def plot(norm, subtitle, save):
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))
fig.suptitle(
r'Magnitude of Change in Phase Space, $\Delta\mathcal{P}(x,p)$',
fontsize=pp.ttfont)
ax[0].set_title(subtitle, fontsize=pp.ttfont - 4)
ax[0].set_xlabel(r'Integration Step, $n$')
ax[0].set_ylabel(
r"$|\Delta\mathcal{P}(x,\pi)| = \sqrt{(\pi_{t} + \pi_{\text{-}t})^2 + (x_{t} - x_{\text{-}t})^2}$"
)
n_steps = norm.size - 1 # norm contains 0th step
steps = np.linspace(0, n_steps, n_steps + 1, True)
ax[0].plot(steps, norm, linestyle='-', color='blue')
pp.save_or_show(save, PLOT_LOC)
pass
def plot(x, y, z, save):
"""Plots a test image of the Bivariate Gaussian
Required Inputs
x,y,z :: arrays :: must all be same length
save :: string / bool :: save location or '' / False
"""
pp = Pretty_Plotter()
pp.s = 1.0
pp._teXify() # LaTeX
fig = plt.figure(figsize=(5, 5))
ax = fig.add_subplot(111)
# create contour plot
c = ax.contourf(x, y, z, 200, cmap=magma)
# axis labels
ax.set_xlabel(r'$\phi_1$', fontsize=pp.axfont)
ax.set_ylabel(r'$\phi_2$', fontsize=pp.axfont)
ax.grid(False) # remove grid
pp.save_or_show(save, PLOT_LOC)
pass
def plot(burn_in, samples, save):
"""Note that samples and burn_in contain the initial conditions"""
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))
name = "SHO"
fig.suptitle(r'Example HMC path sampling the {} potential'.format(name),
fontsize=16)
ax[0].set_title(
r'{} Burn-in Samples shown in orange'.format(burn_in.size-1))
ax[0].set_ylabel(r'Sample, $n$')
ax[0].set_xlabel(r"Position, $x$")
# burn_in includes initial cond.
# samples inclues final burn_in as initial cond.
offst = burn_in.size # burn-in samples
ax[0].plot(burn_in, np.arange(0, offst), #marker='x',
linestyle='-', color='orange', label=r'Burn In')
ax[0].plot(samples, np.arange(offst-1, offst-1 + samples.size), #marker='x',
linestyle='-', color='blue', label=r'Sampling')
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['text.latex.preamble'] = [r"\usepackage{amsmath}"]
pp.params['figure.subplot.top'] = 0.85
pp._updateRC()
fig = plt.figure(figsize=(8,8))
ax = fig.add_subplot(111)
ax.set_xlabel(r'$\mathrm{x_1}$')
ax.set_ylabel(r'$\mathrm{x_2}$')
fig.suptitle(r'Sampling a ring potential with HMC',
fontsize=pp.ttfont)
ax.set_title(r'Showing the burn-in \& first 100 HMC moves',
fontsize=(pp.tfont-4))
plt.grid(True)
x, y, z = bg_xyz
small = 1e-10
mask = z<small
z = np.ma.MaskedArray(z, mask, fill_value=np.nan)
x = np.ma.MaskedArray(x, mask, fill_value=np.nan)
y = np.ma.MaskedArray(y, mask, fill_value=np.nan)
#
levels = MaxNLocator(nbins=300).tick_values(z.min(), z.max())
cmap = plt.get_cmap('viridis')
norm = BoundaryNorm(levels, ncolors=cmap.N, clip=True)
# z = np.ma.array(z, mask=z < .01) # optionally mask to white below certain value
cnt = ax.contourf(x, y, z,
# levels=levels,
# cmap=cmap,
vmin=small,
alpha=.3, antialiased=True)#, norm=LogNorm(vmin=z.min(), vmax=z.max()))
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='grey', linestyle='--'
# marker='o', markerfacecolor='red'
)
l2 = ax.plot(samples[:,0], samples[:,1],
color='blue',
marker='o', markerfacecolor='red'
)
cbar = plt.colorbar(cnt, ax=ax, shrink=0.9)
cbar.ax.set_ylabel(r'Absolute change in Hamiltonian, $|{1 - e^{-\delta H(p,x)}}|$')
pp.save_or_show(save, PLOT_LOC)
pass
def plot(x, y, z, save):
"""Plots a test image of the Bivariate Gaussian
Required Inputs
x,y,z :: arrays :: must all be same length
save :: string / bool :: save location or '' / False
"""
pp = Pretty_Plotter()
pp._teXify() # LaTeX
pp.params['text.latex.preamble'] = [r"\usepackage{amsmath}"]
pp.params['figure.subplot.top'] = 0.85
pp._updateRC()
fig = plt.figure(figsize=(8,8))
ax = fig.add_subplot(111)
# create contour plot
c = ax.contourf(x, y, z, 100, cmap=plasma)
# axis labels
ax.set_xlabel(r'$x_1$')
ax.set_ylabel(r'$x_2$')
ax.grid(False) # remove grid
fig.suptitle( # title
r'Test plot of a 2D Multivariate (Bivariate) Gaussian', fontsize=pp.ttfont)
ax.set_title( # subtitle
r'Parameters: $\mu=\begin{pmatrix}0 & 0\end{pmatrix}$, $\Sigma = \begin{pmatrix} 1.0 & 0.8\\ 0.8 & 1.0 \end{pmatrix}$',
fontsize=pp.tfont-4)
pp.save_or_show(save, PLOT_LOC)
pass
def plot(acns, lines, subtitle, op_name, save):
"""Plots the two-point correlation function
Required Inputs
acs :: {label:(x,y)} :: plots (x,y) as a stem plot with label=label
lines :: {label:(x,y)} :: plots (x,y) as a line with label=label
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
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"Autocorrelation Function for {}".format(op_name),
# fontsize=pp.ttfont)
ax[0].set_title(subtitle, fontsize=pp.ttfont)
ax[0].set_xlabel(r'Fictitious time separation, $s$')
ax[0].set_ylabel(r'Normalised Autocorrelation, $C(s)$') # \
# + r'(\hat{O}_{i+t} - \langle\hat{O}\rangle) \rangle}/{\langle \hat{O}_0^2 \rangle}$')
for label, (x, y, e) in sorted(acns.iteritems()):
c = next(measured_colours)
# for some reason I occisionally need to add a fake plot
# p2 = ax[0].add_patch(Rectangle((0, 0), 0, 0, fc=c, linewidth=0, alpha=.4, label=label))
try:
x, y, e = x[:250], y[:250], e[:250]
if e is not None:
# ax[0].fill_between(x, y-e, y+e, color=c, alpha=0.3, label=label)
ax[0].errorbar(x,
y,
yerr=e,
c=c,
ecolor='k',
ms=3,
fmt='o',
alpha=0.5,
label=label)
else:
ax[0].scatter(x, y, c=c, ms=3, fmt='o', alpha=0.5, label=label)
except Exception, e:
print '\nFailed for "{}"'.format(label)
print 'Wrong types? x:{} y:{} e:{}'.format(type(x), type(y),
type(e))
print '\nError:'
print e
def plot(samples, subtitle, y_label, save, extra_data=[]):
"""Note that samples and burn_in contain the initial conditions
Required Inputs
samples :: the 1D numpy array to plot as a histogram
subtitle :: str :: subtitle for the plot
y_label :: str :: the y axis label
save :: bool :: True saves the plot, False prints to the screen
Optional Inputs
extra_data :: list of dicts :: see below
Expectations
extra_data = [{'f':actual, 'label':theory},
{'f':fitted, 'label':None}]
'f' contains a function with respect to a linear x range (x-axis) and the samples
f(x, samples)
'label' is a string or None
"""
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))
# burn_in includes initial cond.
# samples inclues final burn_in as initial cond.
fig.suptitle(subtitle,
fontsize=16)
ax[0].set_title(r'{} HMC samples'.format(samples.shape[0]), fontsize=pp.ttfont-4)
ax[0].set_ylabel(y_label)
ax[0].set_xlabel(r"Position, $x$")
n, bins, patches = ax[0].hist(samples.ravel(), 50, normed=1, # histogram
facecolor='green', alpha=0.2, label=r'Sampled data')
n = 100 # size of linear space
x = np.linspace(-5, 5, n)
for i in extra_data:
params, fitted = i['f'](x, samples)
ax[0].plot(x, fitted,
linewidth=2., alpha=0.6, label=i['label'].format(*params))
ax[0].legend(loc='best', shadow=True, fontsize = pp.axfont)
ax[0].grid(False)
pp.save_or_show(save, PLOT_LOC)
pass
def plot(lines, 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.s = 1.5
pp._teXify() # LaTeX
fig, ax = plt.subplots(1, figsize = (10, 8))
ax = [ax]
fig.suptitle(r"Showing that $n$ has little effect on $\tau_{\text{int}}$",
fontsize=pp.ttfont+2)
ax[0].set_title(r"HMC; lattice: $(100,)$; $m=0.01$; $M=10^5$; $\vartheta=\frac{\pi}{2}$", fontsize=pp.ttfont)
ax[-1].set_xlabel(r'$\delta\tau$')
ax[0].set_ylabel(r'$\tau_{\text{int}}$')
for line in lines:
m = next(markers)
c = next(measured_colours)
label = line['n_steps']
x = line['step_size']
y = line['itau']
ax[0].scatter(x, y, alpha=0.5, c=c, marker=m, label=int(label))
for a in ax:
a.legend(loc='best', shadow=True, fontsize = pp.axfont)
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(bbox_to_anchor=(0., -0.3, 1., .102), loc=9,
ncol=6, mode="expand", borderaxespad=0.)
fig.subplots_adjust(bottom=0.3)
pp.save_or_show(save, PLOT_LOC)
pass
def plot(burn_in, samples, bg_xyz):
"""Note that samples and burn_in contain the initial conditions"""
pp = Pretty_Plotter()
pp._teXify() # LaTeX
pp.params['text.latex.preamble'] = [r"\usepackage{amsmath}"]
pp.params['figure.subplot.top'] = 0.85
pp._updateRC()
fig = plt.figure(figsize=(8, 8))
ax = fig.add_subplot(111)
ax.set_xlabel(r'$\mathrm{x_1}$')
ax.set_ylabel(r'$\mathrm{x_2}$')
fig.suptitle(r'Sampling Multivariate Gaussian with HMC',
fontsize=pp.ttfont)
ax.set_title(
r'Showing the burn-in \& first 100 HMC moves for:\ $\mu=\begin{pmatrix}0 & 0\end{pmatrix}$, $\Sigma = \begin{pmatrix} 1.0 & 0.8\\ 0.8 & 1.0 \end{pmatrix}$',
fontsize=(pp.tfont - 4))
plt.grid(True)
x, y, z = bg_xyz
# z = np.ma.array(z, mask=z < .01) # optionally mask to white below certain value
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='grey',
linestyle='--'
# marker='o', markerfacecolor='red'
)
l2 = ax.plot(samples[:, 0],
samples[:, 1],
color='blue',
marker='o',
markerfacecolor='red')
cbar = plt.colorbar(p, ax=ax[0], shrink=0.9)
pp.save_or_show(save, PLOT_LOC)
pass
def plot(burn_in, samples, save):
"""Note that samples and burn_in contain the initial conditions"""
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))
name = "QHO"
fig.suptitle(
r'HMC path configurations, sampling the {} potential'.format(name),
fontsize=16)
ax[0].set_title(
r'{} Burn-in configurations shown in grey'.format(burn_in.shape[0] -
1))
ax[0].set_ylabel(r'Time, $\tau$')
ax[0].set_xlabel(r"Position, $x(\tau)$")
for i in xrange(burn_in.shape[0]):
offst = burn_in[i].size + 1 # burn-in samples
ax[0].plot(burn_in[i],
np.arange(1, offst),
linestyle='--',
alpha=.2,
linewidth=3,
color='grey')
for i in xrange(samples.shape[0]):
offst = samples[i].size + 1 # burn-in samples
ax[0].plot(samples[i],
np.arange(1, offst),
linestyle='-',
alpha=.3,
linewidth=3,
color='green')
pp.save_or_show(save, PLOT_LOC)
pass
def plot(lines, subtitles, save):
"""
Required Inputs
lines :: dict :: axis(int): (x(np.ndarray), y(np.ndarray), label(str))
subtitles :: dict :: axis(int): subtitle(str)
save :: bool/str :: string saves the plot as given string, 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(2, sharex=True, figsize=(8, 8))
fig.subplots_adjust(hspace=0.2)
fig.suptitle(
r"Comparing methods of calculating $\mathcal{L}^{-1}F(\beta)$",
fontsize=pp.ttfont)
for i, subtitle in subtitles.iteritems():
ax[i].set_title(subtitle, fontsize=pp.ttfont - 4)
ax[-1].set_xlabel(
r'Fictitious sample time, $t = \sum^j_{i=0}\tau_i \stackrel{j\to\infty}{=} j\bar{\tau} = j \delta \tau \bar{n}$'
)
for i, lines in lines.iteritems():
for w, line in enumerate(lines):
x, y, label = line
style = '--' if not w % 2 else '-'
ax[i].plot(x,
y,
label=label,
linewidth=(w + 1) * 2,
alpha=0.4,
linestyle=style)
for i in ax:
i.grid(True)
i.legend(loc='best', shadow=True, fontsize=pp.tfont, fancybox=True)
i.set_ylabel(r'Autocorrelation, $C(t)$') # same y axis for all
pp.save_or_show(save, PLOT_LOC)
pass
def plot(res, actual, save):
"""Plots 2 stacked figures:
1. The ratio of changes in integrated autocorrelation time
2. The ratio of changes in autocorrelation time
Required Inputs
probs :: dict :: as below
accepts :: dict :: as below
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(2, figsize=(8, 8))
fig.suptitle(
r'Comparisions of \verb|uWerr()| in \verb|python|:$A[X]$ and \verb|matlab|:$U[X]$',
fontsize=pp.ttfont)
ax[0].set_xlabel(r'Integration Window, $w$', fontsize=pp.tfont)
x = np.arange(actual['itau_aav'].size)
ax[0].set_title(r'Measuring the ratio $\Delta = 1 - \frac{U[X]}{A[X]}$',
fontsize=pp.tfont)
ax[0].plot(x, (res['itau_aav'] - actual['itau_aav']) / res['itau_aav'],
label=r'$X = \bar{\bar{\tau}}(w)$')
ax[0].set_ylabel(r'$\Delta$', fontsize=pp.tfont - 2)
ax[0].legend(loc='best', shadow=True, fontsize=pp.tfont, fancybox=True)
diff_acorr = res['acorr'] - actual['acorr']
ax[1].plot(x, diff_acorr / res['acorr'], label=r"$X = \Gamma(t)$")
ax[1].set_ylabel(r"$\Delta$", fontsize=pp.tfont - 2)
ax[1].legend(loc='best', shadow=True, fontsize=pp.tfont, fancybox=True)
ax[1].set_xlabel(r'Autocorrelation Time, $t$', fontsize=pp.tfont)
for i in ax:
i.grid(True)
pp.save_or_show(save, PLOT_LOC)
pass
import matplotlib.ticker as plticker
import numpy as np
from PIL import Image
from scipy.signal import residuez, tf2zpk
from data import store
from plotter import Pretty_Plotter, PLOT_LOC
from common.utils import saveOrDisplay
from theory.autocorrelations import M2_Exp
file_name = __file__
save = False
# start plotting
pp = Pretty_Plotter()
pp._teXify() # LaTeX
pp.params['text.latex.preamble'] = [r"\usepackage{amsmath}"]
pp._updateRC()
dx = (0-2000)/10.
dy = (.0-.05)/5.
fig = plt.figure(figsize=(8,8))
ax = fig.add_subplot(111)
fig.suptitle(r"Verifying theory", fontsize=pp.tfont)
ax.set_title(r'Overlaying functions on an image of a published figure', fontsize=pp.tfont)
ax.set_xlabel(r'$t$', fontsize=pp.tfont)
ax.set_ylabel(r'$C_{M^2}(t)$', fontsize=pp.tfont)
xlim = (0, 2000)
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(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(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
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 anim(burn_in, samples, bg_xyz, save):
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'$Q(\phi_{x}) = e^{-50|\phi_{x}^2 + \tfrac{1}{10}|}$'
ax.set_title(r'Showing {} burn-in \& {} HMC 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)
# z = np.ma.array(z, mask=z < .01) # optionally mask to white below certain value
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',
)
points = ax.plot(samples[0, 0],
samples[0, 1],
color='blue',
alpha=0.7,
ms=3,
linestyle='',
marker='o')
def getCollection(length=None, samples=samples, cmap='magma_r'):
"""Creates a collection from sample chain of shape: (length,dims)
Optional Inputs
length :: int :: the include this many chain samples
"""
if length is None: length = samples[:, 1].size
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(cmap),
norm=plt.Normalize(250, 1500))
lc.set_array(np.arange(length))
lc.set_linewidth(1.)
lc.set_alpha(0.3)
return lc
length = 50
def init():
points.set_data([], [])
return points,
def animate(i): # animation func
# if i==1: del ax.collections[-2] # replace these lines
points.set_data(samples[:i, 0], samples[:i, 1])
# lc = getCollection(length=None)
# col = ax.add_collection(lc)
return points,
anim = animation.FuncAnimation(fig,
animate,
np.arange(length),
interval=50)
plt.show()
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(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
# grab errors
print 'getting errors...'
ans = uWerr(op, a)
_, _, _, itau, itau_diff, _, acns = ans # extract data
my_w = getW(itau, itau_diff, n=n_samples) # get window length
my_err = acorrnErr(acns, my_w, n_samples) # get autocorr errors
my_err *= np.sqrt(n_samples) / np.sqrt(counts)
# theory calclations
if cpp:
th_x = np.linspace(min_sep, max_sep, 1000)
th = np.array([hmc(p, phi, r, i) for i in th_x])
pp = Pretty_Plotter()
pp._teXify()
pp.params['text.latex.preamble'] = [r"\usepackage{amsmath}"]
pp.params['text.latex.preamble'] = [r"\usepackage{mathrsfs}"]
pp._updateRC()
fig = plt.figure(figsize=(8, 8)) # make plot
ax = []
fig, ax = plt.subplots(2, sharex=True, figsize=(8, 8))
ax[-1].set_xlabel(
r'Fictitious time separation, $t : t = m\delta\tau$ for $m\in\mathbb{N}$')
main_title = r'HMC Autocorrelation Data for Exponentially Distributed Trajectories'
info_title = r'Samples: $10^{:d}$ Lattice: ({:d},{:d}), $m={:3.1f}$, $n={:d}$, '.format(
int(np.log10(n_samples)), n, dim, m,
n_steps) + r'$\delta\tau = \frac{2}{m(3\sqrt{3} - \sqrt{15})}\frac{1}{n}$'
th_label = r'Theory: $\mathcal{C}_{\text{HMC}}(t; P_{\text{acc}}=' + r'{:5.3f}, \phi = {:5.3f}, r={:5.3f}'.format(
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(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(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
