ha='left')
# Plot long likelihood histogram
data = logp[start:].flatten()
hist = axes([margin+width+delta, 0.1, 1-2*margin-width-delta, height])
hist.hist(data, bins=40, orientation='horizontal', density=True)
hist.set_ylim(trace.get_ylim())
null_formatter = NullFormatter()
hist.xaxis.set_major_formatter(null_formatter)
hist.yaxis.set_major_formatter(null_formatter)
# Plot chisq fit to log likelihood histogram
float_df, loc, scale = chi2.fit(-data, f0=state.Nvar)
df = int(float_df + 0.5)
pval = kstest(-data, lambda x: chi2.cdf(x, df, loc, scale))
#with open("/tmp/chi", "a") as fd:
# print("chi2 pars for llf", float_df, loc, scale, pval, file=fd)
xmin, xmax = trace.get_ylim()
x = np.linspace(xmin, xmax, 200)
hist.plot(chi2.pdf(-x, df, loc, scale), x, 'r')
def tile_axes(n, size=None):
"""
Creates a tile for the axes which covers as much area of the graph as
possible while keeping the plot shape near the golden ratio.
"""
from pylab import gcf
if size is None:
size = gcf().get_size_inches()
figwidth, figheight = size
# Golden ratio phi is the preferred dimension
# phi = sqrt(5)/2
#
# nw, nh is the number of tiles across and down respectively
# w, h are the sizes of the tiles
#
# w,h = figwidth/nw, figheight/nh
#
# To achieve the golden ratio, set w/h to phi:
# w/h = phi => figwidth/figheight*nh/nw = phi
# => nh/nw = phi * figheight/figwidth
# Must have enough tiles:
# nh*nw > n => nw > n/nh
# => nh**2 > n * phi * figheight/figwidth
# => nh = floor(sqrt(n*phi*figheight/figwidth))
# => nw = ceil(n/nh)
phi = math.sqrt(5)/2
nh = int(math.floor(math.sqrt(n*phi*figheight/figwidth)))
if nh < 1:
nh = 1
nw = int(math.ceil(n/nh))
return nw, nh
def plot_acceptance_rate(state, portion=1.0):
from matplotlib import pyplot as plt
gen, AR = state.acceptance_rate()
if portion != 1.0:
index = int(portion*len(AR))
gen, AR = gen[-index:], AR[-index:]
plt.plot(gen, AR)
plt.xlabel("Generation #")
plt.ylabel("Acceptance rate (%)")
plt.title("DREAM acceptance rate by generation")