def avg_quark_prop(size_list=[8, 8, 8, 8],
cfgs_list=range(200, 1200, 50),
src_type='evenodd_wall',
t0=0,
color_list=[0],
ens_tag='',
prop_tag='eoprop_',
mass=0.5,
figname='',
**lat_kwargs):
"""
This function loads the propagators calculated in :meth:`gauge_tools.examples.staggered_quark_prop`
and averages them. Most key word arguments are similar to those of :meth:`gauge_tools.examples.staggered_quark_prop`,
except for ``figname``, which if not an empyt string, is a signal to create a figure and save it as a pdf in `figname`.
"""
fname_load = lambda ind_cfg: "{}{}m{}_{}.npy".format(
ens_tag, prop_tag, mass, ind_cfg)
fname_save = "{}{}m{}_avg.p".format(ens_tag, prop_tag, mass)
import gauge_tools as gt
lat = gt.lattice(*size_list, **lat_kwargs)
props_list = []
props_projected = []
for n_cfg in cfgs_list:
prop_v_field = np.load(fname_load(n_cfg), allow_pickle=True)
props_list.append(prop_v_field)
props_projected.append(
gt.util.quark.propagator.ks_project_spatialmom(
prop_v_field, color=color_list[0]))
props_proj_gvar = gv.dataset.avg_data(props_projected)
pickle.dump(
dict(mean=gv.mean(props_proj_gvar), cov=gv.evalcov(props_proj_gvar)),
open(fname_save, 'wb'))
avg_quark_prop.props_list = props_list
avg_quark_prop.props_proj_gvar = props_proj_gvar
avg_quark_prop.lat = lat
if figname != '' and PLOTS:
plt.ion()
fig = plt.figure()
plt.errorbar(range(len(props_proj_gvar)),
np.abs(gv.mean(props_proj_gvar)),
gv.sdev(props_proj_gvar),
fmt='.',
label='interacting')
free_theory(gt,
src_type=src_type,
t0=t0,
mass=mass,
color_list=color_list,
print_=False)
plt.title('qaurk propagator in free and interacting theory')
plt.legend()
plt.yscale('log')
fig.savefig(figname, format="pdf")
def gradient_flow(size_list=[8, 8, 8, 8],
cfgs_list=range(200, 1200, 50),
action='W',
max_flowtime=1,
eps=0.01,
save_field=False,
fname_output='',
ens_tag='',
figname='',
**lat_kwargs):
"""
This function uses the gradient flow method to smear the gauge fields,
and calculates the lattice spacing. The topological charge is also calculated but not investigated yet.
***NOTE*** The materials related to the gradeint flow are NOT complete yet.
This function will probably change in the next versions.
"""
fname_load = lambda ind_cfg: "{}{}.npy".format(ens_tag, ind_cfg)
fname_save = lambda ind_cfg: "{}{}_flowtime{}.npy".format(
ens_tag, n_cfg, max_flowtime)
import gauge_tools as gt
lat = gt.lattice(*size_list, action=action, u0=1,
**lat_kwargs) # we do not use tadpole improvement
a_dset = []
for n_cfg in cfgs_list:
T1 = time.time()
U = lat.GF.load_cfg(fname_load(n_cfg))
if fname_output != '':
with open(fname_output, 'a') as fw:
fw.write("#cfg = {}\n".format(n_cfg))
mydict = lat.smear.gradient_flow(U,
lat.actn.calc_staples,
max_flowtime,
eps,
fname=fname_output)
# Note that `U` is already updated inside the lat.smear.gradient_flow function
a = mydict['a']
if save_field:
np.save(fname_save(n_cfg), U)
print(
" cfg={:.6g} is calculated at flowtime {} and saved; yeilds a={} fm (#TIME = {:.4g})"
.format(n_cfg, max_flowtime, a,
time.time() - T1))
else:
print(" a={:.6g} fm\tfor cfg={} (#TIME = {:.4g})".format(
a, n_cfg,
time.time() - T1))
a_dset.append(a)
a = gv.dataset.avg_data(a_dset)
print(" average: a = {} fm".format(a))
gradient_flow.lat = lat
gradient_flow.mydict = mydict
def Landau_gauge(size_list=[8, 8, 8, 8],
cfgs_list=range(200, 1200, 50),
max_itr=1000,
gaugefix_tol=1e-9,
fname_output='',
ens_tag='',
gauge_tag='Landau_',
**lat_kwargs):
"""
This function loads the gauge configurations generated
with functions :meth:`gauge_tools.examples.generate_ensemble` and :meth:`gauge_tools.examples.expand_ensemble`,
fixes the gauge to the Landau gauge them and saves them.
Parameters:
- ``size_list`` ([int]*4): a list of 4 positive integers specifying the lattice size in `[x,y,z,t]` directions.
- ``cfgs_list`` (list): a list of indices of configurations to be loaded for gauge fixing.
- ``max_itr`` (int): maximum number of iteration in gauge fixing.
- ``gaugefix_tol`` (float): the tolerance to hault the process of gauge fixing.
- ``ens_tag`` (str): a unique tag (label) describing the ensemble:\
for details see the parameters of function :meth:`gauge_tools.examples.generate_ensemble`.
- ``gauge_tag`` (str): a string used to construct a file name for saving the gauge-fixed configuration;\
see below for clarification.
- ``fname_output`` (string): if not an empty string, dumps the details of gauge fixing in `fname_output`.
A note on the file names:
from the parameter `ens_tag` this function constructs two file names:
- to load an existing configuration:
`fname_load = "{}{}.npy".format(ens_tag, ind_cfg)`.
- to save the gauge fixed configuration:
`fname_save = "{}{}{}.npy".format(ens_tag, gauge_tag, ind_cfg)`.
"""
fname_load = lambda ind_cfg: "{}{}.npy".format(ens_tag, ind_cfg)
fname_save = lambda ind_cfg: "{}{}{}.npy".format(ens_tag, gauge_tag, n_cfg)
import gauge_tools as gt
lat = gt.lattice(*size_list, **lat_kwargs)
for n_cfg in cfgs_list:
T1 = time.time()
U = lat.GF.load_cfg(fname_load(n_cfg))
if fname_output != '':
with open(fname_output, 'a') as fw:
fw.write("#cfg = {}\n".format(n_cfg))
lat.gaugefix.gaugefix_Landau(U,
max_itr=max_itr,
gaugefix_tol=gaugefix_tol,
fname=fname_output)
# Note that `U` is already updated inside the lat.smear.gradient_flow function
np.save(fname_save(n_cfg), U)
print(" cfg={} gauge-fixed and saved (#TIME = {:.4g})".format(
n_cfg,
time.time() - T1))
Landau_gauge.lat = lat
def measure_Wilson_loops(size_list=[8, 8, 8, 8],
cfgs_list=range(200, 1200, 50),
binsize=1,
ens_tag='',
**lat_kwargs):
"""
This function computes Monte Carlo averages of `a x a` and `a x 2a` Wilson loops
exploiting the gauge configurations generated with functions :meth:`gauge_tools.examples.generate_ensemble` and :meth:`gauge_tools.examples.expand_ensemble`.
This corresponds to the exercise on page 35 of the `lecture notes`_.
For the exercise simply use::
>>> import gauge_tools as gt
>>> gt.examples.measure_Wilson_loops(cfgs_list=range(200,1200,50), ens_tag='W_')
The output looks like::
Calculating averages of 'axa' and 'ax2a' Wilson loops:
'axa':0.49774(96), 'ax2a':0.2606(13)
Parameters:
- ``size_list`` ([int]*4): a list of 4 positive integers specifying the lattice size in `[x,y,z,t]` directions.
- ``cfgs_list`` (list): a list of indices of configurations to be loaded and used for the Monte Carlo averages.
- ``binsize`` (int): bin size used for estimation of uncertainties.
- ``ens_tag`` (str): a unique tag (label) describing the ensemble:\
for details see the parameters of function :meth:`gauge_tools.examples.generate_ensemble`.
"""
fname_lambda = lambda ind_cfg: "{}{}.npy".format(ens_tag, ind_cfg)
import gauge_tools as gt
lat = gt.lattice(*size_list, **lat_kwargs)
calc_a_a = lambda U: lat.meas.avg_planar_loops(U, l1=1, l2=1)
calc_a_2a = lambda U: lat.meas.avg_planar_loops(U, l1=1, l2=2)
fn = lambda U: (calc_a_a(U), calc_a_2a(U))
print("Calculating averages of 'axa' and 'ax2a' Wilson loops:")
T1 = time.time()
avg = lat.MC.eval_fn(fn,
cfgs_list,
fname_lambda,
binsize=binsize,
avg_data=True)
print("'axa':{}, 'ax2a':{}".format(*avg), end=''),
print("\t(#TIME = {:.4g})".format(time.time() - T1))
measure_Wilson_loops.avg = avg
measure_Wilson_loops.lat = lat
def measure_polyakov_loops(size_list=[8, 8, 8, 8],
cfgs_list=range(200, 1200, 50),
binsize=1,
ens_tag='',
**lat_kwargs):
""" This function calculate the polyakov loops on the given configurations.
"""
fname_lambda = lambda ind_cfg: "{}{}.npy".format(ens_tag, ind_cfg)
import gauge_tools as gt
lat = gt.lattice(*size_list, **lat_kwargs)
fn = lambda U: lat.meas.avg_polyakov_loops(U)
print("Calculating averages of polyakov loops:")
T1 = time.time()
avg = lat.MC.eval_fn(fn,
cfgs_list,
fname_lambda,
binsize=binsize,
avg_data=True)
print("<polyakov-loops>: {}".format(avg), end=''),
print("\t(#TIME = {:.4g})".format(time.time() - T1))
measure_polyakov_loops.avg = avg
measure_polyakov_loops.lat = lat
def expand_ensemble(size_list=[8, 8, 8, 8],
beta=5.5,
action='W',
u0=1,
load_ind=None,
n_cfgs=15,
n_skip=50,
eps_hit=0.24,
ens_tag='',
**lat_kwargs):
"""
This function expands an existing ensemble by loading the last (saved) configuration
and updating it to generate more gauge configurations.
Parameters:
similar to the parameters of :meth:`gauge_tools.examples.generate_ensemble` except that instead of `n_therm` and `update_u0`
there is a new parameter called `load_ind` which is the index (`sweep_cntr`) of the gauge configuration
that should be loaded to start with.
Usage:
(1) For generating (and saving) 15 more gauge configurations with Wilson action, one can use::
>>> import gauge_tools as gt
>>> gt.examples.expand_ensemble(load_ind=400, n_cfgs=15, ens_tag='W_')
where it is assumed that the index (`ind_cfg`) of the last saved configurations is 400.
"""
fname_lambda = lambda ind_cfg: "{}{}.npy".format(ens_tag, ind_cfg)
load_kwargs = dict(mode="load&update",
load_fname=fname_lambda(load_ind),
load_ind=load_ind)
import gauge_tools as gt
lat = gt.lattice(*size_list, beta=beta, action=action, u0=u0, **lat_kwargs)
lat.MC.gen_cfgs(n_skip=n_skip,
n_cfgs=n_cfgs,
fname_lambda=fname_lambda,
eps_hit=eps_hit,
**load_kwargs)
expand_ensemble.lat = lat
def staggered_quark_prop(size_list=[8, 8, 8, 8],
cfgs_list=range(200, 1200, 50),
src_type='evenodd_wall',
t0=0,
color_list=[0],
ens_tag='',
gauge_tag='Landau_',
prop_tag='eoprop_',
mass=0.5,
do_smear=True,
smearing_dict={'u0': 0.84},
tadpole=False,
**lat_kwargs):
"""
This function calculating the propagator of a staggered quark.
Here we smear the links before calculating the quark propagator.
One can simply disable the smearing by setting the option `do_smear=False`.
The smearing parameters can be changed by manipulating `smearing_dict`.
Parameters:
- ``size_list`` ([int]*4): a list of 4 positive integers specifying the lattice size in `[x,y,z,t]` directions.
- ``cfgs_list`` (list): a list of indices of configurations to be loaded for further calculations.
- ``src_type`` (str): a string indicating the source type; the available types are\
'point_src', 'corner_wall', 'even_wall', and 'evenodd_wall', and 'evenminusodd_wall'.
- ``t0`` (int): the time slice of the source.
- ``color_list`` (list): the color charge of the source; for now the code only accepts one charge, e.g. [0].
- ``ens_tag`` (str): a unique tag (label) describing the ensemble:\
for details see the parameters of function :meth:`gauge_tools.examples.generate_ensemble`.
- ``gauge_tag`` (str): a string used to construct a file name for laoding the gauge-fixed configuration;\
see below for clarification.
- ``prop_tag`` (str): a string used to construct a file name for saving the propagators;\
see below for clarification.
- ``mass`` (int): the mass of the quark.
- ``do_smear`` (bool): For smearing the links before calculating the quark propagator;\
the default value is `True`.
- ``smearing_dict`` (dict): a dictionary to control the smearing parameters;\
for available options see :meth:`gauge_tools.examples.ape_smear`.
- ``tadpole`` (bool): if `True`, performs a tadpole improvement on the links befor calculating the propagator;\
the default value is `False`.
A note on the file names:
from the parameter `ens_tag` this function constructs two file names:
- to load an existing configuration:\
`fname_load = "{}{}{}.npy".format(ens_tag, gauge_tag, ind_cfg)`.
- to saved the propagator:\
`fname_save = "{}{}m{}_{}.npy".format(ens_tag, prop_tag, mass, ind_cfg)`.
"""
fname_load = lambda ind_cfg: "{}{}{}.npy".format(ens_tag, gauge_tag,
ind_cfg)
fname_save = lambda ind_cfg: "{}{}m{}_{}.npy".format(
ens_tag, prop_tag, mass, ind_cfg)
import gauge_tools as gt
lat = gt.lattice(*size_list, **lat_kwargs)
lat.quark.set_source(src_type, t0=t0, color_list=color_list)
for n_cfg in cfgs_list:
T1 = time.time()
U = lat.GF.load_cfg(fname_load(n_cfg))
if do_smear:
lat.smear.ape_smear(
U, **smearing_dict) # the smearing is performed on `U`
lat.quark.calc_propagator(U, mass, n_restart=1, tadpole=tadpole)
lat.quark.save_propagator(fname_save(n_cfg))
print(
" cfg={} quark propagator is calculated and saved for mass={} (#TIME = {:.4g})"
.format(n_cfg, mass,
time.time() - T1))
staggered_quark_prop.lat = lat
def generate_ensemble(size_list=[8, 8, 8, 8],
beta=5.5,
action='W',
u0=1,
n_therm=200,
n_cfgs=5,
n_skip=50,
eps_hit=0.24,
update_u0=False,
ens_tag='',
**lat_kwargs):
"""
This function generates a new ensemble of gauge configurations.
The default values of the parameters correspond to the exercise on page 35 of the `lecture notes`_.
Parameters:
- ``size_list`` ([int]*4): a list of 4 positive integers specifying the lattice size in `[x,y,z,t]` directions.
- ``action`` (str): `'W'` stands for Wilson action and `'imp'` stand for an improved action.
- ``beta`` (float): the lattice beta; with our convension this beta already contains the tadpole improvement factor.
- ``u0`` (float): the `u0` used for tadpole improvement (irrelevant for the non-improved action).
- ``n_therm`` (int): number of sweeps for thermalizing the gauge configurations.
- ``n_cfgs`` (int): number of gauge configurations requested to be generated and saved.
- ``n_skip`` (int): number of sweeps between two saved configurations.
- ``update_u0`` (bool): if `True` updates the value of `u0` in the process of thermalizing.
- ``ens_tag`` (str): a unique tag (label) describing the ensemble:\
this tag is used to automatically create a file name for saving (loading) a gauge configuration;\
`fname = "{}{}.npy".format(ens_tag, ind_cfg)`, where `ind_cfg` is explained below.
A note on `ind_cfg`:
this index counts the number of all sweeps including the sweeps for thermalization. With the default values\
of the parameters of this function we will have `ind_cfg \in [100,150,200,250,300]`
for 5 gauge configurations that are going to be saved. (`ind_cfg` is nothing but `sweep_cntr` in the code.)
Usage:
(1) For generating 5 gauge configurations with Wilson action, one can simply use::
>>> import gauge_tools as gt
>>> gt.examples.generate_ensemble(n_cfgs=5, ens_tag='W_')
This generates 5 gauge configurations and saves each of them to a seperate file in the current directory.
One can of course change default values of the parameters of the function.
(2) For generating 5 gauge configurations with the improved action, one can change the parameters to something like::
>>> import gauge_tools as gt
>>> gt.examples.generate_ensemble(beta=1.719/0.797**4, u0=0.797, n_cfgs=5, ens_tag='imp_')
(3) One can also let the code dynamically determine the value of `u0`. To this end, for instance one can use
>>> import gauge_tools as gt
>>> gt.examples.generate_ensemble(beta=1.719/0.797**4, update_u0=True, n_cfgs=5, ens_tag='imp_')
"""
fname_lambda = lambda ind_cfg: "{}{}.npy".format(ens_tag, ind_cfg)
import gauge_tools as gt
lat = gt.lattice(*size_list, beta=beta, action=action, u0=u0, **lat_kwargs)
lat.MC.thermalize(n_therm,
fname_lambda=fname_lambda,
update_u0=update_u0,
eps_hit=eps_hit)
lat.MC.gen_cfgs(n_skip=n_skip,
n_cfgs=n_cfgs - 1,
fname_lambda=fname_lambda,
eps_hit=eps_hit)
generate_ensemble.lat = lat
def ape_smear(size_list=[8, 8, 8, 8],
cfgs_list=range(200, 1200, 50),
n_smear=4,
eps_smear=1 / 12.,
u0=0.84,
space_only=True,
project_SU3=True,
ens_tag='',
smear_tag='smear4_',
**lat_kwargs):
"""
This function loads the gauge configurations generated
with functions :meth:`gauge_tools.examples.generate_ensemble` and :meth:`gauge_tools.examples.expand_ensemble`,
smears them and saves them.
This corresponds to the exercise on page 37 of the `lecture notes`_.
For the exercise simply use::
>>> import gauge_tools as gt
>>> gt.examples.ape_smear(cfgs_list=range(200,1200,50), ens_tag='W_')
Parameters:
- ``size_list`` ([int]*4): a list of 4 positive integers specifying the lattice size in `[x,y,z,t]` directions.
- ``cfgs_list`` (list): a list of indices of configurations to be loaded for smearing.
- ``n_smear`` (int): number of smearings.
- ``eps_smear`` (float): the `eps` used for smearing.
- ``u0`` (float): the `u0` used for tadpole improvement.
- ``ens_tag`` (str): a unique tag (label) describing the ensemble:\
for details see the parameters of function :meth:`gauge_tools.examples.generate_ensemble`.
- ``smear_tag`` (str): a string used to construct a file name for saving a smeared gauge configuration;\
see below for clarification.
- ``space_only`` (bool): the default value is `True` indicating that the smearing is going to be done only in spatial planes.\
If set to `False`, the smearing will be performed for termpotal links too,\
and also includes spatial-temporal planes.
- ``project_SU3`` (bool): the default value is `False` indicating that the smeared links are projected to SU(3) in the end.\
Note that the algorithm used here works only for SU(3) gauges.
A note on the file names:
from the parameter `ens_tag` this function constructs two file names:
- to load an existing configuration:
`fname_load = "{}{}.npy".format(ens_tag, ind_cfg)`.
- to save the smeared configuration:
`fname_save = "{}{}{}.npy".format(ens_tag, smear_tag, ind_cfg)`.
"""
fname_load = lambda ind_cfg: "{}{}.npy".format(ens_tag, ind_cfg)
fname_save = lambda ind_cfg: "{}{}{}.npy".format(ens_tag, smear_tag,
ind_cfg)
smearing_dict = dict(eps=eps_smear,
n_smear=n_smear,
u0=u0,
space_only=space_only,
project_SU3=project_SU3)
import gauge_tools as gt
lat = gt.lattice(*size_list, **lat_kwargs)
for n_cfg in cfgs_list:
T1 = time.time()
U = lat.GF.load_cfg(fname_load(n_cfg))
lat.smear.ape_smear(
U, **smearing_dict) # the smearing is performed on `U`
np.save(fname_save(n_cfg), U)
print(" cfg={} is smeard and saved (#TIME = {:.4g})".format(
n_cfg,
time.time() - T1))
ape_smear.lat = lat
def static_potential(size_list=[8, 8, 8, 8],
cfgs_list=range(200, 1200, 50),
max_R=4.1,
max_T=5,
ens_tag='',
smear_tag='',
do_smear=True,
smearing_dict={'u0': 0.84},
figname='',
**lat_kwargs):
"""
This function computes the statice potential from Monte Carlo averages of `R times T` Wilson loops
for different values of `R` and `T`.
This corresponds to the exercise on page 37 of the `lecture notes`_.
Here we smear the links first and then calculate the Wilson loops.
One can simply disable the smearing by setting the option `do_smear=False`.
Note that one can first run :meth:`gauge_tools.examples.ape_smear` to smear the links, save them, and then use them here.
With a combination of the options `ens_tag` and `smear_tag` one can specify the links to be read,
and with the option `do_smear` one can request an in-place smearing. In this case, one can control the
smearing parameters by the `smearing_dict`. The latter one is used by default.
For the exercise simply use::
>>> import gauge_tools as gt
>>> gt.examples.static_potential(cfgs_list=range(200,1200,50), ens_tag='W_', figname='static_W_smear4.pdf')
Parameters:
- ``size_list`` ([int]*4): a list of 4 positive integers specifying the lattice size in `[x,y,z,t]` directions.
- ``cfgs_list`` (list): a list of indices of configurations to be loaded for further calculations.
- ``ens_tag`` (str): a unique tag (label) describing the ensemble:\
for details see the parameters of :meth:`gauge_tools.examples.generate_ensemble`.
- ``smear_tag`` (str): useful if one is going to use the already saved smeared links;\
for details see the parameters of :meth:`gauge_tools.examples.ape_smear`.
Ignore this if the smearing is going to be done in place.
- ``do_smear`` (bool): For smearing the links before calculating the Wilson loops;\
the default value is `True`.
- ``smearing_dict`` (dict) a dictionary to control the smearing parameters;\
for available options see :meth:`gauge_tools.examples.ape_smear`.
- ``max_R`` (float): calculates the static potential for distances `\le max_R`.
- ``max_T`` (int): calculates the static potential for all times `\le max_T`.
- ``figname`` (str): if not an empyt string, creates a figure and saves it as a pdf in `figname`.
"""
import gauge_tools as gt
lat = gt.lattice(*size_list, **lat_kwargs)
#===============
fname_load = lambda ind_cfg: "{}{}{}.npy".format(ens_tag, smear_tag, n_cfg)
fname_save = "{}{}{}.p".format(ens_tag, smear_tag, 'Wilson_loops')
#===============
dset = []
range_T = range(1, 1 + max_T)
range_R, spatial_paths = define_paths(max_R)
func = lambda U: [
lat.meas.avg_RxT_loops(U, path_R, max_T) for path_R in spatial_paths
]
#===============
for n_cfg in cfgs_list:
T1 = time.time()
U = lat.GF.load_cfg(fname_load(n_cfg))
if do_smear:
lat.smear.ape_smear(
U, **smearing_dict) # the smearing is performed on `U`
dset.append(func(U))
print(" RxT is evaluated for cfg={} (#TIME = {:.4g})".format(
n_cfg,
time.time() - T1))
W = gv.dataset.avg_data(dset)
pickle.dump(dict(r=range_R, Wmean=gv.mean(W), Wcov=gv.evalcov(W)),
open(fname_save, 'wb'))
if figname != '' and PLOTS:
V = gv.log(W[:, :-1] / np.roll(W, -1, axis=1)[:, :-1])
plot_static_potential(range_R, V, figname=figname)
static_potential.lat = lat