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