diff --git a/pyerrors/correlators.py b/pyerrors/correlators.py index 3382c26e..c1c66389 100644 --- a/pyerrors/correlators.py +++ b/pyerrors/correlators.py @@ -3,7 +3,7 @@ import numpy as np 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 @@ -41,7 +41,11 @@ class Corr: 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 @@ -101,7 +105,7 @@ class Corr: # 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 @@ -113,17 +117,32 @@ class Corr: 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): @@ -199,20 +218,45 @@ class Corr: 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() @@ -223,13 +267,48 @@ class Corr: 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 @@ -242,7 +321,7 @@ class Corr: 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 @@ -264,7 +343,7 @@ class Corr: 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.") @@ -590,7 +669,6 @@ class Corr: def dump(self, filename, **kwargs): """Dumps the Corr into a pickle file - Parameters ---------- filename : str @@ -599,14 +677,23 @@ class Corr: 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' @@ -640,7 +727,7 @@ class Corr: 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): @@ -663,7 +750,7 @@ class Corr: 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): @@ -696,9 +783,14 @@ class Corr: 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): @@ -728,7 +820,7 @@ class Corr: 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: @@ -809,3 +901,70 @@ class Corr: 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