diff --git a/docs/pyerrors/input/misc.html b/docs/pyerrors/input/misc.html index 1e1873f9..bc5db3ce 100644 --- a/docs/pyerrors/input/misc.html +++ b/docs/pyerrors/input/misc.html @@ -83,180 +83,220 @@ 2import fnmatch 3import re 4import struct - 5import numpy as np # Thinly-wrapped numpy - 6import matplotlib.pyplot as plt - 7from matplotlib import gridspec - 8from ..obs import Obs - 9from ..fits import fit_lin - 10 + 5import warnings + 6import numpy as np # Thinly-wrapped numpy + 7import matplotlib.pyplot as plt + 8from matplotlib import gridspec + 9from ..obs import Obs + 10from ..fits import fit_lin 11 - 12def fit_t0(t2E_dict, fit_range, plot_fit=False): - 13 zero_crossing = np.argmax(np.array( - 14 [o.value for o in t2E_dict.values()]) > 0.0) - 15 - 16 x = list(t2E_dict.keys())[zero_crossing - fit_range: - 17 zero_crossing + fit_range] - 18 y = list(t2E_dict.values())[zero_crossing - fit_range: - 19 zero_crossing + fit_range] - 20 [o.gamma_method() for o in y] - 21 - 22 fit_result = fit_lin(x, y) + 12 + 13def fit_t0(t2E_dict, fit_range, plot_fit=False, observable='t0'): + 14 """Compute the root of (flow-based) data based on a dictionary that contains + 15 the necessary information in key-value pairs a la (flow time: observable at flow time). + 16 + 17 It is assumed that the data is monotonically increasing and passes zero from below. + 18 No exception is thrown if this is not the case (several roots, no monotonic increase). + 19 An exception is thrown if no root can be found in the data. + 20 + 21 A linear fit in the vicinity of the root is performed to exctract the root from the + 22 two fit parameters. 23 - 24 if plot_fit is True: - 25 plt.figure() - 26 gs = gridspec.GridSpec(2, 1, height_ratios=[3, 1], wspace=0.0, hspace=0.0) - 27 ax0 = plt.subplot(gs[0]) - 28 xmore = list(t2E_dict.keys())[zero_crossing - fit_range - 2: zero_crossing + fit_range + 2] - 29 ymore = list(t2E_dict.values())[zero_crossing - fit_range - 2: zero_crossing + fit_range + 2] - 30 [o.gamma_method() for o in ymore] - 31 ax0.errorbar(xmore, [yi.value for yi in ymore], yerr=[yi.dvalue for yi in ymore], fmt='x') - 32 xplot = np.linspace(np.min(x), np.max(x)) - 33 yplot = [fit_result[0] + fit_result[1] * xi for xi in xplot] - 34 [yi.gamma_method() for yi in yplot] - 35 ax0.fill_between(xplot, y1=[yi.value - yi.dvalue for yi in yplot], y2=[yi.value + yi.dvalue for yi in yplot]) - 36 retval = (-fit_result[0] / fit_result[1]) - 37 retval.gamma_method() - 38 ylim = ax0.get_ylim() - 39 ax0.fill_betweenx(ylim, x1=retval.value - retval.dvalue, x2=retval.value + retval.dvalue, color='gray', alpha=0.4) - 40 ax0.set_ylim(ylim) - 41 ax0.set_ylabel(r'$t^2 \langle E(t) \rangle - 0.3 $') - 42 xlim = ax0.get_xlim() + 24 Parameters + 25 ---------- + 26 t2E_dict : dict + 27 Dictionary with pairs of (flow time: observable at flow time) where the flow times + 28 are of type float and the observables of type Obs. + 29 fit_range : int + 30 Number of data points left and right of the zero + 31 crossing to be included in the linear fit. + 32 plot_fit : bool + 33 If true, the fit for the extraction of t0 is shown together with the data. (Default: False) + 34 observable: str + 35 Keyword to identify the observable to print the correct ylabel (if plot_fit is True) + 36 for the observables 't0' and 'w0'. No y label is printed otherwise. (Default: 't0') + 37 + 38 Returns + 39 ------- + 40 root : Obs + 41 The root of the data series. + 42 """ 43 - 44 fit_res = [fit_result[0] + fit_result[1] * xi for xi in x] - 45 residuals = (np.asarray([o.value for o in y]) - [o.value for o in fit_res]) / np.asarray([o.dvalue for o in y]) - 46 ax1 = plt.subplot(gs[1]) - 47 ax1.plot(x, residuals, 'ko', ls='none', markersize=5) - 48 ax1.tick_params(direction='out') - 49 ax1.tick_params(axis="x", bottom=True, top=True, labelbottom=True) - 50 ax1.axhline(y=0.0, ls='--', color='k') - 51 ax1.fill_between(xlim, -1.0, 1.0, alpha=0.1, facecolor='k') - 52 ax1.set_xlim(xlim) - 53 ax1.set_ylabel('Residuals') - 54 ax1.set_xlabel(r'$t/a^2$') + 44 zero_crossing = np.argmax(np.array( + 45 [o.value for o in t2E_dict.values()]) > 0.0) + 46 + 47 if zero_crossing == 0: + 48 raise Exception('Desired flow time not in data') + 49 + 50 x = list(t2E_dict.keys())[zero_crossing - fit_range: + 51 zero_crossing + fit_range] + 52 y = list(t2E_dict.values())[zero_crossing - fit_range: + 53 zero_crossing + fit_range] + 54 [o.gamma_method() for o in y] 55 - 56 plt.draw() - 57 return -fit_result[0] / fit_result[1] + 56 if len(x) < 2 * fit_range: + 57 warnings.warn('Fit range smaller than expected! Fitting from %1.2e to %1.2e' % (x[0], x[-1])) 58 - 59 - 60def read_pbp(path, prefix, **kwargs): - 61 """Read pbp format from given folder structure. - 62 - 63 Parameters - 64 ---------- - 65 r_start : list - 66 list which contains the first config to be read for each replicum - 67 r_stop : list - 68 list which contains the last config to be read for each replicum - 69 - 70 Returns - 71 ------- - 72 result : list[Obs] - 73 list of observables read - 74 """ - 75 - 76 ls = [] - 77 for (dirpath, dirnames, filenames) in os.walk(path): - 78 ls.extend(filenames) - 79 break - 80 - 81 if not ls: - 82 raise Exception('Error, directory not found') + 59 fit_result = fit_lin(x, y) + 60 + 61 if plot_fit is True: + 62 plt.figure() + 63 gs = gridspec.GridSpec(2, 1, height_ratios=[3, 1], wspace=0.0, hspace=0.0) + 64 ax0 = plt.subplot(gs[0]) + 65 xmore = list(t2E_dict.keys())[zero_crossing - fit_range - 2: zero_crossing + fit_range + 2] + 66 ymore = list(t2E_dict.values())[zero_crossing - fit_range - 2: zero_crossing + fit_range + 2] + 67 [o.gamma_method() for o in ymore] + 68 ax0.errorbar(xmore, [yi.value for yi in ymore], yerr=[yi.dvalue for yi in ymore], fmt='x') + 69 xplot = np.linspace(np.min(x), np.max(x)) + 70 yplot = [fit_result[0] + fit_result[1] * xi for xi in xplot] + 71 [yi.gamma_method() for yi in yplot] + 72 ax0.fill_between(xplot, y1=[yi.value - yi.dvalue for yi in yplot], y2=[yi.value + yi.dvalue for yi in yplot]) + 73 retval = (-fit_result[0] / fit_result[1]) + 74 retval.gamma_method() + 75 ylim = ax0.get_ylim() + 76 ax0.fill_betweenx(ylim, x1=retval.value - retval.dvalue, x2=retval.value + retval.dvalue, color='gray', alpha=0.4) + 77 ax0.set_ylim(ylim) + 78 if observable == 't0': + 79 ax0.set_ylabel(r'$t^2 \langle E(t) \rangle - 0.3 $') + 80 elif observable == 'w0': + 81 ax0.set_ylabel(r'$t d(t^2 \langle E(t) \rangle)/dt - 0.3 $') + 82 xlim = ax0.get_xlim() 83 - 84 # Exclude files with different names - 85 for exc in ls: - 86 if not fnmatch.fnmatch(exc, prefix + '*.dat'): - 87 ls = list(set(ls) - set([exc])) - 88 if len(ls) > 1: - 89 ls.sort(key=lambda x: int(re.findall(r'\d+', x[len(prefix):])[0])) - 90 replica = len(ls) - 91 - 92 if 'r_start' in kwargs: - 93 r_start = kwargs.get('r_start') - 94 if len(r_start) != replica: - 95 raise Exception('r_start does not match number of replicas') - 96 # Adjust Configuration numbering to python index - 97 r_start = [o - 1 if o else None for o in r_start] - 98 else: - 99 r_start = [None] * replica -100 -101 if 'r_stop' in kwargs: -102 r_stop = kwargs.get('r_stop') -103 if len(r_stop) != replica: -104 raise Exception('r_stop does not match number of replicas') -105 else: -106 r_stop = [None] * replica -107 -108 print(r'Read <bar{psi}\psi> from', prefix[:-1], ',', replica, 'replica', end='') + 84 fit_res = [fit_result[0] + fit_result[1] * xi for xi in x] + 85 residuals = (np.asarray([o.value for o in y]) - [o.value for o in fit_res]) / np.asarray([o.dvalue for o in y]) + 86 ax1 = plt.subplot(gs[1]) + 87 ax1.plot(x, residuals, 'ko', ls='none', markersize=5) + 88 ax1.tick_params(direction='out') + 89 ax1.tick_params(axis="x", bottom=True, top=True, labelbottom=True) + 90 ax1.axhline(y=0.0, ls='--', color='k') + 91 ax1.fill_between(xlim, -1.0, 1.0, alpha=0.1, facecolor='k') + 92 ax1.set_xlim(xlim) + 93 ax1.set_ylabel('Residuals') + 94 ax1.set_xlabel(r'$t/a^2$') + 95 + 96 plt.draw() + 97 return -fit_result[0] / fit_result[1] + 98 + 99 +100def read_pbp(path, prefix, **kwargs): +101 """Read pbp format from given folder structure. +102 +103 Parameters +104 ---------- +105 r_start : list +106 list which contains the first config to be read for each replicum +107 r_stop : list +108 list which contains the last config to be read for each replicum 109 -110 print_err = 0 -111 if 'print_err' in kwargs: -112 print_err = 1 -113 print() -114 -115 deltas = [] -116 -117 for rep in range(replica): -118 tmp_array = [] -119 with open(path + '/' + ls[rep], 'rb') as fp: +110 Returns +111 ------- +112 result : list[Obs] +113 list of observables read +114 """ +115 +116 ls = [] +117 for (dirpath, dirnames, filenames) in os.walk(path): +118 ls.extend(filenames) +119 break 120 -121 t = fp.read(4) # number of reweighting factors -122 if rep == 0: -123 nrw = struct.unpack('i', t)[0] -124 for k in range(nrw): -125 deltas.append([]) -126 else: -127 if nrw != struct.unpack('i', t)[0]: -128 raise Exception('Error: different number of factors for replicum', rep) -129 -130 for k in range(nrw): -131 tmp_array.append([]) -132 -133 # This block is necessary for openQCD1.6 ms1 files -134 nfct = [] -135 for i in range(nrw): -136 t = fp.read(4) -137 nfct.append(struct.unpack('i', t)[0]) -138 print('nfct: ', nfct) # Hasenbusch factor, 1 for rat reweighting -139 -140 nsrc = [] -141 for i in range(nrw): -142 t = fp.read(4) -143 nsrc.append(struct.unpack('i', t)[0]) -144 -145 # body -146 while True: -147 t = fp.read(4) -148 if len(t) < 4: -149 break -150 if print_err: -151 config_no = struct.unpack('i', t) -152 for i in range(nrw): -153 tmp_nfct = 1.0 -154 for j in range(nfct[i]): -155 t = fp.read(8 * nsrc[i]) -156 t = fp.read(8 * nsrc[i]) -157 tmp_rw = struct.unpack('d' * nsrc[i], t) -158 tmp_nfct *= np.mean(np.asarray(tmp_rw)) -159 if print_err: -160 print(config_no, i, j, np.mean(np.asarray(tmp_rw)), np.std(np.asarray(tmp_rw))) -161 print('Sources:', np.asarray(tmp_rw)) -162 print('Partial factor:', tmp_nfct) -163 tmp_array[i].append(tmp_nfct) -164 -165 for k in range(nrw): -166 deltas[k].append(tmp_array[k][r_start[rep]:r_stop[rep]]) -167 -168 rep_names = [] -169 for entry in ls: -170 truncated_entry = entry.split('.')[0] -171 idx = truncated_entry.index('r') -172 rep_names.append(truncated_entry[:idx] + '|' + truncated_entry[idx:]) -173 print(',', nrw, r'<bar{psi}\psi> with', nsrc, 'sources') -174 result = [] -175 for t in range(nrw): -176 result.append(Obs(deltas[t], rep_names)) -177 -178 return result +121 if not ls: +122 raise Exception('Error, directory not found') +123 +124 # Exclude files with different names +125 for exc in ls: +126 if not fnmatch.fnmatch(exc, prefix + '*.dat'): +127 ls = list(set(ls) - set([exc])) +128 if len(ls) > 1: +129 ls.sort(key=lambda x: int(re.findall(r'\d+', x[len(prefix):])[0])) +130 replica = len(ls) +131 +132 if 'r_start' in kwargs: +133 r_start = kwargs.get('r_start') +134 if len(r_start) != replica: +135 raise Exception('r_start does not match number of replicas') +136 # Adjust Configuration numbering to python index +137 r_start = [o - 1 if o else None for o in r_start] +138 else: +139 r_start = [None] * replica +140 +141 if 'r_stop' in kwargs: +142 r_stop = kwargs.get('r_stop') +143 if len(r_stop) != replica: +144 raise Exception('r_stop does not match number of replicas') +145 else: +146 r_stop = [None] * replica +147 +148 print(r'Read <bar{psi}\psi> from', prefix[:-1], ',', replica, 'replica', end='') +149 +150 print_err = 0 +151 if 'print_err' in kwargs: +152 print_err = 1 +153 print() +154 +155 deltas = [] +156 +157 for rep in range(replica): +158 tmp_array = [] +159 with open(path + '/' + ls[rep], 'rb') as fp: +160 +161 t = fp.read(4) # number of reweighting factors +162 if rep == 0: +163 nrw = struct.unpack('i', t)[0] +164 for k in range(nrw): +165 deltas.append([]) +166 else: +167 if nrw != struct.unpack('i', t)[0]: +168 raise Exception('Error: different number of factors for replicum', rep) +169 +170 for k in range(nrw): +171 tmp_array.append([]) +172 +173 # This block is necessary for openQCD1.6 ms1 files +174 nfct = [] +175 for i in range(nrw): +176 t = fp.read(4) +177 nfct.append(struct.unpack('i', t)[0]) +178 print('nfct: ', nfct) # Hasenbusch factor, 1 for rat reweighting +179 +180 nsrc = [] +181 for i in range(nrw): +182 t = fp.read(4) +183 nsrc.append(struct.unpack('i', t)[0]) +184 +185 # body +186 while True: +187 t = fp.read(4) +188 if len(t) < 4: +189 break +190 if print_err: +191 config_no = struct.unpack('i', t) +192 for i in range(nrw): +193 tmp_nfct = 1.0 +194 for j in range(nfct[i]): +195 t = fp.read(8 * nsrc[i]) +196 t = fp.read(8 * nsrc[i]) +197 tmp_rw = struct.unpack('d' * nsrc[i], t) +198 tmp_nfct *= np.mean(np.asarray(tmp_rw)) +199 if print_err: +200 print(config_no, i, j, np.mean(np.asarray(tmp_rw)), np.std(np.asarray(tmp_rw))) +201 print('Sources:', np.asarray(tmp_rw)) +202 print('Partial factor:', tmp_nfct) +203 tmp_array[i].append(tmp_nfct) +204 +205 for k in range(nrw): +206 deltas[k].append(tmp_array[k][r_start[rep]:r_stop[rep]]) +207 +208 rep_names = [] +209 for entry in ls: +210 truncated_entry = entry.split('.')[0] +211 idx = truncated_entry.index('r') +212 rep_names.append(truncated_entry[:idx] + '|' + truncated_entry[idx:]) +213 print(',', nrw, r'<bar{psi}\psi> with', nsrc, 'sources') +214 result = [] +215 for t in range(nrw): +216 result.append(Obs(deltas[t], rep_names)) +217 +218 return result @@ -266,62 +306,134 @@
def - fit_t0(t2E_dict, fit_range, plot_fit=False): + fit_t0(t2E_dict, fit_range, plot_fit=False, observable='t0'):
- 
13def fit_t0(t2E_dict, fit_range, plot_fit=False):
-14    zero_crossing = np.argmax(np.array(
-15        [o.value for o in t2E_dict.values()]) > 0.0)
-16
-17    x = list(t2E_dict.keys())[zero_crossing - fit_range:
-18                              zero_crossing + fit_range]
-19    y = list(t2E_dict.values())[zero_crossing - fit_range:
-20                                zero_crossing + fit_range]
-21    [o.gamma_method() for o in y]
-22
-23    fit_result = fit_lin(x, y)
+            
14def fit_t0(t2E_dict, fit_range, plot_fit=False, observable='t0'):
+15    """Compute the root of (flow-based) data based on a dictionary that contains
+16    the necessary information in key-value pairs a la (flow time: observable at flow time).
+17
+18    It is assumed that the data is monotonically increasing and passes zero from below.
+19    No exception is thrown if this is not the case (several roots, no monotonic increase).
+20    An exception is thrown if no root can be found in the data.
+21
+22    A linear fit in the vicinity of the root is performed to exctract the root from the
+23    two fit parameters.
 24
-25    if plot_fit is True:
-26        plt.figure()
-27        gs = gridspec.GridSpec(2, 1, height_ratios=[3, 1], wspace=0.0, hspace=0.0)
-28        ax0 = plt.subplot(gs[0])
-29        xmore = list(t2E_dict.keys())[zero_crossing - fit_range - 2: zero_crossing + fit_range + 2]
-30        ymore = list(t2E_dict.values())[zero_crossing - fit_range - 2: zero_crossing + fit_range + 2]
-31        [o.gamma_method() for o in ymore]
-32        ax0.errorbar(xmore, [yi.value for yi in ymore], yerr=[yi.dvalue for yi in ymore], fmt='x')
-33        xplot = np.linspace(np.min(x), np.max(x))
-34        yplot = [fit_result[0] + fit_result[1] * xi for xi in xplot]
-35        [yi.gamma_method() for yi in yplot]
-36        ax0.fill_between(xplot, y1=[yi.value - yi.dvalue for yi in yplot], y2=[yi.value + yi.dvalue for yi in yplot])
-37        retval = (-fit_result[0] / fit_result[1])
-38        retval.gamma_method()
-39        ylim = ax0.get_ylim()
-40        ax0.fill_betweenx(ylim, x1=retval.value - retval.dvalue, x2=retval.value + retval.dvalue, color='gray', alpha=0.4)
-41        ax0.set_ylim(ylim)
-42        ax0.set_ylabel(r'$t^2 \langle E(t) \rangle - 0.3 $')
-43        xlim = ax0.get_xlim()
+25    Parameters
+26    ----------
+27    t2E_dict : dict
+28        Dictionary with pairs of (flow time: observable at flow time) where the flow times
+29        are of type float and the observables of type Obs.
+30    fit_range : int
+31        Number of data points left and right of the zero
+32        crossing to be included in the linear fit.
+33    plot_fit : bool
+34        If true, the fit for the extraction of t0 is shown together with the data. (Default: False)
+35    observable: str
+36        Keyword to identify the observable to print the correct ylabel (if plot_fit is True)
+37        for the observables 't0' and 'w0'. No y label is printed otherwise. (Default: 't0')
+38
+39    Returns
+40    -------
+41    root : Obs
+42        The root of the data series.
+43    """
 44
-45        fit_res = [fit_result[0] + fit_result[1] * xi for xi in x]
-46        residuals = (np.asarray([o.value for o in y]) - [o.value for o in fit_res]) / np.asarray([o.dvalue for o in y])
-47        ax1 = plt.subplot(gs[1])
-48        ax1.plot(x, residuals, 'ko', ls='none', markersize=5)
-49        ax1.tick_params(direction='out')
-50        ax1.tick_params(axis="x", bottom=True, top=True, labelbottom=True)
-51        ax1.axhline(y=0.0, ls='--', color='k')
-52        ax1.fill_between(xlim, -1.0, 1.0, alpha=0.1, facecolor='k')
-53        ax1.set_xlim(xlim)
-54        ax1.set_ylabel('Residuals')
-55        ax1.set_xlabel(r'$t/a^2$')
+45    zero_crossing = np.argmax(np.array(
+46        [o.value for o in t2E_dict.values()]) > 0.0)
+47
+48    if zero_crossing == 0:
+49        raise Exception('Desired flow time not in data')
+50
+51    x = list(t2E_dict.keys())[zero_crossing - fit_range:
+52                              zero_crossing + fit_range]
+53    y = list(t2E_dict.values())[zero_crossing - fit_range:
+54                                zero_crossing + fit_range]
+55    [o.gamma_method() for o in y]
 56
-57        plt.draw()
-58    return -fit_result[0] / fit_result[1]
+57    if len(x) < 2 * fit_range:
+58        warnings.warn('Fit range smaller than expected! Fitting from %1.2e to %1.2e' % (x[0], x[-1]))
+59
+60    fit_result = fit_lin(x, y)
+61
+62    if plot_fit is True:
+63        plt.figure()
+64        gs = gridspec.GridSpec(2, 1, height_ratios=[3, 1], wspace=0.0, hspace=0.0)
+65        ax0 = plt.subplot(gs[0])
+66        xmore = list(t2E_dict.keys())[zero_crossing - fit_range - 2: zero_crossing + fit_range + 2]
+67        ymore = list(t2E_dict.values())[zero_crossing - fit_range - 2: zero_crossing + fit_range + 2]
+68        [o.gamma_method() for o in ymore]
+69        ax0.errorbar(xmore, [yi.value for yi in ymore], yerr=[yi.dvalue for yi in ymore], fmt='x')
+70        xplot = np.linspace(np.min(x), np.max(x))
+71        yplot = [fit_result[0] + fit_result[1] * xi for xi in xplot]
+72        [yi.gamma_method() for yi in yplot]
+73        ax0.fill_between(xplot, y1=[yi.value - yi.dvalue for yi in yplot], y2=[yi.value + yi.dvalue for yi in yplot])
+74        retval = (-fit_result[0] / fit_result[1])
+75        retval.gamma_method()
+76        ylim = ax0.get_ylim()
+77        ax0.fill_betweenx(ylim, x1=retval.value - retval.dvalue, x2=retval.value + retval.dvalue, color='gray', alpha=0.4)
+78        ax0.set_ylim(ylim)
+79        if observable == 't0':
+80            ax0.set_ylabel(r'$t^2 \langle E(t) \rangle - 0.3 $')
+81        elif observable == 'w0':
+82            ax0.set_ylabel(r'$t d(t^2 \langle E(t) \rangle)/dt - 0.3 $')
+83        xlim = ax0.get_xlim()
+84
+85        fit_res = [fit_result[0] + fit_result[1] * xi for xi in x]
+86        residuals = (np.asarray([o.value for o in y]) - [o.value for o in fit_res]) / np.asarray([o.dvalue for o in y])
+87        ax1 = plt.subplot(gs[1])
+88        ax1.plot(x, residuals, 'ko', ls='none', markersize=5)
+89        ax1.tick_params(direction='out')
+90        ax1.tick_params(axis="x", bottom=True, top=True, labelbottom=True)
+91        ax1.axhline(y=0.0, ls='--', color='k')
+92        ax1.fill_between(xlim, -1.0, 1.0, alpha=0.1, facecolor='k')
+93        ax1.set_xlim(xlim)
+94        ax1.set_ylabel('Residuals')
+95        ax1.set_xlabel(r'$t/a^2$')
+96
+97        plt.draw()
+98    return -fit_result[0] / fit_result[1]
 

 
 
-    
+            
Compute the root of (flow-based) data based on a dictionary that contains
+the necessary information in key-value pairs a la (flow time: observable at flow time).

+
+
It is assumed that the data is monotonically increasing and passes zero from below.
+No exception is thrown if this is not the case (several roots, no monotonic increase).
+An exception is thrown if no root can be found in the data.

+
+
A linear fit in the vicinity of the root is performed to exctract the root from the
+two fit parameters.

+
+
Parameters

+
+
    
+
  • t2E_dict (dict):
+Dictionary with pairs of (flow time: observable at flow time) where the flow times
+are of type float and the observables of type Obs.
    • 
+
  • fit_range (int):
+Number of data points left and right of the zero
+crossing to be included in the linear fit.
    • 
+
  • plot_fit (bool):
+If true, the fit for the extraction of t0 is shown together with the data. (Default: False)
    • 
+
  • observable (str):
+Keyword to identify the observable to print the correct ylabel (if plot_fit is True)
+for the observables 't0' and 'w0'. No y label is printed otherwise. (Default: 't0')
    • 
+

+
+
Returns

+
+
    
+
  • root (Obs):
+The root of the data series.
    • 
+

+

+
 
                 
                 

@@ -335,125 +447,125 @@
- 
 61def read_pbp(path, prefix, **kwargs):
- 62    """Read pbp format from given folder structure.
- 63
- 64    Parameters
- 65    ----------
- 66    r_start : list
- 67        list which contains the first config to be read for each replicum
- 68    r_stop : list
- 69        list which contains the last config to be read for each replicum
- 70
- 71    Returns
- 72    -------
- 73    result : list[Obs]
- 74        list of observables read
- 75    """
- 76
- 77    ls = []
- 78    for (dirpath, dirnames, filenames) in os.walk(path):
- 79        ls.extend(filenames)
- 80        break
- 81
- 82    if not ls:
- 83        raise Exception('Error, directory not found')
- 84
- 85    # Exclude files with different names
- 86    for exc in ls:
- 87        if not fnmatch.fnmatch(exc, prefix + '*.dat'):
- 88            ls = list(set(ls) - set([exc]))
- 89    if len(ls) > 1:
- 90        ls.sort(key=lambda x: int(re.findall(r'\d+', x[len(prefix):])[0]))
- 91    replica = len(ls)
- 92
- 93    if 'r_start' in kwargs:
- 94        r_start = kwargs.get('r_start')
- 95        if len(r_start) != replica:
- 96            raise Exception('r_start does not match number of replicas')
- 97        # Adjust Configuration numbering to python index
- 98        r_start = [o - 1 if o else None for o in r_start]
- 99    else:
-100        r_start = [None] * replica
-101
-102    if 'r_stop' in kwargs:
-103        r_stop = kwargs.get('r_stop')
-104        if len(r_stop) != replica:
-105            raise Exception('r_stop does not match number of replicas')
-106    else:
-107        r_stop = [None] * replica
-108
-109    print(r'Read <bar{psi}\psi> from', prefix[:-1], ',', replica, 'replica', end='')
+            
101def read_pbp(path, prefix, **kwargs):
+102    """Read pbp format from given folder structure.
+103
+104    Parameters
+105    ----------
+106    r_start : list
+107        list which contains the first config to be read for each replicum
+108    r_stop : list
+109        list which contains the last config to be read for each replicum
 110
-111    print_err = 0
-112    if 'print_err' in kwargs:
-113        print_err = 1
-114        print()
-115
-116    deltas = []
-117
-118    for rep in range(replica):
-119        tmp_array = []
-120        with open(path + '/' + ls[rep], 'rb') as fp:
+111    Returns
+112    -------
+113    result : list[Obs]
+114        list of observables read
+115    """
+116
+117    ls = []
+118    for (dirpath, dirnames, filenames) in os.walk(path):
+119        ls.extend(filenames)
+120        break
 121
-122            t = fp.read(4)  # number of reweighting factors
-123            if rep == 0:
-124                nrw = struct.unpack('i', t)[0]
-125                for k in range(nrw):
-126                    deltas.append([])
-127            else:
-128                if nrw != struct.unpack('i', t)[0]:
-129                    raise Exception('Error: different number of factors for replicum', rep)
-130
-131            for k in range(nrw):
-132                tmp_array.append([])
-133
-134            # This block is necessary for openQCD1.6 ms1 files
-135            nfct = []
-136            for i in range(nrw):
-137                t = fp.read(4)
-138                nfct.append(struct.unpack('i', t)[0])
-139            print('nfct: ', nfct)  # Hasenbusch factor, 1 for rat reweighting
-140
-141            nsrc = []
-142            for i in range(nrw):
-143                t = fp.read(4)
-144                nsrc.append(struct.unpack('i', t)[0])
-145
-146            # body
-147            while True:
-148                t = fp.read(4)
-149                if len(t) < 4:
-150                    break
-151                if print_err:
-152                    config_no = struct.unpack('i', t)
-153                for i in range(nrw):
-154                    tmp_nfct = 1.0
-155                    for j in range(nfct[i]):
-156                        t = fp.read(8 * nsrc[i])
-157                        t = fp.read(8 * nsrc[i])
-158                        tmp_rw = struct.unpack('d' * nsrc[i], t)
-159                        tmp_nfct *= np.mean(np.asarray(tmp_rw))
-160                        if print_err:
-161                            print(config_no, i, j, np.mean(np.asarray(tmp_rw)), np.std(np.asarray(tmp_rw)))
-162                            print('Sources:', np.asarray(tmp_rw))
-163                            print('Partial factor:', tmp_nfct)
-164                    tmp_array[i].append(tmp_nfct)
-165
-166            for k in range(nrw):
-167                deltas[k].append(tmp_array[k][r_start[rep]:r_stop[rep]])
-168
-169    rep_names = []
-170    for entry in ls:
-171        truncated_entry = entry.split('.')[0]
-172        idx = truncated_entry.index('r')
-173        rep_names.append(truncated_entry[:idx] + '|' + truncated_entry[idx:])
-174    print(',', nrw, r'<bar{psi}\psi> with', nsrc, 'sources')
-175    result = []
-176    for t in range(nrw):
-177        result.append(Obs(deltas[t], rep_names))
-178
-179    return result
+122    if not ls:
+123        raise Exception('Error, directory not found')
+124
+125    # Exclude files with different names
+126    for exc in ls:
+127        if not fnmatch.fnmatch(exc, prefix + '*.dat'):
+128            ls = list(set(ls) - set([exc]))
+129    if len(ls) > 1:
+130        ls.sort(key=lambda x: int(re.findall(r'\d+', x[len(prefix):])[0]))
+131    replica = len(ls)
+132
+133    if 'r_start' in kwargs:
+134        r_start = kwargs.get('r_start')
+135        if len(r_start) != replica:
+136            raise Exception('r_start does not match number of replicas')
+137        # Adjust Configuration numbering to python index
+138        r_start = [o - 1 if o else None for o in r_start]
+139    else:
+140        r_start = [None] * replica
+141
+142    if 'r_stop' in kwargs:
+143        r_stop = kwargs.get('r_stop')
+144        if len(r_stop) != replica:
+145            raise Exception('r_stop does not match number of replicas')
+146    else:
+147        r_stop = [None] * replica
+148
+149    print(r'Read <bar{psi}\psi> from', prefix[:-1], ',', replica, 'replica', end='')
+150
+151    print_err = 0
+152    if 'print_err' in kwargs:
+153        print_err = 1
+154        print()
+155
+156    deltas = []
+157
+158    for rep in range(replica):
+159        tmp_array = []
+160        with open(path + '/' + ls[rep], 'rb') as fp:
+161
+162            t = fp.read(4)  # number of reweighting factors
+163            if rep == 0:
+164                nrw = struct.unpack('i', t)[0]
+165                for k in range(nrw):
+166                    deltas.append([])
+167            else:
+168                if nrw != struct.unpack('i', t)[0]:
+169                    raise Exception('Error: different number of factors for replicum', rep)
+170
+171            for k in range(nrw):
+172                tmp_array.append([])
+173
+174            # This block is necessary for openQCD1.6 ms1 files
+175            nfct = []
+176            for i in range(nrw):
+177                t = fp.read(4)
+178                nfct.append(struct.unpack('i', t)[0])
+179            print('nfct: ', nfct)  # Hasenbusch factor, 1 for rat reweighting
+180
+181            nsrc = []
+182            for i in range(nrw):
+183                t = fp.read(4)
+184                nsrc.append(struct.unpack('i', t)[0])
+185
+186            # body
+187            while True:
+188                t = fp.read(4)
+189                if len(t) < 4:
+190                    break
+191                if print_err:
+192                    config_no = struct.unpack('i', t)
+193                for i in range(nrw):
+194                    tmp_nfct = 1.0
+195                    for j in range(nfct[i]):
+196                        t = fp.read(8 * nsrc[i])
+197                        t = fp.read(8 * nsrc[i])
+198                        tmp_rw = struct.unpack('d' * nsrc[i], t)
+199                        tmp_nfct *= np.mean(np.asarray(tmp_rw))
+200                        if print_err:
+201                            print(config_no, i, j, np.mean(np.asarray(tmp_rw)), np.std(np.asarray(tmp_rw)))
+202                            print('Sources:', np.asarray(tmp_rw))
+203                            print('Partial factor:', tmp_nfct)
+204                    tmp_array[i].append(tmp_nfct)
+205
+206            for k in range(nrw):
+207                deltas[k].append(tmp_array[k][r_start[rep]:r_stop[rep]])
+208
+209    rep_names = []
+210    for entry in ls:
+211        truncated_entry = entry.split('.')[0]
+212        idx = truncated_entry.index('r')
+213        rep_names.append(truncated_entry[:idx] + '|' + truncated_entry[idx:])
+214    print(',', nrw, r'<bar{psi}\psi> with', nsrc, 'sources')
+215    result = []
+216    for t in range(nrw):
+217        result.append(Obs(deltas[t], rep_names))
+218
+219    return result
 

 
 
diff --git a/docs/pyerrors/input/openQCD.html b/docs/pyerrors/input/openQCD.html
index f5b355d2..2d9f02ce 100644
--- a/docs/pyerrors/input/openQCD.html
+++ b/docs/pyerrors/input/openQCD.html
@@ -58,6 +58,9 @@
             
  • 
                     extract_t0
             
    • 
+            
  • 
+                    extract_w0
+            
    • 
             
  • 
                     read_qtop
             
    • 
@@ -325,925 +328,1073 @@
      229    return result
  230
  231
- 232def extract_t0(path, prefix, dtr_read, xmin, spatial_extent, fit_range=5, postfix='ms', **kwargs):
- 233    """Extract t0 from given .ms.dat files. Returns t0 as Obs.
- 234
- 235    It is assumed that all boundary effects have
- 236    sufficiently decayed at x0=xmin.
- 237    The data around the zero crossing of t^2<E> - 0.3
- 238    is fitted with a linear function
- 239    from which the exact root is extracted.
- 240
- 241    It is assumed that one measurement is performed for each config.
- 242    If this is not the case, the resulting idl, as well as the handling
- 243    of r_start, r_stop and r_step is wrong and the user has to correct
- 244    this in the resulting observable.
- 245
- 246    Parameters
- 247    ----------
- 248    path : str
- 249        Path to .ms.dat files
- 250    prefix : str
- 251        Ensemble prefix
- 252    dtr_read : int
- 253        Determines how many trajectories should be skipped
- 254        when reading the ms.dat files.
- 255        Corresponds to dtr_cnfg / dtr_ms in the openQCD input file.
- 256    xmin : int
- 257        First timeslice where the boundary
- 258        effects have sufficiently decayed.
- 259    spatial_extent : int
- 260        spatial extent of the lattice, required for normalization.
- 261    fit_range : int
- 262        Number of data points left and right of the zero
- 263        crossing to be included in the linear fit. (Default: 5)
- 264    postfix : str
- 265        Postfix of measurement file (Default: ms)
- 266    r_start : list
- 267        list which contains the first config to be read for each replicum.
- 268    r_stop : list
- 269        list which contains the last config to be read for each replicum.
- 270    r_step : int
- 271        integer that defines a fixed step size between two measurements (in units of configs)
- 272        If not given, r_step=1 is assumed.
- 273    plaquette : bool
- 274        If true extract the plaquette estimate of t0 instead.
- 275    names : list
- 276        list of names that is assigned to the data according according
- 277        to the order in the file list. Use careful, if you do not provide file names!
- 278    files : list
- 279        list which contains the filenames to be read. No automatic detection of
- 280        files performed if given.
- 281    plot_fit : bool
- 282        If true, the fit for the extraction of t0 is shown together with the data.
- 283    assume_thermalization : bool
- 284        If True: If the first record divided by the distance between two measurements is larger than
- 285        1, it is assumed that this is due to thermalization and the first measurement belongs
- 286        to the first config (default).
- 287        If False: The config numbers are assumed to be traj_number // difference
- 288
- 289    Returns
- 290    -------
- 291    t0 : Obs
- 292        Extracted t0
- 293    """
+ 232def _extract_flowed_energy_density(path, prefix, dtr_read, xmin, spatial_extent, postfix='ms', **kwargs):
+ 233    """Extract a dictionary with the flowed Yang-Mills action density from given .ms.dat files.
+ 234    Returns a dictionary with Obs as values and flow times as keys.
+ 235
+ 236    It is assumed that all boundary effects have
+ 237    sufficiently decayed at x0=xmin.
+ 238
+ 239    It is assumed that one measurement is performed for each config.
+ 240    If this is not the case, the resulting idl, as well as the handling
+ 241    of r_start, r_stop and r_step is wrong and the user has to correct
+ 242    this in the resulting observable.
+ 243
+ 244    Parameters
+ 245    ----------
+ 246    path : str
+ 247        Path to .ms.dat files
+ 248    prefix : str
+ 249        Ensemble prefix
+ 250    dtr_read : int
+ 251        Determines how many trajectories should be skipped
+ 252        when reading the ms.dat files.
+ 253        Corresponds to dtr_cnfg / dtr_ms in the openQCD input file.
+ 254    xmin : int
+ 255        First timeslice where the boundary
+ 256        effects have sufficiently decayed.
+ 257    spatial_extent : int
+ 258        spatial extent of the lattice, required for normalization.
+ 259    postfix : str
+ 260        Postfix of measurement file (Default: ms)
+ 261    r_start : list
+ 262        list which contains the first config to be read for each replicum.
+ 263    r_stop : list
+ 264        list which contains the last config to be read for each replicum.
+ 265    r_step : int
+ 266        integer that defines a fixed step size between two measurements (in units of configs)
+ 267        If not given, r_step=1 is assumed.
+ 268    plaquette : bool
+ 269        If true extract the plaquette estimate of t0 instead.
+ 270    names : list
+ 271        list of names that is assigned to the data according according
+ 272        to the order in the file list. Use careful, if you do not provide file names!
+ 273    files : list
+ 274        list which contains the filenames to be read. No automatic detection of
+ 275        files performed if given.
+ 276    assume_thermalization : bool
+ 277        If True: If the first record divided by the distance between two measurements is larger than
+ 278        1, it is assumed that this is due to thermalization and the first measurement belongs
+ 279        to the first config (default).
+ 280        If False: The config numbers are assumed to be traj_number // difference
+ 281
+ 282    Returns
+ 283    -------
+ 284    E_dict : dictionary
+ 285        Dictionary with the flowed action density at flow times t
+ 286    """
+ 287
+ 288    if 'files' in kwargs:
+ 289        known_files = kwargs.get('files')
+ 290    else:
+ 291        known_files = []
+ 292
+ 293    ls = _find_files(path, prefix, postfix, 'dat', known_files=known_files)
  294
- 295    if 'files' in kwargs:
- 296        known_files = kwargs.get('files')
- 297    else:
- 298        known_files = []
- 299
- 300    ls = _find_files(path, prefix, postfix, 'dat', known_files=known_files)
- 301
- 302    replica = len(ls)
- 303
- 304    if 'r_start' in kwargs:
- 305        r_start = kwargs.get('r_start')
- 306        if len(r_start) != replica:
- 307            raise Exception('r_start does not match number of replicas')
- 308        r_start = [o if o else None for o in r_start]
+ 295    replica = len(ls)
+ 296
+ 297    if 'r_start' in kwargs:
+ 298        r_start = kwargs.get('r_start')
+ 299        if len(r_start) != replica:
+ 300            raise Exception('r_start does not match number of replicas')
+ 301        r_start = [o if o else None for o in r_start]
+ 302    else:
+ 303        r_start = [None] * replica
+ 304
+ 305    if 'r_stop' in kwargs:
+ 306        r_stop = kwargs.get('r_stop')
+ 307        if len(r_stop) != replica:
+ 308            raise Exception('r_stop does not match number of replicas')
  309    else:
- 310        r_start = [None] * replica
+ 310        r_stop = [None] * replica
  311
- 312    if 'r_stop' in kwargs:
- 313        r_stop = kwargs.get('r_stop')
- 314        if len(r_stop) != replica:
- 315            raise Exception('r_stop does not match number of replicas')
- 316    else:
- 317        r_stop = [None] * replica
+ 312    if 'r_step' in kwargs:
+ 313        r_step = kwargs.get('r_step')
+ 314    else:
+ 315        r_step = 1
+ 316
+ 317    print('Extract flowed Yang-Mills action density from', prefix, ',', replica, 'replica')
  318
- 319    if 'r_step' in kwargs:
- 320        r_step = kwargs.get('r_step')
+ 319    if 'names' in kwargs:
+ 320        rep_names = kwargs.get('names')
  321    else:
- 322        r_step = 1
- 323
- 324    print('Extract t0 from', prefix, ',', replica, 'replica')
- 325
- 326    if 'names' in kwargs:
- 327        rep_names = kwargs.get('names')
- 328    else:
- 329        rep_names = []
- 330        for entry in ls:
- 331            truncated_entry = entry.split('.')[0]
- 332            idx = truncated_entry.index('r')
- 333            rep_names.append(truncated_entry[:idx] + '|' + truncated_entry[idx:])
- 334
- 335    Ysum = []
- 336
- 337    configlist = []
- 338    r_start_index = []
- 339    r_stop_index = []
- 340
- 341    for rep in range(replica):
- 342
- 343        with open(path + '/' + ls[rep], 'rb') as fp:
- 344            t = fp.read(12)
- 345            header = struct.unpack('iii', t)
- 346            if rep == 0:
- 347                dn = header[0]
- 348                nn = header[1]
- 349                tmax = header[2]
- 350            elif dn != header[0] or nn != header[1] or tmax != header[2]:
- 351                raise Exception('Replica parameters do not match.')
+ 322        rep_names = []
+ 323        for entry in ls:
+ 324            truncated_entry = entry.split('.')[0]
+ 325            idx = truncated_entry.index('r')
+ 326            rep_names.append(truncated_entry[:idx] + '|' + truncated_entry[idx:])
+ 327
+ 328    Ysum = []
+ 329
+ 330    configlist = []
+ 331    r_start_index = []
+ 332    r_stop_index = []
+ 333
+ 334    for rep in range(replica):
+ 335
+ 336        with open(path + '/' + ls[rep], 'rb') as fp:
+ 337            t = fp.read(12)
+ 338            header = struct.unpack('iii', t)
+ 339            if rep == 0:
+ 340                dn = header[0]
+ 341                nn = header[1]
+ 342                tmax = header[2]
+ 343            elif dn != header[0] or nn != header[1] or tmax != header[2]:
+ 344                raise Exception('Replica parameters do not match.')
+ 345
+ 346            t = fp.read(8)
+ 347            if rep == 0:
+ 348                eps = struct.unpack('d', t)[0]
+ 349                print('Step size:', eps, ', Maximal t value:', dn * (nn) * eps)
+ 350            elif eps != struct.unpack('d', t)[0]:
+ 351                raise Exception('Values for eps do not match among replica.')
  352
- 353            t = fp.read(8)
- 354            if rep == 0:
- 355                eps = struct.unpack('d', t)[0]
- 356                print('Step size:', eps, ', Maximal t value:', dn * (nn) * eps)
- 357            elif eps != struct.unpack('d', t)[0]:
- 358                raise Exception('Values for eps do not match among replica.')
- 359
- 360            Ysl = []
- 361
- 362            configlist.append([])
- 363            while True:
- 364                t = fp.read(4)
- 365                if (len(t) < 4):
- 366                    break
- 367                nc = struct.unpack('i', t)[0]
- 368                configlist[-1].append(nc)
- 369
- 370                t = fp.read(8 * tmax * (nn + 1))
- 371                if kwargs.get('plaquette'):
- 372                    if nc % dtr_read == 0:
- 373                        Ysl.append(struct.unpack('d' * tmax * (nn + 1), t))
- 374                t = fp.read(8 * tmax * (nn + 1))
- 375                if not kwargs.get('plaquette'):
- 376                    if nc % dtr_read == 0:
- 377                        Ysl.append(struct.unpack('d' * tmax * (nn + 1), t))
- 378                t = fp.read(8 * tmax * (nn + 1))
- 379
- 380        Ysum.append([])
- 381        for i, item in enumerate(Ysl):
- 382            Ysum[-1].append([np.mean(item[current + xmin:
- 383                             current + tmax - xmin])
- 384                            for current in range(0, len(item), tmax)])
+ 353            Ysl = []
+ 354
+ 355            configlist.append([])
+ 356            while True:
+ 357                t = fp.read(4)
+ 358                if (len(t) < 4):
+ 359                    break
+ 360                nc = struct.unpack('i', t)[0]
+ 361                configlist[-1].append(nc)
+ 362
+ 363                t = fp.read(8 * tmax * (nn + 1))
+ 364                if kwargs.get('plaquette'):
+ 365                    if nc % dtr_read == 0:
+ 366                        Ysl.append(struct.unpack('d' * tmax * (nn + 1), t))
+ 367                t = fp.read(8 * tmax * (nn + 1))
+ 368                if not kwargs.get('plaquette'):
+ 369                    if nc % dtr_read == 0:
+ 370                        Ysl.append(struct.unpack('d' * tmax * (nn + 1), t))
+ 371                t = fp.read(8 * tmax * (nn + 1))
+ 372
+ 373        Ysum.append([])
+ 374        for i, item in enumerate(Ysl):
+ 375            Ysum[-1].append([np.mean(item[current + xmin:
+ 376                             current + tmax - xmin])
+ 377                            for current in range(0, len(item), tmax)])
+ 378
+ 379        diffmeas = configlist[-1][-1] - configlist[-1][-2]
+ 380        configlist[-1] = [item // diffmeas for item in configlist[-1]]
+ 381        if kwargs.get('assume_thermalization', True) and configlist[-1][0] > 1:
+ 382            warnings.warn('Assume thermalization and that the first measurement belongs to the first config.')
+ 383            offset = configlist[-1][0] - 1
+ 384            configlist[-1] = [item - offset for item in configlist[-1]]
  385
- 386        diffmeas = configlist[-1][-1] - configlist[-1][-2]
- 387        configlist[-1] = [item // diffmeas for item in configlist[-1]]
- 388        if kwargs.get('assume_thermalization', True) and configlist[-1][0] > 1:
- 389            warnings.warn('Assume thermalization and that the first measurement belongs to the first config.')
- 390            offset = configlist[-1][0] - 1
- 391            configlist[-1] = [item - offset for item in configlist[-1]]
- 392
- 393        if r_start[rep] is None:
- 394            r_start_index.append(0)
- 395        else:
- 396            try:
- 397                r_start_index.append(configlist[-1].index(r_start[rep]))
- 398            except ValueError:
- 399                raise Exception('Config %d not in file with range [%d, %d]' % (
- 400                    r_start[rep], configlist[-1][0], configlist[-1][-1])) from None
- 401
- 402        if r_stop[rep] is None:
- 403            r_stop_index.append(len(configlist[-1]) - 1)
- 404        else:
- 405            try:
- 406                r_stop_index.append(configlist[-1].index(r_stop[rep]))
- 407            except ValueError:
- 408                raise Exception('Config %d not in file with range [%d, %d]' % (
- 409                    r_stop[rep], configlist[-1][0], configlist[-1][-1])) from None
- 410
- 411    if np.any([len(np.unique(np.diff(cl))) != 1 for cl in configlist]):
- 412        raise Exception('Irregular spaced data in input file!', [len(np.unique(np.diff(cl))) for cl in configlist])
- 413    stepsizes = [list(np.unique(np.diff(cl)))[0] for cl in configlist]
- 414    if np.any([step != 1 for step in stepsizes]):
- 415        warnings.warn('Stepsize between configurations is greater than one!' + str(stepsizes), RuntimeWarning)
- 416
- 417    idl = [range(configlist[rep][r_start_index[rep]], configlist[rep][r_stop_index[rep]] + 1, r_step) for rep in range(replica)]
- 418    t2E_dict = {}
- 419    for n in range(nn + 1):
- 420        samples = []
- 421        for nrep, rep in enumerate(Ysum):
- 422            samples.append([])
- 423            for cnfg in rep:
- 424                samples[-1].append(cnfg[n])
- 425            samples[-1] = samples[-1][r_start_index[nrep]:r_stop_index[nrep] + 1][::r_step]
- 426        new_obs = Obs(samples, rep_names, idl=idl)
- 427        t2E_dict[n * dn * eps] = (n * dn * eps) ** 2 * new_obs / (spatial_extent ** 3) - 0.3
- 428
- 429    return fit_t0(t2E_dict, fit_range, plot_fit=kwargs.get('plot_fit'))
- 430
- 431
- 432def _parse_array_openQCD2(d, n, size, wa, quadrupel=False):
- 433    arr = []
- 434    if d == 2:
- 435        for i in range(n[0]):
- 436            tmp = wa[i * n[1]:(i + 1) * n[1]]
- 437            if quadrupel:
- 438                tmp2 = []
- 439                for j in range(0, len(tmp), 2):
- 440                    tmp2.append(tmp[j])
- 441                arr.append(tmp2)
- 442            else:
- 443                arr.append(np.asarray(tmp))
- 444
- 445    else:
- 446        raise Exception('Only two-dimensional arrays supported!')
- 447
- 448    return arr
- 449
- 450
- 451def _find_files(path, prefix, postfix, ext, known_files=[]):
- 452    found = []
- 453    files = []
- 454
- 455    if postfix != "":
- 456        if postfix[-1] != ".":
- 457            postfix = postfix + "."
- 458        if postfix[0] != ".":
- 459            postfix = "." + postfix
- 460
- 461    if ext[0] == ".":
- 462        ext = ext[1:]
- 463
- 464    pattern = prefix + "*" + postfix + ext
- 465
- 466    for (dirpath, dirnames, filenames) in os.walk(path + "/"):
- 467        found.extend(filenames)
- 468        break
- 469
- 470    if known_files != []:
- 471        for kf in known_files:
- 472            if kf not in found:
- 473                raise FileNotFoundError("Given file " + kf + " does not exist!")
- 474
- 475        return known_files
- 476
- 477    if not found:
- 478        raise FileNotFoundError(f"Error, directory '{path}' not found")
- 479
- 480    for f in found:
- 481        if fnmatch.fnmatch(f, pattern):
- 482            files.append(f)
+ 386        if r_start[rep] is None:
+ 387            r_start_index.append(0)
+ 388        else:
+ 389            try:
+ 390                r_start_index.append(configlist[-1].index(r_start[rep]))
+ 391            except ValueError:
+ 392                raise Exception('Config %d not in file with range [%d, %d]' % (
+ 393                    r_start[rep], configlist[-1][0], configlist[-1][-1])) from None
+ 394
+ 395        if r_stop[rep] is None:
+ 396            r_stop_index.append(len(configlist[-1]) - 1)
+ 397        else:
+ 398            try:
+ 399                r_stop_index.append(configlist[-1].index(r_stop[rep]))
+ 400            except ValueError:
+ 401                raise Exception('Config %d not in file with range [%d, %d]' % (
+ 402                    r_stop[rep], configlist[-1][0], configlist[-1][-1])) from None
+ 403
+ 404    if np.any([len(np.unique(np.diff(cl))) != 1 for cl in configlist]):
+ 405        raise Exception('Irregular spaced data in input file!', [len(np.unique(np.diff(cl))) for cl in configlist])
+ 406    stepsizes = [list(np.unique(np.diff(cl)))[0] for cl in configlist]
+ 407    if np.any([step != 1 for step in stepsizes]):
+ 408        warnings.warn('Stepsize between configurations is greater than one!' + str(stepsizes), RuntimeWarning)
+ 409
+ 410    idl = [range(configlist[rep][r_start_index[rep]], configlist[rep][r_stop_index[rep]] + 1, r_step) for rep in range(replica)]
+ 411    E_dict = {}
+ 412    for n in range(nn + 1):
+ 413        samples = []
+ 414        for nrep, rep in enumerate(Ysum):
+ 415            samples.append([])
+ 416            for cnfg in rep:
+ 417                samples[-1].append(cnfg[n])
+ 418            samples[-1] = samples[-1][r_start_index[nrep]:r_stop_index[nrep] + 1][::r_step]
+ 419        new_obs = Obs(samples, rep_names, idl=idl)
+ 420        E_dict[n * dn * eps] = new_obs / (spatial_extent ** 3)
+ 421
+ 422    return E_dict
+ 423
+ 424
+ 425def extract_t0(path, prefix, dtr_read, xmin, spatial_extent, fit_range=5, postfix='ms', c=0.3, **kwargs):
+ 426    """Extract t0/a^2 from given .ms.dat files. Returns t0 as Obs.
+ 427
+ 428    It is assumed that all boundary effects have
+ 429    sufficiently decayed at x0=xmin.
+ 430    The data around the zero crossing of t^2<E> - c (where c=0.3 by default)
+ 431    is fitted with a linear function
+ 432    from which the exact root is extracted.
+ 433
+ 434    It is assumed that one measurement is performed for each config.
+ 435    If this is not the case, the resulting idl, as well as the handling
+ 436    of r_start, r_stop and r_step is wrong and the user has to correct
+ 437    this in the resulting observable.
+ 438
+ 439    Parameters
+ 440    ----------
+ 441    path : str
+ 442        Path to .ms.dat files
+ 443    prefix : str
+ 444        Ensemble prefix
+ 445    dtr_read : int
+ 446        Determines how many trajectories should be skipped
+ 447        when reading the ms.dat files.
+ 448        Corresponds to dtr_cnfg / dtr_ms in the openQCD input file.
+ 449    xmin : int
+ 450        First timeslice where the boundary
+ 451        effects have sufficiently decayed.
+ 452    spatial_extent : int
+ 453        spatial extent of the lattice, required for normalization.
+ 454    fit_range : int
+ 455        Number of data points left and right of the zero
+ 456        crossing to be included in the linear fit. (Default: 5)
+ 457    postfix : str
+ 458        Postfix of measurement file (Default: ms)
+ 459    c: float
+ 460        Constant that defines the flow scale. Default 0.3 for t_0, choose 2./3 for t_1.
+ 461    r_start : list
+ 462        list which contains the first config to be read for each replicum.
+ 463    r_stop : list
+ 464        list which contains the last config to be read for each replicum.
+ 465    r_step : int
+ 466        integer that defines a fixed step size between two measurements (in units of configs)
+ 467        If not given, r_step=1 is assumed.
+ 468    plaquette : bool
+ 469        If true extract the plaquette estimate of t0 instead.
+ 470    names : list
+ 471        list of names that is assigned to the data according according
+ 472        to the order in the file list. Use careful, if you do not provide file names!
+ 473    files : list
+ 474        list which contains the filenames to be read. No automatic detection of
+ 475        files performed if given.
+ 476    plot_fit : bool
+ 477        If true, the fit for the extraction of t0 is shown together with the data.
+ 478    assume_thermalization : bool
+ 479        If True: If the first record divided by the distance between two measurements is larger than
+ 480        1, it is assumed that this is due to thermalization and the first measurement belongs
+ 481        to the first config (default).
+ 482        If False: The config numbers are assumed to be traj_number // difference
  483
- 484    if files == []:
- 485        raise Exception("No files found after pattern filter!")
- 486
- 487    files = sort_names(files)
- 488    return files
+ 484    Returns
+ 485    -------
+ 486    t0 : Obs
+ 487        Extracted t0
+ 488    """
  489
- 490
- 491def _read_array_openQCD2(fp):
- 492    t = fp.read(4)
- 493    d = struct.unpack('i', t)[0]
- 494    t = fp.read(4 * d)
- 495    n = struct.unpack('%di' % (d), t)
- 496    t = fp.read(4)
- 497    size = struct.unpack('i', t)[0]
- 498    if size == 4:
- 499        types = 'i'
- 500    elif size == 8:
- 501        types = 'd'
- 502    elif size == 16:
- 503        types = 'dd'
- 504    else:
- 505        raise Exception("Type for size '" + str(size) + "' not known.")
- 506    m = n[0]
- 507    for i in range(1, d):
- 508        m *= n[i]
- 509
- 510    t = fp.read(m * size)
- 511    tmp = struct.unpack('%d%s' % (m, types), t)
- 512
- 513    arr = _parse_array_openQCD2(d, n, size, tmp, quadrupel=True)
- 514    return {'d': d, 'n': n, 'size': size, 'arr': arr}
- 515
- 516
- 517def read_qtop(path, prefix, c, dtr_cnfg=1, version="openQCD", **kwargs):
- 518    """Read the topologial charge based on openQCD gradient flow measurements.
- 519
- 520    Parameters
- 521    ----------
- 522    path : str
- 523        path of the measurement files
- 524    prefix : str
- 525        prefix of the measurement files, e.g. <prefix>_id0_r0.ms.dat.
- 526        Ignored if file names are passed explicitly via keyword files.
- 527    c : double
- 528        Smearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
- 529    dtr_cnfg : int
- 530        (optional) parameter that specifies the number of measurements
- 531        between two configs.
- 532        If it is not set, the distance between two measurements
- 533        in the file is assumed to be the distance between two configurations.
- 534    steps : int
- 535        (optional) Distance between two configurations in units of trajectories /
- 536         cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
- 537    version : str
- 538        Either openQCD or sfqcd, depending on the data.
- 539    L : int
- 540        spatial length of the lattice in L/a.
- 541        HAS to be set if version != sfqcd, since openQCD does not provide
- 542        this in the header
- 543    r_start : list
- 544        list which contains the first config to be read for each replicum.
- 545    r_stop : list
- 546        list which contains the last config to be read for each replicum.
- 547    files : list
- 548        specify the exact files that need to be read
- 549        from path, practical if e.g. only one replicum is needed
- 550    postfix : str
- 551        postfix of the file to read, e.g. '.gfms.dat' for openQCD-files
- 552    names : list
- 553        Alternative labeling for replicas/ensembles.
- 554        Has to have the appropriate length.
- 555    Zeuthen_flow : bool
- 556        (optional) If True, the Zeuthen flow is used for Qtop. Only possible
- 557        for version=='sfqcd' If False, the Wilson flow is used.
- 558    integer_charge : bool
- 559        If True, the charge is rounded towards the nearest integer on each config.
- 560
- 561    Returns
- 562    -------
- 563    result : Obs
- 564        Read topological charge
- 565    """
+ 490    E_dict = _extract_flowed_energy_density(path, prefix, dtr_read, xmin, spatial_extent, postfix, **kwargs)
+ 491    t2E_dict = {}
+ 492    for t in sorted(E_dict.keys()):
+ 493        t2E_dict[t] = t ** 2 * E_dict[t] - c
+ 494
+ 495    return fit_t0(t2E_dict, fit_range, plot_fit=kwargs.get('plot_fit'))
+ 496
+ 497
+ 498def extract_w0(path, prefix, dtr_read, xmin, spatial_extent, fit_range=5, postfix='ms', c=0.3, **kwargs):
+ 499    """Extract w0/a from given .ms.dat files. Returns w0 as Obs.
+ 500
+ 501    It is assumed that all boundary effects have
+ 502    sufficiently decayed at x0=xmin.
+ 503    The data around the zero crossing of t d(t^2<E>)/dt -  (where c=0.3 by default)
+ 504    is fitted with a linear function
+ 505    from which the exact root is extracted.
+ 506
+ 507    It is assumed that one measurement is performed for each config.
+ 508    If this is not the case, the resulting idl, as well as the handling
+ 509    of r_start, r_stop and r_step is wrong and the user has to correct
+ 510    this in the resulting observable.
+ 511
+ 512    Parameters
+ 513    ----------
+ 514    path : str
+ 515        Path to .ms.dat files
+ 516    prefix : str
+ 517        Ensemble prefix
+ 518    dtr_read : int
+ 519        Determines how many trajectories should be skipped
+ 520        when reading the ms.dat files.
+ 521        Corresponds to dtr_cnfg / dtr_ms in the openQCD input file.
+ 522    xmin : int
+ 523        First timeslice where the boundary
+ 524        effects have sufficiently decayed.
+ 525    spatial_extent : int
+ 526        spatial extent of the lattice, required for normalization.
+ 527    fit_range : int
+ 528        Number of data points left and right of the zero
+ 529        crossing to be included in the linear fit. (Default: 5)
+ 530    postfix : str
+ 531        Postfix of measurement file (Default: ms)
+ 532    c: float
+ 533        Constant that defines the flow scale. Default 0.3 for w_0, choose 2./3 for w_1.
+ 534    r_start : list
+ 535        list which contains the first config to be read for each replicum.
+ 536    r_stop : list
+ 537        list which contains the last config to be read for each replicum.
+ 538    r_step : int
+ 539        integer that defines a fixed step size between two measurements (in units of configs)
+ 540        If not given, r_step=1 is assumed.
+ 541    plaquette : bool
+ 542        If true extract the plaquette estimate of w0 instead.
+ 543    names : list
+ 544        list of names that is assigned to the data according according
+ 545        to the order in the file list. Use careful, if you do not provide file names!
+ 546    files : list
+ 547        list which contains the filenames to be read. No automatic detection of
+ 548        files performed if given.
+ 549    plot_fit : bool
+ 550        If true, the fit for the extraction of w0 is shown together with the data.
+ 551    assume_thermalization : bool
+ 552        If True: If the first record divided by the distance between two measurements is larger than
+ 553        1, it is assumed that this is due to thermalization and the first measurement belongs
+ 554        to the first config (default).
+ 555        If False: The config numbers are assumed to be traj_number // difference
+ 556
+ 557    Returns
+ 558    -------
+ 559    w0 : Obs
+ 560        Extracted w0
+ 561    """
+ 562
+ 563    E_dict = _extract_flowed_energy_density(path, prefix, dtr_read, xmin, spatial_extent, postfix, **kwargs)
+ 564
+ 565    ftimes = sorted(E_dict.keys())
  566
- 567    return _read_flow_obs(path, prefix, c, dtr_cnfg=dtr_cnfg, version=version, obspos=0, **kwargs)
- 568
- 569
- 570def read_gf_coupling(path, prefix, c, dtr_cnfg=1, Zeuthen_flow=True, **kwargs):
- 571    """Read the gradient flow coupling based on sfqcd gradient flow measurements. See 1607.06423 for details.
- 572
- 573    Note: The current implementation only works for c=0.3 and T=L. The definition of the coupling in 1607.06423 requires projection to topological charge zero which is not done within this function but has to be performed in a separate step.
- 574
- 575    Parameters
- 576    ----------
- 577    path : str
- 578        path of the measurement files
- 579    prefix : str
- 580        prefix of the measurement files, e.g. <prefix>_id0_r0.ms.dat.
- 581        Ignored if file names are passed explicitly via keyword files.
- 582    c : double
- 583        Smearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
- 584    dtr_cnfg : int
- 585        (optional) parameter that specifies the number of measurements
- 586        between two configs.
- 587        If it is not set, the distance between two measurements
- 588        in the file is assumed to be the distance between two configurations.
- 589    steps : int
- 590        (optional) Distance between two configurations in units of trajectories /
- 591         cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
- 592    r_start : list
- 593        list which contains the first config to be read for each replicum.
- 594    r_stop : list
- 595        list which contains the last config to be read for each replicum.
- 596    files : list
- 597        specify the exact files that need to be read
- 598        from path, practical if e.g. only one replicum is needed
- 599    names : list
- 600        Alternative labeling for replicas/ensembles.
- 601        Has to have the appropriate length.
- 602    postfix : str
- 603        postfix of the file to read, e.g. '.gfms.dat' for openQCD-files
- 604    Zeuthen_flow : bool
- 605        (optional) If True, the Zeuthen flow is used for the coupling. If False, the Wilson flow is used.
- 606    """
- 607
- 608    if c != 0.3:
- 609        raise Exception("The required lattice norm is only implemented for c=0.3 at the moment.")
- 610
- 611    plaq = _read_flow_obs(path, prefix, c, dtr_cnfg=dtr_cnfg, version="sfqcd", obspos=6, sum_t=False, Zeuthen_flow=Zeuthen_flow, integer_charge=False, **kwargs)
- 612    C2x1 = _read_flow_obs(path, prefix, c, dtr_cnfg=dtr_cnfg, version="sfqcd", obspos=7, sum_t=False, Zeuthen_flow=Zeuthen_flow, integer_charge=False, **kwargs)
- 613    L = plaq.tag["L"]
- 614    T = plaq.tag["T"]
- 615
- 616    if T != L:
- 617        raise Exception("The required lattice norm is only implemented for T=L at the moment.")
- 618
- 619    if Zeuthen_flow is not True:
- 620        raise Exception("The required lattice norm is only implemented for the Zeuthen flow at the moment.")
- 621
- 622    t = (c * L) ** 2 / 8
- 623
- 624    normdict = {4: 0.012341170468270,
- 625                6: 0.010162691462430,
- 626                8: 0.009031614807931,
- 627                10: 0.008744966371393,
- 628                12: 0.008650917856809,
- 629                14: 8.611154391267955E-03,
- 630                16: 0.008591758449508,
- 631                20: 0.008575359627103,
- 632                24: 0.008569387847540,
- 633                28: 8.566803713382559E-03,
- 634                32: 0.008565541650006,
- 635                40: 8.564480684962046E-03,
- 636                48: 8.564098025073460E-03,
- 637                64: 8.563853943383087E-03}
+ 567    t2E_dict = {}
+ 568    for t in ftimes:
+ 569        t2E_dict[t] = t ** 2 * E_dict[t]
+ 570
+ 571    tdtt2E_dict = {}
+ 572    tdtt2E_dict[ftimes[0]] = ftimes[0] * (t2E_dict[ftimes[1]] - t2E_dict[ftimes[0]]) / (ftimes[1] - ftimes[0]) - c
+ 573    for i in range(1, len(ftimes) - 1):
+ 574        tdtt2E_dict[ftimes[i]] = ftimes[i] * (t2E_dict[ftimes[i + 1]] - t2E_dict[ftimes[i - 1]]) / (ftimes[i + 1] - ftimes[i - 1]) - c
+ 575    tdtt2E_dict[ftimes[-1]] = ftimes[-1] * (t2E_dict[ftimes[-1]] - t2E_dict[ftimes[-2]]) / (ftimes[-1] - ftimes[-2]) - c
+ 576
+ 577    return np.sqrt(fit_t0(tdtt2E_dict, fit_range, plot_fit=kwargs.get('plot_fit'), observable='w0'))
+ 578
+ 579
+ 580def _parse_array_openQCD2(d, n, size, wa, quadrupel=False):
+ 581    arr = []
+ 582    if d == 2:
+ 583        for i in range(n[0]):
+ 584            tmp = wa[i * n[1]:(i + 1) * n[1]]
+ 585            if quadrupel:
+ 586                tmp2 = []
+ 587                for j in range(0, len(tmp), 2):
+ 588                    tmp2.append(tmp[j])
+ 589                arr.append(tmp2)
+ 590            else:
+ 591                arr.append(np.asarray(tmp))
+ 592
+ 593    else:
+ 594        raise Exception('Only two-dimensional arrays supported!')
+ 595
+ 596    return arr
+ 597
+ 598
+ 599def _find_files(path, prefix, postfix, ext, known_files=[]):
+ 600    found = []
+ 601    files = []
+ 602
+ 603    if postfix != "":
+ 604        if postfix[-1] != ".":
+ 605            postfix = postfix + "."
+ 606        if postfix[0] != ".":
+ 607            postfix = "." + postfix
+ 608
+ 609    if ext[0] == ".":
+ 610        ext = ext[1:]
+ 611
+ 612    pattern = prefix + "*" + postfix + ext
+ 613
+ 614    for (dirpath, dirnames, filenames) in os.walk(path + "/"):
+ 615        found.extend(filenames)
+ 616        break
+ 617
+ 618    if known_files != []:
+ 619        for kf in known_files:
+ 620            if kf not in found:
+ 621                raise FileNotFoundError("Given file " + kf + " does not exist!")
+ 622
+ 623        return known_files
+ 624
+ 625    if not found:
+ 626        raise FileNotFoundError(f"Error, directory '{path}' not found")
+ 627
+ 628    for f in found:
+ 629        if fnmatch.fnmatch(f, pattern):
+ 630            files.append(f)
+ 631
+ 632    if files == []:
+ 633        raise Exception("No files found after pattern filter!")
+ 634
+ 635    files = sort_names(files)
+ 636    return files
+ 637
  638
- 639    return t * t * (5 / 3 * plaq - 1 / 12 * C2x1) / normdict[L]
- 640
- 641
- 642def _read_flow_obs(path, prefix, c, dtr_cnfg=1, version="openQCD", obspos=0, sum_t=True, **kwargs):
- 643    """Read a flow observable based on openQCD gradient flow measurements.
- 644
- 645    Parameters
- 646    ----------
- 647    path : str
- 648        path of the measurement files
- 649    prefix : str
- 650        prefix of the measurement files, e.g. <prefix>_id0_r0.ms.dat.
- 651        Ignored if file names are passed explicitly via keyword files.
- 652    c : double
- 653        Smearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
- 654    dtr_cnfg : int
- 655        (optional) parameter that specifies the number of measurements
- 656        between two configs.
- 657        If it is not set, the distance between two measurements
- 658        in the file is assumed to be the distance between two configurations.
- 659    steps : int
- 660        (optional) Distance between two configurations in units of trajectories /
- 661         cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
- 662    version : str
- 663        Either openQCD or sfqcd, depending on the data.
- 664    obspos : int
- 665        position of the obeservable in the measurement file. Only relevant for sfqcd files.
- 666    sum_t : bool
- 667        If true sum over all timeslices, if false only take the value at T/2.
- 668    L : int
- 669        spatial length of the lattice in L/a.
- 670        HAS to be set if version != sfqcd, since openQCD does not provide
- 671        this in the header
- 672    r_start : list
- 673        list which contains the first config to be read for each replicum.
- 674    r_stop : list
- 675        list which contains the last config to be read for each replicum.
- 676    files : list
- 677        specify the exact files that need to be read
- 678        from path, practical if e.g. only one replicum is needed
- 679    names : list
- 680        Alternative labeling for replicas/ensembles.
- 681        Has to have the appropriate length.
- 682    postfix : str
- 683        postfix of the file to read, e.g. '.gfms.dat' for openQCD-files
- 684    Zeuthen_flow : bool
- 685        (optional) If True, the Zeuthen flow is used for Qtop. Only possible
- 686        for version=='sfqcd' If False, the Wilson flow is used.
- 687    integer_charge : bool
- 688        If True, the charge is rounded towards the nearest integer on each config.
- 689
- 690    Returns
- 691    -------
- 692    result : Obs
- 693        flow observable specified
- 694    """
- 695    known_versions = ["openQCD", "sfqcd"]
- 696
- 697    if version not in known_versions:
- 698        raise Exception("Unknown openQCD version.")
- 699    if "steps" in kwargs:
- 700        steps = kwargs.get("steps")
- 701    if version == "sfqcd":
- 702        if "L" in kwargs:
- 703            supposed_L = kwargs.get("L")
- 704        else:
- 705            supposed_L = None
- 706        postfix = "gfms"
- 707    else:
- 708        if "L" not in kwargs:
- 709            raise Exception("This version of openQCD needs you to provide the spatial length of the lattice as parameter 'L'.")
- 710        else:
- 711            L = kwargs.get("L")
- 712        postfix = "ms"
- 713
- 714    if "postfix" in kwargs:
- 715        postfix = kwargs.get("postfix")
+ 639def _read_array_openQCD2(fp):
+ 640    t = fp.read(4)
+ 641    d = struct.unpack('i', t)[0]
+ 642    t = fp.read(4 * d)
+ 643    n = struct.unpack('%di' % (d), t)
+ 644    t = fp.read(4)
+ 645    size = struct.unpack('i', t)[0]
+ 646    if size == 4:
+ 647        types = 'i'
+ 648    elif size == 8:
+ 649        types = 'd'
+ 650    elif size == 16:
+ 651        types = 'dd'
+ 652    else:
+ 653        raise Exception("Type for size '" + str(size) + "' not known.")
+ 654    m = n[0]
+ 655    for i in range(1, d):
+ 656        m *= n[i]
+ 657
+ 658    t = fp.read(m * size)
+ 659    tmp = struct.unpack('%d%s' % (m, types), t)
+ 660
+ 661    arr = _parse_array_openQCD2(d, n, size, tmp, quadrupel=True)
+ 662    return {'d': d, 'n': n, 'size': size, 'arr': arr}
+ 663
+ 664
+ 665def read_qtop(path, prefix, c, dtr_cnfg=1, version="openQCD", **kwargs):
+ 666    """Read the topologial charge based on openQCD gradient flow measurements.
+ 667
+ 668    Parameters
+ 669    ----------
+ 670    path : str
+ 671        path of the measurement files
+ 672    prefix : str
+ 673        prefix of the measurement files, e.g. <prefix>_id0_r0.ms.dat.
+ 674        Ignored if file names are passed explicitly via keyword files.
+ 675    c : double
+ 676        Smearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
+ 677    dtr_cnfg : int
+ 678        (optional) parameter that specifies the number of measurements
+ 679        between two configs.
+ 680        If it is not set, the distance between two measurements
+ 681        in the file is assumed to be the distance between two configurations.
+ 682    steps : int
+ 683        (optional) Distance between two configurations in units of trajectories /
+ 684         cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
+ 685    version : str
+ 686        Either openQCD or sfqcd, depending on the data.
+ 687    L : int
+ 688        spatial length of the lattice in L/a.
+ 689        HAS to be set if version != sfqcd, since openQCD does not provide
+ 690        this in the header
+ 691    r_start : list
+ 692        list which contains the first config to be read for each replicum.
+ 693    r_stop : list
+ 694        list which contains the last config to be read for each replicum.
+ 695    files : list
+ 696        specify the exact files that need to be read
+ 697        from path, practical if e.g. only one replicum is needed
+ 698    postfix : str
+ 699        postfix of the file to read, e.g. '.gfms.dat' for openQCD-files
+ 700    names : list
+ 701        Alternative labeling for replicas/ensembles.
+ 702        Has to have the appropriate length.
+ 703    Zeuthen_flow : bool
+ 704        (optional) If True, the Zeuthen flow is used for Qtop. Only possible
+ 705        for version=='sfqcd' If False, the Wilson flow is used.
+ 706    integer_charge : bool
+ 707        If True, the charge is rounded towards the nearest integer on each config.
+ 708
+ 709    Returns
+ 710    -------
+ 711    result : Obs
+ 712        Read topological charge
+ 713    """
+ 714
+ 715    return _read_flow_obs(path, prefix, c, dtr_cnfg=dtr_cnfg, version=version, obspos=0, **kwargs)
  716
- 717    if "files" in kwargs:
- 718        known_files = kwargs.get("files")
- 719    else:
- 720        known_files = []
- 721
- 722    files = _find_files(path, prefix, postfix, "dat", known_files=known_files)
- 723
- 724    if 'r_start' in kwargs:
- 725        r_start = kwargs.get('r_start')
- 726        if len(r_start) != len(files):
- 727            raise Exception('r_start does not match number of replicas')
- 728        r_start = [o if o else None for o in r_start]
- 729    else:
- 730        r_start = [None] * len(files)
- 731
- 732    if 'r_stop' in kwargs:
- 733        r_stop = kwargs.get('r_stop')
- 734        if len(r_stop) != len(files):
- 735            raise Exception('r_stop does not match number of replicas')
- 736    else:
- 737        r_stop = [None] * len(files)
- 738    rep_names = []
- 739
- 740    zeuthen = kwargs.get('Zeuthen_flow', False)
- 741    if zeuthen and version not in ['sfqcd']:
- 742        raise Exception('Zeuthen flow can only be used for version==sfqcd')
- 743
- 744    r_start_index = []
- 745    r_stop_index = []
- 746    deltas = []
- 747    configlist = []
- 748    if not zeuthen:
- 749        obspos += 8
- 750    for rep, file in enumerate(files):
- 751        with open(path + "/" + file, "rb") as fp:
- 752
- 753            Q = []
- 754            traj_list = []
- 755            if version in ['sfqcd']:
- 756                t = fp.read(12)
- 757                header = struct.unpack('<iii', t)
- 758                zthfl = header[0]  # Zeuthen flow -> if it's equal to 2 it means that the Zeuthen flow is also 'measured' (apart from the Wilson flow)
- 759                ncs = header[1]  # number of different values for c in t_flow=1/8 c² L² -> measurements done for ncs c's
- 760                tmax = header[2]  # lattice T/a
- 761
- 762                t = fp.read(12)
- 763                Ls = struct.unpack('<iii', t)
- 764                if (Ls[0] == Ls[1] and Ls[1] == Ls[2]):
- 765                    L = Ls[0]
- 766                    if not (supposed_L == L) and supposed_L:
- 767                        raise Exception("It seems the length given in the header and by you contradict each other")
- 768                else:
- 769                    raise Exception("Found more than one spatial length in header!")
- 770
- 771                t = fp.read(16)
- 772                header2 = struct.unpack('<dd', t)
- 773                tol = header2[0]
- 774                cmax = header2[1]  # highest value of c used
- 775
- 776                if c > cmax:
- 777                    raise Exception('Flow has been determined between c=0 and c=%lf with tolerance %lf' % (cmax, tol))
- 778
- 779                if (zthfl == 2):
- 780                    nfl = 2  # number of flows
- 781                else:
- 782                    nfl = 1
- 783                iobs = 8 * nfl  # number of flow observables calculated
- 784
- 785                while True:
- 786                    t = fp.read(4)
- 787                    if (len(t) < 4):
- 788                        break
- 789                    traj_list.append(struct.unpack('i', t)[0])   # trajectory number when measurement was done
- 790
- 791                    for j in range(ncs + 1):
- 792                        for i in range(iobs):
- 793                            t = fp.read(8 * tmax)
- 794                            if (i == obspos):  # determines the flow observable -> i=0 <-> Zeuthen flow
- 795                                Q.append(struct.unpack('d' * tmax, t))
- 796
- 797            else:
- 798                t = fp.read(12)
- 799                header = struct.unpack('<iii', t)
- 800                # step size in integration steps "dnms"
- 801                dn = header[0]
- 802                # number of measurements, so "ntot"/dn
- 803                nn = header[1]
- 804                # lattice T/a
- 805                tmax = header[2]
- 806
- 807                t = fp.read(8)
- 808                eps = struct.unpack('d', t)[0]
- 809
- 810                while True:
- 811                    t = fp.read(4)
- 812                    if (len(t) < 4):
- 813                        break
- 814                    traj_list.append(struct.unpack('i', t)[0])
- 815                    # Wsl
- 816                    t = fp.read(8 * tmax * (nn + 1))
- 817                    # Ysl
- 818                    t = fp.read(8 * tmax * (nn + 1))
- 819                    # Qsl, which is asked for in this method
- 820                    t = fp.read(8 * tmax * (nn + 1))
- 821                    # unpack the array of Qtops,
- 822                    # on each timeslice t=0,...,tmax-1 and the
- 823                    # measurement number in = 0...nn (see README.qcd1)
- 824                    tmpd = struct.unpack('d' * tmax * (nn + 1), t)
- 825                    Q.append(tmpd)
- 826
- 827        if len(np.unique(np.diff(traj_list))) != 1:
- 828            raise Exception("Irregularities in stepsize found")
- 829        else:
- 830            if 'steps' in kwargs:
- 831                if steps != traj_list[1] - traj_list[0]:
- 832                    raise Exception("steps and the found stepsize are not the same")
- 833            else:
- 834                steps = traj_list[1] - traj_list[0]
- 835
- 836        configlist.append([tr // steps // dtr_cnfg for tr in traj_list])
- 837        if configlist[-1][0] > 1:
- 838            offset = configlist[-1][0] - 1
- 839            warnings.warn('Assume thermalization and that the first measurement belongs to the first config. Offset = %d configs (%d trajectories / cycles)' % (
- 840                offset, offset * steps))
- 841            configlist[-1] = [item - offset for item in configlist[-1]]
- 842
- 843        if r_start[rep] is None:
- 844            r_start_index.append(0)
- 845        else:
- 846            try:
- 847                r_start_index.append(configlist[-1].index(r_start[rep]))
- 848            except ValueError:
- 849                raise Exception('Config %d not in file with range [%d, %d]' % (
- 850                    r_start[rep], configlist[-1][0], configlist[-1][-1])) from None
- 851
- 852        if r_stop[rep] is None:
- 853            r_stop_index.append(len(configlist[-1]) - 1)
- 854        else:
- 855            try:
- 856                r_stop_index.append(configlist[-1].index(r_stop[rep]))
- 857            except ValueError:
- 858                raise Exception('Config %d not in file with range [%d, %d]' % (
- 859                    r_stop[rep], configlist[-1][0], configlist[-1][-1])) from None
- 860
- 861        if version in ['sfqcd']:
- 862            cstepsize = cmax / ncs
- 863            index_aim = round(c / cstepsize)
- 864        else:
- 865            t_aim = (c * L) ** 2 / 8
- 866            index_aim = round(t_aim / eps / dn)
- 867
- 868        Q_sum = []
- 869        for i, item in enumerate(Q):
- 870            if sum_t is True:
- 871                Q_sum.append([sum(item[current:current + tmax])
- 872                             for current in range(0, len(item), tmax)])
- 873            else:
- 874                Q_sum.append([item[int(tmax / 2)]])
- 875        Q_top = []
- 876        if version in ['sfqcd']:
- 877            for i in range(len(Q_sum) // (ncs + 1)):
- 878                Q_top.append(Q_sum[i * (ncs + 1) + index_aim][0])
- 879        else:
- 880            for i in range(len(Q) // dtr_cnfg):
- 881                Q_top.append(Q_sum[dtr_cnfg * i][index_aim])
- 882        if len(Q_top) != len(traj_list) // dtr_cnfg:
- 883            raise Exception("qtops and traj_list dont have the same length")
- 884
- 885        if kwargs.get('integer_charge', False):
- 886            Q_top = [round(q) for q in Q_top]
+ 717
+ 718def read_gf_coupling(path, prefix, c, dtr_cnfg=1, Zeuthen_flow=True, **kwargs):
+ 719    """Read the gradient flow coupling based on sfqcd gradient flow measurements. See 1607.06423 for details.
+ 720
+ 721    Note: The current implementation only works for c=0.3 and T=L. The definition of the coupling in 1607.06423 requires projection to topological charge zero which is not done within this function but has to be performed in a separate step.
+ 722
+ 723    Parameters
+ 724    ----------
+ 725    path : str
+ 726        path of the measurement files
+ 727    prefix : str
+ 728        prefix of the measurement files, e.g. <prefix>_id0_r0.ms.dat.
+ 729        Ignored if file names are passed explicitly via keyword files.
+ 730    c : double
+ 731        Smearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
+ 732    dtr_cnfg : int
+ 733        (optional) parameter that specifies the number of measurements
+ 734        between two configs.
+ 735        If it is not set, the distance between two measurements
+ 736        in the file is assumed to be the distance between two configurations.
+ 737    steps : int
+ 738        (optional) Distance between two configurations in units of trajectories /
+ 739         cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
+ 740    r_start : list
+ 741        list which contains the first config to be read for each replicum.
+ 742    r_stop : list
+ 743        list which contains the last config to be read for each replicum.
+ 744    files : list
+ 745        specify the exact files that need to be read
+ 746        from path, practical if e.g. only one replicum is needed
+ 747    names : list
+ 748        Alternative labeling for replicas/ensembles.
+ 749        Has to have the appropriate length.
+ 750    postfix : str
+ 751        postfix of the file to read, e.g. '.gfms.dat' for openQCD-files
+ 752    Zeuthen_flow : bool
+ 753        (optional) If True, the Zeuthen flow is used for the coupling. If False, the Wilson flow is used.
+ 754    """
+ 755
+ 756    if c != 0.3:
+ 757        raise Exception("The required lattice norm is only implemented for c=0.3 at the moment.")
+ 758
+ 759    plaq = _read_flow_obs(path, prefix, c, dtr_cnfg=dtr_cnfg, version="sfqcd", obspos=6, sum_t=False, Zeuthen_flow=Zeuthen_flow, integer_charge=False, **kwargs)
+ 760    C2x1 = _read_flow_obs(path, prefix, c, dtr_cnfg=dtr_cnfg, version="sfqcd", obspos=7, sum_t=False, Zeuthen_flow=Zeuthen_flow, integer_charge=False, **kwargs)
+ 761    L = plaq.tag["L"]
+ 762    T = plaq.tag["T"]
+ 763
+ 764    if T != L:
+ 765        raise Exception("The required lattice norm is only implemented for T=L at the moment.")
+ 766
+ 767    if Zeuthen_flow is not True:
+ 768        raise Exception("The required lattice norm is only implemented for the Zeuthen flow at the moment.")
+ 769
+ 770    t = (c * L) ** 2 / 8
+ 771
+ 772    normdict = {4: 0.012341170468270,
+ 773                6: 0.010162691462430,
+ 774                8: 0.009031614807931,
+ 775                10: 0.008744966371393,
+ 776                12: 0.008650917856809,
+ 777                14: 8.611154391267955E-03,
+ 778                16: 0.008591758449508,
+ 779                20: 0.008575359627103,
+ 780                24: 0.008569387847540,
+ 781                28: 8.566803713382559E-03,
+ 782                32: 0.008565541650006,
+ 783                40: 8.564480684962046E-03,
+ 784                48: 8.564098025073460E-03,
+ 785                64: 8.563853943383087E-03}
+ 786
+ 787    return t * t * (5 / 3 * plaq - 1 / 12 * C2x1) / normdict[L]
+ 788
+ 789
+ 790def _read_flow_obs(path, prefix, c, dtr_cnfg=1, version="openQCD", obspos=0, sum_t=True, **kwargs):
+ 791    """Read a flow observable based on openQCD gradient flow measurements.
+ 792
+ 793    Parameters
+ 794    ----------
+ 795    path : str
+ 796        path of the measurement files
+ 797    prefix : str
+ 798        prefix of the measurement files, e.g. <prefix>_id0_r0.ms.dat.
+ 799        Ignored if file names are passed explicitly via keyword files.
+ 800    c : double
+ 801        Smearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
+ 802    dtr_cnfg : int
+ 803        (optional) parameter that specifies the number of measurements
+ 804        between two configs.
+ 805        If it is not set, the distance between two measurements
+ 806        in the file is assumed to be the distance between two configurations.
+ 807    steps : int
+ 808        (optional) Distance between two configurations in units of trajectories /
+ 809         cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
+ 810    version : str
+ 811        Either openQCD or sfqcd, depending on the data.
+ 812    obspos : int
+ 813        position of the obeservable in the measurement file. Only relevant for sfqcd files.
+ 814    sum_t : bool
+ 815        If true sum over all timeslices, if false only take the value at T/2.
+ 816    L : int
+ 817        spatial length of the lattice in L/a.
+ 818        HAS to be set if version != sfqcd, since openQCD does not provide
+ 819        this in the header
+ 820    r_start : list
+ 821        list which contains the first config to be read for each replicum.
+ 822    r_stop : list
+ 823        list which contains the last config to be read for each replicum.
+ 824    files : list
+ 825        specify the exact files that need to be read
+ 826        from path, practical if e.g. only one replicum is needed
+ 827    names : list
+ 828        Alternative labeling for replicas/ensembles.
+ 829        Has to have the appropriate length.
+ 830    postfix : str
+ 831        postfix of the file to read, e.g. '.gfms.dat' for openQCD-files
+ 832    Zeuthen_flow : bool
+ 833        (optional) If True, the Zeuthen flow is used for Qtop. Only possible
+ 834        for version=='sfqcd' If False, the Wilson flow is used.
+ 835    integer_charge : bool
+ 836        If True, the charge is rounded towards the nearest integer on each config.
+ 837
+ 838    Returns
+ 839    -------
+ 840    result : Obs
+ 841        flow observable specified
+ 842    """
+ 843    known_versions = ["openQCD", "sfqcd"]
+ 844
+ 845    if version not in known_versions:
+ 846        raise Exception("Unknown openQCD version.")
+ 847    if "steps" in kwargs:
+ 848        steps = kwargs.get("steps")
+ 849    if version == "sfqcd":
+ 850        if "L" in kwargs:
+ 851            supposed_L = kwargs.get("L")
+ 852        else:
+ 853            supposed_L = None
+ 854        postfix = "gfms"
+ 855    else:
+ 856        if "L" not in kwargs:
+ 857            raise Exception("This version of openQCD needs you to provide the spatial length of the lattice as parameter 'L'.")
+ 858        else:
+ 859            L = kwargs.get("L")
+ 860        postfix = "ms"
+ 861
+ 862    if "postfix" in kwargs:
+ 863        postfix = kwargs.get("postfix")
+ 864
+ 865    if "files" in kwargs:
+ 866        known_files = kwargs.get("files")
+ 867    else:
+ 868        known_files = []
+ 869
+ 870    files = _find_files(path, prefix, postfix, "dat", known_files=known_files)
+ 871
+ 872    if 'r_start' in kwargs:
+ 873        r_start = kwargs.get('r_start')
+ 874        if len(r_start) != len(files):
+ 875            raise Exception('r_start does not match number of replicas')
+ 876        r_start = [o if o else None for o in r_start]
+ 877    else:
+ 878        r_start = [None] * len(files)
+ 879
+ 880    if 'r_stop' in kwargs:
+ 881        r_stop = kwargs.get('r_stop')
+ 882        if len(r_stop) != len(files):
+ 883            raise Exception('r_stop does not match number of replicas')
+ 884    else:
+ 885        r_stop = [None] * len(files)
+ 886    rep_names = []
  887
- 888        truncated_file = file[:-len(postfix)]
- 889
- 890        if "names" not in kwargs:
- 891            try:
- 892                idx = truncated_file.index('r')
- 893            except Exception:
- 894                if "names" not in kwargs:
- 895                    raise Exception("Automatic recognition of replicum failed, please enter the key word 'names'.")
- 896            ens_name = truncated_file[:idx]
- 897            rep_names.append(ens_name + '|' + truncated_file[idx:].split(".")[0])
- 898        else:
- 899            names = kwargs.get("names")
- 900            rep_names = names
- 901
- 902        deltas.append(Q_top)
- 903
- 904    rep_names = sort_names(rep_names)
- 905
- 906    idl = [range(int(configlist[rep][r_start_index[rep]]), int(configlist[rep][r_stop_index[rep]]) + 1, 1) for rep in range(len(deltas))]
- 907    deltas = [deltas[nrep][r_start_index[nrep]:r_stop_index[nrep] + 1] for nrep in range(len(deltas))]
- 908    result = Obs(deltas, rep_names, idl=idl)
- 909    result.tag = {"T": tmax - 1,
- 910                  "L": L}
- 911    return result
- 912
- 913
- 914def qtop_projection(qtop, target=0):
- 915    """Returns the projection to the topological charge sector defined by target.
- 916
- 917    Parameters
- 918    ----------
- 919    path : Obs
- 920        Topological charge.
- 921    target : int
- 922        Specifies the topological sector to be reweighted to (default 0)
+ 888    zeuthen = kwargs.get('Zeuthen_flow', False)
+ 889    if zeuthen and version not in ['sfqcd']:
+ 890        raise Exception('Zeuthen flow can only be used for version==sfqcd')
+ 891
+ 892    r_start_index = []
+ 893    r_stop_index = []
+ 894    deltas = []
+ 895    configlist = []
+ 896    if not zeuthen:
+ 897        obspos += 8
+ 898    for rep, file in enumerate(files):
+ 899        with open(path + "/" + file, "rb") as fp:
+ 900
+ 901            Q = []
+ 902            traj_list = []
+ 903            if version in ['sfqcd']:
+ 904                t = fp.read(12)
+ 905                header = struct.unpack('<iii', t)
+ 906                zthfl = header[0]  # Zeuthen flow -> if it's equal to 2 it means that the Zeuthen flow is also 'measured' (apart from the Wilson flow)
+ 907                ncs = header[1]  # number of different values for c in t_flow=1/8 c² L² -> measurements done for ncs c's
+ 908                tmax = header[2]  # lattice T/a
+ 909
+ 910                t = fp.read(12)
+ 911                Ls = struct.unpack('<iii', t)
+ 912                if (Ls[0] == Ls[1] and Ls[1] == Ls[2]):
+ 913                    L = Ls[0]
+ 914                    if not (supposed_L == L) and supposed_L:
+ 915                        raise Exception("It seems the length given in the header and by you contradict each other")
+ 916                else:
+ 917                    raise Exception("Found more than one spatial length in header!")
+ 918
+ 919                t = fp.read(16)
+ 920                header2 = struct.unpack('<dd', t)
+ 921                tol = header2[0]
+ 922                cmax = header2[1]  # highest value of c used
  923
- 924    Returns
- 925    -------
- 926    reto : Obs
- 927        projection to the topological charge sector defined by target
- 928    """
- 929    if qtop.reweighted:
- 930        raise Exception('You can not use a reweighted observable for reweighting!')
- 931
- 932    proj_qtop = []
- 933    for n in qtop.deltas:
- 934        proj_qtop.append(np.array([1 if round(qtop.r_values[n] + q) == target else 0 for q in qtop.deltas[n]]))
- 935
- 936    reto = Obs(proj_qtop, qtop.names, idl=[qtop.idl[name] for name in qtop.names])
- 937    return reto
+ 924                if c > cmax:
+ 925                    raise Exception('Flow has been determined between c=0 and c=%lf with tolerance %lf' % (cmax, tol))
+ 926
+ 927                if (zthfl == 2):
+ 928                    nfl = 2  # number of flows
+ 929                else:
+ 930                    nfl = 1
+ 931                iobs = 8 * nfl  # number of flow observables calculated
+ 932
+ 933                while True:
+ 934                    t = fp.read(4)
+ 935                    if (len(t) < 4):
+ 936                        break
+ 937                    traj_list.append(struct.unpack('i', t)[0])   # trajectory number when measurement was done
  938
- 939
- 940def read_qtop_sector(path, prefix, c, target=0, **kwargs):
- 941    """Constructs reweighting factors to a specified topological sector.
- 942
- 943    Parameters
- 944    ----------
- 945    path : str
- 946        path of the measurement files
- 947    prefix : str
- 948        prefix of the measurement files, e.g. <prefix>_id0_r0.ms.dat
- 949    c : double
- 950        Smearing radius in units of the lattice extent, c = sqrt(8 t0) / L
- 951    target : int
- 952        Specifies the topological sector to be reweighted to (default 0)
- 953    dtr_cnfg : int
- 954        (optional) parameter that specifies the number of trajectories
- 955        between two configs.
- 956        if it is not set, the distance between two measurements
- 957        in the file is assumed to be the distance between two configurations.
- 958    steps : int
- 959        (optional) Distance between two configurations in units of trajectories /
- 960         cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
- 961    version : str
- 962        version string of the openQCD (sfqcd) version used to create
- 963        the ensemble. Default is 2.0. May also be set to sfqcd.
- 964    L : int
- 965        spatial length of the lattice in L/a.
- 966        HAS to be set if version != sfqcd, since openQCD does not provide
- 967        this in the header
- 968    r_start : list
- 969        offset of the first ensemble, making it easier to match
- 970        later on with other Obs
- 971    r_stop : list
- 972        last configurations that need to be read (per replicum)
- 973    files : list
- 974        specify the exact files that need to be read
- 975        from path, practical if e.g. only one replicum is needed
- 976    names : list
- 977        Alternative labeling for replicas/ensembles.
- 978        Has to have the appropriate length
- 979    Zeuthen_flow : bool
- 980        (optional) If True, the Zeuthen flow is used for Qtop. Only possible
- 981        for version=='sfqcd' If False, the Wilson flow is used.
- 982
- 983    Returns
- 984    -------
- 985    reto : Obs
- 986        projection to the topological charge sector defined by target
- 987    """
- 988
- 989    if not isinstance(target, int):
- 990        raise Exception("'target' has to be an integer.")
- 991
- 992    kwargs['integer_charge'] = True
- 993    qtop = read_qtop(path, prefix, c, **kwargs)
- 994
- 995    return qtop_projection(qtop, target=target)
- 996
- 997
- 998def read_ms5_xsf(path, prefix, qc, corr, sep="r", **kwargs):
- 999    """
-1000    Read data from files in the specified directory with the specified prefix and quark combination extension, and return a `Corr` object containing the data.
-1001
-1002    Parameters
-1003    ----------
-1004    path : str
-1005        The directory to search for the files in.
-1006    prefix : str
-1007        The prefix to match the files against.
-1008    qc : str
-1009        The quark combination extension to match the files against.
-1010    corr : str
-1011        The correlator to extract data for.
-1012    sep : str, optional
-1013        The separator to use when parsing the replika names.
-1014    **kwargs
-1015        Additional keyword arguments. The following keyword arguments are recognized:
-1016
-1017        - names (List[str]): A list of names to use for the replicas.
-1018
-1019    Returns
-1020    -------
-1021    Corr
-1022        A complex valued `Corr` object containing the data read from the files. In case of boudary to bulk correlators.
-1023    or
-1024    CObs
-1025        A complex valued `CObs` object containing the data read from the files. In case of boudary to boundary correlators.
-1026
-1027
-1028    Raises
-1029    ------
-1030    FileNotFoundError
-1031        If no files matching the specified prefix and quark combination extension are found in the specified directory.
-1032    IOError
-1033        If there is an error reading a file.
-1034    struct.error
-1035        If there is an error unpacking binary data.
-1036    """
+ 939                    for j in range(ncs + 1):
+ 940                        for i in range(iobs):
+ 941                            t = fp.read(8 * tmax)
+ 942                            if (i == obspos):  # determines the flow observable -> i=0 <-> Zeuthen flow
+ 943                                Q.append(struct.unpack('d' * tmax, t))
+ 944
+ 945            else:
+ 946                t = fp.read(12)
+ 947                header = struct.unpack('<iii', t)
+ 948                # step size in integration steps "dnms"
+ 949                dn = header[0]
+ 950                # number of measurements, so "ntot"/dn
+ 951                nn = header[1]
+ 952                # lattice T/a
+ 953                tmax = header[2]
+ 954
+ 955                t = fp.read(8)
+ 956                eps = struct.unpack('d', t)[0]
+ 957
+ 958                while True:
+ 959                    t = fp.read(4)
+ 960                    if (len(t) < 4):
+ 961                        break
+ 962                    traj_list.append(struct.unpack('i', t)[0])
+ 963                    # Wsl
+ 964                    t = fp.read(8 * tmax * (nn + 1))
+ 965                    # Ysl
+ 966                    t = fp.read(8 * tmax * (nn + 1))
+ 967                    # Qsl, which is asked for in this method
+ 968                    t = fp.read(8 * tmax * (nn + 1))
+ 969                    # unpack the array of Qtops,
+ 970                    # on each timeslice t=0,...,tmax-1 and the
+ 971                    # measurement number in = 0...nn (see README.qcd1)
+ 972                    tmpd = struct.unpack('d' * tmax * (nn + 1), t)
+ 973                    Q.append(tmpd)
+ 974
+ 975        if len(np.unique(np.diff(traj_list))) != 1:
+ 976            raise Exception("Irregularities in stepsize found")
+ 977        else:
+ 978            if 'steps' in kwargs:
+ 979                if steps != traj_list[1] - traj_list[0]:
+ 980                    raise Exception("steps and the found stepsize are not the same")
+ 981            else:
+ 982                steps = traj_list[1] - traj_list[0]
+ 983
+ 984        configlist.append([tr // steps // dtr_cnfg for tr in traj_list])
+ 985        if configlist[-1][0] > 1:
+ 986            offset = configlist[-1][0] - 1
+ 987            warnings.warn('Assume thermalization and that the first measurement belongs to the first config. Offset = %d configs (%d trajectories / cycles)' % (
+ 988                offset, offset * steps))
+ 989            configlist[-1] = [item - offset for item in configlist[-1]]
+ 990
+ 991        if r_start[rep] is None:
+ 992            r_start_index.append(0)
+ 993        else:
+ 994            try:
+ 995                r_start_index.append(configlist[-1].index(r_start[rep]))
+ 996            except ValueError:
+ 997                raise Exception('Config %d not in file with range [%d, %d]' % (
+ 998                    r_start[rep], configlist[-1][0], configlist[-1][-1])) from None
+ 999
+1000        if r_stop[rep] is None:
+1001            r_stop_index.append(len(configlist[-1]) - 1)
+1002        else:
+1003            try:
+1004                r_stop_index.append(configlist[-1].index(r_stop[rep]))
+1005            except ValueError:
+1006                raise Exception('Config %d not in file with range [%d, %d]' % (
+1007                    r_stop[rep], configlist[-1][0], configlist[-1][-1])) from None
+1008
+1009        if version in ['sfqcd']:
+1010            cstepsize = cmax / ncs
+1011            index_aim = round(c / cstepsize)
+1012        else:
+1013            t_aim = (c * L) ** 2 / 8
+1014            index_aim = round(t_aim / eps / dn)
+1015
+1016        Q_sum = []
+1017        for i, item in enumerate(Q):
+1018            if sum_t is True:
+1019                Q_sum.append([sum(item[current:current + tmax])
+1020                             for current in range(0, len(item), tmax)])
+1021            else:
+1022                Q_sum.append([item[int(tmax / 2)]])
+1023        Q_top = []
+1024        if version in ['sfqcd']:
+1025            for i in range(len(Q_sum) // (ncs + 1)):
+1026                Q_top.append(Q_sum[i * (ncs + 1) + index_aim][0])
+1027        else:
+1028            for i in range(len(Q) // dtr_cnfg):
+1029                Q_top.append(Q_sum[dtr_cnfg * i][index_aim])
+1030        if len(Q_top) != len(traj_list) // dtr_cnfg:
+1031            raise Exception("qtops and traj_list dont have the same length")
+1032
+1033        if kwargs.get('integer_charge', False):
+1034            Q_top = [round(q) for q in Q_top]
+1035
+1036        truncated_file = file[:-len(postfix)]
 1037
-1038    # found = []
-1039    files = []
-1040    names = []
-1041
-1042    # test if the input is correct
-1043    if qc not in ['dd', 'ud', 'du', 'uu']:
-1044        raise Exception("Unknown quark conbination!")
-1045
-1046    if corr not in ["gS", "gP", "gA", "gV", "gVt", "lA", "lV", "lVt", "lT", "lTt", "g1", "l1"]:
-1047        raise Exception("Unknown correlator!")
-1048
-1049    if "files" in kwargs:
-1050        known_files = kwargs.get("files")
-1051    else:
-1052        known_files = []
-1053    files = _find_files(path, prefix, "ms5_xsf_" + qc, "dat", known_files=known_files)
-1054
-1055    if "names" in kwargs:
-1056        names = kwargs.get("names")
-1057    else:
-1058        for f in files:
-1059            if not sep == "":
-1060                se = f.split(".")[0]
-1061                for s in f.split(".")[1:-2]:
-1062                    se += "." + s
-1063                names.append(se.split(sep)[0] + "|r" + se.split(sep)[1])
-1064            else:
-1065                names.append(prefix)
-1066
-1067    names = sorted(names)
-1068    files = sorted(files)
-1069
-1070    cnfgs = []
-1071    realsamples = []
-1072    imagsamples = []
-1073    repnum = 0
-1074    for file in files:
-1075        with open(path + "/" + file, "rb") as fp:
-1076
-1077            t = fp.read(8)
-1078            kappa = struct.unpack('d', t)[0]
-1079            t = fp.read(8)
-1080            csw = struct.unpack('d', t)[0]
-1081            t = fp.read(8)
-1082            dF = struct.unpack('d', t)[0]
-1083            t = fp.read(8)
-1084            zF = struct.unpack('d', t)[0]
-1085
-1086            t = fp.read(4)
-1087            tmax = struct.unpack('i', t)[0]
-1088            t = fp.read(4)
-1089            bnd = struct.unpack('i', t)[0]
+1038        if "names" not in kwargs:
+1039            try:
+1040                idx = truncated_file.index('r')
+1041            except Exception:
+1042                if "names" not in kwargs:
+1043                    raise Exception("Automatic recognition of replicum failed, please enter the key word 'names'.")
+1044            ens_name = truncated_file[:idx]
+1045            rep_names.append(ens_name + '|' + truncated_file[idx:].split(".")[0])
+1046        else:
+1047            names = kwargs.get("names")
+1048            rep_names = names
+1049
+1050        deltas.append(Q_top)
+1051
+1052    rep_names = sort_names(rep_names)
+1053
+1054    idl = [range(int(configlist[rep][r_start_index[rep]]), int(configlist[rep][r_stop_index[rep]]) + 1, 1) for rep in range(len(deltas))]
+1055    deltas = [deltas[nrep][r_start_index[nrep]:r_stop_index[nrep] + 1] for nrep in range(len(deltas))]
+1056    result = Obs(deltas, rep_names, idl=idl)
+1057    result.tag = {"T": tmax - 1,
+1058                  "L": L}
+1059    return result
+1060
+1061
+1062def qtop_projection(qtop, target=0):
+1063    """Returns the projection to the topological charge sector defined by target.
+1064
+1065    Parameters
+1066    ----------
+1067    path : Obs
+1068        Topological charge.
+1069    target : int
+1070        Specifies the topological sector to be reweighted to (default 0)
+1071
+1072    Returns
+1073    -------
+1074    reto : Obs
+1075        projection to the topological charge sector defined by target
+1076    """
+1077    if qtop.reweighted:
+1078        raise Exception('You can not use a reweighted observable for reweighting!')
+1079
+1080    proj_qtop = []
+1081    for n in qtop.deltas:
+1082        proj_qtop.append(np.array([1 if round(qtop.r_values[n] + q) == target else 0 for q in qtop.deltas[n]]))
+1083
+1084    reto = Obs(proj_qtop, qtop.names, idl=[qtop.idl[name] for name in qtop.names])
+1085    return reto
+1086
+1087
+1088def read_qtop_sector(path, prefix, c, target=0, **kwargs):
+1089    """Constructs reweighting factors to a specified topological sector.
 1090
-1091            placesBI = ["gS", "gP",
-1092                        "gA", "gV",
-1093                        "gVt", "lA",
-1094                        "lV", "lVt",
-1095                        "lT", "lTt"]
-1096            placesBB = ["g1", "l1"]
-1097
-1098            # the chunks have the following structure:
-1099            # confignumber, 10x timedependent complex correlators as doubles, 2x timeindependent complex correlators as doubles
-1100
-1101            chunksize = 4 + (8 * 2 * tmax * 10) + (8 * 2 * 2)
-1102            packstr = '=i' + ('d' * 2 * tmax * 10) + ('d' * 2 * 2)
-1103            cnfgs.append([])
-1104            realsamples.append([])
-1105            imagsamples.append([])
-1106            for t in range(tmax):
-1107                realsamples[repnum].append([])
-1108                imagsamples[repnum].append([])
-1109
-1110            while True:
-1111                cnfgt = fp.read(chunksize)
-1112                if not cnfgt:
-1113                    break
-1114                asascii = struct.unpack(packstr, cnfgt)
-1115                cnfg = asascii[0]
-1116                cnfgs[repnum].append(cnfg)
-1117
-1118                if corr not in placesBB:
-1119                    tmpcorr = asascii[1 + 2 * tmax * placesBI.index(corr):1 + 2 * tmax * placesBI.index(corr) + 2 * tmax]
-1120                else:
-1121                    tmpcorr = asascii[1 + 2 * tmax * len(placesBI) + 2 * placesBB.index(corr):1 + 2 * tmax * len(placesBI) + 2 * placesBB.index(corr) + 2]
-1122
-1123                corrres = [[], []]
-1124                for i in range(len(tmpcorr)):
-1125                    corrres[i % 2].append(tmpcorr[i])
-1126                for t in range(int(len(tmpcorr) / 2)):
-1127                    realsamples[repnum][t].append(corrres[0][t])
-1128                for t in range(int(len(tmpcorr) / 2)):
-1129                    imagsamples[repnum][t].append(corrres[1][t])
-1130        repnum += 1
-1131
-1132    s = "Read correlator " + corr + " from " + str(repnum) + " replika with " + str(len(realsamples[0][t]))
-1133    for rep in range(1, repnum):
-1134        s += ", " + str(len(realsamples[rep][t]))
-1135    s += " samples"
-1136    print(s)
-1137    print("Asserted run parameters:\n T:", tmax, "kappa:", kappa, "csw:", csw, "dF:", dF, "zF:", zF, "bnd:", bnd)
-1138
-1139    # we have the data now... but we need to re format the whole thing and put it into Corr objects.
-1140
-1141    compObs = []
+1091    Parameters
+1092    ----------
+1093    path : str
+1094        path of the measurement files
+1095    prefix : str
+1096        prefix of the measurement files, e.g. <prefix>_id0_r0.ms.dat
+1097    c : double
+1098        Smearing radius in units of the lattice extent, c = sqrt(8 t0) / L
+1099    target : int
+1100        Specifies the topological sector to be reweighted to (default 0)
+1101    dtr_cnfg : int
+1102        (optional) parameter that specifies the number of trajectories
+1103        between two configs.
+1104        if it is not set, the distance between two measurements
+1105        in the file is assumed to be the distance between two configurations.
+1106    steps : int
+1107        (optional) Distance between two configurations in units of trajectories /
+1108         cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
+1109    version : str
+1110        version string of the openQCD (sfqcd) version used to create
+1111        the ensemble. Default is 2.0. May also be set to sfqcd.
+1112    L : int
+1113        spatial length of the lattice in L/a.
+1114        HAS to be set if version != sfqcd, since openQCD does not provide
+1115        this in the header
+1116    r_start : list
+1117        offset of the first ensemble, making it easier to match
+1118        later on with other Obs
+1119    r_stop : list
+1120        last configurations that need to be read (per replicum)
+1121    files : list
+1122        specify the exact files that need to be read
+1123        from path, practical if e.g. only one replicum is needed
+1124    names : list
+1125        Alternative labeling for replicas/ensembles.
+1126        Has to have the appropriate length
+1127    Zeuthen_flow : bool
+1128        (optional) If True, the Zeuthen flow is used for Qtop. Only possible
+1129        for version=='sfqcd' If False, the Wilson flow is used.
+1130
+1131    Returns
+1132    -------
+1133    reto : Obs
+1134        projection to the topological charge sector defined by target
+1135    """
+1136
+1137    if not isinstance(target, int):
+1138        raise Exception("'target' has to be an integer.")
+1139
+1140    kwargs['integer_charge'] = True
+1141    qtop = read_qtop(path, prefix, c, **kwargs)
 1142
-1143    for t in range(int(len(tmpcorr) / 2)):
-1144        compObs.append(CObs(Obs([realsamples[rep][t] for rep in range(repnum)], names=names, idl=cnfgs),
-1145                            Obs([imagsamples[rep][t] for rep in range(repnum)], names=names, idl=cnfgs)))
-1146
-1147    if len(compObs) == 1:
-1148        return compObs[0]
-1149    else:
-1150        return Corr(compObs)
+1143    return qtop_projection(qtop, target=target)
+1144
+1145
+1146def read_ms5_xsf(path, prefix, qc, corr, sep="r", **kwargs):
+1147    """
+1148    Read data from files in the specified directory with the specified prefix and quark combination extension, and return a `Corr` object containing the data.
+1149
+1150    Parameters
+1151    ----------
+1152    path : str
+1153        The directory to search for the files in.
+1154    prefix : str
+1155        The prefix to match the files against.
+1156    qc : str
+1157        The quark combination extension to match the files against.
+1158    corr : str
+1159        The correlator to extract data for.
+1160    sep : str, optional
+1161        The separator to use when parsing the replika names.
+1162    **kwargs
+1163        Additional keyword arguments. The following keyword arguments are recognized:
+1164
+1165        - names (List[str]): A list of names to use for the replicas.
+1166
+1167    Returns
+1168    -------
+1169    Corr
+1170        A complex valued `Corr` object containing the data read from the files. In case of boudary to bulk correlators.
+1171    or
+1172    CObs
+1173        A complex valued `CObs` object containing the data read from the files. In case of boudary to boundary correlators.
+1174
+1175
+1176    Raises
+1177    ------
+1178    FileNotFoundError
+1179        If no files matching the specified prefix and quark combination extension are found in the specified directory.
+1180    IOError
+1181        If there is an error reading a file.
+1182    struct.error
+1183        If there is an error unpacking binary data.
+1184    """
+1185
+1186    # found = []
+1187    files = []
+1188    names = []
+1189
+1190    # test if the input is correct
+1191    if qc not in ['dd', 'ud', 'du', 'uu']:
+1192        raise Exception("Unknown quark conbination!")
+1193
+1194    if corr not in ["gS", "gP", "gA", "gV", "gVt", "lA", "lV", "lVt", "lT", "lTt", "g1", "l1"]:
+1195        raise Exception("Unknown correlator!")
+1196
+1197    if "files" in kwargs:
+1198        known_files = kwargs.get("files")
+1199    else:
+1200        known_files = []
+1201    files = _find_files(path, prefix, "ms5_xsf_" + qc, "dat", known_files=known_files)
+1202
+1203    if "names" in kwargs:
+1204        names = kwargs.get("names")
+1205    else:
+1206        for f in files:
+1207            if not sep == "":
+1208                se = f.split(".")[0]
+1209                for s in f.split(".")[1:-2]:
+1210                    se += "." + s
+1211                names.append(se.split(sep)[0] + "|r" + se.split(sep)[1])
+1212            else:
+1213                names.append(prefix)
+1214
+1215    names = sorted(names)
+1216    files = sorted(files)
+1217
+1218    cnfgs = []
+1219    realsamples = []
+1220    imagsamples = []
+1221    repnum = 0
+1222    for file in files:
+1223        with open(path + "/" + file, "rb") as fp:
+1224
+1225            t = fp.read(8)
+1226            kappa = struct.unpack('d', t)[0]
+1227            t = fp.read(8)
+1228            csw = struct.unpack('d', t)[0]
+1229            t = fp.read(8)
+1230            dF = struct.unpack('d', t)[0]
+1231            t = fp.read(8)
+1232            zF = struct.unpack('d', t)[0]
+1233
+1234            t = fp.read(4)
+1235            tmax = struct.unpack('i', t)[0]
+1236            t = fp.read(4)
+1237            bnd = struct.unpack('i', t)[0]
+1238
+1239            placesBI = ["gS", "gP",
+1240                        "gA", "gV",
+1241                        "gVt", "lA",
+1242                        "lV", "lVt",
+1243                        "lT", "lTt"]
+1244            placesBB = ["g1", "l1"]
+1245
+1246            # the chunks have the following structure:
+1247            # confignumber, 10x timedependent complex correlators as doubles, 2x timeindependent complex correlators as doubles
+1248
+1249            chunksize = 4 + (8 * 2 * tmax * 10) + (8 * 2 * 2)
+1250            packstr = '=i' + ('d' * 2 * tmax * 10) + ('d' * 2 * 2)
+1251            cnfgs.append([])
+1252            realsamples.append([])
+1253            imagsamples.append([])
+1254            for t in range(tmax):
+1255                realsamples[repnum].append([])
+1256                imagsamples[repnum].append([])
+1257
+1258            while True:
+1259                cnfgt = fp.read(chunksize)
+1260                if not cnfgt:
+1261                    break
+1262                asascii = struct.unpack(packstr, cnfgt)
+1263                cnfg = asascii[0]
+1264                cnfgs[repnum].append(cnfg)
+1265
+1266                if corr not in placesBB:
+1267                    tmpcorr = asascii[1 + 2 * tmax * placesBI.index(corr):1 + 2 * tmax * placesBI.index(corr) + 2 * tmax]
+1268                else:
+1269                    tmpcorr = asascii[1 + 2 * tmax * len(placesBI) + 2 * placesBB.index(corr):1 + 2 * tmax * len(placesBI) + 2 * placesBB.index(corr) + 2]
+1270
+1271                corrres = [[], []]
+1272                for i in range(len(tmpcorr)):
+1273                    corrres[i % 2].append(tmpcorr[i])
+1274                for t in range(int(len(tmpcorr) / 2)):
+1275                    realsamples[repnum][t].append(corrres[0][t])
+1276                for t in range(int(len(tmpcorr) / 2)):
+1277                    imagsamples[repnum][t].append(corrres[1][t])
+1278        repnum += 1
+1279
+1280    s = "Read correlator " + corr + " from " + str(repnum) + " replika with " + str(len(realsamples[0][t]))
+1281    for rep in range(1, repnum):
+1282        s += ", " + str(len(realsamples[rep][t]))
+1283    s += " samples"
+1284    print(s)
+1285    print("Asserted run parameters:\n T:", tmax, "kappa:", kappa, "csw:", csw, "dF:", dF, "zF:", zF, "bnd:", bnd)
+1286
+1287    # we have the data now... but we need to re format the whole thing and put it into Corr objects.
+1288
+1289    compObs = []
+1290
+1291    for t in range(int(len(tmpcorr) / 2)):
+1292        compObs.append(CObs(Obs([realsamples[rep][t] for rep in range(repnum)], names=names, idl=cnfgs),
+1293                            Obs([imagsamples[rep][t] for rep in range(repnum)], names=names, idl=cnfgs)))
+1294
+1295    if len(compObs) == 1:
+1296        return compObs[0]
+1297    else:
+1298        return Corr(compObs)
    @@ -1526,218 +1677,91 @@ Reweighting factors read
    def - extract_t0( path, prefix, dtr_read, xmin, spatial_extent, fit_range=5, postfix='ms', **kwargs): + extract_t0( path, prefix, dtr_read, xmin, spatial_extent, fit_range=5, postfix='ms', c=0.3, **kwargs):
    - 
    233def extract_t0(path, prefix, dtr_read, xmin, spatial_extent, fit_range=5, postfix='ms', **kwargs):
-234    """Extract t0 from given .ms.dat files. Returns t0 as Obs.
-235
-236    It is assumed that all boundary effects have
-237    sufficiently decayed at x0=xmin.
-238    The data around the zero crossing of t^2<E> - 0.3
-239    is fitted with a linear function
-240    from which the exact root is extracted.
-241
-242    It is assumed that one measurement is performed for each config.
-243    If this is not the case, the resulting idl, as well as the handling
-244    of r_start, r_stop and r_step is wrong and the user has to correct
-245    this in the resulting observable.
-246
-247    Parameters
-248    ----------
-249    path : str
-250        Path to .ms.dat files
-251    prefix : str
-252        Ensemble prefix
-253    dtr_read : int
-254        Determines how many trajectories should be skipped
-255        when reading the ms.dat files.
-256        Corresponds to dtr_cnfg / dtr_ms in the openQCD input file.
-257    xmin : int
-258        First timeslice where the boundary
-259        effects have sufficiently decayed.
-260    spatial_extent : int
-261        spatial extent of the lattice, required for normalization.
-262    fit_range : int
-263        Number of data points left and right of the zero
-264        crossing to be included in the linear fit. (Default: 5)
-265    postfix : str
-266        Postfix of measurement file (Default: ms)
-267    r_start : list
-268        list which contains the first config to be read for each replicum.
-269    r_stop : list
-270        list which contains the last config to be read for each replicum.
-271    r_step : int
-272        integer that defines a fixed step size between two measurements (in units of configs)
-273        If not given, r_step=1 is assumed.
-274    plaquette : bool
-275        If true extract the plaquette estimate of t0 instead.
-276    names : list
-277        list of names that is assigned to the data according according
-278        to the order in the file list. Use careful, if you do not provide file names!
-279    files : list
-280        list which contains the filenames to be read. No automatic detection of
-281        files performed if given.
-282    plot_fit : bool
-283        If true, the fit for the extraction of t0 is shown together with the data.
-284    assume_thermalization : bool
-285        If True: If the first record divided by the distance between two measurements is larger than
-286        1, it is assumed that this is due to thermalization and the first measurement belongs
-287        to the first config (default).
-288        If False: The config numbers are assumed to be traj_number // difference
-289
-290    Returns
-291    -------
-292    t0 : Obs
-293        Extracted t0
-294    """
-295
-296    if 'files' in kwargs:
-297        known_files = kwargs.get('files')
-298    else:
-299        known_files = []
-300
-301    ls = _find_files(path, prefix, postfix, 'dat', known_files=known_files)
-302
-303    replica = len(ls)
-304
-305    if 'r_start' in kwargs:
-306        r_start = kwargs.get('r_start')
-307        if len(r_start) != replica:
-308            raise Exception('r_start does not match number of replicas')
-309        r_start = [o if o else None for o in r_start]
-310    else:
-311        r_start = [None] * replica
-312
-313    if 'r_stop' in kwargs:
-314        r_stop = kwargs.get('r_stop')
-315        if len(r_stop) != replica:
-316            raise Exception('r_stop does not match number of replicas')
-317    else:
-318        r_stop = [None] * replica
-319
-320    if 'r_step' in kwargs:
-321        r_step = kwargs.get('r_step')
-322    else:
-323        r_step = 1
-324
-325    print('Extract t0 from', prefix, ',', replica, 'replica')
-326
-327    if 'names' in kwargs:
-328        rep_names = kwargs.get('names')
-329    else:
-330        rep_names = []
-331        for entry in ls:
-332            truncated_entry = entry.split('.')[0]
-333            idx = truncated_entry.index('r')
-334            rep_names.append(truncated_entry[:idx] + '|' + truncated_entry[idx:])
-335
-336    Ysum = []
-337
-338    configlist = []
-339    r_start_index = []
-340    r_stop_index = []
-341
-342    for rep in range(replica):
-343
-344        with open(path + '/' + ls[rep], 'rb') as fp:
-345            t = fp.read(12)
-346            header = struct.unpack('iii', t)
-347            if rep == 0:
-348                dn = header[0]
-349                nn = header[1]
-350                tmax = header[2]
-351            elif dn != header[0] or nn != header[1] or tmax != header[2]:
-352                raise Exception('Replica parameters do not match.')
-353
-354            t = fp.read(8)
-355            if rep == 0:
-356                eps = struct.unpack('d', t)[0]
-357                print('Step size:', eps, ', Maximal t value:', dn * (nn) * eps)
-358            elif eps != struct.unpack('d', t)[0]:
-359                raise Exception('Values for eps do not match among replica.')
-360
-361            Ysl = []
-362
-363            configlist.append([])
-364            while True:
-365                t = fp.read(4)
-366                if (len(t) < 4):
-367                    break
-368                nc = struct.unpack('i', t)[0]
-369                configlist[-1].append(nc)
-370
-371                t = fp.read(8 * tmax * (nn + 1))
-372                if kwargs.get('plaquette'):
-373                    if nc % dtr_read == 0:
-374                        Ysl.append(struct.unpack('d' * tmax * (nn + 1), t))
-375                t = fp.read(8 * tmax * (nn + 1))
-376                if not kwargs.get('plaquette'):
-377                    if nc % dtr_read == 0:
-378                        Ysl.append(struct.unpack('d' * tmax * (nn + 1), t))
-379                t = fp.read(8 * tmax * (nn + 1))
-380
-381        Ysum.append([])
-382        for i, item in enumerate(Ysl):
-383            Ysum[-1].append([np.mean(item[current + xmin:
-384                             current + tmax - xmin])
-385                            for current in range(0, len(item), tmax)])
-386
-387        diffmeas = configlist[-1][-1] - configlist[-1][-2]
-388        configlist[-1] = [item // diffmeas for item in configlist[-1]]
-389        if kwargs.get('assume_thermalization', True) and configlist[-1][0] > 1:
-390            warnings.warn('Assume thermalization and that the first measurement belongs to the first config.')
-391            offset = configlist[-1][0] - 1
-392            configlist[-1] = [item - offset for item in configlist[-1]]
-393
-394        if r_start[rep] is None:
-395            r_start_index.append(0)
-396        else:
-397            try:
-398                r_start_index.append(configlist[-1].index(r_start[rep]))
-399            except ValueError:
-400                raise Exception('Config %d not in file with range [%d, %d]' % (
-401                    r_start[rep], configlist[-1][0], configlist[-1][-1])) from None
-402
-403        if r_stop[rep] is None:
-404            r_stop_index.append(len(configlist[-1]) - 1)
-405        else:
-406            try:
-407                r_stop_index.append(configlist[-1].index(r_stop[rep]))
-408            except ValueError:
-409                raise Exception('Config %d not in file with range [%d, %d]' % (
-410                    r_stop[rep], configlist[-1][0], configlist[-1][-1])) from None
-411
-412    if np.any([len(np.unique(np.diff(cl))) != 1 for cl in configlist]):
-413        raise Exception('Irregular spaced data in input file!', [len(np.unique(np.diff(cl))) for cl in configlist])
-414    stepsizes = [list(np.unique(np.diff(cl)))[0] for cl in configlist]
-415    if np.any([step != 1 for step in stepsizes]):
-416        warnings.warn('Stepsize between configurations is greater than one!' + str(stepsizes), RuntimeWarning)
-417
-418    idl = [range(configlist[rep][r_start_index[rep]], configlist[rep][r_stop_index[rep]] + 1, r_step) for rep in range(replica)]
-419    t2E_dict = {}
-420    for n in range(nn + 1):
-421        samples = []
-422        for nrep, rep in enumerate(Ysum):
-423            samples.append([])
-424            for cnfg in rep:
-425                samples[-1].append(cnfg[n])
-426            samples[-1] = samples[-1][r_start_index[nrep]:r_stop_index[nrep] + 1][::r_step]
-427        new_obs = Obs(samples, rep_names, idl=idl)
-428        t2E_dict[n * dn * eps] = (n * dn * eps) ** 2 * new_obs / (spatial_extent ** 3) - 0.3
-429
-430    return fit_t0(t2E_dict, fit_range, plot_fit=kwargs.get('plot_fit'))
+            
    426def extract_t0(path, prefix, dtr_read, xmin, spatial_extent, fit_range=5, postfix='ms', c=0.3, **kwargs):
+427    """Extract t0/a^2 from given .ms.dat files. Returns t0 as Obs.
+428
+429    It is assumed that all boundary effects have
+430    sufficiently decayed at x0=xmin.
+431    The data around the zero crossing of t^2<E> - c (where c=0.3 by default)
+432    is fitted with a linear function
+433    from which the exact root is extracted.
+434
+435    It is assumed that one measurement is performed for each config.
+436    If this is not the case, the resulting idl, as well as the handling
+437    of r_start, r_stop and r_step is wrong and the user has to correct
+438    this in the resulting observable.
+439
+440    Parameters
+441    ----------
+442    path : str
+443        Path to .ms.dat files
+444    prefix : str
+445        Ensemble prefix
+446    dtr_read : int
+447        Determines how many trajectories should be skipped
+448        when reading the ms.dat files.
+449        Corresponds to dtr_cnfg / dtr_ms in the openQCD input file.
+450    xmin : int
+451        First timeslice where the boundary
+452        effects have sufficiently decayed.
+453    spatial_extent : int
+454        spatial extent of the lattice, required for normalization.
+455    fit_range : int
+456        Number of data points left and right of the zero
+457        crossing to be included in the linear fit. (Default: 5)
+458    postfix : str
+459        Postfix of measurement file (Default: ms)
+460    c: float
+461        Constant that defines the flow scale. Default 0.3 for t_0, choose 2./3 for t_1.
+462    r_start : list
+463        list which contains the first config to be read for each replicum.
+464    r_stop : list
+465        list which contains the last config to be read for each replicum.
+466    r_step : int
+467        integer that defines a fixed step size between two measurements (in units of configs)
+468        If not given, r_step=1 is assumed.
+469    plaquette : bool
+470        If true extract the plaquette estimate of t0 instead.
+471    names : list
+472        list of names that is assigned to the data according according
+473        to the order in the file list. Use careful, if you do not provide file names!
+474    files : list
+475        list which contains the filenames to be read. No automatic detection of
+476        files performed if given.
+477    plot_fit : bool
+478        If true, the fit for the extraction of t0 is shown together with the data.
+479    assume_thermalization : bool
+480        If True: If the first record divided by the distance between two measurements is larger than
+481        1, it is assumed that this is due to thermalization and the first measurement belongs
+482        to the first config (default).
+483        If False: The config numbers are assumed to be traj_number // difference
+484
+485    Returns
+486    -------
+487    t0 : Obs
+488        Extracted t0
+489    """
+490
+491    E_dict = _extract_flowed_energy_density(path, prefix, dtr_read, xmin, spatial_extent, postfix, **kwargs)
+492    t2E_dict = {}
+493    for t in sorted(E_dict.keys()):
+494        t2E_dict[t] = t ** 2 * E_dict[t] - c
+495
+496    return fit_t0(t2E_dict, fit_range, plot_fit=kwargs.get('plot_fit'))
 
    
 
 
-            
    Extract t0 from given .ms.dat files. Returns t0 as Obs.
    
+            
    Extract t0/a^2 from given .ms.dat files. Returns t0 as Obs.
    
 
 
    It is assumed that all boundary effects have
 sufficiently decayed at x0=xmin.
-The data around the zero crossing of t^2 - 0.3
+The data around the zero crossing of t^2 - c (where c=0.3 by default)
 is fitted with a linear function
 from which the exact root is extracted.
    
 
@@ -1767,6 +1791,8 @@ Number of data points left and right of the zero
 crossing to be included in the linear fit. (Default: 5)
 
  • postfix (str):
 Postfix of measurement file (Default: ms)
    • 
+
  • c (float):
+Constant that defines the flow scale. Default 0.3 for t_0, choose 2./3 for t_1.
    • 
 
  • r_start (list):
 list which contains the first config to be read for each replicum.
    • 
 
  • r_stop (list):
@@ -1800,6 +1826,170 @@ Extracted t0
    • 
 
    
 
 
+                
+                
    
+                            
+
    
+            
+        def
+        extract_w0(	path,	prefix,	dtr_read,	xmin,	spatial_extent,	fit_range=5,	postfix='ms',	c=0.3,	**kwargs):
+
+                
+
+    
    
+    
+            
    499def extract_w0(path, prefix, dtr_read, xmin, spatial_extent, fit_range=5, postfix='ms', c=0.3, **kwargs):
+500    """Extract w0/a from given .ms.dat files. Returns w0 as Obs.
+501
+502    It is assumed that all boundary effects have
+503    sufficiently decayed at x0=xmin.
+504    The data around the zero crossing of t d(t^2<E>)/dt -  (where c=0.3 by default)
+505    is fitted with a linear function
+506    from which the exact root is extracted.
+507
+508    It is assumed that one measurement is performed for each config.
+509    If this is not the case, the resulting idl, as well as the handling
+510    of r_start, r_stop and r_step is wrong and the user has to correct
+511    this in the resulting observable.
+512
+513    Parameters
+514    ----------
+515    path : str
+516        Path to .ms.dat files
+517    prefix : str
+518        Ensemble prefix
+519    dtr_read : int
+520        Determines how many trajectories should be skipped
+521        when reading the ms.dat files.
+522        Corresponds to dtr_cnfg / dtr_ms in the openQCD input file.
+523    xmin : int
+524        First timeslice where the boundary
+525        effects have sufficiently decayed.
+526    spatial_extent : int
+527        spatial extent of the lattice, required for normalization.
+528    fit_range : int
+529        Number of data points left and right of the zero
+530        crossing to be included in the linear fit. (Default: 5)
+531    postfix : str
+532        Postfix of measurement file (Default: ms)
+533    c: float
+534        Constant that defines the flow scale. Default 0.3 for w_0, choose 2./3 for w_1.
+535    r_start : list
+536        list which contains the first config to be read for each replicum.
+537    r_stop : list
+538        list which contains the last config to be read for each replicum.
+539    r_step : int
+540        integer that defines a fixed step size between two measurements (in units of configs)
+541        If not given, r_step=1 is assumed.
+542    plaquette : bool
+543        If true extract the plaquette estimate of w0 instead.
+544    names : list
+545        list of names that is assigned to the data according according
+546        to the order in the file list. Use careful, if you do not provide file names!
+547    files : list
+548        list which contains the filenames to be read. No automatic detection of
+549        files performed if given.
+550    plot_fit : bool
+551        If true, the fit for the extraction of w0 is shown together with the data.
+552    assume_thermalization : bool
+553        If True: If the first record divided by the distance between two measurements is larger than
+554        1, it is assumed that this is due to thermalization and the first measurement belongs
+555        to the first config (default).
+556        If False: The config numbers are assumed to be traj_number // difference
+557
+558    Returns
+559    -------
+560    w0 : Obs
+561        Extracted w0
+562    """
+563
+564    E_dict = _extract_flowed_energy_density(path, prefix, dtr_read, xmin, spatial_extent, postfix, **kwargs)
+565
+566    ftimes = sorted(E_dict.keys())
+567
+568    t2E_dict = {}
+569    for t in ftimes:
+570        t2E_dict[t] = t ** 2 * E_dict[t]
+571
+572    tdtt2E_dict = {}
+573    tdtt2E_dict[ftimes[0]] = ftimes[0] * (t2E_dict[ftimes[1]] - t2E_dict[ftimes[0]]) / (ftimes[1] - ftimes[0]) - c
+574    for i in range(1, len(ftimes) - 1):
+575        tdtt2E_dict[ftimes[i]] = ftimes[i] * (t2E_dict[ftimes[i + 1]] - t2E_dict[ftimes[i - 1]]) / (ftimes[i + 1] - ftimes[i - 1]) - c
+576    tdtt2E_dict[ftimes[-1]] = ftimes[-1] * (t2E_dict[ftimes[-1]] - t2E_dict[ftimes[-2]]) / (ftimes[-1] - ftimes[-2]) - c
+577
+578    return np.sqrt(fit_t0(tdtt2E_dict, fit_range, plot_fit=kwargs.get('plot_fit'), observable='w0'))
+
    
+
+
+            
    Extract w0/a from given .ms.dat files. Returns w0 as Obs.
    
+
+
    It is assumed that all boundary effects have
+sufficiently decayed at x0=xmin.
+The data around the zero crossing of t d(t^2)/dt -  (where c=0.3 by default)
+is fitted with a linear function
+from which the exact root is extracted.
    
+
+
    It is assumed that one measurement is performed for each config.
+If this is not the case, the resulting idl, as well as the handling
+of r_start, r_stop and r_step is wrong and the user has to correct
+this in the resulting observable.
    
+
+
    Parameters
    
+
+
      
+
    • path (str):
+Path to .ms.dat files
      • 
+
    • prefix (str):
+Ensemble prefix
      • 
+
    • dtr_read (int):
+Determines how many trajectories should be skipped
+when reading the ms.dat files.
+Corresponds to dtr_cnfg / dtr_ms in the openQCD input file.
      • 
+
    • xmin (int):
+First timeslice where the boundary
+effects have sufficiently decayed.
      • 
+
    • spatial_extent (int):
+spatial extent of the lattice, required for normalization.
      • 
+
    • fit_range (int):
+Number of data points left and right of the zero
+crossing to be included in the linear fit. (Default: 5)
      • 
+
    • postfix (str):
+Postfix of measurement file (Default: ms)
      • 
+
    • c (float):
+Constant that defines the flow scale. Default 0.3 for w_0, choose 2./3 for w_1.
      • 
+
    • r_start (list):
+list which contains the first config to be read for each replicum.
      • 
+
    • r_stop (list):
+list which contains the last config to be read for each replicum.
      • 
+
    • r_step (int):
+integer that defines a fixed step size between two measurements (in units of configs)
+If not given, r_step=1 is assumed.
      • 
+
    • plaquette (bool):
+If true extract the plaquette estimate of w0 instead.
      • 
+
    • names (list):
+list of names that is assigned to the data according according
+to the order in the file list. Use careful, if you do not provide file names!
      • 
+
    • files (list):
+list which contains the filenames to be read. No automatic detection of
+files performed if given.
      • 
+
    • plot_fit (bool):
+If true, the fit for the extraction of w0 is shown together with the data.
      • 
+
    • assume_thermalization (bool):
+If True: If the first record divided by the distance between two measurements is larger than
+1, it is assumed that this is due to thermalization and the first measurement belongs
+to the first config (default).
+If False: The config numbers are assumed to be traj_number // difference
      • 
+
    
+
+
    Returns
    
+
+
      
+
    • w0 (Obs):
+Extracted w0
      • 
+
    
+
    
+
+
                 
    
                 
    
                             
@@ -1812,57 +2002,57 @@ Extracted t0
 
     
    
     
-            
    518def read_qtop(path, prefix, c, dtr_cnfg=1, version="openQCD", **kwargs):
-519    """Read the topologial charge based on openQCD gradient flow measurements.
-520
-521    Parameters
-522    ----------
-523    path : str
-524        path of the measurement files
-525    prefix : str
-526        prefix of the measurement files, e.g. <prefix>_id0_r0.ms.dat.
-527        Ignored if file names are passed explicitly via keyword files.
-528    c : double
-529        Smearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
-530    dtr_cnfg : int
-531        (optional) parameter that specifies the number of measurements
-532        between two configs.
-533        If it is not set, the distance between two measurements
-534        in the file is assumed to be the distance between two configurations.
-535    steps : int
-536        (optional) Distance between two configurations in units of trajectories /
-537         cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
-538    version : str
-539        Either openQCD or sfqcd, depending on the data.
-540    L : int
-541        spatial length of the lattice in L/a.
-542        HAS to be set if version != sfqcd, since openQCD does not provide
-543        this in the header
-544    r_start : list
-545        list which contains the first config to be read for each replicum.
-546    r_stop : list
-547        list which contains the last config to be read for each replicum.
-548    files : list
-549        specify the exact files that need to be read
-550        from path, practical if e.g. only one replicum is needed
-551    postfix : str
-552        postfix of the file to read, e.g. '.gfms.dat' for openQCD-files
-553    names : list
-554        Alternative labeling for replicas/ensembles.
-555        Has to have the appropriate length.
-556    Zeuthen_flow : bool
-557        (optional) If True, the Zeuthen flow is used for Qtop. Only possible
-558        for version=='sfqcd' If False, the Wilson flow is used.
-559    integer_charge : bool
-560        If True, the charge is rounded towards the nearest integer on each config.
-561
-562    Returns
-563    -------
-564    result : Obs
-565        Read topological charge
-566    """
-567
-568    return _read_flow_obs(path, prefix, c, dtr_cnfg=dtr_cnfg, version=version, obspos=0, **kwargs)
+            
    666def read_qtop(path, prefix, c, dtr_cnfg=1, version="openQCD", **kwargs):
+667    """Read the topologial charge based on openQCD gradient flow measurements.
+668
+669    Parameters
+670    ----------
+671    path : str
+672        path of the measurement files
+673    prefix : str
+674        prefix of the measurement files, e.g. <prefix>_id0_r0.ms.dat.
+675        Ignored if file names are passed explicitly via keyword files.
+676    c : double
+677        Smearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
+678    dtr_cnfg : int
+679        (optional) parameter that specifies the number of measurements
+680        between two configs.
+681        If it is not set, the distance between two measurements
+682        in the file is assumed to be the distance between two configurations.
+683    steps : int
+684        (optional) Distance between two configurations in units of trajectories /
+685         cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
+686    version : str
+687        Either openQCD or sfqcd, depending on the data.
+688    L : int
+689        spatial length of the lattice in L/a.
+690        HAS to be set if version != sfqcd, since openQCD does not provide
+691        this in the header
+692    r_start : list
+693        list which contains the first config to be read for each replicum.
+694    r_stop : list
+695        list which contains the last config to be read for each replicum.
+696    files : list
+697        specify the exact files that need to be read
+698        from path, practical if e.g. only one replicum is needed
+699    postfix : str
+700        postfix of the file to read, e.g. '.gfms.dat' for openQCD-files
+701    names : list
+702        Alternative labeling for replicas/ensembles.
+703        Has to have the appropriate length.
+704    Zeuthen_flow : bool
+705        (optional) If True, the Zeuthen flow is used for Qtop. Only possible
+706        for version=='sfqcd' If False, the Wilson flow is used.
+707    integer_charge : bool
+708        If True, the charge is rounded towards the nearest integer on each config.
+709
+710    Returns
+711    -------
+712    result : Obs
+713        Read topological charge
+714    """
+715
+716    return _read_flow_obs(path, prefix, c, dtr_cnfg=dtr_cnfg, version=version, obspos=0, **kwargs)
 
    
 
 
@@ -1932,76 +2122,76 @@ Read topological charge
 
     
    
     
-            
    571def read_gf_coupling(path, prefix, c, dtr_cnfg=1, Zeuthen_flow=True, **kwargs):
-572    """Read the gradient flow coupling based on sfqcd gradient flow measurements. See 1607.06423 for details.
-573
-574    Note: The current implementation only works for c=0.3 and T=L. The definition of the coupling in 1607.06423 requires projection to topological charge zero which is not done within this function but has to be performed in a separate step.
-575
-576    Parameters
-577    ----------
-578    path : str
-579        path of the measurement files
-580    prefix : str
-581        prefix of the measurement files, e.g. <prefix>_id0_r0.ms.dat.
-582        Ignored if file names are passed explicitly via keyword files.
-583    c : double
-584        Smearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
-585    dtr_cnfg : int
-586        (optional) parameter that specifies the number of measurements
-587        between two configs.
-588        If it is not set, the distance between two measurements
-589        in the file is assumed to be the distance between two configurations.
-590    steps : int
-591        (optional) Distance between two configurations in units of trajectories /
-592         cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
-593    r_start : list
-594        list which contains the first config to be read for each replicum.
-595    r_stop : list
-596        list which contains the last config to be read for each replicum.
-597    files : list
-598        specify the exact files that need to be read
-599        from path, practical if e.g. only one replicum is needed
-600    names : list
-601        Alternative labeling for replicas/ensembles.
-602        Has to have the appropriate length.
-603    postfix : str
-604        postfix of the file to read, e.g. '.gfms.dat' for openQCD-files
-605    Zeuthen_flow : bool
-606        (optional) If True, the Zeuthen flow is used for the coupling. If False, the Wilson flow is used.
-607    """
-608
-609    if c != 0.3:
-610        raise Exception("The required lattice norm is only implemented for c=0.3 at the moment.")
-611
-612    plaq = _read_flow_obs(path, prefix, c, dtr_cnfg=dtr_cnfg, version="sfqcd", obspos=6, sum_t=False, Zeuthen_flow=Zeuthen_flow, integer_charge=False, **kwargs)
-613    C2x1 = _read_flow_obs(path, prefix, c, dtr_cnfg=dtr_cnfg, version="sfqcd", obspos=7, sum_t=False, Zeuthen_flow=Zeuthen_flow, integer_charge=False, **kwargs)
-614    L = plaq.tag["L"]
-615    T = plaq.tag["T"]
-616
-617    if T != L:
-618        raise Exception("The required lattice norm is only implemented for T=L at the moment.")
-619
-620    if Zeuthen_flow is not True:
-621        raise Exception("The required lattice norm is only implemented for the Zeuthen flow at the moment.")
-622
-623    t = (c * L) ** 2 / 8
-624
-625    normdict = {4: 0.012341170468270,
-626                6: 0.010162691462430,
-627                8: 0.009031614807931,
-628                10: 0.008744966371393,
-629                12: 0.008650917856809,
-630                14: 8.611154391267955E-03,
-631                16: 0.008591758449508,
-632                20: 0.008575359627103,
-633                24: 0.008569387847540,
-634                28: 8.566803713382559E-03,
-635                32: 0.008565541650006,
-636                40: 8.564480684962046E-03,
-637                48: 8.564098025073460E-03,
-638                64: 8.563853943383087E-03}
-639
-640    return t * t * (5 / 3 * plaq - 1 / 12 * C2x1) / normdict[L]
+            
    719def read_gf_coupling(path, prefix, c, dtr_cnfg=1, Zeuthen_flow=True, **kwargs):
+720    """Read the gradient flow coupling based on sfqcd gradient flow measurements. See 1607.06423 for details.
+721
+722    Note: The current implementation only works for c=0.3 and T=L. The definition of the coupling in 1607.06423 requires projection to topological charge zero which is not done within this function but has to be performed in a separate step.
+723
+724    Parameters
+725    ----------
+726    path : str
+727        path of the measurement files
+728    prefix : str
+729        prefix of the measurement files, e.g. <prefix>_id0_r0.ms.dat.
+730        Ignored if file names are passed explicitly via keyword files.
+731    c : double
+732        Smearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
+733    dtr_cnfg : int
+734        (optional) parameter that specifies the number of measurements
+735        between two configs.
+736        If it is not set, the distance between two measurements
+737        in the file is assumed to be the distance between two configurations.
+738    steps : int
+739        (optional) Distance between two configurations in units of trajectories /
+740         cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
+741    r_start : list
+742        list which contains the first config to be read for each replicum.
+743    r_stop : list
+744        list which contains the last config to be read for each replicum.
+745    files : list
+746        specify the exact files that need to be read
+747        from path, practical if e.g. only one replicum is needed
+748    names : list
+749        Alternative labeling for replicas/ensembles.
+750        Has to have the appropriate length.
+751    postfix : str
+752        postfix of the file to read, e.g. '.gfms.dat' for openQCD-files
+753    Zeuthen_flow : bool
+754        (optional) If True, the Zeuthen flow is used for the coupling. If False, the Wilson flow is used.
+755    """
+756
+757    if c != 0.3:
+758        raise Exception("The required lattice norm is only implemented for c=0.3 at the moment.")
+759
+760    plaq = _read_flow_obs(path, prefix, c, dtr_cnfg=dtr_cnfg, version="sfqcd", obspos=6, sum_t=False, Zeuthen_flow=Zeuthen_flow, integer_charge=False, **kwargs)
+761    C2x1 = _read_flow_obs(path, prefix, c, dtr_cnfg=dtr_cnfg, version="sfqcd", obspos=7, sum_t=False, Zeuthen_flow=Zeuthen_flow, integer_charge=False, **kwargs)
+762    L = plaq.tag["L"]
+763    T = plaq.tag["T"]
+764
+765    if T != L:
+766        raise Exception("The required lattice norm is only implemented for T=L at the moment.")
+767
+768    if Zeuthen_flow is not True:
+769        raise Exception("The required lattice norm is only implemented for the Zeuthen flow at the moment.")
+770
+771    t = (c * L) ** 2 / 8
+772
+773    normdict = {4: 0.012341170468270,
+774                6: 0.010162691462430,
+775                8: 0.009031614807931,
+776                10: 0.008744966371393,
+777                12: 0.008650917856809,
+778                14: 8.611154391267955E-03,
+779                16: 0.008591758449508,
+780                20: 0.008575359627103,
+781                24: 0.008569387847540,
+782                28: 8.566803713382559E-03,
+783                32: 0.008565541650006,
+784                40: 8.564480684962046E-03,
+785                48: 8.564098025073460E-03,
+786                64: 8.563853943383087E-03}
+787
+788    return t * t * (5 / 3 * plaq - 1 / 12 * C2x1) / normdict[L]
 
    
 
 
@@ -2057,30 +2247,30 @@ postfix of the file to read, e.g. '.gfms.dat' for openQCD-files
 
     
    
     
-            
    915def qtop_projection(qtop, target=0):
-916    """Returns the projection to the topological charge sector defined by target.
-917
-918    Parameters
-919    ----------
-920    path : Obs
-921        Topological charge.
-922    target : int
-923        Specifies the topological sector to be reweighted to (default 0)
-924
-925    Returns
-926    -------
-927    reto : Obs
-928        projection to the topological charge sector defined by target
-929    """
-930    if qtop.reweighted:
-931        raise Exception('You can not use a reweighted observable for reweighting!')
-932
-933    proj_qtop = []
-934    for n in qtop.deltas:
-935        proj_qtop.append(np.array([1 if round(qtop.r_values[n] + q) == target else 0 for q in qtop.deltas[n]]))
-936
-937    reto = Obs(proj_qtop, qtop.names, idl=[qtop.idl[name] for name in qtop.names])
-938    return reto
+            
    1063def qtop_projection(qtop, target=0):
+1064    """Returns the projection to the topological charge sector defined by target.
+1065
+1066    Parameters
+1067    ----------
+1068    path : Obs
+1069        Topological charge.
+1070    target : int
+1071        Specifies the topological sector to be reweighted to (default 0)
+1072
+1073    Returns
+1074    -------
+1075    reto : Obs
+1076        projection to the topological charge sector defined by target
+1077    """
+1078    if qtop.reweighted:
+1079        raise Exception('You can not use a reweighted observable for reweighting!')
+1080
+1081    proj_qtop = []
+1082    for n in qtop.deltas:
+1083        proj_qtop.append(np.array([1 if round(qtop.r_values[n] + q) == target else 0 for q in qtop.deltas[n]]))
+1084
+1085    reto = Obs(proj_qtop, qtop.names, idl=[qtop.idl[name] for name in qtop.names])
+1086    return reto
 
    
 
 
@@ -2116,62 +2306,62 @@ projection to the topological charge sector defined by target
 
     
    
     
-            
    941def read_qtop_sector(path, prefix, c, target=0, **kwargs):
-942    """Constructs reweighting factors to a specified topological sector.
-943
-944    Parameters
-945    ----------
-946    path : str
-947        path of the measurement files
-948    prefix : str
-949        prefix of the measurement files, e.g. <prefix>_id0_r0.ms.dat
-950    c : double
-951        Smearing radius in units of the lattice extent, c = sqrt(8 t0) / L
-952    target : int
-953        Specifies the topological sector to be reweighted to (default 0)
-954    dtr_cnfg : int
-955        (optional) parameter that specifies the number of trajectories
-956        between two configs.
-957        if it is not set, the distance between two measurements
-958        in the file is assumed to be the distance between two configurations.
-959    steps : int
-960        (optional) Distance between two configurations in units of trajectories /
-961         cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
-962    version : str
-963        version string of the openQCD (sfqcd) version used to create
-964        the ensemble. Default is 2.0. May also be set to sfqcd.
-965    L : int
-966        spatial length of the lattice in L/a.
-967        HAS to be set if version != sfqcd, since openQCD does not provide
-968        this in the header
-969    r_start : list
-970        offset of the first ensemble, making it easier to match
-971        later on with other Obs
-972    r_stop : list
-973        last configurations that need to be read (per replicum)
-974    files : list
-975        specify the exact files that need to be read
-976        from path, practical if e.g. only one replicum is needed
-977    names : list
-978        Alternative labeling for replicas/ensembles.
-979        Has to have the appropriate length
-980    Zeuthen_flow : bool
-981        (optional) If True, the Zeuthen flow is used for Qtop. Only possible
-982        for version=='sfqcd' If False, the Wilson flow is used.
-983
-984    Returns
-985    -------
-986    reto : Obs
-987        projection to the topological charge sector defined by target
-988    """
-989
-990    if not isinstance(target, int):
-991        raise Exception("'target' has to be an integer.")
-992
-993    kwargs['integer_charge'] = True
-994    qtop = read_qtop(path, prefix, c, **kwargs)
-995
-996    return qtop_projection(qtop, target=target)
+            
    1089def read_qtop_sector(path, prefix, c, target=0, **kwargs):
+1090    """Constructs reweighting factors to a specified topological sector.
+1091
+1092    Parameters
+1093    ----------
+1094    path : str
+1095        path of the measurement files
+1096    prefix : str
+1097        prefix of the measurement files, e.g. <prefix>_id0_r0.ms.dat
+1098    c : double
+1099        Smearing radius in units of the lattice extent, c = sqrt(8 t0) / L
+1100    target : int
+1101        Specifies the topological sector to be reweighted to (default 0)
+1102    dtr_cnfg : int
+1103        (optional) parameter that specifies the number of trajectories
+1104        between two configs.
+1105        if it is not set, the distance between two measurements
+1106        in the file is assumed to be the distance between two configurations.
+1107    steps : int
+1108        (optional) Distance between two configurations in units of trajectories /
+1109         cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
+1110    version : str
+1111        version string of the openQCD (sfqcd) version used to create
+1112        the ensemble. Default is 2.0. May also be set to sfqcd.
+1113    L : int
+1114        spatial length of the lattice in L/a.
+1115        HAS to be set if version != sfqcd, since openQCD does not provide
+1116        this in the header
+1117    r_start : list
+1118        offset of the first ensemble, making it easier to match
+1119        later on with other Obs
+1120    r_stop : list
+1121        last configurations that need to be read (per replicum)
+1122    files : list
+1123        specify the exact files that need to be read
+1124        from path, practical if e.g. only one replicum is needed
+1125    names : list
+1126        Alternative labeling for replicas/ensembles.
+1127        Has to have the appropriate length
+1128    Zeuthen_flow : bool
+1129        (optional) If True, the Zeuthen flow is used for Qtop. Only possible
+1130        for version=='sfqcd' If False, the Wilson flow is used.
+1131
+1132    Returns
+1133    -------
+1134    reto : Obs
+1135        projection to the topological charge sector defined by target
+1136    """
+1137
+1138    if not isinstance(target, int):
+1139        raise Exception("'target' has to be an integer.")
+1140
+1141    kwargs['integer_charge'] = True
+1142    qtop = read_qtop(path, prefix, c, **kwargs)
+1143
+1144    return qtop_projection(qtop, target=target)
 
    
 
 
@@ -2240,159 +2430,159 @@ projection to the topological charge sector defined by target
 
     
    
     
-            
     999def read_ms5_xsf(path, prefix, qc, corr, sep="r", **kwargs):
-1000    """
-1001    Read data from files in the specified directory with the specified prefix and quark combination extension, and return a `Corr` object containing the data.
-1002
-1003    Parameters
-1004    ----------
-1005    path : str
-1006        The directory to search for the files in.
-1007    prefix : str
-1008        The prefix to match the files against.
-1009    qc : str
-1010        The quark combination extension to match the files against.
-1011    corr : str
-1012        The correlator to extract data for.
-1013    sep : str, optional
-1014        The separator to use when parsing the replika names.
-1015    **kwargs
-1016        Additional keyword arguments. The following keyword arguments are recognized:
-1017
-1018        - names (List[str]): A list of names to use for the replicas.
-1019
-1020    Returns
-1021    -------
-1022    Corr
-1023        A complex valued `Corr` object containing the data read from the files. In case of boudary to bulk correlators.
-1024    or
-1025    CObs
-1026        A complex valued `CObs` object containing the data read from the files. In case of boudary to boundary correlators.
-1027
-1028
-1029    Raises
-1030    ------
-1031    FileNotFoundError
-1032        If no files matching the specified prefix and quark combination extension are found in the specified directory.
-1033    IOError
-1034        If there is an error reading a file.
-1035    struct.error
-1036        If there is an error unpacking binary data.
-1037    """
-1038
-1039    # found = []
-1040    files = []
-1041    names = []
-1042
-1043    # test if the input is correct
-1044    if qc not in ['dd', 'ud', 'du', 'uu']:
-1045        raise Exception("Unknown quark conbination!")
-1046
-1047    if corr not in ["gS", "gP", "gA", "gV", "gVt", "lA", "lV", "lVt", "lT", "lTt", "g1", "l1"]:
-1048        raise Exception("Unknown correlator!")
-1049
-1050    if "files" in kwargs:
-1051        known_files = kwargs.get("files")
-1052    else:
-1053        known_files = []
-1054    files = _find_files(path, prefix, "ms5_xsf_" + qc, "dat", known_files=known_files)
-1055
-1056    if "names" in kwargs:
-1057        names = kwargs.get("names")
-1058    else:
-1059        for f in files:
-1060            if not sep == "":
-1061                se = f.split(".")[0]
-1062                for s in f.split(".")[1:-2]:
-1063                    se += "." + s
-1064                names.append(se.split(sep)[0] + "|r" + se.split(sep)[1])
-1065            else:
-1066                names.append(prefix)
-1067
-1068    names = sorted(names)
-1069    files = sorted(files)
-1070
-1071    cnfgs = []
-1072    realsamples = []
-1073    imagsamples = []
-1074    repnum = 0
-1075    for file in files:
-1076        with open(path + "/" + file, "rb") as fp:
-1077
-1078            t = fp.read(8)
-1079            kappa = struct.unpack('d', t)[0]
-1080            t = fp.read(8)
-1081            csw = struct.unpack('d', t)[0]
-1082            t = fp.read(8)
-1083            dF = struct.unpack('d', t)[0]
-1084            t = fp.read(8)
-1085            zF = struct.unpack('d', t)[0]
-1086
-1087            t = fp.read(4)
-1088            tmax = struct.unpack('i', t)[0]
-1089            t = fp.read(4)
-1090            bnd = struct.unpack('i', t)[0]
-1091
-1092            placesBI = ["gS", "gP",
-1093                        "gA", "gV",
-1094                        "gVt", "lA",
-1095                        "lV", "lVt",
-1096                        "lT", "lTt"]
-1097            placesBB = ["g1", "l1"]
-1098
-1099            # the chunks have the following structure:
-1100            # confignumber, 10x timedependent complex correlators as doubles, 2x timeindependent complex correlators as doubles
-1101
-1102            chunksize = 4 + (8 * 2 * tmax * 10) + (8 * 2 * 2)
-1103            packstr = '=i' + ('d' * 2 * tmax * 10) + ('d' * 2 * 2)
-1104            cnfgs.append([])
-1105            realsamples.append([])
-1106            imagsamples.append([])
-1107            for t in range(tmax):
-1108                realsamples[repnum].append([])
-1109                imagsamples[repnum].append([])
-1110
-1111            while True:
-1112                cnfgt = fp.read(chunksize)
-1113                if not cnfgt:
-1114                    break
-1115                asascii = struct.unpack(packstr, cnfgt)
-1116                cnfg = asascii[0]
-1117                cnfgs[repnum].append(cnfg)
-1118
-1119                if corr not in placesBB:
-1120                    tmpcorr = asascii[1 + 2 * tmax * placesBI.index(corr):1 + 2 * tmax * placesBI.index(corr) + 2 * tmax]
-1121                else:
-1122                    tmpcorr = asascii[1 + 2 * tmax * len(placesBI) + 2 * placesBB.index(corr):1 + 2 * tmax * len(placesBI) + 2 * placesBB.index(corr) + 2]
-1123
-1124                corrres = [[], []]
-1125                for i in range(len(tmpcorr)):
-1126                    corrres[i % 2].append(tmpcorr[i])
-1127                for t in range(int(len(tmpcorr) / 2)):
-1128                    realsamples[repnum][t].append(corrres[0][t])
-1129                for t in range(int(len(tmpcorr) / 2)):
-1130                    imagsamples[repnum][t].append(corrres[1][t])
-1131        repnum += 1
-1132
-1133    s = "Read correlator " + corr + " from " + str(repnum) + " replika with " + str(len(realsamples[0][t]))
-1134    for rep in range(1, repnum):
-1135        s += ", " + str(len(realsamples[rep][t]))
-1136    s += " samples"
-1137    print(s)
-1138    print("Asserted run parameters:\n T:", tmax, "kappa:", kappa, "csw:", csw, "dF:", dF, "zF:", zF, "bnd:", bnd)
-1139
-1140    # we have the data now... but we need to re format the whole thing and put it into Corr objects.
-1141
-1142    compObs = []
-1143
-1144    for t in range(int(len(tmpcorr) / 2)):
-1145        compObs.append(CObs(Obs([realsamples[rep][t] for rep in range(repnum)], names=names, idl=cnfgs),
-1146                            Obs([imagsamples[rep][t] for rep in range(repnum)], names=names, idl=cnfgs)))
-1147
-1148    if len(compObs) == 1:
-1149        return compObs[0]
-1150    else:
-1151        return Corr(compObs)
+            
    1147def read_ms5_xsf(path, prefix, qc, corr, sep="r", **kwargs):
+1148    """
+1149    Read data from files in the specified directory with the specified prefix and quark combination extension, and return a `Corr` object containing the data.
+1150
+1151    Parameters
+1152    ----------
+1153    path : str
+1154        The directory to search for the files in.
+1155    prefix : str
+1156        The prefix to match the files against.
+1157    qc : str
+1158        The quark combination extension to match the files against.
+1159    corr : str
+1160        The correlator to extract data for.
+1161    sep : str, optional
+1162        The separator to use when parsing the replika names.
+1163    **kwargs
+1164        Additional keyword arguments. The following keyword arguments are recognized:
+1165
+1166        - names (List[str]): A list of names to use for the replicas.
+1167
+1168    Returns
+1169    -------
+1170    Corr
+1171        A complex valued `Corr` object containing the data read from the files. In case of boudary to bulk correlators.
+1172    or
+1173    CObs
+1174        A complex valued `CObs` object containing the data read from the files. In case of boudary to boundary correlators.
+1175
+1176
+1177    Raises
+1178    ------
+1179    FileNotFoundError
+1180        If no files matching the specified prefix and quark combination extension are found in the specified directory.
+1181    IOError
+1182        If there is an error reading a file.
+1183    struct.error
+1184        If there is an error unpacking binary data.
+1185    """
+1186
+1187    # found = []
+1188    files = []
+1189    names = []
+1190
+1191    # test if the input is correct
+1192    if qc not in ['dd', 'ud', 'du', 'uu']:
+1193        raise Exception("Unknown quark conbination!")
+1194
+1195    if corr not in ["gS", "gP", "gA", "gV", "gVt", "lA", "lV", "lVt", "lT", "lTt", "g1", "l1"]:
+1196        raise Exception("Unknown correlator!")
+1197
+1198    if "files" in kwargs:
+1199        known_files = kwargs.get("files")
+1200    else:
+1201        known_files = []
+1202    files = _find_files(path, prefix, "ms5_xsf_" + qc, "dat", known_files=known_files)
+1203
+1204    if "names" in kwargs:
+1205        names = kwargs.get("names")
+1206    else:
+1207        for f in files:
+1208            if not sep == "":
+1209                se = f.split(".")[0]
+1210                for s in f.split(".")[1:-2]:
+1211                    se += "." + s
+1212                names.append(se.split(sep)[0] + "|r" + se.split(sep)[1])
+1213            else:
+1214                names.append(prefix)
+1215
+1216    names = sorted(names)
+1217    files = sorted(files)
+1218
+1219    cnfgs = []
+1220    realsamples = []
+1221    imagsamples = []
+1222    repnum = 0
+1223    for file in files:
+1224        with open(path + "/" + file, "rb") as fp:
+1225
+1226            t = fp.read(8)
+1227            kappa = struct.unpack('d', t)[0]
+1228            t = fp.read(8)
+1229            csw = struct.unpack('d', t)[0]
+1230            t = fp.read(8)
+1231            dF = struct.unpack('d', t)[0]
+1232            t = fp.read(8)
+1233            zF = struct.unpack('d', t)[0]
+1234
+1235            t = fp.read(4)
+1236            tmax = struct.unpack('i', t)[0]
+1237            t = fp.read(4)
+1238            bnd = struct.unpack('i', t)[0]
+1239
+1240            placesBI = ["gS", "gP",
+1241                        "gA", "gV",
+1242                        "gVt", "lA",
+1243                        "lV", "lVt",
+1244                        "lT", "lTt"]
+1245            placesBB = ["g1", "l1"]
+1246
+1247            # the chunks have the following structure:
+1248            # confignumber, 10x timedependent complex correlators as doubles, 2x timeindependent complex correlators as doubles
+1249
+1250            chunksize = 4 + (8 * 2 * tmax * 10) + (8 * 2 * 2)
+1251            packstr = '=i' + ('d' * 2 * tmax * 10) + ('d' * 2 * 2)
+1252            cnfgs.append([])
+1253            realsamples.append([])
+1254            imagsamples.append([])
+1255            for t in range(tmax):
+1256                realsamples[repnum].append([])
+1257                imagsamples[repnum].append([])
+1258
+1259            while True:
+1260                cnfgt = fp.read(chunksize)
+1261                if not cnfgt:
+1262                    break
+1263                asascii = struct.unpack(packstr, cnfgt)
+1264                cnfg = asascii[0]
+1265                cnfgs[repnum].append(cnfg)
+1266
+1267                if corr not in placesBB:
+1268                    tmpcorr = asascii[1 + 2 * tmax * placesBI.index(corr):1 + 2 * tmax * placesBI.index(corr) + 2 * tmax]
+1269                else:
+1270                    tmpcorr = asascii[1 + 2 * tmax * len(placesBI) + 2 * placesBB.index(corr):1 + 2 * tmax * len(placesBI) + 2 * placesBB.index(corr) + 2]
+1271
+1272                corrres = [[], []]
+1273                for i in range(len(tmpcorr)):
+1274                    corrres[i % 2].append(tmpcorr[i])
+1275                for t in range(int(len(tmpcorr) / 2)):
+1276                    realsamples[repnum][t].append(corrres[0][t])
+1277                for t in range(int(len(tmpcorr) / 2)):
+1278                    imagsamples[repnum][t].append(corrres[1][t])
+1279        repnum += 1
+1280
+1281    s = "Read correlator " + corr + " from " + str(repnum) + " replika with " + str(len(realsamples[0][t]))
+1282    for rep in range(1, repnum):
+1283        s += ", " + str(len(realsamples[rep][t]))
+1284    s += " samples"
+1285    print(s)
+1286    print("Asserted run parameters:\n T:", tmax, "kappa:", kappa, "csw:", csw, "dF:", dF, "zF:", zF, "bnd:", bnd)
+1287
+1288    # we have the data now... but we need to re format the whole thing and put it into Corr objects.
+1289
+1290    compObs = []
+1291
+1292    for t in range(int(len(tmpcorr) / 2)):
+1293        compObs.append(CObs(Obs([realsamples[rep][t] for rep in range(repnum)], names=names, idl=cnfgs),
+1294                            Obs([imagsamples[rep][t] for rep in range(repnum)], names=names, idl=cnfgs)))
+1295
+1296    if len(compObs) == 1:
+1297        return compObs[0]
+1298    else:
+1299        return Corr(compObs)
 
    
 
 
diff --git a/docs/search.js b/docs/search.js
index 6daa2304..571bb1e1 100644
--- a/docs/search.js
+++ b/docs/search.js
@@ -1,6 +1,6 @@
 window.pdocSearch = (function(){
 /** elasticlunr - http://weixsong.github.io * Copyright (C) 2017 Oliver Nightingale * Copyright (C) 2017 Wei Song * MIT Licensed */!function(){function e(e){if(null===e||"object"!=typeof e)return e;var t=e.constructor();for(var n in e)e.hasOwnProperty(n)&&(t[n]=e[n]);return t}var t=function(e){var n=new t.Index;return n.pipeline.add(t.trimmer,t.stopWordFilter,t.stemmer),e&&e.call(n,n),n};t.version="0.9.5",lunr=t,t.utils={},t.utils.warn=function(e){return function(t){e.console&&console.warn&&console.warn(t)}}(this),t.utils.toString=function(e){return void 0===e||null===e?"":e.toString()},t.EventEmitter=function(){this.events={}},t.EventEmitter.prototype.addListener=function(){var e=Array.prototype.slice.call(arguments),t=e.pop(),n=e;if("function"!=typeof t)throw new TypeError("last argument must be a function");n.forEach(function(e){this.hasHandler(e)||(this.events[e]=[]),this.events[e].push(t)},this)},t.EventEmitter.prototype.removeListener=function(e,t){if(this.hasHandler(e)){var n=this.events[e].indexOf(t);-1!==n&&(this.events[e].splice(n,1),0==this.events[e].length&&delete this.events[e])}},t.EventEmitter.prototype.emit=function(e){if(this.hasHandler(e)){var t=Array.prototype.slice.call(arguments,1);this.events[e].forEach(function(e){e.apply(void 0,t)},this)}},t.EventEmitter.prototype.hasHandler=function(e){return e in this.events},t.tokenizer=function(e){if(!arguments.length||null===e||void 0===e)return[];if(Array.isArray(e)){var n=e.filter(function(e){return null===e||void 0===e?!1:!0});n=n.map(function(e){return t.utils.toString(e).toLowerCase()});var i=[];return n.forEach(function(e){var n=e.split(t.tokenizer.seperator);i=i.concat(n)},this),i}return e.toString().trim().toLowerCase().split(t.tokenizer.seperator)},t.tokenizer.defaultSeperator=/[\s\-]+/,t.tokenizer.seperator=t.tokenizer.defaultSeperator,t.tokenizer.setSeperator=function(e){null!==e&&void 0!==e&&"object"==typeof e&&(t.tokenizer.seperator=e)},t.tokenizer.resetSeperator=function(){t.tokenizer.seperator=t.tokenizer.defaultSeperator},t.tokenizer.getSeperator=function(){return t.tokenizer.seperator},t.Pipeline=function(){this._queue=[]},t.Pipeline.registeredFunctions={},t.Pipeline.registerFunction=function(e,n){n in t.Pipeline.registeredFunctions&&t.utils.warn("Overwriting existing registered function: "+n),e.label=n,t.Pipeline.registeredFunctions[n]=e},t.Pipeline.getRegisteredFunction=function(e){return e in t.Pipeline.registeredFunctions!=!0?null:t.Pipeline.registeredFunctions[e]},t.Pipeline.warnIfFunctionNotRegistered=function(e){var n=e.label&&e.label in this.registeredFunctions;n||t.utils.warn("Function is not registered with pipeline. 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this.config},t.Configuration.prototype.reset=function(){this.config={}},lunr.SortedSet=function(){this.length=0,this.elements=[]},lunr.SortedSet.load=function(e){var t=new this;return t.elements=e,t.length=e.length,t},lunr.SortedSet.prototype.add=function(){var e,t;for(e=0;e1;){if(r===e)return o;e>r&&(t=o),r>e&&(n=o),i=n-t,o=t+Math.floor(i/2),r=this.elements[o]}return r===e?o:-1},lunr.SortedSet.prototype.locationFor=function(e){for(var t=0,n=this.elements.length,i=n-t,o=t+Math.floor(i/2),r=this.elements[o];i>1;)e>r&&(t=o),r>e&&(n=o),i=n-t,o=t+Math.floor(i/2),r=this.elements[o];return r>e?o:e>r?o+1:void 0},lunr.SortedSet.prototype.intersect=function(e){for(var t=new lunr.SortedSet,n=0,i=0,o=this.length,r=e.length,s=this.elements,u=e.elements;;){if(n>o-1||i>r-1)break;s[n]!==u[i]?s[n]u[i]&&i++:(t.add(s[n]),n++,i++)}return t},lunr.SortedSet.prototype.clone=function(){var e=new lunr.SortedSet;return e.elements=this.toArray(),e.length=e.elements.length,e},lunr.SortedSet.prototype.union=function(e){var t,n,i;this.length>=e.length?(t=this,n=e):(t=e,n=this),i=t.clone();for(var o=0,r=n.toArray();oWhat is pyerrors?\n\n
    pyerrors is a python package for error computation and propagation of Markov chain Monte Carlo data.\nIt is based on the gamma method arXiv:hep-lat/0306017. Some of its features are:
    \n\n
      \n
    • automatic differentiation for exact linear error propagation as suggested in arXiv:1809.01289 (partly based on the autograd package).
      • \n
    • treatment of slow modes in the simulation as suggested in arXiv:1009.5228.
      • \n
    • coherent error propagation for data from different Markov chains.
      • \n
    • non-linear fits with x- and y-errors and exact linear error propagation based on automatic differentiation as introduced in arXiv:1809.01289.
      • \n
    • real and complex matrix operations and their error propagation based on automatic differentiation (Matrix inverse, Cholesky decomposition, calculation of eigenvalues and eigenvectors, singular value decomposition...).
      • \n
    \n\n
    More detailed examples can found in the GitHub repository \"badge\".
    \n\n
    If you use pyerrors for research that leads to a publication please consider citing:
    \n\n
      \n
    • Fabian Joswig, Simon Kuberski, Justus T. Kuhlmann, Jan Neuendorf, pyerrors: a python framework for error analysis of Monte Carlo data. Comput.Phys.Commun. 288 (2023) 108750.
      • \n
    • Ulli Wolff, Monte Carlo errors with less errors. Comput.Phys.Commun. 156 (2004) 143-153, Comput.Phys.Commun. 176 (2007) 383 (erratum).
      • \n
    • Alberto Ramos, Automatic differentiation for error analysis of Monte Carlo data. Comput.Phys.Commun. 238 (2019) 19-35.
      • \n
    \n\n
    and
    \n\n
      \n
    • Stefan Schaefer, Rainer Sommer, Francesco Virotta, Critical slowing down and error analysis in lattice QCD simulations. Nucl.Phys.B 845 (2011) 93-119.
      • \n
    \n\n
    where applicable.
    \n\n
    There exist similar publicly available implementations of gamma method error analysis suites in Fortran, Julia and Python.
    \n\n
    Installation
    \n\n
    Install the most recent release using pip and pypi:
    \n\n
    \n
    pip install pyerrors     # Fresh install\npip install -U pyerrors  # Update\n
    \n
    \n\n
    Install the most recent release using conda and conda-forge:
    \n\n
    \n
    conda install -c conda-forge pyerrors  # Fresh install\nconda update -c conda-forge pyerrors   # Update\n
    \n
    \n\n
    Install the current develop version:
    \n\n
    \n
    pip install git+https://github.com/fjosw/pyerrors.git@develop\n
    \n
    \n\n
    Basic example
    \n\n
    \n
    import numpy as np\nimport pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name']) # Initialize an Obs object\nmy_new_obs = 2 * np.log(my_obs) / my_obs ** 2 # Construct derived Obs object\nmy_new_obs.gamma_method()                     # Estimate the statistical error\nprint(my_new_obs)                             # Print the result to stdout\n> 0.31498(72)\n
    \n
    \n\n
    The Obs class
    \n\n
    pyerrors introduces a new datatype, Obs, which simplifies error propagation and estimation for auto- and cross-correlated data.\nAn Obs object can be initialized with two arguments, the first is a list containing the samples for an observable from a Monte Carlo chain.\nThe samples can either be provided as python list or as numpy array.\nThe second argument is a list containing the names of the respective Monte Carlo chains as strings. These strings uniquely identify a Monte Carlo chain/ensemble. It is crucial for the correct error propagation that observations from the same Monte Carlo history are labeled with the same name. See Multiple ensembles/replica for details.
    \n\n
    \n
    import pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name'])\n
    \n
    \n\n
    Error propagation
    \n\n
    When performing mathematical operations on Obs objects the correct error propagation is intrinsically taken care of using a first order Taylor expansion\n$$\\delta_f^i=\\sum_\\alpha \\bar{f}_\\alpha \\delta_\\alpha^i\\,,\\quad \\delta_\\alpha^i=a_\\alpha^i-\\bar{a}_\\alpha\\,,$$\nas introduced in arXiv:hep-lat/0306017.\nThe required derivatives $\\bar{f}_\\alpha$ are evaluated up to machine precision via automatic differentiation as suggested in arXiv:1809.01289.
    \n\n
    The Obs class is designed such that mathematical numpy functions can be used on Obs just as for regular floats.
    \n\n
    \n
    import numpy as np\nimport pyerrors as pe\n\nmy_obs1 = pe.Obs([samples1], ['ensemble_name'])\nmy_obs2 = pe.Obs([samples2], ['ensemble_name'])\n\nmy_sum = my_obs1 + my_obs2\n\nmy_m_eff = np.log(my_obs1 / my_obs2)\n\niamzero = my_m_eff - my_m_eff\n# Check that value and fluctuations are zero within machine precision\nprint(iamzero == 0.0)\n> True\n
    \n
    \n\n
    Error estimation
    \n\n
    The error estimation within pyerrors is based on the gamma method introduced in arXiv:hep-lat/0306017.\nAfter having arrived at the derived quantity of interest the gamma_method can be called as detailed in the following example.
    \n\n
    \n
    my_sum.gamma_method()\nprint(my_sum)\n> 1.70(57)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 5.72046658e-01 +/- 7.56746598e-02 (33.650%)\n>  t_int         2.71422900e+00 +/- 6.40320983e-01 S = 2.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n
    \n\n
    We use the following definition of the integrated autocorrelation time established in Madras & Sokal 1988\n$$\\tau_\\mathrm{int}=\\frac{1}{2}+\\sum_{t=1}^{W}\\rho(t)\\geq \\frac{1}{2}\\,.$$\nThe window $W$ is determined via the automatic windowing procedure described in arXiv:hep-lat/0306017.\nThe standard value for the parameter $S$ of this automatic windowing procedure is $S=2$. Other values for $S$ can be passed to the gamma_method as parameter.
    \n\n
    \n
    my_sum.gamma_method(S=3.0)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.30675201e-01 +/- 1.04585650e-01 (37.099%)\n>  t_int         3.29909703e+00 +/- 9.77310102e-01 S = 3.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n
    \n\n
    The integrated autocorrelation time $\\tau_\\mathrm{int}$ and the autocorrelation function $\\rho(W)$ can be monitored via the methods pyerrors.obs.Obs.plot_tauint and pyerrors.obs.Obs.plot_rho.
    \n\n
    If the parameter $S$ is set to zero it is assumed that the dataset does not exhibit any autocorrelation and the window size is chosen to be zero.\nIn this case the error estimate is identical to the sample standard error.
    \n\n
    Exponential tails
    \n\n
    Slow modes in the Monte Carlo history can be accounted for by attaching an exponential tail to the autocorrelation function $\\rho$ as suggested in arXiv:1009.5228. The longest autocorrelation time in the history, $\\tau_\\mathrm{exp}$, can be passed to the gamma_method as parameter. In this case the automatic windowing procedure is vacated and the parameter $S$ does not affect the error estimate.
    \n\n
    \n
    my_sum.gamma_method(tau_exp=7.2)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.28097762e-01 +/- 5.79077524e-02 (36.947%)\n>  t_int         3.27218667e+00 +/- 7.99583654e-01 tau_exp = 7.20,  N_sigma = 1\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n
    \n\n
    For the full API see pyerrors.obs.Obs.gamma_method.
    \n\n
    Multiple ensembles/replica
    \n\n
    Error propagation for multiple ensembles (Markov chains with different simulation parameters) is handled automatically. Ensembles are uniquely identified by their name.
    \n\n
    \n
    obs1 = pe.Obs([samples1], ['ensemble1'])\nobs2 = pe.Obs([samples2], ['ensemble2'])\n\nmy_sum = obs1 + obs2\nmy_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 2 ensembles:\n>   \u00b7 Ensemble 'ensemble1' : 1000 configurations (from 1 to 1000)\n>   \u00b7 Ensemble 'ensemble2' : 500 configurations (from 1 to 500)\n
    \n
    \n\n
    Observables from the same Monte Carlo chain have to be initialized with the same name for correct error propagation. If different names were used in this case the data would be treated as statistically independent resulting in loss of relevant information and a potential over or under estimate of the statistical error.
    \n\n
    pyerrors identifies multiple replica (independent Markov chains with identical simulation parameters) by the vertical bar | in the name of the data set.
    \n\n
    \n
    obs1 = pe.Obs([samples1], ['ensemble1|r01'])\nobs2 = pe.Obs([samples2], ['ensemble1|r02'])\n\n> my_sum = obs1 + obs2\n> my_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1'\n>     \u00b7 Replicum 'r01' : 1000 configurations (from 1 to 1000)\n>     \u00b7 Replicum 'r02' : 500 configurations (from 1 to 500)\n
    \n
    \n\n
    Error estimation for multiple ensembles
    \n\n
    In order to keep track of different error analysis parameters for different ensembles one can make use of global dictionaries as detailed in the following example.
    \n\n
    \n
    pe.Obs.S_dict['ensemble1'] = 2.5\npe.Obs.tau_exp_dict['ensemble2'] = 8.0\npe.Obs.tau_exp_dict['ensemble3'] = 2.0\n
    \n
    \n\n
    In case the gamma_method is called without any parameters it will use the values specified in the dictionaries for the respective ensembles.\nPassing arguments to the gamma_method still dominates over the dictionaries.
    \n\n
    Irregular Monte Carlo chains
    \n\n
    Obs objects defined on irregular Monte Carlo chains can be initialized with the parameter idl.
    \n\n
    \n
    # Observable defined on configurations 20 to 519\nobs1 = pe.Obs([samples1], ['ensemble1'], idl=[range(20, 520)])\nobs1.details()\n> Result         9.98319881e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 20 to 519)\n\n# Observable defined on every second configuration between 5 and 1003\nobs2 = pe.Obs([samples2], ['ensemble1'], idl=[range(5, 1005, 2)])\nobs2.details()\n> Result         9.99100712e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 5 to 1003 in steps of 2)\n\n# Observable defined on configurations 2, 9, 28, 29 and 501\nobs3 = pe.Obs([samples3], ['ensemble1'], idl=[[2, 9, 28, 29, 501]])\nobs3.details()\n> Result         1.01718064e+00\n> 5 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 5 configurations (irregular range)\n
    \n
    \n\n
    Obs objects defined on regular and irregular histories of the same ensemble can be combined with each other and the correct error propagation and estimation is automatically taken care of.
    \n\n
    Warning: Irregular Monte Carlo chains can result in odd patterns in the autocorrelation functions.\nMake sure to check the autocorrelation time with e.g. pyerrors.obs.Obs.plot_rho or pyerrors.obs.Obs.plot_tauint.
    \n\n
    For the full API see pyerrors.obs.Obs.
    \n\n
    Correlators
    \n\n
    When one is not interested in single observables but correlation functions, pyerrors offers the Corr class which simplifies the corresponding error propagation and provides the user with a set of standard methods. In order to initialize a Corr objects one needs to arrange the data as a list of Obs
    \n\n
    \n
    my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0      0.7957(80)\n> 1      0.5156(51)\n> 2      0.3227(33)\n> 3      0.2041(21)\n
    \n
    \n\n
    In case the correlation functions are not defined on the outermost timeslices, for example because of fixed boundary conditions, a padding can be introduced.
    \n\n
    \n
    my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3], padding=[1, 1])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0\n> 1      0.7957(80)\n> 2      0.5156(51)\n> 3      0.3227(33)\n> 4      0.2041(21)\n> 5\n
    \n
    \n\n
    The individual entries of a correlator can be accessed via slicing
    \n\n
    \n
    print(my_corr[3])\n> 0.3227(33)\n
    \n
    \n\n
    Error propagation with the Corr class works very similar to Obs objects. Mathematical operations are overloaded and Corr objects can be computed together with other Corr objects, Obs objects or real numbers and integers.
    \n\n
    \n
    my_new_corr = 0.3 * my_corr[2] * my_corr * my_corr + 12 / my_corr\n
    \n
    \n\n
    pyerrors provides the user with a set of regularly used methods for the manipulation of correlator objects:
    \n\n
      \n
    • Corr.gamma_method applies the gamma method to all entries of the correlator.
      • \n
    • Corr.m_eff to construct effective masses. Various variants for periodic and fixed temporal boundary conditions are available.
      • \n
    • Corr.deriv returns the first derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
      • \n
    • Corr.second_deriv returns the second derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
      • \n
    • Corr.symmetric symmetrizes parity even correlations functions, assuming periodic boundary conditions.
      • \n
    • Corr.anti_symmetric anti-symmetrizes parity odd correlations functions, assuming periodic boundary conditions.
      • \n
    • Corr.T_symmetry averages a correlator with its time symmetry partner, assuming fixed boundary conditions.
      • \n
    • Corr.plateau extracts a plateau value from the correlator in a given range.
      • \n
    • Corr.roll periodically shifts the correlator.
      • \n
    • Corr.reverse reverses the time ordering of the correlator.
      • \n
    • Corr.correlate constructs a disconnected correlation function from the correlator and another Corr or Obs object.
      • \n
    • Corr.reweight reweights the correlator.
      • \n
    \n\n
    pyerrors can also handle matrices of correlation functions and extract energy states from these matrices via a generalized eigenvalue problem (see pyerrors.correlators.Corr.GEVP).
    \n\n
    For the full API see pyerrors.correlators.Corr.
    \n\n
    Complex valued observables
    \n\n
    pyerrors can handle complex valued observables via the class pyerrors.obs.CObs.\nCObs are initialized with a real and an imaginary part which both can be Obs valued.
    \n\n
    \n
    my_real_part = pe.Obs([samples1], ['ensemble1'])\nmy_imag_part = pe.Obs([samples2], ['ensemble1'])\n\nmy_cobs = pe.CObs(my_real_part, my_imag_part)\nmy_cobs.gamma_method()\nprint(my_cobs)\n> (0.9959(91)+0.659(28)j)\n
    \n
    \n\n
    Elementary mathematical operations are overloaded and samples are properly propagated as for the Obs class.
    \n\n
    \n
    my_derived_cobs = (my_cobs + my_cobs.conjugate()) / np.abs(my_cobs)\nmy_derived_cobs.gamma_method()\nprint(my_derived_cobs)\n> (1.668(23)+0.0j)\n
    \n
    \n\n
    The Covobs class
    \n\n
    In many projects, auxiliary data that is not based on Monte Carlo chains enters. Examples are experimentally determined mesons masses which are used to set the scale or renormalization constants. These numbers come with an error that has to be propagated through the analysis. The Covobs class allows to define such quantities in pyerrors. Furthermore, external input might consist of correlated quantities. An example are the parameters of an interpolation formula, which are defined via mean values and a covariance matrix between all parameters. The contribution of the interpolation formula to the error of a derived quantity therefore might depend on the complete covariance matrix.
    \n\n
    This concept is built into the definition of Covobs. In pyerrors, external input is defined by $M$ mean values, a $M\\times M$ covariance matrix, where $M=1$ is permissible, and a name that uniquely identifies the covariance matrix. Below, we define the pion mass, based on its mean value and error, 134.9768(5). Note, that the square of the error enters cov_Obs, since the second argument of this function is the covariance matrix of the Covobs.
    \n\n
    \n
    import pyerrors.obs as pe\n\nmpi = pe.cov_Obs(134.9768, 0.0005**2, 'pi^0 mass')\nmpi.gamma_method()\nmpi.details()\n> Result         1.34976800e+02 +/- 5.00000000e-04 +/- 0.00000000e+00 (0.000%)\n>  pi^0 mass     5.00000000e-04\n> 0 samples in 1 ensemble:\n>   \u00b7 Covobs   'pi^0 mass'\n
    \n
    \n\n
    The resulting object mpi is an Obs that contains a Covobs. In the following, it may be handled as any other Obs. The contribution of the covariance matrix to the error of an Obs is determined from the $M \\times M$ covariance matrix $\\Sigma$ and the gradient of the Obs with respect to the external quantities, which is the $1\\times M$ Jacobian matrix $J$, via\n$$s = \\sqrt{J^T \\Sigma J}\\,,$$\nwhere the Jacobian is computed for each derived quantity via automatic differentiation.
    \n\n
    Correlated auxiliary data is defined similarly to above, e.g., via
    \n\n
    \n
    RAP = pe.cov_Obs([16.7457, -19.0475], [[3.49591, -6.07560], [-6.07560, 10.5834]], 'R_AP, 1906.03445, (5.3a)')\nprint(RAP)\n> [Obs[16.7(1.9)], Obs[-19.0(3.3)]]\n
    \n
    \n\n
    where RAP now is a list of two Obs that contains the two correlated parameters.
    \n\n
    Since the gradient of a derived observable with respect to an external covariance matrix is propagated through the entire analysis, the Covobs class allows to quote the derivative of a result with respect to the external quantities. If these derivatives are published together with the result, small shifts in the definition of external quantities, e.g., the definition of the physical point, can be performed a posteriori based on the published information. This may help to compare results of different groups. The gradient of an Obs o with respect to a covariance matrix with the identifying string k may be accessed via
    \n\n
    \n
    o.covobs[k].grad\n
    \n
    \n\n
    Error propagation in iterative algorithms
    \n\n
    pyerrors supports exact linear error propagation for iterative algorithms like various variants of non-linear least squares fits or root finding. The derivatives required for the error propagation are calculated as described in arXiv:1809.01289.
    \n\n
    Least squares fits
    \n\n
    Standard non-linear least square fits with errors on the dependent but not the independent variables can be performed with pyerrors.fits.least_squares. As default solver the Levenberg-Marquardt algorithm implemented in scipy is used.
    \n\n
    Fit functions have to be of the following form
    \n\n
    \n
    import autograd.numpy as anp\n\ndef func(a, x):\n    return a[1] * anp.exp(-a[0] * x)\n
    \n
    \n\n
    It is important that numerical functions refer to autograd.numpy instead of numpy for the automatic differentiation in iterative algorithms to work properly.
    \n\n
    Fits can then be performed via
    \n\n
    \n
    fit_result = pe.fits.least_squares(x, y, func)\nprint("\\n", fit_result)\n> Fit with 2 parameters\n> Method: Levenberg-Marquardt\n> `ftol` termination condition is satisfied.\n> chisquare/d.o.f.: 0.9593035785160936\n\n>  Goodness of fit:\n> \u03c7\u00b2/d.o.f. = 0.959304\n> p-value   = 0.5673\n> Fit parameters:\n> 0      0.0548(28)\n> 1      1.933(64)\n
    \n
    \n\n
    where x is a list or numpy.array of floats and y is a list or numpy.array of Obs.
    \n\n
    Data stored in Corr objects can be fitted directly using the Corr.fit method.
    \n\n
    \n
    my_corr = pe.Corr(y)\nfit_result = my_corr.fit(func, fitrange=[12, 25])\n
    \n
    \n\n
    this can simplify working with absolute fit ranges and takes care of gaps in the data automatically.
    \n\n
    For fit functions with multiple independent variables the fit function can be of the form
    \n\n
    \n
    def func(a, x):\n    (x1, x2) = x\n    return a[0] * x1 ** 2 + a[1] * x2\n
    \n
    \n\n
    pyerrors also supports correlated fits which can be triggered via the parameter correlated_fit=True.\nDetails about how the required covariance matrix is estimated can be found in pyerrors.obs.covariance.
    \n\n
    Direct visualizations of the performed fits can be triggered via resplot=True or qqplot=True. For all available options see pyerrors.fits.least_squares.
    \n\n
    Total least squares fits
    \n\n
    pyerrors can also fit data with errors on both the dependent and independent variables using the total least squares method also referred to orthogonal distance regression as implemented in scipy, see pyerrors.fits.least_squares. The syntax is identical to the standard least squares case, the only difference being that x also has to be a list or numpy.array of Obs.
    \n\n
    For the full API see pyerrors.fits for fits and pyerrors.roots for finding roots of functions.
    \n\n
    Matrix operations
    \n\n
    pyerrors provides wrappers for Obs- and CObs-valued matrix operations based on numpy.linalg. The supported functions include:
    \n\n
      \n
    • inv for the matrix inverse.
      • \n
    • cholseky for the Cholesky decomposition.
      • \n
    • det for the matrix determinant.
      • \n
    • eigh for eigenvalues and eigenvectors of hermitean matrices.
      • \n
    • eig for eigenvalues of general matrices.
      • \n
    • pinv for the Moore-Penrose pseudoinverse.
      • \n
    • svd for the singular-value-decomposition.
      • \n
    \n\n
    For the full API see pyerrors.linalg.
    \n\n
    Export data
    \n\n
    \n\n
    The preferred exported file format within pyerrors is json.gz. Files written to this format are valid JSON files that have been compressed using gzip. The structure of the content is inspired by the dobs format of the ALPHA collaboration. The aim of the format is to facilitate the storage of data in a self-contained way such that, even years after the creation of the file, it is possible to extract all necessary information:
    \n\n
      \n
    • What observables are stored? Possibly: How exactly are they defined.
      • \n
    • How does each single ensemble or external quantity contribute to the error of the observable?
      • \n
    • Who did write the file when and on which machine?
      • \n
    \n\n
    This can be achieved by storing all information in one single file. The export routines of pyerrors are written such that as much information as possible is written automatically as described in the following example
    \n\n
    \n
    my_obs = pe.Obs([samples], ["test_ensemble"])\nmy_obs.tag = "My observable"\n\npe.input.json.dump_to_json(my_obs, "test_output_file", description="This file contains a test observable")\n# For a single observable one can equivalently use the class method dump\nmy_obs.dump("test_output_file", description="This file contains a test observable")\n\ncheck = pe.input.json.load_json("test_output_file")\n\nprint(my_obs == check)\n> True\n
    \n
    \n\n
    The format also allows to directly write out the content of Corr objects or lists and arrays of Obs objects by passing the desired data to pyerrors.input.json.dump_to_json.
    \n\n
    json.gz format specification
    \n\n
    The first entries of the file provide optional auxiliary information:
    \n\n
      \n
    • program is a string that indicates which program was used to write the file.
      • \n
    • version is a string that specifies the version of the format.
      • \n
    • who is a string that specifies the user name of the creator of the file.
      • \n
    • date is a string and contains the creation date of the file.
      • \n
    • host is a string and contains the hostname of the machine where the file has been written.
      • \n
    • description contains information on the content of the file. This field is not filled automatically in pyerrors. The user is advised to provide as detailed information as possible in this field. Examples are: Input files of measurements or simulations, LaTeX formulae or references to publications to specify how the observables have been computed, details on the analysis strategy, ... This field may be any valid JSON type. Strings, arrays or objects (equivalent to dicts in python) are well suited to provide information.
      • \n
    \n\n
    The only necessary entry of the file is the field\n-obsdata, an array that contains the actual data.
    \n\n
    Each entry of the array belongs to a single structure of observables. Currently, these structures can be either of Obs, list, numpy.ndarray, Corr. All Obs inside a structure (with dimension > 0) have to be defined on the same set of configurations. Different structures, that are represented by entries of the array obsdata, are treated independently. Each entry of the array obsdata has the following required entries:
    \n\n
      \n
    • type is a string that specifies the type of the structure. This allows to parse the content to the correct form after reading the file. It is always possible to interpret the content as list of Obs.
      • \n
    • value is an array that contains the mean values of the Obs inside the structure.\nThe following entries are optional:
      • \n
    • layout is a string that specifies the layout of multi-dimensional structures. Examples are \"2, 2\" for a 2x2 dimensional matrix or  \"64, 4, 4\" for a Corr with $T=64$ and 4x4 matrices on each time slices. \"1\" denotes a single Obs. Multi-dimensional structures are stored in row-major format (see below).
      • \n
    • tag is any JSON type. It contains additional information concerning the structure. The tag of an Obs in pyerrors is written here.
      • \n
    • reweighted is a Bool that may be used to specify, whether the Obs in the structure have been reweighted.
      • \n
    • data is an array that contains the data from MC chains. We will define it below.
      • \n
    • cdata is an array that contains the data from external quantities with an error (Covobs in pyerrors). We will define it below.
      • \n
    \n\n
    The array data contains the data from MC chains. Each entry of the array corresponds to one ensemble and contains:
    \n\n
      \n
    • id, a string that contains the name of the ensemble
      • \n
    • replica, an array that contains an entry per replica of the ensemble.
      • \n
    \n\n
    Each entry of replica contains\nname, a string that contains the name of the replica\ndeltas, an array that contains the actual data.
    \n\n
    Each entry in deltas corresponds to one configuration of the replica and has $1+N$ many entries. The first entry is an integer that specifies the configuration number that, together with ensemble and replica name, may be used to uniquely identify the configuration on which the data has been obtained. The following N entries specify the deltas, i.e., the deviation of the observable from the mean value on this configuration, of each Obs inside the structure. Multi-dimensional structures are stored in a row-major format. For primary observables, such as correlation functions, $value + delta_i$ matches the primary data obtained on the configuration.
    \n\n
    The array cdata contains information about the contribution of auxiliary observables, represented by Covobs in pyerrors, to the total error of the observables. Each entry of the array belongs to one auxiliary covariance matrix and contains:
    \n\n
      \n
    • id, a string that identifies the covariance matrix
      • \n
    • layout, a string that defines the dimensions of the $M\\times M$ covariance matrix (has to be \"M, M\" or \"1\").
      • \n
    • cov, an array that contains the $M\\times M$ many entries of the covariance matrix, stored in row-major format.
      • \n
    • grad, an array that contains N entries, one for each Obs inside the structure. Each entry itself is an array, that contains the M gradients of the Nth observable  with respect to the quantity that corresponds to the Mth diagonal entry of the covariance matrix.
      • \n
    \n\n
    A JSON schema that may be used to verify the correctness of a file with respect to the format definition is stored in ./examples/json_schema.json. The schema is a self-descriptive format definition and contains an exemplary file.
    \n\n
    Julia I/O routines for the json.gz format, compatible with ADerrors.jl, can be found here.
    \n"}, "pyerrors.correlators": {"fullname": "pyerrors.correlators", "modulename": "pyerrors.correlators", "kind": "module", "doc": "
    \n"}, "pyerrors.correlators.Corr": {"fullname": "pyerrors.correlators.Corr", "modulename": "pyerrors.correlators", "qualname": "Corr", "kind": "class", "doc": "
    The class for a correlator (time dependent sequence of pe.Obs).
    \n\n
    Everything, this class does, can be achieved using lists or arrays of Obs.\nBut it is simply more convenient to have a dedicated object for correlators.\nOne often wants to add or multiply correlators of the same length at every timeslice and it is inconvenient\nto iterate over all timeslices for every operation. This is especially true, when dealing with matrices.
    \n\n
    The correlator can have two types of content: An Obs at every timeslice OR a GEVP\nmatrix at every timeslice. Other dependency (eg. spatial) are not supported.
    \n"}, "pyerrors.correlators.Corr.__init__": {"fullname": "pyerrors.correlators.Corr.__init__", "modulename": "pyerrors.correlators", "qualname": "Corr.__init__", "kind": "function", "doc": "
    Initialize a Corr object.
    \n\n
    Parameters
    \n\n
      \n
    • data_input (list or array):\nlist of Obs or list of arrays of Obs or array of Corrs
      • \n
    • padding (list, optional):\nList with two entries where the first labels the padding\nat the front of the correlator and the second the padding\nat the back.
      • \n
    • prange (list, optional):\nList containing the first and last timeslice of the plateau\nregion indentified for this correlator.
      • \n
    \n", "signature": "(data_input, padding=[0, 0], prange=None)"}, "pyerrors.correlators.Corr.gamma_method": {"fullname": "pyerrors.correlators.Corr.gamma_method", "modulename": "pyerrors.correlators", "qualname": "Corr.gamma_method", "kind": "function", "doc": "
    Apply the gamma method to the content of the Corr.
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.gm": {"fullname": "pyerrors.correlators.Corr.gm", "modulename": "pyerrors.correlators", "qualname": "Corr.gm", "kind": "function", "doc": "
    Apply the gamma method to the content of the Corr.
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.projected": {"fullname": "pyerrors.correlators.Corr.projected", "modulename": "pyerrors.correlators", "qualname": "Corr.projected", "kind": "function", "doc": "
    We need to project the Correlator with a Vector to get a single value at each timeslice.
    \n\n
    The method can use one or two vectors.\nIf two are specified it returns v1@G@v2 (the order might be very important.)\nBy default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to
    \n", "signature": "(self, vector_l=None, vector_r=None, normalize=False):", "funcdef": "def"}, "pyerrors.correlators.Corr.item": {"fullname": "pyerrors.correlators.Corr.item", "modulename": "pyerrors.correlators", "qualname": "Corr.item", "kind": "function", "doc": "
    Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice.
    \n\n
    Parameters
    \n\n
      \n
    • i (int):\nFirst index to be picked.
      • \n
    • j (int):\nSecond index to be picked.
      • \n
    \n", "signature": "(self, i, j):", "funcdef": "def"}, "pyerrors.correlators.Corr.plottable": {"fullname": "pyerrors.correlators.Corr.plottable", "modulename": "pyerrors.correlators", "qualname": "Corr.plottable", "kind": "function", "doc": "
    Outputs the correlator in a plotable format.
    \n\n
    Outputs three lists containing the timeslice index, the value on each\ntimeslice and the error on each timeslice.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.symmetric": {"fullname": "pyerrors.correlators.Corr.symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.symmetric", "kind": "function", "doc": "
    Symmetrize the correlator around x0=0.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.anti_symmetric": {"fullname": "pyerrors.correlators.Corr.anti_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.anti_symmetric", "kind": "function", "doc": "
    Anti-symmetrize the correlator around x0=0.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.is_matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.is_matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.is_matrix_symmetric", "kind": "function", "doc": "
    Checks whether a correlator matrices is symmetric on every timeslice.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.matrix_symmetric", "kind": "function", "doc": "
    Symmetrizes the correlator matrices on every timeslice.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.GEVP": {"fullname": "pyerrors.correlators.Corr.GEVP", "modulename": "pyerrors.correlators", "qualname": "Corr.GEVP", "kind": "function", "doc": "
    Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors.
    \n\n
    The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the\nlargest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing
    \n\n
    \n
    C.GEVP(t0=2)[0]  # Ground state vector(s)\nC.GEVP(t0=2)[:3]  # Vectors for the lowest three states\n
    \n
    \n\n
    Parameters
    \n\n
      \n
    • t0 (int):\nThe time t0 for the right hand side of the GEVP according to $G(t)v_i=\\lambda_i G(t_0)v_i$
      • \n
    • ts (int):\nfixed time $G(t_s)v_i=\\lambda_i G(t_0)v_i$ if sort=None.\nIf sort=\"Eigenvector\" it gives a reference point for the sorting method.
      • \n
    • sort (string):\nIf this argument is set, a list of self.T vectors per state is returned. If it is set to None, only one vector is returned.\n
        \n
      • \"Eigenvalue\": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice.
        • \n
      • \"Eigenvector\": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state.\nThe reference state is identified by its eigenvalue at $t=t_s$.
        • \n
      • \n
    \n\n
    Other Parameters
    \n\n
      \n
    • state (int):\nReturns only the vector(s) for a specified state. The lowest state is zero.
      • \n
    \n", "signature": "(self, t0, ts=None, sort='Eigenvalue', **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.Eigenvalue": {"fullname": "pyerrors.correlators.Corr.Eigenvalue", "modulename": "pyerrors.correlators", "qualname": "Corr.Eigenvalue", "kind": "function", "doc": "
    Determines the eigenvalue of the GEVP by solving and projecting the correlator
    \n\n
    Parameters
    \n\n
      \n
    • state (int):\nThe state one is interested in ordered by energy. The lowest state is zero.
      • \n
    • All other parameters are identical to the ones of Corr.GEVP.
      • \n
    \n", "signature": "(self, t0, ts=None, state=0, sort='Eigenvalue'):", "funcdef": "def"}, "pyerrors.correlators.Corr.Hankel": {"fullname": "pyerrors.correlators.Corr.Hankel", "modulename": "pyerrors.correlators", "qualname": "Corr.Hankel", "kind": "function", "doc": "
    Constructs an NxN Hankel matrix
    \n\n
    C(t) c(t+1) ... c(t+n-1)\nC(t+1) c(t+2) ... c(t+n)\n.................\nC(t+(n-1)) c(t+n) ... c(t+2(n-1))
    \n\n
    Parameters
    \n\n
      \n
    • N (int):\nDimension of the Hankel matrix
      • \n
    • periodic (bool, optional):\ndetermines whether the matrix is extended periodically
      • \n
    \n", "signature": "(self, N, periodic=False):", "funcdef": "def"}, "pyerrors.correlators.Corr.roll": {"fullname": "pyerrors.correlators.Corr.roll", "modulename": "pyerrors.correlators", "qualname": "Corr.roll", "kind": "function", "doc": "
    Periodically shift the correlator by dt timeslices
    \n\n
    Parameters
    \n\n
      \n
    • dt (int):\nnumber of timeslices
      • \n
    \n", "signature": "(self, dt):", "funcdef": "def"}, "pyerrors.correlators.Corr.reverse": {"fullname": "pyerrors.correlators.Corr.reverse", "modulename": "pyerrors.correlators", "qualname": "Corr.reverse", "kind": "function", "doc": "
    Reverse the time ordering of the Corr
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.thin": {"fullname": "pyerrors.correlators.Corr.thin", "modulename": "pyerrors.correlators", "qualname": "Corr.thin", "kind": "function", "doc": "
    Thin out a correlator to suppress correlations
    \n\n
    Parameters
    \n\n
      \n
    • spacing (int):\nKeep only every 'spacing'th entry of the correlator
      • \n
    • offset (int):\nOffset the equal spacing
      • \n
    \n", "signature": "(self, spacing=2, offset=0):", "funcdef": "def"}, "pyerrors.correlators.Corr.correlate": {"fullname": "pyerrors.correlators.Corr.correlate", "modulename": "pyerrors.correlators", "qualname": "Corr.correlate", "kind": "function", "doc": "
    Correlate the correlator with another correlator or Obs
    \n\n
    Parameters
    \n\n
      \n
    • partner (Obs or Corr):\npartner to correlate the correlator with.\nCan either be an Obs which is correlated with all entries of the\ncorrelator or a Corr of same length.
      • \n
    \n", "signature": "(self, partner):", "funcdef": "def"}, "pyerrors.correlators.Corr.reweight": {"fullname": "pyerrors.correlators.Corr.reweight", "modulename": "pyerrors.correlators", "qualname": "Corr.reweight", "kind": "function", "doc": "
    Reweight the correlator.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl.
      • \n
    \n", "signature": "(self, weight, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.T_symmetry": {"fullname": "pyerrors.correlators.Corr.T_symmetry", "modulename": "pyerrors.correlators", "qualname": "Corr.T_symmetry", "kind": "function", "doc": "
    Return the time symmetry average of the correlator and its partner
    \n\n
    Parameters
    \n\n
      \n
    • partner (Corr):\nTime symmetry partner of the Corr
      • \n
    • partity (int):\nParity quantum number of the correlator, can be +1 or -1
      • \n
    \n", "signature": "(self, partner, parity=1):", "funcdef": "def"}, "pyerrors.correlators.Corr.deriv": {"fullname": "pyerrors.correlators.Corr.deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.deriv", "kind": "function", "doc": "
    Return the first derivative of the correlator with respect to x0.
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, forward, backward, improved, log, default: symmetric
      • \n
    \n", "signature": "(self, variant='symmetric'):", "funcdef": "def"}, "pyerrors.correlators.Corr.second_deriv": {"fullname": "pyerrors.correlators.Corr.second_deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.second_deriv", "kind": "function", "doc": "
    Return the second derivative of the correlator with respect to x0.
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, improved, log, default: symmetric
      • \n
    \n", "signature": "(self, variant='symmetric'):", "funcdef": "def"}, "pyerrors.correlators.Corr.m_eff": {"fullname": "pyerrors.correlators.Corr.m_eff", "modulename": "pyerrors.correlators", "qualname": "Corr.m_eff", "kind": "function", "doc": "
    Returns the effective mass of the correlator as correlator object
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\nlog : uses the standard effective mass log(C(t) / C(t+1))\ncosh, periodic : Use periodicitiy of the correlator by solving C(t) / C(t+1) = cosh(m * (t - T/2)) / cosh(m * (t + 1 - T/2)) for m.\nsinh : Use anti-periodicitiy of the correlator by solving C(t) / C(t+1) = sinh(m * (t - T/2)) / sinh(m * (t + 1 - T/2)) for m.\nSee, e.g., arXiv:1205.5380\narccosh : Uses the explicit form of the symmetrized correlator (not recommended)\nlogsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2
      • \n
    • guess (float):\nguess for the root finder, only relevant for the root variant
      • \n
    \n", "signature": "(self, variant='log', guess=1.0):", "funcdef": "def"}, "pyerrors.correlators.Corr.fit": {"fullname": "pyerrors.correlators.Corr.fit", "modulename": "pyerrors.correlators", "qualname": "Corr.fit", "kind": "function", "doc": "
    Fits function to the data
    \n\n
    Parameters
    \n\n
      \n
    • function (obj):\nfunction to fit to the data. See fits.least_squares for details.
      • \n
    • fitrange (list):\nTwo element list containing the timeslices on which the fit is supposed to start and stop.\nCaution: This range is inclusive as opposed to standard python indexing.\nfitrange=[4, 6] corresponds to the three entries 4, 5 and 6.\nIf not specified, self.prange or all timeslices are used.
      • \n
    • silent (bool):\nDecides whether output is printed to the standard output.
      • \n
    \n", "signature": "(self, function, fitrange=None, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.plateau": {"fullname": "pyerrors.correlators.Corr.plateau", "modulename": "pyerrors.correlators", "qualname": "Corr.plateau", "kind": "function", "doc": "
    Extract a plateau value from a Corr object
    \n\n
    Parameters
    \n\n
      \n
    • plateau_range (list):\nlist with two entries, indicating the first and the last timeslice\nof the plateau region.
      • \n
    • method (str):\nmethod to extract the plateau.\n    'fit' fits a constant to the plateau region\n    'avg', 'average' or 'mean' just average over the given timeslices.
      • \n
    • auto_gamma (bool):\napply gamma_method with default parameters to the Corr. Defaults to None
      • \n
    \n", "signature": "(self, plateau_range=None, method='fit', auto_gamma=False):", "funcdef": "def"}, "pyerrors.correlators.Corr.set_prange": {"fullname": "pyerrors.correlators.Corr.set_prange", "modulename": "pyerrors.correlators", "qualname": "Corr.set_prange", "kind": "function", "doc": "
    Sets the attribute prange of the Corr object.
    \n", "signature": "(self, prange):", "funcdef": "def"}, "pyerrors.correlators.Corr.show": {"fullname": "pyerrors.correlators.Corr.show", "modulename": "pyerrors.correlators", "qualname": "Corr.show", "kind": "function", "doc": "
    Plots the correlator using the tag of the correlator as label if available.
    \n\n
    Parameters
    \n\n
      \n
    • x_range (list):\nlist of two values, determining the range of the x-axis e.g. [4, 8].
      • \n
    • comp (Corr or list of Corr):\nCorrelator or list of correlators which are plotted for comparison.\nThe tags of these correlators are used as labels if available.
      • \n
    • logscale (bool):\nSets y-axis to logscale.
      • \n
    • plateau (Obs):\nPlateau value to be visualized in the figure.
      • \n
    • fit_res (Fit_result):\nFit_result object to be visualized.
      • \n
    • fit_key (str):\nKey for the fit function in Fit_result.fit_function (for combined fits).
      • \n
    • ylabel (str):\nLabel for the y-axis.
      • \n
    • save (str):\npath to file in which the figure should be saved.
      • \n
    • auto_gamma (bool):\nApply the gamma method with standard parameters to all correlators and plateau values before plotting.
      • \n
    • hide_sigma (float):\nHides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.
      • \n
    • references (list):\nList of floating point values that are displayed as horizontal lines for reference.
      • \n
    • title (string):\nOptional title of the figure.
      • \n
    \n", "signature": "(\tself,\tx_range=None,\tcomp=None,\ty_range=None,\tlogscale=False,\tplateau=None,\tfit_res=None,\tfit_key=None,\tylabel=None,\tsave=None,\tauto_gamma=False,\thide_sigma=None,\treferences=None,\ttitle=None):", "funcdef": "def"}, "pyerrors.correlators.Corr.spaghetti_plot": {"fullname": "pyerrors.correlators.Corr.spaghetti_plot", "modulename": "pyerrors.correlators", "qualname": "Corr.spaghetti_plot", "kind": "function", "doc": "
    Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
    \n\n
    Parameters
    \n\n
      \n
    • logscale (bool):\nDetermines whether the scale of the y-axis is logarithmic or standard.
      • \n
    \n", "signature": "(self, logscale=True):", "funcdef": "def"}, "pyerrors.correlators.Corr.dump": {"fullname": "pyerrors.correlators.Corr.dump", "modulename": "pyerrors.correlators", "qualname": "Corr.dump", "kind": "function", "doc": "
    Dumps the Corr into a file of chosen type
    \n\n
    Parameters
    \n\n
      \n
    • filename (str):\nName of the file to be saved.
      • \n
    • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n", "signature": "(self, filename, datatype='json.gz', **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.print": {"fullname": "pyerrors.correlators.Corr.print", "modulename": "pyerrors.correlators", "qualname": "Corr.print", "kind": "function", "doc": "
    \n", "signature": "(self, print_range=None):", "funcdef": "def"}, "pyerrors.correlators.Corr.sqrt": {"fullname": "pyerrors.correlators.Corr.sqrt", "modulename": "pyerrors.correlators", "qualname": "Corr.sqrt", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.log": {"fullname": "pyerrors.correlators.Corr.log", "modulename": "pyerrors.correlators", "qualname": "Corr.log", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.exp": {"fullname": "pyerrors.correlators.Corr.exp", "modulename": "pyerrors.correlators", "qualname": "Corr.exp", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.sin": {"fullname": "pyerrors.correlators.Corr.sin", "modulename": "pyerrors.correlators", "qualname": "Corr.sin", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.cos": {"fullname": "pyerrors.correlators.Corr.cos", "modulename": "pyerrors.correlators", "qualname": "Corr.cos", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.tan": {"fullname": "pyerrors.correlators.Corr.tan", "modulename": "pyerrors.correlators", "qualname": "Corr.tan", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.sinh": {"fullname": "pyerrors.correlators.Corr.sinh", "modulename": "pyerrors.correlators", "qualname": "Corr.sinh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.cosh": {"fullname": "pyerrors.correlators.Corr.cosh", "modulename": "pyerrors.correlators", "qualname": "Corr.cosh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.tanh": {"fullname": "pyerrors.correlators.Corr.tanh", "modulename": "pyerrors.correlators", "qualname": "Corr.tanh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsin": {"fullname": "pyerrors.correlators.Corr.arcsin", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsin", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arccos": {"fullname": "pyerrors.correlators.Corr.arccos", "modulename": "pyerrors.correlators", "qualname": "Corr.arccos", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arctan": {"fullname": "pyerrors.correlators.Corr.arctan", "modulename": "pyerrors.correlators", "qualname": "Corr.arctan", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsinh": {"fullname": "pyerrors.correlators.Corr.arcsinh", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsinh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arccosh": {"fullname": "pyerrors.correlators.Corr.arccosh", "modulename": "pyerrors.correlators", "qualname": "Corr.arccosh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arctanh": {"fullname": "pyerrors.correlators.Corr.arctanh", "modulename": "pyerrors.correlators", "qualname": "Corr.arctanh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.prune": {"fullname": "pyerrors.correlators.Corr.prune", "modulename": "pyerrors.correlators", "qualname": "Corr.prune", "kind": "function", "doc": "
    Project large correlation matrix to lowest states
    \n\n
    This method can be used to reduce the size of an (N x N) correlation matrix\nto (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise\nis still small.
    \n\n
    Parameters
    \n\n
      \n
    • Ntrunc (int):\nRank of the target matrix.
      • \n
    • tproj (int):\nTime where the eigenvectors are evaluated, corresponds to ts in the GEVP method.\nThe default value is 3.
      • \n
    • t0proj (int):\nTime where the correlation matrix is inverted. Choosing t0proj=1 is strongly\ndiscouraged for O(a) improved theories, since the correctness of the procedure\ncannot be granted in this case. The default value is 2.
      • \n
    • basematrix (Corr):\nCorrelation matrix that is used to determine the eigenvectors of the\nlowest states based on a GEVP. basematrix is taken to be the Corr itself if\nis is not specified.
      • \n
    \n\n
    Notes
    \n\n
    We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving\nthe GEVP $$C(t) v_n(t, t_0) = \\lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \\equiv t_\\mathrm{proj}$\nand $t_0 \\equiv t_{0, \\mathrm{proj}}$. The target matrix is projected onto the subspace of the\nresulting eigenvectors $v_n, n=1,\\dots,N_\\mathrm{trunc}$ via\n$$G^\\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large\ncorrelation matrix and to remove some noise that is added by irrelevant operators.\nThis may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated\nbound $t_0 \\leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.
    \n", "signature": "(self, Ntrunc, tproj=3, t0proj=2, basematrix=None):", "funcdef": "def"}, "pyerrors.covobs": {"fullname": "pyerrors.covobs", "modulename": "pyerrors.covobs", "kind": "module", "doc": "
    \n"}, "pyerrors.covobs.Covobs": {"fullname": "pyerrors.covobs.Covobs", "modulename": "pyerrors.covobs", "qualname": "Covobs", "kind": "class", "doc": "
    \n"}, "pyerrors.covobs.Covobs.__init__": {"fullname": "pyerrors.covobs.Covobs.__init__", "modulename": "pyerrors.covobs", "qualname": "Covobs.__init__", "kind": "function", "doc": "
    Initialize Covobs object.
    \n\n
    Parameters
    \n\n
      \n
    • mean (float):\nMean value of the new Obs
      • \n
    • cov (list or array):\n2d Covariance matrix or 1d diagonal entries
      • \n
    • name (str):\nidentifier for the covariance matrix
      • \n
    • pos (int):\nPosition of the variance belonging to mean in cov.\nIs taken to be 1 if cov is 0-dimensional
      • \n
    • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
      • \n
    \n", "signature": "(mean, cov, name, pos=None, grad=None)"}, "pyerrors.covobs.Covobs.errsq": {"fullname": "pyerrors.covobs.Covobs.errsq", "modulename": "pyerrors.covobs", "qualname": "Covobs.errsq", "kind": "function", "doc": "
    Return the variance (= square of the error) of the Covobs
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.dirac": {"fullname": "pyerrors.dirac", "modulename": "pyerrors.dirac", "kind": "module", "doc": "
    \n"}, "pyerrors.dirac.epsilon_tensor": {"fullname": "pyerrors.dirac.epsilon_tensor", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor", "kind": "function", "doc": "
    Rank-3 epsilon tensor
    \n\n
    Based on https://codegolf.stackexchange.com/a/160375
    \n\n
    Returns
    \n\n
      \n
    • elem (int):\nElement (i,j,k) of the epsilon tensor of rank 3
      • \n
    \n", "signature": "(i, j, k):", "funcdef": "def"}, "pyerrors.dirac.epsilon_tensor_rank4": {"fullname": "pyerrors.dirac.epsilon_tensor_rank4", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor_rank4", "kind": "function", "doc": "
    Rank-4 epsilon tensor
    \n\n
    Extension of https://codegolf.stackexchange.com/a/160375
    \n\n
    Returns
    \n\n
      \n
    • elem (int):\nElement (i,j,k,o) of the epsilon tensor of rank 4
      • \n
    \n", "signature": "(i, j, k, o):", "funcdef": "def"}, "pyerrors.dirac.Grid_gamma": {"fullname": "pyerrors.dirac.Grid_gamma", "modulename": "pyerrors.dirac", "qualname": "Grid_gamma", "kind": "function", "doc": "
    Returns gamma matrix in Grid labeling.
    \n", "signature": "(gamma_tag):", "funcdef": "def"}, "pyerrors.fits": {"fullname": "pyerrors.fits", "modulename": "pyerrors.fits", "kind": "module", "doc": "
    \n"}, "pyerrors.fits.Fit_result": {"fullname": "pyerrors.fits.Fit_result", "modulename": "pyerrors.fits", "qualname": "Fit_result", "kind": "class", "doc": "
    Represents fit results.
    \n\n
    Attributes
    \n\n
      \n
    • fit_parameters (list):\nresults for the individual fit parameters,\nalso accessible via indices.
      • \n
    • chisquare_by_dof (float):\nreduced chisquare.
      • \n
    • p_value (float):\np-value of the fit
      • \n
    • t2_p_value (float):\nHotelling t-squared p-value for correlated fits.
      • \n
    \n", "bases": "collections.abc.Sequence"}, "pyerrors.fits.Fit_result.gamma_method": {"fullname": "pyerrors.fits.Fit_result.gamma_method", "modulename": "pyerrors.fits", "qualname": "Fit_result.gamma_method", "kind": "function", "doc": "
    Apply the gamma method to all fit parameters
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.fits.Fit_result.gm": {"fullname": "pyerrors.fits.Fit_result.gm", "modulename": "pyerrors.fits", "qualname": "Fit_result.gm", "kind": "function", "doc": "
    Apply the gamma method to all fit parameters
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.fits.least_squares": {"fullname": "pyerrors.fits.least_squares", "modulename": "pyerrors.fits", "qualname": "least_squares", "kind": "function", "doc": "
    Performs a non-linear fit to y = func(x).\n    ```
    \n\n
    Parameters
    \n\n
      \n
    • For an uncombined fit:
      • \n
    • x (list):\nlist of floats.
      • \n
    • y (list):\nlist of Obs.
      • \n
    • func (object):\nfit function, has to be of the form
      \n\n
      \n
      import autograd.numpy as anp\n\ndef func(a, x):\n   return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
      \n
      \n\n
      For multiple x values func can be of the form
      \n\n
      \n
      def func(a, x):\n   (x1, x2) = x\n   return a[0] * x1 ** 2 + a[1] * x2\n
      \n
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • OR For a combined fit:
      • \n
    • x (dict):\ndict of lists.
      • \n
    • y (dict):\ndict of lists of Obs.
      • \n
    • funcs (dict):\ndict of objects\nfit functions have to be of the form (here a[0] is the common fit parameter)\n```python\nimport autograd.numpy as anp\nfuncs = {\"a\": func_a,\n       \"b\": func_b}
      \n\n
      def func_a(a, x):\n   return a[1] * anp.exp(-a[0] * x)
      \n\n
      def func_b(a, x):\n   return a[2] * anp.exp(-a[0] * x)
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • priors (dict or list, optional):\npriors can either be a dictionary with integer keys and the corresponding priors as values or\na list with an entry for every parameter in the fit. The entries can either be\nObs (e.g. results from a previous fit) or strings containing a value and an error formatted like\n0.548(23), 500(40) or 0.5(0.4)
      • \n
    • silent (bool, optional):\nIf true all output to the console is omitted (default False).
      • \n
    • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for\nnon-linear fits with many parameters. In case of correlated fits the guess is used to perform\nan uncorrelated fit which then serves as guess for the correlated fit.
      • \n
    • method (str, optional):\ncan be used to choose an alternative method for the minimization of chisquare.\nThe possible methods are the ones which can be used for scipy.optimize.minimize and\nmigrad of iminuit. If no method is specified, Levenberg-Marquard is used.\nReliable alternatives are migrad, Powell and Nelder-Mead.
      • \n
    • tol (float, optional):\ncan be used (only for combined fits and methods other than Levenberg-Marquard) to set the tolerance for convergence\nto a different value to either speed up convergence at the cost of a larger error on the fitted parameters (and possibly\ninvalid estimates for parameter uncertainties) or smaller values to get more accurate parameter values\nThe stopping criterion depends on the method, e.g. migrad: edm_max = 0.002 * tol * errordef (EDM criterion: edm < edm_max)
      • \n
    • correlated_fit (bool):\nIf True, use the full inverse covariance matrix in the definition of the chisquare cost function.\nFor details about how the covariance matrix is estimated see pyerrors.obs.covariance.\nIn practice the correlation matrix is Cholesky decomposed and inverted (instead of the covariance matrix).\nThis procedure should be numerically more stable as the correlation matrix is typically better conditioned (Jacobi preconditioning).
      • \n
    • expected_chisquare (bool):\nIf True estimates the expected chisquare which is\ncorrected by effects caused by correlated input data (default False).
      • \n
    • resplot (bool):\nIf True, a plot which displays fit, data and residuals is generated (default False).
      • \n
    • qqplot (bool):\nIf True, a quantile-quantile plot of the fit result is generated (default False).
      • \n
    • num_grad (bool):\nUse numerical differentation instead of automatic differentiation to perform the error propagation (default False).
      • \n
    \n\n
    Returns
    \n\n
      \n
    • output (Fit_result):\nParameters and information on the fitted result.
      • \n
    \n", "signature": "(x, y, func, priors=None, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.fits.total_least_squares": {"fullname": "pyerrors.fits.total_least_squares", "modulename": "pyerrors.fits", "qualname": "total_least_squares", "kind": "function", "doc": "
    Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nlist of Obs, or a tuple of lists of Obs
      • \n
    • y (list):\nlist of Obs. The dvalues of the Obs are used as x- and yerror for the fit.
      • \n
    • func (object):\nfunc has to be of the form
      \n\n
      \n
      import autograd.numpy as anp\n\ndef func(a, x):\n   return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
      \n
      \n\n
      For multiple x values func can be of the form
      \n\n
      \n
      def func(a, x):\n   (x1, x2) = x\n   return a[0] * x1 ** 2 + a[1] * x2\n
      \n
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • silent (bool, optional):\nIf true all output to the console is omitted (default False).
      • \n
    • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for non-linear\nfits with many parameters.
      • \n
    • expected_chisquare (bool):\nIf true prints the expected chisquare which is\ncorrected by effects caused by correlated input data.\nThis can take a while as the full correlation matrix\nhas to be calculated (default False).
      • \n
    • num_grad (bool):\nUse numerical differentation instead of automatic differentiation to perform the error propagation (default False).
      • \n
    \n\n
    Notes
    \n\n
    Based on the orthogonal distance regression module of scipy.
    \n\n
    Returns
    \n\n
      \n
    • output (Fit_result):\nParameters and information on the fitted result.
      • \n
    \n", "signature": "(x, y, func, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.fits.fit_lin": {"fullname": "pyerrors.fits.fit_lin", "modulename": "pyerrors.fits", "qualname": "fit_lin", "kind": "function", "doc": "
    Performs a linear fit to y = n + m * x and returns two Obs n, m.
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nCan either be a list of floats in which case no xerror is assumed, or\na list of Obs, where the dvalues of the Obs are used as xerror for the fit.
      • \n
    • y (list):\nList of Obs, the dvalues of the Obs are used as yerror for the fit.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • fit_parameters (list[Obs]):\nLIist of fitted observables.
      • \n
    \n", "signature": "(x, y, **kwargs):", "funcdef": "def"}, "pyerrors.fits.qqplot": {"fullname": "pyerrors.fits.qqplot", "modulename": "pyerrors.fits", "qualname": "qqplot", "kind": "function", "doc": "
    Generates a quantile-quantile plot of the fit result which can be used to\n   check if the residuals of the fit are gaussian distributed.
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(x, o_y, func, p, title=''):", "funcdef": "def"}, "pyerrors.fits.residual_plot": {"fullname": "pyerrors.fits.residual_plot", "modulename": "pyerrors.fits", "qualname": "residual_plot", "kind": "function", "doc": "
    Generates a plot which compares the fit to the data and displays the corresponding residuals
    \n\n
    For uncorrelated data the residuals are expected to be distributed ~N(0,1).
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(x, y, func, fit_res, title=''):", "funcdef": "def"}, "pyerrors.fits.error_band": {"fullname": "pyerrors.fits.error_band", "modulename": "pyerrors.fits", "qualname": "error_band", "kind": "function", "doc": "
    Calculate the error band for an array of sample values x, for given fit function func with optimized parameters beta.
    \n\n
    Returns
    \n\n
      \n
    • err (np.array(Obs)):\nError band for an array of sample values x
      • \n
    \n", "signature": "(x, func, beta):", "funcdef": "def"}, "pyerrors.fits.ks_test": {"fullname": "pyerrors.fits.ks_test", "modulename": "pyerrors.fits", "qualname": "ks_test", "kind": "function", "doc": "
    Performs a Kolmogorov\u2013Smirnov test for the p-values of all fit object.
    \n\n
    Parameters
    \n\n
      \n
    • objects (list):\nList of fit results to include in the analysis (optional).
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(objects=None):", "funcdef": "def"}, "pyerrors.input": {"fullname": "pyerrors.input", "modulename": "pyerrors.input", "kind": "module", "doc": "
    pyerrors includes an input submodule in which input routines and parsers for the output of various numerical programs are contained.
    \n\n
    Jackknife samples
    \n\n
    For comparison with other analysis workflows pyerrors can also generate jackknife samples from an Obs object or import jackknife samples into an Obs object.\nSee pyerrors.obs.Obs.export_jackknife and pyerrors.obs.import_jackknife for details.
    \n"}, "pyerrors.input.bdio": {"fullname": "pyerrors.input.bdio", "modulename": "pyerrors.input.bdio", "kind": "module", "doc": "
    \n"}, "pyerrors.input.bdio.read_ADerrors": {"fullname": "pyerrors.input.bdio.read_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "read_ADerrors", "kind": "function", "doc": "
    Extract generic MCMC data from a bdio file
    \n\n
    read_ADerrors requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path -- path to the bdio file
      • \n
    • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    \n\n
    Returns
    \n\n
      \n
    • data (List[Obs]):\nExtracted data
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.write_ADerrors": {"fullname": "pyerrors.input.bdio.write_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "write_ADerrors", "kind": "function", "doc": "
    Write Obs to a bdio file according to ADerrors conventions
    \n\n
    read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path -- path to the bdio file
      • \n
    • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    \n\n
    Returns
    \n\n
      \n
    • success (int):\nreturns 0 is successful
      • \n
    \n", "signature": "(obs_list, file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.read_mesons": {"fullname": "pyerrors.input.bdio.read_mesons", "modulename": "pyerrors.input.bdio", "qualname": "read_mesons", "kind": "function", "doc": "
    Extract mesons data from a bdio file and return it as a dictionary
    \n\n
    The dictionary can be accessed with a tuple consisting of (type, source_position, kappa1, kappa2)
    \n\n
    read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path (str):\npath to the bdio file
      • \n
    • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    • start (int):\nThe first configuration to be read (default 1)
      • \n
    • stop (int):\nThe last configuration to be read (default None)
      • \n
    • step (int):\nFixed step size between two measurements (default 1)
      • \n
    • alternative_ensemble_name (str):\nManually overwrite ensemble name
      • \n
    \n\n
    Returns
    \n\n
      \n
    • data (dict):\nExtracted meson data
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.read_dSdm": {"fullname": "pyerrors.input.bdio.read_dSdm", "modulename": "pyerrors.input.bdio", "qualname": "read_dSdm", "kind": "function", "doc": "
    Extract dSdm data from a bdio file and return it as a dictionary
    \n\n
    The dictionary can be accessed with a tuple consisting of (type, kappa)
    \n\n
    read_dSdm requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path (str):\npath to the bdio file
      • \n
    • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    • start (int):\nThe first configuration to be read (default 1)
      • \n
    • stop (int):\nThe last configuration to be read (default None)
      • \n
    • step (int):\nFixed step size between two measurements (default 1)
      • \n
    • alternative_ensemble_name (str):\nManually overwrite ensemble name
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.dobs": {"fullname": "pyerrors.input.dobs", "modulename": "pyerrors.input.dobs", "kind": "module", "doc": "
    \n"}, "pyerrors.input.dobs.create_pobs_string": {"fullname": "pyerrors.input.dobs.create_pobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_pobs_string", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to an xml string\naccording to the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • xml_str (str):\nXML formatted string of the input data
      • \n
    \n", "signature": "(obsl, name, spec='', origin='', symbol=[], enstag=None):", "funcdef": "def"}, "pyerrors.input.dobs.write_pobs": {"fullname": "pyerrors.input.dobs.write_pobs", "modulename": "pyerrors.input.dobs", "qualname": "write_pobs", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
      • \n
    • gz (bool):\nIf True, the output is a gzipped xml. If False, the output is an xml file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(\tobsl,\tfname,\tname,\tspec='',\torigin='',\tsymbol=[],\tenstag=None,\tgz=True):", "funcdef": "def"}, "pyerrors.input.dobs.read_pobs": {"fullname": "pyerrors.input.dobs.read_pobs", "modulename": "pyerrors.input.dobs", "qualname": "read_pobs", "kind": "function", "doc": "
    Import a list of Obs from an xml.gz file in the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • separatior_insertion (str or int):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nNone (default): Replica names remain unchanged.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • res (list[Obs]):\nImported data
      • \n
    • or
      • \n
    • res (dict):\nImported data and meta-data
      • \n
    \n", "signature": "(fname, full_output=False, gz=True, separator_insertion=None):", "funcdef": "def"}, "pyerrors.input.dobs.import_dobs_string": {"fullname": "pyerrors.input.dobs.import_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "import_dobs_string", "kind": "function", "doc": "
    Import a list of Obs from a string in the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • content (str):\nXML string containing the data
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • res (list[Obs]):\nImported data
      • \n
    • or
      • \n
    • res (dict):\nImported data and meta-data
      • \n
    \n", "signature": "(content, full_output=False, separator_insertion=True):", "funcdef": "def"}, "pyerrors.input.dobs.read_dobs": {"fullname": "pyerrors.input.dobs.read_dobs", "modulename": "pyerrors.input.dobs", "qualname": "read_dobs", "kind": "function", "doc": "
    Import a list of Obs from an xml.gz file in the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes XML file.
      • \n
    • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • res (list[Obs]):\nImported data
      • \n
    • or
      • \n
    • res (dict):\nImported data and meta-data
      • \n
    \n", "signature": "(fname, full_output=False, gz=True, separator_insertion=True):", "funcdef": "def"}, "pyerrors.input.dobs.create_dobs_string": {"fullname": "pyerrors.input.dobs.create_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_dobs_string", "kind": "function", "doc": "
    Generate the string for the export of a list of Obs or structures containing Obs\nto a .xml.gz file according to the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically. The separator |is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • who (str):\nProvide the name of the person that exports the data.
      • \n
    • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • xml_str (str):\nXML string generated from the data
      • \n
    \n", "signature": "(\tobsl,\tname,\tspec='dobs v1.0',\torigin='',\tsymbol=[],\twho=None,\tenstags=None):", "funcdef": "def"}, "pyerrors.input.dobs.write_dobs": {"fullname": "pyerrors.input.dobs.write_dobs", "modulename": "pyerrors.input.dobs", "qualname": "write_dobs", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • who (str):\nProvide the name of the person that exports the data.
      • \n
    • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
      • \n
    • gz (bool):\nIf True, the output is a gzipped XML. If False, the output is a XML file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(\tobsl,\tfname,\tname,\tspec='dobs v1.0',\torigin='',\tsymbol=[],\twho=None,\tenstags=None,\tgz=True):", "funcdef": "def"}, "pyerrors.input.hadrons": {"fullname": "pyerrors.input.hadrons", "modulename": "pyerrors.input.hadrons", "kind": "module", "doc": "
    \n"}, "pyerrors.input.hadrons.read_meson_hd5": {"fullname": "pyerrors.input.hadrons.read_meson_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_meson_hd5", "kind": "function", "doc": "
    Read hadrons meson hdf5 file and extract the meson labeled 'meson'
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • meson (str):\nlabel of the meson to be extracted, standard value meson_0 which\ncorresponds to the pseudoscalar pseudoscalar two-point function.
      • \n
    • gammas (tuple of strings):\nInstrad of a meson label one can also provide a tuple of two strings\nindicating the gamma matrices at source and sink.\n(\"Gamma5\", \"Gamma5\") corresponds to the pseudoscalar pseudoscalar\ntwo-point function. The gammas argument dominateds over meson.
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • corr (Corr):\nCorrelator of the source sink combination in question.
      • \n
    \n", "signature": "(path, filestem, ens_id, meson='meson_0', idl=None, gammas=None):", "funcdef": "def"}, "pyerrors.input.hadrons.extract_t0_hd5": {"fullname": "pyerrors.input.hadrons.extract_t0_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "extract_t0_hd5", "kind": "function", "doc": "
    Read hadrons FlowObservables hdf5 file and extract t0
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • obs (str):\nlabel of the observable from which t0 should be extracted.\nOptions: 'Clover energy density' and 'Plaquette energy density'
      • \n
    • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.
      • \n
    \n", "signature": "(\tpath,\tfilestem,\tens_id,\tobs='Clover energy density',\tfit_range=5,\tidl=None,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.hadrons.read_DistillationContraction_hd5": {"fullname": "pyerrors.input.hadrons.read_DistillationContraction_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_DistillationContraction_hd5", "kind": "function", "doc": "
    Read hadrons DistillationContraction hdf5 files in given directory structure
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the directories to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • diagrams (list):\nList of strings of the diagrams to extract, e.g. [\"direct\", \"box\", \"cross\"].
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (dict):\nextracted DistillationContration data
      • \n
    \n", "signature": "(path, ens_id, diagrams=['direct'], idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.Npr_matrix": {"fullname": "pyerrors.input.hadrons.Npr_matrix", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix", "kind": "class", "doc": "
    ndarray(shape, dtype=float, buffer=None, offset=0,\n        strides=None, order=None)
    \n\n
    An array object represents a multidimensional, homogeneous array\nof fixed-size items.  An associated data-type object describes the\nformat of each element in the array (its byte-order, how many bytes it\noccupies in memory, whether it is an integer, a floating point number,\nor something else, etc.)
    \n\n
    Arrays should be constructed using array, zeros or empty (refer\nto the See Also section below).  The parameters given here refer to\na low-level method (ndarray(...)) for instantiating an array.
    \n\n
    For more information, refer to the numpy module and examine the\nmethods and attributes of an array.
    \n\n
    Parameters
    \n\n
      \n
    • (for the __new__ method; see Notes below)
      • \n
    • shape (tuple of ints):\nShape of created array.
      • \n
    • dtype (data-type, optional):\nAny object that can be interpreted as a numpy data type.
      • \n
    • buffer (object exposing buffer interface, optional):\nUsed to fill the array with data.
      • \n
    • offset (int, optional):\nOffset of array data in buffer.
      • \n
    • strides (tuple of ints, optional):\nStrides of data in memory.
      • \n
    • order ({'C', 'F'}, optional):\nRow-major (C-style) or column-major (Fortran-style) order.
      • \n
    \n\n
    Attributes
    \n\n
      \n
    • T (ndarray):\nTranspose of the array.
      • \n
    • data (buffer):\nThe array's elements, in memory.
      • \n
    • dtype (dtype object):\nDescribes the format of the elements in the array.
      • \n
    • flags (dict):\nDictionary containing information related to memory use, e.g.,\n'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc.
      • \n
    • flat (numpy.flatiter object):\nFlattened version of the array as an iterator.  The iterator\nallows assignments, e.g., x.flat = 3 (See ndarray.flat for\nassignment examples; TODO).
      • \n
    • imag (ndarray):\nImaginary part of the array.
      • \n
    • real (ndarray):\nReal part of the array.
      • \n
    • size (int):\nNumber of elements in the array.
      • \n
    • itemsize (int):\nThe memory use of each array element in bytes.
      • \n
    • nbytes (int):\nThe total number of bytes required to store the array data,\ni.e., itemsize * size.
      • \n
    • ndim (int):\nThe array's number of dimensions.
      • \n
    • shape (tuple of ints):\nShape of the array.
      • \n
    • strides (tuple of ints):\nThe step-size required to move from one element to the next in\nmemory. For example, a contiguous (3, 4) array of type\nint16 in C-order has strides (8, 2).  This implies that\nto move from element to element in memory requires jumps of 2 bytes.\nTo move from row-to-row, one needs to jump 8 bytes at a time\n(2 * 4).
      • \n
    • ctypes (ctypes object):\nClass containing properties of the array needed for interaction\nwith ctypes.
      • \n
    • base (ndarray):\nIf the array is a view into another array, that array is its base\n(unless that array is also a view).  The base array is where the\narray data is actually stored.
      • \n
    \n\n
    See Also
    \n\n
    array:  Construct an array. 
    \nzeros:  Create an array, each element of which is zero. 
    \nempty:  Create an array, but leave its allocated memory unchanged (i.e.,\nit contains \"garbage\"). 
    \ndtype:  Create a data-type. 
    \nnumpy.typing.NDArray:  An ndarray alias :term:generic <generic type>\nw.r.t. its dtype.type <numpy.dtype.type>.  
    \n\n
    Notes
    \n\n
    There are two modes of creating an array using __new__:
    \n\n
      \n
    1. If buffer is None, then only shape, dtype, and order\nare used.
      2. \n
    2. If buffer is an object exposing the buffer interface, then\nall keywords are interpreted.
      3. \n
    \n\n
    No __init__ method is needed because the array is fully initialized\nafter the __new__ method.
    \n\n
    Examples
    \n\n
    These examples illustrate the low-level ndarray constructor.  Refer\nto the See Also section above for easier ways of constructing an\nndarray.
    \n\n
    First mode, buffer is None:
    \n\n
    \n
    >>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n       [     nan, 2.5e-323]])\n
    \n
    \n\n
    Second mode:
    \n\n
    \n
    >>> np.ndarray((2,), buffer=np.array([1,2,3]),\n...            offset=np.int_().itemsize,\n...            dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n
    \n
    \n", "bases": "numpy.ndarray"}, "pyerrors.input.hadrons.Npr_matrix.g5H": {"fullname": "pyerrors.input.hadrons.Npr_matrix.g5H", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.g5H", "kind": "variable", "doc": "
    Gamma_5 hermitean conjugate
    \n\n
    Uses the fact that the propagator is gamma5 hermitean, so just the\nin and out momenta of the propagator are exchanged.
    \n"}, "pyerrors.input.hadrons.read_ExternalLeg_hd5": {"fullname": "pyerrors.input.hadrons.read_ExternalLeg_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_ExternalLeg_hd5", "kind": "function", "doc": "
    Read hadrons ExternalLeg hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (Npr_matrix):\nread Cobs-matrix
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.read_Bilinear_hd5": {"fullname": "pyerrors.input.hadrons.read_Bilinear_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Bilinear_hd5", "kind": "function", "doc": "
    Read hadrons Bilinear hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result_dict (dict[Npr_matrix]):\nextracted Bilinears
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.read_Fourquark_hd5": {"fullname": "pyerrors.input.hadrons.read_Fourquark_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Fourquark_hd5", "kind": "function", "doc": "
    Read hadrons FourquarkFullyConnected hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    • vertices (list):\nVertex functions to be extracted.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result_dict (dict):\nextracted fourquark matrizes
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None, vertices=['VA', 'AV']):", "funcdef": "def"}, "pyerrors.input.json": {"fullname": "pyerrors.input.json", "modulename": "pyerrors.input.json", "kind": "module", "doc": "
    \n"}, "pyerrors.input.json.create_json_string": {"fullname": "pyerrors.input.json.create_json_string", "modulename": "pyerrors.input.json", "qualname": "create_json_string", "kind": "function", "doc": "
    Generate the string for the export of a list of Obs or structures containing Obs\nto a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • json_string (str):\nString for export to .json(.gz) file
      • \n
    \n", "signature": "(ol, description='', indent=1):", "funcdef": "def"}, "pyerrors.input.json.dump_to_json": {"fullname": "pyerrors.input.json.dump_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_to_json", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • Null
      • \n
    \n", "signature": "(ol, fname, description='', indent=1, gz=True):", "funcdef": "def"}, "pyerrors.input.json.import_json_string": {"fullname": "pyerrors.input.json.import_json_string", "modulename": "pyerrors.input.json", "qualname": "import_json_string", "kind": "function", "doc": "
    Reconstruct a list of Obs or structures containing Obs from a json string.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
    \n\n
    Parameters
    \n\n
      \n
    • json_string (str):\njson string containing the data.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (list[Obs]):\nreconstructed list of observables from the json string
      • \n
    • or
      • \n
    • result (Obs):\nonly one observable if the list only has one entry
      • \n
    • or
      • \n
    • result (dict):\nif full_output=True
      • \n
    \n", "signature": "(json_string, verbose=True, full_output=False):", "funcdef": "def"}, "pyerrors.input.json.load_json": {"fullname": "pyerrors.input.json.load_json", "modulename": "pyerrors.input.json", "qualname": "load_json", "kind": "function", "doc": "
    Import a list of Obs or structures containing Obs from a .json(.gz) file.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (list[Obs]):\nreconstructed list of observables from the json string
      • \n
    • or
      • \n
    • result (Obs):\nonly one observable if the list only has one entry
      • \n
    • or
      • \n
    • result (dict):\nif full_output=True
      • \n
    \n", "signature": "(fname, verbose=True, gz=True, full_output=False):", "funcdef": "def"}, "pyerrors.input.json.dump_dict_to_json": {"fullname": "pyerrors.input.json.dump_dict_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_dict_to_json", "kind": "function", "doc": "
    Export a dict of Obs or structures containing Obs to a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • od (dict):\nDict of JSON valid structures and objects that will be exported.\nAt the moment, these objects can be either of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    • reps (str):\nSpecify the structure of the placeholder in exported dict to be reps[0-9]+.
      • \n
    • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(od, fname, description='', indent=1, reps='DICTOBS', gz=True):", "funcdef": "def"}, "pyerrors.input.json.load_json_dict": {"fullname": "pyerrors.input.json.load_json_dict", "modulename": "pyerrors.input.json", "qualname": "load_json_dict", "kind": "function", "doc": "
    Import a dict of Obs or structures containing Obs from a .json(.gz) file.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    • reps (str):\nSpecify the structure of the placeholder in imported dict to be reps[0-9]+.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • data (Obs / list / Corr):\nRead data
      • \n
    • or
      • \n
    • data (dict):\nRead data and meta-data
      • \n
    \n", "signature": "(fname, verbose=True, gz=True, full_output=False, reps='DICTOBS'):", "funcdef": "def"}, "pyerrors.input.misc": {"fullname": "pyerrors.input.misc", "modulename": "pyerrors.input.misc", "kind": "module", "doc": "
    \n"}, "pyerrors.input.misc.fit_t0": {"fullname": "pyerrors.input.misc.fit_t0", "modulename": "pyerrors.input.misc", "qualname": "fit_t0", "kind": "function", "doc": "
    \n", "signature": "(t2E_dict, fit_range, plot_fit=False):", "funcdef": "def"}, "pyerrors.input.misc.read_pbp": {"fullname": "pyerrors.input.misc.read_pbp", "modulename": "pyerrors.input.misc", "qualname": "read_pbp", "kind": "function", "doc": "
    Read pbp format from given folder structure.
    \n\n
    Parameters
    \n\n
      \n
    • r_start (list):\nlist which contains the first config to be read for each replicum
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (list[Obs]):\nlist of observables read
      • \n
    \n", "signature": "(path, prefix, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD": {"fullname": "pyerrors.input.openQCD", "modulename": "pyerrors.input.openQCD", "kind": "module", "doc": "
    \n"}, "pyerrors.input.openQCD.read_rwms": {"fullname": "pyerrors.input.openQCD.read_rwms", "modulename": "pyerrors.input.openQCD", "qualname": "read_rwms", "kind": "function", "doc": "
    Read rwms format from given folder structure. Returns a list of length nrw
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath that contains the data files
      • \n
    • prefix (str):\nall files in path that start with prefix are considered as input files.\nMay be used together postfix to consider only special file endings.\nPrefix is ignored, if the keyword 'files' is used.
      • \n
    • version (str):\nversion of openQCD, default 2.0
      • \n
    • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum
      • \n
    • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
      • \n
    • postfix (str):\npostfix of the file to read, e.g. '.ms1' for openQCD-files
      • \n
    • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
      • \n
    • print_err (bool):\nPrint additional information that is useful for debugging.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • rwms (Obs):\nReweighting factors read
      • \n
    \n", "signature": "(path, prefix, version='2.0', names=None, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.extract_t0": {"fullname": "pyerrors.input.openQCD.extract_t0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_t0", "kind": "function", "doc": "
    Extract t0 from given .ms.dat files. Returns t0 as Obs.
    \n\n
    It is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t^2 - 0.3\nis fitted with a linear function\nfrom which the exact root is extracted.
    \n\n
    It is assumed that one measurement is performed for each config.\nIf this is not the case, the resulting idl, as well as the handling\nof r_start, r_stop and r_step is wrong and the user has to correct\nthis in the resulting observable.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nPath to .ms.dat files
      • \n
    • prefix (str):\nEnsemble prefix
      • \n
    • dtr_read (int):\nDetermines how many trajectories should be skipped\nwhen reading the ms.dat files.\nCorresponds to dtr_cnfg / dtr_ms in the openQCD input file.
      • \n
    • xmin (int):\nFirst timeslice where the boundary\neffects have sufficiently decayed.
      • \n
    • spatial_extent (int):\nspatial extent of the lattice, required for normalization.
      • \n
    • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
      • \n
    • postfix (str):\nPostfix of measurement file (Default: ms)
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
      • \n
    • plaquette (bool):\nIf true extract the plaquette estimate of t0 instead.
      • \n
    • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
      • \n
    • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
      • \n
    • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.
      • \n
    • assume_thermalization (bool):\nIf True: If the first record divided by the distance between two measurements is larger than\n1, it is assumed that this is due to thermalization and the first measurement belongs\nto the first config (default).\nIf False: The config numbers are assumed to be traj_number // difference
      • \n
    \n\n
    Returns
    \n\n
      \n
    • t0 (Obs):\nExtracted t0
      • \n
    \n", "signature": "(\tpath,\tprefix,\tdtr_read,\txmin,\tspatial_extent,\tfit_range=5,\tpostfix='ms',\t**kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop": {"fullname": "pyerrors.input.openQCD.read_qtop", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop", "kind": "function", "doc": "
    Read the topologial charge based on openQCD gradient flow measurements.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • version (str):\nEither openQCD or sfqcd, depending on the data.
      • \n
    • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • postfix (str):\npostfix of the file to read, e.g. '.gfms.dat' for openQCD-files
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
      • \n
    • integer_charge (bool):\nIf True, the charge is rounded towards the nearest integer on each config.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (Obs):\nRead topological charge
      • \n
    \n", "signature": "(path, prefix, c, dtr_cnfg=1, version='openQCD', **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_gf_coupling": {"fullname": "pyerrors.input.openQCD.read_gf_coupling", "modulename": "pyerrors.input.openQCD", "qualname": "read_gf_coupling", "kind": "function", "doc": "
    Read the gradient flow coupling based on sfqcd gradient flow measurements. See 1607.06423 for details.
    \n\n
    Note: The current implementation only works for c=0.3 and T=L. The definition of the coupling in 1607.06423 requires projection to topological charge zero which is not done within this function but has to be performed in a separate step.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.
      • \n
    • postfix (str):\npostfix of the file to read, e.g. '.gfms.dat' for openQCD-files
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for the coupling. If False, the Wilson flow is used.
      • \n
    \n", "signature": "(path, prefix, c, dtr_cnfg=1, Zeuthen_flow=True, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.qtop_projection": {"fullname": "pyerrors.input.openQCD.qtop_projection", "modulename": "pyerrors.input.openQCD", "qualname": "qtop_projection", "kind": "function", "doc": "
    Returns the projection to the topological charge sector defined by target.
    \n\n
    Parameters
    \n\n
      \n
    • path (Obs):\nTopological charge.
      • \n
    • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
      • \n
    \n\n
    Returns
    \n\n
      \n
    • reto (Obs):\nprojection to the topological charge sector defined by target
      • \n
    \n", "signature": "(qtop, target=0):", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop_sector": {"fullname": "pyerrors.input.openQCD.read_qtop_sector", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop_sector", "kind": "function", "doc": "
    Constructs reweighting factors to a specified topological sector.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L
      • \n
    • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of trajectories\nbetween two configs.\nif it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • version (str):\nversion string of the openQCD (sfqcd) version used to create\nthe ensemble. Default is 2.0. May also be set to sfqcd.
      • \n
    • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
      • \n
    • r_start (list):\noffset of the first ensemble, making it easier to match\nlater on with other Obs
      • \n
    • r_stop (list):\nlast configurations that need to be read (per replicum)
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • reto (Obs):\nprojection to the topological charge sector defined by target
      • \n
    \n", "signature": "(path, prefix, c, target=0, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_ms5_xsf": {"fullname": "pyerrors.input.openQCD.read_ms5_xsf", "modulename": "pyerrors.input.openQCD", "qualname": "read_ms5_xsf", "kind": "function", "doc": "
    Read data from files in the specified directory with the specified prefix and quark combination extension, and return a Corr object containing the data.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nThe directory to search for the files in.
      • \n
    • prefix (str):\nThe prefix to match the files against.
      • \n
    • qc (str):\nThe quark combination extension to match the files against.
      • \n
    • corr (str):\nThe correlator to extract data for.
      • \n
    • sep (str, optional):\nThe separator to use when parsing the replika names.
      • \n
    • **kwargs: Additional keyword arguments. The following keyword arguments are recognized:
      \n\n
        \n
      • names (List[str]): A list of names to use for the replicas.
        • \n
      • \n
    \n\n
    Returns
    \n\n
      \n
    • Corr: A complex valued Corr object containing the data read from the files. In case of boudary to bulk correlators.
      • \n
    • or
      • \n
    • CObs: A complex valued CObs object containing the data read from the files. In case of boudary to boundary correlators.
      • \n
    \n\n
    Raises
    \n\n
      \n
    • FileNotFoundError: If no files matching the specified prefix and quark combination extension are found in the specified directory.
      • \n
    • IOError: If there is an error reading a file.
      • \n
    • struct.error: If there is an error unpacking binary data.
      • \n
    \n", "signature": "(path, prefix, qc, corr, sep='r', **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas": {"fullname": "pyerrors.input.pandas", "modulename": "pyerrors.input.pandas", "kind": "module", "doc": "
    \n"}, "pyerrors.input.pandas.to_sql": {"fullname": "pyerrors.input.pandas.to_sql", "modulename": "pyerrors.input.pandas", "qualname": "to_sql", "kind": "function", "doc": "
    Write DataFrame including Obs or Corr valued columns to sqlite database.
    \n\n
    Parameters
    \n\n
      \n
    • df (pandas.DataFrame):\nDataframe to be written to the database.
      • \n
    • table_name (str):\nName of the table in the database.
      • \n
    • db (str):\nPath to the sqlite database.
      • \n
    • if exists (str):\nHow to behave if table already exists. Options 'fail', 'replace', 'append'.
      • \n
    • gz (bool):\nIf True the json strings are gzipped.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(df, table_name, db, if_exists='fail', gz=True, **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas.read_sql": {"fullname": "pyerrors.input.pandas.read_sql", "modulename": "pyerrors.input.pandas", "qualname": "read_sql", "kind": "function", "doc": "
    Execute SQL query on sqlite database and obtain DataFrame including Obs or Corr valued columns.
    \n\n
    Parameters
    \n\n
      \n
    • sql (str):\nSQL query to be executed.
      • \n
    • db (str):\nPath to the sqlite database.
      • \n
    • auto_gamma (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • data (pandas.DataFrame):\nDataframe with the content of the sqlite database.
      • \n
    \n", "signature": "(sql, db, auto_gamma=False, **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas.dump_df": {"fullname": "pyerrors.input.pandas.dump_df", "modulename": "pyerrors.input.pandas", "qualname": "dump_df", "kind": "function", "doc": "
    Exports a pandas DataFrame containing Obs valued columns to a (gzipped) csv file.
    \n\n
    Before making use of pandas to_csv functionality Obs objects are serialized via the standardized\njson format of pyerrors.
    \n\n
    Parameters
    \n\n
      \n
    • df (pandas.DataFrame):\nDataframe to be dumped to a file.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • gz (bool):\nIf True, the output is a gzipped csv file. If False, the output is a csv file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(df, fname, gz=True):", "funcdef": "def"}, "pyerrors.input.pandas.load_df": {"fullname": "pyerrors.input.pandas.load_df", "modulename": "pyerrors.input.pandas", "qualname": "load_df", "kind": "function", "doc": "
    Imports a pandas DataFrame from a csv.(gz) file in which Obs objects are serialized as json strings.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • auto_gamma (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • data (pandas.DataFrame):\nDataframe with the content of the sqlite database.
      • \n
    \n", "signature": "(fname, auto_gamma=False, gz=True):", "funcdef": "def"}, "pyerrors.input.sfcf": {"fullname": "pyerrors.input.sfcf", "modulename": "pyerrors.input.sfcf", "kind": "module", "doc": "
    \n"}, "pyerrors.input.sfcf.read_sfcf": {"fullname": "pyerrors.input.sfcf.read_sfcf", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf", "kind": "function", "doc": "
    Read sfcf files from given folder structure.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nPath to the sfcf files.
      • \n
    • prefix (str):\nPrefix of the sfcf files.
      • \n
    • name (str):\nName of the correlation function to read.
      • \n
    • quarks (str):\nLabel of the quarks used in the sfcf input file. e.g. \"quark quark\"\nfor version 0.0 this does NOT need to be given with the typical \" - \"\nthat is present in the output file,\nthis is done automatically for this version
      • \n
    • corr_type (str):\nType of correlation function to read. Can be\n
        \n
      • 'bi' for boundary-inner
        • \n
      • 'bb' for boundary-boundary
        • \n
      • 'bib' for boundary-inner-boundary
        • \n
      • \n
    • noffset (int):\nOffset of the source (only relevant when wavefunctions are used)
      • \n
    • wf (int):\nID of wave function
      • \n
    • wf2 (int):\nID of the second wavefunction\n(only relevant for boundary-to-boundary correlation functions)
      • \n
    • im (bool):\nif True, read imaginary instead of real part\nof the correlation function.
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
      • \n
    • ens_name (str):\nreplaces the name of the ensemble
      • \n
    • version (str):\nversion of SFCF, with which the measurement was done.\nif the compact output option (-c) was specified,\nappend a \"c\" to the version (e.g. \"1.0c\")\nif the append output option (-a) was specified,\nappend an \"a\" to the version
      • \n
    • cfg_separator (str):\nString that separates the ensemble identifier from the configuration number (default 'n').
      • \n
    • replica (list):\nlist of replica to be read, default is all
      • \n
    • files (list):\nlist of files to be read per replica, default is all.\nfor non-compact output format, hand the folders to be read here.
      • \n
    • check_configs (list[list[int]]):\nlist of list of supposed configs, eg. [range(1,1000)]\nfor one replicum with 1000 configs
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (list[Obs]):\nlist of Observables with length T, observable per timeslice.\nbb-type correlators have length 1.
      • \n
    \n", "signature": "(\tpath,\tprefix,\tname,\tquarks='.*',\tcorr_type='bi',\tnoffset=0,\twf=0,\twf2=0,\tversion='1.0c',\tcfg_separator='n',\tsilent=False,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.utils": {"fullname": "pyerrors.input.utils", "modulename": "pyerrors.input.utils", "kind": "module", "doc": "
    \n"}, "pyerrors.input.utils.sort_names": {"fullname": "pyerrors.input.utils.sort_names", "modulename": "pyerrors.input.utils", "qualname": "sort_names", "kind": "function", "doc": "
    Sorts a list of names of replika with searches for r and id in the replikum string.\nIf this search fails, a fallback method is used,\nwhere the strings are simply compared and the first diffeing numeral is used for differentiation.
    \n\n
    Parameters
    \n\n
      \n
    • ll (list):\nlist to sort
      • \n
    \n\n
    Returns
    \n\n
      \n
    • ll (list):\nsorted list
      • \n
    \n", "signature": "(ll):", "funcdef": "def"}, "pyerrors.input.utils.check_idl": {"fullname": "pyerrors.input.utils.check_idl", "modulename": "pyerrors.input.utils", "qualname": "check_idl", "kind": "function", "doc": "
    Checks if list of configurations is contained in an idl
    \n\n
    Parameters
    \n\n
      \n
    • idl (range or list):\nidl of the current replicum
      • \n
    • che (list):\nlist of configurations to be checked against
      • \n
    \n\n
    Returns
    \n\n
      \n
    • miss_str (str):\nstring with integers of which idls are missing
      • \n
    \n", "signature": "(idl, che):", "funcdef": "def"}, "pyerrors.linalg": {"fullname": "pyerrors.linalg", "modulename": "pyerrors.linalg", "kind": "module", "doc": "
    \n"}, "pyerrors.linalg.matmul": {"fullname": "pyerrors.linalg.matmul", "modulename": "pyerrors.linalg", "qualname": "matmul", "kind": "function", "doc": "
    Matrix multiply all operands.
    \n\n
    Parameters
    \n\n
      \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    • This implementation is faster compared to standard multiplication via the @ operator.
      • \n
    \n", "signature": "(*operands):", "funcdef": "def"}, "pyerrors.linalg.jack_matmul": {"fullname": "pyerrors.linalg.jack_matmul", "modulename": "pyerrors.linalg", "qualname": "jack_matmul", "kind": "function", "doc": "
    Matrix multiply both operands making use of the jackknife approximation.
    \n\n
    Parameters
    \n\n
      \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    • For large matrices this is considerably faster compared to matmul.
      • \n
    \n", "signature": "(*operands):", "funcdef": "def"}, "pyerrors.linalg.einsum": {"fullname": "pyerrors.linalg.einsum", "modulename": "pyerrors.linalg", "qualname": "einsum", "kind": "function", "doc": "
    Wrapper for numpy.einsum
    \n\n
    Parameters
    \n\n
      \n
    • subscripts (str):\nSubscripts for summation (see numpy documentation for details)
      • \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    \n", "signature": "(subscripts, *operands):", "funcdef": "def"}, "pyerrors.linalg.inv": {"fullname": "pyerrors.linalg.inv", "modulename": "pyerrors.linalg", "qualname": "inv", "kind": "function", "doc": "
    Inverse of Obs or CObs valued matrices.
    \n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.cholesky": {"fullname": "pyerrors.linalg.cholesky", "modulename": "pyerrors.linalg", "qualname": "cholesky", "kind": "function", "doc": "
    Cholesky decomposition of Obs valued matrices.
    \n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.det": {"fullname": "pyerrors.linalg.det", "modulename": "pyerrors.linalg", "qualname": "det", "kind": "function", "doc": "
    Determinant of Obs valued matrices.
    \n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.eigh": {"fullname": "pyerrors.linalg.eigh", "modulename": "pyerrors.linalg", "qualname": "eigh", "kind": "function", "doc": "
    Computes the eigenvalues and eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.eig": {"fullname": "pyerrors.linalg.eig", "modulename": "pyerrors.linalg", "qualname": "eig", "kind": "function", "doc": "
    Computes the eigenvalues of a given matrix of Obs according to np.linalg.eig.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.pinv": {"fullname": "pyerrors.linalg.pinv", "modulename": "pyerrors.linalg", "qualname": "pinv", "kind": "function", "doc": "
    Computes the Moore-Penrose pseudoinverse of a matrix of Obs.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.svd": {"fullname": "pyerrors.linalg.svd", "modulename": "pyerrors.linalg", "qualname": "svd", "kind": "function", "doc": "
    Computes the singular value decomposition of a matrix of Obs.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.misc": {"fullname": "pyerrors.misc", "modulename": "pyerrors.misc", "kind": "module", "doc": "
    \n"}, "pyerrors.misc.print_config": {"fullname": "pyerrors.misc.print_config", "modulename": "pyerrors.misc", "qualname": "print_config", "kind": "function", "doc": "
    Print information about version of python, pyerrors and dependencies.
    \n", "signature": "():", "funcdef": "def"}, "pyerrors.misc.errorbar": {"fullname": "pyerrors.misc.errorbar", "modulename": "pyerrors.misc", "qualname": "errorbar", "kind": "function", "doc": "
    pyerrors wrapper for the errorbars method of matplotlib
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nA list of x-values which can be Obs.
      • \n
    • y (list):\nA list of y-values which can be Obs.
      • \n
    • axes ((matplotlib.pyplot.axes)):\nThe axes to plot on. default is plt.
      • \n
    \n", "signature": "(\tx,\ty,\taxes=<module 'matplotlib.pyplot' from '/opt/hostedtoolcache/Python/3.10.11/x64/lib/python3.10/site-packages/matplotlib/pyplot.py'>,\t**kwargs):", "funcdef": "def"}, "pyerrors.misc.dump_object": {"fullname": "pyerrors.misc.dump_object", "modulename": "pyerrors.misc", "qualname": "dump_object", "kind": "function", "doc": "
    Dump object into pickle file.
    \n\n
    Parameters
    \n\n
      \n
    • obj (object):\nobject to be saved in the pickle file
      • \n
    • name (str):\nname of the file
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(obj, name, **kwargs):", "funcdef": "def"}, "pyerrors.misc.load_object": {"fullname": "pyerrors.misc.load_object", "modulename": "pyerrors.misc", "qualname": "load_object", "kind": "function", "doc": "
    Load object from pickle file.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the file
      • \n
    \n\n
    Returns
    \n\n
      \n
    • object (Obs):\nLoaded Object
      • \n
    \n", "signature": "(path):", "funcdef": "def"}, "pyerrors.misc.pseudo_Obs": {"fullname": "pyerrors.misc.pseudo_Obs", "modulename": "pyerrors.misc", "qualname": "pseudo_Obs", "kind": "function", "doc": "
    Generate an Obs object with given value, dvalue and name for test purposes
    \n\n
    Parameters
    \n\n
      \n
    • value (float):\ncentral value of the Obs to be generated.
      • \n
    • dvalue (float):\nerror of the Obs to be generated.
      • \n
    • name (str):\nname of the ensemble for which the Obs is to be generated.
      • \n
    • samples (int):\nnumber of samples for the Obs (default 1000).
      • \n
    \n\n
    Returns
    \n\n
      \n
    • res (Obs):\nGenerated Observable
      • \n
    \n", "signature": "(value, dvalue, name, samples=1000):", "funcdef": "def"}, "pyerrors.misc.gen_correlated_data": {"fullname": "pyerrors.misc.gen_correlated_data", "modulename": "pyerrors.misc", "qualname": "gen_correlated_data", "kind": "function", "doc": "
    Generate observables with given covariance and autocorrelation times.
    \n\n
    Parameters
    \n\n
      \n
    • means (list):\nlist containing the mean value of each observable.
      • \n
    • cov (numpy.ndarray):\ncovariance matrix for the data to be generated.
      • \n
    • name (str):\nensemble name for the data to be geneated.
      • \n
    • tau (float or list):\ncan either be a real number or a list with an entry for\nevery dataset.
      • \n
    • samples (int):\nnumber of samples to be generated for each observable.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • corr_obs (list[Obs]):\nGenerated observable list
      • \n
    \n", "signature": "(means, cov, name, tau=0.5, samples=1000):", "funcdef": "def"}, "pyerrors.mpm": {"fullname": "pyerrors.mpm", "modulename": "pyerrors.mpm", "kind": "module", "doc": "
    \n"}, "pyerrors.mpm.matrix_pencil_method": {"fullname": "pyerrors.mpm.matrix_pencil_method", "modulename": "pyerrors.mpm", "qualname": "matrix_pencil_method", "kind": "function", "doc": "
    Matrix pencil method to extract k energy levels from data
    \n\n
    Implementation of the matrix pencil method based on\neq. (2.17) of Y. Hua, T. K. Sarkar, IEEE Trans. Acoust. 38, 814-824 (1990)
    \n\n
    Parameters
    \n\n
      \n
    • data (list):\ncan be a list of Obs for the analysis of a single correlator, or a list of lists\nof Obs if several correlators are to analyzed at once.
      • \n
    • k (int):\nNumber of states to extract (default 1).
      • \n
    • p (int):\nmatrix pencil parameter which filters noise. The optimal value is expected between\nlen(data)/3 and 2*len(data)/3. The computation is more expensive the closer p is\nto len(data)/2 but could possibly suppress more noise (default len(data)//2).
      • \n
    \n\n
    Returns
    \n\n
      \n
    • energy_levels (list[Obs]):\nExtracted energy levels
      • \n
    \n", "signature": "(corrs, k=1, p=None, **kwargs):", "funcdef": "def"}, "pyerrors.obs": {"fullname": "pyerrors.obs", "modulename": "pyerrors.obs", "kind": "module", "doc": "
    \n"}, "pyerrors.obs.Obs": {"fullname": "pyerrors.obs.Obs", "modulename": "pyerrors.obs", "qualname": "Obs", "kind": "class", "doc": "
    Class for a general observable.
    \n\n
    Instances of Obs are the basic objects of a pyerrors error analysis.\nThey are initialized with a list which contains arrays of samples for\ndifferent ensembles/replica and another list of same length which contains\nthe names of the ensembles/replica. Mathematical operations can be\nperformed on instances. The result is another instance of Obs. The error of\nan instance can be computed with the gamma_method. Also contains additional\nmethods for output and visualization of the error calculation.
    \n\n
    Attributes
    \n\n
      \n
    • S_global (float):\nStandard value for S (default 2.0)
      • \n
    • S_dict (dict):\nDictionary for S values. If an entry for a given ensemble\nexists this overwrites the standard value for that ensemble.
      • \n
    • tau_exp_global (float):\nStandard value for tau_exp (default 0.0)
      • \n
    • tau_exp_dict (dict):\nDictionary for tau_exp values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
      • \n
    • N_sigma_global (float):\nStandard value for N_sigma (default 1.0)
      • \n
    • N_sigma_dict (dict):\nDictionary for N_sigma values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
      • \n
    \n"}, "pyerrors.obs.Obs.__init__": {"fullname": "pyerrors.obs.Obs.__init__", "modulename": "pyerrors.obs", "qualname": "Obs.__init__", "kind": "function", "doc": "
    Initialize Obs object.
    \n\n
    Parameters
    \n\n
      \n
    • samples (list):\nlist of numpy arrays containing the Monte Carlo samples
      • \n
    • names (list):\nlist of strings labeling the individual samples
      • \n
    • idl (list, optional):\nlist of ranges or lists on which the samples are defined
      • \n
    \n", "signature": "(samples, names, idl=None, **kwargs)"}, "pyerrors.obs.Obs.gamma_method": {"fullname": "pyerrors.obs.Obs.gamma_method", "modulename": "pyerrors.obs", "qualname": "Obs.gamma_method", "kind": "function", "doc": "
    Estimate the error and related properties of the Obs.
    \n\n
    Parameters
    \n\n
      \n
    • S (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.
      • \n
    • tau_exp (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).
      • \n
    • N_sigma (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).
      • \n
    • fft (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True)
      • \n
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.gm": {"fullname": "pyerrors.obs.Obs.gm", "modulename": "pyerrors.obs", "qualname": "Obs.gm", "kind": "function", "doc": "
    Estimate the error and related properties of the Obs.
    \n\n
    Parameters
    \n\n
      \n
    • S (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.
      • \n
    • tau_exp (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).
      • \n
    • N_sigma (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).
      • \n
    • fft (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True)
      • \n
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.details": {"fullname": "pyerrors.obs.Obs.details", "modulename": "pyerrors.obs", "qualname": "Obs.details", "kind": "function", "doc": "
    Output detailed properties of the Obs.
    \n\n
    Parameters
    \n\n
      \n
    • ens_content (bool):\nprint details about the ensembles and replica if true.
      • \n
    \n", "signature": "(self, ens_content=True):", "funcdef": "def"}, "pyerrors.obs.Obs.reweight": {"fullname": "pyerrors.obs.Obs.reweight", "modulename": "pyerrors.obs", "qualname": "Obs.reweight", "kind": "function", "doc": "
    Reweight the obs with given rewighting factors.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. Default False.
      • \n
    \n", "signature": "(self, weight):", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero_within_error": {"fullname": "pyerrors.obs.Obs.is_zero_within_error", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero_within_error", "kind": "function", "doc": "
    Checks whether the observable is zero within 'sigma' standard errors.
    \n\n
    Parameters
    \n\n
      \n
    • sigma (int):\nNumber of standard errors used for the check.
      • \n
    • Works only properly when the gamma method was run.
      • \n
    \n", "signature": "(self, sigma=1):", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero": {"fullname": "pyerrors.obs.Obs.is_zero", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero", "kind": "function", "doc": "
    Checks whether the observable is zero within a given tolerance.
    \n\n
    Parameters
    \n\n
      \n
    • atol (float):\nAbsolute tolerance (for details see numpy documentation).
      • \n
    \n", "signature": "(self, atol=1e-10):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_tauint": {"fullname": "pyerrors.obs.Obs.plot_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.plot_tauint", "kind": "function", "doc": "
    Plot integrated autocorrelation time for each ensemble.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rho": {"fullname": "pyerrors.obs.Obs.plot_rho", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rho", "kind": "function", "doc": "
    Plot normalized autocorrelation function time for each ensemble.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rep_dist": {"fullname": "pyerrors.obs.Obs.plot_rep_dist", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rep_dist", "kind": "function", "doc": "
    Plot replica distribution for each ensemble with more than one replicum.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_history": {"fullname": "pyerrors.obs.Obs.plot_history", "modulename": "pyerrors.obs", "qualname": "Obs.plot_history", "kind": "function", "doc": "
    Plot derived Monte Carlo history for each ensemble
    \n\n
    Parameters
    \n\n
      \n
    • expand (bool):\nshow expanded history for irregular Monte Carlo chains (default: True).
      • \n
    \n", "signature": "(self, expand=True):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_piechart": {"fullname": "pyerrors.obs.Obs.plot_piechart", "modulename": "pyerrors.obs", "qualname": "Obs.plot_piechart", "kind": "function", "doc": "
    Plot piechart which shows the fractional contribution of each\nensemble to the error and returns a dictionary containing the fractions.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.dump": {"fullname": "pyerrors.obs.Obs.dump", "modulename": "pyerrors.obs", "qualname": "Obs.dump", "kind": "function", "doc": "
    Dump the Obs to a file 'name' of chosen format.
    \n\n
    Parameters
    \n\n
      \n
    • filename (str):\nname of the file to be saved.
      • \n
    • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
      • \n
    • description (str):\nDescription for output file, only relevant for json.gz format.
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n", "signature": "(self, filename, datatype='json.gz', description='', **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.export_jackknife": {"fullname": "pyerrors.obs.Obs.export_jackknife", "modulename": "pyerrors.obs", "qualname": "Obs.export_jackknife", "kind": "function", "doc": "
    Export jackknife samples from the Obs
    \n\n
    Returns
    \n\n
      \n
    • numpy.ndarray: Returns a numpy array of length N + 1 where N is the number of samples\nfor the given ensemble and replicum. The zeroth entry of the array contains\nthe mean value of the Obs, entries 1 to N contain the N jackknife samples\nderived from the Obs. The current implementation only works for observables\ndefined on exactly one ensemble and replicum. The derived jackknife samples\nshould agree with samples from a full jackknife analysis up to O(1/N).
      • \n
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.sqrt": {"fullname": "pyerrors.obs.Obs.sqrt", "modulename": "pyerrors.obs", "qualname": "Obs.sqrt", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.log": {"fullname": "pyerrors.obs.Obs.log", "modulename": "pyerrors.obs", "qualname": "Obs.log", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.exp": {"fullname": "pyerrors.obs.Obs.exp", "modulename": "pyerrors.obs", "qualname": "Obs.exp", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.sin": {"fullname": "pyerrors.obs.Obs.sin", "modulename": "pyerrors.obs", "qualname": "Obs.sin", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.cos": {"fullname": "pyerrors.obs.Obs.cos", "modulename": "pyerrors.obs", "qualname": "Obs.cos", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.tan": {"fullname": "pyerrors.obs.Obs.tan", "modulename": "pyerrors.obs", "qualname": "Obs.tan", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arcsin": {"fullname": "pyerrors.obs.Obs.arcsin", "modulename": "pyerrors.obs", "qualname": "Obs.arcsin", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arccos": {"fullname": "pyerrors.obs.Obs.arccos", "modulename": "pyerrors.obs", "qualname": "Obs.arccos", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arctan": {"fullname": "pyerrors.obs.Obs.arctan", "modulename": "pyerrors.obs", "qualname": "Obs.arctan", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.sinh": {"fullname": "pyerrors.obs.Obs.sinh", "modulename": "pyerrors.obs", "qualname": "Obs.sinh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.cosh": {"fullname": "pyerrors.obs.Obs.cosh", "modulename": "pyerrors.obs", "qualname": "Obs.cosh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.tanh": {"fullname": "pyerrors.obs.Obs.tanh", "modulename": "pyerrors.obs", "qualname": "Obs.tanh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arcsinh": {"fullname": "pyerrors.obs.Obs.arcsinh", "modulename": "pyerrors.obs", "qualname": "Obs.arcsinh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arccosh": {"fullname": "pyerrors.obs.Obs.arccosh", "modulename": "pyerrors.obs", "qualname": "Obs.arccosh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arctanh": {"fullname": "pyerrors.obs.Obs.arctanh", "modulename": "pyerrors.obs", "qualname": "Obs.arctanh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.CObs": {"fullname": "pyerrors.obs.CObs", "modulename": "pyerrors.obs", "qualname": "CObs", "kind": "class", "doc": "
    Class for a complex valued observable.
    \n"}, "pyerrors.obs.CObs.__init__": {"fullname": "pyerrors.obs.CObs.__init__", "modulename": "pyerrors.obs", "qualname": "CObs.__init__", "kind": "function", "doc": "
    \n", "signature": "(real, imag=0.0)"}, "pyerrors.obs.CObs.gamma_method": {"fullname": "pyerrors.obs.CObs.gamma_method", "modulename": "pyerrors.obs", "qualname": "CObs.gamma_method", "kind": "function", "doc": "
    Executes the gamma_method for the real and the imaginary part.
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.CObs.is_zero": {"fullname": "pyerrors.obs.CObs.is_zero", "modulename": "pyerrors.obs", "qualname": "CObs.is_zero", "kind": "function", "doc": "
    Checks whether both real and imaginary part are zero within machine precision.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.CObs.conjugate": {"fullname": "pyerrors.obs.CObs.conjugate", "modulename": "pyerrors.obs", "qualname": "CObs.conjugate", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.derived_observable": {"fullname": "pyerrors.obs.derived_observable", "modulename": "pyerrors.obs", "qualname": "derived_observable", "kind": "function", "doc": "
    Construct a derived Obs according to func(data, **kwargs) using automatic differentiation.
    \n\n
    Parameters
    \n\n
      \n
    • func (object):\narbitrary function of the form func(data, **kwargs). For the\nautomatic differentiation to work, all numpy functions have to have\nthe autograd wrapper (use 'import autograd.numpy as anp').
      • \n
    • data (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
      • \n
    • num_grad (bool):\nif True, numerical derivatives are used instead of autograd\n(default False). To control the numerical differentiation the\nkwargs of numdifftools.step_generators.MaxStepGenerator\ncan be used.
      • \n
    • man_grad (list):\nmanually supply a list or an array which contains the jacobian\nof func. Use cautiously, supplying the wrong derivative will\nnot be intercepted.
      • \n
    \n\n
    Notes
    \n\n
    For simple mathematical operations it can be practical to use anonymous\nfunctions. For the ratio of two observables one can e.g. use
    \n\n
    new_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2])
    \n", "signature": "(func, data, array_mode=False, **kwargs):", "funcdef": "def"}, "pyerrors.obs.reweight": {"fullname": "pyerrors.obs.reweight", "modulename": "pyerrors.obs", "qualname": "reweight", "kind": "function", "doc": "
    Reweight a list of observables.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • obs (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. Default False.
      • \n
    \n", "signature": "(weight, obs, **kwargs):", "funcdef": "def"}, "pyerrors.obs.correlate": {"fullname": "pyerrors.obs.correlate", "modulename": "pyerrors.obs", "qualname": "correlate", "kind": "function", "doc": "
    Correlate two observables.
    \n\n
    Parameters
    \n\n
      \n
    • obs_a (Obs):\nFirst observable
      • \n
    • obs_b (Obs):\nSecond observable
      • \n
    \n\n
    Notes
    \n\n
    Keep in mind to only correlate primary observables which have not been reweighted\nyet. The reweighting has to be applied after correlating the observables.\nCurrently only works if ensembles are identical (this is not strictly necessary).
    \n", "signature": "(obs_a, obs_b):", "funcdef": "def"}, "pyerrors.obs.covariance": {"fullname": "pyerrors.obs.covariance", "modulename": "pyerrors.obs", "qualname": "covariance", "kind": "function", "doc": "
    Calculates the error covariance matrix of a set of observables.
    \n\n
    WARNING: This function should be used with care, especially for observables with support on multiple\n         ensembles with differing autocorrelations. See the notes below for details.
    \n\n
    The gamma method has to be applied first to all observables.
    \n\n
    Parameters
    \n\n
      \n
    • obs (list or numpy.ndarray):\nList or one dimensional array of Obs
      • \n
    • visualize (bool):\nIf True plots the corresponding normalized correlation matrix (default False).
      • \n
    • correlation (bool):\nIf True the correlation matrix instead of the error covariance matrix is returned (default False).
      • \n
    • smooth (None or int):\nIf smooth is an integer 'E' between 2 and the dimension of the matrix minus 1 the eigenvalue\nsmoothing procedure of hep-lat/9412087 is applied to the correlation matrix which leaves the\nlargest E eigenvalues essentially unchanged and smoothes the smaller eigenvalues to avoid extremely\nsmall ones.
      • \n
    \n\n
    Notes
    \n\n
    The error covariance is defined such that it agrees with the squared standard error for two identical observables\n$$\\operatorname{cov}(a,a)=\\sum_{s=1}^N\\delta_a^s\\delta_a^s/N^2=\\Gamma_{aa}(0)/N=\\operatorname{var}(a)/N=\\sigma_a^2$$\nin the absence of autocorrelation.\nThe error covariance is estimated by calculating the correlation matrix assuming no autocorrelation and then rescaling the correlation matrix by the full errors including the previous gamma method estimate for the autocorrelation of the observables. The covariance at windowsize 0 is guaranteed to be positive semi-definite\n$$\\sum_{i,j}v_i\\Gamma_{ij}(0)v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i,j}v_i\\delta_i^s\\delta_j^s v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i}|v_i\\delta_i^s|^2\\geq 0\\,,$$ for every $v\\in\\mathbb{R}^M$, while such an identity does not hold for larger windows/lags.\nFor observables defined on a single ensemble our approximation is equivalent to assuming that the integrated autocorrelation time of an off-diagonal element is equal to the geometric mean of the integrated autocorrelation times of the corresponding diagonal elements.\n$$\\tau_{\\mathrm{int}, ij}=\\sqrt{\\tau_{\\mathrm{int}, i}\\times \\tau_{\\mathrm{int}, j}}$$\nThis construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors).
    \n", "signature": "(obs, visualize=False, correlation=False, smooth=None, **kwargs):", "funcdef": "def"}, "pyerrors.obs.import_jackknife": {"fullname": "pyerrors.obs.import_jackknife", "modulename": "pyerrors.obs", "qualname": "import_jackknife", "kind": "function", "doc": "
    Imports jackknife samples and returns an Obs
    \n\n
    Parameters
    \n\n
      \n
    • jacks (numpy.ndarray):\nnumpy array containing the mean value as zeroth entry and\nthe N jackknife samples as first to Nth entry.
      • \n
    • name (str):\nname of the ensemble the samples are defined on.
      • \n
    \n", "signature": "(jacks, name, idl=None):", "funcdef": "def"}, "pyerrors.obs.merge_obs": {"fullname": "pyerrors.obs.merge_obs", "modulename": "pyerrors.obs", "qualname": "merge_obs", "kind": "function", "doc": "
    Combine all observables in list_of_obs into one new observable
    \n\n
    Parameters
    \n\n
      \n
    • list_of_obs (list):\nlist of the Obs object to be combined
      • \n
    \n\n
    Notes
    \n\n
    It is not possible to combine obs which are based on the same replicum
    \n", "signature": "(list_of_obs):", "funcdef": "def"}, "pyerrors.obs.cov_Obs": {"fullname": "pyerrors.obs.cov_Obs", "modulename": "pyerrors.obs", "qualname": "cov_Obs", "kind": "function", "doc": "
    Create an Obs based on mean(s) and a covariance matrix
    \n\n
    Parameters
    \n\n
      \n
    • mean (list of floats or float):\nN mean value(s) of the new Obs
      • \n
    • cov (list or array):\n2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariance
      • \n
    • name (str):\nidentifier for the covariance matrix
      • \n
    • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
      • \n
    \n", "signature": "(means, cov, name, grad=None):", "funcdef": "def"}, "pyerrors.roots": {"fullname": "pyerrors.roots", "modulename": "pyerrors.roots", "kind": "module", "doc": "
    \n"}, "pyerrors.roots.find_root": {"fullname": "pyerrors.roots.find_root", "modulename": "pyerrors.roots", "qualname": "find_root", "kind": "function", "doc": "
    Finds the root of the function func(x, d) where d is an Obs.
    \n\n
    Parameters
    \n\n
      \n
    • d (Obs):\nObs passed to the function.
      • \n
    • func (object):\nFunction to be minimized. Any numpy functions have to use the autograd.numpy wrapper.\nExample:
      \n\n
      \n
      import autograd.numpy as anp\ndef root_func(x, d):\n   return anp.exp(-x ** 2) - d\n
      \n
      • \n
    • guess (float):\nInitial guess for the minimization.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • res (Obs):\nObs valued root of the function.
      • \n
    \n", "signature": "(d, func, guess=1.0, **kwargs):", "funcdef": "def"}, "pyerrors.version": {"fullname": "pyerrors.version", "modulename": "pyerrors.version", "kind": "module", "doc": "
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    What is pyerrors?
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    \n\n
      \n
    • automatic differentiation for exact linear error propagation as suggested in arXiv:1809.01289 (partly based on the autograd package).
      • \n
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      • \n
    • coherent error propagation for data from different Markov chains.
      • \n
    • non-linear fits with x- and y-errors and exact linear error propagation based on automatic differentiation as introduced in arXiv:1809.01289.
      • \n
    • real and complex matrix operations and their error propagation based on automatic differentiation (Matrix inverse, Cholesky decomposition, calculation of eigenvalues and eigenvectors, singular value decomposition...).
      • \n
    \n\n
    More detailed examples can found in the GitHub repository \"badge\".
    \n\n
    If you use pyerrors for research that leads to a publication please consider citing:
    \n\n
      \n
    • Fabian Joswig, Simon Kuberski, Justus T. Kuhlmann, Jan Neuendorf, pyerrors: a python framework for error analysis of Monte Carlo data. Comput.Phys.Commun. 288 (2023) 108750.
      • \n
    • Ulli Wolff, Monte Carlo errors with less errors. Comput.Phys.Commun. 156 (2004) 143-153, Comput.Phys.Commun. 176 (2007) 383 (erratum).
      • \n
    • Alberto Ramos, Automatic differentiation for error analysis of Monte Carlo data. Comput.Phys.Commun. 238 (2019) 19-35.
      • \n
    \n\n
    and
    \n\n
      \n
    • Stefan Schaefer, Rainer Sommer, Francesco Virotta, Critical slowing down and error analysis in lattice QCD simulations. Nucl.Phys.B 845 (2011) 93-119.
      • \n
    \n\n
    where applicable.
    \n\n
    There exist similar publicly available implementations of gamma method error analysis suites in Fortran, Julia and Python.
    \n\n
    Installation
    \n\n
    Install the most recent release using pip and pypi:
    \n\n
    \n
    pip install pyerrors     # Fresh install\npip install -U pyerrors  # Update\n
    \n
    \n\n
    Install the most recent release using conda and conda-forge:
    \n\n
    \n
    conda install -c conda-forge pyerrors  # Fresh install\nconda update -c conda-forge pyerrors   # Update\n
    \n
    \n\n
    Install the current develop version:
    \n\n
    \n
    pip install git+https://github.com/fjosw/pyerrors.git@develop\n
    \n
    \n\n
    Basic example
    \n\n
    \n
    import numpy as np\nimport pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name']) # Initialize an Obs object\nmy_new_obs = 2 * np.log(my_obs) / my_obs ** 2 # Construct derived Obs object\nmy_new_obs.gamma_method()                     # Estimate the statistical error\nprint(my_new_obs)                             # Print the result to stdout\n> 0.31498(72)\n
    \n
    \n\n
    The Obs class
    \n\n
    pyerrors introduces a new datatype, Obs, which simplifies error propagation and estimation for auto- and cross-correlated data.\nAn Obs object can be initialized with two arguments, the first is a list containing the samples for an observable from a Monte Carlo chain.\nThe samples can either be provided as python list or as numpy array.\nThe second argument is a list containing the names of the respective Monte Carlo chains as strings. These strings uniquely identify a Monte Carlo chain/ensemble. It is crucial for the correct error propagation that observations from the same Monte Carlo history are labeled with the same name. See Multiple ensembles/replica for details.
    \n\n
    \n
    import pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name'])\n
    \n
    \n\n
    Error propagation
    \n\n
    When performing mathematical operations on Obs objects the correct error propagation is intrinsically taken care of using a first order Taylor expansion\n$$\\delta_f^i=\\sum_\\alpha \\bar{f}_\\alpha \\delta_\\alpha^i\\,,\\quad \\delta_\\alpha^i=a_\\alpha^i-\\bar{a}_\\alpha\\,,$$\nas introduced in arXiv:hep-lat/0306017.\nThe required derivatives $\\bar{f}_\\alpha$ are evaluated up to machine precision via automatic differentiation as suggested in arXiv:1809.01289.
    \n\n
    The Obs class is designed such that mathematical numpy functions can be used on Obs just as for regular floats.
    \n\n
    \n
    import numpy as np\nimport pyerrors as pe\n\nmy_obs1 = pe.Obs([samples1], ['ensemble_name'])\nmy_obs2 = pe.Obs([samples2], ['ensemble_name'])\n\nmy_sum = my_obs1 + my_obs2\n\nmy_m_eff = np.log(my_obs1 / my_obs2)\n\niamzero = my_m_eff - my_m_eff\n# Check that value and fluctuations are zero within machine precision\nprint(iamzero == 0.0)\n> True\n
    \n
    \n\n
    Error estimation
    \n\n
    The error estimation within pyerrors is based on the gamma method introduced in arXiv:hep-lat/0306017.\nAfter having arrived at the derived quantity of interest the gamma_method can be called as detailed in the following example.
    \n\n
    \n
    my_sum.gamma_method()\nprint(my_sum)\n> 1.70(57)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 5.72046658e-01 +/- 7.56746598e-02 (33.650%)\n>  t_int         2.71422900e+00 +/- 6.40320983e-01 S = 2.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n
    \n\n
    We use the following definition of the integrated autocorrelation time established in Madras & Sokal 1988\n$$\\tau_\\mathrm{int}=\\frac{1}{2}+\\sum_{t=1}^{W}\\rho(t)\\geq \\frac{1}{2}\\,.$$\nThe window $W$ is determined via the automatic windowing procedure described in arXiv:hep-lat/0306017.\nThe standard value for the parameter $S$ of this automatic windowing procedure is $S=2$. Other values for $S$ can be passed to the gamma_method as parameter.
    \n\n
    \n
    my_sum.gamma_method(S=3.0)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.30675201e-01 +/- 1.04585650e-01 (37.099%)\n>  t_int         3.29909703e+00 +/- 9.77310102e-01 S = 3.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n
    \n\n
    The integrated autocorrelation time $\\tau_\\mathrm{int}$ and the autocorrelation function $\\rho(W)$ can be monitored via the methods pyerrors.obs.Obs.plot_tauint and pyerrors.obs.Obs.plot_rho.
    \n\n
    If the parameter $S$ is set to zero it is assumed that the dataset does not exhibit any autocorrelation and the window size is chosen to be zero.\nIn this case the error estimate is identical to the sample standard error.
    \n\n
    Exponential tails
    \n\n
    Slow modes in the Monte Carlo history can be accounted for by attaching an exponential tail to the autocorrelation function $\\rho$ as suggested in arXiv:1009.5228. The longest autocorrelation time in the history, $\\tau_\\mathrm{exp}$, can be passed to the gamma_method as parameter. In this case the automatic windowing procedure is vacated and the parameter $S$ does not affect the error estimate.
    \n\n
    \n
    my_sum.gamma_method(tau_exp=7.2)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.28097762e-01 +/- 5.79077524e-02 (36.947%)\n>  t_int         3.27218667e+00 +/- 7.99583654e-01 tau_exp = 7.20,  N_sigma = 1\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n
    \n\n
    For the full API see pyerrors.obs.Obs.gamma_method.
    \n\n
    Multiple ensembles/replica
    \n\n
    Error propagation for multiple ensembles (Markov chains with different simulation parameters) is handled automatically. Ensembles are uniquely identified by their name.
    \n\n
    \n
    obs1 = pe.Obs([samples1], ['ensemble1'])\nobs2 = pe.Obs([samples2], ['ensemble2'])\n\nmy_sum = obs1 + obs2\nmy_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 2 ensembles:\n>   \u00b7 Ensemble 'ensemble1' : 1000 configurations (from 1 to 1000)\n>   \u00b7 Ensemble 'ensemble2' : 500 configurations (from 1 to 500)\n
    \n
    \n\n
    Observables from the same Monte Carlo chain have to be initialized with the same name for correct error propagation. If different names were used in this case the data would be treated as statistically independent resulting in loss of relevant information and a potential over or under estimate of the statistical error.
    \n\n
    pyerrors identifies multiple replica (independent Markov chains with identical simulation parameters) by the vertical bar | in the name of the data set.
    \n\n
    \n
    obs1 = pe.Obs([samples1], ['ensemble1|r01'])\nobs2 = pe.Obs([samples2], ['ensemble1|r02'])\n\n> my_sum = obs1 + obs2\n> my_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1'\n>     \u00b7 Replicum 'r01' : 1000 configurations (from 1 to 1000)\n>     \u00b7 Replicum 'r02' : 500 configurations (from 1 to 500)\n
    \n
    \n\n
    Error estimation for multiple ensembles
    \n\n
    In order to keep track of different error analysis parameters for different ensembles one can make use of global dictionaries as detailed in the following example.
    \n\n
    \n
    pe.Obs.S_dict['ensemble1'] = 2.5\npe.Obs.tau_exp_dict['ensemble2'] = 8.0\npe.Obs.tau_exp_dict['ensemble3'] = 2.0\n
    \n
    \n\n
    In case the gamma_method is called without any parameters it will use the values specified in the dictionaries for the respective ensembles.\nPassing arguments to the gamma_method still dominates over the dictionaries.
    \n\n
    Irregular Monte Carlo chains
    \n\n
    Obs objects defined on irregular Monte Carlo chains can be initialized with the parameter idl.
    \n\n
    \n
    # Observable defined on configurations 20 to 519\nobs1 = pe.Obs([samples1], ['ensemble1'], idl=[range(20, 520)])\nobs1.details()\n> Result         9.98319881e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 20 to 519)\n\n# Observable defined on every second configuration between 5 and 1003\nobs2 = pe.Obs([samples2], ['ensemble1'], idl=[range(5, 1005, 2)])\nobs2.details()\n> Result         9.99100712e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 5 to 1003 in steps of 2)\n\n# Observable defined on configurations 2, 9, 28, 29 and 501\nobs3 = pe.Obs([samples3], ['ensemble1'], idl=[[2, 9, 28, 29, 501]])\nobs3.details()\n> Result         1.01718064e+00\n> 5 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 5 configurations (irregular range)\n
    \n
    \n\n
    Obs objects defined on regular and irregular histories of the same ensemble can be combined with each other and the correct error propagation and estimation is automatically taken care of.
    \n\n
    Warning: Irregular Monte Carlo chains can result in odd patterns in the autocorrelation functions.\nMake sure to check the autocorrelation time with e.g. pyerrors.obs.Obs.plot_rho or pyerrors.obs.Obs.plot_tauint.
    \n\n
    For the full API see pyerrors.obs.Obs.
    \n\n
    Correlators
    \n\n
    When one is not interested in single observables but correlation functions, pyerrors offers the Corr class which simplifies the corresponding error propagation and provides the user with a set of standard methods. In order to initialize a Corr objects one needs to arrange the data as a list of Obs
    \n\n
    \n
    my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0      0.7957(80)\n> 1      0.5156(51)\n> 2      0.3227(33)\n> 3      0.2041(21)\n
    \n
    \n\n
    In case the correlation functions are not defined on the outermost timeslices, for example because of fixed boundary conditions, a padding can be introduced.
    \n\n
    \n
    my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3], padding=[1, 1])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0\n> 1      0.7957(80)\n> 2      0.5156(51)\n> 3      0.3227(33)\n> 4      0.2041(21)\n> 5\n
    \n
    \n\n
    The individual entries of a correlator can be accessed via slicing
    \n\n
    \n
    print(my_corr[3])\n> 0.3227(33)\n
    \n
    \n\n
    Error propagation with the Corr class works very similar to Obs objects. Mathematical operations are overloaded and Corr objects can be computed together with other Corr objects, Obs objects or real numbers and integers.
    \n\n
    \n
    my_new_corr = 0.3 * my_corr[2] * my_corr * my_corr + 12 / my_corr\n
    \n
    \n\n
    pyerrors provides the user with a set of regularly used methods for the manipulation of correlator objects:
    \n\n
      \n
    • Corr.gamma_method applies the gamma method to all entries of the correlator.
      • \n
    • Corr.m_eff to construct effective masses. Various variants for periodic and fixed temporal boundary conditions are available.
      • \n
    • Corr.deriv returns the first derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
      • \n
    • Corr.second_deriv returns the second derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
      • \n
    • Corr.symmetric symmetrizes parity even correlations functions, assuming periodic boundary conditions.
      • \n
    • Corr.anti_symmetric anti-symmetrizes parity odd correlations functions, assuming periodic boundary conditions.
      • \n
    • Corr.T_symmetry averages a correlator with its time symmetry partner, assuming fixed boundary conditions.
      • \n
    • Corr.plateau extracts a plateau value from the correlator in a given range.
      • \n
    • Corr.roll periodically shifts the correlator.
      • \n
    • Corr.reverse reverses the time ordering of the correlator.
      • \n
    • Corr.correlate constructs a disconnected correlation function from the correlator and another Corr or Obs object.
      • \n
    • Corr.reweight reweights the correlator.
      • \n
    \n\n
    pyerrors can also handle matrices of correlation functions and extract energy states from these matrices via a generalized eigenvalue problem (see pyerrors.correlators.Corr.GEVP).
    \n\n
    For the full API see pyerrors.correlators.Corr.
    \n\n
    Complex valued observables
    \n\n
    pyerrors can handle complex valued observables via the class pyerrors.obs.CObs.\nCObs are initialized with a real and an imaginary part which both can be Obs valued.
    \n\n
    \n
    my_real_part = pe.Obs([samples1], ['ensemble1'])\nmy_imag_part = pe.Obs([samples2], ['ensemble1'])\n\nmy_cobs = pe.CObs(my_real_part, my_imag_part)\nmy_cobs.gamma_method()\nprint(my_cobs)\n> (0.9959(91)+0.659(28)j)\n
    \n
    \n\n
    Elementary mathematical operations are overloaded and samples are properly propagated as for the Obs class.
    \n\n
    \n
    my_derived_cobs = (my_cobs + my_cobs.conjugate()) / np.abs(my_cobs)\nmy_derived_cobs.gamma_method()\nprint(my_derived_cobs)\n> (1.668(23)+0.0j)\n
    \n
    \n\n
    The Covobs class
    \n\n
    In many projects, auxiliary data that is not based on Monte Carlo chains enters. Examples are experimentally determined mesons masses which are used to set the scale or renormalization constants. These numbers come with an error that has to be propagated through the analysis. The Covobs class allows to define such quantities in pyerrors. Furthermore, external input might consist of correlated quantities. An example are the parameters of an interpolation formula, which are defined via mean values and a covariance matrix between all parameters. The contribution of the interpolation formula to the error of a derived quantity therefore might depend on the complete covariance matrix.
    \n\n
    This concept is built into the definition of Covobs. In pyerrors, external input is defined by $M$ mean values, a $M\\times M$ covariance matrix, where $M=1$ is permissible, and a name that uniquely identifies the covariance matrix. Below, we define the pion mass, based on its mean value and error, 134.9768(5). Note, that the square of the error enters cov_Obs, since the second argument of this function is the covariance matrix of the Covobs.
    \n\n
    \n
    import pyerrors.obs as pe\n\nmpi = pe.cov_Obs(134.9768, 0.0005**2, 'pi^0 mass')\nmpi.gamma_method()\nmpi.details()\n> Result         1.34976800e+02 +/- 5.00000000e-04 +/- 0.00000000e+00 (0.000%)\n>  pi^0 mass     5.00000000e-04\n> 0 samples in 1 ensemble:\n>   \u00b7 Covobs   'pi^0 mass'\n
    \n
    \n\n
    The resulting object mpi is an Obs that contains a Covobs. In the following, it may be handled as any other Obs. The contribution of the covariance matrix to the error of an Obs is determined from the $M \\times M$ covariance matrix $\\Sigma$ and the gradient of the Obs with respect to the external quantities, which is the $1\\times M$ Jacobian matrix $J$, via\n$$s = \\sqrt{J^T \\Sigma J}\\,,$$\nwhere the Jacobian is computed for each derived quantity via automatic differentiation.
    \n\n
    Correlated auxiliary data is defined similarly to above, e.g., via
    \n\n
    \n
    RAP = pe.cov_Obs([16.7457, -19.0475], [[3.49591, -6.07560], [-6.07560, 10.5834]], 'R_AP, 1906.03445, (5.3a)')\nprint(RAP)\n> [Obs[16.7(1.9)], Obs[-19.0(3.3)]]\n
    \n
    \n\n
    where RAP now is a list of two Obs that contains the two correlated parameters.
    \n\n
    Since the gradient of a derived observable with respect to an external covariance matrix is propagated through the entire analysis, the Covobs class allows to quote the derivative of a result with respect to the external quantities. If these derivatives are published together with the result, small shifts in the definition of external quantities, e.g., the definition of the physical point, can be performed a posteriori based on the published information. This may help to compare results of different groups. The gradient of an Obs o with respect to a covariance matrix with the identifying string k may be accessed via
    \n\n
    \n
    o.covobs[k].grad\n
    \n
    \n\n
    Error propagation in iterative algorithms
    \n\n
    pyerrors supports exact linear error propagation for iterative algorithms like various variants of non-linear least squares fits or root finding. The derivatives required for the error propagation are calculated as described in arXiv:1809.01289.
    \n\n
    Least squares fits
    \n\n
    Standard non-linear least square fits with errors on the dependent but not the independent variables can be performed with pyerrors.fits.least_squares. As default solver the Levenberg-Marquardt algorithm implemented in scipy is used.
    \n\n
    Fit functions have to be of the following form
    \n\n
    \n
    import autograd.numpy as anp\n\ndef func(a, x):\n    return a[1] * anp.exp(-a[0] * x)\n
    \n
    \n\n
    It is important that numerical functions refer to autograd.numpy instead of numpy for the automatic differentiation in iterative algorithms to work properly.
    \n\n
    Fits can then be performed via
    \n\n
    \n
    fit_result = pe.fits.least_squares(x, y, func)\nprint("\\n", fit_result)\n> Fit with 2 parameters\n> Method: Levenberg-Marquardt\n> `ftol` termination condition is satisfied.\n> chisquare/d.o.f.: 0.9593035785160936\n\n>  Goodness of fit:\n> \u03c7\u00b2/d.o.f. = 0.959304\n> p-value   = 0.5673\n> Fit parameters:\n> 0      0.0548(28)\n> 1      1.933(64)\n
    \n
    \n\n
    where x is a list or numpy.array of floats and y is a list or numpy.array of Obs.
    \n\n
    Data stored in Corr objects can be fitted directly using the Corr.fit method.
    \n\n
    \n
    my_corr = pe.Corr(y)\nfit_result = my_corr.fit(func, fitrange=[12, 25])\n
    \n
    \n\n
    this can simplify working with absolute fit ranges and takes care of gaps in the data automatically.
    \n\n
    For fit functions with multiple independent variables the fit function can be of the form
    \n\n
    \n
    def func(a, x):\n    (x1, x2) = x\n    return a[0] * x1 ** 2 + a[1] * x2\n
    \n
    \n\n
    pyerrors also supports correlated fits which can be triggered via the parameter correlated_fit=True.\nDetails about how the required covariance matrix is estimated can be found in pyerrors.obs.covariance.
    \n\n
    Direct visualizations of the performed fits can be triggered via resplot=True or qqplot=True. For all available options see pyerrors.fits.least_squares.
    \n\n
    Total least squares fits
    \n\n
    pyerrors can also fit data with errors on both the dependent and independent variables using the total least squares method also referred to orthogonal distance regression as implemented in scipy, see pyerrors.fits.least_squares. The syntax is identical to the standard least squares case, the only difference being that x also has to be a list or numpy.array of Obs.
    \n\n
    For the full API see pyerrors.fits for fits and pyerrors.roots for finding roots of functions.
    \n\n
    Matrix operations
    \n\n
    pyerrors provides wrappers for Obs- and CObs-valued matrix operations based on numpy.linalg. The supported functions include:
    \n\n
      \n
    • inv for the matrix inverse.
      • \n
    • cholseky for the Cholesky decomposition.
      • \n
    • det for the matrix determinant.
      • \n
    • eigh for eigenvalues and eigenvectors of hermitean matrices.
      • \n
    • eig for eigenvalues of general matrices.
      • \n
    • pinv for the Moore-Penrose pseudoinverse.
      • \n
    • svd for the singular-value-decomposition.
      • \n
    \n\n
    For the full API see pyerrors.linalg.
    \n\n
    Export data
    \n\n
    \n\n
    The preferred exported file format within pyerrors is json.gz. Files written to this format are valid JSON files that have been compressed using gzip. The structure of the content is inspired by the dobs format of the ALPHA collaboration. The aim of the format is to facilitate the storage of data in a self-contained way such that, even years after the creation of the file, it is possible to extract all necessary information:
    \n\n
      \n
    • What observables are stored? Possibly: How exactly are they defined.
      • \n
    • How does each single ensemble or external quantity contribute to the error of the observable?
      • \n
    • Who did write the file when and on which machine?
      • \n
    \n\n
    This can be achieved by storing all information in one single file. The export routines of pyerrors are written such that as much information as possible is written automatically as described in the following example
    \n\n
    \n
    my_obs = pe.Obs([samples], ["test_ensemble"])\nmy_obs.tag = "My observable"\n\npe.input.json.dump_to_json(my_obs, "test_output_file", description="This file contains a test observable")\n# For a single observable one can equivalently use the class method dump\nmy_obs.dump("test_output_file", description="This file contains a test observable")\n\ncheck = pe.input.json.load_json("test_output_file")\n\nprint(my_obs == check)\n> True\n
    \n
    \n\n
    The format also allows to directly write out the content of Corr objects or lists and arrays of Obs objects by passing the desired data to pyerrors.input.json.dump_to_json.
    \n\n
    json.gz format specification
    \n\n
    The first entries of the file provide optional auxiliary information:
    \n\n
      \n
    • program is a string that indicates which program was used to write the file.
      • \n
    • version is a string that specifies the version of the format.
      • \n
    • who is a string that specifies the user name of the creator of the file.
      • \n
    • date is a string and contains the creation date of the file.
      • \n
    • host is a string and contains the hostname of the machine where the file has been written.
      • \n
    • description contains information on the content of the file. This field is not filled automatically in pyerrors. The user is advised to provide as detailed information as possible in this field. Examples are: Input files of measurements or simulations, LaTeX formulae or references to publications to specify how the observables have been computed, details on the analysis strategy, ... This field may be any valid JSON type. Strings, arrays or objects (equivalent to dicts in python) are well suited to provide information.
      • \n
    \n\n
    The only necessary entry of the file is the field\n-obsdata, an array that contains the actual data.
    \n\n
    Each entry of the array belongs to a single structure of observables. Currently, these structures can be either of Obs, list, numpy.ndarray, Corr. All Obs inside a structure (with dimension > 0) have to be defined on the same set of configurations. Different structures, that are represented by entries of the array obsdata, are treated independently. Each entry of the array obsdata has the following required entries:
    \n\n
      \n
    • type is a string that specifies the type of the structure. This allows to parse the content to the correct form after reading the file. It is always possible to interpret the content as list of Obs.
      • \n
    • value is an array that contains the mean values of the Obs inside the structure.\nThe following entries are optional:
      • \n
    • layout is a string that specifies the layout of multi-dimensional structures. Examples are \"2, 2\" for a 2x2 dimensional matrix or  \"64, 4, 4\" for a Corr with $T=64$ and 4x4 matrices on each time slices. \"1\" denotes a single Obs. Multi-dimensional structures are stored in row-major format (see below).
      • \n
    • tag is any JSON type. It contains additional information concerning the structure. The tag of an Obs in pyerrors is written here.
      • \n
    • reweighted is a Bool that may be used to specify, whether the Obs in the structure have been reweighted.
      • \n
    • data is an array that contains the data from MC chains. We will define it below.
      • \n
    • cdata is an array that contains the data from external quantities with an error (Covobs in pyerrors). We will define it below.
      • \n
    \n\n
    The array data contains the data from MC chains. Each entry of the array corresponds to one ensemble and contains:
    \n\n
      \n
    • id, a string that contains the name of the ensemble
      • \n
    • replica, an array that contains an entry per replica of the ensemble.
      • \n
    \n\n
    Each entry of replica contains\nname, a string that contains the name of the replica\ndeltas, an array that contains the actual data.
    \n\n
    Each entry in deltas corresponds to one configuration of the replica and has $1+N$ many entries. The first entry is an integer that specifies the configuration number that, together with ensemble and replica name, may be used to uniquely identify the configuration on which the data has been obtained. The following N entries specify the deltas, i.e., the deviation of the observable from the mean value on this configuration, of each Obs inside the structure. Multi-dimensional structures are stored in a row-major format. For primary observables, such as correlation functions, $value + delta_i$ matches the primary data obtained on the configuration.
    \n\n
    The array cdata contains information about the contribution of auxiliary observables, represented by Covobs in pyerrors, to the total error of the observables. Each entry of the array belongs to one auxiliary covariance matrix and contains:
    \n\n
      \n
    • id, a string that identifies the covariance matrix
      • \n
    • layout, a string that defines the dimensions of the $M\\times M$ covariance matrix (has to be \"M, M\" or \"1\").
      • \n
    • cov, an array that contains the $M\\times M$ many entries of the covariance matrix, stored in row-major format.
      • \n
    • grad, an array that contains N entries, one for each Obs inside the structure. Each entry itself is an array, that contains the M gradients of the Nth observable  with respect to the quantity that corresponds to the Mth diagonal entry of the covariance matrix.
      • \n
    \n\n
    A JSON schema that may be used to verify the correctness of a file with respect to the format definition is stored in ./examples/json_schema.json. The schema is a self-descriptive format definition and contains an exemplary file.
    \n\n
    Julia I/O routines for the json.gz format, compatible with ADerrors.jl, can be found here.
    \n"}, "pyerrors.correlators": {"fullname": "pyerrors.correlators", "modulename": "pyerrors.correlators", "kind": "module", "doc": "
    \n"}, "pyerrors.correlators.Corr": {"fullname": "pyerrors.correlators.Corr", "modulename": "pyerrors.correlators", "qualname": "Corr", "kind": "class", "doc": "
    The class for a correlator (time dependent sequence of pe.Obs).
    \n\n
    Everything, this class does, can be achieved using lists or arrays of Obs.\nBut it is simply more convenient to have a dedicated object for correlators.\nOne often wants to add or multiply correlators of the same length at every timeslice and it is inconvenient\nto iterate over all timeslices for every operation. This is especially true, when dealing with matrices.
    \n\n
    The correlator can have two types of content: An Obs at every timeslice OR a GEVP\nmatrix at every timeslice. Other dependency (eg. spatial) are not supported.
    \n"}, "pyerrors.correlators.Corr.__init__": {"fullname": "pyerrors.correlators.Corr.__init__", "modulename": "pyerrors.correlators", "qualname": "Corr.__init__", "kind": "function", "doc": "
    Initialize a Corr object.
    \n\n
    Parameters
    \n\n
      \n
    • data_input (list or array):\nlist of Obs or list of arrays of Obs or array of Corrs
      • \n
    • padding (list, optional):\nList with two entries where the first labels the padding\nat the front of the correlator and the second the padding\nat the back.
      • \n
    • prange (list, optional):\nList containing the first and last timeslice of the plateau\nregion indentified for this correlator.
      • \n
    \n", "signature": "(data_input, padding=[0, 0], prange=None)"}, "pyerrors.correlators.Corr.gamma_method": {"fullname": "pyerrors.correlators.Corr.gamma_method", "modulename": "pyerrors.correlators", "qualname": "Corr.gamma_method", "kind": "function", "doc": "
    Apply the gamma method to the content of the Corr.
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.gm": {"fullname": "pyerrors.correlators.Corr.gm", "modulename": "pyerrors.correlators", "qualname": "Corr.gm", "kind": "function", "doc": "
    Apply the gamma method to the content of the Corr.
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.projected": {"fullname": "pyerrors.correlators.Corr.projected", "modulename": "pyerrors.correlators", "qualname": "Corr.projected", "kind": "function", "doc": "
    We need to project the Correlator with a Vector to get a single value at each timeslice.
    \n\n
    The method can use one or two vectors.\nIf two are specified it returns v1@G@v2 (the order might be very important.)\nBy default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to
    \n", "signature": "(self, vector_l=None, vector_r=None, normalize=False):", "funcdef": "def"}, "pyerrors.correlators.Corr.item": {"fullname": "pyerrors.correlators.Corr.item", "modulename": "pyerrors.correlators", "qualname": "Corr.item", "kind": "function", "doc": "
    Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice.
    \n\n
    Parameters
    \n\n
      \n
    • i (int):\nFirst index to be picked.
      • \n
    • j (int):\nSecond index to be picked.
      • \n
    \n", "signature": "(self, i, j):", "funcdef": "def"}, "pyerrors.correlators.Corr.plottable": {"fullname": "pyerrors.correlators.Corr.plottable", "modulename": "pyerrors.correlators", "qualname": "Corr.plottable", "kind": "function", "doc": "
    Outputs the correlator in a plotable format.
    \n\n
    Outputs three lists containing the timeslice index, the value on each\ntimeslice and the error on each timeslice.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.symmetric": {"fullname": "pyerrors.correlators.Corr.symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.symmetric", "kind": "function", "doc": "
    Symmetrize the correlator around x0=0.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.anti_symmetric": {"fullname": "pyerrors.correlators.Corr.anti_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.anti_symmetric", "kind": "function", "doc": "
    Anti-symmetrize the correlator around x0=0.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.is_matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.is_matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.is_matrix_symmetric", "kind": "function", "doc": "
    Checks whether a correlator matrices is symmetric on every timeslice.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.matrix_symmetric", "kind": "function", "doc": "
    Symmetrizes the correlator matrices on every timeslice.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.GEVP": {"fullname": "pyerrors.correlators.Corr.GEVP", "modulename": "pyerrors.correlators", "qualname": "Corr.GEVP", "kind": "function", "doc": "
    Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors.
    \n\n
    The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the\nlargest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing
    \n\n
    \n
    C.GEVP(t0=2)[0]  # Ground state vector(s)\nC.GEVP(t0=2)[:3]  # Vectors for the lowest three states\n
    \n
    \n\n
    Parameters
    \n\n
      \n
    • t0 (int):\nThe time t0 for the right hand side of the GEVP according to $G(t)v_i=\\lambda_i G(t_0)v_i$
      • \n
    • ts (int):\nfixed time $G(t_s)v_i=\\lambda_i G(t_0)v_i$ if sort=None.\nIf sort=\"Eigenvector\" it gives a reference point for the sorting method.
      • \n
    • sort (string):\nIf this argument is set, a list of self.T vectors per state is returned. If it is set to None, only one vector is returned.\n
        \n
      • \"Eigenvalue\": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice.
        • \n
      • \"Eigenvector\": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state.\nThe reference state is identified by its eigenvalue at $t=t_s$.
        • \n
      • \n
    \n\n
    Other Parameters
    \n\n
      \n
    • state (int):\nReturns only the vector(s) for a specified state. The lowest state is zero.
      • \n
    \n", "signature": "(self, t0, ts=None, sort='Eigenvalue', **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.Eigenvalue": {"fullname": "pyerrors.correlators.Corr.Eigenvalue", "modulename": "pyerrors.correlators", "qualname": "Corr.Eigenvalue", "kind": "function", "doc": "
    Determines the eigenvalue of the GEVP by solving and projecting the correlator
    \n\n
    Parameters
    \n\n
      \n
    • state (int):\nThe state one is interested in ordered by energy. The lowest state is zero.
      • \n
    • All other parameters are identical to the ones of Corr.GEVP.
      • \n
    \n", "signature": "(self, t0, ts=None, state=0, sort='Eigenvalue'):", "funcdef": "def"}, "pyerrors.correlators.Corr.Hankel": {"fullname": "pyerrors.correlators.Corr.Hankel", "modulename": "pyerrors.correlators", "qualname": "Corr.Hankel", "kind": "function", "doc": "
    Constructs an NxN Hankel matrix
    \n\n
    C(t) c(t+1) ... c(t+n-1)\nC(t+1) c(t+2) ... c(t+n)\n.................\nC(t+(n-1)) c(t+n) ... c(t+2(n-1))
    \n\n
    Parameters
    \n\n
      \n
    • N (int):\nDimension of the Hankel matrix
      • \n
    • periodic (bool, optional):\ndetermines whether the matrix is extended periodically
      • \n
    \n", "signature": "(self, N, periodic=False):", "funcdef": "def"}, "pyerrors.correlators.Corr.roll": {"fullname": "pyerrors.correlators.Corr.roll", "modulename": "pyerrors.correlators", "qualname": "Corr.roll", "kind": "function", "doc": "
    Periodically shift the correlator by dt timeslices
    \n\n
    Parameters
    \n\n
      \n
    • dt (int):\nnumber of timeslices
      • \n
    \n", "signature": "(self, dt):", "funcdef": "def"}, "pyerrors.correlators.Corr.reverse": {"fullname": "pyerrors.correlators.Corr.reverse", "modulename": "pyerrors.correlators", "qualname": "Corr.reverse", "kind": "function", "doc": "
    Reverse the time ordering of the Corr
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.thin": {"fullname": "pyerrors.correlators.Corr.thin", "modulename": "pyerrors.correlators", "qualname": "Corr.thin", "kind": "function", "doc": "
    Thin out a correlator to suppress correlations
    \n\n
    Parameters
    \n\n
      \n
    • spacing (int):\nKeep only every 'spacing'th entry of the correlator
      • \n
    • offset (int):\nOffset the equal spacing
      • \n
    \n", "signature": "(self, spacing=2, offset=0):", "funcdef": "def"}, "pyerrors.correlators.Corr.correlate": {"fullname": "pyerrors.correlators.Corr.correlate", "modulename": "pyerrors.correlators", "qualname": "Corr.correlate", "kind": "function", "doc": "
    Correlate the correlator with another correlator or Obs
    \n\n
    Parameters
    \n\n
      \n
    • partner (Obs or Corr):\npartner to correlate the correlator with.\nCan either be an Obs which is correlated with all entries of the\ncorrelator or a Corr of same length.
      • \n
    \n", "signature": "(self, partner):", "funcdef": "def"}, "pyerrors.correlators.Corr.reweight": {"fullname": "pyerrors.correlators.Corr.reweight", "modulename": "pyerrors.correlators", "qualname": "Corr.reweight", "kind": "function", "doc": "
    Reweight the correlator.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl.
      • \n
    \n", "signature": "(self, weight, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.T_symmetry": {"fullname": "pyerrors.correlators.Corr.T_symmetry", "modulename": "pyerrors.correlators", "qualname": "Corr.T_symmetry", "kind": "function", "doc": "
    Return the time symmetry average of the correlator and its partner
    \n\n
    Parameters
    \n\n
      \n
    • partner (Corr):\nTime symmetry partner of the Corr
      • \n
    • partity (int):\nParity quantum number of the correlator, can be +1 or -1
      • \n
    \n", "signature": "(self, partner, parity=1):", "funcdef": "def"}, "pyerrors.correlators.Corr.deriv": {"fullname": "pyerrors.correlators.Corr.deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.deriv", "kind": "function", "doc": "
    Return the first derivative of the correlator with respect to x0.
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, forward, backward, improved, log, default: symmetric
      • \n
    \n", "signature": "(self, variant='symmetric'):", "funcdef": "def"}, "pyerrors.correlators.Corr.second_deriv": {"fullname": "pyerrors.correlators.Corr.second_deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.second_deriv", "kind": "function", "doc": "
    Return the second derivative of the correlator with respect to x0.
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, improved, log, default: symmetric
      • \n
    \n", "signature": "(self, variant='symmetric'):", "funcdef": "def"}, "pyerrors.correlators.Corr.m_eff": {"fullname": "pyerrors.correlators.Corr.m_eff", "modulename": "pyerrors.correlators", "qualname": "Corr.m_eff", "kind": "function", "doc": "
    Returns the effective mass of the correlator as correlator object
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\nlog : uses the standard effective mass log(C(t) / C(t+1))\ncosh, periodic : Use periodicitiy of the correlator by solving C(t) / C(t+1) = cosh(m * (t - T/2)) / cosh(m * (t + 1 - T/2)) for m.\nsinh : Use anti-periodicitiy of the correlator by solving C(t) / C(t+1) = sinh(m * (t - T/2)) / sinh(m * (t + 1 - T/2)) for m.\nSee, e.g., arXiv:1205.5380\narccosh : Uses the explicit form of the symmetrized correlator (not recommended)\nlogsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2
      • \n
    • guess (float):\nguess for the root finder, only relevant for the root variant
      • \n
    \n", "signature": "(self, variant='log', guess=1.0):", "funcdef": "def"}, "pyerrors.correlators.Corr.fit": {"fullname": "pyerrors.correlators.Corr.fit", "modulename": "pyerrors.correlators", "qualname": "Corr.fit", "kind": "function", "doc": "
    Fits function to the data
    \n\n
    Parameters
    \n\n
      \n
    • function (obj):\nfunction to fit to the data. See fits.least_squares for details.
      • \n
    • fitrange (list):\nTwo element list containing the timeslices on which the fit is supposed to start and stop.\nCaution: This range is inclusive as opposed to standard python indexing.\nfitrange=[4, 6] corresponds to the three entries 4, 5 and 6.\nIf not specified, self.prange or all timeslices are used.
      • \n
    • silent (bool):\nDecides whether output is printed to the standard output.
      • \n
    \n", "signature": "(self, function, fitrange=None, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.plateau": {"fullname": "pyerrors.correlators.Corr.plateau", "modulename": "pyerrors.correlators", "qualname": "Corr.plateau", "kind": "function", "doc": "
    Extract a plateau value from a Corr object
    \n\n
    Parameters
    \n\n
      \n
    • plateau_range (list):\nlist with two entries, indicating the first and the last timeslice\nof the plateau region.
      • \n
    • method (str):\nmethod to extract the plateau.\n    'fit' fits a constant to the plateau region\n    'avg', 'average' or 'mean' just average over the given timeslices.
      • \n
    • auto_gamma (bool):\napply gamma_method with default parameters to the Corr. Defaults to None
      • \n
    \n", "signature": "(self, plateau_range=None, method='fit', auto_gamma=False):", "funcdef": "def"}, "pyerrors.correlators.Corr.set_prange": {"fullname": "pyerrors.correlators.Corr.set_prange", "modulename": "pyerrors.correlators", "qualname": "Corr.set_prange", "kind": "function", "doc": "
    Sets the attribute prange of the Corr object.
    \n", "signature": "(self, prange):", "funcdef": "def"}, "pyerrors.correlators.Corr.show": {"fullname": "pyerrors.correlators.Corr.show", "modulename": "pyerrors.correlators", "qualname": "Corr.show", "kind": "function", "doc": "
    Plots the correlator using the tag of the correlator as label if available.
    \n\n
    Parameters
    \n\n
      \n
    • x_range (list):\nlist of two values, determining the range of the x-axis e.g. [4, 8].
      • \n
    • comp (Corr or list of Corr):\nCorrelator or list of correlators which are plotted for comparison.\nThe tags of these correlators are used as labels if available.
      • \n
    • logscale (bool):\nSets y-axis to logscale.
      • \n
    • plateau (Obs):\nPlateau value to be visualized in the figure.
      • \n
    • fit_res (Fit_result):\nFit_result object to be visualized.
      • \n
    • fit_key (str):\nKey for the fit function in Fit_result.fit_function (for combined fits).
      • \n
    • ylabel (str):\nLabel for the y-axis.
      • \n
    • save (str):\npath to file in which the figure should be saved.
      • \n
    • auto_gamma (bool):\nApply the gamma method with standard parameters to all correlators and plateau values before plotting.
      • \n
    • hide_sigma (float):\nHides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.
      • \n
    • references (list):\nList of floating point values that are displayed as horizontal lines for reference.
      • \n
    • title (string):\nOptional title of the figure.
      • \n
    \n", "signature": "(\tself,\tx_range=None,\tcomp=None,\ty_range=None,\tlogscale=False,\tplateau=None,\tfit_res=None,\tfit_key=None,\tylabel=None,\tsave=None,\tauto_gamma=False,\thide_sigma=None,\treferences=None,\ttitle=None):", "funcdef": "def"}, "pyerrors.correlators.Corr.spaghetti_plot": {"fullname": "pyerrors.correlators.Corr.spaghetti_plot", "modulename": "pyerrors.correlators", "qualname": "Corr.spaghetti_plot", "kind": "function", "doc": "
    Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
    \n\n
    Parameters
    \n\n
      \n
    • logscale (bool):\nDetermines whether the scale of the y-axis is logarithmic or standard.
      • \n
    \n", "signature": "(self, logscale=True):", "funcdef": "def"}, "pyerrors.correlators.Corr.dump": {"fullname": "pyerrors.correlators.Corr.dump", "modulename": "pyerrors.correlators", "qualname": "Corr.dump", "kind": "function", "doc": "
    Dumps the Corr into a file of chosen type
    \n\n
    Parameters
    \n\n
      \n
    • filename (str):\nName of the file to be saved.
      • \n
    • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n", "signature": "(self, filename, datatype='json.gz', **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.print": {"fullname": "pyerrors.correlators.Corr.print", "modulename": "pyerrors.correlators", "qualname": "Corr.print", "kind": "function", "doc": "
    \n", "signature": "(self, print_range=None):", "funcdef": "def"}, "pyerrors.correlators.Corr.sqrt": {"fullname": "pyerrors.correlators.Corr.sqrt", "modulename": "pyerrors.correlators", "qualname": "Corr.sqrt", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.log": {"fullname": "pyerrors.correlators.Corr.log", "modulename": "pyerrors.correlators", "qualname": "Corr.log", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.exp": {"fullname": "pyerrors.correlators.Corr.exp", "modulename": "pyerrors.correlators", "qualname": "Corr.exp", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.sin": {"fullname": "pyerrors.correlators.Corr.sin", "modulename": "pyerrors.correlators", "qualname": "Corr.sin", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.cos": {"fullname": "pyerrors.correlators.Corr.cos", "modulename": "pyerrors.correlators", "qualname": "Corr.cos", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.tan": {"fullname": "pyerrors.correlators.Corr.tan", "modulename": "pyerrors.correlators", "qualname": "Corr.tan", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.sinh": {"fullname": "pyerrors.correlators.Corr.sinh", "modulename": "pyerrors.correlators", "qualname": "Corr.sinh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.cosh": {"fullname": "pyerrors.correlators.Corr.cosh", "modulename": "pyerrors.correlators", "qualname": "Corr.cosh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.tanh": {"fullname": "pyerrors.correlators.Corr.tanh", "modulename": "pyerrors.correlators", "qualname": "Corr.tanh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsin": {"fullname": "pyerrors.correlators.Corr.arcsin", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsin", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arccos": {"fullname": "pyerrors.correlators.Corr.arccos", "modulename": "pyerrors.correlators", "qualname": "Corr.arccos", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arctan": {"fullname": "pyerrors.correlators.Corr.arctan", "modulename": "pyerrors.correlators", "qualname": "Corr.arctan", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsinh": {"fullname": "pyerrors.correlators.Corr.arcsinh", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsinh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arccosh": {"fullname": "pyerrors.correlators.Corr.arccosh", "modulename": "pyerrors.correlators", "qualname": "Corr.arccosh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arctanh": {"fullname": "pyerrors.correlators.Corr.arctanh", "modulename": "pyerrors.correlators", "qualname": "Corr.arctanh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.prune": {"fullname": "pyerrors.correlators.Corr.prune", "modulename": "pyerrors.correlators", "qualname": "Corr.prune", "kind": "function", "doc": "
    Project large correlation matrix to lowest states
    \n\n
    This method can be used to reduce the size of an (N x N) correlation matrix\nto (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise\nis still small.
    \n\n
    Parameters
    \n\n
      \n
    • Ntrunc (int):\nRank of the target matrix.
      • \n
    • tproj (int):\nTime where the eigenvectors are evaluated, corresponds to ts in the GEVP method.\nThe default value is 3.
      • \n
    • t0proj (int):\nTime where the correlation matrix is inverted. Choosing t0proj=1 is strongly\ndiscouraged for O(a) improved theories, since the correctness of the procedure\ncannot be granted in this case. The default value is 2.
      • \n
    • basematrix (Corr):\nCorrelation matrix that is used to determine the eigenvectors of the\nlowest states based on a GEVP. basematrix is taken to be the Corr itself if\nis is not specified.
      • \n
    \n\n
    Notes
    \n\n
    We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving\nthe GEVP $$C(t) v_n(t, t_0) = \\lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \\equiv t_\\mathrm{proj}$\nand $t_0 \\equiv t_{0, \\mathrm{proj}}$. The target matrix is projected onto the subspace of the\nresulting eigenvectors $v_n, n=1,\\dots,N_\\mathrm{trunc}$ via\n$$G^\\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large\ncorrelation matrix and to remove some noise that is added by irrelevant operators.\nThis may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated\nbound $t_0 \\leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.
    \n", "signature": "(self, Ntrunc, tproj=3, t0proj=2, basematrix=None):", "funcdef": "def"}, "pyerrors.covobs": {"fullname": "pyerrors.covobs", "modulename": "pyerrors.covobs", "kind": "module", "doc": "
    \n"}, "pyerrors.covobs.Covobs": {"fullname": "pyerrors.covobs.Covobs", "modulename": "pyerrors.covobs", "qualname": "Covobs", "kind": "class", "doc": "
    \n"}, "pyerrors.covobs.Covobs.__init__": {"fullname": "pyerrors.covobs.Covobs.__init__", "modulename": "pyerrors.covobs", "qualname": "Covobs.__init__", "kind": "function", "doc": "
    Initialize Covobs object.
    \n\n
    Parameters
    \n\n
      \n
    • mean (float):\nMean value of the new Obs
      • \n
    • cov (list or array):\n2d Covariance matrix or 1d diagonal entries
      • \n
    • name (str):\nidentifier for the covariance matrix
      • \n
    • pos (int):\nPosition of the variance belonging to mean in cov.\nIs taken to be 1 if cov is 0-dimensional
      • \n
    • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
      • \n
    \n", "signature": "(mean, cov, name, pos=None, grad=None)"}, "pyerrors.covobs.Covobs.errsq": {"fullname": "pyerrors.covobs.Covobs.errsq", "modulename": "pyerrors.covobs", "qualname": "Covobs.errsq", "kind": "function", "doc": "
    Return the variance (= square of the error) of the Covobs
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.dirac": {"fullname": "pyerrors.dirac", "modulename": "pyerrors.dirac", "kind": "module", "doc": "
    \n"}, "pyerrors.dirac.epsilon_tensor": {"fullname": "pyerrors.dirac.epsilon_tensor", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor", "kind": "function", "doc": "
    Rank-3 epsilon tensor
    \n\n
    Based on https://codegolf.stackexchange.com/a/160375
    \n\n
    Returns
    \n\n
      \n
    • elem (int):\nElement (i,j,k) of the epsilon tensor of rank 3
      • \n
    \n", "signature": "(i, j, k):", "funcdef": "def"}, "pyerrors.dirac.epsilon_tensor_rank4": {"fullname": "pyerrors.dirac.epsilon_tensor_rank4", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor_rank4", "kind": "function", "doc": "
    Rank-4 epsilon tensor
    \n\n
    Extension of https://codegolf.stackexchange.com/a/160375
    \n\n
    Returns
    \n\n
      \n
    • elem (int):\nElement (i,j,k,o) of the epsilon tensor of rank 4
      • \n
    \n", "signature": "(i, j, k, o):", "funcdef": "def"}, "pyerrors.dirac.Grid_gamma": {"fullname": "pyerrors.dirac.Grid_gamma", "modulename": "pyerrors.dirac", "qualname": "Grid_gamma", "kind": "function", "doc": "
    Returns gamma matrix in Grid labeling.
    \n", "signature": "(gamma_tag):", "funcdef": "def"}, "pyerrors.fits": {"fullname": "pyerrors.fits", "modulename": "pyerrors.fits", "kind": "module", "doc": "
    \n"}, "pyerrors.fits.Fit_result": {"fullname": "pyerrors.fits.Fit_result", "modulename": "pyerrors.fits", "qualname": "Fit_result", "kind": "class", "doc": "
    Represents fit results.
    \n\n
    Attributes
    \n\n
      \n
    • fit_parameters (list):\nresults for the individual fit parameters,\nalso accessible via indices.
      • \n
    • chisquare_by_dof (float):\nreduced chisquare.
      • \n
    • p_value (float):\np-value of the fit
      • \n
    • t2_p_value (float):\nHotelling t-squared p-value for correlated fits.
      • \n
    \n", "bases": "collections.abc.Sequence"}, "pyerrors.fits.Fit_result.gamma_method": {"fullname": "pyerrors.fits.Fit_result.gamma_method", "modulename": "pyerrors.fits", "qualname": "Fit_result.gamma_method", "kind": "function", "doc": "
    Apply the gamma method to all fit parameters
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.fits.Fit_result.gm": {"fullname": "pyerrors.fits.Fit_result.gm", "modulename": "pyerrors.fits", "qualname": "Fit_result.gm", "kind": "function", "doc": "
    Apply the gamma method to all fit parameters
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.fits.least_squares": {"fullname": "pyerrors.fits.least_squares", "modulename": "pyerrors.fits", "qualname": "least_squares", "kind": "function", "doc": "
    Performs a non-linear fit to y = func(x).\n    ```
    \n\n
    Parameters
    \n\n
      \n
    • For an uncombined fit:
      • \n
    • x (list):\nlist of floats.
      • \n
    • y (list):\nlist of Obs.
      • \n
    • func (object):\nfit function, has to be of the form
      \n\n
      \n
      import autograd.numpy as anp\n\ndef func(a, x):\n   return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
      \n
      \n\n
      For multiple x values func can be of the form
      \n\n
      \n
      def func(a, x):\n   (x1, x2) = x\n   return a[0] * x1 ** 2 + a[1] * x2\n
      \n
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • OR For a combined fit:
      • \n
    • x (dict):\ndict of lists.
      • \n
    • y (dict):\ndict of lists of Obs.
      • \n
    • funcs (dict):\ndict of objects\nfit functions have to be of the form (here a[0] is the common fit parameter)\n```python\nimport autograd.numpy as anp\nfuncs = {\"a\": func_a,\n       \"b\": func_b}
      \n\n
      def func_a(a, x):\n   return a[1] * anp.exp(-a[0] * x)
      \n\n
      def func_b(a, x):\n   return a[2] * anp.exp(-a[0] * x)
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • priors (dict or list, optional):\npriors can either be a dictionary with integer keys and the corresponding priors as values or\na list with an entry for every parameter in the fit. The entries can either be\nObs (e.g. results from a previous fit) or strings containing a value and an error formatted like\n0.548(23), 500(40) or 0.5(0.4)
      • \n
    • silent (bool, optional):\nIf true all output to the console is omitted (default False).
      • \n
    • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for\nnon-linear fits with many parameters. In case of correlated fits the guess is used to perform\nan uncorrelated fit which then serves as guess for the correlated fit.
      • \n
    • method (str, optional):\ncan be used to choose an alternative method for the minimization of chisquare.\nThe possible methods are the ones which can be used for scipy.optimize.minimize and\nmigrad of iminuit. If no method is specified, Levenberg-Marquard is used.\nReliable alternatives are migrad, Powell and Nelder-Mead.
      • \n
    • tol (float, optional):\ncan be used (only for combined fits and methods other than Levenberg-Marquard) to set the tolerance for convergence\nto a different value to either speed up convergence at the cost of a larger error on the fitted parameters (and possibly\ninvalid estimates for parameter uncertainties) or smaller values to get more accurate parameter values\nThe stopping criterion depends on the method, e.g. migrad: edm_max = 0.002 * tol * errordef (EDM criterion: edm < edm_max)
      • \n
    • correlated_fit (bool):\nIf True, use the full inverse covariance matrix in the definition of the chisquare cost function.\nFor details about how the covariance matrix is estimated see pyerrors.obs.covariance.\nIn practice the correlation matrix is Cholesky decomposed and inverted (instead of the covariance matrix).\nThis procedure should be numerically more stable as the correlation matrix is typically better conditioned (Jacobi preconditioning).
      • \n
    • expected_chisquare (bool):\nIf True estimates the expected chisquare which is\ncorrected by effects caused by correlated input data (default False).
      • \n
    • resplot (bool):\nIf True, a plot which displays fit, data and residuals is generated (default False).
      • \n
    • qqplot (bool):\nIf True, a quantile-quantile plot of the fit result is generated (default False).
      • \n
    • num_grad (bool):\nUse numerical differentation instead of automatic differentiation to perform the error propagation (default False).
      • \n
    \n\n
    Returns
    \n\n
      \n
    • output (Fit_result):\nParameters and information on the fitted result.
      • \n
    \n", "signature": "(x, y, func, priors=None, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.fits.total_least_squares": {"fullname": "pyerrors.fits.total_least_squares", "modulename": "pyerrors.fits", "qualname": "total_least_squares", "kind": "function", "doc": "
    Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nlist of Obs, or a tuple of lists of Obs
      • \n
    • y (list):\nlist of Obs. The dvalues of the Obs are used as x- and yerror for the fit.
      • \n
    • func (object):\nfunc has to be of the form
      \n\n
      \n
      import autograd.numpy as anp\n\ndef func(a, x):\n   return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
      \n
      \n\n
      For multiple x values func can be of the form
      \n\n
      \n
      def func(a, x):\n   (x1, x2) = x\n   return a[0] * x1 ** 2 + a[1] * x2\n
      \n
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • silent (bool, optional):\nIf true all output to the console is omitted (default False).
      • \n
    • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for non-linear\nfits with many parameters.
      • \n
    • expected_chisquare (bool):\nIf true prints the expected chisquare which is\ncorrected by effects caused by correlated input data.\nThis can take a while as the full correlation matrix\nhas to be calculated (default False).
      • \n
    • num_grad (bool):\nUse numerical differentation instead of automatic differentiation to perform the error propagation (default False).
      • \n
    \n\n
    Notes
    \n\n
    Based on the orthogonal distance regression module of scipy.
    \n\n
    Returns
    \n\n
      \n
    • output (Fit_result):\nParameters and information on the fitted result.
      • \n
    \n", "signature": "(x, y, func, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.fits.fit_lin": {"fullname": "pyerrors.fits.fit_lin", "modulename": "pyerrors.fits", "qualname": "fit_lin", "kind": "function", "doc": "
    Performs a linear fit to y = n + m * x and returns two Obs n, m.
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nCan either be a list of floats in which case no xerror is assumed, or\na list of Obs, where the dvalues of the Obs are used as xerror for the fit.
      • \n
    • y (list):\nList of Obs, the dvalues of the Obs are used as yerror for the fit.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • fit_parameters (list[Obs]):\nLIist of fitted observables.
      • \n
    \n", "signature": "(x, y, **kwargs):", "funcdef": "def"}, "pyerrors.fits.qqplot": {"fullname": "pyerrors.fits.qqplot", "modulename": "pyerrors.fits", "qualname": "qqplot", "kind": "function", "doc": "
    Generates a quantile-quantile plot of the fit result which can be used to\n   check if the residuals of the fit are gaussian distributed.
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(x, o_y, func, p, title=''):", "funcdef": "def"}, "pyerrors.fits.residual_plot": {"fullname": "pyerrors.fits.residual_plot", "modulename": "pyerrors.fits", "qualname": "residual_plot", "kind": "function", "doc": "
    Generates a plot which compares the fit to the data and displays the corresponding residuals
    \n\n
    For uncorrelated data the residuals are expected to be distributed ~N(0,1).
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(x, y, func, fit_res, title=''):", "funcdef": "def"}, "pyerrors.fits.error_band": {"fullname": "pyerrors.fits.error_band", "modulename": "pyerrors.fits", "qualname": "error_band", "kind": "function", "doc": "
    Calculate the error band for an array of sample values x, for given fit function func with optimized parameters beta.
    \n\n
    Returns
    \n\n
      \n
    • err (np.array(Obs)):\nError band for an array of sample values x
      • \n
    \n", "signature": "(x, func, beta):", "funcdef": "def"}, "pyerrors.fits.ks_test": {"fullname": "pyerrors.fits.ks_test", "modulename": "pyerrors.fits", "qualname": "ks_test", "kind": "function", "doc": "
    Performs a Kolmogorov\u2013Smirnov test for the p-values of all fit object.
    \n\n
    Parameters
    \n\n
      \n
    • objects (list):\nList of fit results to include in the analysis (optional).
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(objects=None):", "funcdef": "def"}, "pyerrors.input": {"fullname": "pyerrors.input", "modulename": "pyerrors.input", "kind": "module", "doc": "
    pyerrors includes an input submodule in which input routines and parsers for the output of various numerical programs are contained.
    \n\n
    Jackknife samples
    \n\n
    For comparison with other analysis workflows pyerrors can also generate jackknife samples from an Obs object or import jackknife samples into an Obs object.\nSee pyerrors.obs.Obs.export_jackknife and pyerrors.obs.import_jackknife for details.
    \n"}, "pyerrors.input.bdio": {"fullname": "pyerrors.input.bdio", "modulename": "pyerrors.input.bdio", "kind": "module", "doc": "
    \n"}, "pyerrors.input.bdio.read_ADerrors": {"fullname": "pyerrors.input.bdio.read_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "read_ADerrors", "kind": "function", "doc": "
    Extract generic MCMC data from a bdio file
    \n\n
    read_ADerrors requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path -- path to the bdio file
      • \n
    • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    \n\n
    Returns
    \n\n
      \n
    • data (List[Obs]):\nExtracted data
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.write_ADerrors": {"fullname": "pyerrors.input.bdio.write_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "write_ADerrors", "kind": "function", "doc": "
    Write Obs to a bdio file according to ADerrors conventions
    \n\n
    read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path -- path to the bdio file
      • \n
    • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    \n\n
    Returns
    \n\n
      \n
    • success (int):\nreturns 0 is successful
      • \n
    \n", "signature": "(obs_list, file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.read_mesons": {"fullname": "pyerrors.input.bdio.read_mesons", "modulename": "pyerrors.input.bdio", "qualname": "read_mesons", "kind": "function", "doc": "
    Extract mesons data from a bdio file and return it as a dictionary
    \n\n
    The dictionary can be accessed with a tuple consisting of (type, source_position, kappa1, kappa2)
    \n\n
    read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path (str):\npath to the bdio file
      • \n
    • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    • start (int):\nThe first configuration to be read (default 1)
      • \n
    • stop (int):\nThe last configuration to be read (default None)
      • \n
    • step (int):\nFixed step size between two measurements (default 1)
      • \n
    • alternative_ensemble_name (str):\nManually overwrite ensemble name
      • \n
    \n\n
    Returns
    \n\n
      \n
    • data (dict):\nExtracted meson data
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.read_dSdm": {"fullname": "pyerrors.input.bdio.read_dSdm", "modulename": "pyerrors.input.bdio", "qualname": "read_dSdm", "kind": "function", "doc": "
    Extract dSdm data from a bdio file and return it as a dictionary
    \n\n
    The dictionary can be accessed with a tuple consisting of (type, kappa)
    \n\n
    read_dSdm requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path (str):\npath to the bdio file
      • \n
    • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    • start (int):\nThe first configuration to be read (default 1)
      • \n
    • stop (int):\nThe last configuration to be read (default None)
      • \n
    • step (int):\nFixed step size between two measurements (default 1)
      • \n
    • alternative_ensemble_name (str):\nManually overwrite ensemble name
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.dobs": {"fullname": "pyerrors.input.dobs", "modulename": "pyerrors.input.dobs", "kind": "module", "doc": "
    \n"}, "pyerrors.input.dobs.create_pobs_string": {"fullname": "pyerrors.input.dobs.create_pobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_pobs_string", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to an xml string\naccording to the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • xml_str (str):\nXML formatted string of the input data
      • \n
    \n", "signature": "(obsl, name, spec='', origin='', symbol=[], enstag=None):", "funcdef": "def"}, "pyerrors.input.dobs.write_pobs": {"fullname": "pyerrors.input.dobs.write_pobs", "modulename": "pyerrors.input.dobs", "qualname": "write_pobs", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
      • \n
    • gz (bool):\nIf True, the output is a gzipped xml. If False, the output is an xml file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(\tobsl,\tfname,\tname,\tspec='',\torigin='',\tsymbol=[],\tenstag=None,\tgz=True):", "funcdef": "def"}, "pyerrors.input.dobs.read_pobs": {"fullname": "pyerrors.input.dobs.read_pobs", "modulename": "pyerrors.input.dobs", "qualname": "read_pobs", "kind": "function", "doc": "
    Import a list of Obs from an xml.gz file in the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • separatior_insertion (str or int):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nNone (default): Replica names remain unchanged.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • res (list[Obs]):\nImported data
      • \n
    • or
      • \n
    • res (dict):\nImported data and meta-data
      • \n
    \n", "signature": "(fname, full_output=False, gz=True, separator_insertion=None):", "funcdef": "def"}, "pyerrors.input.dobs.import_dobs_string": {"fullname": "pyerrors.input.dobs.import_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "import_dobs_string", "kind": "function", "doc": "
    Import a list of Obs from a string in the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • content (str):\nXML string containing the data
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • res (list[Obs]):\nImported data
      • \n
    • or
      • \n
    • res (dict):\nImported data and meta-data
      • \n
    \n", "signature": "(content, full_output=False, separator_insertion=True):", "funcdef": "def"}, "pyerrors.input.dobs.read_dobs": {"fullname": "pyerrors.input.dobs.read_dobs", "modulename": "pyerrors.input.dobs", "qualname": "read_dobs", "kind": "function", "doc": "
    Import a list of Obs from an xml.gz file in the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes XML file.
      • \n
    • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • res (list[Obs]):\nImported data
      • \n
    • or
      • \n
    • res (dict):\nImported data and meta-data
      • \n
    \n", "signature": "(fname, full_output=False, gz=True, separator_insertion=True):", "funcdef": "def"}, "pyerrors.input.dobs.create_dobs_string": {"fullname": "pyerrors.input.dobs.create_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_dobs_string", "kind": "function", "doc": "
    Generate the string for the export of a list of Obs or structures containing Obs\nto a .xml.gz file according to the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically. The separator |is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • who (str):\nProvide the name of the person that exports the data.
      • \n
    • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • xml_str (str):\nXML string generated from the data
      • \n
    \n", "signature": "(\tobsl,\tname,\tspec='dobs v1.0',\torigin='',\tsymbol=[],\twho=None,\tenstags=None):", "funcdef": "def"}, "pyerrors.input.dobs.write_dobs": {"fullname": "pyerrors.input.dobs.write_dobs", "modulename": "pyerrors.input.dobs", "qualname": "write_dobs", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • who (str):\nProvide the name of the person that exports the data.
      • \n
    • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
      • \n
    • gz (bool):\nIf True, the output is a gzipped XML. If False, the output is a XML file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(\tobsl,\tfname,\tname,\tspec='dobs v1.0',\torigin='',\tsymbol=[],\twho=None,\tenstags=None,\tgz=True):", "funcdef": "def"}, "pyerrors.input.hadrons": {"fullname": "pyerrors.input.hadrons", "modulename": "pyerrors.input.hadrons", "kind": "module", "doc": "
    \n"}, "pyerrors.input.hadrons.read_meson_hd5": {"fullname": "pyerrors.input.hadrons.read_meson_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_meson_hd5", "kind": "function", "doc": "
    Read hadrons meson hdf5 file and extract the meson labeled 'meson'
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • meson (str):\nlabel of the meson to be extracted, standard value meson_0 which\ncorresponds to the pseudoscalar pseudoscalar two-point function.
      • \n
    • gammas (tuple of strings):\nInstrad of a meson label one can also provide a tuple of two strings\nindicating the gamma matrices at source and sink.\n(\"Gamma5\", \"Gamma5\") corresponds to the pseudoscalar pseudoscalar\ntwo-point function. The gammas argument dominateds over meson.
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • corr (Corr):\nCorrelator of the source sink combination in question.
      • \n
    \n", "signature": "(path, filestem, ens_id, meson='meson_0', idl=None, gammas=None):", "funcdef": "def"}, "pyerrors.input.hadrons.extract_t0_hd5": {"fullname": "pyerrors.input.hadrons.extract_t0_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "extract_t0_hd5", "kind": "function", "doc": "
    Read hadrons FlowObservables hdf5 file and extract t0
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • obs (str):\nlabel of the observable from which t0 should be extracted.\nOptions: 'Clover energy density' and 'Plaquette energy density'
      • \n
    • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.
      • \n
    \n", "signature": "(\tpath,\tfilestem,\tens_id,\tobs='Clover energy density',\tfit_range=5,\tidl=None,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.hadrons.read_DistillationContraction_hd5": {"fullname": "pyerrors.input.hadrons.read_DistillationContraction_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_DistillationContraction_hd5", "kind": "function", "doc": "
    Read hadrons DistillationContraction hdf5 files in given directory structure
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the directories to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • diagrams (list):\nList of strings of the diagrams to extract, e.g. [\"direct\", \"box\", \"cross\"].
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (dict):\nextracted DistillationContration data
      • \n
    \n", "signature": "(path, ens_id, diagrams=['direct'], idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.Npr_matrix": {"fullname": "pyerrors.input.hadrons.Npr_matrix", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix", "kind": "class", "doc": "
    ndarray(shape, dtype=float, buffer=None, offset=0,\n        strides=None, order=None)
    \n\n
    An array object represents a multidimensional, homogeneous array\nof fixed-size items.  An associated data-type object describes the\nformat of each element in the array (its byte-order, how many bytes it\noccupies in memory, whether it is an integer, a floating point number,\nor something else, etc.)
    \n\n
    Arrays should be constructed using array, zeros or empty (refer\nto the See Also section below).  The parameters given here refer to\na low-level method (ndarray(...)) for instantiating an array.
    \n\n
    For more information, refer to the numpy module and examine the\nmethods and attributes of an array.
    \n\n
    Parameters
    \n\n
      \n
    • (for the __new__ method; see Notes below)
      • \n
    • shape (tuple of ints):\nShape of created array.
      • \n
    • dtype (data-type, optional):\nAny object that can be interpreted as a numpy data type.
      • \n
    • buffer (object exposing buffer interface, optional):\nUsed to fill the array with data.
      • \n
    • offset (int, optional):\nOffset of array data in buffer.
      • \n
    • strides (tuple of ints, optional):\nStrides of data in memory.
      • \n
    • order ({'C', 'F'}, optional):\nRow-major (C-style) or column-major (Fortran-style) order.
      • \n
    \n\n
    Attributes
    \n\n
      \n
    • T (ndarray):\nTranspose of the array.
      • \n
    • data (buffer):\nThe array's elements, in memory.
      • \n
    • dtype (dtype object):\nDescribes the format of the elements in the array.
      • \n
    • flags (dict):\nDictionary containing information related to memory use, e.g.,\n'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc.
      • \n
    • flat (numpy.flatiter object):\nFlattened version of the array as an iterator.  The iterator\nallows assignments, e.g., x.flat = 3 (See ndarray.flat for\nassignment examples; TODO).
      • \n
    • imag (ndarray):\nImaginary part of the array.
      • \n
    • real (ndarray):\nReal part of the array.
      • \n
    • size (int):\nNumber of elements in the array.
      • \n
    • itemsize (int):\nThe memory use of each array element in bytes.
      • \n
    • nbytes (int):\nThe total number of bytes required to store the array data,\ni.e., itemsize * size.
      • \n
    • ndim (int):\nThe array's number of dimensions.
      • \n
    • shape (tuple of ints):\nShape of the array.
      • \n
    • strides (tuple of ints):\nThe step-size required to move from one element to the next in\nmemory. For example, a contiguous (3, 4) array of type\nint16 in C-order has strides (8, 2).  This implies that\nto move from element to element in memory requires jumps of 2 bytes.\nTo move from row-to-row, one needs to jump 8 bytes at a time\n(2 * 4).
      • \n
    • ctypes (ctypes object):\nClass containing properties of the array needed for interaction\nwith ctypes.
      • \n
    • base (ndarray):\nIf the array is a view into another array, that array is its base\n(unless that array is also a view).  The base array is where the\narray data is actually stored.
      • \n
    \n\n
    See Also
    \n\n
    array:  Construct an array. 
    \nzeros:  Create an array, each element of which is zero. 
    \nempty:  Create an array, but leave its allocated memory unchanged (i.e.,\nit contains \"garbage\"). 
    \ndtype:  Create a data-type. 
    \nnumpy.typing.NDArray:  An ndarray alias :term:generic <generic type>\nw.r.t. its dtype.type <numpy.dtype.type>.  
    \n\n
    Notes
    \n\n
    There are two modes of creating an array using __new__:
    \n\n
      \n
    1. If buffer is None, then only shape, dtype, and order\nare used.
      2. \n
    2. If buffer is an object exposing the buffer interface, then\nall keywords are interpreted.
      3. \n
    \n\n
    No __init__ method is needed because the array is fully initialized\nafter the __new__ method.
    \n\n
    Examples
    \n\n
    These examples illustrate the low-level ndarray constructor.  Refer\nto the See Also section above for easier ways of constructing an\nndarray.
    \n\n
    First mode, buffer is None:
    \n\n
    \n
    >>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n       [     nan, 2.5e-323]])\n
    \n
    \n\n
    Second mode:
    \n\n
    \n
    >>> np.ndarray((2,), buffer=np.array([1,2,3]),\n...            offset=np.int_().itemsize,\n...            dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n
    \n
    \n", "bases": "numpy.ndarray"}, "pyerrors.input.hadrons.Npr_matrix.g5H": {"fullname": "pyerrors.input.hadrons.Npr_matrix.g5H", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.g5H", "kind": "variable", "doc": "
    Gamma_5 hermitean conjugate
    \n\n
    Uses the fact that the propagator is gamma5 hermitean, so just the\nin and out momenta of the propagator are exchanged.
    \n"}, "pyerrors.input.hadrons.read_ExternalLeg_hd5": {"fullname": "pyerrors.input.hadrons.read_ExternalLeg_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_ExternalLeg_hd5", "kind": "function", "doc": "
    Read hadrons ExternalLeg hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (Npr_matrix):\nread Cobs-matrix
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.read_Bilinear_hd5": {"fullname": "pyerrors.input.hadrons.read_Bilinear_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Bilinear_hd5", "kind": "function", "doc": "
    Read hadrons Bilinear hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result_dict (dict[Npr_matrix]):\nextracted Bilinears
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.read_Fourquark_hd5": {"fullname": "pyerrors.input.hadrons.read_Fourquark_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Fourquark_hd5", "kind": "function", "doc": "
    Read hadrons FourquarkFullyConnected hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    • vertices (list):\nVertex functions to be extracted.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result_dict (dict):\nextracted fourquark matrizes
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None, vertices=['VA', 'AV']):", "funcdef": "def"}, "pyerrors.input.json": {"fullname": "pyerrors.input.json", "modulename": "pyerrors.input.json", "kind": "module", "doc": "
    \n"}, "pyerrors.input.json.create_json_string": {"fullname": "pyerrors.input.json.create_json_string", "modulename": "pyerrors.input.json", "qualname": "create_json_string", "kind": "function", "doc": "
    Generate the string for the export of a list of Obs or structures containing Obs\nto a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • json_string (str):\nString for export to .json(.gz) file
      • \n
    \n", "signature": "(ol, description='', indent=1):", "funcdef": "def"}, "pyerrors.input.json.dump_to_json": {"fullname": "pyerrors.input.json.dump_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_to_json", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • Null
      • \n
    \n", "signature": "(ol, fname, description='', indent=1, gz=True):", "funcdef": "def"}, "pyerrors.input.json.import_json_string": {"fullname": "pyerrors.input.json.import_json_string", "modulename": "pyerrors.input.json", "qualname": "import_json_string", "kind": "function", "doc": "
    Reconstruct a list of Obs or structures containing Obs from a json string.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
    \n\n
    Parameters
    \n\n
      \n
    • json_string (str):\njson string containing the data.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (list[Obs]):\nreconstructed list of observables from the json string
      • \n
    • or
      • \n
    • result (Obs):\nonly one observable if the list only has one entry
      • \n
    • or
      • \n
    • result (dict):\nif full_output=True
      • \n
    \n", "signature": "(json_string, verbose=True, full_output=False):", "funcdef": "def"}, "pyerrors.input.json.load_json": {"fullname": "pyerrors.input.json.load_json", "modulename": "pyerrors.input.json", "qualname": "load_json", "kind": "function", "doc": "
    Import a list of Obs or structures containing Obs from a .json(.gz) file.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (list[Obs]):\nreconstructed list of observables from the json string
      • \n
    • or
      • \n
    • result (Obs):\nonly one observable if the list only has one entry
      • \n
    • or
      • \n
    • result (dict):\nif full_output=True
      • \n
    \n", "signature": "(fname, verbose=True, gz=True, full_output=False):", "funcdef": "def"}, "pyerrors.input.json.dump_dict_to_json": {"fullname": "pyerrors.input.json.dump_dict_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_dict_to_json", "kind": "function", "doc": "
    Export a dict of Obs or structures containing Obs to a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • od (dict):\nDict of JSON valid structures and objects that will be exported.\nAt the moment, these objects can be either of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    • reps (str):\nSpecify the structure of the placeholder in exported dict to be reps[0-9]+.
      • \n
    • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(od, fname, description='', indent=1, reps='DICTOBS', gz=True):", "funcdef": "def"}, "pyerrors.input.json.load_json_dict": {"fullname": "pyerrors.input.json.load_json_dict", "modulename": "pyerrors.input.json", "qualname": "load_json_dict", "kind": "function", "doc": "
    Import a dict of Obs or structures containing Obs from a .json(.gz) file.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    • reps (str):\nSpecify the structure of the placeholder in imported dict to be reps[0-9]+.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • data (Obs / list / Corr):\nRead data
      • \n
    • or
      • \n
    • data (dict):\nRead data and meta-data
      • \n
    \n", "signature": "(fname, verbose=True, gz=True, full_output=False, reps='DICTOBS'):", "funcdef": "def"}, "pyerrors.input.misc": {"fullname": "pyerrors.input.misc", "modulename": "pyerrors.input.misc", "kind": "module", "doc": "
    \n"}, "pyerrors.input.misc.fit_t0": {"fullname": "pyerrors.input.misc.fit_t0", "modulename": "pyerrors.input.misc", "qualname": "fit_t0", "kind": "function", "doc": "
    Compute the root of (flow-based) data based on a dictionary that contains\nthe necessary information in key-value pairs a la (flow time: observable at flow time).
    \n\n
    It is assumed that the data is monotonically increasing and passes zero from below.\nNo exception is thrown if this is not the case (several roots, no monotonic increase).\nAn exception is thrown if no root can be found in the data.
    \n\n
    A linear fit in the vicinity of the root is performed to exctract the root from the\ntwo fit parameters.
    \n\n
    Parameters
    \n\n
      \n
    • t2E_dict (dict):\nDictionary with pairs of (flow time: observable at flow time) where the flow times\nare of type float and the observables of type Obs.
      • \n
    • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit.
      • \n
    • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data. (Default: False)
      • \n
    • observable (str):\nKeyword to identify the observable to print the correct ylabel (if plot_fit is True)\nfor the observables 't0' and 'w0'. No y label is printed otherwise. (Default: 't0')
      • \n
    \n\n
    Returns
    \n\n
      \n
    • root (Obs):\nThe root of the data series.
      • \n
    \n", "signature": "(t2E_dict, fit_range, plot_fit=False, observable='t0'):", "funcdef": "def"}, "pyerrors.input.misc.read_pbp": {"fullname": "pyerrors.input.misc.read_pbp", "modulename": "pyerrors.input.misc", "qualname": "read_pbp", "kind": "function", "doc": "
    Read pbp format from given folder structure.
    \n\n
    Parameters
    \n\n
      \n
    • r_start (list):\nlist which contains the first config to be read for each replicum
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (list[Obs]):\nlist of observables read
      • \n
    \n", "signature": "(path, prefix, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD": {"fullname": "pyerrors.input.openQCD", "modulename": "pyerrors.input.openQCD", "kind": "module", "doc": "
    \n"}, "pyerrors.input.openQCD.read_rwms": {"fullname": "pyerrors.input.openQCD.read_rwms", "modulename": "pyerrors.input.openQCD", "qualname": "read_rwms", "kind": "function", "doc": "
    Read rwms format from given folder structure. Returns a list of length nrw
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath that contains the data files
      • \n
    • prefix (str):\nall files in path that start with prefix are considered as input files.\nMay be used together postfix to consider only special file endings.\nPrefix is ignored, if the keyword 'files' is used.
      • \n
    • version (str):\nversion of openQCD, default 2.0
      • \n
    • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum
      • \n
    • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
      • \n
    • postfix (str):\npostfix of the file to read, e.g. '.ms1' for openQCD-files
      • \n
    • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
      • \n
    • print_err (bool):\nPrint additional information that is useful for debugging.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • rwms (Obs):\nReweighting factors read
      • \n
    \n", "signature": "(path, prefix, version='2.0', names=None, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.extract_t0": {"fullname": "pyerrors.input.openQCD.extract_t0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_t0", "kind": "function", "doc": "
    Extract t0/a^2 from given .ms.dat files. Returns t0 as Obs.
    \n\n
    It is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t^2 - c (where c=0.3 by default)\nis fitted with a linear function\nfrom which the exact root is extracted.
    \n\n
    It is assumed that one measurement is performed for each config.\nIf this is not the case, the resulting idl, as well as the handling\nof r_start, r_stop and r_step is wrong and the user has to correct\nthis in the resulting observable.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nPath to .ms.dat files
      • \n
    • prefix (str):\nEnsemble prefix
      • \n
    • dtr_read (int):\nDetermines how many trajectories should be skipped\nwhen reading the ms.dat files.\nCorresponds to dtr_cnfg / dtr_ms in the openQCD input file.
      • \n
    • xmin (int):\nFirst timeslice where the boundary\neffects have sufficiently decayed.
      • \n
    • spatial_extent (int):\nspatial extent of the lattice, required for normalization.
      • \n
    • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
      • \n
    • postfix (str):\nPostfix of measurement file (Default: ms)
      • \n
    • c (float):\nConstant that defines the flow scale. Default 0.3 for t_0, choose 2./3 for t_1.
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
      • \n
    • plaquette (bool):\nIf true extract the plaquette estimate of t0 instead.
      • \n
    • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
      • \n
    • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
      • \n
    • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.
      • \n
    • assume_thermalization (bool):\nIf True: If the first record divided by the distance between two measurements is larger than\n1, it is assumed that this is due to thermalization and the first measurement belongs\nto the first config (default).\nIf False: The config numbers are assumed to be traj_number // difference
      • \n
    \n\n
    Returns
    \n\n
      \n
    • t0 (Obs):\nExtracted t0
      • \n
    \n", "signature": "(\tpath,\tprefix,\tdtr_read,\txmin,\tspatial_extent,\tfit_range=5,\tpostfix='ms',\tc=0.3,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.extract_w0": {"fullname": "pyerrors.input.openQCD.extract_w0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_w0", "kind": "function", "doc": "
    Extract w0/a from given .ms.dat files. Returns w0 as Obs.
    \n\n
    It is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t d(t^2)/dt -  (where c=0.3 by default)\nis fitted with a linear function\nfrom which the exact root is extracted.
    \n\n
    It is assumed that one measurement is performed for each config.\nIf this is not the case, the resulting idl, as well as the handling\nof r_start, r_stop and r_step is wrong and the user has to correct\nthis in the resulting observable.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nPath to .ms.dat files
      • \n
    • prefix (str):\nEnsemble prefix
      • \n
    • dtr_read (int):\nDetermines how many trajectories should be skipped\nwhen reading the ms.dat files.\nCorresponds to dtr_cnfg / dtr_ms in the openQCD input file.
      • \n
    • xmin (int):\nFirst timeslice where the boundary\neffects have sufficiently decayed.
      • \n
    • spatial_extent (int):\nspatial extent of the lattice, required for normalization.
      • \n
    • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
      • \n
    • postfix (str):\nPostfix of measurement file (Default: ms)
      • \n
    • c (float):\nConstant that defines the flow scale. Default 0.3 for w_0, choose 2./3 for w_1.
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
      • \n
    • plaquette (bool):\nIf true extract the plaquette estimate of w0 instead.
      • \n
    • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
      • \n
    • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
      • \n
    • plot_fit (bool):\nIf true, the fit for the extraction of w0 is shown together with the data.
      • \n
    • assume_thermalization (bool):\nIf True: If the first record divided by the distance between two measurements is larger than\n1, it is assumed that this is due to thermalization and the first measurement belongs\nto the first config (default).\nIf False: The config numbers are assumed to be traj_number // difference
      • \n
    \n\n
    Returns
    \n\n
      \n
    • w0 (Obs):\nExtracted w0
      • \n
    \n", "signature": "(\tpath,\tprefix,\tdtr_read,\txmin,\tspatial_extent,\tfit_range=5,\tpostfix='ms',\tc=0.3,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop": {"fullname": "pyerrors.input.openQCD.read_qtop", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop", "kind": "function", "doc": "
    Read the topologial charge based on openQCD gradient flow measurements.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • version (str):\nEither openQCD or sfqcd, depending on the data.
      • \n
    • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • postfix (str):\npostfix of the file to read, e.g. '.gfms.dat' for openQCD-files
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
      • \n
    • integer_charge (bool):\nIf True, the charge is rounded towards the nearest integer on each config.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (Obs):\nRead topological charge
      • \n
    \n", "signature": "(path, prefix, c, dtr_cnfg=1, version='openQCD', **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_gf_coupling": {"fullname": "pyerrors.input.openQCD.read_gf_coupling", "modulename": "pyerrors.input.openQCD", "qualname": "read_gf_coupling", "kind": "function", "doc": "
    Read the gradient flow coupling based on sfqcd gradient flow measurements. See 1607.06423 for details.
    \n\n
    Note: The current implementation only works for c=0.3 and T=L. The definition of the coupling in 1607.06423 requires projection to topological charge zero which is not done within this function but has to be performed in a separate step.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.
      • \n
    • postfix (str):\npostfix of the file to read, e.g. '.gfms.dat' for openQCD-files
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for the coupling. If False, the Wilson flow is used.
      • \n
    \n", "signature": "(path, prefix, c, dtr_cnfg=1, Zeuthen_flow=True, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.qtop_projection": {"fullname": "pyerrors.input.openQCD.qtop_projection", "modulename": "pyerrors.input.openQCD", "qualname": "qtop_projection", "kind": "function", "doc": "
    Returns the projection to the topological charge sector defined by target.
    \n\n
    Parameters
    \n\n
      \n
    • path (Obs):\nTopological charge.
      • \n
    • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
      • \n
    \n\n
    Returns
    \n\n
      \n
    • reto (Obs):\nprojection to the topological charge sector defined by target
      • \n
    \n", "signature": "(qtop, target=0):", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop_sector": {"fullname": "pyerrors.input.openQCD.read_qtop_sector", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop_sector", "kind": "function", "doc": "
    Constructs reweighting factors to a specified topological sector.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L
      • \n
    • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of trajectories\nbetween two configs.\nif it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • version (str):\nversion string of the openQCD (sfqcd) version used to create\nthe ensemble. Default is 2.0. May also be set to sfqcd.
      • \n
    • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
      • \n
    • r_start (list):\noffset of the first ensemble, making it easier to match\nlater on with other Obs
      • \n
    • r_stop (list):\nlast configurations that need to be read (per replicum)
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • reto (Obs):\nprojection to the topological charge sector defined by target
      • \n
    \n", "signature": "(path, prefix, c, target=0, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_ms5_xsf": {"fullname": "pyerrors.input.openQCD.read_ms5_xsf", "modulename": "pyerrors.input.openQCD", "qualname": "read_ms5_xsf", "kind": "function", "doc": "
    Read data from files in the specified directory with the specified prefix and quark combination extension, and return a Corr object containing the data.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nThe directory to search for the files in.
      • \n
    • prefix (str):\nThe prefix to match the files against.
      • \n
    • qc (str):\nThe quark combination extension to match the files against.
      • \n
    • corr (str):\nThe correlator to extract data for.
      • \n
    • sep (str, optional):\nThe separator to use when parsing the replika names.
      • \n
    • **kwargs: Additional keyword arguments. The following keyword arguments are recognized:
      \n\n
        \n
      • names (List[str]): A list of names to use for the replicas.
        • \n
      • \n
    \n\n
    Returns
    \n\n
      \n
    • Corr: A complex valued Corr object containing the data read from the files. In case of boudary to bulk correlators.
      • \n
    • or
      • \n
    • CObs: A complex valued CObs object containing the data read from the files. In case of boudary to boundary correlators.
      • \n
    \n\n
    Raises
    \n\n
      \n
    • FileNotFoundError: If no files matching the specified prefix and quark combination extension are found in the specified directory.
      • \n
    • IOError: If there is an error reading a file.
      • \n
    • struct.error: If there is an error unpacking binary data.
      • \n
    \n", "signature": "(path, prefix, qc, corr, sep='r', **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas": {"fullname": "pyerrors.input.pandas", "modulename": "pyerrors.input.pandas", "kind": "module", "doc": "
    \n"}, "pyerrors.input.pandas.to_sql": {"fullname": "pyerrors.input.pandas.to_sql", "modulename": "pyerrors.input.pandas", "qualname": "to_sql", "kind": "function", "doc": "
    Write DataFrame including Obs or Corr valued columns to sqlite database.
    \n\n
    Parameters
    \n\n
      \n
    • df (pandas.DataFrame):\nDataframe to be written to the database.
      • \n
    • table_name (str):\nName of the table in the database.
      • \n
    • db (str):\nPath to the sqlite database.
      • \n
    • if exists (str):\nHow to behave if table already exists. Options 'fail', 'replace', 'append'.
      • \n
    • gz (bool):\nIf True the json strings are gzipped.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(df, table_name, db, if_exists='fail', gz=True, **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas.read_sql": {"fullname": "pyerrors.input.pandas.read_sql", "modulename": "pyerrors.input.pandas", "qualname": "read_sql", "kind": "function", "doc": "
    Execute SQL query on sqlite database and obtain DataFrame including Obs or Corr valued columns.
    \n\n
    Parameters
    \n\n
      \n
    • sql (str):\nSQL query to be executed.
      • \n
    • db (str):\nPath to the sqlite database.
      • \n
    • auto_gamma (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • data (pandas.DataFrame):\nDataframe with the content of the sqlite database.
      • \n
    \n", "signature": "(sql, db, auto_gamma=False, **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas.dump_df": {"fullname": "pyerrors.input.pandas.dump_df", "modulename": "pyerrors.input.pandas", "qualname": "dump_df", "kind": "function", "doc": "
    Exports a pandas DataFrame containing Obs valued columns to a (gzipped) csv file.
    \n\n
    Before making use of pandas to_csv functionality Obs objects are serialized via the standardized\njson format of pyerrors.
    \n\n
    Parameters
    \n\n
      \n
    • df (pandas.DataFrame):\nDataframe to be dumped to a file.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • gz (bool):\nIf True, the output is a gzipped csv file. If False, the output is a csv file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(df, fname, gz=True):", "funcdef": "def"}, "pyerrors.input.pandas.load_df": {"fullname": "pyerrors.input.pandas.load_df", "modulename": "pyerrors.input.pandas", "qualname": "load_df", "kind": "function", "doc": "
    Imports a pandas DataFrame from a csv.(gz) file in which Obs objects are serialized as json strings.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • auto_gamma (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • data (pandas.DataFrame):\nDataframe with the content of the sqlite database.
      • \n
    \n", "signature": "(fname, auto_gamma=False, gz=True):", "funcdef": "def"}, "pyerrors.input.sfcf": {"fullname": "pyerrors.input.sfcf", "modulename": "pyerrors.input.sfcf", "kind": "module", "doc": "
    \n"}, "pyerrors.input.sfcf.read_sfcf": {"fullname": "pyerrors.input.sfcf.read_sfcf", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf", "kind": "function", "doc": "
    Read sfcf files from given folder structure.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nPath to the sfcf files.
      • \n
    • prefix (str):\nPrefix of the sfcf files.
      • \n
    • name (str):\nName of the correlation function to read.
      • \n
    • quarks (str):\nLabel of the quarks used in the sfcf input file. e.g. \"quark quark\"\nfor version 0.0 this does NOT need to be given with the typical \" - \"\nthat is present in the output file,\nthis is done automatically for this version
      • \n
    • corr_type (str):\nType of correlation function to read. Can be\n
        \n
      • 'bi' for boundary-inner
        • \n
      • 'bb' for boundary-boundary
        • \n
      • 'bib' for boundary-inner-boundary
        • \n
      • \n
    • noffset (int):\nOffset of the source (only relevant when wavefunctions are used)
      • \n
    • wf (int):\nID of wave function
      • \n
    • wf2 (int):\nID of the second wavefunction\n(only relevant for boundary-to-boundary correlation functions)
      • \n
    • im (bool):\nif True, read imaginary instead of real part\nof the correlation function.
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
      • \n
    • ens_name (str):\nreplaces the name of the ensemble
      • \n
    • version (str):\nversion of SFCF, with which the measurement was done.\nif the compact output option (-c) was specified,\nappend a \"c\" to the version (e.g. \"1.0c\")\nif the append output option (-a) was specified,\nappend an \"a\" to the version
      • \n
    • cfg_separator (str):\nString that separates the ensemble identifier from the configuration number (default 'n').
      • \n
    • replica (list):\nlist of replica to be read, default is all
      • \n
    • files (list):\nlist of files to be read per replica, default is all.\nfor non-compact output format, hand the folders to be read here.
      • \n
    • check_configs (list[list[int]]):\nlist of list of supposed configs, eg. [range(1,1000)]\nfor one replicum with 1000 configs
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (list[Obs]):\nlist of Observables with length T, observable per timeslice.\nbb-type correlators have length 1.
      • \n
    \n", "signature": "(\tpath,\tprefix,\tname,\tquarks='.*',\tcorr_type='bi',\tnoffset=0,\twf=0,\twf2=0,\tversion='1.0c',\tcfg_separator='n',\tsilent=False,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.utils": {"fullname": "pyerrors.input.utils", "modulename": "pyerrors.input.utils", "kind": "module", "doc": "
    \n"}, "pyerrors.input.utils.sort_names": {"fullname": "pyerrors.input.utils.sort_names", "modulename": "pyerrors.input.utils", "qualname": "sort_names", "kind": "function", "doc": "
    Sorts a list of names of replika with searches for r and id in the replikum string.\nIf this search fails, a fallback method is used,\nwhere the strings are simply compared and the first diffeing numeral is used for differentiation.
    \n\n
    Parameters
    \n\n
      \n
    • ll (list):\nlist to sort
      • \n
    \n\n
    Returns
    \n\n
      \n
    • ll (list):\nsorted list
      • \n
    \n", "signature": "(ll):", "funcdef": "def"}, "pyerrors.input.utils.check_idl": {"fullname": "pyerrors.input.utils.check_idl", "modulename": "pyerrors.input.utils", "qualname": "check_idl", "kind": "function", "doc": "
    Checks if list of configurations is contained in an idl
    \n\n
    Parameters
    \n\n
      \n
    • idl (range or list):\nidl of the current replicum
      • \n
    • che (list):\nlist of configurations to be checked against
      • \n
    \n\n
    Returns
    \n\n
      \n
    • miss_str (str):\nstring with integers of which idls are missing
      • \n
    \n", "signature": "(idl, che):", "funcdef": "def"}, "pyerrors.linalg": {"fullname": "pyerrors.linalg", "modulename": "pyerrors.linalg", "kind": "module", "doc": "
    \n"}, "pyerrors.linalg.matmul": {"fullname": "pyerrors.linalg.matmul", "modulename": "pyerrors.linalg", "qualname": "matmul", "kind": "function", "doc": "
    Matrix multiply all operands.
    \n\n
    Parameters
    \n\n
      \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    • This implementation is faster compared to standard multiplication via the @ operator.
      • \n
    \n", "signature": "(*operands):", "funcdef": "def"}, "pyerrors.linalg.jack_matmul": {"fullname": "pyerrors.linalg.jack_matmul", "modulename": "pyerrors.linalg", "qualname": "jack_matmul", "kind": "function", "doc": "
    Matrix multiply both operands making use of the jackknife approximation.
    \n\n
    Parameters
    \n\n
      \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    • For large matrices this is considerably faster compared to matmul.
      • \n
    \n", "signature": "(*operands):", "funcdef": "def"}, "pyerrors.linalg.einsum": {"fullname": "pyerrors.linalg.einsum", "modulename": "pyerrors.linalg", "qualname": "einsum", "kind": "function", "doc": "
    Wrapper for numpy.einsum
    \n\n
    Parameters
    \n\n
      \n
    • subscripts (str):\nSubscripts for summation (see numpy documentation for details)
      • \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    \n", "signature": "(subscripts, *operands):", "funcdef": "def"}, "pyerrors.linalg.inv": {"fullname": "pyerrors.linalg.inv", "modulename": "pyerrors.linalg", "qualname": "inv", "kind": "function", "doc": "
    Inverse of Obs or CObs valued matrices.
    \n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.cholesky": {"fullname": "pyerrors.linalg.cholesky", "modulename": "pyerrors.linalg", "qualname": "cholesky", "kind": "function", "doc": "
    Cholesky decomposition of Obs valued matrices.
    \n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.det": {"fullname": "pyerrors.linalg.det", "modulename": "pyerrors.linalg", "qualname": "det", "kind": "function", "doc": "
    Determinant of Obs valued matrices.
    \n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.eigh": {"fullname": "pyerrors.linalg.eigh", "modulename": "pyerrors.linalg", "qualname": "eigh", "kind": "function", "doc": "
    Computes the eigenvalues and eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.eig": {"fullname": "pyerrors.linalg.eig", "modulename": "pyerrors.linalg", "qualname": "eig", "kind": "function", "doc": "
    Computes the eigenvalues of a given matrix of Obs according to np.linalg.eig.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.pinv": {"fullname": "pyerrors.linalg.pinv", "modulename": "pyerrors.linalg", "qualname": "pinv", "kind": "function", "doc": "
    Computes the Moore-Penrose pseudoinverse of a matrix of Obs.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.svd": {"fullname": "pyerrors.linalg.svd", "modulename": "pyerrors.linalg", "qualname": "svd", "kind": "function", "doc": "
    Computes the singular value decomposition of a matrix of Obs.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.misc": {"fullname": "pyerrors.misc", "modulename": "pyerrors.misc", "kind": "module", "doc": "
    \n"}, "pyerrors.misc.print_config": {"fullname": "pyerrors.misc.print_config", "modulename": "pyerrors.misc", "qualname": "print_config", "kind": "function", "doc": "
    Print information about version of python, pyerrors and dependencies.
    \n", "signature": "():", "funcdef": "def"}, "pyerrors.misc.errorbar": {"fullname": "pyerrors.misc.errorbar", "modulename": "pyerrors.misc", "qualname": "errorbar", "kind": "function", "doc": "
    pyerrors wrapper for the errorbars method of matplotlib
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nA list of x-values which can be Obs.
      • \n
    • y (list):\nA list of y-values which can be Obs.
      • \n
    • axes ((matplotlib.pyplot.axes)):\nThe axes to plot on. default is plt.
      • \n
    \n", "signature": "(\tx,\ty,\taxes=<module 'matplotlib.pyplot' from '/opt/hostedtoolcache/Python/3.10.11/x64/lib/python3.10/site-packages/matplotlib/pyplot.py'>,\t**kwargs):", "funcdef": "def"}, "pyerrors.misc.dump_object": {"fullname": "pyerrors.misc.dump_object", "modulename": "pyerrors.misc", "qualname": "dump_object", "kind": "function", "doc": "
    Dump object into pickle file.
    \n\n
    Parameters
    \n\n
      \n
    • obj (object):\nobject to be saved in the pickle file
      • \n
    • name (str):\nname of the file
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(obj, name, **kwargs):", "funcdef": "def"}, "pyerrors.misc.load_object": {"fullname": "pyerrors.misc.load_object", "modulename": "pyerrors.misc", "qualname": "load_object", "kind": "function", "doc": "
    Load object from pickle file.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the file
      • \n
    \n\n
    Returns
    \n\n
      \n
    • object (Obs):\nLoaded Object
      • \n
    \n", "signature": "(path):", "funcdef": "def"}, "pyerrors.misc.pseudo_Obs": {"fullname": "pyerrors.misc.pseudo_Obs", "modulename": "pyerrors.misc", "qualname": "pseudo_Obs", "kind": "function", "doc": "
    Generate an Obs object with given value, dvalue and name for test purposes
    \n\n
    Parameters
    \n\n
      \n
    • value (float):\ncentral value of the Obs to be generated.
      • \n
    • dvalue (float):\nerror of the Obs to be generated.
      • \n
    • name (str):\nname of the ensemble for which the Obs is to be generated.
      • \n
    • samples (int):\nnumber of samples for the Obs (default 1000).
      • \n
    \n\n
    Returns
    \n\n
      \n
    • res (Obs):\nGenerated Observable
      • \n
    \n", "signature": "(value, dvalue, name, samples=1000):", "funcdef": "def"}, "pyerrors.misc.gen_correlated_data": {"fullname": "pyerrors.misc.gen_correlated_data", "modulename": "pyerrors.misc", "qualname": "gen_correlated_data", "kind": "function", "doc": "
    Generate observables with given covariance and autocorrelation times.
    \n\n
    Parameters
    \n\n
      \n
    • means (list):\nlist containing the mean value of each observable.
      • \n
    • cov (numpy.ndarray):\ncovariance matrix for the data to be generated.
      • \n
    • name (str):\nensemble name for the data to be geneated.
      • \n
    • tau (float or list):\ncan either be a real number or a list with an entry for\nevery dataset.
      • \n
    • samples (int):\nnumber of samples to be generated for each observable.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • corr_obs (list[Obs]):\nGenerated observable list
      • \n
    \n", "signature": "(means, cov, name, tau=0.5, samples=1000):", "funcdef": "def"}, "pyerrors.mpm": {"fullname": "pyerrors.mpm", "modulename": "pyerrors.mpm", "kind": "module", "doc": "
    \n"}, "pyerrors.mpm.matrix_pencil_method": {"fullname": "pyerrors.mpm.matrix_pencil_method", "modulename": "pyerrors.mpm", "qualname": "matrix_pencil_method", "kind": "function", "doc": "
    Matrix pencil method to extract k energy levels from data
    \n\n
    Implementation of the matrix pencil method based on\neq. (2.17) of Y. Hua, T. K. Sarkar, IEEE Trans. Acoust. 38, 814-824 (1990)
    \n\n
    Parameters
    \n\n
      \n
    • data (list):\ncan be a list of Obs for the analysis of a single correlator, or a list of lists\nof Obs if several correlators are to analyzed at once.
      • \n
    • k (int):\nNumber of states to extract (default 1).
      • \n
    • p (int):\nmatrix pencil parameter which filters noise. The optimal value is expected between\nlen(data)/3 and 2*len(data)/3. The computation is more expensive the closer p is\nto len(data)/2 but could possibly suppress more noise (default len(data)//2).
      • \n
    \n\n
    Returns
    \n\n
      \n
    • energy_levels (list[Obs]):\nExtracted energy levels
      • \n
    \n", "signature": "(corrs, k=1, p=None, **kwargs):", "funcdef": "def"}, "pyerrors.obs": {"fullname": "pyerrors.obs", "modulename": "pyerrors.obs", "kind": "module", "doc": "
    \n"}, "pyerrors.obs.Obs": {"fullname": "pyerrors.obs.Obs", "modulename": "pyerrors.obs", "qualname": "Obs", "kind": "class", "doc": "
    Class for a general observable.
    \n\n
    Instances of Obs are the basic objects of a pyerrors error analysis.\nThey are initialized with a list which contains arrays of samples for\ndifferent ensembles/replica and another list of same length which contains\nthe names of the ensembles/replica. Mathematical operations can be\nperformed on instances. The result is another instance of Obs. The error of\nan instance can be computed with the gamma_method. Also contains additional\nmethods for output and visualization of the error calculation.
    \n\n
    Attributes
    \n\n
      \n
    • S_global (float):\nStandard value for S (default 2.0)
      • \n
    • S_dict (dict):\nDictionary for S values. If an entry for a given ensemble\nexists this overwrites the standard value for that ensemble.
      • \n
    • tau_exp_global (float):\nStandard value for tau_exp (default 0.0)
      • \n
    • tau_exp_dict (dict):\nDictionary for tau_exp values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
      • \n
    • N_sigma_global (float):\nStandard value for N_sigma (default 1.0)
      • \n
    • N_sigma_dict (dict):\nDictionary for N_sigma values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
      • \n
    \n"}, "pyerrors.obs.Obs.__init__": {"fullname": "pyerrors.obs.Obs.__init__", "modulename": "pyerrors.obs", "qualname": "Obs.__init__", "kind": "function", "doc": "
    Initialize Obs object.
    \n\n
    Parameters
    \n\n
      \n
    • samples (list):\nlist of numpy arrays containing the Monte Carlo samples
      • \n
    • names (list):\nlist of strings labeling the individual samples
      • \n
    • idl (list, optional):\nlist of ranges or lists on which the samples are defined
      • \n
    \n", "signature": "(samples, names, idl=None, **kwargs)"}, "pyerrors.obs.Obs.gamma_method": {"fullname": "pyerrors.obs.Obs.gamma_method", "modulename": "pyerrors.obs", "qualname": "Obs.gamma_method", "kind": "function", "doc": "
    Estimate the error and related properties of the Obs.
    \n\n
    Parameters
    \n\n
      \n
    • S (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.
      • \n
    • tau_exp (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).
      • \n
    • N_sigma (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).
      • \n
    • fft (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True)
      • \n
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.gm": {"fullname": "pyerrors.obs.Obs.gm", "modulename": "pyerrors.obs", "qualname": "Obs.gm", "kind": "function", "doc": "
    Estimate the error and related properties of the Obs.
    \n\n
    Parameters
    \n\n
      \n
    • S (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.
      • \n
    • tau_exp (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).
      • \n
    • N_sigma (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).
      • \n
    • fft (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True)
      • \n
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.details": {"fullname": "pyerrors.obs.Obs.details", "modulename": "pyerrors.obs", "qualname": "Obs.details", "kind": "function", "doc": "
    Output detailed properties of the Obs.
    \n\n
    Parameters
    \n\n
      \n
    • ens_content (bool):\nprint details about the ensembles and replica if true.
      • \n
    \n", "signature": "(self, ens_content=True):", "funcdef": "def"}, "pyerrors.obs.Obs.reweight": {"fullname": "pyerrors.obs.Obs.reweight", "modulename": "pyerrors.obs", "qualname": "Obs.reweight", "kind": "function", "doc": "
    Reweight the obs with given rewighting factors.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. Default False.
      • \n
    \n", "signature": "(self, weight):", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero_within_error": {"fullname": "pyerrors.obs.Obs.is_zero_within_error", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero_within_error", "kind": "function", "doc": "
    Checks whether the observable is zero within 'sigma' standard errors.
    \n\n
    Parameters
    \n\n
      \n
    • sigma (int):\nNumber of standard errors used for the check.
      • \n
    • Works only properly when the gamma method was run.
      • \n
    \n", "signature": "(self, sigma=1):", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero": {"fullname": "pyerrors.obs.Obs.is_zero", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero", "kind": "function", "doc": "
    Checks whether the observable is zero within a given tolerance.
    \n\n
    Parameters
    \n\n
      \n
    • atol (float):\nAbsolute tolerance (for details see numpy documentation).
      • \n
    \n", "signature": "(self, atol=1e-10):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_tauint": {"fullname": "pyerrors.obs.Obs.plot_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.plot_tauint", "kind": "function", "doc": "
    Plot integrated autocorrelation time for each ensemble.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rho": {"fullname": "pyerrors.obs.Obs.plot_rho", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rho", "kind": "function", "doc": "
    Plot normalized autocorrelation function time for each ensemble.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rep_dist": {"fullname": "pyerrors.obs.Obs.plot_rep_dist", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rep_dist", "kind": "function", "doc": "
    Plot replica distribution for each ensemble with more than one replicum.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_history": {"fullname": "pyerrors.obs.Obs.plot_history", "modulename": "pyerrors.obs", "qualname": "Obs.plot_history", "kind": "function", "doc": "
    Plot derived Monte Carlo history for each ensemble
    \n\n
    Parameters
    \n\n
      \n
    • expand (bool):\nshow expanded history for irregular Monte Carlo chains (default: True).
      • \n
    \n", "signature": "(self, expand=True):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_piechart": {"fullname": "pyerrors.obs.Obs.plot_piechart", "modulename": "pyerrors.obs", "qualname": "Obs.plot_piechart", "kind": "function", "doc": "
    Plot piechart which shows the fractional contribution of each\nensemble to the error and returns a dictionary containing the fractions.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.dump": {"fullname": "pyerrors.obs.Obs.dump", "modulename": "pyerrors.obs", "qualname": "Obs.dump", "kind": "function", "doc": "
    Dump the Obs to a file 'name' of chosen format.
    \n\n
    Parameters
    \n\n
      \n
    • filename (str):\nname of the file to be saved.
      • \n
    • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
      • \n
    • description (str):\nDescription for output file, only relevant for json.gz format.
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n", "signature": "(self, filename, datatype='json.gz', description='', **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.export_jackknife": {"fullname": "pyerrors.obs.Obs.export_jackknife", "modulename": "pyerrors.obs", "qualname": "Obs.export_jackknife", "kind": "function", "doc": "
    Export jackknife samples from the Obs
    \n\n
    Returns
    \n\n
      \n
    • numpy.ndarray: Returns a numpy array of length N + 1 where N is the number of samples\nfor the given ensemble and replicum. The zeroth entry of the array contains\nthe mean value of the Obs, entries 1 to N contain the N jackknife samples\nderived from the Obs. The current implementation only works for observables\ndefined on exactly one ensemble and replicum. The derived jackknife samples\nshould agree with samples from a full jackknife analysis up to O(1/N).
      • \n
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.sqrt": {"fullname": "pyerrors.obs.Obs.sqrt", "modulename": "pyerrors.obs", "qualname": "Obs.sqrt", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.log": {"fullname": "pyerrors.obs.Obs.log", "modulename": "pyerrors.obs", "qualname": "Obs.log", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.exp": {"fullname": "pyerrors.obs.Obs.exp", "modulename": "pyerrors.obs", "qualname": "Obs.exp", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.sin": {"fullname": "pyerrors.obs.Obs.sin", "modulename": "pyerrors.obs", "qualname": "Obs.sin", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.cos": {"fullname": "pyerrors.obs.Obs.cos", "modulename": "pyerrors.obs", "qualname": "Obs.cos", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.tan": {"fullname": "pyerrors.obs.Obs.tan", "modulename": "pyerrors.obs", "qualname": "Obs.tan", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arcsin": {"fullname": "pyerrors.obs.Obs.arcsin", "modulename": "pyerrors.obs", "qualname": "Obs.arcsin", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arccos": {"fullname": "pyerrors.obs.Obs.arccos", "modulename": "pyerrors.obs", "qualname": "Obs.arccos", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arctan": {"fullname": "pyerrors.obs.Obs.arctan", "modulename": "pyerrors.obs", "qualname": "Obs.arctan", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.sinh": {"fullname": "pyerrors.obs.Obs.sinh", "modulename": "pyerrors.obs", "qualname": "Obs.sinh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.cosh": {"fullname": "pyerrors.obs.Obs.cosh", "modulename": "pyerrors.obs", "qualname": "Obs.cosh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.tanh": {"fullname": "pyerrors.obs.Obs.tanh", "modulename": "pyerrors.obs", "qualname": "Obs.tanh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arcsinh": {"fullname": "pyerrors.obs.Obs.arcsinh", "modulename": "pyerrors.obs", "qualname": "Obs.arcsinh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arccosh": {"fullname": "pyerrors.obs.Obs.arccosh", "modulename": "pyerrors.obs", "qualname": "Obs.arccosh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arctanh": {"fullname": "pyerrors.obs.Obs.arctanh", "modulename": "pyerrors.obs", "qualname": "Obs.arctanh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.CObs": {"fullname": "pyerrors.obs.CObs", "modulename": "pyerrors.obs", "qualname": "CObs", "kind": "class", "doc": "
    Class for a complex valued observable.
    \n"}, "pyerrors.obs.CObs.__init__": {"fullname": "pyerrors.obs.CObs.__init__", "modulename": "pyerrors.obs", "qualname": "CObs.__init__", "kind": "function", "doc": "
    \n", "signature": "(real, imag=0.0)"}, "pyerrors.obs.CObs.gamma_method": {"fullname": "pyerrors.obs.CObs.gamma_method", "modulename": "pyerrors.obs", "qualname": "CObs.gamma_method", "kind": "function", "doc": "
    Executes the gamma_method for the real and the imaginary part.
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.CObs.is_zero": {"fullname": "pyerrors.obs.CObs.is_zero", "modulename": "pyerrors.obs", "qualname": "CObs.is_zero", "kind": "function", "doc": "
    Checks whether both real and imaginary part are zero within machine precision.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.CObs.conjugate": {"fullname": "pyerrors.obs.CObs.conjugate", "modulename": "pyerrors.obs", "qualname": "CObs.conjugate", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.derived_observable": {"fullname": "pyerrors.obs.derived_observable", "modulename": "pyerrors.obs", "qualname": "derived_observable", "kind": "function", "doc": "
    Construct a derived Obs according to func(data, **kwargs) using automatic differentiation.
    \n\n
    Parameters
    \n\n
      \n
    • func (object):\narbitrary function of the form func(data, **kwargs). For the\nautomatic differentiation to work, all numpy functions have to have\nthe autograd wrapper (use 'import autograd.numpy as anp').
      • \n
    • data (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
      • \n
    • num_grad (bool):\nif True, numerical derivatives are used instead of autograd\n(default False). To control the numerical differentiation the\nkwargs of numdifftools.step_generators.MaxStepGenerator\ncan be used.
      • \n
    • man_grad (list):\nmanually supply a list or an array which contains the jacobian\nof func. Use cautiously, supplying the wrong derivative will\nnot be intercepted.
      • \n
    \n\n
    Notes
    \n\n
    For simple mathematical operations it can be practical to use anonymous\nfunctions. For the ratio of two observables one can e.g. use
    \n\n
    new_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2])
    \n", "signature": "(func, data, array_mode=False, **kwargs):", "funcdef": "def"}, "pyerrors.obs.reweight": {"fullname": "pyerrors.obs.reweight", "modulename": "pyerrors.obs", "qualname": "reweight", "kind": "function", "doc": "
    Reweight a list of observables.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • obs (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. Default False.
      • \n
    \n", "signature": "(weight, obs, **kwargs):", "funcdef": "def"}, "pyerrors.obs.correlate": {"fullname": "pyerrors.obs.correlate", "modulename": "pyerrors.obs", "qualname": "correlate", "kind": "function", "doc": "
    Correlate two observables.
    \n\n
    Parameters
    \n\n
      \n
    • obs_a (Obs):\nFirst observable
      • \n
    • obs_b (Obs):\nSecond observable
      • \n
    \n\n
    Notes
    \n\n
    Keep in mind to only correlate primary observables which have not been reweighted\nyet. The reweighting has to be applied after correlating the observables.\nCurrently only works if ensembles are identical (this is not strictly necessary).
    \n", "signature": "(obs_a, obs_b):", "funcdef": "def"}, "pyerrors.obs.covariance": {"fullname": "pyerrors.obs.covariance", "modulename": "pyerrors.obs", "qualname": "covariance", "kind": "function", "doc": "
    Calculates the error covariance matrix of a set of observables.
    \n\n
    WARNING: This function should be used with care, especially for observables with support on multiple\n         ensembles with differing autocorrelations. See the notes below for details.
    \n\n
    The gamma method has to be applied first to all observables.
    \n\n
    Parameters
    \n\n
      \n
    • obs (list or numpy.ndarray):\nList or one dimensional array of Obs
      • \n
    • visualize (bool):\nIf True plots the corresponding normalized correlation matrix (default False).
      • \n
    • correlation (bool):\nIf True the correlation matrix instead of the error covariance matrix is returned (default False).
      • \n
    • smooth (None or int):\nIf smooth is an integer 'E' between 2 and the dimension of the matrix minus 1 the eigenvalue\nsmoothing procedure of hep-lat/9412087 is applied to the correlation matrix which leaves the\nlargest E eigenvalues essentially unchanged and smoothes the smaller eigenvalues to avoid extremely\nsmall ones.
      • \n
    \n\n
    Notes
    \n\n
    The error covariance is defined such that it agrees with the squared standard error for two identical observables\n$$\\operatorname{cov}(a,a)=\\sum_{s=1}^N\\delta_a^s\\delta_a^s/N^2=\\Gamma_{aa}(0)/N=\\operatorname{var}(a)/N=\\sigma_a^2$$\nin the absence of autocorrelation.\nThe error covariance is estimated by calculating the correlation matrix assuming no autocorrelation and then rescaling the correlation matrix by the full errors including the previous gamma method estimate for the autocorrelation of the observables. The covariance at windowsize 0 is guaranteed to be positive semi-definite\n$$\\sum_{i,j}v_i\\Gamma_{ij}(0)v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i,j}v_i\\delta_i^s\\delta_j^s v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i}|v_i\\delta_i^s|^2\\geq 0\\,,$$ for every $v\\in\\mathbb{R}^M$, while such an identity does not hold for larger windows/lags.\nFor observables defined on a single ensemble our approximation is equivalent to assuming that the integrated autocorrelation time of an off-diagonal element is equal to the geometric mean of the integrated autocorrelation times of the corresponding diagonal elements.\n$$\\tau_{\\mathrm{int}, ij}=\\sqrt{\\tau_{\\mathrm{int}, i}\\times \\tau_{\\mathrm{int}, j}}$$\nThis construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors).
    \n", "signature": "(obs, visualize=False, correlation=False, smooth=None, **kwargs):", "funcdef": "def"}, "pyerrors.obs.import_jackknife": {"fullname": "pyerrors.obs.import_jackknife", "modulename": "pyerrors.obs", "qualname": "import_jackknife", "kind": "function", "doc": "
    Imports jackknife samples and returns an Obs
    \n\n
    Parameters
    \n\n
      \n
    • jacks (numpy.ndarray):\nnumpy array containing the mean value as zeroth entry and\nthe N jackknife samples as first to Nth entry.
      • \n
    • name (str):\nname of the ensemble the samples are defined on.
      • \n
    \n", "signature": "(jacks, name, idl=None):", "funcdef": "def"}, "pyerrors.obs.merge_obs": {"fullname": "pyerrors.obs.merge_obs", "modulename": "pyerrors.obs", "qualname": "merge_obs", "kind": "function", "doc": "
    Combine all observables in list_of_obs into one new observable
    \n\n
    Parameters
    \n\n
      \n
    • list_of_obs (list):\nlist of the Obs object to be combined
      • \n
    \n\n
    Notes
    \n\n
    It is not possible to combine obs which are based on the same replicum
    \n", "signature": "(list_of_obs):", "funcdef": "def"}, "pyerrors.obs.cov_Obs": {"fullname": "pyerrors.obs.cov_Obs", "modulename": "pyerrors.obs", "qualname": "cov_Obs", "kind": "function", "doc": "
    Create an Obs based on mean(s) and a covariance matrix
    \n\n
    Parameters
    \n\n
      \n
    • mean (list of floats or float):\nN mean value(s) of the new Obs
      • \n
    • cov (list or array):\n2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariance
      • \n
    • name (str):\nidentifier for the covariance matrix
      • \n
    • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
      • \n
    \n", "signature": "(means, cov, name, grad=None):", "funcdef": "def"}, "pyerrors.roots": {"fullname": "pyerrors.roots", "modulename": "pyerrors.roots", "kind": "module", "doc": "
    \n"}, "pyerrors.roots.find_root": {"fullname": "pyerrors.roots.find_root", "modulename": "pyerrors.roots", "qualname": "find_root", "kind": "function", "doc": "
    Finds the root of the function func(x, d) where d is an Obs.
    \n\n
    Parameters
    \n\n
      \n
    • d (Obs):\nObs passed to the function.
      • \n
    • func (object):\nFunction to be minimized. Any numpy functions have to use the autograd.numpy wrapper.\nExample:
      \n\n
      \n
      import autograd.numpy as anp\ndef root_func(x, d):\n   return anp.exp(-x ** 2) - d\n
      \n
      • \n
    • guess (float):\nInitial guess for the minimization.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • res (Obs):\nObs valued root of the function.
      • \n
    \n", "signature": "(d, func, guess=1.0, **kwargs):", "funcdef": "def"}, "pyerrors.version": {"fullname": "pyerrors.version", "modulename": "pyerrors.version", "kind": "module", "doc": "
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