pp = Pretty_Plotter()
pp._teXify() # LaTeX
pp.params['text.latex.preamble'] = r"\usepackage{amsmath}"
pp._updateRC()
fig = plt.figure(figsize=(8, 8)) # make plot
ax = []
ax.append(fig.add_subplot(111))
ax[0].set_title(
r'Checking stability of $g_W(\tau_W)$ for $\tau_W = \lim_{g_{\text{int}}\to 0} \left[\ln\left(1+\frac{1}{g_{\text{int}}}\right)\right]^{-1}$',
fontsize=pp.ttfont)
ax[0].set_ylabel(r'$g_W(\tau_W) = e^{-1/\tau_W} - \tau_W$')
ax[0].set_xlabel(r'$g_{\text{int}}$')
x = np.linspace(-.2, .1, 1000)
ax[0].plot(x,
np.exp(-1. / np.log(1. + 1. / x.clip(0))) - x,
label=r'$1/0$ = np.inf',
linewidth=2.,
alpha=.4)
ax[0].plot(x,
np.exp(-1. / np.log(1. + 1. / x.clip(np.finfo(float).eps))) - x,
label=r"$1/0$ = `eps'",
linewidth=2.,
alpha=.4)
ax[0].legend(loc='best', shadow=True, fontsize=pp.axfont)
pp.save_or_show(saveOrDisplay(save, __file__), PLOT_LOC)
minor_yticks = np.linspace(0, .05, 5*2+1, endpoint=True)
ax.xaxis.set_ticks(minor_xticks, minor = True)
ax.yaxis.set_ticks(minor_yticks, minor = True)
# Specify different settings for major and minor grids
ax.grid(which = 'minor', alpha = 0.3)
ax.grid(which = 'major', alpha = 0.7)
# im = np.asarray(Image.open('results/figures/archive/misc_appendixA3_acorr_img.png'))
# store.store(im, __file__, '_img')
im = store.load('results/data/numpy_objs/misc_appendixA3_acorr_img.json')
ax.imshow(im, extent=xlim+ylim, aspect='auto', label = r'paper')
m = 0.01
r = iter([np.sqrt(3)*m, .5*m*(3*np.sqrt(3)+np.sqrt(15)), .5*m*(3*np.sqrt(3)-np.sqrt(15))])
f = M2_Exp(next(r), m)
x = np.linspace(0, 1000, 1000, True)
plt.plot(x, f.eval(x), linewidth=4., color='red', alpha=0.6, linestyle="--",
label = r'$r = \sqrt{3}m$')
plt.plot(x, f.eval(x, tau=1/next(r)), linewidth=4., color='green', alpha=0.6, linestyle="--",
label = r'$r = \frac{m}{2}(3\sqrt{3} + \sqrt{15})$')
plt.plot(x, f.eval(x, tau=1/next(r)), linewidth=4., color='blue', alpha=0.6, linestyle="--",
label = r'$r = \frac{m}{2}(3\sqrt{3} - \sqrt{15})$')
ax.legend(loc='lower right', shadow=True, fancybox=True)
pp.save_or_show(saveOrDisplay(save, file_name), PLOT_LOC)
def plot(itau, pacc, acorr, op, tint_th=None, pacc_th=None, op_th=None, save=False):
"""Plots the two-point correlation function
Required Inputs
itau :: {(x,y,e)} :: plots (x,y,e) as error bars
pacc :: {(x,y,e)} :: plots (x,y,e) as error bars
# subtitle :: str :: subtitle for the plot
# op_name :: str :: the name of the operator for the title
save :: bool :: True saves the plot, False prints to the screen
"""
pp = Pretty_Plotter()
pp._teXify() # LaTeX
fig, ax = plt.subplots(3, sharex=True, figsize = (8, 8))
fig.subplots_adjust(hspace=0.1)
fig.suptitle(r"$\langle\rho_t\rangle_t$ and $\tau_{\text{int}}$ varying with $\delta\tau$ for $M^2$",
fontsize=pp.ttfont)
ax[0].set_title(r"HMC; lattice: $(100,)$; $n=20$; $m=0.1$; $M=10^5$", fontsize=pp.ttfont)
ax[-1].set_xlabel(r'$\delta\tau$')
ax[0].set_ylabel(r'$\tau_{\text{int}}$')
x,y,e = itau
ax[0].errorbar(x, y, yerr=e, ecolor='k', ms=3, fmt='o', alpha=0.5)
if tint_th is not None:
if len(tint_th) == 4:
x,y,y_hi,y_lo = tint_th
ax[0].fill_between(x, y_hi, y_lo, color='r', alpha=0.5, label='theory')
else:
x,y = tint_th
ax[0].plot(x, y, c='r', alpha=1, linestyle='--')
ax[1].set_ylabel(r'$\langle\rho_t\rangle_t$')
x,y,e = pacc
ax[1].errorbar(x, y, yerr=e, ecolor='k', ms=3, fmt='o', alpha=0.5)
if pacc_th is not None:
x,y = pacc_th
ax[1].plot(x, y, c='r', alpha=0.7, linestyle='--', label='theory')
# ax[2].set_ylabel(r'$\mathcal{C}_{\mathscr{X}^2}$')
# x,y,e = acorr
# for x_i,y_i,e_i in zip(x,y,e):
# c = next(measured_colours)
# ax[2].plot(np.arange(y_i.size), y_i, color=c, alpha=0.3, label=x_i)
# ax[2].legend(loc='best', shadow=True, fancybox=True)
ax[-1].set_ylabel(r'$\langle M^2_t\rangle_t$')
x,y,e = op
ax[-1].errorbar(x, y, yerr=e, ecolor='k', ms=3, fmt='o', alpha=0.5)
if op_th is not None:
x,y = op_th
ax[-1].plot(x, y, c='r', alpha=0.7, linestyle='--', label='theory')
for a in ax:
a.legend(loc='best', shadow=True, fontsize = pp.axfont)
xi,xf = a.get_xlim()
a.set_xlim(xmin=xi-0.05*(xf-xi)) # give a decent view of the first point
yi,yf = a.get_ylim()
a.set_ylim(ymax=yf + .05*(yf-yi), ymin=yi-.05*(yf-yi)) # give 5% extra room at top
pp.save_or_show(save, PLOT_LOC)
pass
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(scats, lines, subtitle, save):
"""Reproduces figure 1 from [1]
Required Inputs
lines :: {label:(x,y)} :: plots (x,y) as a line with label=label
scats :: {label:(x,y)} :: plots (x,y) as a scatter with label=label
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._updateRC()
fig = plt.figure(figsize=(8, 8)) # make plot
ax = []
ax.append(fig.add_subplot(111))
# fig.suptitle(r'Testing Acceptance Rate', fontsize=pp.ttfont)
ax[0].set_title(subtitle, fontsize=pp.tfont)
ax[-1].set_xlabel(r'Trajectory Length, $\tau=n\delta\tau$')
### add the lines to the plots
ax[0].set_ylabel(r'Average Acceptance, $\langle \rho_t \rangle_t$')
colour = [i for i in random.sample(clist, len(clist))]
ms = [i for i in random.sample(mlist, len(mlist))]
darkclist = [i for i in colors.cnames if 'dark' in i]
darkcolour = [i for i in random.sample(darkclist, len(darkclist))]
lightcolour = map(lambda strng: strng.replace('dark', ''), darkcolour)
cs = iter(colour)
m = iter(ms)
lc = iter(lightcolour)
# clist = [i for i in colors.ColorConverter.colors if i != 'w']
# colour = (i for i in random.sample(clist, len(clist)))
for label, line in lines.iteritems():
ax[0].plot(*line,
linestyle='-',
color=next(lc),
linewidth=2.,
alpha=0.4,
label=label)
for label, scats in scats.iteritems():
x, y, e = scats
ax[0].errorbar(x,
y,
yerr=e,
ecolor='k',
ms=6,
fmt=next(m),
alpha=0.9,
label=label,
c=next(cs),
lw=1,
elinewidth=1)
### place legends
ax[0].legend(loc='best', shadow=True, fontsize=pp.ipfont, fancybox=True)
### formatting
for i in ax:
i.grid(True)
pp.save_or_show(save, PLOT_LOC)
pass
def plot(itau,
pacc,
acorr,
op,
tint_th=None,
pacc_th=None,
op_th=None,
save=False):
"""Plots the two-point correlation function
Required Inputs
itau :: {(x,y,e)} :: plots (x,y,e) as error bars
pacc :: {(x,y,e)} :: plots (x,y,e) as error bars
# subtitle :: str :: subtitle for the plot
# op_name :: str :: the name of the operator for the title
save :: bool :: True saves the plot, False prints to the screen
"""
# annotate minimum values
min_idx = np.argmin(itau[1])
pp = Pretty_Plotter()
pp._teXify() # LaTeX
fig, ax = plt.subplots(3, sharex=True, figsize=(8, 8))
fig.subplots_adjust(hspace=0.1)
fig.suptitle(
r"$\langle\rho_t\rangle_t$ and $\tau_{\text{int}}$ varying with $\delta\tau$ for $X^2$",
fontsize=pp.ttfont)
ax[0].set_title(r"HMC; lattice: $(100,)$; $n=20$; $m=0.1$; $M=10^5$",
fontsize=pp.ttfont)
ax[-1].set_xlabel(r'$\delta\tau$')
ax[0].set_ylabel(r'$\tau_{\text{int}}$')
x, y, e = itau
if len(x) > 100:
ax[0].fill_between(x, y + e, y - e, alpha=0.5, label='Measured')
else:
ax[1].errorbar(x,
y,
yerr=e,
ecolor='k',
ms=3,
fmt='o',
alpha=0.5,
label='Measured')
ax[0].scatter(x[min_idx], y[min_idx], c='r', alpha=1,
label=r'min $\tau_{\text{int}}=' \
+ r'{:8.4f}$ at $\delta\tau={:5.3f}$'.format(y[min_idx],x[min_idx]))
if tint_th is not None:
if len(tint_th) == 4:
x, y, y_hi, y_lo = tint_th
ax[0].fill_between(x,
y_hi,
y_lo,
color='r',
alpha=0.5,
label='Theory')
else:
x, y = tint_th
ax[0].plot(x, y, c='r', alpha=1, linestyle='-')
ax[1].set_ylabel(r'$\langle\rho_t\rangle_t$')
x, y, e = pacc
if len(x) > 100:
ax[1].fill_between(x, y + e, y - e, alpha=0.5, label='Measured')
ax[1].plot(x, y, alpha=0.5)
else:
ax[1].errorbar(x,
y,
yerr=e,
ecolor='k',
ms=3,
fmt='o',
alpha=0.5,
label='Measured')
ax[1].scatter(x[min_idx], y[min_idx], c='r', alpha=1,
label=r'min $\tau_{\text{int}}$' \
+ r' at $\langle\rho_t\rangle_t={:5.3f}\pm{:.1f}$'.format(y[min_idx], e[min_idx]))
if pacc_th is not None:
x, y = pacc_th
ax[1].plot(x, y, c='r', alpha=0.7, linestyle='--', label='Theory')
ax[-1].set_ylabel(r'$\langle X^2_t\rangle_t$')
x, y, e = op
if len(x) > 100:
ax[-1].fill_between(x, y + e, y - e, alpha=0.5, label='Measured')
else:
ax[-1].errorbar(x,
y,
yerr=e,
ecolor='k',
ms=3,
fmt='o',
alpha=0.5,
label='Measured')
if op_th is not None:
x, y = op_th
ax[-1].plot(x, y, c='r', alpha=0.7, linestyle='-', label='Theory')
for a in ax:
xi, xf = a.get_xlim()
a.set_xlim(xmin=xi - 0.01 * (xf - xi), xmax=xf + 0.01 *
(xf - xi)) # give a decent view of the first point
yi, yf = a.get_ylim()
a.set_ylim(ymax=yf + .05 * (yf - yi),
ymin=yi - .05 * (yf - yi)) # give 5% extra room at top
ax[0].legend(loc='upper left', shadow=True, fontsize=pp.axfont)
ax[-1].legend(loc='lower left', shadow=True, fontsize=pp.axfont)
ax[1].legend(loc='best', shadow=True, fontsize=pp.axfont)
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
def plot(burn_in, samples, bg_xyz, save):
"""Note that samples and burn_in contain the initial conditions"""
pp = Pretty_Plotter()
pp._teXify() # LaTeX
pp.params['figure.subplot.top'] = 0.85
pp._updateRC()
fig = plt.figure(figsize=(8, 8))
ax = fig.add_subplot(111)
ax.set_xlabel(r'$\phi_{1}$', fontsize=pp.axfont)
ax.set_ylabel(r'$\phi_{2}$', fontsize=pp.axfont)
# fig.suptitle(r'Sampling a ring potential with HMC',
# fontsize=pp.ttfont)
pot = r'$Q(\phi_{x}) = e^{-50\left|\phi_{x}^2 + 1/10\right|}$'
ax.set_title(r'{} burn-in \& {} MH moves'.format(max(burn_in.shape),
max(samples.shape)),
fontsize=pp.tfont)
plt.grid(False)
x, y, z = bg_xyz
# small = 1e-1
# mask = z<small
# z = np.ma.MaskedArray(-z, mask, fill_value=0)
# x = np.ma.MaskedArray(x, mask, fill_value=np.nan)
# y = np.ma.MaskedArray(y, mask, fill_value=np.nan)
cnt = ax.contourf(x, y, z, 100, cmap=viridis, alpha=.3, antialiased=True)
l0 = ax.plot(burn_in[0, 0],
burn_in[0, 1],
marker='o',
markerfacecolor='green')
l1 = ax.plot(
burn_in[:, 0],
burn_in[:, 1],
color='green',
linestyle='--',
alpha=0.3,
# marker='o', markerfacecolor='red'
)
x, y = samples[:, 0], samples[:, 1]
points = np.array([x, y]).T.reshape(-1, 1, 2)
segments = np.concatenate([points[:-1], points[1:]], axis=1)
lc = LineCollection(segments,
cmap=plt.get_cmap('magma_r'),
norm=plt.Normalize(250, 1500))
lc.set_array(np.arange(samples[:, 1].size))
lc.set_linewidth(1.)
lc.set_alpha(0.3)
ax.add_collection(lc)
l2 = ax.scatter(
samples[:, 0],
samples[:, 1],
color='blue',
alpha=0.7,
s=3,
marker='o',
)
pp.save_or_show(save, PLOT_LOC)
pass
def plot(y1, y2, subtitle, save, all_lines=False):
"""A plot of y1 and y2 as functions of the steps which
are implicit from the length of the arrays
Required Inputs
y1 :: np.array :: conj kinetic energy array
y2 :: np.array :: shape is either (n, 3) or (n,)
subtitle :: string :: subtitle for the plot
save :: bool :: True saves the plot, False prints to the screen
Optional Inputs
all_lines :: bool :: if True, plots hamiltonian as well as all its components
"""
pp = Pretty_Plotter()
pp._teXify() # LaTeX
pp._updateRC()
fig = plt.figure(figsize=(8, 8)) # make plot
ax = []
ax.append(fig.add_subplot(111))
# fig.suptitle(r"Change in Energy during Leap Frog integration",
# fontsize=pp.ttfont)
ax[0].set_title(subtitle, fontsize=pp.ttfont)
ax[0].set_xlabel(r'Number of Leap Frog Steps, $n$', fontsize=pp.axfont)
ax[0].set_ylabel(r'Change in Energy, $\delta E_{n} = E_{n} - E_0$',
fontsize=pp.axfont)
steps = np.linspace(0, y1.size, y1.size, True)
# check for multiple values in the potential
multi_pot = (len(y2.shape) > 1)
print multi_pot, y2.shape
if multi_pot:
action, k, u = zip(*y2)
k = np.asarray(k)
u = np.asarray(u)
else:
action = y2
action = np.asarray(action)
h = ax[0].plot(
steps,
y1 + np.asarray(action), # Full Hamiltonian
label=r"$\delta H_t = \delta T_n + \delta S_t$",
color='blue',
linewidth=5.,
linestyle='-',
alpha=1)
if all_lines:
t = ax[0].plot(
steps,
np.asarray(y1), # Kinetic Energy (conjugate)
label=r'$\delta T_n$',
color='darkred',
linewidth=2.,
linestyle='-',
alpha=1)
if multi_pot:
s = ax[0].plot(
steps,
np.asarray(action), # Potential Energy (Action)
label=
r'$\delta \delta S_n = \sum_{n} (\delta T^{(s)}_n + \delta V^{(s)}_n)$',
color='darkgreen',
linewidth=1.,
linestyle='-',
alpha=1)
t_s = ax[0].plot(
steps,
np.asarray(k), # Kinetic Energy in Action
label=r'$\sum_{n} \delta T^{(s)}_n$',
color='red',
linewidth=1.,
linestyle='--',
alpha=2.)
v_s = ax[0].plot(
steps,
np.asarray(u), # Potential Energy in Action
label=r'$\sum_{n} \delta V^{(s)}_n$',
color='green',
linewidth=1.,
linestyle='--',
alpha=1.)
else:
s = ax[0].plot(
steps,
np.asarray(action), # Potential Energy (Action)
label=r'$\delta S(x,t) = \frac{1}{2}\delta \phi_{n,x}^2$',
color='darkgreen',
linewidth=3.,
linestyle='-',
alpha=1)
# add legend
ax[0].legend(loc='upper left', shadow=True, fontsize=pp.axfont)
pp.save_or_show(save, PLOT_LOC)
pass
def plot(x, lines, subtitle, op_name, save):
"""Plots the two-point correlation function
Required Inputs
x_vals :: list :: list / np.ndarray of angles the routine was run for
lines :: {axis:(y, error)} :: contains (y,error) for each axis
subtitle :: str :: subtitle for the plot
op_name :: str :: the name of the operator for the title
save :: bool :: True saves the plot, False prints to the screen
"""
pp = Pretty_Plotter()
pp._teXify() # LaTeX
pp._updateRC()
ax = []
fig, ax = plt.subplots(4, sharex=True, figsize=(8, 8))
# fig.suptitle(r"Integrated Autocorrelations for " \
# + r"{} and varying $\theta$".format(op_name), fontsize=pp.ttfont)
fig.subplots_adjust(hspace=0.2)
# Add top pseudo-title and bottom shared x-axis label
ax[0].set_title(subtitle, fontsize=pp.tfont)
ax[-1].set_xlabel(r'Mixing angle, $\vartheta$')
ax[0].set_ylabel(r'$\tau_{\text{int}}$')
ax[1].set_ylabel(r'$\langle X^2\rangle_{t}$')
ax[2].set_ylabel(r'Int. window, $w$')
ax[3].set_ylabel(r'$\langle \rho_t\rangle_t$')
def formatFunc(tic, tic_loc):
return r"${}\pi$".format(tic)
ax[-1].get_xaxis().set_major_formatter(ticker.FuncFormatter(formatFunc))
# Fix colours: A bug sometimes forces all colours the same
colour = (i
for i in random.sample(clist, len(clist))) # defined top of file
for k, v in lines.iteritems():
for i, (y, err, label) in enumerate(v):
if i > 0:
s = '--'
c = 'r'
else:
s = '-'
c = next(colour)
if err is None:
ax[k].plot(x, y, c=c, lw=1., alpha=1, label=label, linestyle=s)
else:
y = np.asarray(y)
err = np.asarray(err)
ax[k].fill_between(x,
y - err,
y + err,
color=c,
alpha=1,
label=label)
# ax[k].errorbar(x, y, yerr=err, c=c, ecolor='k', ms=3, fmt='o', alpha=0.5,
# label=label)
if i == 0:
yi, yf = ax[k].get_ylim()
ax[k].set_ylim(ymax=yf + .05 * (yf - yi),
ymin=yi - .05 * (yf - yi))
ax[k].legend(loc='best', shadow=True, fontsize=pp.axfont)
pp.save_or_show(save, PLOT_LOC)
pass
def plot(c_fn, errs, th_x_sq, spacing, subtitle, logscale, save):
"""Plots the two-point correlation function
Required Inputs
c_fn :: np.array :: correlation function
err :: np.array :: errs in c_fn
spacing :: float :: the lattice spacing
subtitle :: string :: subtitle for the plot
save :: bool :: True saves the plot, False prints to the screen
logscale :: bool :: adds a logscale
Optional Inputs
all_lines :: bool :: if True, plots hamiltonian as well as all its components
"""
pp = Pretty_Plotter()
pp._teXify() # LaTeX
pp._updateRC()
fig = plt.figure(figsize=(8, 8)) # make plot
ax = []
ax.append(fig.add_subplot(111))
# fig.suptitle(r"Two-Point Correlation Function, $\langle x(0)x(\tau)\rangle$",
# fontsize=pp.ttfont)
ax[0].set_title(subtitle)
ax[0].set_xlabel(r'Lattice Separation, $ia$')
ax[0].set_ylabel(r'$\langle \phi_{t,x}\phi_{t,x+i} \rangle_{t,x}$')
steps = np.linspace(0, spacing * c_fn.size, c_fn.size,
False) # get x values
# log_y = np.log(c_fn) # regress for logarithmic scale
# mask = np.isfinite(log_y) # handles negatives in the logarithm
# x = steps[mask]
# y = log_y[mask]
# linear regression of the exponential curve
# m, c, r_val, p_val, std_err = stats.linregress(x, y)
# fit = np.exp(m*steps + c)
if th_x_sq is not None:
th = ax[0].plot(steps,
th_x_sq,
color='green',
linewidth=3.,
linestyle='-',
alpha=0.2,
label=r'Theoretical prediction')
# bf = ax[0].plot(steps, fit, color='blue',
# linewidth=3., linestyle = '-', alpha=0.2, label=r'fit: $y = e^{'\
# + '{:.2f}x'.format(m)+'}e^{'+'{:.2f}'.format(c) + r'}$')
# err = c_fn*np.exp(c_fn)*errs
f = ax[0].errorbar(steps,
c_fn,
yerr=errs,
ecolor='k',
ms=3,
fmt='o',
alpha=0.6,
label='Measured Data')
ax[0].set_xlim(xmin=0)
if logscale: ax[0].set_yscale("log", nonposy='clip')
ax[0].legend(loc='best', shadow=True, fontsize=pp.axfont)
pp.save_or_show(save, PLOT_LOC)
pass
