def coreFunc(a):
"""runs the below for an angle, a
Allows multiprocessing across a range of values for a
"""
i, a = a
model = Model(x0,
pot=pot,
spacing=spacing,
rng=rng,
step_size=step_size,
n_steps=n_steps,
rand_steps=rand_steps)
c = acorr.Autocorrelations_1d(model)
c.runModel(n_samples=n_samples,
n_burn_in=n_burn_in,
mixing_angle=a,
verbose=True,
verb_pos=i)
store.store(c.model.samples, file_name, '_samples')
store.store(c.model.traj, file_name, '_trajs')
acs = c.getAcorr(separations,
opFn,
norm=False,
prll_map=prll_map,
max_sep=50) # non norm for uWerr
# get parameters generated
traj = np.cumsum(c.trajs)
p = c.model.p_acc
xx = c.op_mean
acorr_seps = c.acorr_ficticous_time
acorr_counts = c.acorr_counts
store.store(p, file_name, '_probs')
store.store(acs, file_name, '_acs')
ans = errors.uWerr(c.op_samples, acorr=acs) # get errors
_, _, _, itau, itau_diff, _, acns = ans # extract data
w = errors.getW(itau, itau_diff, n=n_samples) # get window length
acns_err = errors.acorrnErr(acns, w, n_samples) # get error estimates
if rand_steps: # correct for N being different for each correlation
acns_err *= np.sqrt(n_samples) / acorr_counts
return xx, acns, acns_err, p, w, traj, acorr_seps
def main(x0, pot, file_name, n_samples, n_burn_in,
mixing_angles, step_sizes, separations, opFn ,n_steps = 1,
tintTh=None, paccTh = None, opTh = None, plot_res=1000,
save = False):
"""A wrapper function
Required Inputs
x0 :: np.array :: initial position input to the HMC algorithm
pot :: potential class :: defined in hmc.potentials
file_name :: string :: the final plot will be saved with a similar name if save=True
n_samples :: int :: number of HMC samples
n_burn_in :: int :: number of burn in samples
mixing_angles :: iterable :: mixing angles for the HMC algorithm
angle_labels :: list :: list of labels for the angles provided
opFn :: func :: function for autocorellations - takes one input: samples
op_name :: str :: name of opFn for plotting
separations :: iterable :: lengths of autocorellations
max_sep :: float :: define the max separation
Optional Inputs
rand_steps :: bool :: probability of with prob
step_size :: float :: MDMC step size
n_steps :: int :: number of MDMC steps
spacing :: float :: lattice spacing
acFunc :: func :: function for evaluating autocorrelations
save :: bool :: True saves the plot, False prints to the screen
"""
# required declarations. If no lines are provided this still allows iteration for 0 times
lines = {} # contains the label as the key and a tuple as (x,y) data in the entry
acs = {}
rng = np.random.RandomState()
print 'Running Model: {}'.format(file_name)
def coreFunc(a):
"""runs the below for an angle, a
Allows multiprocessing across a range of values for a
"""
i,d,a = a
model = Model(x0, pot=pot, rng=rng, step_size = d,
n_steps = n_steps, rand_steps=False)
c = acorr.Autocorrelations_1d(model)
c.runModel(n_samples=n_samples, n_burn_in=n_burn_in, mixing_angle = a, verbose=False, verb_pos=i)
acs = c.getAcorr(separations, opFn, norm = False)
# get parameters generated
pacc = c.model.p_acc
pacc_err = np.std(c.model.sampler.accept.accept_rates)
ans = errors.uWerr(c.op_samples, acorr=acs) # get errors
op_av, op_diff, _, itau, itau_diff, _, acns = ans # extract data
w = errors.getW(itau, itau_diff, n=n_samples) # get window length
if not np.isnan(w):
acns_err = errors.acorrnErr(acns, w, n_samples) # get error estimates
acs = acns
else:
acns_err = np.full(acs.shape, np.nan)
itau = itau_diff = np.nan
return op_av, op_diff, acs, acns_err, itau, itau_diff, pacc, pacc_err, w
# use multiprocessings
elms = step_sizes.size*mixing_angles.size
combinations = np.zeros((elms,3))
combinations[:,1:] = np.array(np.meshgrid(step_sizes, mixing_angles)).T.reshape(-1,2)
combinations[:,0] = np.arange(elms)
ans = prll_map(coreFunc, combinations, verbose=True)
print 'Finished Running Model: {}'.format(file_name)
# results have now been obtained. This operation is a dimension shuffle
# Currently the first iterable dimension contains one copy of each item
# Want to split into separate arrays each of length n
op_av, op_diff, acs, acns_err, itau, itau_diff, pacc, pacc_err, w = zip(*ans)
op_av = np.array(op_av)
op_diff = np.array(op_diff)
acs = np.array(acs)
acns_err = np.array(acns_err)
itau = np.array(itau)
itau_diff = np.array(itau_diff)
pacc = np.array(pacc)
pacc_err = np.array(pacc_err).ravel()
w = np.array(w)
# Bundle all data ready for Plot() and store data as .pkl or .json for future use
all_plot = {'itau':(step_sizes, itau, itau_diff),
'pacc':(step_sizes, pacc, pacc_err),
'acorr':(step_sizes, acs, acns_err),
'op':(step_sizes, op_av, op_diff)
}
max_step = step_sizes[-1]
min_step = step_sizes[0]
step_sizes_th = np.linspace(min_step, max_step, plot_res)
if paccTh is not None:
accs = np.asarray(map(paccTh,step_sizes_th))
all_plot['pacc_th'] = (step_sizes_th, accs)
if tintTh is not None:
# itau = np.asarray([tintTh(dtau,acc) for dtau, acc in zip(step_sizes_th, pacc)])
# itau_hi = np.asarray([tintTh(dtau,acc) for dtau, acc in zip(step_sizes_th, pacc+pacc_err)])
# itau_lo = np.asarray([tintTh(dtau,acc) for dtau, acc in zip(step_sizes_th, pacc-pacc_err)])
# all_plot['tint_th'] = (step_sizes_th, itau, itau_hi, itau_lo)
itau = np.asarray([tintTh(dtau,acc) for dtau, acc in zip(step_sizes_th, accs)])
all_plot['tint_th'] = (step_sizes_th, itau)
# do the same for the X^2 operators
if opTh is not None:
all_plot['op_th'] = (step_sizes_th, np.asarray(map(opTh,step_sizes_th)))
store.store(all_plot, file_name, '_allPlot')
plot(save = saveOrDisplay(save, file_name), **all_plot)
def main(x0,
pot,
file_name,
n_samples,
n_burn_in,
mixing_angles,
angle_labels,
opFn,
op_name,
separations,
rand_steps=False,
step_size=.5,
n_steps=1,
spacing=1.,
acFunc=None,
save=False):
"""A wrapper function
Required Inputs
x0 :: np.array :: initial position input to the HMC algorithm
pot :: potential class :: defined in hmc.potentials
file_name :: string :: the final plot will be saved with a similar name if save=True
n_samples :: int :: number of HMC samples
n_burn_in :: int :: number of burn in samples
mixing_angles :: iterable :: mixing angles for the HMC algorithm
angle_labels :: list :: list of labels for the angles provided
opFn :: func :: function for autocorellations - takes one input: samples
op_name :: str :: name of opFn for plotting
separations :: iterable :: lengths of autocorellations
max_sep :: float :: define the max separation
Optional Inputs
rand_steps :: bool :: True for exponential distribution of MDMC steps
step_size :: float :: MDMC step size
n_steps :: int :: number of MDMC steps
spacing :: float :: lattice spacing
acFunc :: func :: function for evaluating autocorrelations
save :: bool :: True saves the plot, False prints to the screen
"""
al = len(mixing_angles) # the number of mixing angles
send_prll = prll_map if al == 1 else None
# required declarations. If no lines are provided this still allows iteration for 0 times
lines = {
} # contains the label as the key and a tuple as (x,y) data in the entry
acs = {}
if not isinstance(separations, np.ndarray):
separations = np.asarray(separations)
rng = np.random.RandomState()
subtitle = r"Potential: {}; Lattice: ${}$; $a={:.1f}; \delta\tau={:.2f}; n={}; m={:.1f}$".format(
pot.name, x0.shape, spacing, step_size, n_steps, pot.m)
print 'Running Model: {}'.format(file_name)
def coreFunc(a):
"""runs the below for an angle, a
Allows multiprocessing across a range of values for a
"""
i, a = a
model = Model(x0,
pot=pot,
spacing=spacing,
rng=rng,
step_size=step_size,
n_steps=n_steps,
rand_steps=rand_steps)
c = acorr.Autocorrelations_1d(model)
c.runModel(n_samples=n_samples,
n_burn_in=n_burn_in,
mixing_angle=a,
verbose=True,
verb_pos=i)
store.store(c.model.samples, file_name, '_samples')
store.store(c.model.traj, file_name, '_trajs')
acs = c.getAcorr(separations,
opFn,
norm=False,
prll_map=prll_map,
max_sep=50) # non norm for uWerr
# get parameters generated
traj = np.cumsum(c.trajs)
p = c.model.p_acc
xx = c.op_mean
acorr_seps = c.acorr_ficticous_time
acorr_counts = c.acorr_counts
store.store(p, file_name, '_probs')
store.store(acs, file_name, '_acs')
ans = errors.uWerr(c.op_samples, acorr=acs) # get errors
_, _, _, itau, itau_diff, _, acns = ans # extract data
w = errors.getW(itau, itau_diff, n=n_samples) # get window length
acns_err = errors.acorrnErr(acns, w, n_samples) # get error estimates
if rand_steps: # correct for N being different for each correlation
acns_err *= np.sqrt(n_samples) / acorr_counts
return xx, acns, acns_err, p, w, traj, acorr_seps
# use multiprocessing
if al == 1: # don't use multiprocessing for just 1 mixing angle
a = mixing_angles[0]
ans = [coreFunc((i, a)) for i, a in enumerate(mixing_angles)]
else: # use multiprocessing for a number of mixing angles
ans = prll_map(coreFunc, zip(range(al), mixing_angles), verbose=False)
#
print 'Finished Running Model: {}'.format(file_name)
# results have now been obtained. This operation is a dimension shuffle
# Currently the first iterable dimension contains one copy of each item
# Want to split into separate arrays each of length n
xx, acns, acns_err, ps, ws, ts, acxs = zip(*ans)
print 'trajs:'
print ts
print '\n' * al # hack to avoid overlapping with the progress bar from multiprocessing
out = lambda p, x, a: '> measured at angle:{:3.1f}: <x(0)x(0)> = {}; <P_acc> = {:4.2f}'.format(
a, x, p)
for p, x, a in zip(ps, xx, mixing_angles):
print out(p, x, a) # print output as defined above
# Decide a good total length for the plot
w = np.max(ws) # same length for all theory and measured data
print 'Window is:{}'.format(w)
if np.isnan(w):
alen = int(len(separations) / 2)
else:
alen = 2 * w
# Create Dictionary for Plotting Measured Data
aclabel = r'Measured: $C_{\mathscr{X}^2}(s; ' \
+ r'\langle\rho_t\rangle_t'+r'={:4.2f}; '.format(p)
yelpwx = zip(acns, acns_err, angle_labels, ps, ws,
acxs) # this is an iterable of all a/c plot values
# create the dictionary item to pass to plot()
acns = {
aclabel + r'\vartheta = {})$'.format(l): (x[:alen], y[:alen], e[:alen])
for y, e, l, p, w_i, x in yelpwx
}
if acFunc is not None: # Create Dictionary for Plotting Theory
fx_f = np.max(np.asarray(
[a[:alen]
for a in acxs])) # last trajectory separation length to plot
fx_res = step_size * 0.1 # points per x-value
fx_points = fx_f / fx_res + 1 # number of points to use
fx = np.linspace(0, fx_f, fx_points,
True) # create the x-axis for the theory
windowed_ps = ps[:alen] # windowed acceptance probabilities
# calculcate theory across all tau, varying p_acc and normalise
normFn = lambda pt: np.array(
[acFunc(t=xi, pa=pt[0], theta=pt[1])
for xi in fx]) / acFunc(t=0, pa=pt[0], theta=pt[1])
fs = map(normFn, zip(
ps, mixing_angles)) # map the a/c function to acceptance & angles
th_label = r'Theory: $C_{\mathscr{X}^2}(s\sim \text{Exp}(\frac{1}{r}); \langle\rho_t\rangle_t = '
pfl = zip(
ps, fs,
angle_labels) # this is an iterable of all theory plot values
pfl = pfl[:alen] # cut to the same window length as x-axis
# create the dictionary item to pass to plot()
lines = {
th_label + r'{:4.2f}; \theta = {})$'.format(p, l): (fx, f)
for p, f, l in pfl if f is not None
}
else:
pass # lines = {} has been declared at the top so will allow the iteration in plot()
# Bundle all data ready for Plot() and store data as .pkl or .json for future use
all_plot = {
'acns': acns,
'lines': lines,
'subtitle': subtitle,
'op_name': op_name
}
store.store(all_plot, file_name, '_allPlot')
plot(acns, lines, subtitle, op_name, save=saveOrDisplay(save, file_name))
def main(x0,
pot,
file_name,
n_rng,
n_samples=1000,
n_burn_in=25,
step_size=0.2,
save=False):
"""A wrapper function
Required Inputs
x0 :: np.array :: initial position input to the HMC algorithm
pot :: pot. cls :: defined in hmc.potentials
file_name :: string :: the final plot will be saved with a similar name if save=True
n_rng :: int arr :: array of number of leapfrog step sizes
Optional Inputs
n_samples :: int :: number of HMC samples
n_burn_in :: int :: number of burn in samples
save :: bool :: bool :: True saves the plot, False prints to the screen
step_size :: int :: Leap Frog step size
"""
lines = {
} # contains the label as the key and a tuple as (x,y) data in the entry
scats = {}
print 'Running Model: {}'.format(file_name)
# f = np.vectorize(lambda t: accHMC1dFree(t, step_size, 0, np.arange(1, x0.size+1)))
f = np.vectorize(lambda t: HMC1dfVm0lf0(t, step_size, x0.size))
x_fine = np.linspace(0, n_rng[-1] * step_size, 101, True)
theory1 = f(x_fine)
label = r'$\text{erfc}\left( \frac{\delta\tau^2}{2}' \
+ r' \sqrt{ 2 p^{2}_{0,1} N \sigma^{(2)}_{m^2} } \right)$'
lines[label] = (x_fine, theory1)
def coreFunc(n_steps):
"""function for multiprocessing support
Required Inputs
n_steps :: int :: the number of LF steps
"""
model = Model(x0.copy(),
pot,
step_size=step_size,
n_steps=n_steps,
accept_kwargs={'get_delta_hs': True})
model.sampler.accept.store_acceptance = True
prob = 1.
delta_hs = 1.
av_dh = -1
accept_rates = []
delta_hs = []
samples = []
while av_dh < 0:
model.run(n_samples=n_samples, n_burn_in=n_burn_in)
accept_rates += model.sampler.accept.accept_rates[n_burn_in:]
delta_hs += model.sampler.accept.delta_hs[n_burn_in:]
samples.append(model.samples.copy())
av_dh = np.mean(delta_hs)
if av_dh < 0: tqdm.write('running again -ve av_dh')
accept_rates = np.asarray(accept_rates)
samples = np.concatenate(tuple(samples), axis=0)
prob = accept_rates.mean()
meas_av_exp_dh = np.asscalar((1. / np.exp(delta_hs)).mean())
# ans = errors.uWerr(accept_rates) # get errors
# f_aav, f_diff, _, itau, itau_diff, _, acns = ans # extract data
mean = accept_rates.mean()
err = np.std(accept_rates) / np.sqrt(n_samples)
th_err = np.std(accept_rates) / np.sqrt(n_samples)
theory = acceptance(dtau=step_size, delta_h=av_dh)
return mean, theory, err, th_err
# use multi-core support to speed up
ans = prll_map(coreFunc, n_rng, verbose=True)
print 'Finished Running Model: {}'.format(file_name)
prob, theory, errs, th_err = zip(*ans)
x = np.asarray(n_rng) * step_size
# theories[r'$p_{HMC}$'] = (x2, theory2)
scats[r'$\text{erfc}(\sqrt{\langle \delta H_t \rangle}/2)$'] = (x, theory,
th_err)
scats[r'Measured'] = (x, prob, errs)
# one long subtitle - long as can't mix LaTeX and .format()
subtitle = '\centering Potential: {}, Lattice: {}'.format(pot.name, x0.shape) \
+ r', $\delta\tau = ' + '{:4.2f}$'.format(step_size)
all_plot = {'lines': lines, 'scats': scats, 'subtitle': subtitle}
store.store(all_plot, file_name, '_allPlot')
plot(
lines=lines,
scats=scats,
subtitle=subtitle,
save=saveOrDisplay(save, file_name),
)
pass
def main(x0,
pot,
file_name,
n_samples,
n_burn_in,
mixing_angle,
angle_labels,
opFn,
op_name,
rand_steps=False,
step_size=.5,
n_steps=1,
spacing=1.,
itauFunc=None,
separations=range(5000),
acTheory=None,
max_sep=None,
save=False):
"""Takes a function: opFn. Runs HMC-MCMC. Runs opFn on HMC samples.
Calculates Autocorrelation + Errors on opFn.
Required Inputs
x0 :: np.array :: initial position input to the HMC algorithm
pot :: potential class :: defined in hmc.potentials
file_name :: string :: final plot will be saved with a similar name if save=True
n_samples :: int :: number of HMC samples
n_burn_in :: int :: number of burn in samples
mixing_angle :: iterable :: mixing angles for the HMC algorithm
angle_labels :: list :: list of angle label text for legend plotting
opFn :: func :: a function to run over samples
op_name :: str :: label for the operator for plotting
Optional Inputs
rand_steps :: bool :: probability of with prob
step_size :: float :: MDMC step size
n_steps :: int :: number of MDMC steps
spacing ::float :: lattice spacing
save :: bool :: True saves the plot, False prints to the screen
acTheory :: func :: acTheory(t, pa, theta) takes in acceptance prob., time, angle
separations :: range / nparray :: the number of separations for A/C
max_sep :: float :: the maximum separation tom consider for autocorrelations
"""
rng = np.random.RandomState()
multi_angle = len(mixing_angle) > 1 # see if multiprocessing is needed
print 'Running Model: {}'.format(file_name)
# output to print to screen
out = lambda p,x,a: '> measured at angle:{:3.1f}:'.format(a) \
+ ' <x^2>_L = {}; <P_acc>_HMC = {:4.2f}'.format(x, p)
if not multi_angle:
mixing_angle = mixing_angle[0]
model = Model(
x0,
pot=pot,
spacing=spacing, # set up model
rng=rng,
step_size=step_size,
n_steps=n_steps,
rand_steps=rand_steps)
c = acorr.Autocorrelations_1d(model) # set up autocorrs
c.runModel(
n_samples=n_samples,
n_burn_in=n_burn_in, # run MCMC
mixing_angle=mixing_angle,
verbose=True)
acs = c.getAcorr(separations, opFn, norm=False, prll_map=prll_map)
cfn = c.op_samples
# get parameters generated
traj = c.model.traj # get trajectory lengths for each LF step
p = c.model.p_acc # get acceptance rates at each M-H step
xx = np.average(
c.op_samples) # get average of the function run over the samples
if itauFunc:
t = itauFunc(tau=(n_steps * step_size),
m=1,
pa=p,
theta=mixing_angle)
else:
t = None
if acTheory is not None:
ac_th = np.asarray(
[acTheory(t, p, mixing_angle) for t in c.acorr_ficticous_time])
else:
ac_th = None
ans = errors.uWerr(cfn, acorr=acs)
x, gta, w = preparePlot(cfn,
ans,
n=n_samples,
itau_theory=t,
mcore=False,
acn_theory=ac_th)
window_fns, int_ac_fns, acorr_fns = [[item] for item in gta]
ws = [w] # makes compatible with multiproc
x_lst = [x] # again same as last two lines
print out(p, xx, mixing_angle)
else: # use multicore support
def coreFunc(a):
"""runs the below for an angle, a"""
i, a = a
model = Model(
x0,
pot=pot,
spacing=spacing, # set up model
rng=rng,
step_size=step_size,
n_steps=n_steps,
rand_steps=rand_steps)
c = acorr.Autocorrelations_1d(model) # set up autocorrs
c.runModel(
n_samples=n_samples,
n_burn_in=n_burn_in, # run MCMC
mixing_angle=a,
verbose=True,
verb_pos=i)
acs = c.getAcorr(separations,
opFn,
norm=False,
prll_map=None,
ac=acs,
max_itau=max_itau)
cfn = c.op_samples
# get parameters generated
p = c.model.p_acc # get acceptance rates at each M-H step
xx = np.average(
cfn) # get average of the function run over the samples
ans = errors.uWerr(cfn, acorr=acs)
if itauFunc:
t = itauFunc(tau=n_steps * step_size, m=1, pa=p, theta=a)
else:
t = None
if acTheory is not None:
th_x = np.linspace(0, c.acorr_ficticous_time, 10000)
ac_th = np.asarray([th_x, [acTheory(t, p, a) for t in th_x]])
else:
ac_th = None
x, gta, w = preparePlot(cfn,
n=n_samples,
itau_theory=t,
mcore=True,
acn_theory=ac_th)
return xx, traj, p, x, gta, w
#
# use multiprocessing
l = len(mixing_angle) # number of mixing angles
ans = prll_map(coreFunc, zip(range(l), mixing_angle), verbose=False)
# unpack from multiprocessing
xx, traj, ps, x_lst, gtas, ws = zip(*ans)
print '\n' * l # hack to avoid text overlapping in terminal
for p, x, a in zip(
ps, xx, mixing_angle): # print intermediate results to screen
print out(p, x, a)
window_fns, int_ac_fns, acorr_fns = zip(
*gtas) # separate out to respective lists
lines = {
0: window_fns,
1: int_ac_fns,
2: acorr_fns
} # create a dictionary for plotting
#
print 'Finished Running Model: {}'.format(file_name)
subtitle = r"Potential: {}; Lattice Shape: ".format(pot.name) \
+ r"${}$; $a={:.1f}; \delta\tau={:.1f}; n={}$".format(
x0.shape, spacing, step_size, n_steps)
# all_plot contains all necessary keyword arguments
all_plot = {
'lines_d': lines,
'x_lst': x_lst,
'ws': ws,
'subtitle': subtitle,
'mcore': multi_angle,
'angle_labels': angle_labels,
'op_name': op_name
}
store.store(all_plot, file_name, '_allPlot')
plot(lines_d=lines,
x_lst=x_lst,
ws=ws,
subtitle=subtitle,
mcore=multi_angle,
angle_labels=angle_labels,
op_name=op_name,
save=saveOrDisplay(save, file_name))
pass
def main(x0,
pot,
file_name,
n_samples,
n_burn_in,
angle_fracs,
opFn,
op_name,
rand_steps=False,
step_size=.1,
n_steps=1,
spacing=1.,
iTauTheory=None,
pacc_theory=None,
op_theory=None,
save=False):
"""Takes a function: opFn. Runs HMC-MCMC. Runs opFn on GHMC samples.
Calculates Integrated Autocorrelation + Errors across a number of angles
Required Inputs
x0 :: np.array :: initial position input to the HMC algorithm
pot :: potential class :: defined in hmc.potentials
file_name :: string :: final plot will be saved with a similar name if save=True
n_samples :: int :: number of HMC samples
n_burn_in :: int :: number of burn in samples
angle_fracs :: iterable :: list of values: n, for mixing angles of nπ
opFn :: func :: a function o run over samples
op_name :: str :: label for the operator for plotting
Optional Inputs
rand_steps :: bool :: probability of with prob
step_size :: float :: MDMC step size
n_steps :: int :: number of MDMC steps
spacing :: float :: lattice spacing
iTauTheory :: func :: a function for theoretical integrated autocorrelation
pacc_theory :: float :: a value for theoretical acceptance probability
op_theory :: float :: a value for the operator at 0 separation
save :: bool :: True saves the plot, False prints to the screen
"""
if not isinstance(angle_fracs, np.ndarray):
angle_fracs = np.asarray(angle_fracs)
if not hasattr(n_samples, '__iter__'):
n_samples = [n_samples] * angle_fracs.size
rng = np.random.RandomState()
angls = np.pi * angle_fracs
print 'Running Model: {}'.format(file_name)
explicit_prog = (angls.size <= 16)
def coreFunc(a):
"""runs the below for an angle, a"""
i, a, n_samples = a
model = Model(
x0,
pot=pot,
spacing=spacing, # set up model
rng=rng,
step_size=step_size,
n_steps=n_steps,
rand_steps=rand_steps)
c = acorr.Autocorrelations_1d(model) # set up autocorrs
c.runModel(
n_samples=n_samples,
n_burn_in=n_burn_in, # run MCMC
mixing_angle=a,
verbose=explicit_prog,
verb_pos=i)
cfn = opFn(c.model.samples) # run func on HMC samples
# get parameters generated
p = c.model.p_acc # get acceptance rates at each M-H step
# Calculating integrated autocorrelations
ans = errors.uWerr(cfn)
xx, f_diff, _, itau, itau_diff, itaus, _ = ans
w = errors.getW(itau, itau_diff, n=cfn.shape[0])
out = itau, itau_diff, f_diff, w
return xx, p, itau, itau_diff, f_diff, w
#
ans = prll_map(coreFunc,
zip(range(angle_fracs.size), angls, n_samples),
verbose=1 - explicit_prog)
# unpack from multiprocessing
xx_lst, p_lst, itau_lst, itau_diffs_lst, f_diff_lst, w_lst = zip(*ans)
print '\n' * angle_fracs.size * explicit_prog # hack to avoid overlapping!
print 'Finished Running Model: {}'.format(file_name)
subtitle = r"Potential: {}; Lattice: ".format(pot.name) \
+ r"${}$; $a={:.1f}; \delta\tau={:.1f}; n={}$".format(
x0.shape, spacing, step_size, n_steps)
# Create dictionary item for the measured data
lines = { # format is [(y, Errorbar, label)] if no errorbars then None
0: [(itau_lst, itau_diffs_lst, r'Measured')],
1: [(xx_lst, f_diff_lst, r'Measured')],
2: [(w_lst, None, r'Measured')],
3: [(p_lst, None, r'Measured')]
}
# append theory lines to each dictionary list item
# add theory for integrated autocorrelations if provided
if iTauTheory is not None:
vFn = lambda pt: iTauTheory(
tau=n_steps * step_size, m=pot.m, pa=pt[0], theta=pt[1])
f = map(vFn, zip(p_lst,
angls)) # map the a/c function to acceptance & angles
lines[0].append((f, None, r'Theory'))
if op_theory is not None:
f = np.full(angls.shape, op_theory)
lines[1].append((f, None, r'Theory'))
# add theory for acceptance probabilities
if pacc_theory is not None:
f = np.full(angls.shape, pacc_theory)
lines[3].append((f, None, 'Theory'))
all_plot = {
'lines': lines,
'x': angle_fracs,
'subtitle': subtitle,
'op_name': op_name
}
if save: store.store(all_plot, file_name, '_allPlot')
# enter as keyword arguments
plot(save=saveOrDisplay(save, file_name), **all_plot)
pass