From dc60784c314374c406e5c00e90fc85a3e796daab Mon Sep 17 00:00:00 2001 From: fjosw Date: Tue, 18 Jan 2022 16:36:51 +0000 Subject: [PATCH] Documentation updated --- docs/pyerrors/correlators.html | 700 ++++++++++++++++++++++++++++----- docs/search.js | 2 +- 2 files changed, 597 insertions(+), 105 deletions(-) diff --git a/docs/pyerrors/correlators.html b/docs/pyerrors/correlators.html index 502bbbc0..a3f979d6 100644 --- a/docs/pyerrors/correlators.html +++ b/docs/pyerrors/correlators.html @@ -86,6 +86,9 @@
  • Eigenvalue
    • +
  • + Hankel +
  • roll
    • @@ -173,9 +176,24 @@
  • arctanh
    • +
  • + real +
    • +
  • + imag +
    • +
  • + sort_vectors +
    • +
  • + permutation +
    • +
  • + GEVP_solver +
    • @@ -200,7 +218,7 @@ import autograd.numpy as anp import matplotlib.pyplot as plt import scipy.linalg -from .obs import Obs, reweight, correlate +from .obs import Obs, reweight, correlate, CObs from .misc import dump_object from .fits import least_squares from .linalg import eigh, inv, cholesky @@ -238,7 +256,11 @@ if not isinstance(data_input, list): raise TypeError('Corr__init__ expects a list of timeslices.') - if all([isinstance(item, Obs) for item in data_input]): + + # data_input can have multiple shapes. The simplest one is a list of Obs. + # We check, if this is the case + if all([(isinstance(item, Obs) or isinstance(item, CObs)) for item in data_input]): + self.content = [np.asarray([item]) for item in data_input] self.N = 1 @@ -298,7 +320,7 @@ # 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 projected(self, vector_l=None, vector_r=None): + def projected(self, vector_l=None, vector_r=None, normalize=False): if self.N == 1: raise Exception("Trying to project a Corr, that already has N=1.") # This Exception is in no way necessary. One could just return self @@ -310,17 +332,32 @@ 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 vector_l.shape == vector_r.shape == (self.N,): - raise Exception("Vectors are of wrong shape!") + 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) + # if (not (0.95 < vector_r @ vector_r < 1.05)) or (not (0.95 < vector_l @ vector_l < 1.05)): + # print("Vectors are normalized before projection!") - # We always normalize before projecting! But we only raise a warning, when it is clear, they where not meant to be normalized. - if (not (0.95 < vector_r @ vector_r < 1.05)) or (not (0.95 < vector_l @ vector_l < 1.05)): - print("Vectors are normalized before projection!") + newcontent = [None if (item is None) else np.asarray([vector_l.T @ item @ vector_r]) for item in self.content] - vector_l, vector_r = vector_l / np.sqrt((vector_l @ vector_l)), vector_r / np.sqrt(vector_r @ vector_r) + 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 (item is None) else np.asarray([vector_l.T @ item @ vector_r]) for item in self.content] + 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 sum(self): @@ -396,20 +433,45 @@ if self.N == 1: raise Exception("Trying to symmetrize a smearing matrix, that already has N=1.") - # We also include a simple GEVP method based on Scipy.linalg - def GEVP(self, t0, ts, state=1): - 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 + # There are two ways, the GEVP metod can be called. + # 1. return_list=False will return a single eigenvector, normalized according to V*C(t_0)*V=1 + # 2. return_list=True will return a new eigenvector for every timeslice. The time t_s is used to order the vectors according to. arXiv:2004.10472 [hep-lat] + def GEVP(self, t0, ts, state=0, sorting="Eigenvalue", return_list=False): + if not return_list: + 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_val, sp_vec = scipy.linalg.eig(Gt, G0) - sp_vec = sp_vec[:, np.argsort(sp_val)[-state]] # We only want the eigenvector belonging to the selected state - sp_vec = sp_vec / np.sqrt(sp_vec @ sp_vec) - return sp_vec + sp_vecs = GEVP_solver(Gt, G0) + sp_vec = sp_vecs[state] + return sp_vec + if return_list: + 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 sorting == "Eigenvalue": + sp_vec = sp_vecs[state] + all_vecs.append(sp_vec) + else: + all_vecs.append(sp_vecs) + except "Failure to solve for one timeslice": # This could contain a check for real eigenvectors + all_vecs.append(None) + if sorting == "Eigenvector": + 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.smearing_symmetric() @@ -420,13 +482,48 @@ LTi = inv(LT) newcontent = [] for t in range(self.T): - Gt = G.content[t] - M = Li @ Gt @ LTi - eigenvalues = eigh(M)[0] - eigenvalue = eigenvalues[-state] - newcontent.append(eigenvalue) + 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)) + + 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): + if i >= self.T: + return 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 @@ -439,7 +536,7 @@ def reverse(self): """Reverse the time ordering of the Corr""" - return Corr(self.content[::-1]) + return Corr(self.content[:: -1]) def correlate(self, partner): """Correlate the correlator with another correlator or Obs @@ -461,7 +558,7 @@ 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): + 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.") @@ -787,7 +884,6 @@ def dump(self, filename, **kwargs): """Dumps the Corr into a pickle file - Parameters ---------- filename : str @@ -796,14 +892,23 @@ specifies a custom path for the file (default '.') """ dump_object(self, filename, **kwargs) + return 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 + # This avoids a crash for N>1. I do not know, what else to do here. I like the list representation for N==1. We could print only one "smearing" or one matrix. Printing everything will just + # be a wall of numbers. + if range[1]: range[1] += 1 content_string += 'x0/a\tCorr(x0/a)\n------------------\n' @@ -837,7 +942,7 @@ newcontent.append(self.content[t] + y.content[t]) return Corr(newcontent) - elif isinstance(y, Obs) or isinstance(y, int) or isinstance(y, float): + elif isinstance(y, Obs) or isinstance(y, int) or isinstance(y, float) or isinstance(y, CObs): newcontent = [] for t in range(self.T): if (self.content[t] is None): @@ -860,7 +965,7 @@ newcontent.append(self.content[t] * y.content[t]) return Corr(newcontent) - elif isinstance(y, Obs) or isinstance(y, int) or isinstance(y, float): + elif isinstance(y, Obs) or isinstance(y, int) or isinstance(y, float) or isinstance(y, CObs): newcontent = [] for t in range(self.T): if (self.content[t] is None): @@ -893,9 +998,14 @@ raise Exception("Division returns completely undefined correlator") return Corr(newcontent) - elif isinstance(y, Obs): - if y.value == 0: - raise Exception('Division by zero will return undefined correlator') + elif isinstance(y, Obs) or isinstance(y, 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): @@ -925,7 +1035,7 @@ return self + (-y) def __pow__(self, y): - if isinstance(y, Obs) or isinstance(y, int) or isinstance(y, float): + if isinstance(y, Obs) or isinstance(y, int) or isinstance(y, float) or isinstance(y, CObs): newcontent = [None if (item is None) else item**y for item in self.content] return Corr(newcontent, prange=self.prange) else: @@ -1006,6 +1116,73 @@ 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 = permutation([i for i in range(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 + # print("best perm", best_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 permutation(lst): # Shamelessly copied + if len(lst) == 1: + return [lst] + ll = [] + for i in range(len(lst)): + m = lst[i] + remLst = lst[:i] + lst[i + 1:] + # Generating all permutations where m is first + for p in permutation(remLst): + ll.append([m] + p) + return ll + + +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 @@ -1053,7 +1230,11 @@ if not isinstance(data_input, list): raise TypeError('Corr__init__ expects a list of timeslices.') - if all([isinstance(item, Obs) for item in data_input]): + + # data_input can have multiple shapes. The simplest one is a list of Obs. + # We check, if this is the case + if all([(isinstance(item, Obs) or isinstance(item, CObs)) for item in data_input]): + self.content = [np.asarray([item]) for item in data_input] self.N = 1 @@ -1113,7 +1294,7 @@ # 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 projected(self, vector_l=None, vector_r=None): + def projected(self, vector_l=None, vector_r=None, normalize=False): if self.N == 1: raise Exception("Trying to project a Corr, that already has N=1.") # This Exception is in no way necessary. One could just return self @@ -1125,17 +1306,32 @@ 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 vector_l.shape == vector_r.shape == (self.N,): - raise Exception("Vectors are of wrong shape!") + 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) + # if (not (0.95 < vector_r @ vector_r < 1.05)) or (not (0.95 < vector_l @ vector_l < 1.05)): + # print("Vectors are normalized before projection!") - # We always normalize before projecting! But we only raise a warning, when it is clear, they where not meant to be normalized. - if (not (0.95 < vector_r @ vector_r < 1.05)) or (not (0.95 < vector_l @ vector_l < 1.05)): - print("Vectors are normalized before projection!") + newcontent = [None if (item is None) else np.asarray([vector_l.T @ item @ vector_r]) for item in self.content] - vector_l, vector_r = vector_l / np.sqrt((vector_l @ vector_l)), vector_r / np.sqrt(vector_r @ vector_r) + 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 (item is None) else np.asarray([vector_l.T @ item @ vector_r]) for item in self.content] + 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 sum(self): @@ -1211,20 +1407,45 @@ if self.N == 1: raise Exception("Trying to symmetrize a smearing matrix, that already has N=1.") - # We also include a simple GEVP method based on Scipy.linalg - def GEVP(self, t0, ts, state=1): - 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 + # There are two ways, the GEVP metod can be called. + # 1. return_list=False will return a single eigenvector, normalized according to V*C(t_0)*V=1 + # 2. return_list=True will return a new eigenvector for every timeslice. The time t_s is used to order the vectors according to. arXiv:2004.10472 [hep-lat] + def GEVP(self, t0, ts, state=0, sorting="Eigenvalue", return_list=False): + if not return_list: + 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_val, sp_vec = scipy.linalg.eig(Gt, G0) - sp_vec = sp_vec[:, np.argsort(sp_val)[-state]] # We only want the eigenvector belonging to the selected state - sp_vec = sp_vec / np.sqrt(sp_vec @ sp_vec) - return sp_vec + sp_vecs = GEVP_solver(Gt, G0) + sp_vec = sp_vecs[state] + return sp_vec + if return_list: + 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 sorting == "Eigenvalue": + sp_vec = sp_vecs[state] + all_vecs.append(sp_vec) + else: + all_vecs.append(sp_vecs) + except "Failure to solve for one timeslice": # This could contain a check for real eigenvectors + all_vecs.append(None) + if sorting == "Eigenvector": + 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.smearing_symmetric() @@ -1235,13 +1456,48 @@ LTi = inv(LT) newcontent = [] for t in range(self.T): - Gt = G.content[t] - M = Li @ Gt @ LTi - eigenvalues = eigh(M)[0] - eigenvalue = eigenvalues[-state] - newcontent.append(eigenvalue) + 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)) + + 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): + if i >= self.T: + return 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 @@ -1254,7 +1510,7 @@ def reverse(self): """Reverse the time ordering of the Corr""" - return Corr(self.content[::-1]) + return Corr(self.content[:: -1]) def correlate(self, partner): """Correlate the correlator with another correlator or Obs @@ -1276,7 +1532,7 @@ 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): + 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.") @@ -1602,7 +1858,6 @@ def dump(self, filename, **kwargs): """Dumps the Corr into a pickle file - Parameters ---------- filename : str @@ -1611,14 +1866,23 @@ specifies a custom path for the file (default '.') """ dump_object(self, filename, **kwargs) + return 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 + # This avoids a crash for N>1. I do not know, what else to do here. I like the list representation for N==1. We could print only one "smearing" or one matrix. Printing everything will just + # be a wall of numbers. + if range[1]: range[1] += 1 content_string += 'x0/a\tCorr(x0/a)\n------------------\n' @@ -1652,7 +1916,7 @@ newcontent.append(self.content[t] + y.content[t]) return Corr(newcontent) - elif isinstance(y, Obs) or isinstance(y, int) or isinstance(y, float): + elif isinstance(y, Obs) or isinstance(y, int) or isinstance(y, float) or isinstance(y, CObs): newcontent = [] for t in range(self.T): if (self.content[t] is None): @@ -1675,7 +1939,7 @@ newcontent.append(self.content[t] * y.content[t]) return Corr(newcontent) - elif isinstance(y, Obs) or isinstance(y, int) or isinstance(y, float): + elif isinstance(y, Obs) or isinstance(y, int) or isinstance(y, float) or isinstance(y, CObs): newcontent = [] for t in range(self.T): if (self.content[t] is None): @@ -1708,9 +1972,14 @@ raise Exception("Division returns completely undefined correlator") return Corr(newcontent) - elif isinstance(y, Obs): - if y.value == 0: - raise Exception('Division by zero will return undefined correlator') + elif isinstance(y, Obs) or isinstance(y, 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): @@ -1740,7 +2009,7 @@ return self + (-y) def __pow__(self, y): - if isinstance(y, Obs) or isinstance(y, int) or isinstance(y, float): + if isinstance(y, Obs) or isinstance(y, int) or isinstance(y, float) or isinstance(y, CObs): newcontent = [None if (item is None) else item**y for item in self.content] return Corr(newcontent, prange=self.prange) else: @@ -1821,6 +2090,26 @@ 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) @@ -1864,7 +2153,11 @@ smearing matrix at every timeslice. Other dependency (eg. spatial) are not suppo if not isinstance(data_input, list): raise TypeError('Corr__init__ expects a list of timeslices.') - if all([isinstance(item, Obs) for item in data_input]): + + # data_input can have multiple shapes. The simplest one is a list of Obs. + # We check, if this is the case + if all([(isinstance(item, Obs) or isinstance(item, CObs)) for item in data_input]): + self.content = [np.asarray([item]) for item in data_input] self.N = 1 @@ -1955,12 +2248,12 @@ region indentified for this correlator. def - projected(self, vector_l=None, vector_r=None): + projected(self, vector_l=None, vector_r=None, normalize=False):
    View Source - 
        def projected(self, vector_l=None, vector_r=None):
+            
        def projected(self, vector_l=None, vector_r=None, normalize=False):
         if self.N == 1:
             raise Exception("Trying to project a Corr, that already has N=1.")
             # This Exception is in no way necessary. One could just return self
@@ -1972,17 +2265,32 @@ region indentified for this correlator.
             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 vector_l.shape == vector_r.shape == (self.N,):
-            raise Exception("Vectors are of wrong shape!")
+        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)
+            # if (not (0.95 < vector_r @ vector_r < 1.05)) or (not (0.95 < vector_l @ vector_l < 1.05)):
+                # print("Vectors are normalized before projection!")
 
-        # We always normalize before projecting! But we only raise a warning, when it is clear, they where not meant to be normalized.
-        if (not (0.95 < vector_r @ vector_r < 1.05)) or (not (0.95 < vector_l @ vector_l < 1.05)):
-            print("Vectors are normalized before projection!")
+            newcontent = [None if (item is None) else np.asarray([vector_l.T @ item @ vector_r]) for item in self.content]
 
-        vector_l, vector_r = vector_l / np.sqrt((vector_l @ vector_l)), vector_r / np.sqrt(vector_r @ vector_r)
+        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 (item is None) else np.asarray([vector_l.T @ item @ vector_r]) for item in self.content]
+            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)
 
    
 
@@ -2167,24 +2475,47 @@ timeslice and the error on each timeslice.
    
 
         
             def
-            GEVP(self, t0, ts, state=1):
+            GEVP(self, t0, ts, state=0, sorting='Eigenvalue', return_list=False):
    View Source - 
        def GEVP(self, t0, ts, state=1):
-        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
+            
        def GEVP(self, t0, ts, state=0, sorting="Eigenvalue", return_list=False):
+        if not return_list:
+            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_val, sp_vec = scipy.linalg.eig(Gt, G0)
-        sp_vec = sp_vec[:, np.argsort(sp_val)[-state]]  # We only want the eigenvector belonging to the selected state
-        sp_vec = sp_vec / np.sqrt(sp_vec @ sp_vec)
-        return sp_vec
+            sp_vecs = GEVP_solver(Gt, G0)
+            sp_vec = sp_vecs[state]
+            return sp_vec
+        if return_list:
+            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 sorting == "Eigenvalue":
+                        sp_vec = sp_vecs[state]
+                        all_vecs.append(sp_vec)
+                    else:
+                        all_vecs.append(sp_vecs)
+                except "Failure to solve for one timeslice":   # This could contain a check for real eigenvectors
+                    all_vecs.append(None)
+            if sorting == "Eigenvector":
+                all_vecs = sort_vectors(all_vecs, ts)
+                all_vecs = [a[state] for a in all_vecs]
+
+        return all_vecs
    @@ -2211,11 +2542,14 @@ timeslice and the error on each timeslice.

    LTi = inv(LT) newcontent = [] for t in range(self.T): - Gt = G.content[t] - M = Li @ Gt @ LTi - eigenvalues = eigh(M)[0] - eigenvalue = eigenvalues[-state] - newcontent.append(eigenvalue) + 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) @@ -2223,6 +2557,54 @@ timeslice and the error on each timeslice.

    + +
    +
    #   + + + 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))
+
+        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):
+            if i >= self.T:
+                return 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)
+
    + +
    + + +
    #   @@ -2271,7 +2653,7 @@ number of timeslices View Source 
        def reverse(self):
         """Reverse the time ordering of the Corr"""
-        return Corr(self.content[::-1])
+        return Corr(self.content[:: -1])
    @@ -2311,7 +2693,7 @@ number of timeslices 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): + 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.") @@ -2920,7 +3302,6 @@ path to file in which the figure should be saved View Source 
        def dump(self, filename, **kwargs):
         """Dumps the Corr into a pickle file
-
         Parameters
         ----------
         filename : str
@@ -2929,6 +3310,7 @@ path to file in which the figure should be saved
             specifies a custom path for the file (default '.')
         """
         dump_object(self, filename, **kwargs)
+        return
    @@ -3253,6 +3635,116 @@ specifies a custom path for the file (default '.') +
    +
    #   + + real +
    + + + +
    +
    +
    #   + + imag +
    + + + +
    + +
    +
    #   + + + def + sort_vectors(vec_set, ts): +
    + +
    + View Source + 
    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 = permutation([i for i in range(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
+            # print("best perm", best_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 + permutation(lst): +
    + +
    + View Source + 
    def permutation(lst):  # Shamelessly copied
+    if len(lst) == 1:
+        return [lst]
+    ll = []
+    for i in range(len(lst)):
+        m = lst[i]
+        remLst = lst[:i] + lst[i + 1:]
+        # Generating all permutations where m is first
+        for p in permutation(remLst):
+            ll.append([m] + p)
+    return ll
+
    + +
    + + + +
    +
    +
    #   + + + def + GEVP_solver(Gt, G0): +
    + +
    + View Source + 
    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
+
    + +
    + + +