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Feat/flow (#176)
* fix: String conversion of Obs can now handle a dvalue that is NaN or inf * Feat: Added extraction of w0/a from openQCD files * Removed unnecessary round in w0 routine * Improved error handling in fit_t0 * Allowed to change the reference flow time in t0 and w0 determinations. * Added doc string to fit_t0
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s-kuberski
GitHub
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5155effbbf
commit
3198088f9c
3 changed files with 216 additions and 17 deletions
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@ -2,6 +2,7 @@ import os
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import fnmatch
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import re
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import struct
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import warnings
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import numpy as np # Thinly-wrapped numpy
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import matplotlib.pyplot as plt
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from matplotlib import gridspec
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@ -9,16 +10,52 @@ from ..obs import Obs
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from ..fits import fit_lin
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def fit_t0(t2E_dict, fit_range, plot_fit=False):
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def fit_t0(t2E_dict, fit_range, plot_fit=False, observable='t0'):
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"""Compute the root of (flow-based) data based on a dictionary that contains
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the necessary information in key-value pairs a la (flow time: observable at flow time).
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It is assumed that the data is monotonically increasing and passes zero from below.
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No exception is thrown if this is not the case (several roots, no monotonic increase).
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An exception is thrown if no root can be found in the data.
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A linear fit in the vicinity of the root is performed to exctract the root from the
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two fit parameters.
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Parameters
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----------
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t2E_dict : dict
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Dictionary with pairs of (flow time: observable at flow time) where the flow times
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are of type float and the observables of type Obs.
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fit_range : int
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Number of data points left and right of the zero
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crossing to be included in the linear fit.
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plot_fit : bool
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If true, the fit for the extraction of t0 is shown together with the data. (Default: False)
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observable: str
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Keyword to identify the observable to print the correct ylabel (if plot_fit is True)
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for the observables 't0' and 'w0'. No y label is printed otherwise. (Default: 't0')
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Returns
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-------
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root : Obs
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The root of the data series.
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"""
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zero_crossing = np.argmax(np.array(
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[o.value for o in t2E_dict.values()]) > 0.0)
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if zero_crossing == 0:
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raise Exception('Desired flow time not in data')
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x = list(t2E_dict.keys())[zero_crossing - fit_range:
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zero_crossing + fit_range]
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y = list(t2E_dict.values())[zero_crossing - fit_range:
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zero_crossing + fit_range]
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[o.gamma_method() for o in y]
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if len(x) < 2 * fit_range:
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warnings.warn('Fit range smaller than expected! Fitting from %1.2e to %1.2e' % (x[0], x[-1]))
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fit_result = fit_lin(x, y)
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if plot_fit is True:
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@ -38,7 +75,10 @@ def fit_t0(t2E_dict, fit_range, plot_fit=False):
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ylim = ax0.get_ylim()
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ax0.fill_betweenx(ylim, x1=retval.value - retval.dvalue, x2=retval.value + retval.dvalue, color='gray', alpha=0.4)
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ax0.set_ylim(ylim)
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if observable == 't0':
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ax0.set_ylabel(r'$t^2 \langle E(t) \rangle - 0.3 $')
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elif observable == 'w0':
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ax0.set_ylabel(r'$t d(t^2 \langle E(t) \rangle)/dt - 0.3 $')
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xlim = ax0.get_xlim()
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fit_res = [fit_result[0] + fit_result[1] * xi for xi in x]
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@ -229,14 +229,12 @@ def read_rwms(path, prefix, version='2.0', names=None, **kwargs):
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return result
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def extract_t0(path, prefix, dtr_read, xmin, spatial_extent, fit_range=5, postfix='ms', **kwargs):
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"""Extract t0 from given .ms.dat files. Returns t0 as Obs.
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def _extract_flowed_energy_density(path, prefix, dtr_read, xmin, spatial_extent, postfix='ms', **kwargs):
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"""Extract a dictionary with the flowed Yang-Mills action density from given .ms.dat files.
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Returns a dictionary with Obs as values and flow times as keys.
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It is assumed that all boundary effects have
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sufficiently decayed at x0=xmin.
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The data around the zero crossing of t^2<E> - 0.3
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is fitted with a linear function
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from which the exact root is extracted.
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It is assumed that one measurement is performed for each config.
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If this is not the case, the resulting idl, as well as the handling
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@ -258,9 +256,6 @@ def extract_t0(path, prefix, dtr_read, xmin, spatial_extent, fit_range=5, postfi
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effects have sufficiently decayed.
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spatial_extent : int
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spatial extent of the lattice, required for normalization.
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fit_range : int
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Number of data points left and right of the zero
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crossing to be included in the linear fit. (Default: 5)
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postfix : str
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Postfix of measurement file (Default: ms)
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r_start : list
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@ -278,8 +273,6 @@ def extract_t0(path, prefix, dtr_read, xmin, spatial_extent, fit_range=5, postfi
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files : list
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list which contains the filenames to be read. No automatic detection of
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files performed if given.
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plot_fit : bool
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If true, the fit for the extraction of t0 is shown together with the data.
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assume_thermalization : bool
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If True: If the first record divided by the distance between two measurements is larger than
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1, it is assumed that this is due to thermalization and the first measurement belongs
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@ -288,8 +281,8 @@ def extract_t0(path, prefix, dtr_read, xmin, spatial_extent, fit_range=5, postfi
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Returns
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-------
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t0 : Obs
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Extracted t0
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E_dict : dictionary
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Dictionary with the flowed action density at flow times t
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"""
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if 'files' in kwargs:
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@ -321,7 +314,7 @@ def extract_t0(path, prefix, dtr_read, xmin, spatial_extent, fit_range=5, postfi
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else:
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r_step = 1
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print('Extract t0 from', prefix, ',', replica, 'replica')
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print('Extract flowed Yang-Mills action density from', prefix, ',', replica, 'replica')
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if 'names' in kwargs:
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rep_names = kwargs.get('names')
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@ -415,7 +408,7 @@ def extract_t0(path, prefix, dtr_read, xmin, spatial_extent, fit_range=5, postfi
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warnings.warn('Stepsize between configurations is greater than one!' + str(stepsizes), RuntimeWarning)
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idl = [range(configlist[rep][r_start_index[rep]], configlist[rep][r_stop_index[rep]] + 1, r_step) for rep in range(replica)]
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t2E_dict = {}
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E_dict = {}
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for n in range(nn + 1):
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samples = []
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for nrep, rep in enumerate(Ysum):
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@ -424,11 +417,166 @@ def extract_t0(path, prefix, dtr_read, xmin, spatial_extent, fit_range=5, postfi
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samples[-1].append(cnfg[n])
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samples[-1] = samples[-1][r_start_index[nrep]:r_stop_index[nrep] + 1][::r_step]
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new_obs = Obs(samples, rep_names, idl=idl)
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t2E_dict[n * dn * eps] = (n * dn * eps) ** 2 * new_obs / (spatial_extent ** 3) - 0.3
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E_dict[n * dn * eps] = new_obs / (spatial_extent ** 3)
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return E_dict
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def extract_t0(path, prefix, dtr_read, xmin, spatial_extent, fit_range=5, postfix='ms', c=0.3, **kwargs):
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"""Extract t0/a^2 from given .ms.dat files. Returns t0 as Obs.
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It is assumed that all boundary effects have
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sufficiently decayed at x0=xmin.
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The data around the zero crossing of t^2<E> - c (where c=0.3 by default)
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is fitted with a linear function
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from which the exact root is extracted.
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It is assumed that one measurement is performed for each config.
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If this is not the case, the resulting idl, as well as the handling
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of r_start, r_stop and r_step is wrong and the user has to correct
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this in the resulting observable.
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Parameters
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----------
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path : str
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Path to .ms.dat files
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prefix : str
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Ensemble prefix
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dtr_read : int
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Determines how many trajectories should be skipped
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when reading the ms.dat files.
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Corresponds to dtr_cnfg / dtr_ms in the openQCD input file.
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xmin : int
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First timeslice where the boundary
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effects have sufficiently decayed.
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spatial_extent : int
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spatial extent of the lattice, required for normalization.
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fit_range : int
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Number of data points left and right of the zero
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crossing to be included in the linear fit. (Default: 5)
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postfix : str
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Postfix of measurement file (Default: ms)
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c: float
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Constant that defines the flow scale. Default 0.3 for t_0, choose 2./3 for t_1.
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r_start : list
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list which contains the first config to be read for each replicum.
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r_stop : list
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list which contains the last config to be read for each replicum.
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r_step : int
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integer that defines a fixed step size between two measurements (in units of configs)
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If not given, r_step=1 is assumed.
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plaquette : bool
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If true extract the plaquette estimate of t0 instead.
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names : list
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list of names that is assigned to the data according according
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to the order in the file list. Use careful, if you do not provide file names!
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files : list
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list which contains the filenames to be read. No automatic detection of
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files performed if given.
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plot_fit : bool
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If true, the fit for the extraction of t0 is shown together with the data.
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assume_thermalization : bool
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If True: If the first record divided by the distance between two measurements is larger than
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1, it is assumed that this is due to thermalization and the first measurement belongs
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to the first config (default).
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If False: The config numbers are assumed to be traj_number // difference
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Returns
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-------
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t0 : Obs
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Extracted t0
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"""
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E_dict = _extract_flowed_energy_density(path, prefix, dtr_read, xmin, spatial_extent, postfix, **kwargs)
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t2E_dict = {}
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for t in sorted(E_dict.keys()):
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t2E_dict[t] = t ** 2 * E_dict[t] - c
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return fit_t0(t2E_dict, fit_range, plot_fit=kwargs.get('plot_fit'))
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def extract_w0(path, prefix, dtr_read, xmin, spatial_extent, fit_range=5, postfix='ms', c=0.3, **kwargs):
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"""Extract w0/a from given .ms.dat files. Returns w0 as Obs.
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It is assumed that all boundary effects have
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sufficiently decayed at x0=xmin.
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The data around the zero crossing of t d(t^2<E>)/dt - (where c=0.3 by default)
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is fitted with a linear function
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from which the exact root is extracted.
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It is assumed that one measurement is performed for each config.
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If this is not the case, the resulting idl, as well as the handling
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of r_start, r_stop and r_step is wrong and the user has to correct
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this in the resulting observable.
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Parameters
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----------
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path : str
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Path to .ms.dat files
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prefix : str
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Ensemble prefix
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dtr_read : int
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Determines how many trajectories should be skipped
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when reading the ms.dat files.
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Corresponds to dtr_cnfg / dtr_ms in the openQCD input file.
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xmin : int
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First timeslice where the boundary
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effects have sufficiently decayed.
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spatial_extent : int
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spatial extent of the lattice, required for normalization.
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fit_range : int
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Number of data points left and right of the zero
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crossing to be included in the linear fit. (Default: 5)
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postfix : str
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Postfix of measurement file (Default: ms)
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c: float
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Constant that defines the flow scale. Default 0.3 for w_0, choose 2./3 for w_1.
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r_start : list
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list which contains the first config to be read for each replicum.
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r_stop : list
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list which contains the last config to be read for each replicum.
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r_step : int
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integer that defines a fixed step size between two measurements (in units of configs)
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If not given, r_step=1 is assumed.
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plaquette : bool
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If true extract the plaquette estimate of w0 instead.
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names : list
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list of names that is assigned to the data according according
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to the order in the file list. Use careful, if you do not provide file names!
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files : list
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list which contains the filenames to be read. No automatic detection of
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files performed if given.
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plot_fit : bool
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If true, the fit for the extraction of w0 is shown together with the data.
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assume_thermalization : bool
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If True: If the first record divided by the distance between two measurements is larger than
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1, it is assumed that this is due to thermalization and the first measurement belongs
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to the first config (default).
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If False: The config numbers are assumed to be traj_number // difference
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Returns
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-------
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w0 : Obs
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Extracted w0
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"""
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E_dict = _extract_flowed_energy_density(path, prefix, dtr_read, xmin, spatial_extent, postfix, **kwargs)
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ftimes = sorted(E_dict.keys())
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t2E_dict = {}
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for t in ftimes:
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t2E_dict[t] = t ** 2 * E_dict[t]
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tdtt2E_dict = {}
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tdtt2E_dict[ftimes[0]] = ftimes[0] * (t2E_dict[ftimes[1]] - t2E_dict[ftimes[0]]) / (ftimes[1] - ftimes[0]) - c
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for i in range(1, len(ftimes) - 1):
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tdtt2E_dict[ftimes[i]] = ftimes[i] * (t2E_dict[ftimes[i + 1]] - t2E_dict[ftimes[i - 1]]) / (ftimes[i + 1] - ftimes[i - 1]) - c
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tdtt2E_dict[ftimes[-1]] = ftimes[-1] * (t2E_dict[ftimes[-1]] - t2E_dict[ftimes[-2]]) / (ftimes[-1] - ftimes[-2]) - c
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return np.sqrt(fit_t0(tdtt2E_dict, fit_range, plot_fit=kwargs.get('plot_fit'), observable='w0'))
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def _parse_array_openQCD2(d, n, size, wa, quadrupel=False):
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arr = []
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if d == 2:
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@ -54,6 +54,7 @@ def test_rwms():
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files = ['openqcd2r1.ms.dat']
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names = ['openqcd2|r1']
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t0 = pe.input.openQCD.extract_t0(path, '', dtr_read=3, xmin=0, spatial_extent=4, files=files, names=names, fit_range=2)
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assert(np.isclose(t0.value, 0.3816208266076627))
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t0 = pe.input.openQCD.extract_t0(path, prefix, dtr_read=3, xmin=0, spatial_extent=4, r_start=[1])
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repname = list(rwfo[0].idl.keys())[0]
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assert(t0.idl[repname] == range(1, 10))
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@ -64,6 +65,16 @@ def test_rwms():
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pe.input.openQCD.extract_t0(path, '', dtr_read=3, xmin=0, spatial_extent=4, files=files, names=names, fit_range=2, plot_fit=True)
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with pytest.raises(Exception):
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pe.input.openQCD.extract_t0(path, '', dtr_read=3, xmin=0, spatial_extent=4, files=files, names=names, fit_range=2, c=14)
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# w0
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w0 = pe.input.openQCD.extract_w0(path, '', dtr_read=3, xmin=0, spatial_extent=4, files=files, names=names, fit_range=2, plot_fit=True)
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assert(np.isclose(w0.value, 0.5220124285820434))
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with pytest.raises(Exception):
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pe.input.openQCD.extract_w0(path, '', dtr_read=3, xmin=0, spatial_extent=4, files=files, names=names, fit_range=2, c=14)
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def test_Qtop():
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path = './tests//data/openqcd_test/'
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