pyerrors.correlators
1import warnings 2from itertools import permutations 3import numpy as np 4import autograd.numpy as anp 5import matplotlib.pyplot as plt 6import scipy.linalg 7from .obs import Obs, reweight, correlate, CObs 8from .misc import dump_object, _assert_equal_properties 9from .fits import least_squares 10from .roots import find_root 11 12 13class Corr: 14 """The class for a correlator (time dependent sequence of pe.Obs). 15 16 Everything, this class does, can be achieved using lists or arrays of Obs. 17 But it is simply more convenient to have a dedicated object for correlators. 18 One often wants to add or multiply correlators of the same length at every timeslice and it is inconvenient 19 to iterate over all timeslices for every operation. This is especially true, when dealing with matrices. 20 21 The correlator can have two types of content: An Obs at every timeslice OR a GEVP 22 matrix at every timeslice. Other dependency (eg. spatial) are not supported. 23 24 """ 25 26 def __init__(self, data_input, padding=[0, 0], prange=None): 27 """ Initialize a Corr object. 28 29 Parameters 30 ---------- 31 data_input : list or array 32 list of Obs or list of arrays of Obs or array of Corrs 33 padding : list, optional 34 List with two entries where the first labels the padding 35 at the front of the correlator and the second the padding 36 at the back. 37 prange : list, optional 38 List containing the first and last timeslice of the plateau 39 region indentified for this correlator. 40 """ 41 42 if isinstance(data_input, np.ndarray): 43 44 # This only works, if the array fulfills the conditions below 45 if not len(data_input.shape) == 2 and data_input.shape[0] == data_input.shape[1]: 46 raise Exception("Incompatible array shape") 47 if not all([isinstance(item, Corr) for item in data_input.flatten()]): 48 raise Exception("If the input is an array, its elements must be of type pe.Corr") 49 if not all([item.N == 1 for item in data_input.flatten()]): 50 raise Exception("Can only construct matrix correlator from single valued correlators") 51 if not len(set([item.T for item in data_input.flatten()])) == 1: 52 raise Exception("All input Correlators must be defined over the same timeslices.") 53 54 T = data_input[0, 0].T 55 N = data_input.shape[0] 56 input_as_list = [] 57 for t in range(T): 58 if any([(item.content[t] is None) for item in data_input.flatten()]): 59 if not all([(item.content[t] is None) for item in data_input.flatten()]): 60 warnings.warn("Input ill-defined at different timeslices. Conversion leads to data loss!", RuntimeWarning) 61 input_as_list.append(None) 62 else: 63 array_at_timeslace = np.empty([N, N], dtype="object") 64 for i in range(N): 65 for j in range(N): 66 array_at_timeslace[i, j] = data_input[i, j][t] 67 input_as_list.append(array_at_timeslace) 68 data_input = input_as_list 69 70 if isinstance(data_input, list): 71 72 if all([isinstance(item, (Obs, CObs)) or item is None for item in data_input]): 73 _assert_equal_properties([o for o in data_input if o is not None]) 74 self.content = [np.asarray([item]) if item is not None else None for item in data_input] 75 self.N = 1 76 77 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]): 78 self.content = data_input 79 noNull = [a for a in self.content if not (a is None)] # To check if the matrices are correct for all undefined elements 80 self.N = noNull[0].shape[0] 81 if self.N > 1 and noNull[0].shape[0] != noNull[0].shape[1]: 82 raise Exception("Smearing matrices are not NxN") 83 if (not all([item.shape == noNull[0].shape for item in noNull])): 84 raise Exception("Items in data_input are not of identical shape." + str(noNull)) 85 else: 86 raise Exception("data_input contains item of wrong type") 87 else: 88 raise Exception("Data input was not given as list or correct array") 89 90 self.tag = None 91 92 # An undefined timeslice is represented by the None object 93 self.content = [None] * padding[0] + self.content + [None] * padding[1] 94 self.T = len(self.content) 95 self.prange = prange 96 97 def __getitem__(self, idx): 98 """Return the content of timeslice idx""" 99 if self.content[idx] is None: 100 return None 101 elif len(self.content[idx]) == 1: 102 return self.content[idx][0] 103 else: 104 return self.content[idx] 105 106 @property 107 def reweighted(self): 108 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]]) 109 if np.all(bool_array == 1): 110 return True 111 elif np.all(bool_array == 0): 112 return False 113 else: 114 raise Exception("Reweighting status of correlator corrupted.") 115 116 def gamma_method(self, **kwargs): 117 """Apply the gamma method to the content of the Corr.""" 118 for item in self.content: 119 if not (item is None): 120 if self.N == 1: 121 item[0].gamma_method(**kwargs) 122 else: 123 for i in range(self.N): 124 for j in range(self.N): 125 item[i, j].gamma_method(**kwargs) 126 127 gm = gamma_method 128 129 def projected(self, vector_l=None, vector_r=None, normalize=False): 130 """We need to project the Correlator with a Vector to get a single value at each timeslice. 131 132 The method can use one or two vectors. 133 If two are specified it returns v1@G@v2 (the order might be very important.) 134 By default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to 135 """ 136 if self.N == 1: 137 raise Exception("Trying to project a Corr, that already has N=1.") 138 139 if vector_l is None: 140 vector_l, vector_r = np.asarray([1.] + (self.N - 1) * [0.]), np.asarray([1.] + (self.N - 1) * [0.]) 141 elif (vector_r is None): 142 vector_r = vector_l 143 if isinstance(vector_l, list) and not isinstance(vector_r, list): 144 if len(vector_l) != self.T: 145 raise Exception("Length of vector list must be equal to T") 146 vector_r = [vector_r] * self.T 147 if isinstance(vector_r, list) and not isinstance(vector_l, list): 148 if len(vector_r) != self.T: 149 raise Exception("Length of vector list must be equal to T") 150 vector_l = [vector_l] * self.T 151 152 if not isinstance(vector_l, list): 153 if not vector_l.shape == vector_r.shape == (self.N,): 154 raise Exception("Vectors are of wrong shape!") 155 if normalize: 156 vector_l, vector_r = vector_l / np.sqrt((vector_l @ vector_l)), vector_r / np.sqrt(vector_r @ vector_r) 157 newcontent = [None if _check_for_none(self, item) else np.asarray([vector_l.T @ item @ vector_r]) for item in self.content] 158 159 else: 160 # There are no checks here yet. There are so many possible scenarios, where this can go wrong. 161 if normalize: 162 for t in range(self.T): 163 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]) 164 165 newcontent = [None if (_check_for_none(self, self.content[t]) 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)] 166 return Corr(newcontent) 167 168 def item(self, i, j): 169 """Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice. 170 171 Parameters 172 ---------- 173 i : int 174 First index to be picked. 175 j : int 176 Second index to be picked. 177 """ 178 if self.N == 1: 179 raise Exception("Trying to pick item from projected Corr") 180 newcontent = [None if (item is None) else item[i, j] for item in self.content] 181 return Corr(newcontent) 182 183 def plottable(self): 184 """Outputs the correlator in a plotable format. 185 186 Outputs three lists containing the timeslice index, the value on each 187 timeslice and the error on each timeslice. 188 """ 189 if self.N != 1: 190 raise Exception("Can only make Corr[N=1] plottable") 191 x_list = [x for x in range(self.T) if not self.content[x] is None] 192 y_list = [y[0].value for y in self.content if y is not None] 193 y_err_list = [y[0].dvalue for y in self.content if y is not None] 194 195 return x_list, y_list, y_err_list 196 197 def symmetric(self): 198 """ Symmetrize the correlator around x0=0.""" 199 if self.N != 1: 200 raise Exception('symmetric cannot be safely applied to multi-dimensional correlators.') 201 if self.T % 2 != 0: 202 raise Exception("Can not symmetrize odd T") 203 204 if np.argmax(np.abs(self.content)) != 0: 205 warnings.warn("Correlator does not seem to be symmetric around x0=0.", RuntimeWarning) 206 207 newcontent = [self.content[0]] 208 for t in range(1, self.T): 209 if (self.content[t] is None) or (self.content[self.T - t] is None): 210 newcontent.append(None) 211 else: 212 newcontent.append(0.5 * (self.content[t] + self.content[self.T - t])) 213 if (all([x is None for x in newcontent])): 214 raise Exception("Corr could not be symmetrized: No redundant values") 215 return Corr(newcontent, prange=self.prange) 216 217 def anti_symmetric(self): 218 """Anti-symmetrize the correlator around x0=0.""" 219 if self.N != 1: 220 raise Exception('anti_symmetric cannot be safely applied to multi-dimensional correlators.') 221 if self.T % 2 != 0: 222 raise Exception("Can not symmetrize odd T") 223 224 test = 1 * self 225 test.gamma_method() 226 if not all([o.is_zero_within_error(3) for o in test.content[0]]): 227 warnings.warn("Correlator does not seem to be anti-symmetric around x0=0.", RuntimeWarning) 228 229 newcontent = [self.content[0]] 230 for t in range(1, self.T): 231 if (self.content[t] is None) or (self.content[self.T - t] is None): 232 newcontent.append(None) 233 else: 234 newcontent.append(0.5 * (self.content[t] - self.content[self.T - t])) 235 if (all([x is None for x in newcontent])): 236 raise Exception("Corr could not be symmetrized: No redundant values") 237 return Corr(newcontent, prange=self.prange) 238 239 def is_matrix_symmetric(self): 240 """Checks whether a correlator matrices is symmetric on every timeslice.""" 241 if self.N == 1: 242 raise Exception("Only works for correlator matrices.") 243 for t in range(self.T): 244 if self[t] is None: 245 continue 246 for i in range(self.N): 247 for j in range(i + 1, self.N): 248 if self[t][i, j] is self[t][j, i]: 249 continue 250 if hash(self[t][i, j]) != hash(self[t][j, i]): 251 return False 252 return True 253 254 def matrix_symmetric(self): 255 """Symmetrizes the correlator matrices on every timeslice.""" 256 if self.N == 1: 257 raise Exception("Trying to symmetrize a correlator matrix, that already has N=1.") 258 if self.is_matrix_symmetric(): 259 return 1.0 * self 260 else: 261 transposed = [None if _check_for_none(self, G) else G.T for G in self.content] 262 return 0.5 * (Corr(transposed) + self) 263 264 def GEVP(self, t0, ts=None, sort="Eigenvalue", **kwargs): 265 r'''Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors. 266 267 The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the 268 largest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing 269 ```python 270 C.GEVP(t0=2)[0] # Ground state vector(s) 271 C.GEVP(t0=2)[:3] # Vectors for the lowest three states 272 ``` 273 274 Parameters 275 ---------- 276 t0 : int 277 The time t0 for the right hand side of the GEVP according to $G(t)v_i=\lambda_i G(t_0)v_i$ 278 ts : int 279 fixed time $G(t_s)v_i=\lambda_i G(t_0)v_i$ if sort=None. 280 If sort="Eigenvector" it gives a reference point for the sorting method. 281 sort : string 282 If this argument is set, a list of self.T vectors per state is returned. If it is set to None, only one vector is returned. 283 - "Eigenvalue": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice. 284 - "Eigenvector": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state. 285 The reference state is identified by its eigenvalue at $t=t_s$. 286 287 Other Parameters 288 ---------------- 289 state : int 290 Returns only the vector(s) for a specified state. The lowest state is zero. 291 ''' 292 293 if self.N == 1: 294 raise Exception("GEVP methods only works on correlator matrices and not single correlators.") 295 if ts is not None: 296 if (ts <= t0): 297 raise Exception("ts has to be larger than t0.") 298 299 if "sorted_list" in kwargs: 300 warnings.warn("Argument 'sorted_list' is deprecated, use 'sort' instead.", DeprecationWarning) 301 sort = kwargs.get("sorted_list") 302 303 if self.is_matrix_symmetric(): 304 symmetric_corr = self 305 else: 306 symmetric_corr = self.matrix_symmetric() 307 308 G0 = np.vectorize(lambda x: x.value)(symmetric_corr[t0]) 309 np.linalg.cholesky(G0) # Check if matrix G0 is positive-semidefinite. 310 311 if sort is None: 312 if (ts is None): 313 raise Exception("ts is required if sort=None.") 314 if (self.content[t0] is None) or (self.content[ts] is None): 315 raise Exception("Corr not defined at t0/ts.") 316 Gt = np.vectorize(lambda x: x.value)(symmetric_corr[ts]) 317 reordered_vecs = _GEVP_solver(Gt, G0) 318 319 elif sort in ["Eigenvalue", "Eigenvector"]: 320 if sort == "Eigenvalue" and ts is not None: 321 warnings.warn("ts has no effect when sorting by eigenvalue is chosen.", RuntimeWarning) 322 all_vecs = [None] * (t0 + 1) 323 for t in range(t0 + 1, self.T): 324 try: 325 Gt = np.vectorize(lambda x: x.value)(symmetric_corr[t]) 326 all_vecs.append(_GEVP_solver(Gt, G0)) 327 except Exception: 328 all_vecs.append(None) 329 if sort == "Eigenvector": 330 if ts is None: 331 raise Exception("ts is required for the Eigenvector sorting method.") 332 all_vecs = _sort_vectors(all_vecs, ts) 333 334 reordered_vecs = [[v[s] if v is not None else None for v in all_vecs] for s in range(self.N)] 335 else: 336 raise Exception("Unkown value for 'sort'.") 337 338 if "state" in kwargs: 339 return reordered_vecs[kwargs.get("state")] 340 else: 341 return reordered_vecs 342 343 def Eigenvalue(self, t0, ts=None, state=0, sort="Eigenvalue"): 344 """Determines the eigenvalue of the GEVP by solving and projecting the correlator 345 346 Parameters 347 ---------- 348 state : int 349 The state one is interested in ordered by energy. The lowest state is zero. 350 351 All other parameters are identical to the ones of Corr.GEVP. 352 """ 353 vec = self.GEVP(t0, ts=ts, sort=sort)[state] 354 return self.projected(vec) 355 356 def Hankel(self, N, periodic=False): 357 """Constructs an NxN Hankel matrix 358 359 C(t) c(t+1) ... c(t+n-1) 360 C(t+1) c(t+2) ... c(t+n) 361 ................. 362 C(t+(n-1)) c(t+n) ... c(t+2(n-1)) 363 364 Parameters 365 ---------- 366 N : int 367 Dimension of the Hankel matrix 368 periodic : bool, optional 369 determines whether the matrix is extended periodically 370 """ 371 372 if self.N != 1: 373 raise Exception("Multi-operator Prony not implemented!") 374 375 array = np.empty([N, N], dtype="object") 376 new_content = [] 377 for t in range(self.T): 378 new_content.append(array.copy()) 379 380 def wrap(i): 381 while i >= self.T: 382 i -= self.T 383 return i 384 385 for t in range(self.T): 386 for i in range(N): 387 for j in range(N): 388 if periodic: 389 new_content[t][i, j] = self.content[wrap(t + i + j)][0] 390 elif (t + i + j) >= self.T: 391 new_content[t] = None 392 else: 393 new_content[t][i, j] = self.content[t + i + j][0] 394 395 return Corr(new_content) 396 397 def roll(self, dt): 398 """Periodically shift the correlator by dt timeslices 399 400 Parameters 401 ---------- 402 dt : int 403 number of timeslices 404 """ 405 return Corr(list(np.roll(np.array(self.content, dtype=object), dt))) 406 407 def reverse(self): 408 """Reverse the time ordering of the Corr""" 409 return Corr(self.content[:: -1]) 410 411 def thin(self, spacing=2, offset=0): 412 """Thin out a correlator to suppress correlations 413 414 Parameters 415 ---------- 416 spacing : int 417 Keep only every 'spacing'th entry of the correlator 418 offset : int 419 Offset the equal spacing 420 """ 421 new_content = [] 422 for t in range(self.T): 423 if (offset + t) % spacing != 0: 424 new_content.append(None) 425 else: 426 new_content.append(self.content[t]) 427 return Corr(new_content) 428 429 def correlate(self, partner): 430 """Correlate the correlator with another correlator or Obs 431 432 Parameters 433 ---------- 434 partner : Obs or Corr 435 partner to correlate the correlator with. 436 Can either be an Obs which is correlated with all entries of the 437 correlator or a Corr of same length. 438 """ 439 if self.N != 1: 440 raise Exception("Only one-dimensional correlators can be safely correlated.") 441 new_content = [] 442 for x0, t_slice in enumerate(self.content): 443 if _check_for_none(self, t_slice): 444 new_content.append(None) 445 else: 446 if isinstance(partner, Corr): 447 if _check_for_none(partner, partner.content[x0]): 448 new_content.append(None) 449 else: 450 new_content.append(np.array([correlate(o, partner.content[x0][0]) for o in t_slice])) 451 elif isinstance(partner, Obs): # Should this include CObs? 452 new_content.append(np.array([correlate(o, partner) for o in t_slice])) 453 else: 454 raise Exception("Can only correlate with an Obs or a Corr.") 455 456 return Corr(new_content) 457 458 def reweight(self, weight, **kwargs): 459 """Reweight the correlator. 460 461 Parameters 462 ---------- 463 weight : Obs 464 Reweighting factor. An Observable that has to be defined on a superset of the 465 configurations in obs[i].idl for all i. 466 all_configs : bool 467 if True, the reweighted observables are normalized by the average of 468 the reweighting factor on all configurations in weight.idl and not 469 on the configurations in obs[i].idl. 470 """ 471 if self.N != 1: 472 raise Exception("Reweighting only implemented for one-dimensional correlators.") 473 new_content = [] 474 for t_slice in self.content: 475 if _check_for_none(self, t_slice): 476 new_content.append(None) 477 else: 478 new_content.append(np.array(reweight(weight, t_slice, **kwargs))) 479 return Corr(new_content) 480 481 def T_symmetry(self, partner, parity=+1): 482 """Return the time symmetry average of the correlator and its partner 483 484 Parameters 485 ---------- 486 partner : Corr 487 Time symmetry partner of the Corr 488 partity : int 489 Parity quantum number of the correlator, can be +1 or -1 490 """ 491 if self.N != 1: 492 raise Exception("T_symmetry only implemented for one-dimensional correlators.") 493 if not isinstance(partner, Corr): 494 raise Exception("T partner has to be a Corr object.") 495 if parity not in [+1, -1]: 496 raise Exception("Parity has to be +1 or -1.") 497 T_partner = parity * partner.reverse() 498 499 t_slices = [] 500 test = (self - T_partner) 501 test.gamma_method() 502 for x0, t_slice in enumerate(test.content): 503 if t_slice is not None: 504 if not t_slice[0].is_zero_within_error(5): 505 t_slices.append(x0) 506 if t_slices: 507 warnings.warn("T symmetry partners do not agree within 5 sigma on time slices " + str(t_slices) + ".", RuntimeWarning) 508 509 return (self + T_partner) / 2 510 511 def deriv(self, variant="symmetric"): 512 """Return the first derivative of the correlator with respect to x0. 513 514 Parameters 515 ---------- 516 variant : str 517 decides which definition of the finite differences derivative is used. 518 Available choice: symmetric, forward, backward, improved, log, default: symmetric 519 """ 520 if self.N != 1: 521 raise Exception("deriv only implemented for one-dimensional correlators.") 522 if variant == "symmetric": 523 newcontent = [] 524 for t in range(1, self.T - 1): 525 if (self.content[t - 1] is None) or (self.content[t + 1] is None): 526 newcontent.append(None) 527 else: 528 newcontent.append(0.5 * (self.content[t + 1] - self.content[t - 1])) 529 if (all([x is None for x in newcontent])): 530 raise Exception('Derivative is undefined at all timeslices') 531 return Corr(newcontent, padding=[1, 1]) 532 elif variant == "forward": 533 newcontent = [] 534 for t in range(self.T - 1): 535 if (self.content[t] is None) or (self.content[t + 1] is None): 536 newcontent.append(None) 537 else: 538 newcontent.append(self.content[t + 1] - self.content[t]) 539 if (all([x is None for x in newcontent])): 540 raise Exception("Derivative is undefined at all timeslices") 541 return Corr(newcontent, padding=[0, 1]) 542 elif variant == "backward": 543 newcontent = [] 544 for t in range(1, self.T): 545 if (self.content[t - 1] is None) or (self.content[t] is None): 546 newcontent.append(None) 547 else: 548 newcontent.append(self.content[t] - self.content[t - 1]) 549 if (all([x is None for x in newcontent])): 550 raise Exception("Derivative is undefined at all timeslices") 551 return Corr(newcontent, padding=[1, 0]) 552 elif variant == "improved": 553 newcontent = [] 554 for t in range(2, self.T - 2): 555 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): 556 newcontent.append(None) 557 else: 558 newcontent.append((1 / 12) * (self.content[t - 2] - 8 * self.content[t - 1] + 8 * self.content[t + 1] - self.content[t + 2])) 559 if (all([x is None for x in newcontent])): 560 raise Exception('Derivative is undefined at all timeslices') 561 return Corr(newcontent, padding=[2, 2]) 562 elif variant == 'log': 563 newcontent = [] 564 for t in range(self.T): 565 if (self.content[t] is None) or (self.content[t] <= 0): 566 newcontent.append(None) 567 else: 568 newcontent.append(np.log(self.content[t])) 569 if (all([x is None for x in newcontent])): 570 raise Exception("Log is undefined at all timeslices") 571 logcorr = Corr(newcontent) 572 return self * logcorr.deriv('symmetric') 573 else: 574 raise Exception("Unknown variant.") 575 576 def second_deriv(self, variant="symmetric"): 577 """Return the second derivative of the correlator with respect to x0. 578 579 Parameters 580 ---------- 581 variant : str 582 decides which definition of the finite differences derivative is used. 583 Available choice: symmetric, improved, log, default: symmetric 584 """ 585 if self.N != 1: 586 raise Exception("second_deriv only implemented for one-dimensional correlators.") 587 if variant == "symmetric": 588 newcontent = [] 589 for t in range(1, self.T - 1): 590 if (self.content[t - 1] is None) or (self.content[t + 1] is None): 591 newcontent.append(None) 592 else: 593 newcontent.append((self.content[t + 1] - 2 * self.content[t] + self.content[t - 1])) 594 if (all([x is None for x in newcontent])): 595 raise Exception("Derivative is undefined at all timeslices") 596 return Corr(newcontent, padding=[1, 1]) 597 elif variant == "improved": 598 newcontent = [] 599 for t in range(2, self.T - 2): 600 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): 601 newcontent.append(None) 602 else: 603 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])) 604 if (all([x is None for x in newcontent])): 605 raise Exception("Derivative is undefined at all timeslices") 606 return Corr(newcontent, padding=[2, 2]) 607 elif variant == 'log': 608 newcontent = [] 609 for t in range(self.T): 610 if (self.content[t] is None) or (self.content[t] <= 0): 611 newcontent.append(None) 612 else: 613 newcontent.append(np.log(self.content[t])) 614 if (all([x is None for x in newcontent])): 615 raise Exception("Log is undefined at all timeslices") 616 logcorr = Corr(newcontent) 617 return self * (logcorr.second_deriv('symmetric') + (logcorr.deriv('symmetric'))**2) 618 else: 619 raise Exception("Unknown variant.") 620 621 def m_eff(self, variant='log', guess=1.0): 622 """Returns the effective mass of the correlator as correlator object 623 624 Parameters 625 ---------- 626 variant : str 627 log : uses the standard effective mass log(C(t) / C(t+1)) 628 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. 629 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. 630 See, e.g., arXiv:1205.5380 631 arccosh : Uses the explicit form of the symmetrized correlator (not recommended) 632 logsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2 633 guess : float 634 guess for the root finder, only relevant for the root variant 635 """ 636 if self.N != 1: 637 raise Exception('Correlator must be projected before getting m_eff') 638 if variant == 'log': 639 newcontent = [] 640 for t in range(self.T - 1): 641 if ((self.content[t] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0): 642 newcontent.append(None) 643 elif self.content[t][0].value / self.content[t + 1][0].value < 0: 644 newcontent.append(None) 645 else: 646 newcontent.append(self.content[t] / self.content[t + 1]) 647 if (all([x is None for x in newcontent])): 648 raise Exception('m_eff is undefined at all timeslices') 649 650 return np.log(Corr(newcontent, padding=[0, 1])) 651 652 elif variant == 'logsym': 653 newcontent = [] 654 for t in range(1, self.T - 1): 655 if ((self.content[t - 1] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0): 656 newcontent.append(None) 657 elif self.content[t - 1][0].value / self.content[t + 1][0].value < 0: 658 newcontent.append(None) 659 else: 660 newcontent.append(self.content[t - 1] / self.content[t + 1]) 661 if (all([x is None for x in newcontent])): 662 raise Exception('m_eff is undefined at all timeslices') 663 664 return np.log(Corr(newcontent, padding=[1, 1])) / 2 665 666 elif variant in ['periodic', 'cosh', 'sinh']: 667 if variant in ['periodic', 'cosh']: 668 func = anp.cosh 669 else: 670 func = anp.sinh 671 672 def root_function(x, d): 673 return func(x * (t - self.T / 2)) / func(x * (t + 1 - self.T / 2)) - d 674 675 newcontent = [] 676 for t in range(self.T - 1): 677 if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 1][0].value == 0): 678 newcontent.append(None) 679 # Fill the two timeslices in the middle of the lattice with their predecessors 680 elif variant == 'sinh' and t in [self.T / 2, self.T / 2 - 1]: 681 newcontent.append(newcontent[-1]) 682 elif self.content[t][0].value / self.content[t + 1][0].value < 0: 683 newcontent.append(None) 684 else: 685 newcontent.append(np.abs(find_root(self.content[t][0] / self.content[t + 1][0], root_function, guess=guess))) 686 if (all([x is None for x in newcontent])): 687 raise Exception('m_eff is undefined at all timeslices') 688 689 return Corr(newcontent, padding=[0, 1]) 690 691 elif variant == 'arccosh': 692 newcontent = [] 693 for t in range(1, self.T - 1): 694 if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t - 1] is None) or (self.content[t][0].value == 0): 695 newcontent.append(None) 696 else: 697 newcontent.append((self.content[t + 1] + self.content[t - 1]) / (2 * self.content[t])) 698 if (all([x is None for x in newcontent])): 699 raise Exception("m_eff is undefined at all timeslices") 700 return np.arccosh(Corr(newcontent, padding=[1, 1])) 701 702 else: 703 raise Exception('Unknown variant.') 704 705 def fit(self, function, fitrange=None, silent=False, **kwargs): 706 r'''Fits function to the data 707 708 Parameters 709 ---------- 710 function : obj 711 function to fit to the data. See fits.least_squares for details. 712 fitrange : list 713 Two element list containing the timeslices on which the fit is supposed to start and stop. 714 Caution: This range is inclusive as opposed to standard python indexing. 715 `fitrange=[4, 6]` corresponds to the three entries 4, 5 and 6. 716 If not specified, self.prange or all timeslices are used. 717 silent : bool 718 Decides whether output is printed to the standard output. 719 ''' 720 if self.N != 1: 721 raise Exception("Correlator must be projected before fitting") 722 723 if fitrange is None: 724 if self.prange: 725 fitrange = self.prange 726 else: 727 fitrange = [0, self.T - 1] 728 else: 729 if not isinstance(fitrange, list): 730 raise Exception("fitrange has to be a list with two elements") 731 if len(fitrange) != 2: 732 raise Exception("fitrange has to have exactly two elements [fit_start, fit_stop]") 733 734 xs = [x for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None] 735 ys = [self.content[x][0] for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None] 736 result = least_squares(xs, ys, function, silent=silent, **kwargs) 737 return result 738 739 def plateau(self, plateau_range=None, method="fit", auto_gamma=False): 740 """ Extract a plateau value from a Corr object 741 742 Parameters 743 ---------- 744 plateau_range : list 745 list with two entries, indicating the first and the last timeslice 746 of the plateau region. 747 method : str 748 method to extract the plateau. 749 'fit' fits a constant to the plateau region 750 'avg', 'average' or 'mean' just average over the given timeslices. 751 auto_gamma : bool 752 apply gamma_method with default parameters to the Corr. Defaults to None 753 """ 754 if not plateau_range: 755 if self.prange: 756 plateau_range = self.prange 757 else: 758 raise Exception("no plateau range provided") 759 if self.N != 1: 760 raise Exception("Correlator must be projected before getting a plateau.") 761 if (all([self.content[t] is None for t in range(plateau_range[0], plateau_range[1] + 1)])): 762 raise Exception("plateau is undefined at all timeslices in plateaurange.") 763 if auto_gamma: 764 self.gamma_method() 765 if method == "fit": 766 def const_func(a, t): 767 return a[0] 768 return self.fit(const_func, plateau_range)[0] 769 elif method in ["avg", "average", "mean"]: 770 returnvalue = np.mean([item[0] for item in self.content[plateau_range[0]:plateau_range[1] + 1] if item is not None]) 771 return returnvalue 772 773 else: 774 raise Exception("Unsupported plateau method: " + method) 775 776 def set_prange(self, prange): 777 """Sets the attribute prange of the Corr object.""" 778 if not len(prange) == 2: 779 raise Exception("prange must be a list or array with two values") 780 if not ((isinstance(prange[0], int)) and (isinstance(prange[1], int))): 781 raise Exception("Start and end point must be integers") 782 if not (0 <= prange[0] <= self.T and 0 <= prange[1] <= self.T and prange[0] < prange[1]): 783 raise Exception("Start and end point must define a range in the interval 0,T") 784 785 self.prange = prange 786 return 787 788 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, hide_sigma=None, references=None, title=None): 789 """Plots the correlator using the tag of the correlator as label if available. 790 791 Parameters 792 ---------- 793 x_range : list 794 list of two values, determining the range of the x-axis e.g. [4, 8]. 795 comp : Corr or list of Corr 796 Correlator or list of correlators which are plotted for comparison. 797 The tags of these correlators are used as labels if available. 798 logscale : bool 799 Sets y-axis to logscale. 800 plateau : Obs 801 Plateau value to be visualized in the figure. 802 fit_res : Fit_result 803 Fit_result object to be visualized. 804 ylabel : str 805 Label for the y-axis. 806 save : str 807 path to file in which the figure should be saved. 808 auto_gamma : bool 809 Apply the gamma method with standard parameters to all correlators and plateau values before plotting. 810 hide_sigma : float 811 Hides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors. 812 references : list 813 List of floating point values that are displayed as horizontal lines for reference. 814 title : string 815 Optional title of the figure. 816 """ 817 if self.N != 1: 818 raise Exception("Correlator must be projected before plotting") 819 820 if auto_gamma: 821 self.gamma_method() 822 823 if x_range is None: 824 x_range = [0, self.T - 1] 825 826 fig = plt.figure() 827 ax1 = fig.add_subplot(111) 828 829 x, y, y_err = self.plottable() 830 if hide_sigma: 831 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 832 else: 833 hide_from = None 834 ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=self.tag) 835 if logscale: 836 ax1.set_yscale('log') 837 else: 838 if y_range is None: 839 try: 840 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)]) 841 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)]) 842 ax1.set_ylim([y_min - 0.1 * (y_max - y_min), y_max + 0.1 * (y_max - y_min)]) 843 except Exception: 844 pass 845 else: 846 ax1.set_ylim(y_range) 847 if comp: 848 if isinstance(comp, (Corr, list)): 849 for corr in comp if isinstance(comp, list) else [comp]: 850 if auto_gamma: 851 corr.gamma_method() 852 x, y, y_err = corr.plottable() 853 if hide_sigma: 854 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 855 else: 856 hide_from = None 857 ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=corr.tag, mfc=plt.rcParams['axes.facecolor']) 858 else: 859 raise Exception("'comp' must be a correlator or a list of correlators.") 860 861 if plateau: 862 if isinstance(plateau, Obs): 863 if auto_gamma: 864 plateau.gamma_method() 865 ax1.axhline(y=plateau.value, linewidth=2, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--', label=str(plateau)) 866 ax1.axhspan(plateau.value - plateau.dvalue, plateau.value + plateau.dvalue, alpha=0.25, color=plt.rcParams['text.color'], ls='-') 867 else: 868 raise Exception("'plateau' must be an Obs") 869 870 if references: 871 if isinstance(references, list): 872 for ref in references: 873 ax1.axhline(y=ref, linewidth=1, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--') 874 else: 875 raise Exception("'references' must be a list of floating pint values.") 876 877 if self.prange: 878 ax1.axvline(self.prange[0], 0, 1, ls='-', marker=',') 879 ax1.axvline(self.prange[1], 0, 1, ls='-', marker=',') 880 881 if fit_res: 882 x_samples = np.arange(x_range[0], x_range[1] + 1, 0.05) 883 ax1.plot(x_samples, 884 fit_res.fit_function([o.value for o in fit_res.fit_parameters], x_samples), 885 ls='-', marker=',', lw=2) 886 887 ax1.set_xlabel(r'$x_0 / a$') 888 if ylabel: 889 ax1.set_ylabel(ylabel) 890 ax1.set_xlim([x_range[0] - 0.5, x_range[1] + 0.5]) 891 892 handles, labels = ax1.get_legend_handles_labels() 893 if labels: 894 ax1.legend() 895 896 if title: 897 plt.title(title) 898 899 plt.draw() 900 901 if save: 902 if isinstance(save, str): 903 fig.savefig(save, bbox_inches='tight') 904 else: 905 raise Exception("'save' has to be a string.") 906 907 def spaghetti_plot(self, logscale=True): 908 """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations. 909 910 Parameters 911 ---------- 912 logscale : bool 913 Determines whether the scale of the y-axis is logarithmic or standard. 914 """ 915 if self.N != 1: 916 raise Exception("Correlator needs to be projected first.") 917 918 mc_names = list(set([item for sublist in [sum(map(o[0].e_content.get, o[0].mc_names), []) for o in self.content if o is not None] for item in sublist])) 919 x0_vals = [n for (n, o) in zip(np.arange(self.T), self.content) if o is not None] 920 921 for name in mc_names: 922 data = np.array([o[0].deltas[name] + o[0].r_values[name] for o in self.content if o is not None]).T 923 924 fig = plt.figure() 925 ax = fig.add_subplot(111) 926 for dat in data: 927 ax.plot(x0_vals, dat, ls='-', marker='') 928 929 if logscale is True: 930 ax.set_yscale('log') 931 932 ax.set_xlabel(r'$x_0 / a$') 933 plt.title(name) 934 plt.draw() 935 936 def dump(self, filename, datatype="json.gz", **kwargs): 937 """Dumps the Corr into a file of chosen type 938 Parameters 939 ---------- 940 filename : str 941 Name of the file to be saved. 942 datatype : str 943 Format of the exported file. Supported formats include 944 "json.gz" and "pickle" 945 path : str 946 specifies a custom path for the file (default '.') 947 """ 948 if datatype == "json.gz": 949 from .input.json import dump_to_json 950 if 'path' in kwargs: 951 file_name = kwargs.get('path') + '/' + filename 952 else: 953 file_name = filename 954 dump_to_json(self, file_name) 955 elif datatype == "pickle": 956 dump_object(self, filename, **kwargs) 957 else: 958 raise Exception("Unknown datatype " + str(datatype)) 959 960 def print(self, print_range=None): 961 print(self.__repr__(print_range)) 962 963 def __repr__(self, print_range=None): 964 if print_range is None: 965 print_range = [0, None] 966 967 content_string = "" 968 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 969 970 if self.tag is not None: 971 content_string += "Description: " + self.tag + "\n" 972 if self.N != 1: 973 return content_string 974 if isinstance(self[0], CObs): 975 return content_string 976 977 if print_range[1]: 978 print_range[1] += 1 979 content_string += 'x0/a\tCorr(x0/a)\n------------------\n' 980 for i, sub_corr in enumerate(self.content[print_range[0]:print_range[1]]): 981 if sub_corr is None: 982 content_string += str(i + print_range[0]) + '\n' 983 else: 984 content_string += str(i + print_range[0]) 985 for element in sub_corr: 986 content_string += '\t' + ' ' * int(element >= 0) + str(element) 987 content_string += '\n' 988 return content_string 989 990 def __str__(self): 991 return self.__repr__() 992 993 # We define the basic operations, that can be performed with correlators. 994 # While */+- get defined here, they only work for Corr*Obs and not Obs*Corr. 995 # This is because Obs*Corr checks Obs.__mul__ first and does not catch an exception. 996 # One could try and tell Obs to check if the y in __mul__ is a Corr and 997 998 def __add__(self, y): 999 if isinstance(y, Corr): 1000 if ((self.N != y.N) or (self.T != y.T)): 1001 raise Exception("Addition of Corrs with different shape") 1002 newcontent = [] 1003 for t in range(self.T): 1004 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): 1005 newcontent.append(None) 1006 else: 1007 newcontent.append(self.content[t] + y.content[t]) 1008 return Corr(newcontent) 1009 1010 elif isinstance(y, (Obs, int, float, CObs)): 1011 newcontent = [] 1012 for t in range(self.T): 1013 if _check_for_none(self, self.content[t]): 1014 newcontent.append(None) 1015 else: 1016 newcontent.append(self.content[t] + y) 1017 return Corr(newcontent, prange=self.prange) 1018 elif isinstance(y, np.ndarray): 1019 if y.shape == (self.T,): 1020 return Corr(list((np.array(self.content).T + y).T)) 1021 else: 1022 raise ValueError("operands could not be broadcast together") 1023 else: 1024 raise TypeError("Corr + wrong type") 1025 1026 def __mul__(self, y): 1027 if isinstance(y, Corr): 1028 if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): 1029 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") 1030 newcontent = [] 1031 for t in range(self.T): 1032 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): 1033 newcontent.append(None) 1034 else: 1035 newcontent.append(self.content[t] * y.content[t]) 1036 return Corr(newcontent) 1037 1038 elif isinstance(y, (Obs, int, float, CObs)): 1039 newcontent = [] 1040 for t in range(self.T): 1041 if _check_for_none(self, self.content[t]): 1042 newcontent.append(None) 1043 else: 1044 newcontent.append(self.content[t] * y) 1045 return Corr(newcontent, prange=self.prange) 1046 elif isinstance(y, np.ndarray): 1047 if y.shape == (self.T,): 1048 return Corr(list((np.array(self.content).T * y).T)) 1049 else: 1050 raise ValueError("operands could not be broadcast together") 1051 else: 1052 raise TypeError("Corr * wrong type") 1053 1054 def __truediv__(self, y): 1055 if isinstance(y, Corr): 1056 if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): 1057 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") 1058 newcontent = [] 1059 for t in range(self.T): 1060 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): 1061 newcontent.append(None) 1062 else: 1063 newcontent.append(self.content[t] / y.content[t]) 1064 for t in range(self.T): 1065 if _check_for_none(self, newcontent[t]): 1066 continue 1067 if np.isnan(np.sum(newcontent[t]).value): 1068 newcontent[t] = None 1069 1070 if all([item is None for item in newcontent]): 1071 raise Exception("Division returns completely undefined correlator") 1072 return Corr(newcontent) 1073 1074 elif isinstance(y, (Obs, CObs)): 1075 if isinstance(y, Obs): 1076 if y.value == 0: 1077 raise Exception('Division by zero will return undefined correlator') 1078 if isinstance(y, CObs): 1079 if y.is_zero(): 1080 raise Exception('Division by zero will return undefined correlator') 1081 1082 newcontent = [] 1083 for t in range(self.T): 1084 if _check_for_none(self, self.content[t]): 1085 newcontent.append(None) 1086 else: 1087 newcontent.append(self.content[t] / y) 1088 return Corr(newcontent, prange=self.prange) 1089 1090 elif isinstance(y, (int, float)): 1091 if y == 0: 1092 raise Exception('Division by zero will return undefined correlator') 1093 newcontent = [] 1094 for t in range(self.T): 1095 if _check_for_none(self, self.content[t]): 1096 newcontent.append(None) 1097 else: 1098 newcontent.append(self.content[t] / y) 1099 return Corr(newcontent, prange=self.prange) 1100 elif isinstance(y, np.ndarray): 1101 if y.shape == (self.T,): 1102 return Corr(list((np.array(self.content).T / y).T)) 1103 else: 1104 raise ValueError("operands could not be broadcast together") 1105 else: 1106 raise TypeError('Corr / wrong type') 1107 1108 def __neg__(self): 1109 newcontent = [None if _check_for_none(self, item) else -1. * item for item in self.content] 1110 return Corr(newcontent, prange=self.prange) 1111 1112 def __sub__(self, y): 1113 return self + (-y) 1114 1115 def __pow__(self, y): 1116 if isinstance(y, (Obs, int, float, CObs)): 1117 newcontent = [None if _check_for_none(self, item) else item**y for item in self.content] 1118 return Corr(newcontent, prange=self.prange) 1119 else: 1120 raise TypeError('Type of exponent not supported') 1121 1122 def __abs__(self): 1123 newcontent = [None if _check_for_none(self, item) else np.abs(item) for item in self.content] 1124 return Corr(newcontent, prange=self.prange) 1125 1126 # The numpy functions: 1127 def sqrt(self): 1128 return self ** 0.5 1129 1130 def log(self): 1131 newcontent = [None if _check_for_none(self, item) else np.log(item) for item in self.content] 1132 return Corr(newcontent, prange=self.prange) 1133 1134 def exp(self): 1135 newcontent = [None if _check_for_none(self, item) else np.exp(item) for item in self.content] 1136 return Corr(newcontent, prange=self.prange) 1137 1138 def _apply_func_to_corr(self, func): 1139 newcontent = [None if _check_for_none(self, item) else func(item) for item in self.content] 1140 for t in range(self.T): 1141 if _check_for_none(self, newcontent[t]): 1142 continue 1143 tmp_sum = np.sum(newcontent[t]) 1144 if hasattr(tmp_sum, "value"): 1145 if np.isnan(tmp_sum.value): 1146 newcontent[t] = None 1147 if all([item is None for item in newcontent]): 1148 raise Exception('Operation returns undefined correlator') 1149 return Corr(newcontent) 1150 1151 def sin(self): 1152 return self._apply_func_to_corr(np.sin) 1153 1154 def cos(self): 1155 return self._apply_func_to_corr(np.cos) 1156 1157 def tan(self): 1158 return self._apply_func_to_corr(np.tan) 1159 1160 def sinh(self): 1161 return self._apply_func_to_corr(np.sinh) 1162 1163 def cosh(self): 1164 return self._apply_func_to_corr(np.cosh) 1165 1166 def tanh(self): 1167 return self._apply_func_to_corr(np.tanh) 1168 1169 def arcsin(self): 1170 return self._apply_func_to_corr(np.arcsin) 1171 1172 def arccos(self): 1173 return self._apply_func_to_corr(np.arccos) 1174 1175 def arctan(self): 1176 return self._apply_func_to_corr(np.arctan) 1177 1178 def arcsinh(self): 1179 return self._apply_func_to_corr(np.arcsinh) 1180 1181 def arccosh(self): 1182 return self._apply_func_to_corr(np.arccosh) 1183 1184 def arctanh(self): 1185 return self._apply_func_to_corr(np.arctanh) 1186 1187 # Right hand side operations (require tweak in main module to work) 1188 def __radd__(self, y): 1189 return self + y 1190 1191 def __rsub__(self, y): 1192 return -self + y 1193 1194 def __rmul__(self, y): 1195 return self * y 1196 1197 def __rtruediv__(self, y): 1198 return (self / y) ** (-1) 1199 1200 @property 1201 def real(self): 1202 def return_real(obs_OR_cobs): 1203 if isinstance(obs_OR_cobs.flatten()[0], CObs): 1204 return np.vectorize(lambda x: x.real)(obs_OR_cobs) 1205 else: 1206 return obs_OR_cobs 1207 1208 return self._apply_func_to_corr(return_real) 1209 1210 @property 1211 def imag(self): 1212 def return_imag(obs_OR_cobs): 1213 if isinstance(obs_OR_cobs.flatten()[0], CObs): 1214 return np.vectorize(lambda x: x.imag)(obs_OR_cobs) 1215 else: 1216 return obs_OR_cobs * 0 # So it stays the right type 1217 1218 return self._apply_func_to_corr(return_imag) 1219 1220 def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None): 1221 r''' Project large correlation matrix to lowest states 1222 1223 This method can be used to reduce the size of an (N x N) correlation matrix 1224 to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise 1225 is still small. 1226 1227 Parameters 1228 ---------- 1229 Ntrunc: int 1230 Rank of the target matrix. 1231 tproj: int 1232 Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method. 1233 The default value is 3. 1234 t0proj: int 1235 Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly 1236 discouraged for O(a) improved theories, since the correctness of the procedure 1237 cannot be granted in this case. The default value is 2. 1238 basematrix : Corr 1239 Correlation matrix that is used to determine the eigenvectors of the 1240 lowest states based on a GEVP. basematrix is taken to be the Corr itself if 1241 is is not specified. 1242 1243 Notes 1244 ----- 1245 We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving 1246 the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$ 1247 and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the 1248 resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via 1249 $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large 1250 correlation matrix and to remove some noise that is added by irrelevant operators. 1251 This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated 1252 bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$. 1253 ''' 1254 1255 if self.N == 1: 1256 raise Exception('Method cannot be applied to one-dimensional correlators.') 1257 if basematrix is None: 1258 basematrix = self 1259 if Ntrunc >= basematrix.N: 1260 raise Exception('Cannot truncate using Ntrunc <= %d' % (basematrix.N)) 1261 if basematrix.N != self.N: 1262 raise Exception('basematrix and targetmatrix have to be of the same size.') 1263 1264 evecs = basematrix.GEVP(t0proj, tproj, sort=None)[:Ntrunc] 1265 1266 tmpmat = np.empty((Ntrunc, Ntrunc), dtype=object) 1267 rmat = [] 1268 for t in range(basematrix.T): 1269 for i in range(Ntrunc): 1270 for j in range(Ntrunc): 1271 tmpmat[i][j] = evecs[i].T @ self[t] @ evecs[j] 1272 rmat.append(np.copy(tmpmat)) 1273 1274 newcontent = [None if (self.content[t] is None) else rmat[t] for t in range(self.T)] 1275 return Corr(newcontent) 1276 1277 1278def _sort_vectors(vec_set, ts): 1279 """Helper function used to find a set of Eigenvectors consistent over all timeslices""" 1280 reference_sorting = np.array(vec_set[ts]) 1281 N = reference_sorting.shape[0] 1282 sorted_vec_set = [] 1283 for t in range(len(vec_set)): 1284 if vec_set[t] is None: 1285 sorted_vec_set.append(None) 1286 elif not t == ts: 1287 perms = [list(o) for o in permutations([i for i in range(N)], N)] 1288 best_score = 0 1289 for perm in perms: 1290 current_score = 1 1291 for k in range(N): 1292 new_sorting = reference_sorting.copy() 1293 new_sorting[perm[k], :] = vec_set[t][k] 1294 current_score *= abs(np.linalg.det(new_sorting)) 1295 if current_score > best_score: 1296 best_score = current_score 1297 best_perm = perm 1298 sorted_vec_set.append([vec_set[t][k] for k in best_perm]) 1299 else: 1300 sorted_vec_set.append(vec_set[t]) 1301 1302 return sorted_vec_set 1303 1304 1305def _check_for_none(corr, entry): 1306 """Checks if entry for correlator corr is None""" 1307 return len(list(filter(None, np.asarray(entry).flatten()))) < corr.N ** 2 1308 1309 1310def _GEVP_solver(Gt, G0): 1311 """Helper function for solving the GEVP and sorting the eigenvectors. 1312 1313 The helper function assumes that both provided matrices are symmetric and 1314 only processes the lower triangular part of both matrices. In case the matrices 1315 are not symmetric the upper triangular parts are effectively discarded.""" 1316 return scipy.linalg.eigh(Gt, G0, lower=True)[1].T[::-1]
14class Corr: 15 """The class for a correlator (time dependent sequence of pe.Obs). 16 17 Everything, this class does, can be achieved using lists or arrays of Obs. 18 But it is simply more convenient to have a dedicated object for correlators. 19 One often wants to add or multiply correlators of the same length at every timeslice and it is inconvenient 20 to iterate over all timeslices for every operation. This is especially true, when dealing with matrices. 21 22 The correlator can have two types of content: An Obs at every timeslice OR a GEVP 23 matrix at every timeslice. Other dependency (eg. spatial) are not supported. 24 25 """ 26 27 def __init__(self, data_input, padding=[0, 0], prange=None): 28 """ Initialize a Corr object. 29 30 Parameters 31 ---------- 32 data_input : list or array 33 list of Obs or list of arrays of Obs or array of Corrs 34 padding : list, optional 35 List with two entries where the first labels the padding 36 at the front of the correlator and the second the padding 37 at the back. 38 prange : list, optional 39 List containing the first and last timeslice of the plateau 40 region indentified for this correlator. 41 """ 42 43 if isinstance(data_input, np.ndarray): 44 45 # This only works, if the array fulfills the conditions below 46 if not len(data_input.shape) == 2 and data_input.shape[0] == data_input.shape[1]: 47 raise Exception("Incompatible array shape") 48 if not all([isinstance(item, Corr) for item in data_input.flatten()]): 49 raise Exception("If the input is an array, its elements must be of type pe.Corr") 50 if not all([item.N == 1 for item in data_input.flatten()]): 51 raise Exception("Can only construct matrix correlator from single valued correlators") 52 if not len(set([item.T for item in data_input.flatten()])) == 1: 53 raise Exception("All input Correlators must be defined over the same timeslices.") 54 55 T = data_input[0, 0].T 56 N = data_input.shape[0] 57 input_as_list = [] 58 for t in range(T): 59 if any([(item.content[t] is None) for item in data_input.flatten()]): 60 if not all([(item.content[t] is None) for item in data_input.flatten()]): 61 warnings.warn("Input ill-defined at different timeslices. Conversion leads to data loss!", RuntimeWarning) 62 input_as_list.append(None) 63 else: 64 array_at_timeslace = np.empty([N, N], dtype="object") 65 for i in range(N): 66 for j in range(N): 67 array_at_timeslace[i, j] = data_input[i, j][t] 68 input_as_list.append(array_at_timeslace) 69 data_input = input_as_list 70 71 if isinstance(data_input, list): 72 73 if all([isinstance(item, (Obs, CObs)) or item is None for item in data_input]): 74 _assert_equal_properties([o for o in data_input if o is not None]) 75 self.content = [np.asarray([item]) if item is not None else None for item in data_input] 76 self.N = 1 77 78 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]): 79 self.content = data_input 80 noNull = [a for a in self.content if not (a is None)] # To check if the matrices are correct for all undefined elements 81 self.N = noNull[0].shape[0] 82 if self.N > 1 and noNull[0].shape[0] != noNull[0].shape[1]: 83 raise Exception("Smearing matrices are not NxN") 84 if (not all([item.shape == noNull[0].shape for item in noNull])): 85 raise Exception("Items in data_input are not of identical shape." + str(noNull)) 86 else: 87 raise Exception("data_input contains item of wrong type") 88 else: 89 raise Exception("Data input was not given as list or correct array") 90 91 self.tag = None 92 93 # An undefined timeslice is represented by the None object 94 self.content = [None] * padding[0] + self.content + [None] * padding[1] 95 self.T = len(self.content) 96 self.prange = prange 97 98 def __getitem__(self, idx): 99 """Return the content of timeslice idx""" 100 if self.content[idx] is None: 101 return None 102 elif len(self.content[idx]) == 1: 103 return self.content[idx][0] 104 else: 105 return self.content[idx] 106 107 @property 108 def reweighted(self): 109 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]]) 110 if np.all(bool_array == 1): 111 return True 112 elif np.all(bool_array == 0): 113 return False 114 else: 115 raise Exception("Reweighting status of correlator corrupted.") 116 117 def gamma_method(self, **kwargs): 118 """Apply the gamma method to the content of the Corr.""" 119 for item in self.content: 120 if not (item is None): 121 if self.N == 1: 122 item[0].gamma_method(**kwargs) 123 else: 124 for i in range(self.N): 125 for j in range(self.N): 126 item[i, j].gamma_method(**kwargs) 127 128 gm = gamma_method 129 130 def projected(self, vector_l=None, vector_r=None, normalize=False): 131 """We need to project the Correlator with a Vector to get a single value at each timeslice. 132 133 The method can use one or two vectors. 134 If two are specified it returns v1@G@v2 (the order might be very important.) 135 By default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to 136 """ 137 if self.N == 1: 138 raise Exception("Trying to project a Corr, that already has N=1.") 139 140 if vector_l is None: 141 vector_l, vector_r = np.asarray([1.] + (self.N - 1) * [0.]), np.asarray([1.] + (self.N - 1) * [0.]) 142 elif (vector_r is None): 143 vector_r = vector_l 144 if isinstance(vector_l, list) and not isinstance(vector_r, list): 145 if len(vector_l) != self.T: 146 raise Exception("Length of vector list must be equal to T") 147 vector_r = [vector_r] * self.T 148 if isinstance(vector_r, list) and not isinstance(vector_l, list): 149 if len(vector_r) != self.T: 150 raise Exception("Length of vector list must be equal to T") 151 vector_l = [vector_l] * self.T 152 153 if not isinstance(vector_l, list): 154 if not vector_l.shape == vector_r.shape == (self.N,): 155 raise Exception("Vectors are of wrong shape!") 156 if normalize: 157 vector_l, vector_r = vector_l / np.sqrt((vector_l @ vector_l)), vector_r / np.sqrt(vector_r @ vector_r) 158 newcontent = [None if _check_for_none(self, item) else np.asarray([vector_l.T @ item @ vector_r]) for item in self.content] 159 160 else: 161 # There are no checks here yet. There are so many possible scenarios, where this can go wrong. 162 if normalize: 163 for t in range(self.T): 164 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]) 165 166 newcontent = [None if (_check_for_none(self, self.content[t]) 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)] 167 return Corr(newcontent) 168 169 def item(self, i, j): 170 """Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice. 171 172 Parameters 173 ---------- 174 i : int 175 First index to be picked. 176 j : int 177 Second index to be picked. 178 """ 179 if self.N == 1: 180 raise Exception("Trying to pick item from projected Corr") 181 newcontent = [None if (item is None) else item[i, j] for item in self.content] 182 return Corr(newcontent) 183 184 def plottable(self): 185 """Outputs the correlator in a plotable format. 186 187 Outputs three lists containing the timeslice index, the value on each 188 timeslice and the error on each timeslice. 189 """ 190 if self.N != 1: 191 raise Exception("Can only make Corr[N=1] plottable") 192 x_list = [x for x in range(self.T) if not self.content[x] is None] 193 y_list = [y[0].value for y in self.content if y is not None] 194 y_err_list = [y[0].dvalue for y in self.content if y is not None] 195 196 return x_list, y_list, y_err_list 197 198 def symmetric(self): 199 """ Symmetrize the correlator around x0=0.""" 200 if self.N != 1: 201 raise Exception('symmetric cannot be safely applied to multi-dimensional correlators.') 202 if self.T % 2 != 0: 203 raise Exception("Can not symmetrize odd T") 204 205 if np.argmax(np.abs(self.content)) != 0: 206 warnings.warn("Correlator does not seem to be symmetric around x0=0.", RuntimeWarning) 207 208 newcontent = [self.content[0]] 209 for t in range(1, self.T): 210 if (self.content[t] is None) or (self.content[self.T - t] is None): 211 newcontent.append(None) 212 else: 213 newcontent.append(0.5 * (self.content[t] + self.content[self.T - t])) 214 if (all([x is None for x in newcontent])): 215 raise Exception("Corr could not be symmetrized: No redundant values") 216 return Corr(newcontent, prange=self.prange) 217 218 def anti_symmetric(self): 219 """Anti-symmetrize the correlator around x0=0.""" 220 if self.N != 1: 221 raise Exception('anti_symmetric cannot be safely applied to multi-dimensional correlators.') 222 if self.T % 2 != 0: 223 raise Exception("Can not symmetrize odd T") 224 225 test = 1 * self 226 test.gamma_method() 227 if not all([o.is_zero_within_error(3) for o in test.content[0]]): 228 warnings.warn("Correlator does not seem to be anti-symmetric around x0=0.", RuntimeWarning) 229 230 newcontent = [self.content[0]] 231 for t in range(1, self.T): 232 if (self.content[t] is None) or (self.content[self.T - t] is None): 233 newcontent.append(None) 234 else: 235 newcontent.append(0.5 * (self.content[t] - self.content[self.T - t])) 236 if (all([x is None for x in newcontent])): 237 raise Exception("Corr could not be symmetrized: No redundant values") 238 return Corr(newcontent, prange=self.prange) 239 240 def is_matrix_symmetric(self): 241 """Checks whether a correlator matrices is symmetric on every timeslice.""" 242 if self.N == 1: 243 raise Exception("Only works for correlator matrices.") 244 for t in range(self.T): 245 if self[t] is None: 246 continue 247 for i in range(self.N): 248 for j in range(i + 1, self.N): 249 if self[t][i, j] is self[t][j, i]: 250 continue 251 if hash(self[t][i, j]) != hash(self[t][j, i]): 252 return False 253 return True 254 255 def matrix_symmetric(self): 256 """Symmetrizes the correlator matrices on every timeslice.""" 257 if self.N == 1: 258 raise Exception("Trying to symmetrize a correlator matrix, that already has N=1.") 259 if self.is_matrix_symmetric(): 260 return 1.0 * self 261 else: 262 transposed = [None if _check_for_none(self, G) else G.T for G in self.content] 263 return 0.5 * (Corr(transposed) + self) 264 265 def GEVP(self, t0, ts=None, sort="Eigenvalue", **kwargs): 266 r'''Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors. 267 268 The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the 269 largest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing 270 ```python 271 C.GEVP(t0=2)[0] # Ground state vector(s) 272 C.GEVP(t0=2)[:3] # Vectors for the lowest three states 273 ``` 274 275 Parameters 276 ---------- 277 t0 : int 278 The time t0 for the right hand side of the GEVP according to $G(t)v_i=\lambda_i G(t_0)v_i$ 279 ts : int 280 fixed time $G(t_s)v_i=\lambda_i G(t_0)v_i$ if sort=None. 281 If sort="Eigenvector" it gives a reference point for the sorting method. 282 sort : string 283 If this argument is set, a list of self.T vectors per state is returned. If it is set to None, only one vector is returned. 284 - "Eigenvalue": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice. 285 - "Eigenvector": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state. 286 The reference state is identified by its eigenvalue at $t=t_s$. 287 288 Other Parameters 289 ---------------- 290 state : int 291 Returns only the vector(s) for a specified state. The lowest state is zero. 292 ''' 293 294 if self.N == 1: 295 raise Exception("GEVP methods only works on correlator matrices and not single correlators.") 296 if ts is not None: 297 if (ts <= t0): 298 raise Exception("ts has to be larger than t0.") 299 300 if "sorted_list" in kwargs: 301 warnings.warn("Argument 'sorted_list' is deprecated, use 'sort' instead.", DeprecationWarning) 302 sort = kwargs.get("sorted_list") 303 304 if self.is_matrix_symmetric(): 305 symmetric_corr = self 306 else: 307 symmetric_corr = self.matrix_symmetric() 308 309 G0 = np.vectorize(lambda x: x.value)(symmetric_corr[t0]) 310 np.linalg.cholesky(G0) # Check if matrix G0 is positive-semidefinite. 311 312 if sort is None: 313 if (ts is None): 314 raise Exception("ts is required if sort=None.") 315 if (self.content[t0] is None) or (self.content[ts] is None): 316 raise Exception("Corr not defined at t0/ts.") 317 Gt = np.vectorize(lambda x: x.value)(symmetric_corr[ts]) 318 reordered_vecs = _GEVP_solver(Gt, G0) 319 320 elif sort in ["Eigenvalue", "Eigenvector"]: 321 if sort == "Eigenvalue" and ts is not None: 322 warnings.warn("ts has no effect when sorting by eigenvalue is chosen.", RuntimeWarning) 323 all_vecs = [None] * (t0 + 1) 324 for t in range(t0 + 1, self.T): 325 try: 326 Gt = np.vectorize(lambda x: x.value)(symmetric_corr[t]) 327 all_vecs.append(_GEVP_solver(Gt, G0)) 328 except Exception: 329 all_vecs.append(None) 330 if sort == "Eigenvector": 331 if ts is None: 332 raise Exception("ts is required for the Eigenvector sorting method.") 333 all_vecs = _sort_vectors(all_vecs, ts) 334 335 reordered_vecs = [[v[s] if v is not None else None for v in all_vecs] for s in range(self.N)] 336 else: 337 raise Exception("Unkown value for 'sort'.") 338 339 if "state" in kwargs: 340 return reordered_vecs[kwargs.get("state")] 341 else: 342 return reordered_vecs 343 344 def Eigenvalue(self, t0, ts=None, state=0, sort="Eigenvalue"): 345 """Determines the eigenvalue of the GEVP by solving and projecting the correlator 346 347 Parameters 348 ---------- 349 state : int 350 The state one is interested in ordered by energy. The lowest state is zero. 351 352 All other parameters are identical to the ones of Corr.GEVP. 353 """ 354 vec = self.GEVP(t0, ts=ts, sort=sort)[state] 355 return self.projected(vec) 356 357 def Hankel(self, N, periodic=False): 358 """Constructs an NxN Hankel matrix 359 360 C(t) c(t+1) ... c(t+n-1) 361 C(t+1) c(t+2) ... c(t+n) 362 ................. 363 C(t+(n-1)) c(t+n) ... c(t+2(n-1)) 364 365 Parameters 366 ---------- 367 N : int 368 Dimension of the Hankel matrix 369 periodic : bool, optional 370 determines whether the matrix is extended periodically 371 """ 372 373 if self.N != 1: 374 raise Exception("Multi-operator Prony not implemented!") 375 376 array = np.empty([N, N], dtype="object") 377 new_content = [] 378 for t in range(self.T): 379 new_content.append(array.copy()) 380 381 def wrap(i): 382 while i >= self.T: 383 i -= self.T 384 return i 385 386 for t in range(self.T): 387 for i in range(N): 388 for j in range(N): 389 if periodic: 390 new_content[t][i, j] = self.content[wrap(t + i + j)][0] 391 elif (t + i + j) >= self.T: 392 new_content[t] = None 393 else: 394 new_content[t][i, j] = self.content[t + i + j][0] 395 396 return Corr(new_content) 397 398 def roll(self, dt): 399 """Periodically shift the correlator by dt timeslices 400 401 Parameters 402 ---------- 403 dt : int 404 number of timeslices 405 """ 406 return Corr(list(np.roll(np.array(self.content, dtype=object), dt))) 407 408 def reverse(self): 409 """Reverse the time ordering of the Corr""" 410 return Corr(self.content[:: -1]) 411 412 def thin(self, spacing=2, offset=0): 413 """Thin out a correlator to suppress correlations 414 415 Parameters 416 ---------- 417 spacing : int 418 Keep only every 'spacing'th entry of the correlator 419 offset : int 420 Offset the equal spacing 421 """ 422 new_content = [] 423 for t in range(self.T): 424 if (offset + t) % spacing != 0: 425 new_content.append(None) 426 else: 427 new_content.append(self.content[t]) 428 return Corr(new_content) 429 430 def correlate(self, partner): 431 """Correlate the correlator with another correlator or Obs 432 433 Parameters 434 ---------- 435 partner : Obs or Corr 436 partner to correlate the correlator with. 437 Can either be an Obs which is correlated with all entries of the 438 correlator or a Corr of same length. 439 """ 440 if self.N != 1: 441 raise Exception("Only one-dimensional correlators can be safely correlated.") 442 new_content = [] 443 for x0, t_slice in enumerate(self.content): 444 if _check_for_none(self, t_slice): 445 new_content.append(None) 446 else: 447 if isinstance(partner, Corr): 448 if _check_for_none(partner, partner.content[x0]): 449 new_content.append(None) 450 else: 451 new_content.append(np.array([correlate(o, partner.content[x0][0]) for o in t_slice])) 452 elif isinstance(partner, Obs): # Should this include CObs? 453 new_content.append(np.array([correlate(o, partner) for o in t_slice])) 454 else: 455 raise Exception("Can only correlate with an Obs or a Corr.") 456 457 return Corr(new_content) 458 459 def reweight(self, weight, **kwargs): 460 """Reweight the correlator. 461 462 Parameters 463 ---------- 464 weight : Obs 465 Reweighting factor. An Observable that has to be defined on a superset of the 466 configurations in obs[i].idl for all i. 467 all_configs : bool 468 if True, the reweighted observables are normalized by the average of 469 the reweighting factor on all configurations in weight.idl and not 470 on the configurations in obs[i].idl. 471 """ 472 if self.N != 1: 473 raise Exception("Reweighting only implemented for one-dimensional correlators.") 474 new_content = [] 475 for t_slice in self.content: 476 if _check_for_none(self, t_slice): 477 new_content.append(None) 478 else: 479 new_content.append(np.array(reweight(weight, t_slice, **kwargs))) 480 return Corr(new_content) 481 482 def T_symmetry(self, partner, parity=+1): 483 """Return the time symmetry average of the correlator and its partner 484 485 Parameters 486 ---------- 487 partner : Corr 488 Time symmetry partner of the Corr 489 partity : int 490 Parity quantum number of the correlator, can be +1 or -1 491 """ 492 if self.N != 1: 493 raise Exception("T_symmetry only implemented for one-dimensional correlators.") 494 if not isinstance(partner, Corr): 495 raise Exception("T partner has to be a Corr object.") 496 if parity not in [+1, -1]: 497 raise Exception("Parity has to be +1 or -1.") 498 T_partner = parity * partner.reverse() 499 500 t_slices = [] 501 test = (self - T_partner) 502 test.gamma_method() 503 for x0, t_slice in enumerate(test.content): 504 if t_slice is not None: 505 if not t_slice[0].is_zero_within_error(5): 506 t_slices.append(x0) 507 if t_slices: 508 warnings.warn("T symmetry partners do not agree within 5 sigma on time slices " + str(t_slices) + ".", RuntimeWarning) 509 510 return (self + T_partner) / 2 511 512 def deriv(self, variant="symmetric"): 513 """Return the first derivative of the correlator with respect to x0. 514 515 Parameters 516 ---------- 517 variant : str 518 decides which definition of the finite differences derivative is used. 519 Available choice: symmetric, forward, backward, improved, log, default: symmetric 520 """ 521 if self.N != 1: 522 raise Exception("deriv only implemented for one-dimensional correlators.") 523 if variant == "symmetric": 524 newcontent = [] 525 for t in range(1, self.T - 1): 526 if (self.content[t - 1] is None) or (self.content[t + 1] is None): 527 newcontent.append(None) 528 else: 529 newcontent.append(0.5 * (self.content[t + 1] - self.content[t - 1])) 530 if (all([x is None for x in newcontent])): 531 raise Exception('Derivative is undefined at all timeslices') 532 return Corr(newcontent, padding=[1, 1]) 533 elif variant == "forward": 534 newcontent = [] 535 for t in range(self.T - 1): 536 if (self.content[t] is None) or (self.content[t + 1] is None): 537 newcontent.append(None) 538 else: 539 newcontent.append(self.content[t + 1] - self.content[t]) 540 if (all([x is None for x in newcontent])): 541 raise Exception("Derivative is undefined at all timeslices") 542 return Corr(newcontent, padding=[0, 1]) 543 elif variant == "backward": 544 newcontent = [] 545 for t in range(1, self.T): 546 if (self.content[t - 1] is None) or (self.content[t] is None): 547 newcontent.append(None) 548 else: 549 newcontent.append(self.content[t] - self.content[t - 1]) 550 if (all([x is None for x in newcontent])): 551 raise Exception("Derivative is undefined at all timeslices") 552 return Corr(newcontent, padding=[1, 0]) 553 elif variant == "improved": 554 newcontent = [] 555 for t in range(2, self.T - 2): 556 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): 557 newcontent.append(None) 558 else: 559 newcontent.append((1 / 12) * (self.content[t - 2] - 8 * self.content[t - 1] + 8 * self.content[t + 1] - self.content[t + 2])) 560 if (all([x is None for x in newcontent])): 561 raise Exception('Derivative is undefined at all timeslices') 562 return Corr(newcontent, padding=[2, 2]) 563 elif variant == 'log': 564 newcontent = [] 565 for t in range(self.T): 566 if (self.content[t] is None) or (self.content[t] <= 0): 567 newcontent.append(None) 568 else: 569 newcontent.append(np.log(self.content[t])) 570 if (all([x is None for x in newcontent])): 571 raise Exception("Log is undefined at all timeslices") 572 logcorr = Corr(newcontent) 573 return self * logcorr.deriv('symmetric') 574 else: 575 raise Exception("Unknown variant.") 576 577 def second_deriv(self, variant="symmetric"): 578 """Return the second derivative of the correlator with respect to x0. 579 580 Parameters 581 ---------- 582 variant : str 583 decides which definition of the finite differences derivative is used. 584 Available choice: symmetric, improved, log, default: symmetric 585 """ 586 if self.N != 1: 587 raise Exception("second_deriv only implemented for one-dimensional correlators.") 588 if variant == "symmetric": 589 newcontent = [] 590 for t in range(1, self.T - 1): 591 if (self.content[t - 1] is None) or (self.content[t + 1] is None): 592 newcontent.append(None) 593 else: 594 newcontent.append((self.content[t + 1] - 2 * self.content[t] + self.content[t - 1])) 595 if (all([x is None for x in newcontent])): 596 raise Exception("Derivative is undefined at all timeslices") 597 return Corr(newcontent, padding=[1, 1]) 598 elif variant == "improved": 599 newcontent = [] 600 for t in range(2, self.T - 2): 601 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): 602 newcontent.append(None) 603 else: 604 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])) 605 if (all([x is None for x in newcontent])): 606 raise Exception("Derivative is undefined at all timeslices") 607 return Corr(newcontent, padding=[2, 2]) 608 elif variant == 'log': 609 newcontent = [] 610 for t in range(self.T): 611 if (self.content[t] is None) or (self.content[t] <= 0): 612 newcontent.append(None) 613 else: 614 newcontent.append(np.log(self.content[t])) 615 if (all([x is None for x in newcontent])): 616 raise Exception("Log is undefined at all timeslices") 617 logcorr = Corr(newcontent) 618 return self * (logcorr.second_deriv('symmetric') + (logcorr.deriv('symmetric'))**2) 619 else: 620 raise Exception("Unknown variant.") 621 622 def m_eff(self, variant='log', guess=1.0): 623 """Returns the effective mass of the correlator as correlator object 624 625 Parameters 626 ---------- 627 variant : str 628 log : uses the standard effective mass log(C(t) / C(t+1)) 629 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. 630 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. 631 See, e.g., arXiv:1205.5380 632 arccosh : Uses the explicit form of the symmetrized correlator (not recommended) 633 logsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2 634 guess : float 635 guess for the root finder, only relevant for the root variant 636 """ 637 if self.N != 1: 638 raise Exception('Correlator must be projected before getting m_eff') 639 if variant == 'log': 640 newcontent = [] 641 for t in range(self.T - 1): 642 if ((self.content[t] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0): 643 newcontent.append(None) 644 elif self.content[t][0].value / self.content[t + 1][0].value < 0: 645 newcontent.append(None) 646 else: 647 newcontent.append(self.content[t] / self.content[t + 1]) 648 if (all([x is None for x in newcontent])): 649 raise Exception('m_eff is undefined at all timeslices') 650 651 return np.log(Corr(newcontent, padding=[0, 1])) 652 653 elif variant == 'logsym': 654 newcontent = [] 655 for t in range(1, self.T - 1): 656 if ((self.content[t - 1] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0): 657 newcontent.append(None) 658 elif self.content[t - 1][0].value / self.content[t + 1][0].value < 0: 659 newcontent.append(None) 660 else: 661 newcontent.append(self.content[t - 1] / self.content[t + 1]) 662 if (all([x is None for x in newcontent])): 663 raise Exception('m_eff is undefined at all timeslices') 664 665 return np.log(Corr(newcontent, padding=[1, 1])) / 2 666 667 elif variant in ['periodic', 'cosh', 'sinh']: 668 if variant in ['periodic', 'cosh']: 669 func = anp.cosh 670 else: 671 func = anp.sinh 672 673 def root_function(x, d): 674 return func(x * (t - self.T / 2)) / func(x * (t + 1 - self.T / 2)) - d 675 676 newcontent = [] 677 for t in range(self.T - 1): 678 if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 1][0].value == 0): 679 newcontent.append(None) 680 # Fill the two timeslices in the middle of the lattice with their predecessors 681 elif variant == 'sinh' and t in [self.T / 2, self.T / 2 - 1]: 682 newcontent.append(newcontent[-1]) 683 elif self.content[t][0].value / self.content[t + 1][0].value < 0: 684 newcontent.append(None) 685 else: 686 newcontent.append(np.abs(find_root(self.content[t][0] / self.content[t + 1][0], root_function, guess=guess))) 687 if (all([x is None for x in newcontent])): 688 raise Exception('m_eff is undefined at all timeslices') 689 690 return Corr(newcontent, padding=[0, 1]) 691 692 elif variant == 'arccosh': 693 newcontent = [] 694 for t in range(1, self.T - 1): 695 if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t - 1] is None) or (self.content[t][0].value == 0): 696 newcontent.append(None) 697 else: 698 newcontent.append((self.content[t + 1] + self.content[t - 1]) / (2 * self.content[t])) 699 if (all([x is None for x in newcontent])): 700 raise Exception("m_eff is undefined at all timeslices") 701 return np.arccosh(Corr(newcontent, padding=[1, 1])) 702 703 else: 704 raise Exception('Unknown variant.') 705 706 def fit(self, function, fitrange=None, silent=False, **kwargs): 707 r'''Fits function to the data 708 709 Parameters 710 ---------- 711 function : obj 712 function to fit to the data. See fits.least_squares for details. 713 fitrange : list 714 Two element list containing the timeslices on which the fit is supposed to start and stop. 715 Caution: This range is inclusive as opposed to standard python indexing. 716 `fitrange=[4, 6]` corresponds to the three entries 4, 5 and 6. 717 If not specified, self.prange or all timeslices are used. 718 silent : bool 719 Decides whether output is printed to the standard output. 720 ''' 721 if self.N != 1: 722 raise Exception("Correlator must be projected before fitting") 723 724 if fitrange is None: 725 if self.prange: 726 fitrange = self.prange 727 else: 728 fitrange = [0, self.T - 1] 729 else: 730 if not isinstance(fitrange, list): 731 raise Exception("fitrange has to be a list with two elements") 732 if len(fitrange) != 2: 733 raise Exception("fitrange has to have exactly two elements [fit_start, fit_stop]") 734 735 xs = [x for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None] 736 ys = [self.content[x][0] for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None] 737 result = least_squares(xs, ys, function, silent=silent, **kwargs) 738 return result 739 740 def plateau(self, plateau_range=None, method="fit", auto_gamma=False): 741 """ Extract a plateau value from a Corr object 742 743 Parameters 744 ---------- 745 plateau_range : list 746 list with two entries, indicating the first and the last timeslice 747 of the plateau region. 748 method : str 749 method to extract the plateau. 750 'fit' fits a constant to the plateau region 751 'avg', 'average' or 'mean' just average over the given timeslices. 752 auto_gamma : bool 753 apply gamma_method with default parameters to the Corr. Defaults to None 754 """ 755 if not plateau_range: 756 if self.prange: 757 plateau_range = self.prange 758 else: 759 raise Exception("no plateau range provided") 760 if self.N != 1: 761 raise Exception("Correlator must be projected before getting a plateau.") 762 if (all([self.content[t] is None for t in range(plateau_range[0], plateau_range[1] + 1)])): 763 raise Exception("plateau is undefined at all timeslices in plateaurange.") 764 if auto_gamma: 765 self.gamma_method() 766 if method == "fit": 767 def const_func(a, t): 768 return a[0] 769 return self.fit(const_func, plateau_range)[0] 770 elif method in ["avg", "average", "mean"]: 771 returnvalue = np.mean([item[0] for item in self.content[plateau_range[0]:plateau_range[1] + 1] if item is not None]) 772 return returnvalue 773 774 else: 775 raise Exception("Unsupported plateau method: " + method) 776 777 def set_prange(self, prange): 778 """Sets the attribute prange of the Corr object.""" 779 if not len(prange) == 2: 780 raise Exception("prange must be a list or array with two values") 781 if not ((isinstance(prange[0], int)) and (isinstance(prange[1], int))): 782 raise Exception("Start and end point must be integers") 783 if not (0 <= prange[0] <= self.T and 0 <= prange[1] <= self.T and prange[0] < prange[1]): 784 raise Exception("Start and end point must define a range in the interval 0,T") 785 786 self.prange = prange 787 return 788 789 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, hide_sigma=None, references=None, title=None): 790 """Plots the correlator using the tag of the correlator as label if available. 791 792 Parameters 793 ---------- 794 x_range : list 795 list of two values, determining the range of the x-axis e.g. [4, 8]. 796 comp : Corr or list of Corr 797 Correlator or list of correlators which are plotted for comparison. 798 The tags of these correlators are used as labels if available. 799 logscale : bool 800 Sets y-axis to logscale. 801 plateau : Obs 802 Plateau value to be visualized in the figure. 803 fit_res : Fit_result 804 Fit_result object to be visualized. 805 ylabel : str 806 Label for the y-axis. 807 save : str 808 path to file in which the figure should be saved. 809 auto_gamma : bool 810 Apply the gamma method with standard parameters to all correlators and plateau values before plotting. 811 hide_sigma : float 812 Hides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors. 813 references : list 814 List of floating point values that are displayed as horizontal lines for reference. 815 title : string 816 Optional title of the figure. 817 """ 818 if self.N != 1: 819 raise Exception("Correlator must be projected before plotting") 820 821 if auto_gamma: 822 self.gamma_method() 823 824 if x_range is None: 825 x_range = [0, self.T - 1] 826 827 fig = plt.figure() 828 ax1 = fig.add_subplot(111) 829 830 x, y, y_err = self.plottable() 831 if hide_sigma: 832 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 833 else: 834 hide_from = None 835 ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=self.tag) 836 if logscale: 837 ax1.set_yscale('log') 838 else: 839 if y_range is None: 840 try: 841 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)]) 842 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)]) 843 ax1.set_ylim([y_min - 0.1 * (y_max - y_min), y_max + 0.1 * (y_max - y_min)]) 844 except Exception: 845 pass 846 else: 847 ax1.set_ylim(y_range) 848 if comp: 849 if isinstance(comp, (Corr, list)): 850 for corr in comp if isinstance(comp, list) else [comp]: 851 if auto_gamma: 852 corr.gamma_method() 853 x, y, y_err = corr.plottable() 854 if hide_sigma: 855 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 856 else: 857 hide_from = None 858 ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=corr.tag, mfc=plt.rcParams['axes.facecolor']) 859 else: 860 raise Exception("'comp' must be a correlator or a list of correlators.") 861 862 if plateau: 863 if isinstance(plateau, Obs): 864 if auto_gamma: 865 plateau.gamma_method() 866 ax1.axhline(y=plateau.value, linewidth=2, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--', label=str(plateau)) 867 ax1.axhspan(plateau.value - plateau.dvalue, plateau.value + plateau.dvalue, alpha=0.25, color=plt.rcParams['text.color'], ls='-') 868 else: 869 raise Exception("'plateau' must be an Obs") 870 871 if references: 872 if isinstance(references, list): 873 for ref in references: 874 ax1.axhline(y=ref, linewidth=1, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--') 875 else: 876 raise Exception("'references' must be a list of floating pint values.") 877 878 if self.prange: 879 ax1.axvline(self.prange[0], 0, 1, ls='-', marker=',') 880 ax1.axvline(self.prange[1], 0, 1, ls='-', marker=',') 881 882 if fit_res: 883 x_samples = np.arange(x_range[0], x_range[1] + 1, 0.05) 884 ax1.plot(x_samples, 885 fit_res.fit_function([o.value for o in fit_res.fit_parameters], x_samples), 886 ls='-', marker=',', lw=2) 887 888 ax1.set_xlabel(r'$x_0 / a$') 889 if ylabel: 890 ax1.set_ylabel(ylabel) 891 ax1.set_xlim([x_range[0] - 0.5, x_range[1] + 0.5]) 892 893 handles, labels = ax1.get_legend_handles_labels() 894 if labels: 895 ax1.legend() 896 897 if title: 898 plt.title(title) 899 900 plt.draw() 901 902 if save: 903 if isinstance(save, str): 904 fig.savefig(save, bbox_inches='tight') 905 else: 906 raise Exception("'save' has to be a string.") 907 908 def spaghetti_plot(self, logscale=True): 909 """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations. 910 911 Parameters 912 ---------- 913 logscale : bool 914 Determines whether the scale of the y-axis is logarithmic or standard. 915 """ 916 if self.N != 1: 917 raise Exception("Correlator needs to be projected first.") 918 919 mc_names = list(set([item for sublist in [sum(map(o[0].e_content.get, o[0].mc_names), []) for o in self.content if o is not None] for item in sublist])) 920 x0_vals = [n for (n, o) in zip(np.arange(self.T), self.content) if o is not None] 921 922 for name in mc_names: 923 data = np.array([o[0].deltas[name] + o[0].r_values[name] for o in self.content if o is not None]).T 924 925 fig = plt.figure() 926 ax = fig.add_subplot(111) 927 for dat in data: 928 ax.plot(x0_vals, dat, ls='-', marker='') 929 930 if logscale is True: 931 ax.set_yscale('log') 932 933 ax.set_xlabel(r'$x_0 / a$') 934 plt.title(name) 935 plt.draw() 936 937 def dump(self, filename, datatype="json.gz", **kwargs): 938 """Dumps the Corr into a file of chosen type 939 Parameters 940 ---------- 941 filename : str 942 Name of the file to be saved. 943 datatype : str 944 Format of the exported file. Supported formats include 945 "json.gz" and "pickle" 946 path : str 947 specifies a custom path for the file (default '.') 948 """ 949 if datatype == "json.gz": 950 from .input.json import dump_to_json 951 if 'path' in kwargs: 952 file_name = kwargs.get('path') + '/' + filename 953 else: 954 file_name = filename 955 dump_to_json(self, file_name) 956 elif datatype == "pickle": 957 dump_object(self, filename, **kwargs) 958 else: 959 raise Exception("Unknown datatype " + str(datatype)) 960 961 def print(self, print_range=None): 962 print(self.__repr__(print_range)) 963 964 def __repr__(self, print_range=None): 965 if print_range is None: 966 print_range = [0, None] 967 968 content_string = "" 969 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 970 971 if self.tag is not None: 972 content_string += "Description: " + self.tag + "\n" 973 if self.N != 1: 974 return content_string 975 if isinstance(self[0], CObs): 976 return content_string 977 978 if print_range[1]: 979 print_range[1] += 1 980 content_string += 'x0/a\tCorr(x0/a)\n------------------\n' 981 for i, sub_corr in enumerate(self.content[print_range[0]:print_range[1]]): 982 if sub_corr is None: 983 content_string += str(i + print_range[0]) + '\n' 984 else: 985 content_string += str(i + print_range[0]) 986 for element in sub_corr: 987 content_string += '\t' + ' ' * int(element >= 0) + str(element) 988 content_string += '\n' 989 return content_string 990 991 def __str__(self): 992 return self.__repr__() 993 994 # We define the basic operations, that can be performed with correlators. 995 # While */+- get defined here, they only work for Corr*Obs and not Obs*Corr. 996 # This is because Obs*Corr checks Obs.__mul__ first and does not catch an exception. 997 # One could try and tell Obs to check if the y in __mul__ is a Corr and 998 999 def __add__(self, y): 1000 if isinstance(y, Corr): 1001 if ((self.N != y.N) or (self.T != y.T)): 1002 raise Exception("Addition of Corrs with different shape") 1003 newcontent = [] 1004 for t in range(self.T): 1005 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): 1006 newcontent.append(None) 1007 else: 1008 newcontent.append(self.content[t] + y.content[t]) 1009 return Corr(newcontent) 1010 1011 elif isinstance(y, (Obs, int, float, CObs)): 1012 newcontent = [] 1013 for t in range(self.T): 1014 if _check_for_none(self, self.content[t]): 1015 newcontent.append(None) 1016 else: 1017 newcontent.append(self.content[t] + y) 1018 return Corr(newcontent, prange=self.prange) 1019 elif isinstance(y, np.ndarray): 1020 if y.shape == (self.T,): 1021 return Corr(list((np.array(self.content).T + y).T)) 1022 else: 1023 raise ValueError("operands could not be broadcast together") 1024 else: 1025 raise TypeError("Corr + wrong type") 1026 1027 def __mul__(self, y): 1028 if isinstance(y, Corr): 1029 if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): 1030 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") 1031 newcontent = [] 1032 for t in range(self.T): 1033 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): 1034 newcontent.append(None) 1035 else: 1036 newcontent.append(self.content[t] * y.content[t]) 1037 return Corr(newcontent) 1038 1039 elif isinstance(y, (Obs, int, float, CObs)): 1040 newcontent = [] 1041 for t in range(self.T): 1042 if _check_for_none(self, self.content[t]): 1043 newcontent.append(None) 1044 else: 1045 newcontent.append(self.content[t] * y) 1046 return Corr(newcontent, prange=self.prange) 1047 elif isinstance(y, np.ndarray): 1048 if y.shape == (self.T,): 1049 return Corr(list((np.array(self.content).T * y).T)) 1050 else: 1051 raise ValueError("operands could not be broadcast together") 1052 else: 1053 raise TypeError("Corr * wrong type") 1054 1055 def __truediv__(self, y): 1056 if isinstance(y, Corr): 1057 if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): 1058 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") 1059 newcontent = [] 1060 for t in range(self.T): 1061 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): 1062 newcontent.append(None) 1063 else: 1064 newcontent.append(self.content[t] / y.content[t]) 1065 for t in range(self.T): 1066 if _check_for_none(self, newcontent[t]): 1067 continue 1068 if np.isnan(np.sum(newcontent[t]).value): 1069 newcontent[t] = None 1070 1071 if all([item is None for item in newcontent]): 1072 raise Exception("Division returns completely undefined correlator") 1073 return Corr(newcontent) 1074 1075 elif isinstance(y, (Obs, CObs)): 1076 if isinstance(y, Obs): 1077 if y.value == 0: 1078 raise Exception('Division by zero will return undefined correlator') 1079 if isinstance(y, CObs): 1080 if y.is_zero(): 1081 raise Exception('Division by zero will return undefined correlator') 1082 1083 newcontent = [] 1084 for t in range(self.T): 1085 if _check_for_none(self, self.content[t]): 1086 newcontent.append(None) 1087 else: 1088 newcontent.append(self.content[t] / y) 1089 return Corr(newcontent, prange=self.prange) 1090 1091 elif isinstance(y, (int, float)): 1092 if y == 0: 1093 raise Exception('Division by zero will return undefined correlator') 1094 newcontent = [] 1095 for t in range(self.T): 1096 if _check_for_none(self, self.content[t]): 1097 newcontent.append(None) 1098 else: 1099 newcontent.append(self.content[t] / y) 1100 return Corr(newcontent, prange=self.prange) 1101 elif isinstance(y, np.ndarray): 1102 if y.shape == (self.T,): 1103 return Corr(list((np.array(self.content).T / y).T)) 1104 else: 1105 raise ValueError("operands could not be broadcast together") 1106 else: 1107 raise TypeError('Corr / wrong type') 1108 1109 def __neg__(self): 1110 newcontent = [None if _check_for_none(self, item) else -1. * item for item in self.content] 1111 return Corr(newcontent, prange=self.prange) 1112 1113 def __sub__(self, y): 1114 return self + (-y) 1115 1116 def __pow__(self, y): 1117 if isinstance(y, (Obs, int, float, CObs)): 1118 newcontent = [None if _check_for_none(self, item) else item**y for item in self.content] 1119 return Corr(newcontent, prange=self.prange) 1120 else: 1121 raise TypeError('Type of exponent not supported') 1122 1123 def __abs__(self): 1124 newcontent = [None if _check_for_none(self, item) else np.abs(item) for item in self.content] 1125 return Corr(newcontent, prange=self.prange) 1126 1127 # The numpy functions: 1128 def sqrt(self): 1129 return self ** 0.5 1130 1131 def log(self): 1132 newcontent = [None if _check_for_none(self, item) else np.log(item) for item in self.content] 1133 return Corr(newcontent, prange=self.prange) 1134 1135 def exp(self): 1136 newcontent = [None if _check_for_none(self, item) else np.exp(item) for item in self.content] 1137 return Corr(newcontent, prange=self.prange) 1138 1139 def _apply_func_to_corr(self, func): 1140 newcontent = [None if _check_for_none(self, item) else func(item) for item in self.content] 1141 for t in range(self.T): 1142 if _check_for_none(self, newcontent[t]): 1143 continue 1144 tmp_sum = np.sum(newcontent[t]) 1145 if hasattr(tmp_sum, "value"): 1146 if np.isnan(tmp_sum.value): 1147 newcontent[t] = None 1148 if all([item is None for item in newcontent]): 1149 raise Exception('Operation returns undefined correlator') 1150 return Corr(newcontent) 1151 1152 def sin(self): 1153 return self._apply_func_to_corr(np.sin) 1154 1155 def cos(self): 1156 return self._apply_func_to_corr(np.cos) 1157 1158 def tan(self): 1159 return self._apply_func_to_corr(np.tan) 1160 1161 def sinh(self): 1162 return self._apply_func_to_corr(np.sinh) 1163 1164 def cosh(self): 1165 return self._apply_func_to_corr(np.cosh) 1166 1167 def tanh(self): 1168 return self._apply_func_to_corr(np.tanh) 1169 1170 def arcsin(self): 1171 return self._apply_func_to_corr(np.arcsin) 1172 1173 def arccos(self): 1174 return self._apply_func_to_corr(np.arccos) 1175 1176 def arctan(self): 1177 return self._apply_func_to_corr(np.arctan) 1178 1179 def arcsinh(self): 1180 return self._apply_func_to_corr(np.arcsinh) 1181 1182 def arccosh(self): 1183 return self._apply_func_to_corr(np.arccosh) 1184 1185 def arctanh(self): 1186 return self._apply_func_to_corr(np.arctanh) 1187 1188 # Right hand side operations (require tweak in main module to work) 1189 def __radd__(self, y): 1190 return self + y 1191 1192 def __rsub__(self, y): 1193 return -self + y 1194 1195 def __rmul__(self, y): 1196 return self * y 1197 1198 def __rtruediv__(self, y): 1199 return (self / y) ** (-1) 1200 1201 @property 1202 def real(self): 1203 def return_real(obs_OR_cobs): 1204 if isinstance(obs_OR_cobs.flatten()[0], CObs): 1205 return np.vectorize(lambda x: x.real)(obs_OR_cobs) 1206 else: 1207 return obs_OR_cobs 1208 1209 return self._apply_func_to_corr(return_real) 1210 1211 @property 1212 def imag(self): 1213 def return_imag(obs_OR_cobs): 1214 if isinstance(obs_OR_cobs.flatten()[0], CObs): 1215 return np.vectorize(lambda x: x.imag)(obs_OR_cobs) 1216 else: 1217 return obs_OR_cobs * 0 # So it stays the right type 1218 1219 return self._apply_func_to_corr(return_imag) 1220 1221 def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None): 1222 r''' Project large correlation matrix to lowest states 1223 1224 This method can be used to reduce the size of an (N x N) correlation matrix 1225 to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise 1226 is still small. 1227 1228 Parameters 1229 ---------- 1230 Ntrunc: int 1231 Rank of the target matrix. 1232 tproj: int 1233 Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method. 1234 The default value is 3. 1235 t0proj: int 1236 Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly 1237 discouraged for O(a) improved theories, since the correctness of the procedure 1238 cannot be granted in this case. The default value is 2. 1239 basematrix : Corr 1240 Correlation matrix that is used to determine the eigenvectors of the 1241 lowest states based on a GEVP. basematrix is taken to be the Corr itself if 1242 is is not specified. 1243 1244 Notes 1245 ----- 1246 We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving 1247 the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$ 1248 and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the 1249 resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via 1250 $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large 1251 correlation matrix and to remove some noise that is added by irrelevant operators. 1252 This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated 1253 bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$. 1254 ''' 1255 1256 if self.N == 1: 1257 raise Exception('Method cannot be applied to one-dimensional correlators.') 1258 if basematrix is None: 1259 basematrix = self 1260 if Ntrunc >= basematrix.N: 1261 raise Exception('Cannot truncate using Ntrunc <= %d' % (basematrix.N)) 1262 if basematrix.N != self.N: 1263 raise Exception('basematrix and targetmatrix have to be of the same size.') 1264 1265 evecs = basematrix.GEVP(t0proj, tproj, sort=None)[:Ntrunc] 1266 1267 tmpmat = np.empty((Ntrunc, Ntrunc), dtype=object) 1268 rmat = [] 1269 for t in range(basematrix.T): 1270 for i in range(Ntrunc): 1271 for j in range(Ntrunc): 1272 tmpmat[i][j] = evecs[i].T @ self[t] @ evecs[j] 1273 rmat.append(np.copy(tmpmat)) 1274 1275 newcontent = [None if (self.content[t] is None) else rmat[t] for t in range(self.T)] 1276 return Corr(newcontent)
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.
27 def __init__(self, data_input, padding=[0, 0], prange=None): 28 """ Initialize a Corr object. 29 30 Parameters 31 ---------- 32 data_input : list or array 33 list of Obs or list of arrays of Obs or array of Corrs 34 padding : list, optional 35 List with two entries where the first labels the padding 36 at the front of the correlator and the second the padding 37 at the back. 38 prange : list, optional 39 List containing the first and last timeslice of the plateau 40 region indentified for this correlator. 41 """ 42 43 if isinstance(data_input, np.ndarray): 44 45 # This only works, if the array fulfills the conditions below 46 if not len(data_input.shape) == 2 and data_input.shape[0] == data_input.shape[1]: 47 raise Exception("Incompatible array shape") 48 if not all([isinstance(item, Corr) for item in data_input.flatten()]): 49 raise Exception("If the input is an array, its elements must be of type pe.Corr") 50 if not all([item.N == 1 for item in data_input.flatten()]): 51 raise Exception("Can only construct matrix correlator from single valued correlators") 52 if not len(set([item.T for item in data_input.flatten()])) == 1: 53 raise Exception("All input Correlators must be defined over the same timeslices.") 54 55 T = data_input[0, 0].T 56 N = data_input.shape[0] 57 input_as_list = [] 58 for t in range(T): 59 if any([(item.content[t] is None) for item in data_input.flatten()]): 60 if not all([(item.content[t] is None) for item in data_input.flatten()]): 61 warnings.warn("Input ill-defined at different timeslices. Conversion leads to data loss!", RuntimeWarning) 62 input_as_list.append(None) 63 else: 64 array_at_timeslace = np.empty([N, N], dtype="object") 65 for i in range(N): 66 for j in range(N): 67 array_at_timeslace[i, j] = data_input[i, j][t] 68 input_as_list.append(array_at_timeslace) 69 data_input = input_as_list 70 71 if isinstance(data_input, list): 72 73 if all([isinstance(item, (Obs, CObs)) or item is None for item in data_input]): 74 _assert_equal_properties([o for o in data_input if o is not None]) 75 self.content = [np.asarray([item]) if item is not None else None for item in data_input] 76 self.N = 1 77 78 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]): 79 self.content = data_input 80 noNull = [a for a in self.content if not (a is None)] # To check if the matrices are correct for all undefined elements 81 self.N = noNull[0].shape[0] 82 if self.N > 1 and noNull[0].shape[0] != noNull[0].shape[1]: 83 raise Exception("Smearing matrices are not NxN") 84 if (not all([item.shape == noNull[0].shape for item in noNull])): 85 raise Exception("Items in data_input are not of identical shape." + str(noNull)) 86 else: 87 raise Exception("data_input contains item of wrong type") 88 else: 89 raise Exception("Data input was not given as list or correct array") 90 91 self.tag = None 92 93 # An undefined timeslice is represented by the None object 94 self.content = [None] * padding[0] + self.content + [None] * padding[1] 95 self.T = len(self.content) 96 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.
117 def gamma_method(self, **kwargs): 118 """Apply the gamma method to the content of the Corr.""" 119 for item in self.content: 120 if not (item is None): 121 if self.N == 1: 122 item[0].gamma_method(**kwargs) 123 else: 124 for i in range(self.N): 125 for j in range(self.N): 126 item[i, j].gamma_method(**kwargs)
Apply the gamma method to the content of the Corr.
117 def gamma_method(self, **kwargs): 118 """Apply the gamma method to the content of the Corr.""" 119 for item in self.content: 120 if not (item is None): 121 if self.N == 1: 122 item[0].gamma_method(**kwargs) 123 else: 124 for i in range(self.N): 125 for j in range(self.N): 126 item[i, j].gamma_method(**kwargs)
Apply the gamma method to the content of the Corr.
130 def projected(self, vector_l=None, vector_r=None, normalize=False): 131 """We need to project the Correlator with a Vector to get a single value at each timeslice. 132 133 The method can use one or two vectors. 134 If two are specified it returns v1@G@v2 (the order might be very important.) 135 By default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to 136 """ 137 if self.N == 1: 138 raise Exception("Trying to project a Corr, that already has N=1.") 139 140 if vector_l is None: 141 vector_l, vector_r = np.asarray([1.] + (self.N - 1) * [0.]), np.asarray([1.] + (self.N - 1) * [0.]) 142 elif (vector_r is None): 143 vector_r = vector_l 144 if isinstance(vector_l, list) and not isinstance(vector_r, list): 145 if len(vector_l) != self.T: 146 raise Exception("Length of vector list must be equal to T") 147 vector_r = [vector_r] * self.T 148 if isinstance(vector_r, list) and not isinstance(vector_l, list): 149 if len(vector_r) != self.T: 150 raise Exception("Length of vector list must be equal to T") 151 vector_l = [vector_l] * self.T 152 153 if not isinstance(vector_l, list): 154 if not vector_l.shape == vector_r.shape == (self.N,): 155 raise Exception("Vectors are of wrong shape!") 156 if normalize: 157 vector_l, vector_r = vector_l / np.sqrt((vector_l @ vector_l)), vector_r / np.sqrt(vector_r @ vector_r) 158 newcontent = [None if _check_for_none(self, item) else np.asarray([vector_l.T @ item @ vector_r]) for item in self.content] 159 160 else: 161 # There are no checks here yet. There are so many possible scenarios, where this can go wrong. 162 if normalize: 163 for t in range(self.T): 164 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]) 165 166 newcontent = [None if (_check_for_none(self, self.content[t]) 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)] 167 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
169 def item(self, i, j): 170 """Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice. 171 172 Parameters 173 ---------- 174 i : int 175 First index to be picked. 176 j : int 177 Second index to be picked. 178 """ 179 if self.N == 1: 180 raise Exception("Trying to pick item from projected Corr") 181 newcontent = [None if (item is None) else item[i, j] for item in self.content] 182 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.
184 def plottable(self): 185 """Outputs the correlator in a plotable format. 186 187 Outputs three lists containing the timeslice index, the value on each 188 timeslice and the error on each timeslice. 189 """ 190 if self.N != 1: 191 raise Exception("Can only make Corr[N=1] plottable") 192 x_list = [x for x in range(self.T) if not self.content[x] is None] 193 y_list = [y[0].value for y in self.content if y is not None] 194 y_err_list = [y[0].dvalue for y in self.content if y is not None] 195 196 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.
198 def symmetric(self): 199 """ Symmetrize the correlator around x0=0.""" 200 if self.N != 1: 201 raise Exception('symmetric cannot be safely applied to multi-dimensional correlators.') 202 if self.T % 2 != 0: 203 raise Exception("Can not symmetrize odd T") 204 205 if np.argmax(np.abs(self.content)) != 0: 206 warnings.warn("Correlator does not seem to be symmetric around x0=0.", RuntimeWarning) 207 208 newcontent = [self.content[0]] 209 for t in range(1, self.T): 210 if (self.content[t] is None) or (self.content[self.T - t] is None): 211 newcontent.append(None) 212 else: 213 newcontent.append(0.5 * (self.content[t] + self.content[self.T - t])) 214 if (all([x is None for x in newcontent])): 215 raise Exception("Corr could not be symmetrized: No redundant values") 216 return Corr(newcontent, prange=self.prange)
Symmetrize the correlator around x0=0.
218 def anti_symmetric(self): 219 """Anti-symmetrize the correlator around x0=0.""" 220 if self.N != 1: 221 raise Exception('anti_symmetric cannot be safely applied to multi-dimensional correlators.') 222 if self.T % 2 != 0: 223 raise Exception("Can not symmetrize odd T") 224 225 test = 1 * self 226 test.gamma_method() 227 if not all([o.is_zero_within_error(3) for o in test.content[0]]): 228 warnings.warn("Correlator does not seem to be anti-symmetric around x0=0.", RuntimeWarning) 229 230 newcontent = [self.content[0]] 231 for t in range(1, self.T): 232 if (self.content[t] is None) or (self.content[self.T - t] is None): 233 newcontent.append(None) 234 else: 235 newcontent.append(0.5 * (self.content[t] - self.content[self.T - t])) 236 if (all([x is None for x in newcontent])): 237 raise Exception("Corr could not be symmetrized: No redundant values") 238 return Corr(newcontent, prange=self.prange)
Anti-symmetrize the correlator around x0=0.
240 def is_matrix_symmetric(self): 241 """Checks whether a correlator matrices is symmetric on every timeslice.""" 242 if self.N == 1: 243 raise Exception("Only works for correlator matrices.") 244 for t in range(self.T): 245 if self[t] is None: 246 continue 247 for i in range(self.N): 248 for j in range(i + 1, self.N): 249 if self[t][i, j] is self[t][j, i]: 250 continue 251 if hash(self[t][i, j]) != hash(self[t][j, i]): 252 return False 253 return True
Checks whether a correlator matrices is symmetric on every timeslice.
255 def matrix_symmetric(self): 256 """Symmetrizes the correlator matrices on every timeslice.""" 257 if self.N == 1: 258 raise Exception("Trying to symmetrize a correlator matrix, that already has N=1.") 259 if self.is_matrix_symmetric(): 260 return 1.0 * self 261 else: 262 transposed = [None if _check_for_none(self, G) else G.T for G in self.content] 263 return 0.5 * (Corr(transposed) + self)
Symmetrizes the correlator matrices on every timeslice.
265 def GEVP(self, t0, ts=None, sort="Eigenvalue", **kwargs): 266 r'''Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors. 267 268 The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the 269 largest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing 270 ```python 271 C.GEVP(t0=2)[0] # Ground state vector(s) 272 C.GEVP(t0=2)[:3] # Vectors for the lowest three states 273 ``` 274 275 Parameters 276 ---------- 277 t0 : int 278 The time t0 for the right hand side of the GEVP according to $G(t)v_i=\lambda_i G(t_0)v_i$ 279 ts : int 280 fixed time $G(t_s)v_i=\lambda_i G(t_0)v_i$ if sort=None. 281 If sort="Eigenvector" it gives a reference point for the sorting method. 282 sort : string 283 If this argument is set, a list of self.T vectors per state is returned. If it is set to None, only one vector is returned. 284 - "Eigenvalue": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice. 285 - "Eigenvector": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state. 286 The reference state is identified by its eigenvalue at $t=t_s$. 287 288 Other Parameters 289 ---------------- 290 state : int 291 Returns only the vector(s) for a specified state. The lowest state is zero. 292 ''' 293 294 if self.N == 1: 295 raise Exception("GEVP methods only works on correlator matrices and not single correlators.") 296 if ts is not None: 297 if (ts <= t0): 298 raise Exception("ts has to be larger than t0.") 299 300 if "sorted_list" in kwargs: 301 warnings.warn("Argument 'sorted_list' is deprecated, use 'sort' instead.", DeprecationWarning) 302 sort = kwargs.get("sorted_list") 303 304 if self.is_matrix_symmetric(): 305 symmetric_corr = self 306 else: 307 symmetric_corr = self.matrix_symmetric() 308 309 G0 = np.vectorize(lambda x: x.value)(symmetric_corr[t0]) 310 np.linalg.cholesky(G0) # Check if matrix G0 is positive-semidefinite. 311 312 if sort is None: 313 if (ts is None): 314 raise Exception("ts is required if sort=None.") 315 if (self.content[t0] is None) or (self.content[ts] is None): 316 raise Exception("Corr not defined at t0/ts.") 317 Gt = np.vectorize(lambda x: x.value)(symmetric_corr[ts]) 318 reordered_vecs = _GEVP_solver(Gt, G0) 319 320 elif sort in ["Eigenvalue", "Eigenvector"]: 321 if sort == "Eigenvalue" and ts is not None: 322 warnings.warn("ts has no effect when sorting by eigenvalue is chosen.", RuntimeWarning) 323 all_vecs = [None] * (t0 + 1) 324 for t in range(t0 + 1, self.T): 325 try: 326 Gt = np.vectorize(lambda x: x.value)(symmetric_corr[t]) 327 all_vecs.append(_GEVP_solver(Gt, G0)) 328 except Exception: 329 all_vecs.append(None) 330 if sort == "Eigenvector": 331 if ts is None: 332 raise Exception("ts is required for the Eigenvector sorting method.") 333 all_vecs = _sort_vectors(all_vecs, ts) 334 335 reordered_vecs = [[v[s] if v is not None else None for v in all_vecs] for s in range(self.N)] 336 else: 337 raise Exception("Unkown value for 'sort'.") 338 339 if "state" in kwargs: 340 return reordered_vecs[kwargs.get("state")] 341 else: 342 return reordered_vecs
Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors.
The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the largest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing
C.GEVP(t0=2)[0] # Ground state vector(s)
C.GEVP(t0=2)[:3] # Vectors for the lowest three states
Parameters
- t0 (int): The time t0 for the right hand side of the GEVP according to $G(t)v_i=\lambda_i G(t_0)v_i$
- ts (int): fixed time $G(t_s)v_i=\lambda_i G(t_0)v_i$ if sort=None. If sort="Eigenvector" it gives a reference point for the sorting method.
- sort (string):
If this argument is set, a list of self.T vectors per state is returned. If it is set to None, only one vector is returned.
- "Eigenvalue": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice.
- "Eigenvector": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state. The reference state is identified by its eigenvalue at $t=t_s$.
Other Parameters
- state (int): Returns only the vector(s) for a specified state. The lowest state is zero.
344 def Eigenvalue(self, t0, ts=None, state=0, sort="Eigenvalue"): 345 """Determines the eigenvalue of the GEVP by solving and projecting the correlator 346 347 Parameters 348 ---------- 349 state : int 350 The state one is interested in ordered by energy. The lowest state is zero. 351 352 All other parameters are identical to the ones of Corr.GEVP. 353 """ 354 vec = self.GEVP(t0, ts=ts, sort=sort)[state] 355 return self.projected(vec)
Determines the eigenvalue of the GEVP by solving and projecting the correlator
Parameters
- state (int): The state one is interested in ordered by energy. The lowest state is zero.
- All other parameters are identical to the ones of Corr.GEVP.
357 def Hankel(self, N, periodic=False): 358 """Constructs an NxN Hankel matrix 359 360 C(t) c(t+1) ... c(t+n-1) 361 C(t+1) c(t+2) ... c(t+n) 362 ................. 363 C(t+(n-1)) c(t+n) ... c(t+2(n-1)) 364 365 Parameters 366 ---------- 367 N : int 368 Dimension of the Hankel matrix 369 periodic : bool, optional 370 determines whether the matrix is extended periodically 371 """ 372 373 if self.N != 1: 374 raise Exception("Multi-operator Prony not implemented!") 375 376 array = np.empty([N, N], dtype="object") 377 new_content = [] 378 for t in range(self.T): 379 new_content.append(array.copy()) 380 381 def wrap(i): 382 while i >= self.T: 383 i -= self.T 384 return i 385 386 for t in range(self.T): 387 for i in range(N): 388 for j in range(N): 389 if periodic: 390 new_content[t][i, j] = self.content[wrap(t + i + j)][0] 391 elif (t + i + j) >= self.T: 392 new_content[t] = None 393 else: 394 new_content[t][i, j] = self.content[t + i + j][0] 395 396 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
398 def roll(self, dt): 399 """Periodically shift the correlator by dt timeslices 400 401 Parameters 402 ---------- 403 dt : int 404 number of timeslices 405 """ 406 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
408 def reverse(self): 409 """Reverse the time ordering of the Corr""" 410 return Corr(self.content[:: -1])
Reverse the time ordering of the Corr
412 def thin(self, spacing=2, offset=0): 413 """Thin out a correlator to suppress correlations 414 415 Parameters 416 ---------- 417 spacing : int 418 Keep only every 'spacing'th entry of the correlator 419 offset : int 420 Offset the equal spacing 421 """ 422 new_content = [] 423 for t in range(self.T): 424 if (offset + t) % spacing != 0: 425 new_content.append(None) 426 else: 427 new_content.append(self.content[t]) 428 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
430 def correlate(self, partner): 431 """Correlate the correlator with another correlator or Obs 432 433 Parameters 434 ---------- 435 partner : Obs or Corr 436 partner to correlate the correlator with. 437 Can either be an Obs which is correlated with all entries of the 438 correlator or a Corr of same length. 439 """ 440 if self.N != 1: 441 raise Exception("Only one-dimensional correlators can be safely correlated.") 442 new_content = [] 443 for x0, t_slice in enumerate(self.content): 444 if _check_for_none(self, t_slice): 445 new_content.append(None) 446 else: 447 if isinstance(partner, Corr): 448 if _check_for_none(partner, partner.content[x0]): 449 new_content.append(None) 450 else: 451 new_content.append(np.array([correlate(o, partner.content[x0][0]) for o in t_slice])) 452 elif isinstance(partner, Obs): # Should this include CObs? 453 new_content.append(np.array([correlate(o, partner) for o in t_slice])) 454 else: 455 raise Exception("Can only correlate with an Obs or a Corr.") 456 457 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.
459 def reweight(self, weight, **kwargs): 460 """Reweight the correlator. 461 462 Parameters 463 ---------- 464 weight : Obs 465 Reweighting factor. An Observable that has to be defined on a superset of the 466 configurations in obs[i].idl for all i. 467 all_configs : bool 468 if True, the reweighted observables are normalized by the average of 469 the reweighting factor on all configurations in weight.idl and not 470 on the configurations in obs[i].idl. 471 """ 472 if self.N != 1: 473 raise Exception("Reweighting only implemented for one-dimensional correlators.") 474 new_content = [] 475 for t_slice in self.content: 476 if _check_for_none(self, t_slice): 477 new_content.append(None) 478 else: 479 new_content.append(np.array(reweight(weight, t_slice, **kwargs))) 480 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.
482 def T_symmetry(self, partner, parity=+1): 483 """Return the time symmetry average of the correlator and its partner 484 485 Parameters 486 ---------- 487 partner : Corr 488 Time symmetry partner of the Corr 489 partity : int 490 Parity quantum number of the correlator, can be +1 or -1 491 """ 492 if self.N != 1: 493 raise Exception("T_symmetry only implemented for one-dimensional correlators.") 494 if not isinstance(partner, Corr): 495 raise Exception("T partner has to be a Corr object.") 496 if parity not in [+1, -1]: 497 raise Exception("Parity has to be +1 or -1.") 498 T_partner = parity * partner.reverse() 499 500 t_slices = [] 501 test = (self - T_partner) 502 test.gamma_method() 503 for x0, t_slice in enumerate(test.content): 504 if t_slice is not None: 505 if not t_slice[0].is_zero_within_error(5): 506 t_slices.append(x0) 507 if t_slices: 508 warnings.warn("T symmetry partners do not agree within 5 sigma on time slices " + str(t_slices) + ".", RuntimeWarning) 509 510 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
512 def deriv(self, variant="symmetric"): 513 """Return the first derivative of the correlator with respect to x0. 514 515 Parameters 516 ---------- 517 variant : str 518 decides which definition of the finite differences derivative is used. 519 Available choice: symmetric, forward, backward, improved, log, default: symmetric 520 """ 521 if self.N != 1: 522 raise Exception("deriv only implemented for one-dimensional correlators.") 523 if variant == "symmetric": 524 newcontent = [] 525 for t in range(1, self.T - 1): 526 if (self.content[t - 1] is None) or (self.content[t + 1] is None): 527 newcontent.append(None) 528 else: 529 newcontent.append(0.5 * (self.content[t + 1] - self.content[t - 1])) 530 if (all([x is None for x in newcontent])): 531 raise Exception('Derivative is undefined at all timeslices') 532 return Corr(newcontent, padding=[1, 1]) 533 elif variant == "forward": 534 newcontent = [] 535 for t in range(self.T - 1): 536 if (self.content[t] is None) or (self.content[t + 1] is None): 537 newcontent.append(None) 538 else: 539 newcontent.append(self.content[t + 1] - self.content[t]) 540 if (all([x is None for x in newcontent])): 541 raise Exception("Derivative is undefined at all timeslices") 542 return Corr(newcontent, padding=[0, 1]) 543 elif variant == "backward": 544 newcontent = [] 545 for t in range(1, self.T): 546 if (self.content[t - 1] is None) or (self.content[t] is None): 547 newcontent.append(None) 548 else: 549 newcontent.append(self.content[t] - self.content[t - 1]) 550 if (all([x is None for x in newcontent])): 551 raise Exception("Derivative is undefined at all timeslices") 552 return Corr(newcontent, padding=[1, 0]) 553 elif variant == "improved": 554 newcontent = [] 555 for t in range(2, self.T - 2): 556 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): 557 newcontent.append(None) 558 else: 559 newcontent.append((1 / 12) * (self.content[t - 2] - 8 * self.content[t - 1] + 8 * self.content[t + 1] - self.content[t + 2])) 560 if (all([x is None for x in newcontent])): 561 raise Exception('Derivative is undefined at all timeslices') 562 return Corr(newcontent, padding=[2, 2]) 563 elif variant == 'log': 564 newcontent = [] 565 for t in range(self.T): 566 if (self.content[t] is None) or (self.content[t] <= 0): 567 newcontent.append(None) 568 else: 569 newcontent.append(np.log(self.content[t])) 570 if (all([x is None for x in newcontent])): 571 raise Exception("Log is undefined at all timeslices") 572 logcorr = Corr(newcontent) 573 return self * logcorr.deriv('symmetric') 574 else: 575 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, log, default: symmetric
577 def second_deriv(self, variant="symmetric"): 578 """Return the second derivative of the correlator with respect to x0. 579 580 Parameters 581 ---------- 582 variant : str 583 decides which definition of the finite differences derivative is used. 584 Available choice: symmetric, improved, log, default: symmetric 585 """ 586 if self.N != 1: 587 raise Exception("second_deriv only implemented for one-dimensional correlators.") 588 if variant == "symmetric": 589 newcontent = [] 590 for t in range(1, self.T - 1): 591 if (self.content[t - 1] is None) or (self.content[t + 1] is None): 592 newcontent.append(None) 593 else: 594 newcontent.append((self.content[t + 1] - 2 * self.content[t] + self.content[t - 1])) 595 if (all([x is None for x in newcontent])): 596 raise Exception("Derivative is undefined at all timeslices") 597 return Corr(newcontent, padding=[1, 1]) 598 elif variant == "improved": 599 newcontent = [] 600 for t in range(2, self.T - 2): 601 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): 602 newcontent.append(None) 603 else: 604 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])) 605 if (all([x is None for x in newcontent])): 606 raise Exception("Derivative is undefined at all timeslices") 607 return Corr(newcontent, padding=[2, 2]) 608 elif variant == 'log': 609 newcontent = [] 610 for t in range(self.T): 611 if (self.content[t] is None) or (self.content[t] <= 0): 612 newcontent.append(None) 613 else: 614 newcontent.append(np.log(self.content[t])) 615 if (all([x is None for x in newcontent])): 616 raise Exception("Log is undefined at all timeslices") 617 logcorr = Corr(newcontent) 618 return self * (logcorr.second_deriv('symmetric') + (logcorr.deriv('symmetric'))**2) 619 else: 620 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, log, default: symmetric
622 def m_eff(self, variant='log', guess=1.0): 623 """Returns the effective mass of the correlator as correlator object 624 625 Parameters 626 ---------- 627 variant : str 628 log : uses the standard effective mass log(C(t) / C(t+1)) 629 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. 630 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. 631 See, e.g., arXiv:1205.5380 632 arccosh : Uses the explicit form of the symmetrized correlator (not recommended) 633 logsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2 634 guess : float 635 guess for the root finder, only relevant for the root variant 636 """ 637 if self.N != 1: 638 raise Exception('Correlator must be projected before getting m_eff') 639 if variant == 'log': 640 newcontent = [] 641 for t in range(self.T - 1): 642 if ((self.content[t] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0): 643 newcontent.append(None) 644 elif self.content[t][0].value / self.content[t + 1][0].value < 0: 645 newcontent.append(None) 646 else: 647 newcontent.append(self.content[t] / self.content[t + 1]) 648 if (all([x is None for x in newcontent])): 649 raise Exception('m_eff is undefined at all timeslices') 650 651 return np.log(Corr(newcontent, padding=[0, 1])) 652 653 elif variant == 'logsym': 654 newcontent = [] 655 for t in range(1, self.T - 1): 656 if ((self.content[t - 1] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0): 657 newcontent.append(None) 658 elif self.content[t - 1][0].value / self.content[t + 1][0].value < 0: 659 newcontent.append(None) 660 else: 661 newcontent.append(self.content[t - 1] / self.content[t + 1]) 662 if (all([x is None for x in newcontent])): 663 raise Exception('m_eff is undefined at all timeslices') 664 665 return np.log(Corr(newcontent, padding=[1, 1])) / 2 666 667 elif variant in ['periodic', 'cosh', 'sinh']: 668 if variant in ['periodic', 'cosh']: 669 func = anp.cosh 670 else: 671 func = anp.sinh 672 673 def root_function(x, d): 674 return func(x * (t - self.T / 2)) / func(x * (t + 1 - self.T / 2)) - d 675 676 newcontent = [] 677 for t in range(self.T - 1): 678 if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 1][0].value == 0): 679 newcontent.append(None) 680 # Fill the two timeslices in the middle of the lattice with their predecessors 681 elif variant == 'sinh' and t in [self.T / 2, self.T / 2 - 1]: 682 newcontent.append(newcontent[-1]) 683 elif self.content[t][0].value / self.content[t + 1][0].value < 0: 684 newcontent.append(None) 685 else: 686 newcontent.append(np.abs(find_root(self.content[t][0] / self.content[t + 1][0], root_function, guess=guess))) 687 if (all([x is None for x in newcontent])): 688 raise Exception('m_eff is undefined at all timeslices') 689 690 return Corr(newcontent, padding=[0, 1]) 691 692 elif variant == 'arccosh': 693 newcontent = [] 694 for t in range(1, self.T - 1): 695 if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t - 1] is None) or (self.content[t][0].value == 0): 696 newcontent.append(None) 697 else: 698 newcontent.append((self.content[t + 1] + self.content[t - 1]) / (2 * self.content[t])) 699 if (all([x is None for x in newcontent])): 700 raise Exception("m_eff is undefined at all timeslices") 701 return np.arccosh(Corr(newcontent, padding=[1, 1])) 702 703 else: 704 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) logsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2
- guess (float): guess for the root finder, only relevant for the root variant
706 def fit(self, function, fitrange=None, silent=False, **kwargs): 707 r'''Fits function to the data 708 709 Parameters 710 ---------- 711 function : obj 712 function to fit to the data. See fits.least_squares for details. 713 fitrange : list 714 Two element list containing the timeslices on which the fit is supposed to start and stop. 715 Caution: This range is inclusive as opposed to standard python indexing. 716 `fitrange=[4, 6]` corresponds to the three entries 4, 5 and 6. 717 If not specified, self.prange or all timeslices are used. 718 silent : bool 719 Decides whether output is printed to the standard output. 720 ''' 721 if self.N != 1: 722 raise Exception("Correlator must be projected before fitting") 723 724 if fitrange is None: 725 if self.prange: 726 fitrange = self.prange 727 else: 728 fitrange = [0, self.T - 1] 729 else: 730 if not isinstance(fitrange, list): 731 raise Exception("fitrange has to be a list with two elements") 732 if len(fitrange) != 2: 733 raise Exception("fitrange has to have exactly two elements [fit_start, fit_stop]") 734 735 xs = [x for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None] 736 ys = [self.content[x][0] for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None] 737 result = least_squares(xs, ys, function, silent=silent, **kwargs) 738 return result
Fits function to the data
Parameters
- function (obj): function to fit to the data. See fits.least_squares for details.
- fitrange (list):
Two element list containing the timeslices on which the fit is supposed to start and stop.
Caution: This range is inclusive as opposed to standard python indexing.
fitrange=[4, 6]
corresponds to the three entries 4, 5 and 6. If not specified, self.prange or all timeslices are used. - silent (bool): Decides whether output is printed to the standard output.
740 def plateau(self, plateau_range=None, method="fit", auto_gamma=False): 741 """ Extract a plateau value from a Corr object 742 743 Parameters 744 ---------- 745 plateau_range : list 746 list with two entries, indicating the first and the last timeslice 747 of the plateau region. 748 method : str 749 method to extract the plateau. 750 'fit' fits a constant to the plateau region 751 'avg', 'average' or 'mean' just average over the given timeslices. 752 auto_gamma : bool 753 apply gamma_method with default parameters to the Corr. Defaults to None 754 """ 755 if not plateau_range: 756 if self.prange: 757 plateau_range = self.prange 758 else: 759 raise Exception("no plateau range provided") 760 if self.N != 1: 761 raise Exception("Correlator must be projected before getting a plateau.") 762 if (all([self.content[t] is None for t in range(plateau_range[0], plateau_range[1] + 1)])): 763 raise Exception("plateau is undefined at all timeslices in plateaurange.") 764 if auto_gamma: 765 self.gamma_method() 766 if method == "fit": 767 def const_func(a, t): 768 return a[0] 769 return self.fit(const_func, plateau_range)[0] 770 elif method in ["avg", "average", "mean"]: 771 returnvalue = np.mean([item[0] for item in self.content[plateau_range[0]:plateau_range[1] + 1] if item is not None]) 772 return returnvalue 773 774 else: 775 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
777 def set_prange(self, prange): 778 """Sets the attribute prange of the Corr object.""" 779 if not len(prange) == 2: 780 raise Exception("prange must be a list or array with two values") 781 if not ((isinstance(prange[0], int)) and (isinstance(prange[1], int))): 782 raise Exception("Start and end point must be integers") 783 if not (0 <= prange[0] <= self.T and 0 <= prange[1] <= self.T and prange[0] < prange[1]): 784 raise Exception("Start and end point must define a range in the interval 0,T") 785 786 self.prange = prange 787 return
Sets the attribute prange of the Corr object.
789 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, hide_sigma=None, references=None, title=None): 790 """Plots the correlator using the tag of the correlator as label if available. 791 792 Parameters 793 ---------- 794 x_range : list 795 list of two values, determining the range of the x-axis e.g. [4, 8]. 796 comp : Corr or list of Corr 797 Correlator or list of correlators which are plotted for comparison. 798 The tags of these correlators are used as labels if available. 799 logscale : bool 800 Sets y-axis to logscale. 801 plateau : Obs 802 Plateau value to be visualized in the figure. 803 fit_res : Fit_result 804 Fit_result object to be visualized. 805 ylabel : str 806 Label for the y-axis. 807 save : str 808 path to file in which the figure should be saved. 809 auto_gamma : bool 810 Apply the gamma method with standard parameters to all correlators and plateau values before plotting. 811 hide_sigma : float 812 Hides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors. 813 references : list 814 List of floating point values that are displayed as horizontal lines for reference. 815 title : string 816 Optional title of the figure. 817 """ 818 if self.N != 1: 819 raise Exception("Correlator must be projected before plotting") 820 821 if auto_gamma: 822 self.gamma_method() 823 824 if x_range is None: 825 x_range = [0, self.T - 1] 826 827 fig = plt.figure() 828 ax1 = fig.add_subplot(111) 829 830 x, y, y_err = self.plottable() 831 if hide_sigma: 832 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 833 else: 834 hide_from = None 835 ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=self.tag) 836 if logscale: 837 ax1.set_yscale('log') 838 else: 839 if y_range is None: 840 try: 841 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)]) 842 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)]) 843 ax1.set_ylim([y_min - 0.1 * (y_max - y_min), y_max + 0.1 * (y_max - y_min)]) 844 except Exception: 845 pass 846 else: 847 ax1.set_ylim(y_range) 848 if comp: 849 if isinstance(comp, (Corr, list)): 850 for corr in comp if isinstance(comp, list) else [comp]: 851 if auto_gamma: 852 corr.gamma_method() 853 x, y, y_err = corr.plottable() 854 if hide_sigma: 855 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 856 else: 857 hide_from = None 858 ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=corr.tag, mfc=plt.rcParams['axes.facecolor']) 859 else: 860 raise Exception("'comp' must be a correlator or a list of correlators.") 861 862 if plateau: 863 if isinstance(plateau, Obs): 864 if auto_gamma: 865 plateau.gamma_method() 866 ax1.axhline(y=plateau.value, linewidth=2, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--', label=str(plateau)) 867 ax1.axhspan(plateau.value - plateau.dvalue, plateau.value + plateau.dvalue, alpha=0.25, color=plt.rcParams['text.color'], ls='-') 868 else: 869 raise Exception("'plateau' must be an Obs") 870 871 if references: 872 if isinstance(references, list): 873 for ref in references: 874 ax1.axhline(y=ref, linewidth=1, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--') 875 else: 876 raise Exception("'references' must be a list of floating pint values.") 877 878 if self.prange: 879 ax1.axvline(self.prange[0], 0, 1, ls='-', marker=',') 880 ax1.axvline(self.prange[1], 0, 1, ls='-', marker=',') 881 882 if fit_res: 883 x_samples = np.arange(x_range[0], x_range[1] + 1, 0.05) 884 ax1.plot(x_samples, 885 fit_res.fit_function([o.value for o in fit_res.fit_parameters], x_samples), 886 ls='-', marker=',', lw=2) 887 888 ax1.set_xlabel(r'$x_0 / a$') 889 if ylabel: 890 ax1.set_ylabel(ylabel) 891 ax1.set_xlim([x_range[0] - 0.5, x_range[1] + 0.5]) 892 893 handles, labels = ax1.get_legend_handles_labels() 894 if labels: 895 ax1.legend() 896 897 if title: 898 plt.title(title) 899 900 plt.draw() 901 902 if save: 903 if isinstance(save, str): 904 fig.savefig(save, bbox_inches='tight') 905 else: 906 raise Exception("'save' has to be a string.")
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.
- hide_sigma (float): Hides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.
- references (list): List of floating point values that are displayed as horizontal lines for reference.
- title (string): Optional title of the figure.
908 def spaghetti_plot(self, logscale=True): 909 """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations. 910 911 Parameters 912 ---------- 913 logscale : bool 914 Determines whether the scale of the y-axis is logarithmic or standard. 915 """ 916 if self.N != 1: 917 raise Exception("Correlator needs to be projected first.") 918 919 mc_names = list(set([item for sublist in [sum(map(o[0].e_content.get, o[0].mc_names), []) for o in self.content if o is not None] for item in sublist])) 920 x0_vals = [n for (n, o) in zip(np.arange(self.T), self.content) if o is not None] 921 922 for name in mc_names: 923 data = np.array([o[0].deltas[name] + o[0].r_values[name] for o in self.content if o is not None]).T 924 925 fig = plt.figure() 926 ax = fig.add_subplot(111) 927 for dat in data: 928 ax.plot(x0_vals, dat, ls='-', marker='') 929 930 if logscale is True: 931 ax.set_yscale('log') 932 933 ax.set_xlabel(r'$x_0 / a$') 934 plt.title(name) 935 plt.draw()
Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
Parameters
- logscale (bool): Determines whether the scale of the y-axis is logarithmic or standard.
937 def dump(self, filename, datatype="json.gz", **kwargs): 938 """Dumps the Corr into a file of chosen type 939 Parameters 940 ---------- 941 filename : str 942 Name of the file to be saved. 943 datatype : str 944 Format of the exported file. Supported formats include 945 "json.gz" and "pickle" 946 path : str 947 specifies a custom path for the file (default '.') 948 """ 949 if datatype == "json.gz": 950 from .input.json import dump_to_json 951 if 'path' in kwargs: 952 file_name = kwargs.get('path') + '/' + filename 953 else: 954 file_name = filename 955 dump_to_json(self, file_name) 956 elif datatype == "pickle": 957 dump_object(self, filename, **kwargs) 958 else: 959 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 '.')
1221 def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None): 1222 r''' Project large correlation matrix to lowest states 1223 1224 This method can be used to reduce the size of an (N x N) correlation matrix 1225 to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise 1226 is still small. 1227 1228 Parameters 1229 ---------- 1230 Ntrunc: int 1231 Rank of the target matrix. 1232 tproj: int 1233 Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method. 1234 The default value is 3. 1235 t0proj: int 1236 Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly 1237 discouraged for O(a) improved theories, since the correctness of the procedure 1238 cannot be granted in this case. The default value is 2. 1239 basematrix : Corr 1240 Correlation matrix that is used to determine the eigenvectors of the 1241 lowest states based on a GEVP. basematrix is taken to be the Corr itself if 1242 is is not specified. 1243 1244 Notes 1245 ----- 1246 We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving 1247 the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$ 1248 and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the 1249 resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via 1250 $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large 1251 correlation matrix and to remove some noise that is added by irrelevant operators. 1252 This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated 1253 bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$. 1254 ''' 1255 1256 if self.N == 1: 1257 raise Exception('Method cannot be applied to one-dimensional correlators.') 1258 if basematrix is None: 1259 basematrix = self 1260 if Ntrunc >= basematrix.N: 1261 raise Exception('Cannot truncate using Ntrunc <= %d' % (basematrix.N)) 1262 if basematrix.N != self.N: 1263 raise Exception('basematrix and targetmatrix have to be of the same size.') 1264 1265 evecs = basematrix.GEVP(t0proj, tproj, sort=None)[:Ntrunc] 1266 1267 tmpmat = np.empty((Ntrunc, Ntrunc), dtype=object) 1268 rmat = [] 1269 for t in range(basematrix.T): 1270 for i in range(Ntrunc): 1271 for j in range(Ntrunc): 1272 tmpmat[i][j] = evecs[i].T @ self[t] @ evecs[j] 1273 rmat.append(np.copy(tmpmat)) 1274 1275 newcontent = [None if (self.content[t] is None) else rmat[t] for t in range(self.T)] 1276 return Corr(newcontent)
Project large correlation matrix to lowest states
This method can be used to reduce the size of an (N x N) correlation matrix to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise is still small.
Parameters
- Ntrunc (int): Rank of the target matrix.
- tproj (int): Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method. The default value is 3.
- t0proj (int): Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly discouraged for O(a) improved theories, since the correctness of the procedure cannot be granted in this case. The default value is 2.
- basematrix (Corr): Correlation matrix that is used to determine the eigenvectors of the lowest states based on a GEVP. basematrix is taken to be the Corr itself if is is not specified.
Notes
We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$ and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large correlation matrix and to remove some noise that is added by irrelevant operators. This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.