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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 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 (cholesky decomposition, calculation of eigenvalues and eigenvectors, singular value decomposition...)
    • \n
\n\n

Getting started

\n\n
import numpy as np\nimport pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name'])\nmy_new_obs = 2 * np.log(my_obs) / my_obs\nmy_new_obs.gamma_method()\nmy_new_obs.details()\nprint(my_new_obs)\n
\n\n

The Obs class

\n\n

pyerrors.obs.Obs

\n\n
import pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name'])\n
\n\n

Multiple ensembles/replica

\n\n

Error propagation for multiple ensembles (Markov chains with different simulation parameters) is handeled automatically. Ensembles are uniquely identified by their name.

\n\n

Example:

\n\n
obs1 = pe.Obs([samples1], ['ensemble1'])\nobs2 = pe.Obs([samples1], ['ensemble2'])\n\nmy_sum = obs1 + obs2\nmy_sum.details()\n> Result         2.00596631e+00 +/- 0.00000000e+00 +/- 0.00000000e+00 (0.000%)\n> 1500 samples in 2 ensembles:\n>    ensemble1: ['ensemble1']\n>    ensemble2: ['ensemble2']\n
\n\n

pyerrors identifies multiple replica (independent Markov chains with identical simulation parameters) by the vertical bar | in the name of the dataset.

\n\n

Example:

\n\n
obs1 = pe.Obs([samples1], ['ensemble1|r01'])\nobs2 = pe.Obs([samples1], ['ensemble1|r02'])\n\nmy_sum = obs1 + obs2\nmy_sum.details()\n> Result         2.00596631e+00 +/- 0.00000000e+00 +/- 0.00000000e+00 (0.000%)\n> 1500 samples in 1 ensemble:\n>    ensemble1: ['ensemble1|r01', 'ensemble1|r02']\n
\n\n

Irregular Monte Carlo chains

\n\n

Irregular Monte Carlo chains can be initilized with the parameter idl.

\n\n

Example:

\n\n
# Observable defined on configurations 20 to 519\nobs1 = pe.Obs([samples1], ['ensemble1'], idl=[range(20, 520)])\n# Observable defined on every second configuration between 5 and 1003\nobs2 = pe.Obs([samples2], ['ensemble1'], idl=[range(5, 1005, 2)])\n# Observable defined on configurations 2, 9, 28, 29 and 501\nobs3 = pe.Obs([samples3], ['ensemble1'], idl=[[2, 9, 28, 29, 501]])\n
\n\n

Warning: Irregular Monte Carlo chains can result in odd patterns in the autocorrelation functions.\nMake sure to check the with e.g. pyerrors.obs.Obs.plot_rho or pyerrors.obs.Obs.plot_tauint.

\n\n

Error propagation

\n\n

Automatic differentiation, cite Alberto,

\n\n

numpy overloaded

\n\n
import numpy as np\nimport pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name'])\nmy_new_obs = 2 * np.log(my_obs) / my_obs\nmy_new_obs.gamma_method()\nmy_new_obs.details()\n
\n\n

Error estimation

\n\n

pyerrors.obs.Obs.gamma_method

\n\n

$\\delta_i\\delta_j$

\n\n

Exponential tails

\n\n

Covariance

\n\n

Correlators

\n\n

pyerrors.correlators.Corr

\n\n

Optimization / fits / roots

\n\n

pyerrors.fits\npyerrors.roots

\n\n

Complex observables

\n\n

pyerrors.obs.CObs

\n\n

Matrix operations

\n\n

pyerrors.linalg

\n\n

Input

\n\n

pyerrors.input

\n"}, "pyerrors.correlators": {"fullname": "pyerrors.correlators", "modulename": "pyerrors.correlators", "qualname": "", "type": "module", "doc": "

\n"}, "pyerrors.correlators.Corr": {"fullname": "pyerrors.correlators.Corr", "modulename": "pyerrors.correlators", "qualname": "Corr", "type": "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 inconvinient\nto iterate over all timeslices for every operation. This is especially true, when dealing with smearing matrices.

\n\n

The correlator can have two types of content: An Obs at every timeslice OR a GEVP\nsmearing matrix at every timeslice. Other dependency (eg. spacial) are not supported.

\n"}, "pyerrors.correlators.Corr.__init__": {"fullname": "pyerrors.correlators.Corr.__init__", "modulename": "pyerrors.correlators", "qualname": "Corr.__init__", "type": "function", "doc": "

\n", "parameters": ["self", "data_input", "padding_front", "padding_back", "prange"], "funcdef": "def"}, "pyerrors.correlators.Corr.reweighted": {"fullname": "pyerrors.correlators.Corr.reweighted", "modulename": "pyerrors.correlators", "qualname": "Corr.reweighted", "type": "variable", "doc": "

\n"}, "pyerrors.correlators.Corr.gamma_method": {"fullname": "pyerrors.correlators.Corr.gamma_method", "modulename": "pyerrors.correlators", "qualname": "Corr.gamma_method", "type": "function", "doc": "

Apply the gamma method to the content of the Corr.

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.projected": {"fullname": "pyerrors.correlators.Corr.projected", "modulename": "pyerrors.correlators", "qualname": "Corr.projected", "type": "function", "doc": "

\n", "parameters": ["self", "vector_l", "vector_r"], "funcdef": "def"}, "pyerrors.correlators.Corr.sum": {"fullname": "pyerrors.correlators.Corr.sum", "modulename": "pyerrors.correlators", "qualname": "Corr.sum", "type": "function", "doc": "

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.smearing": {"fullname": "pyerrors.correlators.Corr.smearing", "modulename": "pyerrors.correlators", "qualname": "Corr.smearing", "type": "function", "doc": "

\n", "parameters": ["self", "i", "j"], "funcdef": "def"}, "pyerrors.correlators.Corr.plottable": {"fullname": "pyerrors.correlators.Corr.plottable", "modulename": "pyerrors.correlators", "qualname": "Corr.plottable", "type": "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", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.symmetric": {"fullname": "pyerrors.correlators.Corr.symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.symmetric", "type": "function", "doc": "

Symmetrize the correlator around x0=0.

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.anti_symmetric": {"fullname": "pyerrors.correlators.Corr.anti_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.anti_symmetric", "type": "function", "doc": "

Anti-symmetrize the correlator around x0=0.

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.smearing_symmetric": {"fullname": "pyerrors.correlators.Corr.smearing_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.smearing_symmetric", "type": "function", "doc": "

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.GEVP": {"fullname": "pyerrors.correlators.Corr.GEVP", "modulename": "pyerrors.correlators", "qualname": "Corr.GEVP", "type": "function", "doc": "

\n", "parameters": ["self", "t0", "ts", "state"], "funcdef": "def"}, "pyerrors.correlators.Corr.Eigenvalue": {"fullname": "pyerrors.correlators.Corr.Eigenvalue", "modulename": "pyerrors.correlators", "qualname": "Corr.Eigenvalue", "type": "function", "doc": "

\n", "parameters": ["self", "t0", "state"], "funcdef": "def"}, "pyerrors.correlators.Corr.roll": {"fullname": "pyerrors.correlators.Corr.roll", "modulename": "pyerrors.correlators", "qualname": "Corr.roll", "type": "function", "doc": "

Periodically shift the correlator by dt timeslices

\n\n
Parameters
\n\n
    \n
  • dt (int):\nnumber of timeslices
    • \n
\n", "parameters": ["self", "dt"], "funcdef": "def"}, "pyerrors.correlators.Corr.reverse": {"fullname": "pyerrors.correlators.Corr.reverse", "modulename": "pyerrors.correlators", "qualname": "Corr.reverse", "type": "function", "doc": "

Reverse the time ordering of the Corr

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.correlate": {"fullname": "pyerrors.correlators.Corr.correlate", "modulename": "pyerrors.correlators", "qualname": "Corr.correlate", "type": "function", "doc": "

Correlate the correlator with another correlator or Obs

\n", "parameters": ["self", "partner"], "funcdef": "def"}, "pyerrors.correlators.Corr.reweight": {"fullname": "pyerrors.correlators.Corr.reweight", "modulename": "pyerrors.correlators", "qualname": "Corr.reweight", "type": "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", "parameters": ["self", "weight", "kwargs"], "funcdef": "def"}, "pyerrors.correlators.Corr.T_symmetry": {"fullname": "pyerrors.correlators.Corr.T_symmetry", "modulename": "pyerrors.correlators", "qualname": "Corr.T_symmetry", "type": "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", "parameters": ["self", "partner", "parity"], "funcdef": "def"}, "pyerrors.correlators.Corr.deriv": {"fullname": "pyerrors.correlators.Corr.deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.deriv", "type": "function", "doc": "

Return the first derivative of the correlator with respect to x0.

\n\n
Parameters
\n\n
    \n
  • symmetric (bool):\ndecides whether symmertic of simple finite differences are used. Default: True
    • \n
\n", "parameters": ["self", "symmetric"], "funcdef": "def"}, "pyerrors.correlators.Corr.second_deriv": {"fullname": "pyerrors.correlators.Corr.second_deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.second_deriv", "type": "function", "doc": "

Return the second derivative of the correlator with respect to x0.

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.m_eff": {"fullname": "pyerrors.correlators.Corr.m_eff", "modulename": "pyerrors.correlators", "qualname": "Corr.m_eff", "type": "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 : 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
    • \n
  • guess (float):\nguess for the root finder, only relevant for the root variant
    • \n
\n", "parameters": ["self", "variant", "guess"], "funcdef": "def"}, "pyerrors.correlators.Corr.fit": {"fullname": "pyerrors.correlators.Corr.fit", "modulename": "pyerrors.correlators", "qualname": "Corr.fit", "type": "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):\nRange in which the function is to be fitted to the data.\nIf not specified, self.prange or all timeslices are used.
    • \n
  • silent (bool):\nDecides whether output is printed to the standard output.
    • \n
\n", "parameters": ["self", "function", "fitrange", "silent", "kwargs"], "funcdef": "def"}, "pyerrors.correlators.Corr.plateau": {"fullname": "pyerrors.correlators.Corr.plateau", "modulename": "pyerrors.correlators", "qualname": "Corr.plateau", "type": "function", "doc": "

Extract a plateu 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
\n", "parameters": ["self", "plateau_range", "method"], "funcdef": "def"}, "pyerrors.correlators.Corr.set_prange": {"fullname": "pyerrors.correlators.Corr.set_prange", "modulename": "pyerrors.correlators", "qualname": "Corr.set_prange", "type": "function", "doc": "

Sets the attribute prange of the Corr object.

\n", "parameters": ["self", "prange"], "funcdef": "def"}, "pyerrors.correlators.Corr.show": {"fullname": "pyerrors.correlators.Corr.show", "modulename": "pyerrors.correlators", "qualname": "Corr.show", "type": "function", "doc": "

Plots the correlator, uses tag 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.
    • \n
  • logscale (bool):\nSets y-axis to logscale
    • \n
  • plateau (Obs):\nplateau to be visualized in the figure
    • \n
  • fit_res (Fit_result):\nFit_result object to be visualized
    • \n
  • ylabel (str):\nLabel for the y-axis
    • \n
  • save (str):\npath to file in which the figure should be saved
    • \n
\n", "parameters": ["self", "x_range", "comp", "y_range", "logscale", "plateau", "fit_res", "ylabel", "save"], "funcdef": "def"}, "pyerrors.correlators.Corr.dump": {"fullname": "pyerrors.correlators.Corr.dump", "modulename": "pyerrors.correlators", "qualname": "Corr.dump", "type": "function", "doc": "

Dumps the Corr into a pickel file

\n\n
Parameters
\n\n
    \n
  • filename (str):\nName of the file
    • \n
\n", "parameters": ["self", "filename"], "funcdef": "def"}, "pyerrors.correlators.Corr.print": {"fullname": "pyerrors.correlators.Corr.print", "modulename": "pyerrors.correlators", "qualname": "Corr.print", "type": "function", "doc": "

\n", "parameters": ["self", "range"], "funcdef": "def"}, "pyerrors.correlators.Corr.sqrt": {"fullname": "pyerrors.correlators.Corr.sqrt", "modulename": "pyerrors.correlators", "qualname": "Corr.sqrt", "type": "function", "doc": "

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.log": {"fullname": "pyerrors.correlators.Corr.log", "modulename": "pyerrors.correlators", "qualname": "Corr.log", "type": "function", "doc": "

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.exp": {"fullname": "pyerrors.correlators.Corr.exp", "modulename": "pyerrors.correlators", "qualname": "Corr.exp", "type": "function", "doc": "

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.sin": {"fullname": "pyerrors.correlators.Corr.sin", "modulename": "pyerrors.correlators", "qualname": "Corr.sin", "type": "function", "doc": "

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.cos": {"fullname": "pyerrors.correlators.Corr.cos", "modulename": "pyerrors.correlators", "qualname": "Corr.cos", "type": "function", "doc": "

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.tan": {"fullname": "pyerrors.correlators.Corr.tan", "modulename": "pyerrors.correlators", "qualname": "Corr.tan", "type": "function", "doc": "

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.sinh": {"fullname": "pyerrors.correlators.Corr.sinh", "modulename": "pyerrors.correlators", "qualname": "Corr.sinh", "type": "function", "doc": "

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.cosh": {"fullname": "pyerrors.correlators.Corr.cosh", "modulename": "pyerrors.correlators", "qualname": "Corr.cosh", "type": "function", "doc": "

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.tanh": {"fullname": "pyerrors.correlators.Corr.tanh", "modulename": "pyerrors.correlators", "qualname": "Corr.tanh", "type": "function", "doc": "

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.arcsin": {"fullname": "pyerrors.correlators.Corr.arcsin", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsin", "type": "function", "doc": "

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.arccos": {"fullname": "pyerrors.correlators.Corr.arccos", "modulename": "pyerrors.correlators", "qualname": "Corr.arccos", "type": "function", "doc": "

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.arctan": {"fullname": "pyerrors.correlators.Corr.arctan", "modulename": "pyerrors.correlators", "qualname": "Corr.arctan", "type": "function", "doc": "

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.arcsinh": {"fullname": "pyerrors.correlators.Corr.arcsinh", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsinh", "type": "function", "doc": "

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.arccosh": {"fullname": "pyerrors.correlators.Corr.arccosh", "modulename": "pyerrors.correlators", "qualname": "Corr.arccosh", "type": "function", "doc": "

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.arctanh": {"fullname": "pyerrors.correlators.Corr.arctanh", "modulename": "pyerrors.correlators", "qualname": "Corr.arctanh", "type": "function", "doc": "

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.dirac": {"fullname": "pyerrors.dirac", "modulename": "pyerrors.dirac", "qualname": "", "type": "module", "doc": "

\n"}, "pyerrors.dirac.Grid_gamma": {"fullname": "pyerrors.dirac.Grid_gamma", "modulename": "pyerrors.dirac", "qualname": "Grid_gamma", "type": "function", "doc": "

Returns gamma matrix in Grid labeling.

\n", "parameters": ["gamma_tag"], "funcdef": "def"}, "pyerrors.fits": {"fullname": "pyerrors.fits", "modulename": "pyerrors.fits", "qualname": "", "type": "module", "doc": "

\n"}, "pyerrors.fits.Fit_result": {"fullname": "pyerrors.fits.Fit_result", "modulename": "pyerrors.fits", "qualname": "Fit_result", "type": "class", "doc": "

Represents fit results.

\n\n
Attributes
\n\n
    \n
  • fit_parameters (list):\nresults for the individual fit parameters,\nalso accesible via indices.
    • \n
\n"}, "pyerrors.fits.Fit_result.__init__": {"fullname": "pyerrors.fits.Fit_result.__init__", "modulename": "pyerrors.fits", "qualname": "Fit_result.__init__", "type": "function", "doc": "

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.fits.Fit_result.gamma_method": {"fullname": "pyerrors.fits.Fit_result.gamma_method", "modulename": "pyerrors.fits", "qualname": "Fit_result.gamma_method", "type": "function", "doc": "

Apply the gamma method to all fit parameters

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.fits.least_squares": {"fullname": "pyerrors.fits.least_squares", "modulename": "pyerrors.fits", "qualname": "least_squares", "type": "function", "doc": "

Performs a non-linear fit to y = func(x).

\n\n
Parameters
\n\n
    \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
    def func(a, x):\n   y = a[0] + a[1] * x + a[2] * anp.sinh(x)\n   return y\n
    \n\n

    For multiple x values func can be of the form

    \n\n
    def func(a, x):\n   (x1, x2) = x\n   return a[0] * x1 ** 2 + a[1] * x2\n
    \n\n

    It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work

    • \n
  • priors (list, optional):\npriors has to be a 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)\nIt is important for the subsequent error estimation that the e_tag for the gamma method is large\nenough.
    • \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\n non-linear fits with many parameters.
    • \n
  • method (str):\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
  • 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
  • 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
\n", "parameters": ["x", "y", "func", "priors", "silent", "kwargs"], "funcdef": "def"}, "pyerrors.fits.total_least_squares": {"fullname": "pyerrors.fits.total_least_squares", "modulename": "pyerrors.fits", "qualname": "total_least_squares", "type": "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
    def func(a, x):\n   y = a[0] + a[1] * x + a[2] * anp.sinh(x)\n   return y\n
    \n\n

    For multiple x values func can be of the form

    \n\n
    def func(a, x):\n   (x1, x2) = x\n   return a[0] * x1 ** 2 + a[1] * x2\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
  • Based on the orthogonal distance regression module of scipy
    • \n
\n", "parameters": ["x", "y", "func", "silent", "kwargs"], "funcdef": "def"}, "pyerrors.fits.prior_fit": {"fullname": "pyerrors.fits.prior_fit", "modulename": "pyerrors.fits", "qualname": "prior_fit", "type": "function", "doc": "

\n", "parameters": ["x", "y", "func", "priors", "silent", "kwargs"], "funcdef": "def"}, "pyerrors.fits.standard_fit": {"fullname": "pyerrors.fits.standard_fit", "modulename": "pyerrors.fits", "qualname": "standard_fit", "type": "function", "doc": "

\n", "parameters": ["x", "y", "func", "silent", "kwargs"], "funcdef": "def"}, "pyerrors.fits.odr_fit": {"fullname": "pyerrors.fits.odr_fit", "modulename": "pyerrors.fits", "qualname": "odr_fit", "type": "function", "doc": "

\n", "parameters": ["x", "y", "func", "silent", "kwargs"], "funcdef": "def"}, "pyerrors.fits.fit_lin": {"fullname": "pyerrors.fits.fit_lin", "modulename": "pyerrors.fits", "qualname": "fit_lin", "type": "function", "doc": "

Performs a linear fit to y = n + m * x and returns two Obs n, m.

\n\n

y has to be a list of Obs, the dvalues of the Obs are used as yerror for the fit.\nx can 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", "parameters": ["x", "y", "kwargs"], "funcdef": "def"}, "pyerrors.fits.qqplot": {"fullname": "pyerrors.fits.qqplot", "modulename": "pyerrors.fits", "qualname": "qqplot", "type": "function", "doc": "

Generates a quantile-quantile plot of the fit result which can be used to\ncheck if the residuals of the fit are gaussian distributed.

\n", "parameters": ["x", "o_y", "func", "p"], "funcdef": "def"}, "pyerrors.fits.residual_plot": {"fullname": "pyerrors.fits.residual_plot", "modulename": "pyerrors.fits", "qualname": "residual_plot", "type": "function", "doc": "

Generates a plot which compares the fit to the data and displays the corresponding residuals

\n", "parameters": ["x", "y", "func", "fit_res"], "funcdef": "def"}, "pyerrors.fits.covariance_matrix": {"fullname": "pyerrors.fits.covariance_matrix", "modulename": "pyerrors.fits", "qualname": "covariance_matrix", "type": "function", "doc": "

Returns the covariance matrix of y.

\n", "parameters": ["y"], "funcdef": "def"}, "pyerrors.fits.error_band": {"fullname": "pyerrors.fits.error_band", "modulename": "pyerrors.fits", "qualname": "error_band", "type": "function", "doc": "

Returns the error band for an array of sample values x, for given fit function func with optimized parameters beta.

\n", "parameters": ["x", "func", "beta"], "funcdef": "def"}, "pyerrors.fits.ks_test": {"fullname": "pyerrors.fits.ks_test", "modulename": "pyerrors.fits", "qualname": "ks_test", "type": "function", "doc": "

Performs a Kolmogorov\u2013Smirnov test for the Q-values of all fit object.

\n\n

If no list is given all Obs in memory are used.

\n\n

Disclaimer: The determination of the individual Q-values as well as this function have not been tested yet.

\n", "parameters": ["obs"], "funcdef": "def"}, "pyerrors.fits.fit_general": {"fullname": "pyerrors.fits.fit_general", "modulename": "pyerrors.fits", "qualname": "fit_general", "type": "function", "doc": "

Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.

\n\n

Plausibility of the results should be checked. To control the numerical differentiation\nthe kwargs of numdifftools.step_generators.MaxStepGenerator can be used.

\n\n

func has to be of the form

\n\n

def func(a, x):\n y = a[0] + a[1] * x + a[2] * np.sinh(x)\n return y

\n\n

y has to be a list of Obs, the dvalues of the Obs are used as yerror for the fit.\nx can 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\n
Keyword arguments
\n\n

silent -- If true all output to the console is omitted (default False).\ninitial_guess -- can provide an initial guess for the input parameters. Relevant for non-linear fits\n with many parameters.

\n", "parameters": ["x", "y", "func", "silent", "kwargs"], "funcdef": "def"}, "pyerrors.input": {"fullname": "pyerrors.input", "modulename": "pyerrors.input", "qualname": "", "type": "module", "doc": "

\n"}, "pyerrors.input.bdio": {"fullname": "pyerrors.input.bdio", "modulename": "pyerrors.input.bdio", "qualname": "", "type": "module", "doc": "

\n"}, "pyerrors.input.bdio.read_ADerrors": {"fullname": "pyerrors.input.bdio.read_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "read_ADerrors", "type": "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", "parameters": ["file_path", "bdio_path", "kwargs"], "funcdef": "def"}, "pyerrors.input.bdio.write_ADerrors": {"fullname": "pyerrors.input.bdio.write_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "write_ADerrors", "type": "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", "parameters": ["obs_list", "file_path", "bdio_path", "kwargs"], "funcdef": "def"}, "pyerrors.input.bdio.read_mesons": {"fullname": "pyerrors.input.bdio.read_mesons", "modulename": "pyerrors.input.bdio", "qualname": "read_mesons", "type": "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 -- path to the bdio file
    • \n
  • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
    • \n
  • stop -- stops reading at given configuration number (default None)
    • \n
  • alternative_ensemble_name -- Manually overwrite ensemble name
    • \n
\n", "parameters": ["file_path", "bdio_path", "kwargs"], "funcdef": "def"}, "pyerrors.input.bdio.read_dSdm": {"fullname": "pyerrors.input.bdio.read_dSdm", "modulename": "pyerrors.input.bdio", "qualname": "read_dSdm", "type": "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 -- path to the bdio file
    • \n
  • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
    • \n
  • stop -- stops reading at given configuration number (default None)
    • \n
\n", "parameters": ["file_path", "bdio_path", "kwargs"], "funcdef": "def"}, "pyerrors.input.hadrons": {"fullname": "pyerrors.input.hadrons", "modulename": "pyerrors.input.hadrons", "qualname": "", "type": "module", "doc": "

\n"}, "pyerrors.input.hadrons.read_meson_hd5": {"fullname": "pyerrors.input.hadrons.read_meson_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_meson_hd5", "type": "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
  • tree (str):\nLabel of the upmost directory in the hdf5 file, default 'meson'\nfor outputs of the Meson module. Can be altered to read input\nfrom other modules with similar structures.
    • \n
\n", "parameters": ["path", "filestem", "ens_id", "meson", "tree"], "funcdef": "def"}, "pyerrors.input.hadrons.read_ExternalLeg_hd5": {"fullname": "pyerrors.input.hadrons.read_ExternalLeg_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_ExternalLeg_hd5", "type": "function", "doc": "

Read hadrons ExternalLeg hdf5 file and output an array of CObs

\n\n
Parameters
\n\n
    \n
  • path -- path to the files to read
    • \n
  • filestem -- namestem of the files to read
    • \n
  • ens_id -- name of the ensemble, required for internal bookkeeping
    • \n
  • order -- order in which the array is to be reshaped,: 'F' for the first index changing fastest (9 4x4 matrices) default.\n'C' for the last index changing fastest (16 3x3 matrices),
    • \n
\n", "parameters": ["path", "filestem", "ens_id", "order"], "funcdef": "def"}, "pyerrors.input.hadrons.read_Bilinear_hd5": {"fullname": "pyerrors.input.hadrons.read_Bilinear_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Bilinear_hd5", "type": "function", "doc": "

Read hadrons Bilinear hdf5 file and output an array of CObs

\n\n
Parameters
\n\n
    \n
  • path -- path to the files to read
    • \n
  • filestem -- namestem of the files to read
    • \n
  • ens_id -- name of the ensemble, required for internal bookkeeping
    • \n
  • order -- order in which the array is to be reshaped,: 'F' for the first index changing fastest (9 4x4 matrices) default.\n'C' for the last index changing fastest (16 3x3 matrices),
    • \n
\n", "parameters": ["path", "filestem", "ens_id", "order"], "funcdef": "def"}, "pyerrors.input.misc": {"fullname": "pyerrors.input.misc", "modulename": "pyerrors.input.misc", "qualname": "", "type": "module", "doc": "

\n"}, "pyerrors.input.misc.read_pbp": {"fullname": "pyerrors.input.misc.read_pbp", "modulename": "pyerrors.input.misc", "qualname": "read_pbp", "type": "function", "doc": "

Read pbp format from given folder structure. Returns a list of length nrw

\n\n
Keyword arguments
\n\n

r_start -- list which contains the first config to be read for each replicum\nr_stop -- list which contains the last config to be read for each replicum

\n", "parameters": ["path", "prefix", "kwargs"], "funcdef": "def"}, "pyerrors.input.openQCD": {"fullname": "pyerrors.input.openQCD", "modulename": "pyerrors.input.openQCD", "qualname": "", "type": "module", "doc": "

\n"}, "pyerrors.input.openQCD.read_rwms": {"fullname": "pyerrors.input.openQCD.read_rwms", "modulename": "pyerrors.input.openQCD", "qualname": "read_rwms", "type": "function", "doc": "

Read rwms format from given folder structure. Returns a list of length nrw

\n\n
Parameters
\n\n
    \n
  • version (str):\nversion of openQCD, default 2.0
    • \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
  • postfix (str):\npostfix of the file to read, e.g. '.ms1' for openQCD-files
    • \n
\n", "parameters": ["path", "prefix", "version", "names", "kwargs"], "funcdef": "def"}, "pyerrors.input.openQCD.extract_t0": {"fullname": "pyerrors.input.openQCD.extract_t0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_t0", "type": "function", "doc": "

Extract t0 from given .ms.dat files. Returns t0 as Obs.

\n\n

It is assumed that all boundary effects have sufficiently decayed at x0=xmin.\nThe data around the zero crossing of t^2 - 0.3 is fitted with a linear function\nfrom which the exact root is extracted.\nOnly works with openQCD v 1.2.

\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 when reading the ms.dat files.\nCorresponds to dtr_cnfg / dtr_ms in the openQCD input file.
    • \n
  • xmin (int):\nFirst timeslice where the boundary effects 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 crossing to be included in the linear fit. (Default: 5)
    • \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
  • plaquette (bool):\nIf true extract the plaquette estimate of t0 instead.
    • \n
\n", "parameters": ["path", "prefix", "dtr_read", "xmin", "spatial_extent", "fit_range", "kwargs"], "funcdef": "def"}, "pyerrors.input.sfcf": {"fullname": "pyerrors.input.sfcf", "modulename": "pyerrors.input.sfcf", "qualname": "", "type": "module", "doc": "

\n"}, "pyerrors.input.sfcf.read_sfcf": {"fullname": "pyerrors.input.sfcf.read_sfcf", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf", "type": "function", "doc": "

Read sfcf C format from given folder structure.

\n\n
Parameters
\n\n
    \n
  • im -- if True, read imaginary instead of real part of the correlation function.
    • \n
  • single -- if True, read a boundary-to-boundary correlation function with a single value
    • \n
  • b2b -- if True, read a time-dependent boundary-to-boundary correlation function
    • \n
  • names -- Alternative labeling for replicas/ensembles. Has to have the appropriate length
    • \n
\n", "parameters": ["path", "prefix", "name", "kwargs"], "funcdef": "def"}, "pyerrors.input.sfcf.read_sfcf_c": {"fullname": "pyerrors.input.sfcf.read_sfcf_c", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf_c", "type": "function", "doc": "

Read sfcf c format from given folder structure.

\n\n
Parameters
\n\n
    \n
  • quarks -- Label of the quarks used in the sfcf input file
    • \n
  • noffset -- Offset of the source (only relevant when wavefunctions are used)
    • \n
  • wf -- ID of wave function
    • \n
  • wf2 -- ID of the second wavefunction (only relevant for boundary-to-boundary correlation functions)
    • \n
  • im -- if True, read imaginary instead of real part of the correlation function.
    • \n
  • b2b -- if True, read a time-dependent boundary-to-boundary correlation function
    • \n
  • names -- Alternative labeling for replicas/ensembles. Has to have the appropriate length
    • \n
  • ens_name (str):\nreplaces the name of the ensemble
    • \n
\n", "parameters": ["path", "prefix", "name", "quarks", "noffset", "wf", "wf2", "kwargs"], "funcdef": "def"}, "pyerrors.input.sfcf.read_qtop": {"fullname": "pyerrors.input.sfcf.read_qtop", "modulename": "pyerrors.input.sfcf", "qualname": "read_qtop", "type": "function", "doc": "

Read qtop format from given folder structure.

\n\n
Parameters
\n\n
    \n
  • target -- specifies the topological sector to be reweighted to (default 0)
    • \n
  • full -- if true read the charge instead of the reweighting factor.
    • \n
\n", "parameters": ["path", "prefix", "kwargs"], "funcdef": "def"}, "pyerrors.jackknifing": {"fullname": "pyerrors.jackknifing", "modulename": "pyerrors.jackknifing", "qualname": "", "type": "module", "doc": "

\n"}, "pyerrors.jackknifing.Jack": {"fullname": "pyerrors.jackknifing.Jack", "modulename": "pyerrors.jackknifing", "qualname": "Jack", "type": "class", "doc": "

\n"}, "pyerrors.jackknifing.Jack.__init__": {"fullname": "pyerrors.jackknifing.Jack.__init__", "modulename": "pyerrors.jackknifing", "qualname": "Jack.__init__", "type": "function", "doc": "

\n", "parameters": ["self", "value", "jacks"], "funcdef": "def"}, "pyerrors.jackknifing.Jack.print": {"fullname": "pyerrors.jackknifing.Jack.print", "modulename": "pyerrors.jackknifing", "qualname": "Jack.print", "type": "function", "doc": "

Print basic properties of the Jack.

\n", "parameters": ["self", "kwargs"], "funcdef": "def"}, "pyerrors.jackknifing.Jack.plot_tauint": {"fullname": "pyerrors.jackknifing.Jack.plot_tauint", "modulename": "pyerrors.jackknifing", "qualname": "Jack.plot_tauint", "type": "function", "doc": "

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.jackknifing.Jack.plot_history": {"fullname": "pyerrors.jackknifing.Jack.plot_history", "modulename": "pyerrors.jackknifing", "qualname": "Jack.plot_history", "type": "function", "doc": "

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.jackknifing.Jack.dump": {"fullname": "pyerrors.jackknifing.Jack.dump", "modulename": "pyerrors.jackknifing", "qualname": "Jack.dump", "type": "function", "doc": "

Dump the Jack to a pickle file 'name'.

\n\n

Keyword arguments:\npath -- specifies a custom path for the file (default '.')

\n", "parameters": ["self", "name", "kwargs"], "funcdef": "def"}, "pyerrors.jackknifing.generate_jack": {"fullname": "pyerrors.jackknifing.generate_jack", "modulename": "pyerrors.jackknifing", "qualname": "generate_jack", "type": "function", "doc": "

\n", "parameters": ["obs", "kwargs"], "funcdef": "def"}, "pyerrors.jackknifing.derived_jack": {"fullname": "pyerrors.jackknifing.derived_jack", "modulename": "pyerrors.jackknifing", "qualname": "derived_jack", "type": "function", "doc": "

Construct a derived Jack according to func(data, **kwargs).

\n\n
Parameters
\n\n
    \n
  • func -- arbitrary function of the form func(data, **kwargs). For the automatic differentiation to work,: all numpy functions have to have the autograd wrapper (use 'import autograd.numpy as np').
    • \n
  • data -- list of Jacks, e.g. [jack1, jack2, jack3].
    • \n
\n\n
Notes
\n\n

For simple mathematical operations it can be practical to use anonymous functions.\nFor the ratio of two jacks one can e.g. use

\n\n

new_jack = derived_jack(lambda x : x[0] / x[1], [jack1, jack2])

\n", "parameters": ["func", "data", "kwargs"], "funcdef": "def"}, "pyerrors.linalg": {"fullname": "pyerrors.linalg", "modulename": "pyerrors.linalg", "qualname": "", "type": "module", "doc": "

\n"}, "pyerrors.linalg.derived_array": {"fullname": "pyerrors.linalg.derived_array", "modulename": "pyerrors.linalg", "qualname": "derived_array", "type": "function", "doc": "

Construct a derived Obs according to func(data, **kwargs) of matrix value data\nusing automatic differentiation.

\n\n
Parameters
\n\n
    \n
  • func -- arbitrary function of the form func(data, **kwargs). For the: automatic differentiation to work, all numpy functions have to have\nthe autograd wrapper (use 'import autograd.numpy as anp').
    • \n
  • data -- list of Obs, e.g. [obs1, obs2, obs3].
    • \n
  • man_grad -- manually supply a list or an array which contains the jacobian: of func. Use cautiously, supplying the wrong derivative will\nnot be intercepted.
    • \n
\n", "parameters": ["func", "data", "kwargs"], "funcdef": "def"}, "pyerrors.linalg.matmul": {"fullname": "pyerrors.linalg.matmul", "modulename": "pyerrors.linalg", "qualname": "matmul", "type": "function", "doc": "

Matrix multiply all operands.

\n\n

Supports real and complex valued matrices and is faster compared to\nstandard multiplication via the @ operator.

\n", "parameters": ["operands"], "funcdef": "def"}, "pyerrors.linalg.inv": {"fullname": "pyerrors.linalg.inv", "modulename": "pyerrors.linalg", "qualname": "inv", "type": "function", "doc": "

Inverse of Obs or CObs valued matrices.

\n", "parameters": ["x"], "funcdef": "def"}, "pyerrors.linalg.cholesky": {"fullname": "pyerrors.linalg.cholesky", "modulename": "pyerrors.linalg", "qualname": "cholesky", "type": "function", "doc": "

Cholesky decompostion of Obs or CObs valued matrices.

\n", "parameters": ["x"], "funcdef": "def"}, "pyerrors.linalg.scalar_mat_op": {"fullname": "pyerrors.linalg.scalar_mat_op", "modulename": "pyerrors.linalg", "qualname": "scalar_mat_op", "type": "function", "doc": "

Computes the matrix to scalar operation op to a given matrix of Obs.

\n", "parameters": ["op", "obs", "kwargs"], "funcdef": "def"}, "pyerrors.linalg.eigh": {"fullname": "pyerrors.linalg.eigh", "modulename": "pyerrors.linalg", "qualname": "eigh", "type": "function", "doc": "

Computes the eigenvalues and eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh.

\n", "parameters": ["obs", "kwargs"], "funcdef": "def"}, "pyerrors.linalg.eig": {"fullname": "pyerrors.linalg.eig", "modulename": "pyerrors.linalg", "qualname": "eig", "type": "function", "doc": "

Computes the eigenvalues of a given matrix of Obs according to np.linalg.eig.

\n", "parameters": ["obs", "kwargs"], "funcdef": "def"}, "pyerrors.linalg.pinv": {"fullname": "pyerrors.linalg.pinv", "modulename": "pyerrors.linalg", "qualname": "pinv", "type": "function", "doc": "

Computes the Moore-Penrose pseudoinverse of a matrix of Obs.

\n", "parameters": ["obs", "kwargs"], "funcdef": "def"}, "pyerrors.linalg.svd": {"fullname": "pyerrors.linalg.svd", "modulename": "pyerrors.linalg", "qualname": "svd", "type": "function", "doc": "

Computes the singular value decomposition of a matrix of Obs.

\n", "parameters": ["obs", "kwargs"], "funcdef": "def"}, "pyerrors.linalg.slogdet": {"fullname": "pyerrors.linalg.slogdet", "modulename": "pyerrors.linalg", "qualname": "slogdet", "type": "function", "doc": "

Computes the determinant of a matrix of Obs via np.linalg.slogdet.

\n", "parameters": ["obs", "kwargs"], "funcdef": "def"}, "pyerrors.linalg.grad_eig": {"fullname": "pyerrors.linalg.grad_eig", "modulename": "pyerrors.linalg", "qualname": "grad_eig", "type": "function", "doc": "

Gradient of a general square (complex valued) matrix

\n", "parameters": ["ans", "x"], "funcdef": "def"}, "pyerrors.misc": {"fullname": "pyerrors.misc", "modulename": "pyerrors.misc", "qualname": "", "type": "module", "doc": "

\n"}, "pyerrors.misc.gen_correlated_data": {"fullname": "pyerrors.misc.gen_correlated_data", "modulename": "pyerrors.misc", "qualname": "gen_correlated_data", "type": "function", "doc": "

Generate observables with given covariance and autocorrelation times.

\n\n
Parameters
\n\n
    \n
  • means -- list containing the mean value of each observable.
    • \n
  • cov -- covariance matrix for the data to be geneated.
    • \n
  • name -- ensemble name for the data to be geneated.
    • \n
  • tau -- can either be a real number or a list with an entry for: every dataset.
    • \n
  • samples -- number of samples to be generated for each observable.
    • \n
\n", "parameters": ["means", "cov", "name", "tau", "samples"], "funcdef": "def"}, "pyerrors.mpm": {"fullname": "pyerrors.mpm", "modulename": "pyerrors.mpm", "qualname": "", "type": "module", "doc": "

\n"}, "pyerrors.mpm.matrix_pencil_method": {"fullname": "pyerrors.mpm.matrix_pencil_method", "modulename": "pyerrors.mpm", "qualname": "matrix_pencil_method", "type": "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 -- can be a list of Obs for the analysis of a single correlator, or a list of lists: of Obs if several correlators are to analyzed at once.
    • \n
  • k -- Number of states to extract (default 1).
    • \n
  • p -- matrix pencil parameter which filters noise. The optimal value is expected between: len(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", "parameters": ["corrs", "k", "p", "kwargs"], "funcdef": "def"}, "pyerrors.mpm.matrix_pencil_method_old": {"fullname": "pyerrors.mpm.matrix_pencil_method_old", "modulename": "pyerrors.mpm", "qualname": "matrix_pencil_method_old", "type": "function", "doc": "

Older impleentation of the matrix pencil method with pencil p on given data to\n extract energy levels.

\n\n
Parameters
\n\n
    \n
  • data -- lists of Obs, where the nth entry is considered to be the correlation function: at x0=n+offset.
    • \n
  • p -- matrix pencil parameter which corresponds to the number of energy levels to extract.: higher values for p can help decreasing noise.
    • \n
  • noise_level -- If this argument is not None an additional prefiltering via singular: value decomposition is performed in which all singular values below 10^(-noise_level)\ntimes the largest singular value are discarded. This increases the computation time.
    • \n
  • verbose -- if larger than zero details about the noise filtering are printed to stdout: (default 1)
    • \n
\n", "parameters": ["data", "p", "noise_level", "verbose", "kwargs"], "funcdef": "def"}, "pyerrors.npr": {"fullname": "pyerrors.npr", "modulename": "pyerrors.npr", "qualname": "", "type": "module", "doc": "

\n"}, "pyerrors.npr.Npr_matrix": {"fullname": "pyerrors.npr.Npr_matrix", "modulename": "pyerrors.npr", "qualname": "Npr_matrix", "type": "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: A :term:generic <generic type> version\nof ndarray.

\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
>>> 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

Second mode:

\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"}, "pyerrors.npr.Npr_matrix.__init__": {"fullname": "pyerrors.npr.Npr_matrix.__init__", "modulename": "pyerrors.npr", "qualname": "Npr_matrix.__init__", "type": "function", "doc": "

\n", "parameters": [], "funcdef": "def"}, "pyerrors.npr.Npr_matrix.g5H": {"fullname": "pyerrors.npr.Npr_matrix.g5H", "modulename": "pyerrors.npr", "qualname": "Npr_matrix.g5H", "type": "variable", "doc": "

Gamma_5 hermitean conjugate

\n\n

Returns gamma_5 @ M.T.conj() @ gamma_5 and exchanges in and out going\nmomenta. Works only for 12x12 matrices.

\n"}, "pyerrors.npr.inv_propagator": {"fullname": "pyerrors.npr.inv_propagator", "modulename": "pyerrors.npr", "qualname": "inv_propagator", "type": "function", "doc": "

Inverts a 12x12 quark propagator

\n", "parameters": ["prop"], "funcdef": "def"}, "pyerrors.npr.Zq": {"fullname": "pyerrors.npr.Zq", "modulename": "pyerrors.npr", "qualname": "Zq", "type": "function", "doc": "

Calculates the quark field renormalization constant Zq

\n\n
Parameters
\n\n
    \n
  • inv_prop (array):\nInverted 12x12 quark propagator
    • \n
  • fermion (str):\nFermion type for which the tree-level propagator is used\n in the calculation of Zq. Default Wilson.
    • \n
\n", "parameters": ["inv_prop", "fermion"], "funcdef": "def"}, "pyerrors.obs": {"fullname": "pyerrors.obs", "modulename": "pyerrors.obs", "qualname": "", "type": "module", "doc": "

\n"}, "pyerrors.obs.Obs": {"fullname": "pyerrors.obs.Obs", "modulename": "pyerrors.obs", "qualname": "Obs", "type": "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"}, "pyerrors.obs.Obs.__init__": {"fullname": "pyerrors.obs.Obs.__init__", "modulename": "pyerrors.obs", "qualname": "Obs.__init__", "type": "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 indivdual samples
    • \n
  • idl (list, optional):\nlist of ranges or lists on which the samples are defined
    • \n
  • means (list, optional):\nlist of mean values for the case that the mean values were\nalready subtracted from the samples
    • \n
\n", "parameters": ["self", "samples", "names", "idl", "means", "kwargs"], "funcdef": "def"}, "pyerrors.obs.Obs.S_global": {"fullname": "pyerrors.obs.Obs.S_global", "modulename": "pyerrors.obs", "qualname": "Obs.S_global", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.S_dict": {"fullname": "pyerrors.obs.Obs.S_dict", "modulename": "pyerrors.obs", "qualname": "Obs.S_dict", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.tau_exp_global": {"fullname": "pyerrors.obs.Obs.tau_exp_global", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_global", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.tau_exp_dict": {"fullname": "pyerrors.obs.Obs.tau_exp_dict", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_dict", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.N_sigma_global": {"fullname": "pyerrors.obs.Obs.N_sigma_global", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_global", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.filter_eps": {"fullname": "pyerrors.obs.Obs.filter_eps", "modulename": "pyerrors.obs", "qualname": "Obs.filter_eps", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.names": {"fullname": "pyerrors.obs.Obs.names", "modulename": "pyerrors.obs", "qualname": "Obs.names", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.shape": {"fullname": "pyerrors.obs.Obs.shape", "modulename": "pyerrors.obs", "qualname": "Obs.shape", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.r_values": {"fullname": "pyerrors.obs.Obs.r_values", "modulename": "pyerrors.obs", "qualname": "Obs.r_values", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.deltas": {"fullname": "pyerrors.obs.Obs.deltas", "modulename": "pyerrors.obs", "qualname": "Obs.deltas", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.idl": {"fullname": "pyerrors.obs.Obs.idl", "modulename": "pyerrors.obs", "qualname": "Obs.idl", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.is_merged": {"fullname": "pyerrors.obs.Obs.is_merged", "modulename": "pyerrors.obs", "qualname": "Obs.is_merged", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.N": {"fullname": "pyerrors.obs.Obs.N", "modulename": "pyerrors.obs", "qualname": "Obs.N", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.ddvalue": {"fullname": "pyerrors.obs.Obs.ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.ddvalue", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.reweighted": {"fullname": "pyerrors.obs.Obs.reweighted", "modulename": "pyerrors.obs", "qualname": "Obs.reweighted", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.tag": {"fullname": "pyerrors.obs.Obs.tag", "modulename": "pyerrors.obs", "qualname": "Obs.tag", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.value": {"fullname": "pyerrors.obs.Obs.value", "modulename": "pyerrors.obs", "qualname": "Obs.value", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.dvalue": {"fullname": "pyerrors.obs.Obs.dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.dvalue", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_names": {"fullname": "pyerrors.obs.Obs.e_names", "modulename": "pyerrors.obs", "qualname": "Obs.e_names", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_content": {"fullname": "pyerrors.obs.Obs.e_content", "modulename": "pyerrors.obs", "qualname": "Obs.e_content", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.gamma_method": {"fullname": "pyerrors.obs.Obs.gamma_method", "modulename": "pyerrors.obs", "qualname": "Obs.gamma_method", "type": "function", "doc": "

Calculate 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), can be\na float or an array of floats for different ensembles
    • \n
  • tau_exp (float):\npositive value triggers the critical slowing down analysis\n(default 0.0), can be a float or an array of floats for different\nensembles
    • \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", "parameters": ["self", "kwargs"], "funcdef": "def"}, "pyerrors.obs.Obs.expand_deltas": {"fullname": "pyerrors.obs.Obs.expand_deltas", "modulename": "pyerrors.obs", "qualname": "Obs.expand_deltas", "type": "function", "doc": "

Expand deltas defined on idx to a regular, contiguous range, where holes are filled by 0.\n If idx is of type range, the deltas are not changed

\n\n
Parameters
\n\n
    \n
  • deltas -- List of fluctuations
    • \n
  • idx -- List or range of configs on which the deltas are defined.
    • \n
  • shape -- Number of configs in idx.
    • \n
\n", "parameters": ["self", "deltas", "idx", "shape"], "funcdef": "def"}, "pyerrors.obs.Obs.calc_gamma": {"fullname": "pyerrors.obs.Obs.calc_gamma", "modulename": "pyerrors.obs", "qualname": "Obs.calc_gamma", "type": "function", "doc": "

Calculate Gamma_{AA} from the deltas, which are defined on idx.\n idx is assumed to be a contiguous range (possibly with a stepsize != 1)

\n\n
Parameters
\n\n
    \n
  • deltas -- List of fluctuations
    • \n
  • idx -- List or range of configs on which the deltas are defined.
    • \n
  • shape -- Number of configs in idx.
    • \n
  • w_max -- Upper bound for the summation window
    • \n
  • fft -- boolean, which determines whether the fft algorithm is used for: the computation of the autocorrelation function
    • \n
\n", "parameters": ["self", "deltas", "idx", "shape", "w_max", "fft"], "funcdef": "def"}, "pyerrors.obs.Obs.print": {"fullname": "pyerrors.obs.Obs.print", "modulename": "pyerrors.obs", "qualname": "Obs.print", "type": "function", "doc": "

\n", "parameters": ["self", "level"], "funcdef": "def"}, "pyerrors.obs.Obs.details": {"fullname": "pyerrors.obs.Obs.details", "modulename": "pyerrors.obs", "qualname": "Obs.details", "type": "function", "doc": "

Output detailed properties of the Obs.

\n", "parameters": ["self", "ens_content"], "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", "type": "function", "doc": "

Checks whether the observable is zero within 'sigma' standard errors.

\n\n

Works only properly when the gamma method was run.

\n", "parameters": ["self", "sigma"], "funcdef": "def"}, "pyerrors.obs.Obs.is_zero": {"fullname": "pyerrors.obs.Obs.is_zero", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero", "type": "function", "doc": "

Checks whether the observable is zero within machine precision.

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.plot_tauint": {"fullname": "pyerrors.obs.Obs.plot_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.plot_tauint", "type": "function", "doc": "

Plot integrated autocorrelation time for each ensemble.

\n", "parameters": ["self", "save"], "funcdef": "def"}, "pyerrors.obs.Obs.plot_rho": {"fullname": "pyerrors.obs.Obs.plot_rho", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rho", "type": "function", "doc": "

Plot normalized autocorrelation function time for each ensemble.

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.plot_rep_dist": {"fullname": "pyerrors.obs.Obs.plot_rep_dist", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rep_dist", "type": "function", "doc": "

Plot replica distribution for each ensemble with more than one replicum.

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.plot_history": {"fullname": "pyerrors.obs.Obs.plot_history", "modulename": "pyerrors.obs", "qualname": "Obs.plot_history", "type": "function", "doc": "

Plot derived Monte Carlo history for each ensemble.

\n", "parameters": ["self", "expand"], "funcdef": "def"}, "pyerrors.obs.Obs.plot_piechart": {"fullname": "pyerrors.obs.Obs.plot_piechart", "modulename": "pyerrors.obs", "qualname": "Obs.plot_piechart", "type": "function", "doc": "

Plot piechart which shows the fractional contribution of each\nensemble to the error and returns a dictionary containing the fractions.

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.dump": {"fullname": "pyerrors.obs.Obs.dump", "modulename": "pyerrors.obs", "qualname": "Obs.dump", "type": "function", "doc": "

Dump the Obs to a pickle file 'name'.

\n\n
Parameters
\n\n
    \n
  • path (str):\nspecifies a custom path for the file (default '.')
    • \n
\n", "parameters": ["self", "name", "kwargs"], "funcdef": "def"}, "pyerrors.obs.Obs.sqrt": {"fullname": "pyerrors.obs.Obs.sqrt", "modulename": "pyerrors.obs", "qualname": "Obs.sqrt", "type": "function", "doc": "

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.log": {"fullname": "pyerrors.obs.Obs.log", "modulename": "pyerrors.obs", "qualname": "Obs.log", "type": "function", "doc": "

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.exp": {"fullname": "pyerrors.obs.Obs.exp", "modulename": "pyerrors.obs", "qualname": "Obs.exp", "type": "function", "doc": "

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.sin": {"fullname": "pyerrors.obs.Obs.sin", "modulename": "pyerrors.obs", "qualname": "Obs.sin", "type": "function", "doc": "

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.cos": {"fullname": "pyerrors.obs.Obs.cos", "modulename": "pyerrors.obs", "qualname": "Obs.cos", "type": "function", "doc": "

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.tan": {"fullname": "pyerrors.obs.Obs.tan", "modulename": "pyerrors.obs", "qualname": "Obs.tan", "type": "function", "doc": "

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.arcsin": {"fullname": "pyerrors.obs.Obs.arcsin", "modulename": "pyerrors.obs", "qualname": "Obs.arcsin", "type": "function", "doc": "

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.arccos": {"fullname": "pyerrors.obs.Obs.arccos", "modulename": "pyerrors.obs", "qualname": "Obs.arccos", "type": "function", "doc": "

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.arctan": {"fullname": "pyerrors.obs.Obs.arctan", "modulename": "pyerrors.obs", "qualname": "Obs.arctan", "type": "function", "doc": "

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.sinh": {"fullname": "pyerrors.obs.Obs.sinh", "modulename": "pyerrors.obs", "qualname": "Obs.sinh", "type": "function", "doc": "

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.cosh": {"fullname": "pyerrors.obs.Obs.cosh", "modulename": "pyerrors.obs", "qualname": "Obs.cosh", "type": "function", "doc": "

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.tanh": {"fullname": "pyerrors.obs.Obs.tanh", "modulename": "pyerrors.obs", "qualname": "Obs.tanh", "type": "function", "doc": "

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.arcsinh": {"fullname": "pyerrors.obs.Obs.arcsinh", "modulename": "pyerrors.obs", "qualname": "Obs.arcsinh", "type": "function", "doc": "

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.arccosh": {"fullname": "pyerrors.obs.Obs.arccosh", "modulename": "pyerrors.obs", "qualname": "Obs.arccosh", "type": "function", "doc": "

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.arctanh": {"fullname": "pyerrors.obs.Obs.arctanh", "modulename": "pyerrors.obs", "qualname": "Obs.arctanh", "type": "function", "doc": "

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.sinc": {"fullname": "pyerrors.obs.Obs.sinc", "modulename": "pyerrors.obs", "qualname": "Obs.sinc", "type": "function", "doc": "

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.N_sigma": {"fullname": "pyerrors.obs.Obs.N_sigma", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.S": {"fullname": "pyerrors.obs.Obs.S", "modulename": "pyerrors.obs", "qualname": "Obs.S", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_ddvalue": {"fullname": "pyerrors.obs.Obs.e_ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_ddvalue", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_drho": {"fullname": "pyerrors.obs.Obs.e_drho", "modulename": "pyerrors.obs", "qualname": "Obs.e_drho", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_dtauint": {"fullname": "pyerrors.obs.Obs.e_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_dtauint", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_dvalue": {"fullname": "pyerrors.obs.Obs.e_dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_dvalue", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_n_dtauint": {"fullname": "pyerrors.obs.Obs.e_n_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_dtauint", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_n_tauint": {"fullname": "pyerrors.obs.Obs.e_n_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_tauint", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_rho": {"fullname": "pyerrors.obs.Obs.e_rho", "modulename": "pyerrors.obs", "qualname": "Obs.e_rho", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_tauint": {"fullname": "pyerrors.obs.Obs.e_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_tauint", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_windowsize": {"fullname": "pyerrors.obs.Obs.e_windowsize", "modulename": "pyerrors.obs", "qualname": "Obs.e_windowsize", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.tau_exp": {"fullname": "pyerrors.obs.Obs.tau_exp", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp", "type": "variable", "doc": "

\n"}, "pyerrors.obs.CObs": {"fullname": "pyerrors.obs.CObs", "modulename": "pyerrors.obs", "qualname": "CObs", "type": "class", "doc": "

Class for a complex valued observable.

\n"}, "pyerrors.obs.CObs.__init__": {"fullname": "pyerrors.obs.CObs.__init__", "modulename": "pyerrors.obs", "qualname": "CObs.__init__", "type": "function", "doc": "

\n", "parameters": ["self", "real", "imag"], "funcdef": "def"}, "pyerrors.obs.CObs.tag": {"fullname": "pyerrors.obs.CObs.tag", "modulename": "pyerrors.obs", "qualname": "CObs.tag", "type": "variable", "doc": "

\n"}, "pyerrors.obs.CObs.real": {"fullname": "pyerrors.obs.CObs.real", "modulename": "pyerrors.obs", "qualname": "CObs.real", "type": "variable", "doc": "

\n"}, "pyerrors.obs.CObs.imag": {"fullname": "pyerrors.obs.CObs.imag", "modulename": "pyerrors.obs", "qualname": "CObs.imag", "type": "variable", "doc": "

\n"}, "pyerrors.obs.CObs.gamma_method": {"fullname": "pyerrors.obs.CObs.gamma_method", "modulename": "pyerrors.obs", "qualname": "CObs.gamma_method", "type": "function", "doc": "

Executes the gamma_method for the real and the imaginary part.

\n", "parameters": ["self", "kwargs"], "funcdef": "def"}, "pyerrors.obs.CObs.is_zero": {"fullname": "pyerrors.obs.CObs.is_zero", "modulename": "pyerrors.obs", "qualname": "CObs.is_zero", "type": "function", "doc": "

Checks whether both real and imaginary part are zero within machine precision.

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.CObs.conjugate": {"fullname": "pyerrors.obs.CObs.conjugate", "modulename": "pyerrors.obs", "qualname": "CObs.conjugate", "type": "function", "doc": "

\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.merge_idx": {"fullname": "pyerrors.obs.merge_idx", "modulename": "pyerrors.obs", "qualname": "merge_idx", "type": "function", "doc": "

Returns the union of all lists in idl

\n\n
Parameters
\n\n
    \n
  • idl (list):\nList of lists or ranges.
    • \n
\n", "parameters": ["idl"], "funcdef": "def"}, "pyerrors.obs.expand_deltas_for_merge": {"fullname": "pyerrors.obs.expand_deltas_for_merge", "modulename": "pyerrors.obs", "qualname": "expand_deltas_for_merge", "type": "function", "doc": "

Expand deltas defined on idx to the list of configs that is defined by new_idx.\n New, empy entries are filled by 0. If idx and new_idx are of type range, the smallest\n common divisor of the step sizes is used as new step size.

\n\n
Parameters
\n\n
    \n
  • deltas (list):\nList of fluctuations
    • \n
  • idx (list):\nList or range of configs on which the deltas are defined.\nHas to be a subset of new_idx.
    • \n
  • shape (list):\nNumber of configs in idx.
    • \n
  • new_idx (list):\nList of configs that defines the new range.
    • \n
\n", "parameters": ["deltas", "idx", "shape", "new_idx"], "funcdef": "def"}, "pyerrors.obs.filter_zeroes": {"fullname": "pyerrors.obs.filter_zeroes", "modulename": "pyerrors.obs", "qualname": "filter_zeroes", "type": "function", "doc": "

Filter out all configurations with vanishing fluctuation such that they do not\n contribute to the error estimate anymore. Returns the new names, deltas and\n idl according to the filtering.\n A fluctuation is considered to be vanishing, if it is smaller than eps times\n the mean of the absolute values of all deltas in one list.

\n\n
Parameters
\n\n
    \n
  • names (list):\nList of names
    • \n
  • deltas (dict):\nDict lists of fluctuations
    • \n
  • idx (dict):\nDict of lists or ranges of configs on which the deltas are defined.\nHas to be a subset of new_idx.
    • \n
  • eps (float):\nPrefactor that enters the filter criterion.
    • \n
\n", "parameters": ["names", "deltas", "idl", "eps"], "funcdef": "def"}, "pyerrors.obs.derived_observable": {"fullname": "pyerrors.obs.derived_observable", "modulename": "pyerrors.obs", "qualname": "derived_observable", "type": "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", "parameters": ["func", "data", "kwargs"], "funcdef": "def"}, "pyerrors.obs.reduce_deltas": {"fullname": "pyerrors.obs.reduce_deltas", "modulename": "pyerrors.obs", "qualname": "reduce_deltas", "type": "function", "doc": "

Extract deltas defined on idx_old on all configs of idx_new.

\n\n
Parameters
\n\n
    \n
  • deltas (list):\nList of fluctuations
    • \n
  • idx_old (list):\nList or range of configs on which the deltas are defined
    • \n
  • idx_new (list):\nList of configs for which we want to extract the deltas.\nHas to be a subset of idx_old.
    • \n
\n", "parameters": ["deltas", "idx_old", "idx_new"], "funcdef": "def"}, "pyerrors.obs.reweight": {"fullname": "pyerrors.obs.reweight", "modulename": "pyerrors.obs", "qualname": "reweight", "type": "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.
    • \n
\n", "parameters": ["weight", "obs", "kwargs"], "funcdef": "def"}, "pyerrors.obs.correlate": {"fullname": "pyerrors.obs.correlate", "modulename": "pyerrors.obs", "qualname": "correlate", "type": "function", "doc": "

Correlate two observables.

\n\n
Parameters
\n\n
    \n
  • obs_a (Obs):\nFirst observable
    • \n
  • obs_b (Obs):\nSecond observable
    • \n
  • Keep in mind to only correlate primary observables which have not been reweighted
    • \n
  • yet. The reweighting has to be applied after correlating the observables.
    • \n
  • Currently only works if ensembles are identical. This is not really necessary.
    • \n
\n", "parameters": ["obs_a", "obs_b"], "funcdef": "def"}, "pyerrors.obs.covariance": {"fullname": "pyerrors.obs.covariance", "modulename": "pyerrors.obs", "qualname": "covariance", "type": "function", "doc": "

Calculates the covariance of two observables.

\n\n

covariance(obs, obs) is equal to obs.dvalue ** 2\nThe gamma method has to be applied first to both observables.

\n\n

If abs(covariance(obs1, obs2)) > obs1.dvalue * obs2.dvalue, the covariance\nis constrained to the maximum value in order to make sure that covariance\nmatrices are positive semidefinite.

\n\n
Parameters
\n\n
    \n
  • correlation (bool):\nif true the correlation instead of the covariance is\nreturned (default False)
    • \n
\n", "parameters": ["obs1", "obs2", "correlation", "kwargs"], "funcdef": "def"}, "pyerrors.obs.covariance2": {"fullname": "pyerrors.obs.covariance2", "modulename": "pyerrors.obs", "qualname": "covariance2", "type": "function", "doc": "

Alternative implementation of the covariance of two observables.

\n\n

covariance(obs, obs) is equal to obs.dvalue ** 2\nThe gamma method has to be applied first to both observables.

\n\n

If abs(covariance(obs1, obs2)) > obs1.dvalue * obs2.dvalue, the covariance\nis constrained to the maximum value in order to make sure that covariance\nmatrices are positive semidefinite.

\n\n
Keyword arguments
\n\n

correlation -- if true the correlation instead of the covariance is\n returned (default False)

\n", "parameters": ["obs1", "obs2", "correlation", "kwargs"], "funcdef": "def"}, "pyerrors.obs.covariance3": {"fullname": "pyerrors.obs.covariance3", "modulename": "pyerrors.obs", "qualname": "covariance3", "type": "function", "doc": "

Another alternative implementation of the covariance of two observables.

\n\n

covariance2(obs, obs) is equal to obs.dvalue ** 2\nCurrently only works if ensembles are identical.\nThe gamma method has to be applied first to both observables.

\n\n

If abs(covariance2(obs1, obs2)) > obs1.dvalue * obs2.dvalue, the covariance\nis constrained to the maximum value in order to make sure that covariance\nmatrices are positive semidefinite.

\n\n
Keyword arguments
\n\n

correlation -- if true the correlation instead of the covariance is\n returned (default False)\nplot -- if true, the integrated autocorrelation time for each ensemble is\n plotted.

\n", "parameters": ["obs1", "obs2", "correlation", "kwargs"], "funcdef": "def"}, "pyerrors.obs.pseudo_Obs": {"fullname": "pyerrors.obs.pseudo_Obs", "modulename": "pyerrors.obs", "qualname": "pseudo_Obs", "type": "function", "doc": "

Generate a pseudo Obs with given value, dvalue and name

\n\n

The standard number of samples is a 1000. This can be adjusted.

\n", "parameters": ["value", "dvalue", "name", "samples"], "funcdef": "def"}, "pyerrors.obs.dump_object": {"fullname": "pyerrors.obs.dump_object", "modulename": "pyerrors.obs", "qualname": "dump_object", "type": "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", "parameters": ["obj", "name", "kwargs"], "funcdef": "def"}, "pyerrors.obs.load_object": {"fullname": "pyerrors.obs.load_object", "modulename": "pyerrors.obs", "qualname": "load_object", "type": "function", "doc": "

Load object from pickle file.

\n", "parameters": ["path"], "funcdef": "def"}, "pyerrors.obs.merge_obs": {"fullname": "pyerrors.obs.merge_obs", "modulename": "pyerrors.obs", "qualname": "merge_obs", "type": "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
  • It is not possible to combine obs which are based on the same replicum
    • \n
\n", "parameters": ["list_of_obs"], "funcdef": "def"}, "pyerrors.roots": {"fullname": "pyerrors.roots", "modulename": "pyerrors.roots", "qualname": "", "type": "module", "doc": "

\n"}, "pyerrors.roots.find_root": {"fullname": "pyerrors.roots.find_root", "modulename": "pyerrors.roots", "qualname": "find_root", "type": "function", "doc": "

Finds the root of the function func(x, d) where d is an Obs.

\n\n
Parameters
\n\n
    \n
  • d -- Obs passed to the function.
    • \n
  • func -- Function to be minimized. Any numpy functions have to use the autograd.numpy wrapper
    • \n
  • guess -- Initial guess for the minimization.
    • \n
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{"docs": {}, "df": 0, "k": {"1": {"docs": {"pyerrors.jackknifing.derived_jack": {"tf": 1.4142135623730951}}, "df": 1}, "2": {"docs": {"pyerrors.jackknifing.derived_jack": {"tf": 1.4142135623730951}}, "df": 1}, "3": {"docs": {"pyerrors.jackknifing.derived_jack": {"tf": 1}}, "df": 1}, "docs": {"pyerrors.jackknifing.Jack.print": {"tf": 1}, "pyerrors.jackknifing.Jack.dump": {"tf": 1}, "pyerrors.jackknifing.derived_jack": {"tf": 1.7320508075688772}}, "df": 3}, "o": {"docs": {}, "df": 0, "b": {"docs": {}, "df": 0, "i": {"docs": {}, "df": 0, "a": {"docs": {}, "df": 0, "n": {"docs": {"pyerrors.linalg.derived_array": {"tf": 1}, "pyerrors.obs.derived_observable": {"tf": 1}}, "df": 2}}}}}}}, "u": {"docs": {}, "df": 0, "m": {"docs": {}, "df": 0, "p": {"docs": {"pyerrors.npr.Npr_matrix": {"tf": 1.4142135623730951}}, "df": 1}}}}, "_": {"docs": {}, "df": 0, "_": {"docs": {}, "df": 0, "n": {"docs": {}, "df": 0, "e": {"docs": {}, "df": 0, "w": {"docs": {}, "df": 0, "_": {"docs": {}, "df": 0, "_": {"docs": {"pyerrors.npr.Npr_matrix": {"tf": 1.7320508075688772}}, "df": 1}}}}}, "i": {"docs": {}, "df": 0, "n": {"docs": {}, "df": 0, "i": {"docs": {}, "df": 0, "t": {"docs": {}, "df": 0, "_": {"docs": {}, "df": 0, "_": {"docs": {"pyerrors.npr.Npr_matrix": {"tf": 1}}, "df": 1}}}}}}}}}}}, "pipeline": ["trimmer", "stopWordFilter", "stemmer"], "_isPrebuiltIndex": true}; // mirrored in build-search-index.js (part 1) // Also split on html tags. this is a cheap heuristic, but good enough. elasticlunr.tokenizer.setSeperator(/[\s\-.;&]+|<[^>]*>/); let searchIndex; if (docs._isPrebuiltIndex) { console.info("using precompiled search index"); searchIndex = elasticlunr.Index.load(docs); } else { console.time("building search index"); // mirrored in build-search-index.js (part 2) searchIndex = elasticlunr(function () { this.addField("qualname"); this.addField("fullname"); this.addField("doc"); this.setRef("fullname"); }); for (let doc of docs) { searchIndex.addDoc(doc); } console.timeEnd("building search index"); } return (term) => searchIndex.search(term, { fields: { qualname: {boost: 4}, fullname: {boost: 2}, doc: {boost: 1}, }, expand: true }); })();