# pyerrors.correlators

View Source

    import warnings
    from itertools import permutations
    import numpy as np
    import autograd.numpy as anp
    import matplotlib.pyplot as plt
    import scipy.linalg
    from .obs import Obs, reweight, correlate, CObs
    from .misc import dump_object, _assert_equal_properties
    from .fits import least_squares
    from .linalg import eigh, inv, cholesky
    from .roots import find_root

    class Corr:
        """The class for a correlator (time dependent sequence of pe.Obs).

        Everything, this class does, can be achieved using lists or arrays of Obs.
        But it is simply more convenient to have a dedicated object for correlators.
        One often wants to add or multiply correlators of the same length at every timeslice and it is inconvenient
        to iterate over all timeslices for every operation. This is especially true, when dealing with matrices.

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

        """

        def __init__(self, data_input, padding=[0, 0], prange=None):
            """ Initialize a Corr object.

            Parameters
            ----------
            data_input : list or array
                list of Obs or list of arrays of Obs or array of Corrs
            padding : list, optional
                List with two entries where the first labels the padding
                at the front of the correlator and the second the padding
                at the back.
            prange : list, optional
                List containing the first and last timeslice of the plateau
                region indentified for this correlator.
            """

            if isinstance(data_input, np.ndarray):

                # This only works, if the array fulfills the conditions below
                if not len(data_input.shape) == 2 and data_input.shape[0] == data_input.shape[1]:
                    raise Exception("Incompatible array shape")
                if not all([isinstance(item, Corr) for item in data_input.flatten()]):
                    raise Exception("If the input is an array, its elements must be of type pe.Corr")
                if not all([item.N == 1 for item in data_input.flatten()]):
                    raise Exception("Can only construct matrix correlator from single valued correlators")
                if not len(set([item.T for item in data_input.flatten()])) == 1:
                    raise Exception("All input Correlators must be defined over the same timeslices.")

                T = data_input[0, 0].T
                N = data_input.shape[0]
                input_as_list = []
                for t in range(T):
                    if any([(item.content[t] is None) for item in data_input.flatten()]):
                        if not all([(item.content[t] is None) for item in data_input.flatten()]):
                            warnings.warn("Input ill-defined at different timeslices. Conversion leads to data loss!", RuntimeWarning)
                        input_as_list.append(None)
                    else:
                        array_at_timeslace = np.empty([N, N], dtype="object")
                        for i in range(N):
                            for j in range(N):
                                array_at_timeslace[i, j] = data_input[i, j][t]
                        input_as_list.append(array_at_timeslace)
                data_input = input_as_list

            if isinstance(data_input, list):

                if all([isinstance(item, (Obs, CObs)) for item in data_input]):
                    _assert_equal_properties(data_input)
                    self.content = [np.asarray([item]) for item in data_input]
                if all([isinstance(item, (Obs, CObs)) or item is None for item in data_input]):
                    _assert_equal_properties([o for o in data_input if o is not None])
                    self.content = [np.asarray([item]) if item is not None else None for item in data_input]
                    self.N = 1

                elif all([isinstance(item, np.ndarray) or item is None for item in data_input]) and any([isinstance(item, np.ndarray) for item in data_input]):
                    self.content = data_input
                    noNull = [a for a in self.content if not (a is None)]  # To check if the matrices are correct for all undefined elements
                    self.N = noNull[0].shape[0]
                    if self.N > 1 and noNull[0].shape[0] != noNull[0].shape[1]:
                        raise Exception("Smearing matrices are not NxN")
                    if (not all([item.shape == noNull[0].shape for item in noNull])):
                        raise Exception("Items in data_input are not of identical shape." + str(noNull))
                else:
                    raise Exception("data_input contains item of wrong type")
            else:
                raise Exception("Data input was not given as list or correct array")

            self.tag = None

            # An undefined timeslice is represented by the None object
            self.content = [None] * padding[0] + self.content + [None] * padding[1]
            self.T = len(self.content)
            self.prange = prange

        def __getitem__(self, idx):
            """Return the content of timeslice idx"""
            if self.content[idx] is None:
                return None
            elif len(self.content[idx]) == 1:
                return self.content[idx][0]
            else:
                return self.content[idx]

        @property
        def reweighted(self):
            bool_array = np.array([list(map(lambda x: x.reweighted, o)) for o in [x for x in self.content if x is not None]])
            if np.all(bool_array == 1):
                return True
            elif np.all(bool_array == 0):
                return False
            else:
                raise Exception("Reweighting status of correlator corrupted.")

        def gamma_method(self, **kwargs):
            """Apply the gamma method to the content of the Corr."""
            for item in self.content:
                if not(item is None):
                    if self.N == 1:
                        item[0].gamma_method(**kwargs)
                    else:
                        for i in range(self.N):
                            for j in range(self.N):
                                item[i, j].gamma_method(**kwargs)

        def projected(self, vector_l=None, vector_r=None, normalize=False):
            """We need to project the Correlator with a Vector to get a single value at each timeslice.

            The method can use one or two vectors.
            If two are specified it returns v1@G@v2 (the order might be very important.)
            By default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to
            """
            if self.N == 1:
                raise Exception("Trying to project a Corr, that already has N=1.")

            if vector_l is None:
                vector_l, vector_r = np.asarray([1.] + (self.N - 1) * [0.]), np.asarray([1.] + (self.N - 1) * [0.])
            elif(vector_r is None):
                vector_r = vector_l
            if isinstance(vector_l, list) and not isinstance(vector_r, list):
                if len(vector_l) != self.T:
                    raise Exception("Length of vector list must be equal to T")
                vector_r = [vector_r] * self.T
            if isinstance(vector_r, list) and not isinstance(vector_l, list):
                if len(vector_r) != self.T:
                    raise Exception("Length of vector list must be equal to T")
                vector_l = [vector_l] * self.T

            if not isinstance(vector_l, list):
                if not vector_l.shape == vector_r.shape == (self.N,):
                    raise Exception("Vectors are of wrong shape!")
                if normalize:
                    vector_l, vector_r = vector_l / np.sqrt((vector_l @ vector_l)), vector_r / np.sqrt(vector_r @ vector_r)
                newcontent = [None if (item is None) else np.asarray([vector_l.T @ item @ vector_r]) for item in self.content]

            else:
                # There are no checks here yet. There are so many possible scenarios, where this can go wrong.
                if normalize:
                    for t in range(self.T):
                        vector_l[t], vector_r[t] = vector_l[t] / np.sqrt((vector_l[t] @ vector_l[t])), vector_r[t] / np.sqrt(vector_r[t] @ vector_r[t])

                newcontent = [None if (self.content[t] is None or vector_l[t] is None or vector_r[t] is None) else np.asarray([vector_l[t].T @ self.content[t] @ vector_r[t]]) for t in range(self.T)]
            return Corr(newcontent)

        def item(self, i, j):
            """Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice.

            Parameters
            ----------
            i : int
                First index to be picked.
            j : int
                Second index to be picked.
            """
            if self.N == 1:
                raise Exception("Trying to pick item from projected Corr")
            newcontent = [None if(item is None) else item[i, j] for item in self.content]
            return Corr(newcontent)

        def plottable(self):
            """Outputs the correlator in a plotable format.

            Outputs three lists containing the timeslice index, the value on each
            timeslice and the error on each timeslice.
            """
            if self.N != 1:
                raise Exception("Can only make Corr[N=1] plottable")
            x_list = [x for x in range(self.T) if not self.content[x] is None]
            y_list = [y[0].value for y in self.content if y is not None]
            y_err_list = [y[0].dvalue for y in self.content if y is not None]

            return x_list, y_list, y_err_list

        def symmetric(self):
            """ Symmetrize the correlator around x0=0."""
            if self.T % 2 != 0:
                raise Exception("Can not symmetrize odd T")

            if np.argmax(np.abs(self.content)) != 0:
                warnings.warn("Correlator does not seem to be symmetric around x0=0.", RuntimeWarning)

            newcontent = [self.content[0]]
            for t in range(1, self.T):
                if (self.content[t] is None) or (self.content[self.T - t] is None):
                    newcontent.append(None)
                else:
                    newcontent.append(0.5 * (self.content[t] + self.content[self.T - t]))
            if(all([x is None for x in newcontent])):
                raise Exception("Corr could not be symmetrized: No redundant values")
            return Corr(newcontent, prange=self.prange)

        def anti_symmetric(self):
            """Anti-symmetrize the correlator around x0=0."""
            if self.T % 2 != 0:
                raise Exception("Can not symmetrize odd T")

            test = 1 * self
            test.gamma_method()
            if not all([o.is_zero_within_error(3) for o in test.content[0]]):
                warnings.warn("Correlator does not seem to be anti-symmetric around x0=0.", RuntimeWarning)

            newcontent = [self.content[0]]
            for t in range(1, self.T):
                if (self.content[t] is None) or (self.content[self.T - t] is None):
                    newcontent.append(None)
                else:
                    newcontent.append(0.5 * (self.content[t] - self.content[self.T - t]))
            if(all([x is None for x in newcontent])):
                raise Exception("Corr could not be symmetrized: No redundant values")
            return Corr(newcontent, prange=self.prange)

        def matrix_symmetric(self):
            """Symmetrizes the correlator matrices on every timeslice."""
            if self.N > 1:
                transposed = [None if (G is None) else G.T for G in self.content]
                return 0.5 * (Corr(transposed) + self)
            if self.N == 1:
                raise Exception("Trying to symmetrize a correlator matrix, that already has N=1.")

        def GEVP(self, t0, ts=None, state=0, sorted_list=None):
            """Solve the general eigenvalue problem on the current correlator

            Parameters
            ----------
            t0 : int
                The time t0 for G(t)v= lambda G(t_0)v
            ts : int
                fixed time G(t_s)v= lambda G(t_0)v  if return_list=False
                If return_list=True and sorting=Eigenvector it gives a reference point for the sorting method.
            state : int
                The state one is interested in ordered by energy. The lowest state is zero.
            sorted_list : string
                if this argument is set, a list of vectors (len=self.T) is returned. If it is left as None, only one vector is returned.
                 "Eigenvalue"  -  The eigenvector is chosen according to which einvenvalue it belongs individually on every timeslice.
                 "Eigenvector" -  Use the method described in arXiv:2004.10472 [hep-lat] to find the set of v(t) belonging to the state.
                                     The referense state is identified by its eigenvalue at t=ts
            """
            if sorted_list is None:
                if (ts is None):
                    raise Exception("ts is required if sorted_list=None")
                if (self.content[t0] is None) or (self.content[ts] is None):
                    raise Exception("Corr not defined at t0/ts")
                G0, Gt = np.empty([self.N, self.N], dtype="double"), np.empty([self.N, self.N], dtype="double")
                for i in range(self.N):
                    for j in range(self.N):
                        G0[i, j] = self.content[t0][i, j].value
                        Gt[i, j] = self.content[ts][i, j].value

                sp_vecs = _GEVP_solver(Gt, G0)
                sp_vec = sp_vecs[state]
                return sp_vec
            else:

                all_vecs = []
                for t in range(self.T):
                    try:
                        G0, Gt = np.empty([self.N, self.N], dtype="double"), np.empty([self.N, self.N], dtype="double")
                        for i in range(self.N):
                            for j in range(self.N):
                                G0[i, j] = self.content[t0][i, j].value
                                Gt[i, j] = self.content[t][i, j].value

                        sp_vecs = _GEVP_solver(Gt, G0)
                        if sorted_list == "Eigenvalue":
                            sp_vec = sp_vecs[state]
                            all_vecs.append(sp_vec)
                        else:
                            all_vecs.append(sp_vecs)
                    except Exception:
                        all_vecs.append(None)
                if sorted_list == "Eigenvector":
                    if (ts is None):
                        raise Exception("ts is required for the Eigenvector sorting method.")
                    all_vecs = _sort_vectors(all_vecs, ts)
                    all_vecs = [a[state] for a in all_vecs]

            return all_vecs

        def Eigenvalue(self, t0, state=1):
            G = self.matrix_symmetric()
            G0 = G.content[t0]
            L = cholesky(G0)
            Li = inv(L)
            LT = L.T
            LTi = inv(LT)
            newcontent = []
            for t in range(self.T):
                if self.content[t] is None:
                    newcontent.append(None)
                else:
                    Gt = G.content[t]
                    M = Li @ Gt @ LTi
                    eigenvalues = eigh(M)[0]
                    eigenvalue = eigenvalues[-state]
                    newcontent.append(eigenvalue)
            return Corr(newcontent)

        def Hankel(self, N, periodic=False):
            """Constructs an NxN Hankel matrix

            C(t) c(t+1) ... c(t+n-1)
            C(t+1) c(t+2) ... c(t+n)
            .................
            C(t+(n-1)) c(t+n) ... c(t+2(n-1))

            Parameters
            ----------
            N : int
                Dimension of the Hankel matrix
            periodic : bool, optional
                determines whether the matrix is extended periodically
            """

            if self.N != 1:
                raise Exception("Multi-operator Prony not implemented!")

            array = np.empty([N, N], dtype="object")
            new_content = []
            for t in range(self.T):
                new_content.append(array.copy())

            def wrap(i):
                while i >= self.T:
                    i -= self.T
                return i

            for t in range(self.T):
                for i in range(N):
                    for j in range(N):
                        if periodic:
                            new_content[t][i, j] = self.content[wrap(t + i + j)][0]
                        elif (t + i + j) >= self.T:
                            new_content[t] = None
                        else:
                            new_content[t][i, j] = self.content[t + i + j][0]

            return Corr(new_content)

        def roll(self, dt):
            """Periodically shift the correlator by dt timeslices

            Parameters
            ----------
            dt : int
                number of timeslices
            """
            return Corr(list(np.roll(np.array(self.content, dtype=object), dt)))

        def reverse(self):
            """Reverse the time ordering of the Corr"""
            return Corr(self.content[:: -1])

        def thin(self, spacing=2, offset=0):
            """Thin out a correlator to suppress correlations

            Parameters
            ----------
            spacing : int
                Keep only every 'spacing'th entry of the correlator
            offset : int
                Offset the equal spacing
            """
            new_content = []
            for t in range(self.T):
                if (offset + t) % spacing != 0:
                    new_content.append(None)
                else:
                    new_content.append(self.content[t])
            return Corr(new_content)

        def correlate(self, partner):
            """Correlate the correlator with another correlator or Obs

            Parameters
            ----------
            partner : Obs or Corr
                partner to correlate the correlator with.
                Can either be an Obs which is correlated with all entries of the
                correlator or a Corr of same length.
            """
            new_content = []
            for x0, t_slice in enumerate(self.content):
                if t_slice is None:
                    new_content.append(None)
                else:
                    if isinstance(partner, Corr):
                        if partner.content[x0] is None:
                            new_content.append(None)
                        else:
                            new_content.append(np.array([correlate(o, partner.content[x0][0]) for o in t_slice]))
                    elif isinstance(partner, Obs):  # Should this include CObs?
                        new_content.append(np.array([correlate(o, partner) for o in t_slice]))
                    else:
                        raise Exception("Can only correlate with an Obs or a Corr.")

            return Corr(new_content)

        def reweight(self, weight, **kwargs):
            """Reweight the correlator.

            Parameters
            ----------
            weight : Obs
                Reweighting factor. An Observable that has to be defined on a superset of the
                configurations in obs[i].idl for all i.
            all_configs : bool
                if True, the reweighted observables are normalized by the average of
                the reweighting factor on all configurations in weight.idl and not
                on the configurations in obs[i].idl.
            """
            new_content = []
            for t_slice in self.content:
                if t_slice is None:
                    new_content.append(None)
                else:
                    new_content.append(np.array(reweight(weight, t_slice, **kwargs)))
            return Corr(new_content)

        def T_symmetry(self, partner, parity=+1):
            """Return the time symmetry average of the correlator and its partner

            Parameters
            ----------
            partner : Corr
                Time symmetry partner of the Corr
            partity : int
                Parity quantum number of the correlator, can be +1 or -1
            """
            if not isinstance(partner, Corr):
                raise Exception("T partner has to be a Corr object.")
            if parity not in [+1, -1]:
                raise Exception("Parity has to be +1 or -1.")
            T_partner = parity * partner.reverse()

            t_slices = []
            test = (self - T_partner)
            test.gamma_method()
            for x0, t_slice in enumerate(test.content):
                if t_slice is not None:
                    if not t_slice[0].is_zero_within_error(5):
                        t_slices.append(x0)
            if t_slices:
                warnings.warn("T symmetry partners do not agree within 5 sigma on time slices " + str(t_slices) + ".", RuntimeWarning)

            return (self + T_partner) / 2

        def deriv(self, variant="symmetric"):
            """Return the first derivative of the correlator with respect to x0.

            Parameters
            ----------
            variant : str
                decides which definition of the finite differences derivative is used.
                Available choice: symmetric, forward, backward, improved, default: symmetric
            """
            if variant == "symmetric":
                newcontent = []
                for t in range(1, self.T - 1):
                    if (self.content[t - 1] is None) or (self.content[t + 1] is None):
                        newcontent.append(None)
                    else:
                        newcontent.append(0.5 * (self.content[t + 1] - self.content[t - 1]))
                if(all([x is None for x in newcontent])):
                    raise Exception('Derivative is undefined at all timeslices')
                return Corr(newcontent, padding=[1, 1])
            elif variant == "forward":
                newcontent = []
                for t in range(self.T - 1):
                    if (self.content[t] is None) or (self.content[t + 1] is None):
                        newcontent.append(None)
                    else:
                        newcontent.append(self.content[t + 1] - self.content[t])
                if(all([x is None for x in newcontent])):
                    raise Exception("Derivative is undefined at all timeslices")
                return Corr(newcontent, padding=[0, 1])
            elif variant == "backward":
                newcontent = []
                for t in range(1, self.T):
                    if (self.content[t - 1] is None) or (self.content[t] is None):
                        newcontent.append(None)
                    else:
                        newcontent.append(self.content[t] - self.content[t - 1])
                if(all([x is None for x in newcontent])):
                    raise Exception("Derivative is undefined at all timeslices")
                return Corr(newcontent, padding=[1, 0])
            elif variant == "improved":
                newcontent = []
                for t in range(2, self.T - 2):
                    if (self.content[t - 2] is None) or (self.content[t - 1] is None) or (self.content[t + 1] is None) or (self.content[t + 2] is None):
                        newcontent.append(None)
                    else:
                        newcontent.append((1 / 12) * (self.content[t - 2] - 8 * self.content[t - 1] + 8 * self.content[t + 1] - self.content[t + 2]))
                if(all([x is None for x in newcontent])):
                    raise Exception('Derivative is undefined at all timeslices')
                return Corr(newcontent, padding=[2, 2])
            else:
                raise Exception("Unknown variant.")

        def second_deriv(self, variant="symmetric"):
            """Return the second derivative of the correlator with respect to x0.

            Parameters
            ----------
            variant : str
                decides which definition of the finite differences derivative is used.
                Available choice: symmetric, improved, default: symmetric
            """
            if variant == "symmetric":
                newcontent = []
                for t in range(1, self.T - 1):
                    if (self.content[t - 1] is None) or (self.content[t + 1] is None):
                        newcontent.append(None)
                    else:
                        newcontent.append((self.content[t + 1] - 2 * self.content[t] + self.content[t - 1]))
                if(all([x is None for x in newcontent])):
                    raise Exception("Derivative is undefined at all timeslices")
                return Corr(newcontent, padding=[1, 1])
            elif variant == "improved":
                newcontent = []
                for t in range(2, self.T - 2):
                    if (self.content[t - 2] is None) or (self.content[t - 1] is None) or (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 2] is None):
                        newcontent.append(None)
                    else:
                        newcontent.append((1 / 12) * (-self.content[t + 2] + 16 * self.content[t + 1] - 30 * self.content[t] + 16 * self.content[t - 1] - self.content[t - 2]))
                if(all([x is None for x in newcontent])):
                    raise Exception("Derivative is undefined at all timeslices")
                return Corr(newcontent, padding=[2, 2])
            else:
                raise Exception("Unknown variant.")

        def m_eff(self, variant='log', guess=1.0):
            """Returns the effective mass of the correlator as correlator object

            Parameters
            ----------
            variant : str
                log : uses the standard effective mass log(C(t) / C(t+1))
                cosh, 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.
                sinh : 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.
                See, e.g., arXiv:1205.5380
                arccosh : Uses the explicit form of the symmetrized correlator (not recommended)
            guess : float
                guess for the root finder, only relevant for the root variant
            """
            if self.N != 1:
                raise Exception('Correlator must be projected before getting m_eff')
            if variant == 'log':
                newcontent = []
                for t in range(self.T - 1):
                    if (self.content[t] is None) or (self.content[t + 1] is None):
                        newcontent.append(None)
                    else:
                        newcontent.append(self.content[t] / self.content[t + 1])
                if(all([x is None for x in newcontent])):
                    raise Exception('m_eff is undefined at all timeslices')

                return np.log(Corr(newcontent, padding=[0, 1]))

            elif variant in ['periodic', 'cosh', 'sinh']:
                if variant in ['periodic', 'cosh']:
                    func = anp.cosh
                else:
                    func = anp.sinh

                def root_function(x, d):
                    return func(x * (t - self.T / 2)) / func(x * (t + 1 - self.T / 2)) - d

                newcontent = []
                for t in range(self.T - 1):
                    if (self.content[t] is None) or (self.content[t + 1] is None):
                        newcontent.append(None)
                    # Fill the two timeslices in the middle of the lattice with their predecessors
                    elif variant == 'sinh' and t in [self.T / 2, self.T / 2 - 1]:
                        newcontent.append(newcontent[-1])
                    else:
                        newcontent.append(np.abs(find_root(self.content[t][0] / self.content[t + 1][0], root_function, guess=guess)))
                if(all([x is None for x in newcontent])):
                    raise Exception('m_eff is undefined at all timeslices')

                return Corr(newcontent, padding=[0, 1])

            elif variant == 'arccosh':
                newcontent = []
                for t in range(1, self.T - 1):
                    if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t - 1] is None):
                        newcontent.append(None)
                    else:
                        newcontent.append((self.content[t + 1] + self.content[t - 1]) / (2 * self.content[t]))
                if(all([x is None for x in newcontent])):
                    raise Exception("m_eff is undefined at all timeslices")
                return np.arccosh(Corr(newcontent, padding=[1, 1]))

            else:
                raise Exception('Unknown variant.')

        def fit(self, function, fitrange=None, silent=False, **kwargs):
            """Fits function to the data

            Parameters
            ----------
            function : obj
                function to fit to the data. See fits.least_squares for details.
            fitrange : list
                Range in which the function is to be fitted to the data.
                If not specified, self.prange or all timeslices are used.
            silent : bool
                Decides whether output is printed to the standard output.
            """
            if self.N != 1:
                raise Exception("Correlator must be projected before fitting")

            if fitrange is None:
                if self.prange:
                    fitrange = self.prange
                else:
                    fitrange = [0, self.T - 1]

            xs = [x for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None]
            ys = [self.content[x][0] for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None]
            result = least_squares(xs, ys, function, silent=silent, **kwargs)
            return result

        def plateau(self, plateau_range=None, method="fit", auto_gamma=False):
            """ Extract a plateau value from a Corr object

            Parameters
            ----------
            plateau_range : list
                list with two entries, indicating the first and the last timeslice
                of the plateau region.
            method : str
                method to extract the plateau.
                    'fit' fits a constant to the plateau region
                    'avg', 'average' or 'mean' just average over the given timeslices.
            auto_gamma : bool
                apply gamma_method with default parameters to the Corr. Defaults to None
            """
            if not plateau_range:
                if self.prange:
                    plateau_range = self.prange
                else:
                    raise Exception("no plateau range provided")
            if self.N != 1:
                raise Exception("Correlator must be projected before getting a plateau.")
            if(all([self.content[t] is None for t in range(plateau_range[0], plateau_range[1] + 1)])):
                raise Exception("plateau is undefined at all timeslices in plateaurange.")
            if auto_gamma:
                self.gamma_method()
            if method == "fit":
                def const_func(a, t):
                    return a[0]
                return self.fit(const_func, plateau_range)[0]
            elif method in ["avg", "average", "mean"]:
                returnvalue = np.mean([item[0] for item in self.content[plateau_range[0]:plateau_range[1] + 1] if item is not None])
                return returnvalue

            else:
                raise Exception("Unsupported plateau method: " + method)

        def set_prange(self, prange):
            """Sets the attribute prange of the Corr object."""
            if not len(prange) == 2:
                raise Exception("prange must be a list or array with two values")
            if not ((isinstance(prange[0], int)) and (isinstance(prange[1], int))):
                raise Exception("Start and end point must be integers")
            if not (0 <= prange[0] <= self.T and 0 <= prange[1] <= self.T and prange[0] < prange[1]):
                raise Exception("Start and end point must define a range in the interval 0,T")

            self.prange = prange
            return

        def show(self, x_range=None, comp=None, y_range=None, logscale=False, plateau=None, fit_res=None, ylabel=None, save=None, auto_gamma=False):
            """Plots the correlator using the tag of the correlator as label if available.

            Parameters
            ----------
            x_range : list
                list of two values, determining the range of the x-axis e.g. [4, 8]
            comp : Corr or list of Corr
                Correlator or list of correlators which are plotted for comparison.
                The tags of these correlators are used as labels if available.
            logscale : bool
                Sets y-axis to logscale
            plateau : Obs
                Plateau value to be visualized in the figure
            fit_res : Fit_result
                Fit_result object to be visualized
            ylabel : str
                Label for the y-axis
            save : str
                path to file in which the figure should be saved
            auto_gamma : bool
                Apply the gamma method with standard parameters to all correlators and plateau values before plotting.
            """
            if self.N != 1:
                raise Exception("Correlator must be projected before plotting")

            if auto_gamma:
                self.gamma_method()

            if x_range is None:
                x_range = [0, self.T - 1]

            fig = plt.figure()
            ax1 = fig.add_subplot(111)

            x, y, y_err = self.plottable()
            ax1.errorbar(x, y, y_err, label=self.tag)
            if logscale:
                ax1.set_yscale('log')
            else:
                if y_range is None:
                    try:
                        y_min = min([(x[0].value - x[0].dvalue) for x in self.content[x_range[0]: x_range[1] + 1] if (x is not None) and x[0].dvalue < 2 * np.abs(x[0].value)])
                        y_max = max([(x[0].value + x[0].dvalue) for x in self.content[x_range[0]: x_range[1] + 1] if (x is not None) and x[0].dvalue < 2 * np.abs(x[0].value)])
                        ax1.set_ylim([y_min - 0.1 * (y_max - y_min), y_max + 0.1 * (y_max - y_min)])
                    except Exception:
                        pass
                else:
                    ax1.set_ylim(y_range)
            if comp:
                if isinstance(comp, (Corr, list)):
                    for corr in comp if isinstance(comp, list) else [comp]:
                        if auto_gamma:
                            corr.gamma_method()
                        x, y, y_err = corr.plottable()
                        plt.errorbar(x, y, y_err, label=corr.tag, mfc=plt.rcParams['axes.facecolor'])
                else:
                    raise Exception("'comp' must be a correlator or a list of correlators.")

            if plateau:
                if isinstance(plateau, Obs):
                    if auto_gamma:
                        plateau.gamma_method()
                    ax1.axhline(y=plateau.value, linewidth=2, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--', label=str(plateau))
                    ax1.axhspan(plateau.value - plateau.dvalue, plateau.value + plateau.dvalue, alpha=0.25, color=plt.rcParams['text.color'], ls='-')
                else:
                    raise Exception("'plateau' must be an Obs")
            if self.prange:
                ax1.axvline(self.prange[0], 0, 1, ls='-', marker=',')
                ax1.axvline(self.prange[1], 0, 1, ls='-', marker=',')

            if fit_res:
                x_samples = np.arange(x_range[0], x_range[1] + 1, 0.05)
                ax1.plot(x_samples,
                         fit_res.fit_function([o.value for o in fit_res.fit_parameters], x_samples),
                         ls='-', marker=',', lw=2)

            ax1.set_xlabel(r'$x_0 / a$')
            if ylabel:
                ax1.set_ylabel(ylabel)
            ax1.set_xlim([x_range[0] - 0.5, x_range[1] + 0.5])

            handles, labels = ax1.get_legend_handles_labels()
            if labels:
                ax1.legend()
            plt.draw()

            if save:
                if isinstance(save, str):
                    fig.savefig(save)
                else:
                    raise Exception("'save' has to be a string.")

            return

        def dump(self, filename, datatype="json.gz", **kwargs):
            """Dumps the Corr into a file of chosen type
            Parameters
            ----------
            filename : str
                Name of the file to be saved.
            datatype : str
                Format of the exported file. Supported formats include
                "json.gz" and "pickle"
            path : str
                specifies a custom path for the file (default '.')
            """
            if datatype == "json.gz":
                from .input.json import dump_to_json
                if 'path' in kwargs:
                    file_name = kwargs.get('path') + '/' + filename
                else:
                    file_name = filename
                dump_to_json(self, file_name)
            elif datatype == "pickle":
                dump_object(self, filename, **kwargs)
            else:
                raise Exception("Unknown datatype " + str(datatype))

        def print(self, range=[0, None]):
            print(self.__repr__(range))

        def __repr__(self, range=[0, None]):
            content_string = ""

            content_string += "Corr T=" + str(self.T) + " N=" + str(self.N) + "\n"  # +" filled with"+ str(type(self.content[0][0])) there should be a good solution here

            if self.tag is not None:
                content_string += "Description: " + self.tag + "\n"
            if self.N != 1:
                return content_string

            if range[1]:
                range[1] += 1
            content_string += 'x0/a\tCorr(x0/a)\n------------------\n'
            for i, sub_corr in enumerate(self.content[range[0]:range[1]]):
                if sub_corr is None:
                    content_string += str(i + range[0]) + '\n'
                else:
                    content_string += str(i + range[0])
                    for element in sub_corr:
                        content_string += '\t' + ' ' * int(element >= 0) + str(element)
                    content_string += '\n'
            return content_string

        def __str__(self):
            return self.__repr__()

        # We define the basic operations, that can be performed with correlators.
        # While */+- get defined here, they only work for Corr*Obs and not Obs*Corr.
        # This is because Obs*Corr checks Obs.__mul__ first and does not catch an exception.
        # One could try and tell Obs to check if the y in __mul__ is a Corr and

        def __add__(self, y):
            if isinstance(y, Corr):
                if ((self.N != y.N) or (self.T != y.T)):
                    raise Exception("Addition of Corrs with different shape")
                newcontent = []
                for t in range(self.T):
                    if (self.content[t] is None) or (y.content[t] is None):
                        newcontent.append(None)
                    else:
                        newcontent.append(self.content[t] + y.content[t])
                return Corr(newcontent)

            elif isinstance(y, (Obs, int, float, CObs)):
                newcontent = []
                for t in range(self.T):
                    if (self.content[t] is None):
                        newcontent.append(None)
                    else:
                        newcontent.append(self.content[t] + y)
                return Corr(newcontent, prange=self.prange)
            else:
                raise TypeError("Corr + wrong type")

        def __mul__(self, y):
            if isinstance(y, Corr):
                if not((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T):
                    raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T")
                newcontent = []
                for t in range(self.T):
                    if (self.content[t] is None) or (y.content[t] is None):
                        newcontent.append(None)
                    else:
                        newcontent.append(self.content[t] * y.content[t])
                return Corr(newcontent)

            elif isinstance(y, (Obs, int, float, CObs)):
                newcontent = []
                for t in range(self.T):
                    if (self.content[t] is None):
                        newcontent.append(None)
                    else:
                        newcontent.append(self.content[t] * y)
                return Corr(newcontent, prange=self.prange)
            else:
                raise TypeError("Corr * wrong type")

        def __truediv__(self, y):
            if isinstance(y, Corr):
                if not((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T):
                    raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T")
                newcontent = []
                for t in range(self.T):
                    if (self.content[t] is None) or (y.content[t] is None):
                        newcontent.append(None)
                    else:
                        newcontent.append(self.content[t] / y.content[t])
                for t in range(self.T):
                    if newcontent[t] is None:
                        continue
                    if np.isnan(np.sum(newcontent[t]).value):
                        newcontent[t] = None

                if all([item is None for item in newcontent]):
                    raise Exception("Division returns completely undefined correlator")
                return Corr(newcontent)

            elif isinstance(y, (Obs, CObs)):
                if isinstance(y, Obs):
                    if y.value == 0:
                        raise Exception('Division by zero will return undefined correlator')
                if isinstance(y, CObs):
                    if y.is_zero():
                        raise Exception('Division by zero will return undefined correlator')

                newcontent = []
                for t in range(self.T):
                    if (self.content[t] is None):
                        newcontent.append(None)
                    else:
                        newcontent.append(self.content[t] / y)
                return Corr(newcontent, prange=self.prange)

            elif isinstance(y, (int, float)):
                if y == 0:
                    raise Exception('Division by zero will return undefined correlator')
                newcontent = []
                for t in range(self.T):
                    if (self.content[t] is None):
                        newcontent.append(None)
                    else:
                        newcontent.append(self.content[t] / y)
                return Corr(newcontent, prange=self.prange)
            else:
                raise TypeError('Corr / wrong type')

        def __neg__(self):
            newcontent = [None if (item is None) else -1. * item for item in self.content]
            return Corr(newcontent, prange=self.prange)

        def __sub__(self, y):
            return self + (-y)

        def __pow__(self, y):
            if isinstance(y, (Obs, int, float, CObs)):
                newcontent = [None if (item is None) else item**y for item in self.content]
                return Corr(newcontent, prange=self.prange)
            else:
                raise TypeError('Type of exponent not supported')

        def __abs__(self):
            newcontent = [None if (item is None) else np.abs(item) for item in self.content]
            return Corr(newcontent, prange=self.prange)

        # The numpy functions:
        def sqrt(self):
            return self**0.5

        def log(self):
            newcontent = [None if (item is None) else np.log(item) for item in self.content]
            return Corr(newcontent, prange=self.prange)

        def exp(self):
            newcontent = [None if (item is None) else np.exp(item) for item in self.content]
            return Corr(newcontent, prange=self.prange)

        def _apply_func_to_corr(self, func):
            newcontent = [None if (item is None) else func(item) for item in self.content]
            for t in range(self.T):
                if newcontent[t] is None:
                    continue
                if np.isnan(np.sum(newcontent[t]).value):
                    newcontent[t] = None
            if all([item is None for item in newcontent]):
                raise Exception('Operation returns undefined correlator')
            return Corr(newcontent)

        def sin(self):
            return self._apply_func_to_corr(np.sin)

        def cos(self):
            return self._apply_func_to_corr(np.cos)

        def tan(self):
            return self._apply_func_to_corr(np.tan)

        def sinh(self):
            return self._apply_func_to_corr(np.sinh)

        def cosh(self):
            return self._apply_func_to_corr(np.cosh)

        def tanh(self):
            return self._apply_func_to_corr(np.tanh)

        def arcsin(self):
            return self._apply_func_to_corr(np.arcsin)

        def arccos(self):
            return self._apply_func_to_corr(np.arccos)

        def arctan(self):
            return self._apply_func_to_corr(np.arctan)

        def arcsinh(self):
            return self._apply_func_to_corr(np.arcsinh)

        def arccosh(self):
            return self._apply_func_to_corr(np.arccosh)

        def arctanh(self):
            return self._apply_func_to_corr(np.arctanh)

        # Right hand side operations (require tweak in main module to work)
        def __radd__(self, y):
            return self + y

        def __rsub__(self, y):
            return -self + y

        def __rmul__(self, y):
            return self * y

        def __rtruediv__(self, y):
            return (self / y) ** (-1)

        @property
        def real(self):
            def return_real(obs_OR_cobs):
                if isinstance(obs_OR_cobs, CObs):
                    return obs_OR_cobs.real
                else:
                    return obs_OR_cobs

            return self._apply_func_to_corr(return_real)

        @property
        def imag(self):
            def return_imag(obs_OR_cobs):
                if isinstance(obs_OR_cobs, CObs):
                    return obs_OR_cobs.imag
                else:
                    return obs_OR_cobs * 0  # So it stays the right type

            return self._apply_func_to_corr(return_imag)

    def _sort_vectors(vec_set, ts):
        """Helper function used to find a set of Eigenvectors consistent over all timeslices"""
        reference_sorting = np.array(vec_set[ts])
        N = reference_sorting.shape[0]
        sorted_vec_set = []
        for t in range(len(vec_set)):
            if vec_set[t] is None:
                sorted_vec_set.append(None)
            elif not t == ts:
                perms = [list(o) for o in permutations([i for i in range(N)], N)]
                best_score = 0
                for perm in perms:
                    current_score = 1
                    for k in range(N):
                        new_sorting = reference_sorting.copy()
                        new_sorting[perm[k], :] = vec_set[t][k]
                        current_score *= abs(np.linalg.det(new_sorting))
                    if current_score > best_score:
                        best_score = current_score
                        best_perm = perm
                sorted_vec_set.append([vec_set[t][k] for k in best_perm])
            else:
                sorted_vec_set.append(vec_set[t])

        return sorted_vec_set

    def _GEVP_solver(Gt, G0):  # Just so normalization an sorting does not need to be repeated. Here we could later put in some checks
        sp_val, sp_vecs = scipy.linalg.eig(Gt, G0)
        sp_vecs = [sp_vecs[:, np.argsort(sp_val)[-i]] for i in range(1, sp_vecs.shape[0] + 1)]
        sp_vecs = [v / np.sqrt((v.T @ G0 @ v)) for v in sp_vecs]
        return sp_vecs

class Corr:
View Source

    class Corr:
        """The class for a correlator (time dependent sequence of pe.Obs).

        Everything, this class does, can be achieved using lists or arrays of Obs.
        But it is simply more convenient to have a dedicated object for correlators.
        One often wants to add or multiply correlators of the same length at every timeslice and it is inconvenient
        to iterate over all timeslices for every operation. This is especially true, when dealing with matrices.

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

        """

        def __init__(self, data_input, padding=[0, 0], prange=None):
            """ Initialize a Corr object.

            Parameters
            ----------
            data_input : list or array
                list of Obs or list of arrays of Obs or array of Corrs
            padding : list, optional
                List with two entries where the first labels the padding
                at the front of the correlator and the second the padding
                at the back.
            prange : list, optional
                List containing the first and last timeslice of the plateau
                region indentified for this correlator.
            """

            if isinstance(data_input, np.ndarray):

                # This only works, if the array fulfills the conditions below
                if not len(data_input.shape) == 2 and data_input.shape[0] == data_input.shape[1]:
                    raise Exception("Incompatible array shape")
                if not all([isinstance(item, Corr) for item in data_input.flatten()]):
                    raise Exception("If the input is an array, its elements must be of type pe.Corr")
                if not all([item.N == 1 for item in data_input.flatten()]):
                    raise Exception("Can only construct matrix correlator from single valued correlators")
                if not len(set([item.T for item in data_input.flatten()])) == 1:
                    raise Exception("All input Correlators must be defined over the same timeslices.")

                T = data_input[0, 0].T
                N = data_input.shape[0]
                input_as_list = []
                for t in range(T):
                    if any([(item.content[t] is None) for item in data_input.flatten()]):
                        if not all([(item.content[t] is None) for item in data_input.flatten()]):
                            warnings.warn("Input ill-defined at different timeslices. Conversion leads to data loss!", RuntimeWarning)
                        input_as_list.append(None)
                    else:
                        array_at_timeslace = np.empty([N, N], dtype="object")
                        for i in range(N):
                            for j in range(N):
                                array_at_timeslace[i, j] = data_input[i, j][t]
                        input_as_list.append(array_at_timeslace)
                data_input = input_as_list

            if isinstance(data_input, list):

                if all([isinstance(item, (Obs, CObs)) for item in data_input]):
                    _assert_equal_properties(data_input)
                    self.content = [np.asarray([item]) for item in data_input]
                if all([isinstance(item, (Obs, CObs)) or item is None for item in data_input]):
                    _assert_equal_properties([o for o in data_input if o is not None])
                    self.content = [np.asarray([item]) if item is not None else None for item in data_input]
                    self.N = 1

                elif all([isinstance(item, np.ndarray) or item is None for item in data_input]) and any([isinstance(item, np.ndarray) for item in data_input]):
                    self.content = data_input
                    noNull = [a for a in self.content if not (a is None)]  # To check if the matrices are correct for all undefined elements
                    self.N = noNull[0].shape[0]
                    if self.N > 1 and noNull[0].shape[0] != noNull[0].shape[1]:
                        raise Exception("Smearing matrices are not NxN")
                    if (not all([item.shape == noNull[0].shape for item in noNull])):
                        raise Exception("Items in data_input are not of identical shape." + str(noNull))
                else:
                    raise Exception("data_input contains item of wrong type")
            else:
                raise Exception("Data input was not given as list or correct array")

            self.tag = None

            # An undefined timeslice is represented by the None object
            self.content = [None] * padding[0] + self.content + [None] * padding[1]
            self.T = len(self.content)
            self.prange = prange

        def __getitem__(self, idx):
            """Return the content of timeslice idx"""
            if self.content[idx] is None:
                return None
            elif len(self.content[idx]) == 1:
                return self.content[idx][0]
            else:
                return self.content[idx]

        @property
        def reweighted(self):
            bool_array = np.array([list(map(lambda x: x.reweighted, o)) for o in [x for x in self.content if x is not None]])
            if np.all(bool_array == 1):
                return True
            elif np.all(bool_array == 0):
                return False
            else:
                raise Exception("Reweighting status of correlator corrupted.")

        def gamma_method(self, **kwargs):
            """Apply the gamma method to the content of the Corr."""
            for item in self.content:
                if not(item is None):
                    if self.N == 1:
                        item[0].gamma_method(**kwargs)
                    else:
                        for i in range(self.N):
                            for j in range(self.N):
                                item[i, j].gamma_method(**kwargs)

        def projected(self, vector_l=None, vector_r=None, normalize=False):
            """We need to project the Correlator with a Vector to get a single value at each timeslice.

            The method can use one or two vectors.
            If two are specified it returns v1@G@v2 (the order might be very important.)
            By default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to
            """
            if self.N == 1:
                raise Exception("Trying to project a Corr, that already has N=1.")

            if vector_l is None:
                vector_l, vector_r = np.asarray([1.] + (self.N - 1) * [0.]), np.asarray([1.] + (self.N - 1) * [0.])
            elif(vector_r is None):
                vector_r = vector_l
            if isinstance(vector_l, list) and not isinstance(vector_r, list):
                if len(vector_l) != self.T:
                    raise Exception("Length of vector list must be equal to T")
                vector_r = [vector_r] * self.T
            if isinstance(vector_r, list) and not isinstance(vector_l, list):
                if len(vector_r) != self.T:
                    raise Exception("Length of vector list must be equal to T")
                vector_l = [vector_l] * self.T

            if not isinstance(vector_l, list):
                if not vector_l.shape == vector_r.shape == (self.N,):
                    raise Exception("Vectors are of wrong shape!")
                if normalize:
                    vector_l, vector_r = vector_l / np.sqrt((vector_l @ vector_l)), vector_r / np.sqrt(vector_r @ vector_r)
                newcontent = [None if (item is None) else np.asarray([vector_l.T @ item @ vector_r]) for item in self.content]

            else:
                # There are no checks here yet. There are so many possible scenarios, where this can go wrong.
                if normalize:
                    for t in range(self.T):
                        vector_l[t], vector_r[t] = vector_l[t] / np.sqrt((vector_l[t] @ vector_l[t])), vector_r[t] / np.sqrt(vector_r[t] @ vector_r[t])

                newcontent = [None if (self.content[t] is None or vector_l[t] is None or vector_r[t] is None) else np.asarray([vector_l[t].T @ self.content[t] @ vector_r[t]]) for t in range(self.T)]
            return Corr(newcontent)

        def item(self, i, j):
            """Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice.

            Parameters
            ----------
            i : int
                First index to be picked.
            j : int
                Second index to be picked.
            """
            if self.N == 1:
                raise Exception("Trying to pick item from projected Corr")
            newcontent = [None if(item is None) else item[i, j] for item in self.content]
            return Corr(newcontent)

        def plottable(self):
            """Outputs the correlator in a plotable format.

            Outputs three lists containing the timeslice index, the value on each
            timeslice and the error on each timeslice.
            """
            if self.N != 1:
                raise Exception("Can only make Corr[N=1] plottable")
            x_list = [x for x in range(self.T) if not self.content[x] is None]
            y_list = [y[0].value for y in self.content if y is not None]
            y_err_list = [y[0].dvalue for y in self.content if y is not None]

            return x_list, y_list, y_err_list

        def symmetric(self):
            """ Symmetrize the correlator around x0=0."""
            if self.T % 2 != 0:
                raise Exception("Can not symmetrize odd T")

            if np.argmax(np.abs(self.content)) != 0:
                warnings.warn("Correlator does not seem to be symmetric around x0=0.", RuntimeWarning)

            newcontent = [self.content[0]]
            for t in range(1, self.T):
                if (self.content[t] is None) or (self.content[self.T - t] is None):
                    newcontent.append(None)
                else:
                    newcontent.append(0.5 * (self.content[t] + self.content[self.T - t]))
            if(all([x is None for x in newcontent])):
                raise Exception("Corr could not be symmetrized: No redundant values")
            return Corr(newcontent, prange=self.prange)

        def anti_symmetric(self):
            """Anti-symmetrize the correlator around x0=0."""
            if self.T % 2 != 0:
                raise Exception("Can not symmetrize odd T")

            test = 1 * self
            test.gamma_method()
            if not all([o.is_zero_within_error(3) for o in test.content[0]]):
                warnings.warn("Correlator does not seem to be anti-symmetric around x0=0.", RuntimeWarning)

            newcontent = [self.content[0]]
            for t in range(1, self.T):
                if (self.content[t] is None) or (self.content[self.T - t] is None):
                    newcontent.append(None)
                else:
                    newcontent.append(0.5 * (self.content[t] - self.content[self.T - t]))
            if(all([x is None for x in newcontent])):
                raise Exception("Corr could not be symmetrized: No redundant values")
            return Corr(newcontent, prange=self.prange)

        def matrix_symmetric(self):
            """Symmetrizes the correlator matrices on every timeslice."""
            if self.N > 1:
                transposed = [None if (G is None) else G.T for G in self.content]
                return 0.5 * (Corr(transposed) + self)
            if self.N == 1:
                raise Exception("Trying to symmetrize a correlator matrix, that already has N=1.")

        def GEVP(self, t0, ts=None, state=0, sorted_list=None):
            """Solve the general eigenvalue problem on the current correlator

            Parameters
            ----------
            t0 : int
                The time t0 for G(t)v= lambda G(t_0)v
            ts : int
                fixed time G(t_s)v= lambda G(t_0)v  if return_list=False
                If return_list=True and sorting=Eigenvector it gives a reference point for the sorting method.
            state : int
                The state one is interested in ordered by energy. The lowest state is zero.
            sorted_list : string
                if this argument is set, a list of vectors (len=self.T) is returned. If it is left as None, only one vector is returned.
                 "Eigenvalue"  -  The eigenvector is chosen according to which einvenvalue it belongs individually on every timeslice.
                 "Eigenvector" -  Use the method described in arXiv:2004.10472 [hep-lat] to find the set of v(t) belonging to the state.
                                     The referense state is identified by its eigenvalue at t=ts
            """
            if sorted_list is None:
                if (ts is None):
                    raise Exception("ts is required if sorted_list=None")
                if (self.content[t0] is None) or (self.content[ts] is None):
                    raise Exception("Corr not defined at t0/ts")
                G0, Gt = np.empty([self.N, self.N], dtype="double"), np.empty([self.N, self.N], dtype="double")
                for i in range(self.N):
                    for j in range(self.N):
                        G0[i, j] = self.content[t0][i, j].value
                        Gt[i, j] = self.content[ts][i, j].value

                sp_vecs = _GEVP_solver(Gt, G0)
                sp_vec = sp_vecs[state]
                return sp_vec
            else:

                all_vecs = []
                for t in range(self.T):
                    try:
                        G0, Gt = np.empty([self.N, self.N], dtype="double"), np.empty([self.N, self.N], dtype="double")
                        for i in range(self.N):
                            for j in range(self.N):
                                G0[i, j] = self.content[t0][i, j].value
                                Gt[i, j] = self.content[t][i, j].value

                        sp_vecs = _GEVP_solver(Gt, G0)
                        if sorted_list == "Eigenvalue":
                            sp_vec = sp_vecs[state]
                            all_vecs.append(sp_vec)
                        else:
                            all_vecs.append(sp_vecs)
                    except Exception:
                        all_vecs.append(None)
                if sorted_list == "Eigenvector":
                    if (ts is None):
                        raise Exception("ts is required for the Eigenvector sorting method.")
                    all_vecs = _sort_vectors(all_vecs, ts)
                    all_vecs = [a[state] for a in all_vecs]

            return all_vecs

        def Eigenvalue(self, t0, state=1):
            G = self.matrix_symmetric()
            G0 = G.content[t0]
            L = cholesky(G0)
            Li = inv(L)
            LT = L.T
            LTi = inv(LT)
            newcontent = []
            for t in range(self.T):
                if self.content[t] is None:
                    newcontent.append(None)
                else:
                    Gt = G.content[t]
                    M = Li @ Gt @ LTi
                    eigenvalues = eigh(M)[0]
                    eigenvalue = eigenvalues[-state]
                    newcontent.append(eigenvalue)
            return Corr(newcontent)

        def Hankel(self, N, periodic=False):
            """Constructs an NxN Hankel matrix

            C(t) c(t+1) ... c(t+n-1)
            C(t+1) c(t+2) ... c(t+n)
            .................
            C(t+(n-1)) c(t+n) ... c(t+2(n-1))

            Parameters
            ----------
            N : int
                Dimension of the Hankel matrix
            periodic : bool, optional
                determines whether the matrix is extended periodically
            """

            if self.N != 1:
                raise Exception("Multi-operator Prony not implemented!")

            array = np.empty([N, N], dtype="object")
            new_content = []
            for t in range(self.T):
                new_content.append(array.copy())

            def wrap(i):
                while i >= self.T:
                    i -= self.T
                return i

            for t in range(self.T):
                for i in range(N):
                    for j in range(N):
                        if periodic:
                            new_content[t][i, j] = self.content[wrap(t + i + j)][0]
                        elif (t + i + j) >= self.T:
                            new_content[t] = None
                        else:
                            new_content[t][i, j] = self.content[t + i + j][0]

            return Corr(new_content)

        def roll(self, dt):
            """Periodically shift the correlator by dt timeslices

            Parameters
            ----------
            dt : int
                number of timeslices
            """
            return Corr(list(np.roll(np.array(self.content, dtype=object), dt)))

        def reverse(self):
            """Reverse the time ordering of the Corr"""
            return Corr(self.content[:: -1])

        def thin(self, spacing=2, offset=0):
            """Thin out a correlator to suppress correlations

            Parameters
            ----------
            spacing : int
                Keep only every 'spacing'th entry of the correlator
            offset : int
                Offset the equal spacing
            """
            new_content = []
            for t in range(self.T):
                if (offset + t) % spacing != 0:
                    new_content.append(None)
                else:
                    new_content.append(self.content[t])
            return Corr(new_content)

        def correlate(self, partner):
            """Correlate the correlator with another correlator or Obs

            Parameters
            ----------
            partner : Obs or Corr
                partner to correlate the correlator with.
                Can either be an Obs which is correlated with all entries of the
                correlator or a Corr of same length.
            """
            new_content = []
            for x0, t_slice in enumerate(self.content):
                if t_slice is None:
                    new_content.append(None)
                else:
                    if isinstance(partner, Corr):
                        if partner.content[x0] is None:
                            new_content.append(None)
                        else:
                            new_content.append(np.array([correlate(o, partner.content[x0][0]) for o in t_slice]))
                    elif isinstance(partner, Obs):  # Should this include CObs?
                        new_content.append(np.array([correlate(o, partner) for o in t_slice]))
                    else:
                        raise Exception("Can only correlate with an Obs or a Corr.")

            return Corr(new_content)

        def reweight(self, weight, **kwargs):
            """Reweight the correlator.

            Parameters
            ----------
            weight : Obs
                Reweighting factor. An Observable that has to be defined on a superset of the
                configurations in obs[i].idl for all i.
            all_configs : bool
                if True, the reweighted observables are normalized by the average of
                the reweighting factor on all configurations in weight.idl and not
                on the configurations in obs[i].idl.
            """
            new_content = []
            for t_slice in self.content:
                if t_slice is None:
                    new_content.append(None)
                else:
                    new_content.append(np.array(reweight(weight, t_slice, **kwargs)))
            return Corr(new_content)

        def T_symmetry(self, partner, parity=+1):
            """Return the time symmetry average of the correlator and its partner

            Parameters
            ----------
            partner : Corr
                Time symmetry partner of the Corr
            partity : int
                Parity quantum number of the correlator, can be +1 or -1
            """
            if not isinstance(partner, Corr):
                raise Exception("T partner has to be a Corr object.")
            if parity not in [+1, -1]:
                raise Exception("Parity has to be +1 or -1.")
            T_partner = parity * partner.reverse()

            t_slices = []
            test = (self - T_partner)
            test.gamma_method()
            for x0, t_slice in enumerate(test.content):
                if t_slice is not None:
                    if not t_slice[0].is_zero_within_error(5):
                        t_slices.append(x0)
            if t_slices:
                warnings.warn("T symmetry partners do not agree within 5 sigma on time slices " + str(t_slices) + ".", RuntimeWarning)

            return (self + T_partner) / 2

        def deriv(self, variant="symmetric"):
            """Return the first derivative of the correlator with respect to x0.

            Parameters
            ----------
            variant : str
                decides which definition of the finite differences derivative is used.
                Available choice: symmetric, forward, backward, improved, default: symmetric
            """
            if variant == "symmetric":
                newcontent = []
                for t in range(1, self.T - 1):
                    if (self.content[t - 1] is None) or (self.content[t + 1] is None):
                        newcontent.append(None)
                    else:
                        newcontent.append(0.5 * (self.content[t + 1] - self.content[t - 1]))
                if(all([x is None for x in newcontent])):
                    raise Exception('Derivative is undefined at all timeslices')
                return Corr(newcontent, padding=[1, 1])
            elif variant == "forward":
                newcontent = []
                for t in range(self.T - 1):
                    if (self.content[t] is None) or (self.content[t + 1] is None):
                        newcontent.append(None)
                    else:
                        newcontent.append(self.content[t + 1] - self.content[t])
                if(all([x is None for x in newcontent])):
                    raise Exception("Derivative is undefined at all timeslices")
                return Corr(newcontent, padding=[0, 1])
            elif variant == "backward":
                newcontent = []
                for t in range(1, self.T):
                    if (self.content[t - 1] is None) or (self.content[t] is None):
                        newcontent.append(None)
                    else:
                        newcontent.append(self.content[t] - self.content[t - 1])
                if(all([x is None for x in newcontent])):
                    raise Exception("Derivative is undefined at all timeslices")
                return Corr(newcontent, padding=[1, 0])
            elif variant == "improved":
                newcontent = []
                for t in range(2, self.T - 2):
                    if (self.content[t - 2] is None) or (self.content[t - 1] is None) or (self.content[t + 1] is None) or (self.content[t + 2] is None):
                        newcontent.append(None)
                    else:
                        newcontent.append((1 / 12) * (self.content[t - 2] - 8 * self.content[t - 1] + 8 * self.content[t + 1] - self.content[t + 2]))
                if(all([x is None for x in newcontent])):
                    raise Exception('Derivative is undefined at all timeslices')
                return Corr(newcontent, padding=[2, 2])
            else:
                raise Exception("Unknown variant.")

        def second_deriv(self, variant="symmetric"):
            """Return the second derivative of the correlator with respect to x0.

            Parameters
            ----------
            variant : str
                decides which definition of the finite differences derivative is used.
                Available choice: symmetric, improved, default: symmetric
            """
            if variant == "symmetric":
                newcontent = []
                for t in range(1, self.T - 1):
                    if (self.content[t - 1] is None) or (self.content[t + 1] is None):
                        newcontent.append(None)
                    else:
                        newcontent.append((self.content[t + 1] - 2 * self.content[t] + self.content[t - 1]))
                if(all([x is None for x in newcontent])):
                    raise Exception("Derivative is undefined at all timeslices")
                return Corr(newcontent, padding=[1, 1])
            elif variant == "improved":
                newcontent = []
                for t in range(2, self.T - 2):
                    if (self.content[t - 2] is None) or (self.content[t - 1] is None) or (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 2] is None):
                        newcontent.append(None)
                    else:
                        newcontent.append((1 / 12) * (-self.content[t + 2] + 16 * self.content[t + 1] - 30 * self.content[t] + 16 * self.content[t - 1] - self.content[t - 2]))
                if(all([x is None for x in newcontent])):
                    raise Exception("Derivative is undefined at all timeslices")
                return Corr(newcontent, padding=[2, 2])
            else:
                raise Exception("Unknown variant.")

        def m_eff(self, variant='log', guess=1.0):
            """Returns the effective mass of the correlator as correlator object

            Parameters
            ----------
            variant : str
                log : uses the standard effective mass log(C(t) / C(t+1))
                cosh, 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.
                sinh : 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.
                See, e.g., arXiv:1205.5380
                arccosh : Uses the explicit form of the symmetrized correlator (not recommended)
            guess : float
                guess for the root finder, only relevant for the root variant
            """
            if self.N != 1:
                raise Exception('Correlator must be projected before getting m_eff')
            if variant == 'log':
                newcontent = []
                for t in range(self.T - 1):
                    if (self.content[t] is None) or (self.content[t + 1] is None):
                        newcontent.append(None)
                    else:
                        newcontent.append(self.content[t] / self.content[t + 1])
                if(all([x is None for x in newcontent])):
                    raise Exception('m_eff is undefined at all timeslices')

                return np.log(Corr(newcontent, padding=[0, 1]))

            elif variant in ['periodic', 'cosh', 'sinh']:
                if variant in ['periodic', 'cosh']:
                    func = anp.cosh
                else:
                    func = anp.sinh

                def root_function(x, d):
                    return func(x * (t - self.T / 2)) / func(x * (t + 1 - self.T / 2)) - d

                newcontent = []
                for t in range(self.T - 1):
                    if (self.content[t] is None) or (self.content[t + 1] is None):
                        newcontent.append(None)
                    # Fill the two timeslices in the middle of the lattice with their predecessors
                    elif variant == 'sinh' and t in [self.T / 2, self.T / 2 - 1]:
                        newcontent.append(newcontent[-1])
                    else:
                        newcontent.append(np.abs(find_root(self.content[t][0] / self.content[t + 1][0], root_function, guess=guess)))
                if(all([x is None for x in newcontent])):
                    raise Exception('m_eff is undefined at all timeslices')

                return Corr(newcontent, padding=[0, 1])

            elif variant == 'arccosh':
                newcontent = []
                for t in range(1, self.T - 1):
                    if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t - 1] is None):
                        newcontent.append(None)
                    else:
                        newcontent.append((self.content[t + 1] + self.content[t - 1]) / (2 * self.content[t]))
                if(all([x is None for x in newcontent])):
                    raise Exception("m_eff is undefined at all timeslices")
                return np.arccosh(Corr(newcontent, padding=[1, 1]))

            else:
                raise Exception('Unknown variant.')

        def fit(self, function, fitrange=None, silent=False, **kwargs):
            """Fits function to the data

            Parameters
            ----------
            function : obj
                function to fit to the data. See fits.least_squares for details.
            fitrange : list
                Range in which the function is to be fitted to the data.
                If not specified, self.prange or all timeslices are used.
            silent : bool
                Decides whether output is printed to the standard output.
            """
            if self.N != 1:
                raise Exception("Correlator must be projected before fitting")

            if fitrange is None:
                if self.prange:
                    fitrange = self.prange
                else:
                    fitrange = [0, self.T - 1]

            xs = [x for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None]
            ys = [self.content[x][0] for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None]
            result = least_squares(xs, ys, function, silent=silent, **kwargs)
            return result

        def plateau(self, plateau_range=None, method="fit", auto_gamma=False):
            """ Extract a plateau value from a Corr object

            Parameters
            ----------
            plateau_range : list
                list with two entries, indicating the first and the last timeslice
                of the plateau region.
            method : str
                method to extract the plateau.
                    'fit' fits a constant to the plateau region
                    'avg', 'average' or 'mean' just average over the given timeslices.
            auto_gamma : bool
                apply gamma_method with default parameters to the Corr. Defaults to None
            """
            if not plateau_range:
                if self.prange:
                    plateau_range = self.prange
                else:
                    raise Exception("no plateau range provided")
            if self.N != 1:
                raise Exception("Correlator must be projected before getting a plateau.")
            if(all([self.content[t] is None for t in range(plateau_range[0], plateau_range[1] + 1)])):
                raise Exception("plateau is undefined at all timeslices in plateaurange.")
            if auto_gamma:
                self.gamma_method()
            if method == "fit":
                def const_func(a, t):
                    return a[0]
                return self.fit(const_func, plateau_range)[0]
            elif method in ["avg", "average", "mean"]:
                returnvalue = np.mean([item[0] for item in self.content[plateau_range[0]:plateau_range[1] + 1] if item is not None])
                return returnvalue

            else:
                raise Exception("Unsupported plateau method: " + method)

        def set_prange(self, prange):
            """Sets the attribute prange of the Corr object."""
            if not len(prange) == 2:
                raise Exception("prange must be a list or array with two values")
            if not ((isinstance(prange[0], int)) and (isinstance(prange[1], int))):
                raise Exception("Start and end point must be integers")
            if not (0 <= prange[0] <= self.T and 0 <= prange[1] <= self.T and prange[0] < prange[1]):
                raise Exception("Start and end point must define a range in the interval 0,T")

            self.prange = prange
            return

        def show(self, x_range=None, comp=None, y_range=None, logscale=False, plateau=None, fit_res=None, ylabel=None, save=None, auto_gamma=False):
            """Plots the correlator using the tag of the correlator as label if available.

            Parameters
            ----------
            x_range : list
                list of two values, determining the range of the x-axis e.g. [4, 8]
            comp : Corr or list of Corr
                Correlator or list of correlators which are plotted for comparison.
                The tags of these correlators are used as labels if available.
            logscale : bool
                Sets y-axis to logscale
            plateau : Obs
                Plateau value to be visualized in the figure
            fit_res : Fit_result
                Fit_result object to be visualized
            ylabel : str
                Label for the y-axis
            save : str
                path to file in which the figure should be saved
            auto_gamma : bool
                Apply the gamma method with standard parameters to all correlators and plateau values before plotting.
            """
            if self.N != 1:
                raise Exception("Correlator must be projected before plotting")

            if auto_gamma:
                self.gamma_method()

            if x_range is None:
                x_range = [0, self.T - 1]

            fig = plt.figure()
            ax1 = fig.add_subplot(111)

            x, y, y_err = self.plottable()
            ax1.errorbar(x, y, y_err, label=self.tag)
            if logscale:
                ax1.set_yscale('log')
            else:
                if y_range is None:
                    try:
                        y_min = min([(x[0].value - x[0].dvalue) for x in self.content[x_range[0]: x_range[1] + 1] if (x is not None) and x[0].dvalue < 2 * np.abs(x[0].value)])
                        y_max = max([(x[0].value + x[0].dvalue) for x in self.content[x_range[0]: x_range[1] + 1] if (x is not None) and x[0].dvalue < 2 * np.abs(x[0].value)])
                        ax1.set_ylim([y_min - 0.1 * (y_max - y_min), y_max + 0.1 * (y_max - y_min)])
                    except Exception:
                        pass
                else:
                    ax1.set_ylim(y_range)
            if comp:
                if isinstance(comp, (Corr, list)):
                    for corr in comp if isinstance(comp, list) else [comp]:
                        if auto_gamma:
                            corr.gamma_method()
                        x, y, y_err = corr.plottable()
                        plt.errorbar(x, y, y_err, label=corr.tag, mfc=plt.rcParams['axes.facecolor'])
                else:
                    raise Exception("'comp' must be a correlator or a list of correlators.")

            if plateau:
                if isinstance(plateau, Obs):
                    if auto_gamma:
                        plateau.gamma_method()
                    ax1.axhline(y=plateau.value, linewidth=2, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--', label=str(plateau))
                    ax1.axhspan(plateau.value - plateau.dvalue, plateau.value + plateau.dvalue, alpha=0.25, color=plt.rcParams['text.color'], ls='-')
                else:
                    raise Exception("'plateau' must be an Obs")
            if self.prange:
                ax1.axvline(self.prange[0], 0, 1, ls='-', marker=',')
                ax1.axvline(self.prange[1], 0, 1, ls='-', marker=',')

            if fit_res:
                x_samples = np.arange(x_range[0], x_range[1] + 1, 0.05)
                ax1.plot(x_samples,
                         fit_res.fit_function([o.value for o in fit_res.fit_parameters], x_samples),
                         ls='-', marker=',', lw=2)

            ax1.set_xlabel(r'$x_0 / a$')
            if ylabel:
                ax1.set_ylabel(ylabel)
            ax1.set_xlim([x_range[0] - 0.5, x_range[1] + 0.5])

            handles, labels = ax1.get_legend_handles_labels()
            if labels:
                ax1.legend()
            plt.draw()

            if save:
                if isinstance(save, str):
                    fig.savefig(save)
                else:
                    raise Exception("'save' has to be a string.")

            return

        def dump(self, filename, datatype="json.gz", **kwargs):
            """Dumps the Corr into a file of chosen type
            Parameters
            ----------
            filename : str
                Name of the file to be saved.
            datatype : str
                Format of the exported file. Supported formats include
                "json.gz" and "pickle"
            path : str
                specifies a custom path for the file (default '.')
            """
            if datatype == "json.gz":
                from .input.json import dump_to_json
                if 'path' in kwargs:
                    file_name = kwargs.get('path') + '/' + filename
                else:
                    file_name = filename
                dump_to_json(self, file_name)
            elif datatype == "pickle":
                dump_object(self, filename, **kwargs)
            else:
                raise Exception("Unknown datatype " + str(datatype))

        def print(self, range=[0, None]):
            print(self.__repr__(range))

        def __repr__(self, range=[0, None]):
            content_string = ""

            content_string += "Corr T=" + str(self.T) + " N=" + str(self.N) + "\n"  # +" filled with"+ str(type(self.content[0][0])) there should be a good solution here

            if self.tag is not None:
                content_string += "Description: " + self.tag + "\n"
            if self.N != 1:
                return content_string

            if range[1]:
                range[1] += 1
            content_string += 'x0/a\tCorr(x0/a)\n------------------\n'
            for i, sub_corr in enumerate(self.content[range[0]:range[1]]):
                if sub_corr is None:
                    content_string += str(i + range[0]) + '\n'
                else:
                    content_string += str(i + range[0])
                    for element in sub_corr:
                        content_string += '\t' + ' ' * int(element >= 0) + str(element)
                    content_string += '\n'
            return content_string

        def __str__(self):
            return self.__repr__()

        # We define the basic operations, that can be performed with correlators.
        # While */+- get defined here, they only work for Corr*Obs and not Obs*Corr.
        # This is because Obs*Corr checks Obs.__mul__ first and does not catch an exception.
        # One could try and tell Obs to check if the y in __mul__ is a Corr and

        def __add__(self, y):
            if isinstance(y, Corr):
                if ((self.N != y.N) or (self.T != y.T)):
                    raise Exception("Addition of Corrs with different shape")
                newcontent = []
                for t in range(self.T):
                    if (self.content[t] is None) or (y.content[t] is None):
                        newcontent.append(None)
                    else:
                        newcontent.append(self.content[t] + y.content[t])
                return Corr(newcontent)

            elif isinstance(y, (Obs, int, float, CObs)):
                newcontent = []
                for t in range(self.T):
                    if (self.content[t] is None):
                        newcontent.append(None)
                    else:
                        newcontent.append(self.content[t] + y)
                return Corr(newcontent, prange=self.prange)
            else:
                raise TypeError("Corr + wrong type")

        def __mul__(self, y):
            if isinstance(y, Corr):
                if not((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T):
                    raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T")
                newcontent = []
                for t in range(self.T):
                    if (self.content[t] is None) or (y.content[t] is None):
                        newcontent.append(None)
                    else:
                        newcontent.append(self.content[t] * y.content[t])
                return Corr(newcontent)

            elif isinstance(y, (Obs, int, float, CObs)):
                newcontent = []
                for t in range(self.T):
                    if (self.content[t] is None):
                        newcontent.append(None)
                    else:
                        newcontent.append(self.content[t] * y)
                return Corr(newcontent, prange=self.prange)
            else:
                raise TypeError("Corr * wrong type")

        def __truediv__(self, y):
            if isinstance(y, Corr):
                if not((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T):
                    raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T")
                newcontent = []
                for t in range(self.T):
                    if (self.content[t] is None) or (y.content[t] is None):
                        newcontent.append(None)
                    else:
                        newcontent.append(self.content[t] / y.content[t])
                for t in range(self.T):
                    if newcontent[t] is None:
                        continue
                    if np.isnan(np.sum(newcontent[t]).value):
                        newcontent[t] = None

                if all([item is None for item in newcontent]):
                    raise Exception("Division returns completely undefined correlator")
                return Corr(newcontent)

            elif isinstance(y, (Obs, CObs)):
                if isinstance(y, Obs):
                    if y.value == 0:
                        raise Exception('Division by zero will return undefined correlator')
                if isinstance(y, CObs):
                    if y.is_zero():
                        raise Exception('Division by zero will return undefined correlator')

                newcontent = []
                for t in range(self.T):
                    if (self.content[t] is None):
                        newcontent.append(None)
                    else:
                        newcontent.append(self.content[t] / y)
                return Corr(newcontent, prange=self.prange)

            elif isinstance(y, (int, float)):
                if y == 0:
                    raise Exception('Division by zero will return undefined correlator')
                newcontent = []
                for t in range(self.T):
                    if (self.content[t] is None):
                        newcontent.append(None)
                    else:
                        newcontent.append(self.content[t] / y)
                return Corr(newcontent, prange=self.prange)
            else:
                raise TypeError('Corr / wrong type')

        def __neg__(self):
            newcontent = [None if (item is None) else -1. * item for item in self.content]
            return Corr(newcontent, prange=self.prange)

        def __sub__(self, y):
            return self + (-y)

        def __pow__(self, y):
            if isinstance(y, (Obs, int, float, CObs)):
                newcontent = [None if (item is None) else item**y for item in self.content]
                return Corr(newcontent, prange=self.prange)
            else:
                raise TypeError('Type of exponent not supported')

        def __abs__(self):
            newcontent = [None if (item is None) else np.abs(item) for item in self.content]
            return Corr(newcontent, prange=self.prange)

        # The numpy functions:
        def sqrt(self):
            return self**0.5

        def log(self):
            newcontent = [None if (item is None) else np.log(item) for item in self.content]
            return Corr(newcontent, prange=self.prange)

        def exp(self):
            newcontent = [None if (item is None) else np.exp(item) for item in self.content]
            return Corr(newcontent, prange=self.prange)

        def _apply_func_to_corr(self, func):
            newcontent = [None if (item is None) else func(item) for item in self.content]
            for t in range(self.T):
                if newcontent[t] is None:
                    continue
                if np.isnan(np.sum(newcontent[t]).value):
                    newcontent[t] = None
            if all([item is None for item in newcontent]):
                raise Exception('Operation returns undefined correlator')
            return Corr(newcontent)

        def sin(self):
            return self._apply_func_to_corr(np.sin)

        def cos(self):
            return self._apply_func_to_corr(np.cos)

        def tan(self):
            return self._apply_func_to_corr(np.tan)

        def sinh(self):
            return self._apply_func_to_corr(np.sinh)

        def cosh(self):
            return self._apply_func_to_corr(np.cosh)

        def tanh(self):
            return self._apply_func_to_corr(np.tanh)

        def arcsin(self):
            return self._apply_func_to_corr(np.arcsin)

        def arccos(self):
            return self._apply_func_to_corr(np.arccos)

        def arctan(self):
            return self._apply_func_to_corr(np.arctan)

        def arcsinh(self):
            return self._apply_func_to_corr(np.arcsinh)

        def arccosh(self):
            return self._apply_func_to_corr(np.arccosh)

        def arctanh(self):
            return self._apply_func_to_corr(np.arctanh)

        # Right hand side operations (require tweak in main module to work)
        def __radd__(self, y):
            return self + y

        def __rsub__(self, y):
            return -self + y

        def __rmul__(self, y):
            return self * y

        def __rtruediv__(self, y):
            return (self / y) ** (-1)

        @property
        def real(self):
            def return_real(obs_OR_cobs):
                if isinstance(obs_OR_cobs, CObs):
                    return obs_OR_cobs.real
                else:
                    return obs_OR_cobs

            return self._apply_func_to_corr(return_real)

        @property
        def imag(self):
            def return_imag(obs_OR_cobs):
                if isinstance(obs_OR_cobs, CObs):
                    return obs_OR_cobs.imag
                else:
                    return obs_OR_cobs * 0  # So it stays the right type

            return self._apply_func_to_corr(return_imag)

The class for a correlator (time dependent sequence of pe.Obs).

Everything, this class does, can be achieved using lists or arrays of Obs. But it is simply more convenient to have a dedicated object for correlators. One often wants to add or multiply correlators of the same length at every timeslice and it is inconvenient to iterate over all timeslices for every operation. This is especially true, when dealing with matrices.

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

Corr(data_input, padding=[0, 0], prange=None)
View Source

        def __init__(self, data_input, padding=[0, 0], prange=None):
            """ Initialize a Corr object.

            Parameters
            ----------
            data_input : list or array
                list of Obs or list of arrays of Obs or array of Corrs
            padding : list, optional
                List with two entries where the first labels the padding
                at the front of the correlator and the second the padding
                at the back.
            prange : list, optional
                List containing the first and last timeslice of the plateau
                region indentified for this correlator.
            """

            if isinstance(data_input, np.ndarray):

                # This only works, if the array fulfills the conditions below
                if not len(data_input.shape) == 2 and data_input.shape[0] == data_input.shape[1]:
                    raise Exception("Incompatible array shape")
                if not all([isinstance(item, Corr) for item in data_input.flatten()]):
                    raise Exception("If the input is an array, its elements must be of type pe.Corr")
                if not all([item.N == 1 for item in data_input.flatten()]):
                    raise Exception("Can only construct matrix correlator from single valued correlators")
                if not len(set([item.T for item in data_input.flatten()])) == 1:
                    raise Exception("All input Correlators must be defined over the same timeslices.")

                T = data_input[0, 0].T
                N = data_input.shape[0]
                input_as_list = []
                for t in range(T):
                    if any([(item.content[t] is None) for item in data_input.flatten()]):
                        if not all([(item.content[t] is None) for item in data_input.flatten()]):
                            warnings.warn("Input ill-defined at different timeslices. Conversion leads to data loss!", RuntimeWarning)
                        input_as_list.append(None)
                    else:
                        array_at_timeslace = np.empty([N, N], dtype="object")
                        for i in range(N):
                            for j in range(N):
                                array_at_timeslace[i, j] = data_input[i, j][t]
                        input_as_list.append(array_at_timeslace)
                data_input = input_as_list

            if isinstance(data_input, list):

                if all([isinstance(item, (Obs, CObs)) for item in data_input]):
                    _assert_equal_properties(data_input)
                    self.content = [np.asarray([item]) for item in data_input]
                if all([isinstance(item, (Obs, CObs)) or item is None for item in data_input]):
                    _assert_equal_properties([o for o in data_input if o is not None])
                    self.content = [np.asarray([item]) if item is not None else None for item in data_input]
                    self.N = 1

                elif all([isinstance(item, np.ndarray) or item is None for item in data_input]) and any([isinstance(item, np.ndarray) for item in data_input]):
                    self.content = data_input
                    noNull = [a for a in self.content if not (a is None)]  # To check if the matrices are correct for all undefined elements
                    self.N = noNull[0].shape[0]
                    if self.N > 1 and noNull[0].shape[0] != noNull[0].shape[1]:
                        raise Exception("Smearing matrices are not NxN")
                    if (not all([item.shape == noNull[0].shape for item in noNull])):
                        raise Exception("Items in data_input are not of identical shape." + str(noNull))
                else:
                    raise Exception("data_input contains item of wrong type")
            else:
                raise Exception("Data input was not given as list or correct array")

            self.tag = None

            # An undefined timeslice is represented by the None object
            self.content = [None] * padding[0] + self.content + [None] * padding[1]
            self.T = len(self.content)
            self.prange = prange

Initialize a Corr object.

###### Parameters

- data_input (list or array): list of Obs or list of arrays of Obs or array of Corrs
- padding (list, optional): List with two entries where the first labels the padding at the front of the correlator and the second the padding at the back.
- prange (list, optional): List containing the first and last timeslice of the plateau region indentified for this correlator.

reweighted
def gamma_method(self, **kwargs):
View Source

        def gamma_method(self, **kwargs):
            """Apply the gamma method to the content of the Corr."""
            for item in self.content:
                if not(item is None):
                    if self.N == 1:
                        item[0].gamma_method(**kwargs)
                    else:
                        for i in range(self.N):
                            for j in range(self.N):
                                item[i, j].gamma_method(**kwargs)

Apply the gamma method to the content of the Corr.

def projected(self, vector_l=None, vector_r=None, normalize=False):
View Source

        def projected(self, vector_l=None, vector_r=None, normalize=False):
            """We need to project the Correlator with a Vector to get a single value at each timeslice.

            The method can use one or two vectors.
            If two are specified it returns v1@G@v2 (the order might be very important.)
            By default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to
            """
            if self.N == 1:
                raise Exception("Trying to project a Corr, that already has N=1.")

            if vector_l is None:
                vector_l, vector_r = np.asarray([1.] + (self.N - 1) * [0.]), np.asarray([1.] + (self.N - 1) * [0.])
            elif(vector_r is None):
                vector_r = vector_l
            if isinstance(vector_l, list) and not isinstance(vector_r, list):
                if len(vector_l) != self.T:
                    raise Exception("Length of vector list must be equal to T")
                vector_r = [vector_r] * self.T
            if isinstance(vector_r, list) and not isinstance(vector_l, list):
                if len(vector_r) != self.T:
                    raise Exception("Length of vector list must be equal to T")
                vector_l = [vector_l] * self.T

            if not isinstance(vector_l, list):
                if not vector_l.shape == vector_r.shape == (self.N,):
                    raise Exception("Vectors are of wrong shape!")
                if normalize:
                    vector_l, vector_r = vector_l / np.sqrt((vector_l @ vector_l)), vector_r / np.sqrt(vector_r @ vector_r)
                newcontent = [None if (item is None) else np.asarray([vector_l.T @ item @ vector_r]) for item in self.content]

            else:
                # There are no checks here yet. There are so many possible scenarios, where this can go wrong.
                if normalize:
                    for t in range(self.T):
                        vector_l[t], vector_r[t] = vector_l[t] / np.sqrt((vector_l[t] @ vector_l[t])), vector_r[t] / np.sqrt(vector_r[t] @ vector_r[t])

                newcontent = [None if (self.content[t] is None or vector_l[t] is None or vector_r[t] is None) else np.asarray([vector_l[t].T @ self.content[t] @ vector_r[t]]) for t in range(self.T)]
            return Corr(newcontent)

We need to project the Correlator with a Vector to get a single value at each timeslice.

The method can use one or two vectors. If two are specified it returns v1@G@v2 (the order might be very important.) By default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to

def item(self, i, j):
View Source

        def item(self, i, j):
            """Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice.

            Parameters
            ----------
            i : int
                First index to be picked.
            j : int
                Second index to be picked.
            """
            if self.N == 1:
                raise Exception("Trying to pick item from projected Corr")
            newcontent = [None if(item is None) else item[i, j] for item in self.content]
            return Corr(newcontent)

Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice.

###### Parameters

- i (int): First index to be picked.
- j (int): Second index to be picked.

def plottable(self):
View Source

        def plottable(self):
            """Outputs the correlator in a plotable format.

            Outputs three lists containing the timeslice index, the value on each
            timeslice and the error on each timeslice.
            """
            if self.N != 1:
                raise Exception("Can only make Corr[N=1] plottable")
            x_list = [x for x in range(self.T) if not self.content[x] is None]
            y_list = [y[0].value for y in self.content if y is not None]
            y_err_list = [y[0].dvalue for y in self.content if y is not None]

            return x_list, y_list, y_err_list

Outputs the correlator in a plotable format.

Outputs three lists containing the timeslice index, the value on each timeslice and the error on each timeslice.

def symmetric(self):
View Source

        def symmetric(self):
            """ Symmetrize the correlator around x0=0."""
            if self.T % 2 != 0:
                raise Exception("Can not symmetrize odd T")

            if np.argmax(np.abs(self.content)) != 0:
                warnings.warn("Correlator does not seem to be symmetric around x0=0.", RuntimeWarning)

            newcontent = [self.content[0]]
            for t in range(1, self.T):
                if (self.content[t] is None) or (self.content[self.T - t] is None):
                    newcontent.append(None)
                else:
                    newcontent.append(0.5 * (self.content[t] + self.content[self.T - t]))
            if(all([x is None for x in newcontent])):
                raise Exception("Corr could not be symmetrized: No redundant values")
            return Corr(newcontent, prange=self.prange)

Symmetrize the correlator around x0=0.

def anti_symmetric(self):
View Source

        def anti_symmetric(self):
            """Anti-symmetrize the correlator around x0=0."""
            if self.T % 2 != 0:
                raise Exception("Can not symmetrize odd T")

            test = 1 * self
            test.gamma_method()
            if not all([o.is_zero_within_error(3) for o in test.content[0]]):
                warnings.warn("Correlator does not seem to be anti-symmetric around x0=0.", RuntimeWarning)

            newcontent = [self.content[0]]
            for t in range(1, self.T):
                if (self.content[t] is None) or (self.content[self.T - t] is None):
                    newcontent.append(None)
                else:
                    newcontent.append(0.5 * (self.content[t] - self.content[self.T - t]))
            if(all([x is None for x in newcontent])):
                raise Exception("Corr could not be symmetrized: No redundant values")
            return Corr(newcontent, prange=self.prange)

Anti-symmetrize the correlator around x0=0.

def matrix_symmetric(self):
View Source

        def matrix_symmetric(self):
            """Symmetrizes the correlator matrices on every timeslice."""
            if self.N > 1:
                transposed = [None if (G is None) else G.T for G in self.content]
                return 0.5 * (Corr(transposed) + self)
            if self.N == 1:
                raise Exception("Trying to symmetrize a correlator matrix, that already has N=1.")

Symmetrizes the correlator matrices on every timeslice.

def GEVP(self, t0, ts=None, state=0, sorted_list=None):
View Source

        def GEVP(self, t0, ts=None, state=0, sorted_list=None):
            """Solve the general eigenvalue problem on the current correlator

            Parameters
            ----------
            t0 : int
                The time t0 for G(t)v= lambda G(t_0)v
            ts : int
                fixed time G(t_s)v= lambda G(t_0)v  if return_list=False
                If return_list=True and sorting=Eigenvector it gives a reference point for the sorting method.
            state : int
                The state one is interested in ordered by energy. The lowest state is zero.
            sorted_list : string
                if this argument is set, a list of vectors (len=self.T) is returned. If it is left as None, only one vector is returned.
                 "Eigenvalue"  -  The eigenvector is chosen according to which einvenvalue it belongs individually on every timeslice.
                 "Eigenvector" -  Use the method described in arXiv:2004.10472 [hep-lat] to find the set of v(t) belonging to the state.
                                     The referense state is identified by its eigenvalue at t=ts
            """
            if sorted_list is None:
                if (ts is None):
                    raise Exception("ts is required if sorted_list=None")
                if (self.content[t0] is None) or (self.content[ts] is None):
                    raise Exception("Corr not defined at t0/ts")
                G0, Gt = np.empty([self.N, self.N], dtype="double"), np.empty([self.N, self.N], dtype="double")
                for i in range(self.N):
                    for j in range(self.N):
                        G0[i, j] = self.content[t0][i, j].value
                        Gt[i, j] = self.content[ts][i, j].value

                sp_vecs = _GEVP_solver(Gt, G0)
                sp_vec = sp_vecs[state]
                return sp_vec
            else:

                all_vecs = []
                for t in range(self.T):
                    try:
                        G0, Gt = np.empty([self.N, self.N], dtype="double"), np.empty([self.N, self.N], dtype="double")
                        for i in range(self.N):
                            for j in range(self.N):
                                G0[i, j] = self.content[t0][i, j].value
                                Gt[i, j] = self.content[t][i, j].value

                        sp_vecs = _GEVP_solver(Gt, G0)
                        if sorted_list == "Eigenvalue":
                            sp_vec = sp_vecs[state]
                            all_vecs.append(sp_vec)
                        else:
                            all_vecs.append(sp_vecs)
                    except Exception:
                        all_vecs.append(None)
                if sorted_list == "Eigenvector":
                    if (ts is None):
                        raise Exception("ts is required for the Eigenvector sorting method.")
                    all_vecs = _sort_vectors(all_vecs, ts)
                    all_vecs = [a[state] for a in all_vecs]

            return all_vecs

Solve the general eigenvalue problem on the current correlator

###### Parameters

- t0 (int): The time t0 for G(t)v= lambda G(t_0)v
- ts (int): fixed time G(t_s)v= lambda G(t_0)v if return_list=False If return_list=True and sorting=Eigenvector it gives a reference point for the sorting method.
- state (int): The state one is interested in ordered by energy. The lowest state is zero.
- sorted_list (string): if this argument is set, a list of vectors (len=self.T) is returned. If it is left as None, only one vector is returned. "Eigenvalue" - The eigenvector is chosen according to which einvenvalue it belongs individually on every timeslice. "Eigenvector" - Use the method described in arXiv:2004.10472 [hep-lat] to find the set of v(t) belonging to the state. The referense state is identified by its eigenvalue at t=ts

def Eigenvalue(self, t0, state=1):
View Source

        def Eigenvalue(self, t0, state=1):
            G = self.matrix_symmetric()
            G0 = G.content[t0]
            L = cholesky(G0)
            Li = inv(L)
            LT = L.T
            LTi = inv(LT)
            newcontent = []
            for t in range(self.T):
                if self.content[t] is None:
                    newcontent.append(None)
                else:
                    Gt = G.content[t]
                    M = Li @ Gt @ LTi
                    eigenvalues = eigh(M)[0]
                    eigenvalue = eigenvalues[-state]
                    newcontent.append(eigenvalue)
            return Corr(newcontent)

def Hankel(self, N, periodic=False):
View Source

        def Hankel(self, N, periodic=False):
            """Constructs an NxN Hankel matrix

            C(t) c(t+1) ... c(t+n-1)
            C(t+1) c(t+2) ... c(t+n)
            .................
            C(t+(n-1)) c(t+n) ... c(t+2(n-1))

            Parameters
            ----------
            N : int
                Dimension of the Hankel matrix
            periodic : bool, optional
                determines whether the matrix is extended periodically
            """

            if self.N != 1:
                raise Exception("Multi-operator Prony not implemented!")

            array = np.empty([N, N], dtype="object")
            new_content = []
            for t in range(self.T):
                new_content.append(array.copy())

            def wrap(i):
                while i >= self.T:
                    i -= self.T
                return i

            for t in range(self.T):
                for i in range(N):
                    for j in range(N):
                        if periodic:
                            new_content[t][i, j] = self.content[wrap(t + i + j)][0]
                        elif (t + i + j) >= self.T:
                            new_content[t] = None
                        else:
                            new_content[t][i, j] = self.content[t + i + j][0]

            return Corr(new_content)

Constructs an NxN Hankel matrix

C(t) c(t+1) ... c(t+n-1) C(t+1) c(t+2) ... c(t+n) ................. C(t+(n-1)) c(t+n) ... c(t+2(n-1))

###### Parameters

- N (int): Dimension of the Hankel matrix
- periodic (bool, optional): determines whether the matrix is extended periodically

def roll(self, dt):
View Source

        def roll(self, dt):
            """Periodically shift the correlator by dt timeslices

            Parameters
            ----------
            dt : int
                number of timeslices
            """
            return Corr(list(np.roll(np.array(self.content, dtype=object), dt)))

Periodically shift the correlator by dt timeslices

###### Parameters

- dt (int): number of timeslices

def reverse(self):
View Source

        def reverse(self):
            """Reverse the time ordering of the Corr"""
            return Corr(self.content[:: -1])

Reverse the time ordering of the Corr

def thin(self, spacing=2, offset=0):
View Source

        def thin(self, spacing=2, offset=0):
            """Thin out a correlator to suppress correlations

            Parameters
            ----------
            spacing : int
                Keep only every 'spacing'th entry of the correlator
            offset : int
                Offset the equal spacing
            """
            new_content = []
            for t in range(self.T):
                if (offset + t) % spacing != 0:
                    new_content.append(None)
                else:
                    new_content.append(self.content[t])
            return Corr(new_content)

Thin out a correlator to suppress correlations

###### Parameters

- spacing (int): Keep only every 'spacing'th entry of the correlator
- offset (int): Offset the equal spacing

def correlate(self, partner):
View Source

        def correlate(self, partner):
            """Correlate the correlator with another correlator or Obs

            Parameters
            ----------
            partner : Obs or Corr
                partner to correlate the correlator with.
                Can either be an Obs which is correlated with all entries of the
                correlator or a Corr of same length.
            """
            new_content = []
            for x0, t_slice in enumerate(self.content):
                if t_slice is None:
                    new_content.append(None)
                else:
                    if isinstance(partner, Corr):
                        if partner.content[x0] is None:
                            new_content.append(None)
                        else:
                            new_content.append(np.array([correlate(o, partner.content[x0][0]) for o in t_slice]))
                    elif isinstance(partner, Obs):  # Should this include CObs?
                        new_content.append(np.array([correlate(o, partner) for o in t_slice]))
                    else:
                        raise Exception("Can only correlate with an Obs or a Corr.")

            return Corr(new_content)

Correlate the correlator with another correlator or Obs

###### Parameters

- partner (Obs or Corr): partner to correlate the correlator with. Can either be an Obs which is correlated with all entries of the correlator or a Corr of same length.

def reweight(self, weight, **kwargs):
View Source

        def reweight(self, weight, **kwargs):
            """Reweight the correlator.

            Parameters
            ----------
            weight : Obs
                Reweighting factor. An Observable that has to be defined on a superset of the
                configurations in obs[i].idl for all i.
            all_configs : bool
                if True, the reweighted observables are normalized by the average of
                the reweighting factor on all configurations in weight.idl and not
                on the configurations in obs[i].idl.
            """
            new_content = []
            for t_slice in self.content:
                if t_slice is None:
                    new_content.append(None)
                else:
                    new_content.append(np.array(reweight(weight, t_slice, **kwargs)))
            return Corr(new_content)

Reweight the correlator.

###### Parameters

- weight (Obs): Reweighting factor. An Observable that has to be defined on a superset of the configurations in obs[i].idl for all i.
- all_configs (bool): if True, the reweighted observables are normalized by the average of the reweighting factor on all configurations in weight.idl and not on the configurations in obs[i].idl.

def T_symmetry(self, partner, parity=1):
View Source

        def T_symmetry(self, partner, parity=+1):
            """Return the time symmetry average of the correlator and its partner

            Parameters
            ----------
            partner : Corr
                Time symmetry partner of the Corr
            partity : int
                Parity quantum number of the correlator, can be +1 or -1
            """
            if not isinstance(partner, Corr):
                raise Exception("T partner has to be a Corr object.")
            if parity not in [+1, -1]:
                raise Exception("Parity has to be +1 or -1.")
            T_partner = parity * partner.reverse()

            t_slices = []
            test = (self - T_partner)
            test.gamma_method()
            for x0, t_slice in enumerate(test.content):
                if t_slice is not None:
                    if not t_slice[0].is_zero_within_error(5):
                        t_slices.append(x0)
            if t_slices:
                warnings.warn("T symmetry partners do not agree within 5 sigma on time slices " + str(t_slices) + ".", RuntimeWarning)

            return (self + T_partner) / 2

Return the time symmetry average of the correlator and its partner

###### Parameters

- partner (Corr): Time symmetry partner of the Corr
- partity (int): Parity quantum number of the correlator, can be +1 or -1

def deriv(self, variant='symmetric'):
View Source

        def deriv(self, variant="symmetric"):
            """Return the first derivative of the correlator with respect to x0.

            Parameters
            ----------
            variant : str
                decides which definition of the finite differences derivative is used.
                Available choice: symmetric, forward, backward, improved, default: symmetric
            """
            if variant == "symmetric":
                newcontent = []
                for t in range(1, self.T - 1):
                    if (self.content[t - 1] is None) or (self.content[t + 1] is None):
                        newcontent.append(None)
                    else:
                        newcontent.append(0.5 * (self.content[t + 1] - self.content[t - 1]))
                if(all([x is None for x in newcontent])):
                    raise Exception('Derivative is undefined at all timeslices')
                return Corr(newcontent, padding=[1, 1])
            elif variant == "forward":
                newcontent = []
                for t in range(self.T - 1):
                    if (self.content[t] is None) or (self.content[t + 1] is None):
                        newcontent.append(None)
                    else:
                        newcontent.append(self.content[t + 1] - self.content[t])
                if(all([x is None for x in newcontent])):
                    raise Exception("Derivative is undefined at all timeslices")
                return Corr(newcontent, padding=[0, 1])
            elif variant == "backward":
                newcontent = []
                for t in range(1, self.T):
                    if (self.content[t - 1] is None) or (self.content[t] is None):
                        newcontent.append(None)
                    else:
                        newcontent.append(self.content[t] - self.content[t - 1])
                if(all([x is None for x in newcontent])):
                    raise Exception("Derivative is undefined at all timeslices")
                return Corr(newcontent, padding=[1, 0])
            elif variant == "improved":
                newcontent = []
                for t in range(2, self.T - 2):
                    if (self.content[t - 2] is None) or (self.content[t - 1] is None) or (self.content[t + 1] is None) or (self.content[t + 2] is None):
                        newcontent.append(None)
                    else:
                        newcontent.append((1 / 12) * (self.content[t - 2] - 8 * self.content[t - 1] + 8 * self.content[t + 1] - self.content[t + 2]))
                if(all([x is None for x in newcontent])):
                    raise Exception('Derivative is undefined at all timeslices')
                return Corr(newcontent, padding=[2, 2])
            else:
                raise Exception("Unknown variant.")

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

###### Parameters

- variant (str): decides which definition of the finite differences derivative is used. Available choice: symmetric, forward, backward, improved, default: symmetric

def second_deriv(self, variant='symmetric'):
View Source

        def second_deriv(self, variant="symmetric"):
            """Return the second derivative of the correlator with respect to x0.

            Parameters
            ----------
            variant : str
                decides which definition of the finite differences derivative is used.
                Available choice: symmetric, improved, default: symmetric
            """
            if variant == "symmetric":
                newcontent = []
                for t in range(1, self.T - 1):
                    if (self.content[t - 1] is None) or (self.content[t + 1] is None):
                        newcontent.append(None)
                    else:
                        newcontent.append((self.content[t + 1] - 2 * self.content[t] + self.content[t - 1]))
                if(all([x is None for x in newcontent])):
                    raise Exception("Derivative is undefined at all timeslices")
                return Corr(newcontent, padding=[1, 1])
            elif variant == "improved":
                newcontent = []
                for t in range(2, self.T - 2):
                    if (self.content[t - 2] is None) or (self.content[t - 1] is None) or (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 2] is None):
                        newcontent.append(None)
                    else:
                        newcontent.append((1 / 12) * (-self.content[t + 2] + 16 * self.content[t + 1] - 30 * self.content[t] + 16 * self.content[t - 1] - self.content[t - 2]))
                if(all([x is None for x in newcontent])):
                    raise Exception("Derivative is undefined at all timeslices")
                return Corr(newcontent, padding=[2, 2])
            else:
                raise Exception("Unknown variant.")

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

###### Parameters

- variant (str): decides which definition of the finite differences derivative is used. Available choice: symmetric, improved, default: symmetric

def m_eff(self, variant='log', guess=1.0):
View Source

        def m_eff(self, variant='log', guess=1.0):
            """Returns the effective mass of the correlator as correlator object

            Parameters
            ----------
            variant : str
                log : uses the standard effective mass log(C(t) / C(t+1))
                cosh, 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.
                sinh : 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.
                See, e.g., arXiv:1205.5380
                arccosh : Uses the explicit form of the symmetrized correlator (not recommended)
            guess : float
                guess for the root finder, only relevant for the root variant
            """
            if self.N != 1:
                raise Exception('Correlator must be projected before getting m_eff')
            if variant == 'log':
                newcontent = []
                for t in range(self.T - 1):
                    if (self.content[t] is None) or (self.content[t + 1] is None):
                        newcontent.append(None)
                    else:
                        newcontent.append(self.content[t] / self.content[t + 1])
                if(all([x is None for x in newcontent])):
                    raise Exception('m_eff is undefined at all timeslices')

                return np.log(Corr(newcontent, padding=[0, 1]))

            elif variant in ['periodic', 'cosh', 'sinh']:
                if variant in ['periodic', 'cosh']:
                    func = anp.cosh
                else:
                    func = anp.sinh

                def root_function(x, d):
                    return func(x * (t - self.T / 2)) / func(x * (t + 1 - self.T / 2)) - d

                newcontent = []
                for t in range(self.T - 1):
                    if (self.content[t] is None) or (self.content[t + 1] is None):
                        newcontent.append(None)
                    # Fill the two timeslices in the middle of the lattice with their predecessors
                    elif variant == 'sinh' and t in [self.T / 2, self.T / 2 - 1]:
                        newcontent.append(newcontent[-1])
                    else:
                        newcontent.append(np.abs(find_root(self.content[t][0] / self.content[t + 1][0], root_function, guess=guess)))
                if(all([x is None for x in newcontent])):
                    raise Exception('m_eff is undefined at all timeslices')

                return Corr(newcontent, padding=[0, 1])

            elif variant == 'arccosh':
                newcontent = []
                for t in range(1, self.T - 1):
                    if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t - 1] is None):
                        newcontent.append(None)
                    else:
                        newcontent.append((self.content[t + 1] + self.content[t - 1]) / (2 * self.content[t]))
                if(all([x is None for x in newcontent])):
                    raise Exception("m_eff is undefined at all timeslices")
                return np.arccosh(Corr(newcontent, padding=[1, 1]))

            else:
                raise Exception('Unknown variant.')

Returns the effective mass of the correlator as correlator object

###### Parameters

- variant (str): log : uses the standard effective mass log(C(t) / C(t+1)) cosh, 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. sinh : 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. See, e.g., arXiv:1205.5380 arccosh : Uses the explicit form of the symmetrized correlator (not recommended)
- guess (float): guess for the root finder, only relevant for the root variant

def fit(self, function, fitrange=None, silent=False, **kwargs):
View Source

        def fit(self, function, fitrange=None, silent=False, **kwargs):
            """Fits function to the data

            Parameters
            ----------
            function : obj
                function to fit to the data. See fits.least_squares for details.
            fitrange : list
                Range in which the function is to be fitted to the data.
                If not specified, self.prange or all timeslices are used.
            silent : bool
                Decides whether output is printed to the standard output.
            """
            if self.N != 1:
                raise Exception("Correlator must be projected before fitting")

            if fitrange is None:
                if self.prange:
                    fitrange = self.prange
                else:
                    fitrange = [0, self.T - 1]

            xs = [x for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None]
            ys = [self.content[x][0] for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None]
            result = least_squares(xs, ys, function, silent=silent, **kwargs)
            return result

Fits function to the data

###### Parameters

- function (obj): function to fit to the data. See fits.least_squares for details.
- fitrange (list): Range in which the function is to be fitted to the data. If not specified, self.prange or all timeslices are used.
- silent (bool): Decides whether output is printed to the standard output.

def plateau(self, plateau_range=None, method='fit', auto_gamma=False):
View Source

        def plateau(self, plateau_range=None, method="fit", auto_gamma=False):
            """ Extract a plateau value from a Corr object

            Parameters
            ----------
            plateau_range : list
                list with two entries, indicating the first and the last timeslice
                of the plateau region.
            method : str
                method to extract the plateau.
                    'fit' fits a constant to the plateau region
                    'avg', 'average' or 'mean' just average over the given timeslices.
            auto_gamma : bool
                apply gamma_method with default parameters to the Corr. Defaults to None
            """
            if not plateau_range:
                if self.prange:
                    plateau_range = self.prange
                else:
                    raise Exception("no plateau range provided")
            if self.N != 1:
                raise Exception("Correlator must be projected before getting a plateau.")
            if(all([self.content[t] is None for t in range(plateau_range[0], plateau_range[1] + 1)])):
                raise Exception("plateau is undefined at all timeslices in plateaurange.")
            if auto_gamma:
                self.gamma_method()
            if method == "fit":
                def const_func(a, t):
                    return a[0]
                return self.fit(const_func, plateau_range)[0]
            elif method in ["avg", "average", "mean"]:
                returnvalue = np.mean([item[0] for item in self.content[plateau_range[0]:plateau_range[1] + 1] if item is not None])
                return returnvalue

            else:
                raise Exception("Unsupported plateau method: " + method)

Extract a plateau value from a Corr object

###### Parameters

- plateau_range (list): list with two entries, indicating the first and the last timeslice of the plateau region.
- method (str): method to extract the plateau. 'fit' fits a constant to the plateau region 'avg', 'average' or 'mean' just average over the given timeslices.
- auto_gamma (bool): apply gamma_method with default parameters to the Corr. Defaults to None

def set_prange(self, prange):
View Source

        def set_prange(self, prange):
            """Sets the attribute prange of the Corr object."""
            if not len(prange) == 2:
                raise Exception("prange must be a list or array with two values")
            if not ((isinstance(prange[0], int)) and (isinstance(prange[1], int))):
                raise Exception("Start and end point must be integers")
            if not (0 <= prange[0] <= self.T and 0 <= prange[1] <= self.T and prange[0] < prange[1]):
                raise Exception("Start and end point must define a range in the interval 0,T")

            self.prange = prange
            return

Sets the attribute prange of the Corr object.

def show( self, x_range=None, comp=None, y_range=None, logscale=False, plateau=None, fit_res=None, ylabel=None, save=None, auto_gamma=False ):
View Source

        def show(self, x_range=None, comp=None, y_range=None, logscale=False, plateau=None, fit_res=None, ylabel=None, save=None, auto_gamma=False):
            """Plots the correlator using the tag of the correlator as label if available.

            Parameters
            ----------
            x_range : list
                list of two values, determining the range of the x-axis e.g. [4, 8]
            comp : Corr or list of Corr
                Correlator or list of correlators which are plotted for comparison.
                The tags of these correlators are used as labels if available.
            logscale : bool
                Sets y-axis to logscale
            plateau : Obs
                Plateau value to be visualized in the figure
            fit_res : Fit_result
                Fit_result object to be visualized
            ylabel : str
                Label for the y-axis
            save : str
                path to file in which the figure should be saved
            auto_gamma : bool
                Apply the gamma method with standard parameters to all correlators and plateau values before plotting.
            """
            if self.N != 1:
                raise Exception("Correlator must be projected before plotting")

            if auto_gamma:
                self.gamma_method()

            if x_range is None:
                x_range = [0, self.T - 1]

            fig = plt.figure()
            ax1 = fig.add_subplot(111)

            x, y, y_err = self.plottable()
            ax1.errorbar(x, y, y_err, label=self.tag)
            if logscale:
                ax1.set_yscale('log')
            else:
                if y_range is None:
                    try:
                        y_min = min([(x[0].value - x[0].dvalue) for x in self.content[x_range[0]: x_range[1] + 1] if (x is not None) and x[0].dvalue < 2 * np.abs(x[0].value)])
                        y_max = max([(x[0].value + x[0].dvalue) for x in self.content[x_range[0]: x_range[1] + 1] if (x is not None) and x[0].dvalue < 2 * np.abs(x[0].value)])
                        ax1.set_ylim([y_min - 0.1 * (y_max - y_min), y_max + 0.1 * (y_max - y_min)])
                    except Exception:
                        pass
                else:
                    ax1.set_ylim(y_range)
            if comp:
                if isinstance(comp, (Corr, list)):
                    for corr in comp if isinstance(comp, list) else [comp]:
                        if auto_gamma:
                            corr.gamma_method()
                        x, y, y_err = corr.plottable()
                        plt.errorbar(x, y, y_err, label=corr.tag, mfc=plt.rcParams['axes.facecolor'])
                else:
                    raise Exception("'comp' must be a correlator or a list of correlators.")

            if plateau:
                if isinstance(plateau, Obs):
                    if auto_gamma:
                        plateau.gamma_method()
                    ax1.axhline(y=plateau.value, linewidth=2, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--', label=str(plateau))
                    ax1.axhspan(plateau.value - plateau.dvalue, plateau.value + plateau.dvalue, alpha=0.25, color=plt.rcParams['text.color'], ls='-')
                else:
                    raise Exception("'plateau' must be an Obs")
            if self.prange:
                ax1.axvline(self.prange[0], 0, 1, ls='-', marker=',')
                ax1.axvline(self.prange[1], 0, 1, ls='-', marker=',')

            if fit_res:
                x_samples = np.arange(x_range[0], x_range[1] + 1, 0.05)
                ax1.plot(x_samples,
                         fit_res.fit_function([o.value for o in fit_res.fit_parameters], x_samples),
                         ls='-', marker=',', lw=2)

            ax1.set_xlabel(r'$x_0 / a$')
            if ylabel:
                ax1.set_ylabel(ylabel)
            ax1.set_xlim([x_range[0] - 0.5, x_range[1] + 0.5])

            handles, labels = ax1.get_legend_handles_labels()
            if labels:
                ax1.legend()
            plt.draw()

            if save:
                if isinstance(save, str):
                    fig.savefig(save)
                else:
                    raise Exception("'save' has to be a string.")

            return

Plots the correlator using the tag of the correlator as label if available.

###### Parameters

- x_range (list): list of two values, determining the range of the x-axis e.g. [4, 8]
- comp (Corr or list of Corr): Correlator or list of correlators which are plotted for comparison. The tags of these correlators are used as labels if available.
- logscale (bool): Sets y-axis to logscale
- plateau (Obs): Plateau value to be visualized in the figure
- fit_res (Fit_result): Fit_result object to be visualized
- ylabel (str): Label for the y-axis
- save (str): path to file in which the figure should be saved
- auto_gamma (bool): Apply the gamma method with standard parameters to all correlators and plateau values before plotting.

def dump(self, filename, datatype='json.gz', **kwargs):
View Source

        def dump(self, filename, datatype="json.gz", **kwargs):
            """Dumps the Corr into a file of chosen type
            Parameters
            ----------
            filename : str
                Name of the file to be saved.
            datatype : str
                Format of the exported file. Supported formats include
                "json.gz" and "pickle"
            path : str
                specifies a custom path for the file (default '.')
            """
            if datatype == "json.gz":
                from .input.json import dump_to_json
                if 'path' in kwargs:
                    file_name = kwargs.get('path') + '/' + filename
                else:
                    file_name = filename
                dump_to_json(self, file_name)
            elif datatype == "pickle":
                dump_object(self, filename, **kwargs)
            else:
                raise Exception("Unknown datatype " + str(datatype))

Dumps the Corr into a file of chosen type

###### Parameters

- filename (str): Name of the file to be saved.
- datatype (str): Format of the exported file. Supported formats include "json.gz" and "pickle"
- path (str): specifies a custom path for the file (default '.')

def print(self, range=[0, None]):
View Source

        def print(self, range=[0, None]):
            print(self.__repr__(range))

def sqrt(self):
View Source

        def sqrt(self):
            return self**0.5

def log(self):
View Source

        def log(self):
            newcontent = [None if (item is None) else np.log(item) for item in self.content]
            return Corr(newcontent, prange=self.prange)

def exp(self):
View Source

        def exp(self):
            newcontent = [None if (item is None) else np.exp(item) for item in self.content]
            return Corr(newcontent, prange=self.prange)

def sin(self):
View Source

        def sin(self):
            return self._apply_func_to_corr(np.sin)

def cos(self):
View Source

        def cos(self):
            return self._apply_func_to_corr(np.cos)

def tan(self):
View Source

        def tan(self):
            return self._apply_func_to_corr(np.tan)

def sinh(self):
View Source

        def sinh(self):
            return self._apply_func_to_corr(np.sinh)

def cosh(self):
View Source

        def cosh(self):
            return self._apply_func_to_corr(np.cosh)

def tanh(self):
View Source

        def tanh(self):
            return self._apply_func_to_corr(np.tanh)

def arcsin(self):
View Source

        def arcsin(self):
            return self._apply_func_to_corr(np.arcsin)

def arccos(self):
View Source

        def arccos(self):
            return self._apply_func_to_corr(np.arccos)

def arctan(self):
View Source

        def arctan(self):
            return self._apply_func_to_corr(np.arctan)

def arcsinh(self):
View Source

        def arcsinh(self):
            return self._apply_func_to_corr(np.arcsinh)

def arccosh(self):
View Source

        def arccosh(self):
            return self._apply_func_to_corr(np.arccosh)

def arctanh(self):
View Source

        def arctanh(self):
            return self._apply_func_to_corr(np.arctanh)

real
imag