def plot(
probs,
accepts,
h_olds,
h_news,
exp_delta_hs,
subtitle,
labels,
save,
h_mdmc=None,
mdmc_deltaH=None, # for mdmc additions
):
"""Plots 3 stacked figures:
1. the acceptance probability at each step
2. the hamiltonian (old, new) at each step
3. the exp{-delta H} at each step
Overlayed with red bars is each instance in which a configuration was rejected
by the Metropolis-Hastings accept/reject step
Required Inputs
probs :: np.array :: acc. probs
accepts :: np.array :: array of boolean acceptances (True = accepted)
h_olds :: np.array :: old hamiltonian at each step
h_news :: np.array :: new hamiltonian at each step
exp_delta_hs :: np.array :: exp{-delta H} at each step
h_mdmc :: np.array ::
mdmc_deltaH :: np.array ::
subtitle :: str :: the subtitle to put in ax[0].set_title()
save :: bool :: True saves the plot, False prints to the screen
"""
pp = Pretty_Plotter()
pp._teXify() # LaTeX
# pp.params['text.latex.preamble'] = [r"\usepackage{amsmath}"]
pp._updateRC()
fig, ax = plt.subplots(3, sharex=True, figsize=(8, 8))
# fig.suptitle(r'Data from {} Metropolis acceptance steps'.format(len(probs)),
# fontsize=pp.ttfont)
fig.subplots_adjust(hspace=0.2)
l = probs.size # length of HMC trajectory - lots rely on this being at the top
### Add top pseudo-title and bottom shared x-axis label
ax[0].set_title(subtitle, fontsize=pp.tfont)
ax[-1].set_xlabel(r'Markov Time, $j$')
### add the rejection points in the background
xrng = range(1, l + 1) # calculate xrange to match length
for a in ax: # iterate over each axis
for x, val in zip(xrng, accepts): # iterate over all rejection points
if val == False:
a.axvline(x=x, linewidth=4, color='red', alpha=0.2)
### add the lines to the plots
ax[0].set_ylabel(r'Hamiltonian, $H_j$')
ax[0].plot(xrng,
h_olds,
linestyle='-',
color='blue',
linewidth=2.,
alpha=1,
label=r'$H_{j-1}$')
# ax[0].plot(xrng, h_news, linestyle='-', color='green', linewidth=2., alpha=0.4,
# label=r'$H(t)$')
ax[1].set_ylabel(r'$\exp{-\delta H_j}$')
ax[1].plot(xrng,
exp_delta_hs,
linestyle='-',
color='blue',
linewidth=2.,
alpha=1,
label=r'$\exp{ -\delta H_t}$')
ax[2].set_ylabel(r'Acceptance $\rho_j$')
ax[2].plot(xrng, probs, linestyle='-', color='blue', linewidth=2., alpha=1)
### test to see if we will plot all the intermediate MDMC steps
plot_mdmc = (h_mdmc is not None) & (mdmc_deltaH is not None)
if plot_mdmc: # all these functions rely on l being calculated!!
# functions to calculate the staggering of y and x
# for the MDMC. Staggering means calculating the start and
# end points of each single trajectory consisting of 1 MDMC integration
n = h_mdmc.size / l - 1 # this calculates n_steps for the MDMC (in a backwards way)
staggered_xi = np.arange(0, l)
staggered_xf = np.arange(1, l + 1)
staggered_y = lambda arr, offset: arr[0 + offset::(n + 1)]
remove_links = lambda arr: [
None if (i) % (n + 1) == 0 else a for i, a in enumerate(arr)
]
## calculate a linear space as a fraction of the HMC trajectory
mdmc_x = np.asarray([
np.linspace(i, j, n + 1)
for i, j in zip(range(0, l), range(1, l + 1))
])
mdmc_x = mdmc_x.flatten()
ax[0].plot(mdmc_x,
remove_links(h_mdmc),
linestyle='--',
color='green',
linewidth=1,
alpha=1,
label=r'MDMC: $H_{j+1}$')
ax[0].scatter(staggered_xi,
staggered_y(h_mdmc, 0),
color='red',
marker='o',
alpha=1,
label=r'Start MDMC')
ax[0].scatter(staggered_xf,
staggered_y(h_mdmc, n),
color='red',
marker='x',
alpha=1,
label=r'End MDMC')
ax[1].plot(mdmc_x,
remove_links(mdmc_deltaH),
linestyle='--',
color='blue',
linewidth=1.,
alpha=1,
label=r'MDMC: $\exp{ -\delta H_{j+1}$')
ax[1].scatter(staggered_xi,
staggered_y(mdmc_deltaH, 0),
color='red',
marker='o',
alpha=1,
label=r'Start MDMC')
ax[1].scatter(staggered_xf,
staggered_y(mdmc_deltaH, n),
color='red',
marker='x',
alpha=1,
label=r'End MDMC')
### adds labels to the plots
for i, text in labels.iteritems():
pp.add_label(ax[i], text, fontsize=pp.tfont)
### place legends
ax[0].legend(loc='upper left',
shadow=True,
fontsize=pp.ipfont,
fancybox=True)
ax[1].legend(loc='upper left',
shadow=True,
fontsize=pp.ipfont,
fancybox=True)
### formatting
for i in ax:
i.grid(True)
# ax[1].set_yscale("log", nonposy='clip') # set logarithmic y-scale
pp.save_or_show(save, PLOT_LOC)
pass
def plot(lines_d, x_lst, ws, subtitle, mcore, angle_labels, op_name, save):
"""Plots the two-point correlation function
Required Inputs
x_lst :: list :: list of x_values for each angle that was run
lines_d :: {axis:[(y,label)]} :: plots (y,error,label) for each list item
ws :: list :: list of integration windows
subtitle :: str :: subtitle for the plot
mcore :: bool :: are there multicore operations? (>1 mixing angles)
op_name :: str :: the name of the operator for the title
angle_labels :: list :: the angle label text for legend plotting
save :: bool :: True saves the plot, False prints to the screen
"""
pp = Pretty_Plotter()
pp._teXify() # LaTeX
pp.params['text.latex.preamble'] = r"\usepackage{amsfonts}"
pp.params['text.latex.preamble'] = r"\usepackage{amsmath}"
pp._updateRC()
fig = plt.figure(figsize=(8, 8)) # make plot
ax = []
fig, ax = plt.subplots(3, sharex=True, figsize=(8, 8))
fig.suptitle(r"Autocorrelation and Errors for {}".format(op_name),
fontsize=pp.ttfont)
fig.subplots_adjust(hspace=0.1)
# Add top pseudo-title and bottom shared x-axis label
ax[0].set_title(subtitle, fontsize=pp.tfont)
ax[-1].set_xlabel(r'Window Length')
if not mcore: # don't want clutter in a multiple plot env.
for a in range(1, len(ax)): # Add the Window stop point as a red line
# there is only one window item if not multiple lines
ax[a].axvline(x=ws[0], linewidth=4, color='red', alpha=0.1)
ax[0].set_ylabel(r'$g(w)$')
ax[1].set_ylabel(r'$\tau_{\text{int}}(w)$')
ax[2].set_ylabel(r'Autocorrelation, $\Gamma(t)$')
#### plot for the 0th axis ####
line_list = lines_d[0]
axis = ax[0]
theory_colours = iter(colour)
measured_colours = iter(colour)
for x, lines in zip(x_lst, line_list):
m = next(marker) # get next marker style
c = next(measured_colours) # get next colour
th_c = next(theory_colours)
# split into y function, errors in y and label
y, e, l = lines # in this case there are no errors or labels used
# allow plots in diff colours for +/
yp = y.copy()
yp[yp < 0] = np.nan # hide negative values
ym = y.copy()
ym[ym >= 0] = np.nan # hide positive values
if not mcore:
axis.scatter(x,
yp,
marker='o',
color='g',
linewidth=2.,
alpha=0.6,
label=r'$g(t) \ge 0$')
axis.scatter(x,
ym,
marker='x',
color='r',
linewidth=2.,
alpha=0.6,
label=r'$g(t) < 0$')
else:
axis.plot(x, yp, color=c, lw=1., alpha=0.6) # label with the angle
axis.plot(x, ym, color='r', lw=1., alpha=0.6)
once_label = None # set to blank so don't get multiple copies
if not mcore: axis.legend(loc='best', shadow=True, fontsize=pp.axfont)
#### plot the 1st axis ###
# there is no angle label on the lines themselves on this axis
# because the colours are synchronised across each plot
# so the label on the bottom axis is enough
line_list = lines_d[1]
axis = ax[1]
theory_colours = iter(colour)
measured_colours = iter(colour)
for x, lines in zip(x_lst, line_list):
m = next(marker) # get next marker style
c = next(measured_colours) # get next colour
th_c = next(theory_colours)
y, e, l, t = lines # split into y function, errors, label and theory
# try:
# axis.fill_between(x, y-e, y+e, color=c, alpha=0.5)
# except:
# print "errors are dodgy"
axis.errorbar(x,
y,
yerr=e,
markersize=3,
color=c,
fmt=m,
alpha=0.5,
ecolor='k')
if t is not None:
axis.axhline(y=t, linewidth=1, color=th_c, linestyle='--')
# Only add informative label if there is only one line
# adds a pretty text box above the middle plot with info
# contained in the variable l - assigned in preparePlot()
if not mcore: pp.add_label(axis, l, fontsize=pp.tfont)
#### plot the 2nd axis ###
# This plot explicitly list the labels for all the angles
line_list = lines_d[2]
axis = ax[2]
theory_colours = iter(colour)
measured_colours = iter(colour)
for x, lines, a in zip(x_lst, line_list, angle_labels):
m = next(marker) # get next marker style
c = next(measured_colours) # get next colour
th_c = next(theory_colours)
y, e, l, t = lines # split into y function, errors in y and label
try: # errors when there are low number of sims
axis.fill_between(x, y - e, y + e, color=c, alpha=0.6, label=a)
# axis.errorbar(x, y, yerr=e, label = a,
# markersize=3, color=c, fmt=m, alpha=0.5, ecolor='k')
except: # avoid crashing
print 'Too few MCMC simulations to plot autocorrelations for: {}'.format(
a)
if t is not None:
axis.plot(x,
t,
linewidth=1.2,
alpha=0.9,
color=th_c,
linestyle='--',
label='Theoretical')
axis.legend(loc='best', shadow=True, fontsize=pp.axfont)
#### start outdated section ####
## this won't work after the changes but shows the general idea of fitting a curve
#
# for i in range(1, len(lines)): # add best fit lines
# x, y = lines[i][:2]
# popt, pcov = curve_fit(expFit, x, y) # approx A+Bexp(-t/C)
# if not mcore:
# l_th = r'Fit: $f(t) = {:.1f} + {:.1f}'.format(popt[0], popt[1]) \
# + r'e^{-t/' +'{:.2f}'.format(popt[2]) + r'}$'
# else:
# l_th = None
# ax[i].plot(x, expFit(x, *popt), label = l_th,
# linestyle = '-', color=c, linewidth=2., alpha=.5)
#### end outdated section ####
# fix the limits so the plots have nice room
xi, xf = ax[2].get_xlim()
ax[2].set_xlim(xmin=xi - .05 * (xf - xi)) # decent view of the first point
for a in ax: # 5% extra room at top & add legend
yi, yf = a.get_ylim()
a.set_ylim(ymax=yf + .05 * (yf - yi), ymin=yi - .05 * (yf - yi))
ax[-1].set_ylim(ymax=2)
pp.save_or_show(save, PLOT_LOC)
pass