245 def GEVP ( self , t0 , ts = None , state = 0 , sorted_list = "Eigenvalue" ):
-246 """Solve the general eigenvalue problem on the current correlator
+ 245 def GEVP ( self , t0 , ts = None , sort = "Eigenvalue" , ** kwargs ):
+246 r '''Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors.
247 248 Parameters
-249 ----------
-250 t0 : int
-251 The time t0 for G(t)v= lambda G(t_0)v
-252 ts : int
-253 fixed time G(t_s)v= lambda G(t_0)v if return_list=False
-254 If return_list=True and sorting=Eigenvector it gives a reference point for the sorting method.
-255 state : int
-256 The state one is interested in, ordered by energy. The lowest state is zero.
-257 sorted_list : string
-258 if this argument is set, a list of vectors (len=self.T) is returned. If it is left as None, only one vector is returned.
-259 "Eigenvalue" - The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice.
-260 "Eigenvector" - Use the method described in arXiv:2004.10472 [hep-lat] to find the set of v(t) belonging to the state.
-261 The reference state is identified by its eigenvalue at t=ts
-262 """
-263 264 if self . N == 1 :
-265 raise Exception ( "GEVP methods only works on correlator matrices and not single correlators." )
-266 267 symmetric_corr = self . matrix_symmetric ()
-268 if sorted_list is None :
-269 if ( ts is None ):
-270 raise Exception ( "ts is required if sorted_list=None." )
-271 if ( ts <= t0 ):
-272 raise Exception ( "ts has to be larger than t0." )
-273 if ( self . content [ t0 ] is None ) or ( self . content [ ts ] is None ):
-274 raise Exception ( "Corr not defined at t0/ts." )
-275 G0 , Gt = np . empty ([ self . N , self . N ], dtype = "double" ), np . empty ([ self . N , self . N ], dtype = "double" )
-276 for i in range ( self . N ):
-277 for j in range ( self . N ):
-278 G0 [ i , j ] = symmetric_corr [ t0 ][ i , j ] . value
-279 Gt [ i , j ] = symmetric_corr [ ts ][ i , j ] . value
-280 281 sp_vecs = _GEVP_solver ( Gt , G0 )
-282 sp_vec = sp_vecs [ state ]
-283 return sp_vec
-284 elif sorted_list in [ "Eigenvalue" , "Eigenvector" ]:
-285 if sorted_list == "Eigenvalue" and ts is not None :
-286 warnings . warn ( "ts has no effect when sorting by eigenvalue is chosen." , RuntimeWarning )
-287 all_vecs = [ None ] * ( t0 + 1 )
-288 for t in range ( t0 + 1 , self . T ):
-289 try :
-290 G0 , Gt = np . empty ([ self . N , self . N ], dtype = "double" ), np . empty ([ self . N , self . N ], dtype = "double" )
-291 for i in range ( self . N ):
-292 for j in range ( self . N ):
-293 G0 [ i , j ] = symmetric_corr [ t0 ][ i , j ] . value
-294 Gt [ i , j ] = symmetric_corr [ t ][ i , j ] . value
+248 The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the
+249 largest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing
+250 ```python
+251 C.GEVP(t0=2)[0] # Ground state vector(s)
+252 C.GEVP(t0=2)[:3] # Vectors for the lowest three states
+253 ```
+254 255 Parameters
+256 ----------
+257 t0 : int
+258 The time t0 for the right hand side of the GEVP according to $G(t)v_i=\lambda_i G(t_0)v_i$
+259 ts : int
+260 fixed time $G(t_s)v_i=\lambda_i G(t_0)v_i$ if sort=None.
+261 If sort="Eigenvector" it gives a reference point for the sorting method.
+262 sort : string
+263 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.
+264 - "Eigenvalue": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice.
+265 - "Eigenvector": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state.
+266 The reference state is identified by its eigenvalue at $t=t_s$.
+267 268 Other Parameters
+269 ----------------
+270 state : int
+271 Returns only the vector(s) for a specified state. The lowest state is zero.
+272 '''
+273 274 if self . N == 1 :
+275 raise Exception ( "GEVP methods only works on correlator matrices and not single correlators." )
+276 if ts is not None :
+277 if ( ts <= t0 ):
+278 raise Exception ( "ts has to be larger than t0." )
+279 280 if "sorted_list" in kwargs :
+281 warnings . warn ( "Argument 'sorted_list' is deprecated, use 'sort' instead." , DeprecationWarning )
+282 sort = kwargs . get ( "sorted_list" )
+283 284 symmetric_corr = self . matrix_symmetric ()
+285 if sort is None :
+286 if ( ts is None ):
+287 raise Exception ( "ts is required if sort=None." )
+288 if ( self . content [ t0 ] is None ) or ( self . content [ ts ] is None ):
+289 raise Exception ( "Corr not defined at t0/ts." )
+290 G0 , Gt = np . empty ([ self . N , self . N ], dtype = "double" ), np . empty ([ self . N , self . N ], dtype = "double" )
+291 for i in range ( self . N ):
+292 for j in range ( self . N ):
+293 G0 [ i , j ] = symmetric_corr [ t0 ][ i , j ] . value
+294 Gt [ i , j ] = symmetric_corr [ ts ][ i , j ] . value
295 296 sp_vecs = _GEVP_solver ( Gt , G0 )
-297 if sorted_list == "Eigenvalue" :
-298 sp_vec = sp_vecs [ state ]
-299 all_vecs . append ( sp_vec )
-300 else :
-301 all_vecs . append ( sp_vecs )
-302 except Exception :
-303 all_vecs . append ( None )
-304 if sorted_list == "Eigenvector" :
-305 if ( ts is None ):
-306 raise Exception ( "ts is required for the Eigenvector sorting method." )
-307 all_vecs = _sort_vectors ( all_vecs , ts )
-308 all_vecs = [ a [ state ] if a is not None else None for a in all_vecs ]
-309 else :
-310 raise Exception ( "Unkown value for 'sorted_list'." )
-311 312 return all_vecs
+296 reordered_vecs = _GEVP_solver ( Gt , G0 )
+297 298 elif sort in [ "Eigenvalue" , "Eigenvector" ]:
+299 if sort == "Eigenvalue" and ts is not None :
+300 warnings . warn ( "ts has no effect when sorting by eigenvalue is chosen." , RuntimeWarning )
+301 all_vecs = [ None ] * ( t0 + 1 )
+302 for t in range ( t0 + 1 , self . T ):
+303 try :
+304 G0 , Gt = np . empty ([ self . N , self . N ], dtype = "double" ), np . empty ([ self . N , self . N ], dtype = "double" )
+305 for i in range ( self . N ):
+306 for j in range ( self . N ):
+307 G0 [ i , j ] = symmetric_corr [ t0 ][ i , j ] . value
+308 Gt [ i , j ] = symmetric_corr [ t ][ i , j ] . value
+309 310 all_vecs . append ( _GEVP_solver ( Gt , G0 ))
+311 except Exception :
+312 all_vecs . append ( None )
+313 if sort == "Eigenvector" :
+314 if ( ts is None ):
+315 raise Exception ( "ts is required for the Eigenvector sorting method." )
+316 all_vecs = _sort_vectors ( all_vecs , ts )
+317 318 reordered_vecs = [[ v [ s ] if v is not None else None for v in all_vecs ] for s in range ( self . N )]
+319 else :
+320 raise Exception ( "Unkown value for 'sort'." )
+321 322 if "state" in kwargs :
+323 return reordered_vecs [ kwargs . get ( "state" )]
+324 else :
+325 return reordered_vecs
Solve the general eigenvalue problem on the current correlator
+
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 G(t)v= lambda G(t_0)vts (int):
-fixed time G(t_s)v= lambda G(t_0)v if return_list=False
-If return_list=True and sorting=Eigenvector it gives a reference point for the sorting method.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):
-The state one is interested in, ordered by energy. The lowest state is zero.sorted_list (string):
-if this argument is set, a list of vectors (len=self.T) is returned. If it is left as None, only one vector is returned.
-"Eigenvalue" - The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice.
-"Eigenvector" - Use the method described in arXiv:2004.10472 [hep-lat] to find the set of v(t) belonging to the state.
- The reference state is identified by its eigenvalue at t=ts
@@ -3140,32 +3175,24 @@ if this argument is set, a list of vectors (len=self.T) is returned. If it is le
def
- Eigenvalue (self , t0 , ts = None , state = 0 , sorted_list = None
+ Eigenvalue (self , t0 , ts = None , state = 0 , sort = 'Eigenvalue'
View Source
-
314 def Eigenvalue ( self , t0 , ts = None , state = 0 , sorted_list = None ):
-315 """Determines the eigenvalue of the GEVP by solving and projecting the correlator
-316 317 Parameters
-318 ----------
-319 t0 : int
-320 The time t0 for G(t)v= lambda G(t_0)v
-321 ts : int
-322 fixed time G(t_s)v= lambda G(t_0)v if return_list=False
-323 If return_list=True and sorting=Eigenvector it gives a reference point for the sorting method.
-324 state : int
-325 The state one is interested in ordered by energy. The lowest state is zero.
-326 sorted_list : string
-327 if this argument is set, a list of vectors (len=self.T) is returned. If it is left as None, only one vector is returned.
-328 "Eigenvalue" - The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice.
-329 "Eigenvector" - Use the method described in arXiv:2004.10472 [hep-lat] to find the set of v(t) belonging to the state.
-330 The reference state is identified by its eigenvalue at t=ts
-331 """
-332 vec = self . GEVP ( t0 , ts = ts , state = state , sorted_list = sorted_list )
-333 return self . projected ( vec )
+ 327 def Eigenvalue ( self , t0 , ts = None , state = 0 , sort = "Eigenvalue" ):
+328 """Determines the eigenvalue of the GEVP by solving and projecting the correlator
+329 330 Parameters
+331 ----------
+332 state : int
+333 The state one is interested in ordered by energy. The lowest state is zero.
+334 335 All other parameters are identical to the ones of Corr.GEVP.
+336 """
+337 vec = self . GEVP ( t0 , ts = ts , sort = sort )[ state ]
+338 return self . projected ( vec )
Parameters
-t0 (int):
-The time t0 for G(t)v= lambda G(t_0)vts (int):
-fixed time G(t_s)v= lambda G(t_0)v if return_list=False
-If return_list=True and sorting=Eigenvector it gives a reference point for the sorting method.state (int):
The state one is interested in ordered by energy. The lowest state is zero.sorted_list (string):
-if this argument is set, a list of vectors (len=self.T) is returned. If it is left as None, only one vector is returned.
-"Eigenvalue" - The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice.
-"Eigenvector" - Use the method described in arXiv:2004.10472 [hep-lat] to find the set of v(t) belonging to the state.
- The reference state is identified by its eigenvalue at t=tsAll other parameters are identical to the ones of Corr.GEVP .
@@ -3202,46 +3220,46 @@ if this argument is set, a list of vectors (len=self.T) is returned. If it is le
335 def Hankel ( self , N , periodic = False ):
-336 """Constructs an NxN Hankel matrix
-337 338 C(t) c(t+1) ... c(t+n-1)
-339 C(t+1) c(t+2) ... c(t+n)
-340 .................
-341 C(t+(n-1)) c(t+n) ... c(t+2(n-1))
+ 340 def Hankel ( self , N , periodic = False ):
+341 """Constructs an NxN Hankel matrix
342 343 Parameters
-344 ----------
-345 N : int
-346 Dimension of the Hankel matrix
-347 periodic : bool, optional
-348 determines whether the matrix is extended periodically
-349 """
-350 351 if self . N != 1 :
-352 raise Exception ( "Multi-operator Prony not implemented!" )
-353 354 array = np . empty ([ N , N ], dtype = "object" )
-355 new_content = []
-356 for t in range ( self . T ):
-357 new_content . append ( array . copy ())
+343 C(t) c(t+1) ... c(t+n-1)
+344 C(t+1) c(t+2) ... c(t+n)
+345 .................
+346 C(t+(n-1)) c(t+n) ... c(t+2(n-1))
+347 348 Parameters
+349 ----------
+350 N : int
+351 Dimension of the Hankel matrix
+352 periodic : bool, optional
+353 determines whether the matrix is extended periodically
+354 """
+355 356 if self . N != 1 :
+357 raise Exception ( "Multi-operator Prony not implemented!" )
358 359 def wrap ( i ):
-360 while i >= self . T :
-361 i -= self . T
-362 return i
+359 array = np . empty ([ N , N ], dtype = "object" )
+360 new_content = []
+361 for t in range ( self . T ):
+362 new_content . append ( array . copy ())
363 364 for t in range ( self . T ):
-365 for i in range ( N ):
-366 for j in range ( N ):
-367 if periodic :
-368 new_content [ t ][ i , j ] = self . content [ wrap ( t + i + j )][ 0 ]
-369 elif ( t + i + j ) >= self . T :
-370 new_content [ t ] = None
-371 else :
-372 new_content [ t ][ i , j ] = self . content [ t + i + j ][ 0 ]
-373 374 return Corr ( new_content )
+364 def wrap ( i ):
+365 while i >= self . T :
+366 i -= self . T
+367 return i
+368 369 for t in range ( self . T ):
+370 for i in range ( N ):
+371 for j in range ( N ):
+372 if periodic :
+373 new_content [ t ][ i , j ] = self . content [ wrap ( t + i + j )][ 0 ]
+374 elif ( t + i + j ) >= self . T :
+375 new_content [ t ] = None
+376 else :
+377 new_content [ t ][ i , j ] = self . content [ t + i + j ][ 0 ]
+378 379 return Corr ( new_content )
376 def roll ( self , dt ):
-377 """Periodically shift the correlator by dt timeslices
-378 379 Parameters
-380 ----------
-381 dt : int
-382 number of timeslices
-383 """
-384 return Corr ( list ( np . roll ( np . array ( self . content , dtype = object ), dt )))
+ 381 def roll ( self , dt ):
+382 """Periodically shift the correlator by dt timeslices
+383 384 Parameters
+385 ----------
+386 dt : int
+387 number of timeslices
+388 """
+389 return Corr ( list ( np . roll ( np . array ( self . content , dtype = object ), dt )))
386 def reverse ( self ):
-387 """Reverse the time ordering of the Corr"""
-388 return Corr ( self . content [:: - 1 ])
+ 391 def reverse ( self ):
+392 """Reverse the time ordering of the Corr"""
+393 return Corr ( self . content [:: - 1 ])
390 def thin ( self , spacing = 2 , offset = 0 ):
-391 """Thin out a correlator to suppress correlations
-392 393 Parameters
-394 ----------
-395 spacing : int
-396 Keep only every 'spacing'th entry of the correlator
-397 offset : int
-398 Offset the equal spacing
-399 """
-400 new_content = []
-401 for t in range ( self . T ):
-402 if ( offset + t ) % spacing != 0 :
-403 new_content . append ( None )
-404 else :
-405 new_content . append ( self . content [ t ])
-406 return Corr ( new_content )
+ 395 def thin ( self , spacing = 2 , offset = 0 ):
+396 """Thin out a correlator to suppress correlations
+397 398 Parameters
+399 ----------
+400 spacing : int
+401 Keep only every 'spacing'th entry of the correlator
+402 offset : int
+403 Offset the equal spacing
+404 """
+405 new_content = []
+406 for t in range ( self . T ):
+407 if ( offset + t ) % spacing != 0 :
+408 new_content . append ( None )
+409 else :
+410 new_content . append ( self . content [ t ])
+411 return Corr ( new_content )
408 def correlate ( self , partner ):
-409 """Correlate the correlator with another correlator or Obs
-410 411 Parameters
-412 ----------
-413 partner : Obs or Corr
-414 partner to correlate the correlator with.
-415 Can either be an Obs which is correlated with all entries of the
-416 correlator or a Corr of same length.
-417 """
-418 new_content = []
-419 for x0 , t_slice in enumerate ( self . content ):
-420 if t_slice is None :
-421 new_content . append ( None )
-422 else :
-423 if isinstance ( partner , Corr ):
-424 if partner . content [ x0 ] is None :
-425 new_content . append ( None )
-426 else :
-427 new_content . append ( np . array ([ correlate ( o , partner . content [ x0 ][ 0 ]) for o in t_slice ]))
-428 elif isinstance ( partner , Obs ): # Should this include CObs?
-429 new_content . append ( np . array ([ correlate ( o , partner ) for o in t_slice ]))
-430 else :
-431 raise Exception ( "Can only correlate with an Obs or a Corr." )
-432 433 return Corr ( new_content )
+ 413 def correlate ( self , partner ):
+414 """Correlate the correlator with another correlator or Obs
+415 416 Parameters
+417 ----------
+418 partner : Obs or Corr
+419 partner to correlate the correlator with.
+420 Can either be an Obs which is correlated with all entries of the
+421 correlator or a Corr of same length.
+422 """
+423 new_content = []
+424 for x0 , t_slice in enumerate ( self . content ):
+425 if t_slice is None :
+426 new_content . append ( None )
+427 else :
+428 if isinstance ( partner , Corr ):
+429 if partner . content [ x0 ] is None :
+430 new_content . append ( None )
+431 else :
+432 new_content . append ( np . array ([ correlate ( o , partner . content [ x0 ][ 0 ]) for o in t_slice ]))
+433 elif isinstance ( partner , Obs ): # Should this include CObs?
+434 new_content . append ( np . array ([ correlate ( o , partner ) for o in t_slice ]))
+435 else :
+436 raise Exception ( "Can only correlate with an Obs or a Corr." )
+437 438 return Corr ( new_content )
435 def reweight ( self , weight , ** kwargs ):
-436 """Reweight the correlator.
-437 438 Parameters
-439 ----------
-440 weight : Obs
-441 Reweighting factor. An Observable that has to be defined on a superset of the
-442 configurations in obs[i].idl for all i.
-443 all_configs : bool
-444 if True, the reweighted observables are normalized by the average of
-445 the reweighting factor on all configurations in weight.idl and not
-446 on the configurations in obs[i].idl.
-447 """
-448 new_content = []
-449 for t_slice in self . content :
-450 if t_slice is None :
-451 new_content . append ( None )
-452 else :
-453 new_content . append ( np . array ( reweight ( weight , t_slice , ** kwargs )))
-454 return Corr ( new_content )
+ 440 def reweight ( self , weight , ** kwargs ):
+441 """Reweight the correlator.
+442 443 Parameters
+444 ----------
+445 weight : Obs
+446 Reweighting factor. An Observable that has to be defined on a superset of the
+447 configurations in obs[i].idl for all i.
+448 all_configs : bool
+449 if True, the reweighted observables are normalized by the average of
+450 the reweighting factor on all configurations in weight.idl and not
+451 on the configurations in obs[i].idl.
+452 """
+453 new_content = []
+454 for t_slice in self . content :
+455 if t_slice is None :
+456 new_content . append ( None )
+457 else :
+458 new_content . append ( np . array ( reweight ( weight , t_slice , ** kwargs )))
+459 return Corr ( new_content )
456 def T_symmetry ( self , partner , parity =+ 1 ):
-457 """Return the time symmetry average of the correlator and its partner
-458 459 Parameters
-460 ----------
-461 partner : Corr
-462 Time symmetry partner of the Corr
-463 partity : int
-464 Parity quantum number of the correlator, can be +1 or -1
-465 """
-466 if not isinstance ( partner , Corr ):
-467 raise Exception ( "T partner has to be a Corr object." )
-468 if parity not in [ + 1 , - 1 ]:
-469 raise Exception ( "Parity has to be +1 or -1." )
-470 T_partner = parity * partner . reverse ()
-471 472 t_slices = []
-473 test = ( self - T_partner )
-474 test . gamma_method ()
-475 for x0 , t_slice in enumerate ( test . content ):
-476 if t_slice is not None :
-477 if not t_slice [ 0 ] . is_zero_within_error ( 5 ):
-478 t_slices . append ( x0 )
-479 if t_slices :
-480 warnings . warn ( "T symmetry partners do not agree within 5 sigma on time slices " + str ( t_slices ) + "." , RuntimeWarning )
-481 482 return ( self + T_partner ) / 2
+ 461 def T_symmetry ( self , partner , parity =+ 1 ):
+462 """Return the time symmetry average of the correlator and its partner
+463 464 Parameters
+465 ----------
+466 partner : Corr
+467 Time symmetry partner of the Corr
+468 partity : int
+469 Parity quantum number of the correlator, can be +1 or -1
+470 """
+471 if not isinstance ( partner , Corr ):
+472 raise Exception ( "T partner has to be a Corr object." )
+473 if parity not in [ + 1 , - 1 ]:
+474 raise Exception ( "Parity has to be +1 or -1." )
+475 T_partner = parity * partner . reverse ()
+476 477 t_slices = []
+478 test = ( self - T_partner )
+479 test . gamma_method ()
+480 for x0 , t_slice in enumerate ( test . content ):
+481 if t_slice is not None :
+482 if not t_slice [ 0 ] . is_zero_within_error ( 5 ):
+483 t_slices . append ( x0 )
+484 if t_slices :
+485 warnings . warn ( "T symmetry partners do not agree within 5 sigma on time slices " + str ( t_slices ) + "." , RuntimeWarning )
+486 487 return ( self + T_partner ) / 2
484 def deriv ( self , variant = "symmetric" ):
-485 """Return the first derivative of the correlator with respect to x0.
-486 487 Parameters
-488 ----------
-489 variant : str
-490 decides which definition of the finite differences derivative is used.
-491 Available choice: symmetric, forward, backward, improved, default: symmetric
-492 """
-493 if variant == "symmetric" :
-494 newcontent = []
-495 for t in range ( 1 , self . T - 1 ):
-496 if ( self . content [ t - 1 ] is None ) or ( self . content [ t + 1 ] is None ):
-497 newcontent . append ( None )
-498 else :
-499 newcontent . append ( 0.5 * ( self . content [ t + 1 ] - self . content [ t - 1 ]))
-500 if ( all ([ x is None for x in newcontent ])):
-501 raise Exception ( 'Derivative is undefined at all timeslices' )
-502 return Corr ( newcontent , padding = [ 1 , 1 ])
-503 elif variant == "forward" :
-504 newcontent = []
-505 for t in range ( self . T - 1 ):
-506 if ( self . content [ t ] is None ) or ( self . content [ t + 1 ] is None ):
-507 newcontent . append ( None )
-508 else :
-509 newcontent . append ( self . content [ t + 1 ] - self . content [ t ])
-510 if ( all ([ x is None for x in newcontent ])):
-511 raise Exception ( "Derivative is undefined at all timeslices" )
-512 return Corr ( newcontent , padding = [ 0 , 1 ])
-513 elif variant == "backward" :
-514 newcontent = []
-515 for t in range ( 1 , self . T ):
-516 if ( self . content [ t - 1 ] is None ) or ( self . content [ t ] is None ):
-517 newcontent . append ( None )
-518 else :
-519 newcontent . append ( self . content [ t ] - self . content [ t - 1 ])
-520 if ( all ([ x is None for x in newcontent ])):
-521 raise Exception ( "Derivative is undefined at all timeslices" )
-522 return Corr ( newcontent , padding = [ 1 , 0 ])
-523 elif variant == "improved" :
-524 newcontent = []
-525 for t in range ( 2 , self . T - 2 ):
-526 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 ):
-527 newcontent . append ( None )
-528 else :
-529 newcontent . append (( 1 / 12 ) * ( self . content [ t - 2 ] - 8 * self . content [ t - 1 ] + 8 * self . content [ t + 1 ] - self . content [ t + 2 ]))
-530 if ( all ([ x is None for x in newcontent ])):
-531 raise Exception ( 'Derivative is undefined at all timeslices' )
-532 return Corr ( newcontent , padding = [ 2 , 2 ])
-533 else :
-534 raise Exception ( "Unknown variant." )
+ 489 def deriv ( self , variant = "symmetric" ):
+490 """Return the first derivative of the correlator with respect to x0.
+491 492 Parameters
+493 ----------
+494 variant : str
+495 decides which definition of the finite differences derivative is used.
+496 Available choice: symmetric, forward, backward, improved, default: symmetric
+497 """
+498 if variant == "symmetric" :
+499 newcontent = []
+500 for t in range ( 1 , self . T - 1 ):
+501 if ( self . content [ t - 1 ] is None ) or ( self . content [ t + 1 ] is None ):
+502 newcontent . append ( None )
+503 else :
+504 newcontent . append ( 0.5 * ( self . content [ t + 1 ] - self . content [ t - 1 ]))
+505 if ( all ([ x is None for x in newcontent ])):
+506 raise Exception ( 'Derivative is undefined at all timeslices' )
+507 return Corr ( newcontent , padding = [ 1 , 1 ])
+508 elif variant == "forward" :
+509 newcontent = []
+510 for t in range ( self . T - 1 ):
+511 if ( self . content [ t ] is None ) or ( self . content [ t + 1 ] is None ):
+512 newcontent . append ( None )
+513 else :
+514 newcontent . append ( self . content [ t + 1 ] - self . content [ t ])
+515 if ( all ([ x is None for x in newcontent ])):
+516 raise Exception ( "Derivative is undefined at all timeslices" )
+517 return Corr ( newcontent , padding = [ 0 , 1 ])
+518 elif variant == "backward" :
+519 newcontent = []
+520 for t in range ( 1 , self . T ):
+521 if ( self . content [ t - 1 ] is None ) or ( self . content [ t ] is None ):
+522 newcontent . append ( None )
+523 else :
+524 newcontent . append ( self . content [ t ] - self . content [ t - 1 ])
+525 if ( all ([ x is None for x in newcontent ])):
+526 raise Exception ( "Derivative is undefined at all timeslices" )
+527 return Corr ( newcontent , padding = [ 1 , 0 ])
+528 elif variant == "improved" :
+529 newcontent = []
+530 for t in range ( 2 , self . T - 2 ):
+531 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 ):
+532 newcontent . append ( None )
+533 else :
+534 newcontent . append (( 1 / 12 ) * ( self . content [ t - 2 ] - 8 * self . content [ t - 1 ] + 8 * self . content [ t + 1 ] - self . content [ t + 2 ]))
+535 if ( all ([ x is None for x in newcontent ])):
+536 raise Exception ( 'Derivative is undefined at all timeslices' )
+537 return Corr ( newcontent , padding = [ 2 , 2 ])
+538 else :
+539 raise Exception ( "Unknown variant." )
536 def second_deriv ( self , variant = "symmetric" ):
-537 """Return the second derivative of the correlator with respect to x0.
-538 539 Parameters
-540 ----------
-541 variant : str
-542 decides which definition of the finite differences derivative is used.
-543 Available choice: symmetric, improved, default: symmetric
-544 """
-545 if variant == "symmetric" :
-546 newcontent = []
-547 for t in range ( 1 , self . T - 1 ):
-548 if ( self . content [ t - 1 ] is None ) or ( self . content [ t + 1 ] is None ):
-549 newcontent . append ( None )
-550 else :
-551 newcontent . append (( self . content [ t + 1 ] - 2 * self . content [ t ] + self . content [ t - 1 ]))
-552 if ( all ([ x is None for x in newcontent ])):
-553 raise Exception ( "Derivative is undefined at all timeslices" )
-554 return Corr ( newcontent , padding = [ 1 , 1 ])
-555 elif variant == "improved" :
-556 newcontent = []
-557 for t in range ( 2 , self . T - 2 ):
-558 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 ):
-559 newcontent . append ( None )
-560 else :
-561 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 ]))
-562 if ( all ([ x is None for x in newcontent ])):
-563 raise Exception ( "Derivative is undefined at all timeslices" )
-564 return Corr ( newcontent , padding = [ 2 , 2 ])
-565 else :
-566 raise Exception ( "Unknown variant." )
+ 541 def second_deriv ( self , variant = "symmetric" ):
+542 """Return the second derivative of the correlator with respect to x0.
+543 544 Parameters
+545 ----------
+546 variant : str
+547 decides which definition of the finite differences derivative is used.
+548 Available choice: symmetric, improved, default: symmetric
+549 """
+550 if variant == "symmetric" :
+551 newcontent = []
+552 for t in range ( 1 , self . T - 1 ):
+553 if ( self . content [ t - 1 ] is None ) or ( self . content [ t + 1 ] is None ):
+554 newcontent . append ( None )
+555 else :
+556 newcontent . append (( self . content [ t + 1 ] - 2 * self . content [ t ] + self . content [ t - 1 ]))
+557 if ( all ([ x is None for x in newcontent ])):
+558 raise Exception ( "Derivative is undefined at all timeslices" )
+559 return Corr ( newcontent , padding = [ 1 , 1 ])
+560 elif variant == "improved" :
+561 newcontent = []
+562 for t in range ( 2 , self . T - 2 ):
+563 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 ):
+564 newcontent . append ( None )
+565 else :
+566 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 ]))
+567 if ( all ([ x is None for x in newcontent ])):
+568 raise Exception ( "Derivative is undefined at all timeslices" )
+569 return Corr ( newcontent , padding = [ 2 , 2 ])
+570 else :
+571 raise Exception ( "Unknown variant." )
568 def m_eff ( self , variant = 'log' , guess = 1.0 ):
-569 """Returns the effective mass of the correlator as correlator object
-570 571 Parameters
-572 ----------
-573 variant : str
-574 log : uses the standard effective mass log(C(t) / C(t+1))
-575 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.
-576 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.
-577 See, e.g., arXiv:1205.5380
-578 arccosh : Uses the explicit form of the symmetrized correlator (not recommended)
-579 guess : float
-580 guess for the root finder, only relevant for the root variant
-581 """
-582 if self . N != 1 :
-583 raise Exception ( 'Correlator must be projected before getting m_eff' )
-584 if variant == 'log' :
-585 newcontent = []
-586 for t in range ( self . T - 1 ):
-587 if ( self . content [ t ] is None ) or ( self . content [ t + 1 ] is None ):
-588 newcontent . append ( None )
-589 else :
-590 newcontent . append ( self . content [ t ] / self . content [ t + 1 ])
-591 if ( all ([ x is None for x in newcontent ])):
-592 raise Exception ( 'm_eff is undefined at all timeslices' )
-593 594 return np . log ( Corr ( newcontent , padding = [ 0 , 1 ]))
-595 596 elif variant in [ 'periodic' , 'cosh' , 'sinh' ]:
-597 if variant in [ 'periodic' , 'cosh' ]:
-598 func = anp . cosh
-599 else :
-600 func = anp . sinh
-601 602 def root_function ( x , d ):
-603 return func ( x * ( t - self . T / 2 )) / func ( x * ( t + 1 - self . T / 2 )) - d
-604 605 newcontent = []
-606 for t in range ( self . T - 1 ):
-607 if ( self . content [ t ] is None ) or ( self . content [ t + 1 ] is None ):
-608 newcontent . append ( None )
-609 # Fill the two timeslices in the middle of the lattice with their predecessors
-610 elif variant == 'sinh' and t in [ self . T / 2 , self . T / 2 - 1 ]:
-611 newcontent . append ( newcontent [ - 1 ])
-612 else :
-613 newcontent . append ( np . abs ( find_root ( self . content [ t ][ 0 ] / self . content [ t + 1 ][ 0 ], root_function , guess = guess )))
-614 if ( all ([ x is None for x in newcontent ])):
-615 raise Exception ( 'm_eff is undefined at all timeslices' )
-616 617 return Corr ( newcontent , padding = [ 0 , 1 ])
-618 619 elif variant == 'arccosh' :
-620 newcontent = []
-621 for t in range ( 1 , self . T - 1 ):
-622 if ( self . content [ t ] is None ) or ( self . content [ t + 1 ] is None ) or ( self . content [ t - 1 ] is None ):
-623 newcontent . append ( None )
-624 else :
-625 newcontent . append (( self . content [ t + 1 ] + self . content [ t - 1 ]) / ( 2 * self . content [ t ]))
-626 if ( all ([ x is None for x in newcontent ])):
-627 raise Exception ( "m_eff is undefined at all timeslices" )
-628 return np . arccosh ( Corr ( newcontent , padding = [ 1 , 1 ]))
-629 630 else :
-631 raise Exception ( 'Unknown variant.' )
+ 573 def m_eff ( self , variant = 'log' , guess = 1.0 ):
+574 """Returns the effective mass of the correlator as correlator object
+575 576 Parameters
+577 ----------
+578 variant : str
+579 log : uses the standard effective mass log(C(t) / C(t+1))
+580 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.
+581 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.
+582 See, e.g., arXiv:1205.5380
+583 arccosh : Uses the explicit form of the symmetrized correlator (not recommended)
+584 guess : float
+585 guess for the root finder, only relevant for the root variant
+586 """
+587 if self . N != 1 :
+588 raise Exception ( 'Correlator must be projected before getting m_eff' )
+589 if variant == 'log' :
+590 newcontent = []
+591 for t in range ( self . T - 1 ):
+592 if ( self . content [ t ] is None ) or ( self . content [ t + 1 ] is None ):
+593 newcontent . append ( None )
+594 else :
+595 newcontent . append ( self . content [ t ] / self . content [ t + 1 ])
+596 if ( all ([ x is None for x in newcontent ])):
+597 raise Exception ( 'm_eff is undefined at all timeslices' )
+598 599 return np . log ( Corr ( newcontent , padding = [ 0 , 1 ]))
+600 601 elif variant in [ 'periodic' , 'cosh' , 'sinh' ]:
+602 if variant in [ 'periodic' , 'cosh' ]:
+603 func = anp . cosh
+604 else :
+605 func = anp . sinh
+606 607 def root_function ( x , d ):
+608 return func ( x * ( t - self . T / 2 )) / func ( x * ( t + 1 - self . T / 2 )) - d
+609 610 newcontent = []
+611 for t in range ( self . T - 1 ):
+612 if ( self . content [ t ] is None ) or ( self . content [ t + 1 ] is None ):
+613 newcontent . append ( None )
+614 # Fill the two timeslices in the middle of the lattice with their predecessors
+615 elif variant == 'sinh' and t in [ self . T / 2 , self . T / 2 - 1 ]:
+616 newcontent . append ( newcontent [ - 1 ])
+617 else :
+618 newcontent . append ( np . abs ( find_root ( self . content [ t ][ 0 ] / self . content [ t + 1 ][ 0 ], root_function , guess = guess )))
+619 if ( all ([ x is None for x in newcontent ])):
+620 raise Exception ( 'm_eff is undefined at all timeslices' )
+621 622 return Corr ( newcontent , padding = [ 0 , 1 ])
+623 624 elif variant == 'arccosh' :
+625 newcontent = []
+626 for t in range ( 1 , self . T - 1 ):
+627 if ( self . content [ t ] is None ) or ( self . content [ t + 1 ] is None ) or ( self . content [ t - 1 ] is None ):
+628 newcontent . append ( None )
+629 else :
+630 newcontent . append (( self . content [ t + 1 ] + self . content [ t - 1 ]) / ( 2 * self . content [ t ]))
+631 if ( all ([ x is None for x in newcontent ])):
+632 raise Exception ( "m_eff is undefined at all timeslices" )
+633 return np . arccosh ( Corr ( newcontent , padding = [ 1 , 1 ]))
+634 635 else :
+636 raise Exception ( 'Unknown variant.' )
633 def fit ( self , function , fitrange = None , silent = False , ** kwargs ):
-634 r '''Fits function to the data
-635 636 Parameters
-637 ----------
-638 function : obj
-639 function to fit to the data. See fits.least_squares for details.
-640 fitrange : list
-641 Two element list containing the timeslices on which the fit is supposed to start and stop.
-642 Caution: This range is inclusive as opposed to standard python indexing.
-643 `fitrange=[4, 6]` corresponds to the three entries 4, 5 and 6.
-644 If not specified, self.prange or all timeslices are used.
-645 silent : bool
-646 Decides whether output is printed to the standard output.
-647 '''
-648 if self . N != 1 :
-649 raise Exception ( "Correlator must be projected before fitting" )
-650 651 if fitrange is None :
-652 if self . prange :
-653 fitrange = self . prange
-654 else :
-655 fitrange = [ 0 , self . T - 1 ]
-656 else :
-657 if not isinstance ( fitrange , list ):
-658 raise Exception ( "fitrange has to be a list with two elements" )
-659 if len ( fitrange ) != 2 :
-660 raise Exception ( "fitrange has to have exactly two elements [fit_start, fit_stop]" )
-661 662 xs = [ x for x in range ( fitrange [ 0 ], fitrange [ 1 ] + 1 ) if not self . content [ x ] is None ]
-663 ys = [ self . content [ x ][ 0 ] for x in range ( fitrange [ 0 ], fitrange [ 1 ] + 1 ) if not self . content [ x ] is None ]
-664 result = least_squares ( xs , ys , function , silent = silent , ** kwargs )
-665 return result
+ 638 def fit ( self , function , fitrange = None , silent = False , ** kwargs ):
+639 r '''Fits function to the data
+640 641 Parameters
+642 ----------
+643 function : obj
+644 function to fit to the data. See fits.least_squares for details.
+645 fitrange : list
+646 Two element list containing the timeslices on which the fit is supposed to start and stop.
+647 Caution: This range is inclusive as opposed to standard python indexing.
+648 `fitrange=[4, 6]` corresponds to the three entries 4, 5 and 6.
+649 If not specified, self.prange or all timeslices are used.
+650 silent : bool
+651 Decides whether output is printed to the standard output.
+652 '''
+653 if self . N != 1 :
+654 raise Exception ( "Correlator must be projected before fitting" )
+655 656 if fitrange is None :
+657 if self . prange :
+658 fitrange = self . prange
+659 else :
+660 fitrange = [ 0 , self . T - 1 ]
+661 else :
+662 if not isinstance ( fitrange , list ):
+663 raise Exception ( "fitrange has to be a list with two elements" )
+664 if len ( fitrange ) != 2 :
+665 raise Exception ( "fitrange has to have exactly two elements [fit_start, fit_stop]" )
+666 667 xs = [ x for x in range ( fitrange [ 0 ], fitrange [ 1 ] + 1 ) if not self . content [ x ] is None ]
+668 ys = [ self . content [ x ][ 0 ] for x in range ( fitrange [ 0 ], fitrange [ 1 ] + 1 ) if not self . content [ x ] is None ]
+669 result = least_squares ( xs , ys , function , silent = silent , ** kwargs )
+670 return result
667 def plateau ( self , plateau_range = None , method = "fit" , auto_gamma = False ):
-668 """ Extract a plateau value from a Corr object
-669 670 Parameters
-671 ----------
-672 plateau_range : list
-673 list with two entries, indicating the first and the last timeslice
-674 of the plateau region.
-675 method : str
-676 method to extract the plateau.
-677 'fit' fits a constant to the plateau region
-678 'avg', 'average' or 'mean' just average over the given timeslices.
-679 auto_gamma : bool
-680 apply gamma_method with default parameters to the Corr. Defaults to None
-681 """
-682 if not plateau_range :
-683 if self . prange :
-684 plateau_range = self . prange
-685 else :
-686 raise Exception ( "no plateau range provided" )
-687 if self . N != 1 :
-688 raise Exception ( "Correlator must be projected before getting a plateau." )
-689 if ( all ([ self . content [ t ] is None for t in range ( plateau_range [ 0 ], plateau_range [ 1 ] + 1 )])):
-690 raise Exception ( "plateau is undefined at all timeslices in plateaurange." )
-691 if auto_gamma :
-692 self . gamma_method ()
-693 if method == "fit" :
-694 def const_func ( a , t ):
-695 return a [ 0 ]
-696 return self . fit ( const_func , plateau_range )[ 0 ]
-697 elif method in [ "avg" , "average" , "mean" ]:
-698 returnvalue = np . mean ([ item [ 0 ] for item in self . content [ plateau_range [ 0 ]: plateau_range [ 1 ] + 1 ] if item is not None ])
-699 return returnvalue
-700 701 else :
-702 raise Exception ( "Unsupported plateau method: " + method )
+ 672 def plateau ( self , plateau_range = None , method = "fit" , auto_gamma = False ):
+673 """ Extract a plateau value from a Corr object
+674 675 Parameters
+676 ----------
+677 plateau_range : list
+678 list with two entries, indicating the first and the last timeslice
+679 of the plateau region.
+680 method : str
+681 method to extract the plateau.
+682 'fit' fits a constant to the plateau region
+683 'avg', 'average' or 'mean' just average over the given timeslices.
+684 auto_gamma : bool
+685 apply gamma_method with default parameters to the Corr. Defaults to None
+686 """
+687 if not plateau_range :
+688 if self . prange :
+689 plateau_range = self . prange
+690 else :
+691 raise Exception ( "no plateau range provided" )
+692 if self . N != 1 :
+693 raise Exception ( "Correlator must be projected before getting a plateau." )
+694 if ( all ([ self . content [ t ] is None for t in range ( plateau_range [ 0 ], plateau_range [ 1 ] + 1 )])):
+695 raise Exception ( "plateau is undefined at all timeslices in plateaurange." )
+696 if auto_gamma :
+697 self . gamma_method ()
+698 if method == "fit" :
+699 def const_func ( a , t ):
+700 return a [ 0 ]
+701 return self . fit ( const_func , plateau_range )[ 0 ]
+702 elif method in [ "avg" , "average" , "mean" ]:
+703 returnvalue = np . mean ([ item [ 0 ] for item in self . content [ plateau_range [ 0 ]: plateau_range [ 1 ] + 1 ] if item is not None ])
+704 return returnvalue
+705 706 else :
+707 raise Exception ( "Unsupported plateau method: " + method )
704 def set_prange ( self , prange ):
-705 """Sets the attribute prange of the Corr object."""
-706 if not len ( prange ) == 2 :
-707 raise Exception ( "prange must be a list or array with two values" )
-708 if not (( isinstance ( prange [ 0 ], int )) and ( isinstance ( prange [ 1 ], int ))):
-709 raise Exception ( "Start and end point must be integers" )
-710 if not ( 0 <= prange [ 0 ] <= self . T and 0 <= prange [ 1 ] <= self . T and prange [ 0 ] < prange [ 1 ]):
-711 raise Exception ( "Start and end point must define a range in the interval 0,T" )
-712 713 self . prange = prange
-714 return
+ 709 def set_prange ( self , prange ):
+710 """Sets the attribute prange of the Corr object."""
+711 if not len ( prange ) == 2 :
+712 raise Exception ( "prange must be a list or array with two values" )
+713 if not (( isinstance ( prange [ 0 ], int )) and ( isinstance ( prange [ 1 ], int ))):
+714 raise Exception ( "Start and end point must be integers" )
+715 if not ( 0 <= prange [ 0 ] <= self . T and 0 <= prange [ 1 ] <= self . T and prange [ 0 ] < prange [ 1 ]):
+716 raise Exception ( "Start and end point must define a range in the interval 0,T" )
+717 718 self . prange = prange
+719 return
716 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 ):
-717 """Plots the correlator using the tag of the correlator as label if available.
-718 719 Parameters
-720 ----------
-721 x_range : list
-722 list of two values, determining the range of the x-axis e.g. [4, 8]
-723 comp : Corr or list of Corr
-724 Correlator or list of correlators which are plotted for comparison.
-725 The tags of these correlators are used as labels if available.
-726 logscale : bool
-727 Sets y-axis to logscale
-728 plateau : Obs
-729 Plateau value to be visualized in the figure
-730 fit_res : Fit_result
-731 Fit_result object to be visualized
-732 ylabel : str
-733 Label for the y-axis
-734 save : str
-735 path to file in which the figure should be saved
-736 auto_gamma : bool
-737 Apply the gamma method with standard parameters to all correlators and plateau values before plotting.
-738 hide_sigma : float
-739 Hides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.
-740 references : list
-741 List of floating point values that are displayed as horizontal lines for reference.
-742 """
-743 if self . N != 1 :
-744 raise Exception ( "Correlator must be projected before plotting" )
-745 746 if auto_gamma :
-747 self . gamma_method ()
-748 749 if x_range is None :
-750 x_range = [ 0 , self . T - 1 ]
-751 752 fig = plt . figure ()
-753 ax1 = fig . add_subplot ( 111 )
-754 755 x , y , y_err = self . plottable ()
-756 if hide_sigma :
-757 hide_from = np . argmax (( hide_sigma * np . array ( y_err )) > np . abs ( y )) - 1
-758 else :
-759 hide_from = None
-760 ax1 . errorbar ( x [: hide_from ], y [: hide_from ], y_err [: hide_from ], label = self . tag )
-761 if logscale :
-762 ax1 . set_yscale ( 'log' )
+ 721 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 ):
+722 """Plots the correlator using the tag of the correlator as label if available.
+723 724 Parameters
+725 ----------
+726 x_range : list
+727 list of two values, determining the range of the x-axis e.g. [4, 8]
+728 comp : Corr or list of Corr
+729 Correlator or list of correlators which are plotted for comparison.
+730 The tags of these correlators are used as labels if available.
+731 logscale : bool
+732 Sets y-axis to logscale
+733 plateau : Obs
+734 Plateau value to be visualized in the figure
+735 fit_res : Fit_result
+736 Fit_result object to be visualized
+737 ylabel : str
+738 Label for the y-axis
+739 save : str
+740 path to file in which the figure should be saved
+741 auto_gamma : bool
+742 Apply the gamma method with standard parameters to all correlators and plateau values before plotting.
+743 hide_sigma : float
+744 Hides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.
+745 references : list
+746 List of floating point values that are displayed as horizontal lines for reference.
+747 """
+748 if self . N != 1 :
+749 raise Exception ( "Correlator must be projected before plotting" )
+750 751 if auto_gamma :
+752 self . gamma_method ()
+753 754 if x_range is None :
+755 x_range = [ 0 , self . T - 1 ]
+756 757 fig = plt . figure ()
+758 ax1 = fig . add_subplot ( 111 )
+759 760 x , y , y_err = self . plottable ()
+761 if hide_sigma :
+762 hide_from = np . argmax (( hide_sigma * np . array ( y_err )) > np . abs ( y )) - 1
763 else :
-764 if y_range is None :
-765 try :
-766 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 )])
-767 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 )])
-768 ax1 . set_ylim ([ y_min - 0.1 * ( y_max - y_min ), y_max + 0.1 * ( y_max - y_min )])
-769 except Exception :
-770 pass
-771 else :
-772 ax1 . set_ylim ( y_range )
-773 if comp :
-774 if isinstance ( comp , ( Corr , list )):
-775 for corr in comp if isinstance ( comp , list ) else [ comp ]:
-776 if auto_gamma :
-777 corr . gamma_method ()
-778 x , y , y_err = corr . plottable ()
-779 if hide_sigma :
-780 hide_from = np . argmax (( hide_sigma * np . array ( y_err )) > np . abs ( y )) - 1
-781 else :
-782 hide_from = None
-783 plt . errorbar ( x [: hide_from ], y [: hide_from ], y_err [: hide_from ], label = corr . tag , mfc = plt . rcParams [ 'axes.facecolor' ])
-784 else :
-785 raise Exception ( "'comp' must be a correlator or a list of correlators." )
-786 787 if plateau :
-788 if isinstance ( plateau , Obs ):
-789 if auto_gamma :
-790 plateau . gamma_method ()
-791 ax1 . axhline ( y = plateau . value , linewidth = 2 , color = plt . rcParams [ 'text.color' ], alpha = 0.6 , marker = ',' , ls = '--' , label = str ( plateau ))
-792 ax1 . axhspan ( plateau . value - plateau . dvalue , plateau . value + plateau . dvalue , alpha = 0.25 , color = plt . rcParams [ 'text.color' ], ls = '-' )
-793 else :
-794 raise Exception ( "'plateau' must be an Obs" )
-795 796 if references :
-797 if isinstance ( references , list ):
-798 for ref in references :
-799 ax1 . axhline ( y = ref , linewidth = 1 , color = plt . rcParams [ 'text.color' ], alpha = 0.6 , marker = ',' , ls = '--' )
-800 else :
-801 raise Exception ( "'references' must be a list of floating pint values." )
-802 803 if self . prange :
-804 ax1 . axvline ( self . prange [ 0 ], 0 , 1 , ls = '-' , marker = ',' )
-805 ax1 . axvline ( self . prange [ 1 ], 0 , 1 , ls = '-' , marker = ',' )
-806 807 if fit_res :
-808 x_samples = np . arange ( x_range [ 0 ], x_range [ 1 ] + 1 , 0.05 )
-809 ax1 . plot ( x_samples ,
-810 fit_res . fit_function ([ o . value for o in fit_res . fit_parameters ], x_samples ),
-811 ls = '-' , marker = ',' , lw = 2 )
-812 813 ax1 . set_xlabel ( r '$x_0 / a$' )
-814 if ylabel :
-815 ax1 . set_ylabel ( ylabel )
-816 ax1 . set_xlim ([ x_range [ 0 ] - 0.5 , x_range [ 1 ] + 0.5 ])
+764 hide_from = None
+765 ax1 . errorbar ( x [: hide_from ], y [: hide_from ], y_err [: hide_from ], label = self . tag )
+766 if logscale :
+767 ax1 . set_yscale ( 'log' )
+768 else :
+769 if y_range is None :
+770 try :
+771 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 )])
+772 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 )])
+773 ax1 . set_ylim ([ y_min - 0.1 * ( y_max - y_min ), y_max + 0.1 * ( y_max - y_min )])
+774 except Exception :
+775 pass
+776 else :
+777 ax1 . set_ylim ( y_range )
+778 if comp :
+779 if isinstance ( comp , ( Corr , list )):
+780 for corr in comp if isinstance ( comp , list ) else [ comp ]:
+781 if auto_gamma :
+782 corr . gamma_method ()
+783 x , y , y_err = corr . plottable ()
+784 if hide_sigma :
+785 hide_from = np . argmax (( hide_sigma * np . array ( y_err )) > np . abs ( y )) - 1
+786 else :
+787 hide_from = None
+788 plt . errorbar ( x [: hide_from ], y [: hide_from ], y_err [: hide_from ], label = corr . tag , mfc = plt . rcParams [ 'axes.facecolor' ])
+789 else :
+790 raise Exception ( "'comp' must be a correlator or a list of correlators." )
+791 792 if plateau :
+793 if isinstance ( plateau , Obs ):
+794 if auto_gamma :
+795 plateau . gamma_method ()
+796 ax1 . axhline ( y = plateau . value , linewidth = 2 , color = plt . rcParams [ 'text.color' ], alpha = 0.6 , marker = ',' , ls = '--' , label = str ( plateau ))
+797 ax1 . axhspan ( plateau . value - plateau . dvalue , plateau . value + plateau . dvalue , alpha = 0.25 , color = plt . rcParams [ 'text.color' ], ls = '-' )
+798 else :
+799 raise Exception ( "'plateau' must be an Obs" )
+800 801 if references :
+802 if isinstance ( references , list ):
+803 for ref in references :
+804 ax1 . axhline ( y = ref , linewidth = 1 , color = plt . rcParams [ 'text.color' ], alpha = 0.6 , marker = ',' , ls = '--' )
+805 else :
+806 raise Exception ( "'references' must be a list of floating pint values." )
+807 808 if self . prange :
+809 ax1 . axvline ( self . prange [ 0 ], 0 , 1 , ls = '-' , marker = ',' )
+810 ax1 . axvline ( self . prange [ 1 ], 0 , 1 , ls = '-' , marker = ',' )
+811 812 if fit_res :
+813 x_samples = np . arange ( x_range [ 0 ], x_range [ 1 ] + 1 , 0.05 )
+814 ax1 . plot ( x_samples ,
+815 fit_res . fit_function ([ o . value for o in fit_res . fit_parameters ], x_samples ),
+816 ls = '-' , marker = ',' , lw = 2 )
817 818 handles , labels = ax1 . get_legend_handles_labels ()
-819 if labels :
-820 ax1 . legend ()
-821 plt . draw ()
+818 ax1 . set_xlabel ( r '$x_0 / a$' )
+819 if ylabel :
+820 ax1 . set_ylabel ( ylabel )
+821 ax1 . set_xlim ([ x_range [ 0 ] - 0.5 , x_range [ 1 ] + 0.5 ])
822 823 if save :
-824 if isinstance ( save , str ):
-825 fig . savefig ( save )
-826 else :
-827 raise Exception ( "'save' has to be a string." )
+823 handles , labels = ax1 . get_legend_handles_labels ()
+824 if labels :
+825 ax1 . legend ()
+826 plt . draw ()
+827 828 if save :
+829 if isinstance ( save , str ):
+830 fig . savefig ( save )
+831 else :
+832 raise Exception ( "'save' has to be a string." )
829 def spaghetti_plot ( self , logscale = True ):
-830 """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
-831 832 Parameters
-833 ----------
-834 logscale : bool
-835 Determines whether the scale of the y-axis is logarithmic or standard.
-836 """
-837 if self . N != 1 :
-838 raise Exception ( "Correlator needs to be projected first." )
-839 840 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 ]))
-841 x0_vals = [ n for ( n , o ) in zip ( np . arange ( self . T ), self . content ) if o is not None ]
-842 843 for name in mc_names :
-844 data = np . array ([ o [ 0 ] . deltas [ name ] + o [ 0 ] . r_values [ name ] for o in self . content if o is not None ]) . T
-845 846 fig = plt . figure ()
-847 ax = fig . add_subplot ( 111 )
-848 for dat in data :
-849 ax . plot ( x0_vals , dat , ls = '-' , marker = '' )
+ 834 def spaghetti_plot ( self , logscale = True ):
+835 """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
+836 837 Parameters
+838 ----------
+839 logscale : bool
+840 Determines whether the scale of the y-axis is logarithmic or standard.
+841 """
+842 if self . N != 1 :
+843 raise Exception ( "Correlator needs to be projected first." )
+844 845 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 ]))
+846 x0_vals = [ n for ( n , o ) in zip ( np . arange ( self . T ), self . content ) if o is not None ]
+847 848 for name in mc_names :
+849 data = np . array ([ o [ 0 ] . deltas [ name ] + o [ 0 ] . r_values [ name ] for o in self . content if o is not None ]) . T
850 851 if logscale is True :
-852 ax . set_yscale ( 'log' )
-853 854 ax . set_xlabel ( r '$x_0 / a$' )
-855 plt . title ( name )
-856 plt . draw ()
+851 fig = plt . figure ()
+852 ax = fig . add_subplot ( 111 )
+853 for dat in data :
+854 ax . plot ( x0_vals , dat , ls = '-' , marker = '' )
+855 856 if logscale is True :
+857 ax . set_yscale ( 'log' )
+858 859 ax . set_xlabel ( r '$x_0 / a$' )
+860 plt . title ( name )
+861 plt . draw ()
858 def dump ( self , filename , datatype = "json.gz" , ** kwargs ):
-859 """Dumps the Corr into a file of chosen type
-860 Parameters
-861 ----------
-862 filename : str
-863 Name of the file to be saved.
-864 datatype : str
-865 Format of the exported file. Supported formats include
-866 "json.gz" and "pickle"
-867 path : str
-868 specifies a custom path for the file (default '.')
-869 """
-870 if datatype == "json.gz" :
-871 from .input.json import dump_to_json
-872 if 'path' in kwargs :
-873 file_name = kwargs . get ( 'path' ) + '/' + filename
-874 else :
-875 file_name = filename
-876 dump_to_json ( self , file_name )
-877 elif datatype == "pickle" :
-878 dump_object ( self , filename , ** kwargs )
-879 else :
-880 raise Exception ( "Unknown datatype " + str ( datatype ))
+ 863 def dump ( self , filename , datatype = "json.gz" , ** kwargs ):
+864 """Dumps the Corr into a file of chosen type
+865 Parameters
+866 ----------
+867 filename : str
+868 Name of the file to be saved.
+869 datatype : str
+870 Format of the exported file. Supported formats include
+871 "json.gz" and "pickle"
+872 path : str
+873 specifies a custom path for the file (default '.')
+874 """
+875 if datatype == "json.gz" :
+876 from .input.json import dump_to_json
+877 if 'path' in kwargs :
+878 file_name = kwargs . get ( 'path' ) + '/' + filename
+879 else :
+880 file_name = filename
+881 dump_to_json ( self , file_name )
+882 elif datatype == "pickle" :
+883 dump_object ( self , filename , ** kwargs )
+884 else :
+885 raise Exception ( "Unknown datatype " + str ( datatype ))
882 def print ( self , range = [ 0 , None ]):
-883 print ( self . __repr__ ( range ))
+ 887 def print ( self , range = [ 0 , None ]):
+888 print ( self . __repr__ ( range ))
1045 def sqrt ( self ):
-1046 return self ** 0.5
+ 1050 def sqrt ( self ):
+1051 return self ** 0.5
1048 def log ( self ):
-1049 newcontent = [ None if ( item is None ) else np . log ( item ) for item in self . content ]
-1050 return Corr ( newcontent , prange = self . prange )
+ 1053 def log ( self ):
+1054 newcontent = [ None if ( item is None ) else np . log ( item ) for item in self . content ]
+1055 return Corr ( newcontent , prange = self . prange )
1052 def exp ( self ):
-1053 newcontent = [ None if ( item is None ) else np . exp ( item ) for item in self . content ]
-1054 return Corr ( newcontent , prange = self . prange )
+ 1057 def exp ( self ):
+1058 newcontent = [ None if ( item is None ) else np . exp ( item ) for item in self . content ]
+1059 return Corr ( newcontent , prange = self . prange )
1067 def sin ( self ):
-1068 return self . _apply_func_to_corr ( np . sin )
+ 1072 def sin ( self ):
+1073 return self . _apply_func_to_corr ( np . sin )
1070 def cos ( self ):
-1071 return self . _apply_func_to_corr ( np . cos )
+ 1075 def cos ( self ):
+1076 return self . _apply_func_to_corr ( np . cos )
1073 def tan ( self ):
-1074 return self . _apply_func_to_corr ( np . tan )
+ 1078 def tan ( self ):
+1079 return self . _apply_func_to_corr ( np . tan )
1076 def sinh ( self ):
-1077 return self . _apply_func_to_corr ( np . sinh )
+ 1081 def sinh ( self ):
+1082 return self . _apply_func_to_corr ( np . sinh )
1079 def cosh ( self ):
-1080 return self . _apply_func_to_corr ( np . cosh )
+ 1084 def cosh ( self ):
+1085 return self . _apply_func_to_corr ( np . cosh )
1082 def tanh ( self ):
-1083 return self . _apply_func_to_corr ( np . tanh )
+ 1087 def tanh ( self ):
+1088 return self . _apply_func_to_corr ( np . tanh )
1085 def arcsin ( self ):
-1086 return self . _apply_func_to_corr ( np . arcsin )
+ 1090 def arcsin ( self ):
+1091 return self . _apply_func_to_corr ( np . arcsin )
1088 def arccos ( self ):
-1089 return self . _apply_func_to_corr ( np . arccos )
+ 1093 def arccos ( self ):
+1094 return self . _apply_func_to_corr ( np . arccos )
1091 def arctan ( self ):
-1092 return self . _apply_func_to_corr ( np . arctan )
+ 1096 def arctan ( self ):
+1097 return self . _apply_func_to_corr ( np . arctan )
1094 def arcsinh ( self ):
-1095 return self . _apply_func_to_corr ( np . arcsinh )
+ 1099 def arcsinh ( self ):
+1100 return self . _apply_func_to_corr ( np . arcsinh )
1097 def arccosh ( self ):
-1098 return self . _apply_func_to_corr ( np . arccosh )
+ 1102 def arccosh ( self ):
+1103 return self . _apply_func_to_corr ( np . arccosh )
1100 def arctanh ( self ):
-1101 return self . _apply_func_to_corr ( np . arctanh )
+ 1105 def arctanh ( self ):
+1106 return self . _apply_func_to_corr ( np . arctanh )
1136 def prune ( self , Ntrunc , tproj = 3 , t0proj = 2 , basematrix = None ):
-1137 r ''' Project large correlation matrix to lowest states
-1138 1139 This method can be used to reduce the size of an (N x N) correlation matrix
-1140 to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise
-1141 is still small.
-1142 1143 Parameters
-1144 ----------
-1145 Ntrunc: int
-1146 Rank of the target matrix.
-1147 tproj: int
-1148 Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method.
-1149 The default value is 3.
-1150 t0proj: int
-1151 Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly
-1152 discouraged for O(a) improved theories, since the correctness of the procedure
-1153 cannot be granted in this case. The default value is 2.
-1154 basematrix : Corr
-1155 Correlation matrix that is used to determine the eigenvectors of the
-1156 lowest states based on a GEVP. basematrix is taken to be the Corr itself if
-1157 is is not specified.
-1158 1159 Notes
-1160 -----
-1161 We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving
-1162 the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$
-1163 and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the
-1164 resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via
-1165 $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large
-1166 correlation matrix and to remove some noise that is added by irrelevant operators.
-1167 This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated
-1168 bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.
-1169 '''
-1170 1171 if self . N == 1 :
-1172 raise Exception ( 'Method cannot be applied to one-dimensional correlators.' )
-1173 if basematrix is None :
-1174 basematrix = self
-1175 if Ntrunc >= basematrix . N :
-1176 raise Exception ( 'Cannot truncate using Ntrunc <= %d ' % ( basematrix . N ))
-1177 if basematrix . N != self . N :
-1178 raise Exception ( 'basematrix and targetmatrix have to be of the same size.' )
-1179 1180 evecs = []
-1181 for i in range ( Ntrunc ):
-1182 evecs . append ( basematrix . GEVP ( t0proj , tproj , state = i , sorted_list = None ))
-1183 1184 tmpmat = np . empty (( Ntrunc , Ntrunc ), dtype = object )
-1185 rmat = []
-1186 for t in range ( basematrix . T ):
-1187 for i in range ( Ntrunc ):
-1188 for j in range ( Ntrunc ):
-1189 tmpmat [ i ][ j ] = evecs [ i ] . T @ self [ t ] @ evecs [ j ]
-1190 rmat . append ( np . copy ( tmpmat ))
-1191 1192 newcontent = [ None if ( self . content [ t ] is None ) else rmat [ t ] for t in range ( self . T )]
-1193 return Corr ( newcontent )
+ 1141 def prune ( self , Ntrunc , tproj = 3 , t0proj = 2 , basematrix = None ):
+1142 r ''' Project large correlation matrix to lowest states
+1143 1144 This method can be used to reduce the size of an (N x N) correlation matrix
+1145 to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise
+1146 is still small.
+1147 1148 Parameters
+1149 ----------
+1150 Ntrunc: int
+1151 Rank of the target matrix.
+1152 tproj: int
+1153 Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method.
+1154 The default value is 3.
+1155 t0proj: int
+1156 Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly
+1157 discouraged for O(a) improved theories, since the correctness of the procedure
+1158 cannot be granted in this case. The default value is 2.
+1159 basematrix : Corr
+1160 Correlation matrix that is used to determine the eigenvectors of the
+1161 lowest states based on a GEVP. basematrix is taken to be the Corr itself if
+1162 is is not specified.
+1163 1164 Notes
+1165 -----
+1166 We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving
+1167 the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$
+1168 and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the
+1169 resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via
+1170 $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large
+1171 correlation matrix and to remove some noise that is added by irrelevant operators.
+1172 This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated
+1173 bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.
+1174 '''
+1175 1176 if self . N == 1 :
+1177 raise Exception ( 'Method cannot be applied to one-dimensional correlators.' )
+1178 if basematrix is None :
+1179 basematrix = self
+1180 if Ntrunc >= basematrix . N :
+1181 raise Exception ( 'Cannot truncate using Ntrunc <= %d ' % ( basematrix . N ))
+1182 if basematrix . N != self . N :
+1183 raise Exception ( 'basematrix and targetmatrix have to be of the same size.' )
+1184 1185 evecs = basematrix . GEVP ( t0proj , tproj , sort = None )[: Ntrunc ]
+1186 1187 tmpmat = np . empty (( Ntrunc , Ntrunc ), dtype = object )
+1188 rmat = []
+1189 for t in range ( basematrix . T ):
+1190 for i in range ( Ntrunc ):
+1191 for j in range ( Ntrunc ):
+1192 tmpmat [ i ][ j ] = evecs [ i ] . T @ self [ t ] @ evecs [ j ]
+1193 rmat . append ( np . copy ( tmpmat ))
+1194 1195 newcontent = [ None if ( self . content [ t ] is None ) else rmat [ t ] for t in range ( self . T )]
+1196 return Corr ( newcontent )
0&&t.push(e);for(var i in n)"docs"!==i&&"df"!==i&&this.expandToken(e+i,t,n[i]);return t},t.InvertedIndex.prototype.toJSON=function(){return{root:this.root}},t.Configuration=function(e,n){var e=e||"";if(void 0==n||null==n)throw new Error("fields should not be null");this.config={};var i;try{i=JSON.parse(e),this.buildUserConfig(i,n)}catch(o){t.utils.warn("user configuration parse failed, will use default configuration"),this.buildDefaultConfig(n)}},t.Configuration.prototype.buildDefaultConfig=function(e){this.reset(),e.forEach(function(e){this.config[e]={boost:1,bool:"OR",expand:!1}},this)},t.Configuration.prototype.buildUserConfig=function(e,n){var i="OR",o=!1;if(this.reset(),"bool"in e&&(i=e.bool||i),"expand"in e&&(o=e.expand||o),"fields"in e)for(var r in e.fields)if(n.indexOf(r)>-1){var s=e.fields[r],u=o;void 0!=s.expand&&(u=s.expand),this.config[r]={boost:s.boost||0===s.boost?s.boost:1,bool:s.bool||i,expand:u}}else t.utils.warn("field name in user configuration not found in index instance fields");else this.addAllFields2UserConfig(i,o,n)},t.Configuration.prototype.addAllFields2UserConfig=function(e,t,n){n.forEach(function(n){this.config[n]={boost:1,bool:e,expand:t}},this)},t.Configuration.prototype.get=function(){return this.config},t.Configuration.prototype.reset=function(){this.config={}},lunr.SortedSet=function(){this.length=0,this.elements=[]},lunr.SortedSet.load=function(e){var t=new this;return t.elements=e,t.length=e.length,t},lunr.SortedSet.prototype.add=function(){var e,t;for(e=0;e1;){if(r===e)return o;e>r&&(t=o),r>e&&(n=o),i=n-t,o=t+Math.floor(i/2),r=this.elements[o]}return r===e?o:-1},lunr.SortedSet.prototype.locationFor=function(e){for(var t=0,n=this.elements.length,i=n-t,o=t+Math.floor(i/2),r=this.elements[o];i>1;)e>r&&(t=o),r>e&&(n=o),i=n-t,o=t+Math.floor(i/2),r=this.elements[o];return r>e?o:e>r?o+1:void 0},lunr.SortedSet.prototype.intersect=function(e){for(var t=new lunr.SortedSet,n=0,i=0,o=this.length,r=e.length,s=this.elements,u=e.elements;;){if(n>o-1||i>r-1)break;s[n]!==u[i]?s[n]u[i]&&i++:(t.add(s[n]),n++,i++)}return t},lunr.SortedSet.prototype.clone=function(){var e=new lunr.SortedSet;return e.elements=this.toArray(),e.length=e.elements.length,e},lunr.SortedSet.prototype.union=function(e){var t,n,i;this.length>=e.length?(t=this,n=e):(t=e,n=this),i=t.clone();for(var o=0,r=n.toArray();oWhat is pyerrors?\n\npyerrors is a python package for error computation and propagation of Markov chain Monte Carlo data.\nIt is based on the gamma method arXiv:hep-lat/0306017 . Some of its features are:
\n\n\nautomatic differentiation for exact liner error propagation as suggested in arXiv:1809.01289 (partly based on the autograd package). \ntreatment of slow modes in the simulation as suggested in arXiv:1009.5228 . \ncoherent error propagation for data from different Markov chains. \nnon-linear fits with x- and y-errors and exact linear error propagation based on automatic differentiation as introduced in arXiv:1809.01289 . \nreal and complex matrix operations and their error propagation based on automatic differentiation (Matrix inverse, Cholesky decomposition, calculation of eigenvalues and eigenvectors, singular value decomposition...). \n \n\nThere exist similar publicly available implementations of gamma method error analysis suites in Fortran , Julia and Python .
\n\nBasic example \n\nimport numpy as np \nimport pyerrors as pe \n\nmy_obs = pe . Obs ([ samples ], [ 'ensemble_name' ]) # Initialize an Obs object \nmy_new_obs = 2 * np . log ( my_obs ) / my_obs ** 2 # Construct derived Obs object \nmy_new_obs . gamma_method () # Estimate the statistical error \nprint ( my_new_obs ) # Print the result to stdout \n> 0.31498 ( 72 ) \nThe Obs class \n\npyerrors introduces a new datatype, Obs, which simplifies error propagation and estimation for auto- and cross-correlated data.\nAn Obs object can be initialized with two arguments, the first is a list containing the samples for an observable from a Monte Carlo chain.\nThe samples can either be provided as python list or as numpy array.\nThe second argument is a list containing the names of the respective Monte Carlo chains as strings. These strings uniquely identify a Monte Carlo chain/ensemble.
\n\nimport pyerrors as pe \n\nmy_obs = pe . Obs ([ samples ], [ 'ensemble_name' ]) \nError propagation \n\nWhen performing mathematical operations on Obs objects the correct error propagation is intrinsically taken care of using a first order Taylor expansion\n$$\\delta_f^i=\\sum_\\alpha \\bar{f}_\\alpha \\delta_\\alpha^i\\,,\\quad \\delta_\\alpha^i=a_\\alpha^i-\\bar{a}_\\alpha\\,,$$\nas introduced in arXiv:hep-lat/0306017 .\nThe required derivatives $\\bar{f}_\\alpha$ are evaluated up to machine precision via automatic differentiation as suggested in arXiv:1809.01289 .
\n\nThe Obs class is designed such that mathematical numpy functions can be used on Obs just as for regular floats.
\n\nimport numpy as np \nimport pyerrors as pe \n\nmy_obs1 = pe . Obs ([ samples1 ], [ 'ensemble_name' ]) \nmy_obs2 = pe . Obs ([ samples2 ], [ 'ensemble_name' ]) \n\nmy_sum = my_obs1 + my_obs2 \n\nmy_m_eff = np . log ( my_obs1 / my_obs2 ) \n\niamzero = my_m_eff - my_m_eff \n# Check that value and fluctuations are zero within machine precision \nprint ( iamzero == 0.0 ) \n> True \nError estimation \n\nThe error estimation within pyerrors is based on the gamma method introduced in arXiv:hep-lat/0306017 .\nAfter having arrived at the derived quantity of interest the gamma_method can be called as detailed in the following example.
\n\nmy_sum . gamma_method () \nprint ( my_sum ) \n> 1.70 ( 57 ) \nmy_sum . details () \n> Result 1.70000000e+00 +/- 5.72046658e-01 +/- 7.56746598e-02 ( 33.650 % ) \n> t_int 2.71422900e+00 +/- 6.40320983e-01 S = 2.00 \n> 1000 samples in 1 ensemble : \n> \u00b7 Ensemble 'ensemble_name' : 1000 configurations ( from 1 to 1000 ) \nWe use the following definition of the integrated autocorrelation time established in Madras & Sokal 1988 \n$$\\tau_\\mathrm{int}=\\frac{1}{2}+\\sum_{t=1}^{W}\\rho(t)\\geq \\frac{1}{2}\\,.$$\nThe window $W$ is determined via the automatic windowing procedure described in arXiv:hep-lat/0306017 .\nThe standard value for the parameter $S$ of this automatic windowing procedure is $S=2$. Other values for $S$ can be passed to the gamma_method as parameter.
\n\nmy_sum . gamma_method ( S = 3.0 ) \nmy_sum . details () \n> Result 1.70000000e+00 +/- 6.30675201e-01 +/- 1.04585650e-01 ( 37.099 % ) \n> t_int 3.29909703e+00 +/- 9.77310102e-01 S = 3.00 \n> 1000 samples in 1 ensemble : \n> \u00b7 Ensemble 'ensemble_name' : 1000 configurations ( from 1 to 1000 ) \nThe integrated autocorrelation time $\\tau_\\mathrm{int}$ and the autocorrelation function $\\rho(W)$ can be monitored via the methods pyerrors.obs.Obs.plot_tauint and pyerrors.obs.Obs.plot_tauint.
\n\nIf the parameter $S$ is set to zero it is assumed that the dataset does not exhibit any autocorrelation and the windowsize is chosen to be zero.\nIn this case the error estimate is identical to the sample standard error.
\n\nExponential tails \n\nSlow modes in the Monte Carlo history can be accounted for by attaching an exponential tail to the autocorrelation function $\\rho$ as suggested in arXiv:1009.5228 . The longest autocorrelation time in the history, $\\tau_\\mathrm{exp}$, can be passed to the gamma_method as parameter. In this case the automatic windowing procedure is vacated and the parameter $S$ does not affect the error estimate.
\n\nmy_sum . gamma_method ( tau_exp = 7.2 ) \nmy_sum . details () \n> Result 1.70000000e+00 +/- 6.28097762e-01 +/- 5.79077524e-02 ( 36.947 % ) \n> t_int 3.27218667e+00 +/- 7.99583654e-01 tau_exp = 7.20 , N_sigma = 1 \n> 1000 samples in 1 ensemble : \n> \u00b7 Ensemble 'ensemble_name' : 1000 configurations ( from 1 to 1000 ) \nFor the full API see pyerrors.obs.Obs.gamma_method.
\n\nMultiple ensembles/replica \n\nError propagation for multiple ensembles (Markov chains with different simulation parameters) is handled automatically. Ensembles are uniquely identified by their name.
\n\nobs1 = pe . Obs ([ samples1 ], [ 'ensemble1' ]) \nobs2 = pe . Obs ([ samples2 ], [ 'ensemble2' ]) \n\nmy_sum = obs1 + obs2 \nmy_sum . details () \n> Result 2.00697958e+00 \n> 1500 samples in 2 ensembles : \n> \u00b7 Ensemble 'ensemble1' : 1000 configurations ( from 1 to 1000 ) \n> \u00b7 Ensemble 'ensemble2' : 500 configurations ( from 1 to 500 ) \npyerrors identifies multiple replica (independent Markov chains with identical simulation parameters) by the vertical bar | in the name of the data set.
\n\nobs1 = pe . Obs ([ samples1 ], [ 'ensemble1|r01' ]) \nobs2 = pe . Obs ([ samples2 ], [ 'ensemble1|r02' ]) \n\n> my_sum = obs1 + obs2 \n> my_sum . details () \n> Result 2.00697958e+00 \n> 1500 samples in 1 ensemble : \n> \u00b7 Ensemble 'ensemble1' \n> \u00b7 Replicum 'r01' : 1000 configurations ( from 1 to 1000 ) \n> \u00b7 Replicum 'r02' : 500 configurations ( from 1 to 500 ) \nError estimation for multiple ensembles \n\nIn order to keep track of different error analysis parameters for different ensembles one can make use of global dictionaries as detailed in the following example.
\n\npe . Obs . S_dict [ 'ensemble1' ] = 2.5 \npe . Obs . tau_exp_dict [ 'ensemble2' ] = 8.0 \npe . Obs . tau_exp_dict [ 'ensemble3' ] = 2.0 \nIn case the gamma_method is called without any parameters it will use the values specified in the dictionaries for the respective ensembles.\nPassing arguments to the gamma_method still dominates over the dictionaries.
\n\nIrregular Monte Carlo chains \n\nObs objects defined on irregular Monte Carlo chains can be initialized with the parameter idl.
\n\n# Observable defined on configurations 20 to 519 \nobs1 = pe . Obs ([ samples1 ], [ 'ensemble1' ], idl = [ range ( 20 , 520 )]) \nobs1 . details () \n> Result 9.98319881e-01 \n> 500 samples in 1 ensemble : \n> \u00b7 Ensemble 'ensemble1' : 500 configurations ( from 20 to 519 ) \n\n# Observable defined on every second configuration between 5 and 1003 \nobs2 = pe . Obs ([ samples2 ], [ 'ensemble1' ], idl = [ range ( 5 , 1005 , 2 )]) \nobs2 . details () \n> Result 9.99100712e-01 \n> 500 samples in 1 ensemble : \n> \u00b7 Ensemble 'ensemble1' : 500 configurations ( from 5 to 1003 in steps of 2 ) \n\n# Observable defined on configurations 2, 9, 28, 29 and 501 \nobs3 = pe . Obs ([ samples3 ], [ 'ensemble1' ], idl = [[ 2 , 9 , 28 , 29 , 501 ]]) \nobs3 . details () \n> Result 1.01718064e+00 \n> 5 samples in 1 ensemble : \n> \u00b7 Ensemble 'ensemble1' : 5 configurations ( irregular range ) \nObs objects defined on regular and irregular histories of the same ensemble can be combined with each other and the correct error propagation and estimation is automatically taken care of.
\n\nWarning: Irregular Monte Carlo chains can result in odd patterns in the autocorrelation functions.\nMake sure to check the autocorrelation time with e.g. pyerrors.obs.Obs.plot_rho or pyerrors.obs.Obs.plot_tauint.
\n\nFor the full API see pyerrors.obs.Obs.
\n\nCorrelators \n\nWhen one is not interested in single observables but correlation functions, pyerrors offers the Corr class which simplifies the corresponding error propagation and provides the user with a set of standard methods. In order to initialize a Corr objects one needs to arrange the data as a list of Obs
\n\nmy_corr = pe . Corr ([ obs_0 , obs_1 , obs_2 , obs_3 ]) \nprint ( my_corr ) \n> x0 / a Corr ( x0 / a ) \n> ------------------ \n> 0 0.7957 ( 80 ) \n> 1 0.5156 ( 51 ) \n> 2 0.3227 ( 33 ) \n> 3 0.2041 ( 21 ) \nIn case the correlation functions are not defined on the outermost timeslices, for example because of fixed boundary conditions, a padding can be introduced.
\n\nmy_corr = pe . Corr ([ obs_0 , obs_1 , obs_2 , obs_3 ], padding = [ 1 , 1 ]) \nprint ( my_corr ) \n> x0 / a Corr ( x0 / a ) \n> ------------------ \n> 0 \n> 1 0.7957 ( 80 ) \n> 2 0.5156 ( 51 ) \n> 3 0.3227 ( 33 ) \n> 4 0.2041 ( 21 ) \n> 5 \nThe individual entries of a correlator can be accessed via slicing
\n\nprint ( my_corr [ 3 ]) \n> 0.3227 ( 33 ) \nError propagation with the Corr class works very similar to Obs objects. Mathematical operations are overloaded and Corr objects can be computed together with other Corr objects, Obs objects or real numbers and integers.
\n\nmy_new_corr = 0.3 * my_corr [ 2 ] * my_corr * my_corr + 12 / my_corr \npyerrors provides the user with a set of regularly used methods for the manipulation of correlator objects:
\n\n\nCorr.gamma_method applies the gamma method to all entries of the correlator.Corr.m_eff to construct effective masses. Various variants for periodic and fixed temporal boundary conditions are available.Corr.deriv returns the first derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.Corr.second_deriv returns the second derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.Corr.symmetric symmetrizes parity even correlations functions, assuming periodic boundary conditions.Corr.anti_symmetric anti-symmetrizes parity odd correlations functions, assuming periodic boundary conditions.Corr.T_symmetry averages a correlator with its time symmetry partner, assuming fixed boundary conditions.Corr.plateau extracts a plateau value from the correlator in a given range.Corr.roll periodically shifts the correlator.Corr.reverse reverses the time ordering of the correlator.Corr.correlate constructs a disconnected correlation function from the correlator and another Corr or Obs object.Corr.reweight reweights the correlator. \n\npyerrors can also handle matrices of correlation functions and extract energy states from these matrices via a generalized eigenvalue problem (see pyerrors.correlators.Corr.GEVP).
\n\nFor the full API see pyerrors.correlators.Corr.
\n\nComplex valued observables \n\npyerrors can handle complex valued observables via the class pyerrors.obs.CObs.\nCObs are initialized with a real and an imaginary part which both can be Obs valued.
\n\nmy_real_part = pe . Obs ([ samples1 ], [ 'ensemble1' ]) \nmy_imag_part = pe . Obs ([ samples2 ], [ 'ensemble1' ]) \n\nmy_cobs = pe . CObs ( my_real_part , my_imag_part ) \nmy_cobs . gamma_method () \nprint ( my_cobs ) \n> ( 0.9959 ( 91 ) + 0.659 ( 28 ) j ) \nElementary mathematical operations are overloaded and samples are properly propagated as for the Obs class.
\n\nmy_derived_cobs = ( my_cobs + my_cobs . conjugate ()) / np . abs ( my_cobs ) \nmy_derived_cobs . gamma_method () \nprint ( my_derived_cobs ) \n> ( 1.668 ( 23 ) + 0.0 j ) \nThe Covobs class \n\nIn many projects, auxiliary data that is not based on Monte Carlo chains enters. Examples are experimentally determined mesons masses which are used to set the scale or renormalization constants. These numbers come with an error that has to be propagated through the analysis. The Covobs class allows to define such quantities in pyerrors. Furthermore, external input might consist of correlated quantities. An example are the parameters of an interpolation formula, which are defined via mean values and a covariance matrix between all parameters. The contribution of the interpolation formula to the error of a derived quantity therefore might depend on the complete covariance matrix.
\n\nThis concept is built into the definition of Covobs. In pyerrors, external input is defined by $M$ mean values, a $M\\times M$ covariance matrix, where $M=1$ is permissible, and a name that uniquely identifies the covariance matrix. Below, we define the pion mass, based on its mean value and error, 134.9768(5). Note, that the square of the error enters cov_Obs, since the second argument of this function is the covariance matrix of the Covobs.
\n\nimport pyerrors.obs as pe \n\nmpi = pe . cov_Obs ( 134.9768 , 0.0005 ** 2 , 'pi^0 mass' ) \nmpi . gamma_method () \nmpi . details () \n> Result 1.34976800e+02 +/- 5.00000000e-04 +/- 0.00000000e+00 ( 0.000 % ) \n> pi ^ 0 mass 5.00000000e-04 \n> 0 samples in 1 ensemble : \n> \u00b7 Covobs 'pi^0 mass' \nThe resulting object mpi is an Obs that contains a Covobs. In the following, it may be handled as any other Obs. The contribution of the covariance matrix to the error of an Obs is determined from the $M \\times M$ covariance matrix $\\Sigma$ and the gradient of the Obs with respect to the external quantities, which is the $1\\times M$ Jacobian matrix $J$, via\n$$s = \\sqrt{J^T \\Sigma J}\\,,$$\nwhere the Jacobian is computed for each derived quantity via automatic differentiation.
\n\nCorrelated auxiliary data is defined similarly to above, e.g., via
\n\nRAP = pe . cov_Obs ([ 16.7457 , - 19.0475 ], [[ 3.49591 , - 6.07560 ], [ - 6.07560 , 10.5834 ]], 'R_AP, 1906.03445, (5.3a)' ) \nprint ( RAP ) \n> [ Obs [ 16.7 ( 1.9 )], Obs [ - 19.0 ( 3.3 )]] \nwhere RAP now is a list of two Obs that contains the two correlated parameters.
\n\nSince the gradient of a derived observable with respect to an external covariance matrix is propagated through the entire analysis, the Covobs class allows to quote the derivative of a result with respect to the external quantities. If these derivatives are published together with the result, small shifts in the definition of external quantities, e.g., the definition of the physical point, can be performed a posteriori based on the published information. This may help to compare results of different groups. The gradient of an Obs o with respect to a covariance matrix with the identifying string k may be accessed via
\n\n\n\nError propagation in iterative algorithms \n\npyerrors supports exact linear error propagation for iterative algorithms like various variants of non-linear least sqaures fits or root finding. The derivatives required for the error propagation are calculated as described in arXiv:1809.01289 .
\n\nLeast squares fits \n\nStandard non-linear least square fits with errors on the dependent but not the independent variables can be performed with pyerrors.fits.least_squares. As default solver the Levenberg-Marquardt algorithm implemented in scipy is used.
\n\nFit functions have to be of the following form
\n\nimport autograd.numpy as anp \n\ndef func ( a , x ): \n return a [ 1 ] * anp . exp ( - a [ 0 ] * x ) \nIt is important that numerical functions refer to autograd.numpy instead of numpy for the automatic differentiation in iterative algorithms to work properly.
\n\nFits can then be performed via
\n\nfit_result = pe . fits . least_squares ( x , y , func ) \nprint ( " \\n " , fit_result ) \n> Fit with 2 parameters \n> Method : Levenberg - Marquardt \n> ` ftol ` termination condition is satisfied . \n> chisquare / d . o . f . : 0.9593035785160936 \n\n> Goodness of fit : \n> \u03c7 \u00b2 / d . o . f . = 0.959304 \n> p - value = 0.5673 \n> Fit parameters : \n> 0 0.0548 ( 28 ) \n> 1 1.933 ( 64 ) \nwhere x is a list or numpy.array of floats and y is a list or numpy.array of Obs.
\n\nData stored in Corr objects can be fitted directly using the Corr.fit method.
\n\nmy_corr = pe . Corr ( y ) \nfit_result = my_corr . fit ( func , fitrange = [ 12 , 25 ]) \nthis can simplify working with absolute fit ranges and takes care of gaps in the data automatically.
\n\nFor fit functions with multiple independent variables the fit function can be of the form
\n\ndef func ( a , x ): \n ( x1 , x2 ) = x \n return a [ 0 ] * x1 ** 2 + a [ 1 ] * x2 \npyerrors also supports correlated fits which can be triggered via the parameter correlated_fit=True.\nDetails about how the required covariance matrix is estimated can be found in pyerrors.obs.covariance.
\n\nDirect visualizations of the performed fits can be triggered via resplot=True or qqplot=True. For all available options see pyerrors.fits.least_squares.
\n\nTotal least squares fits \n\npyerrors can also fit data with errors on both the dependent and independent variables using the total least squares method also referred to orthogonal distance regression as implemented in scipy , see pyerrors.fits.least_squares. The syntax is identical to the standard least squares case, the only diffrence being that x also has to be a list or numpy.array of Obs.
\n\nFor the full API see pyerrors.fits for fits and pyerrors.roots for finding roots of functions.
\n\nMatrix operations \n\npyerrors provides wrappers for Obs- and CObs-valued matrix operations based on numpy.linalg. The supported functions include:
\n\n\ninv for the matrix inverse.cholseky for the Cholesky decomposition.det for the matrix determinant.eigh for eigenvalues and eigenvectors of hermitean matrices.eig for eigenvalues of general matrices.pinv for the Moore-Penrose pseudoinverse.svd for the singular-value-decomposition. \n\nFor the full API see pyerrors.linalg.
\n\nExport data \n\nThe preferred exported file format within pyerrors is json.gz. Files written to this format are valid JSON files that have been compressed using gzip. The structure of the content is inspired by the dobs format of the ALPHA collaboration. The aim of the format is to facilitate the storage of data in a self-contained way such that, even years after the creation of the file, it is possible to extract all necessary information:
\n\n\nWhat observables are stored? Possibly: How exactly are they defined. \nHow does each single ensemble or external quantity contribute to the error of the observable? \nWho did write the file when and on which machine? \n \n\nThis can be achieved by storing all information in one single file. The export routines of pyerrors are written such that as much information as possible is written automatically as described in the following example
\n\nmy_obs = pe . Obs ([ samples ], [ "test_ensemble" ]) \nmy_obs . tag = "My observable" \n\npe . input . json . dump_to_json ( my_obs , "test_output_file" , description = "This file contains a test observable" ) \n# For a single observable one can equivalently use the class method dump \nmy_obs . dump ( "test_output_file" , description = "This file contains a test observable" ) \n\ncheck = pe . input . json . load_json ( "test_output_file" ) \n\nprint ( my_obs == check ) \n> True \nThe format also allows to directly write out the content of Corr objects or lists and arrays of Obs objects by passing the desired data to pyerrors.input.json.dump_to_json.
\n\n\n\nThe first entries of the file provide optional auxiliary information:
\n\n\nprogram is a string that indicates which program was used to write the file.version is a string that specifies the version of the format.who is a string that specifies the user name of the creator of the file.date is a string and contains the creation date of the file.host is a string and contains the hostname of the machine where the file has been written.description contains information on the content of the file. This field is not filled automatically in pyerrors. The user is advised to provide as detailed information as possible in this field. Examples are: Input files of measurements or simulations, LaTeX formulae or references to publications to specify how the observables have been computed, details on the analysis strategy, ... This field may be any valid JSON type. Strings, arrays or objects (equivalent to dicts in python) are well suited to provide information. \n\nThe only necessary entry of the file is the field\n-obsdata, an array that contains the actual data.
\n\nEach entry of the array belongs to a single structure of observables. Currently, these structures can be either of Obs, list, numpy.ndarray, Corr. All Obs inside a structure (with dimension > 0) have to be defined on the same set of configurations. Different structures, that are represented by entries of the array obsdata, are treated independently. Each entry of the array obsdata has the following required entries:
\n\n\ntype is a string that specifies the type of the structure. This allows to parse the content to the correct form after reading the file. It is always possible to interpret the content as list of Obs.value is an array that contains the mean values of the Obs inside the structure.\nThe following entries are optional:layout is a string that specifies the layout of multi-dimensional structures. Examples are \"2, 2\" for a 2x2 dimensional matrix or \"64, 4, 4\" for a Corr with $T=64$ and 4x4 matrices on each time slices. \"1\" denotes a single Obs. Multi-dimensional structures are stored in row-major format (see below).tag is any JSON type. It contains additional information concerning the structure. The tag of an Obs in pyerrors is written here.reweighted is a Bool that may be used to specify, whether the Obs in the structure have been reweighted.data is an array that contains the data from MC chains. We will define it below.cdata is an array that contains the data from external quantities with an error (Covobs in pyerrors). We will define it below. \n\nThe array data contains the data from MC chains. Each entry of the array corresponds to one ensemble and contains:
\n\n\nid, a string that contains the name of the ensemblereplica, an array that contains an entry per replica of the ensemble. \n\nEach entry of replica contains\nname, a string that contains the name of the replica\ndeltas, an array that contains the actual data.
\n\nEach entry in deltas corresponds to one configuration of the replica and has $1+N$ many entries. The first entry is an integer that specifies the configuration number that, together with ensemble and replica name, may be used to uniquely identify the configuration on which the data has been obtained. The following N entries specify the deltas, i.e., the deviation of the observable from the mean value on this configuration, of each Obs inside the structure. Multi-dimensional structures are stored in a row-major format. For primary observables, such as correlation functions, $value + delta_i$ matches the primary data obtained on the configuration.
\n\nThe array cdata contains information about the contribution of auxiliary observables, represented by Covobs in pyerrors, to the total error of the observables. Each entry of the array belongs to one auxiliary covariance matrix and contains:
\n\n\nid, a string that identifies the covariance matrixlayout, a string that defines the dimensions of the $M\\times M$ covariance matrix (has to be \"M, M\" or \"1\").cov, an array that contains the $M\\times M$ many entries of the covariance matrix, stored in row-major format.grad, an array that contains N entries, one for each Obs inside the structure. Each entry itself is an array, that contains the M gradients of the Nth observable with respect to the quantity that corresponds to the Mth diagonal entry of the covariance matrix. \n\nA JSON schema that may be used to verify the correctness of a file with respect to the format definition is stored in ./examples/json_schema.json. The schema is a self-descriptive format definition and contains an exemplary file.
\n\nJulia I/O routines for the json.gz format, compatible with ADerrors.jl , can be found here .
\n\nCiting \n\nIf you use pyerrors for research that leads to a publication please consider citing:
\n\n\nUlli Wolff, Monte Carlo errors with less errors . Comput.Phys.Commun. 156 (2004) 143-153, Comput.Phys.Commun. 176 (2007) 383 (erratum). \nStefan Schaefer, Rainer Sommer, Francesco Virotta, Critical slowing down and error analysis in lattice QCD simulations . Nucl.Phys.B 845 (2011) 93-119. \nAlberto Ramos, Automatic differentiation for error analysis of Monte Carlo data . Comput.Phys.Commun. 238 (2019) 19-35. \n \n"}, "pyerrors.correlators": {"fullname": "pyerrors.correlators", "modulename": "pyerrors.correlators", "type": "module", "doc": "
\n"}, "pyerrors.correlators.Corr": {"fullname": "pyerrors.correlators.Corr", "modulename": "pyerrors.correlators", "qualname": "Corr", "type": "class", "doc": "The class for a correlator (time dependent sequence of pe.Obs).
\n\nEverything, this class does, can be achieved using lists or arrays of Obs.\nBut it is simply more convenient to have a dedicated object for correlators.\nOne often wants to add or multiply correlators of the same length at every timeslice and it is inconvenient\nto iterate over all timeslices for every operation. This is especially true, when dealing with matrices.
\n\nThe correlator can have two types of content: An Obs at every timeslice OR a GEVP\nmatrix at every timeslice. Other dependency (eg. spatial) are not supported.
\n"}, "pyerrors.correlators.Corr.__init__": {"fullname": "pyerrors.correlators.Corr.__init__", "modulename": "pyerrors.correlators", "qualname": "Corr.__init__", "type": "function", "doc": "Initialize a Corr object.
\n\nParameters \n\n\ndata_input (list or array):\nlist of Obs or list of arrays of Obs or array of Corrspadding (list, optional):\nList with two entries where the first labels the padding\nat the front of the correlator and the second the padding\nat the back.prange (list, optional):\nList containing the first and last timeslice of the plateau\nregion indentified for this correlator. \n", "signature": "(self, data_input, padding=[0, 0], prange=None)", "funcdef": "def"}, "pyerrors.correlators.Corr.reweighted": {"fullname": "pyerrors.correlators.Corr.reweighted", "modulename": "pyerrors.correlators", "qualname": "Corr.reweighted", "type": "variable", "doc": "
\n"}, "pyerrors.correlators.Corr.gamma_method": {"fullname": "pyerrors.correlators.Corr.gamma_method", "modulename": "pyerrors.correlators", "qualname": "Corr.gamma_method", "type": "function", "doc": "Apply the gamma method to the content of the Corr.
\n", "signature": "(self, **kwargs)", "funcdef": "def"}, "pyerrors.correlators.Corr.projected": {"fullname": "pyerrors.correlators.Corr.projected", "modulename": "pyerrors.correlators", "qualname": "Corr.projected", "type": "function", "doc": "We need to project the Correlator with a Vector to get a single value at each timeslice.
\n\nThe method can use one or two vectors.\nIf two are specified it returns v1@G@v2 (the order might be very important.)\nBy default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to
\n", "signature": "(self, vector_l=None, vector_r=None, normalize=False)", "funcdef": "def"}, "pyerrors.correlators.Corr.item": {"fullname": "pyerrors.correlators.Corr.item", "modulename": "pyerrors.correlators", "qualname": "Corr.item", "type": "function", "doc": "Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice.
\n\nParameters \n\n\ni (int):\nFirst index to be picked.j (int):\nSecond index to be picked. \n", "signature": "(self, i, j)", "funcdef": "def"}, "pyerrors.correlators.Corr.plottable": {"fullname": "pyerrors.correlators.Corr.plottable", "modulename": "pyerrors.correlators", "qualname": "Corr.plottable", "type": "function", "doc": "Outputs the correlator in a plotable format.
\n\nOutputs three lists containing the timeslice index, the value on each\ntimeslice and the error on each timeslice.
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.symmetric": {"fullname": "pyerrors.correlators.Corr.symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.symmetric", "type": "function", "doc": "Symmetrize the correlator around x0=0.
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.anti_symmetric": {"fullname": "pyerrors.correlators.Corr.anti_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.anti_symmetric", "type": "function", "doc": "Anti-symmetrize the correlator around x0=0.
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.matrix_symmetric", "type": "function", "doc": "Symmetrizes the correlator matrices on every timeslice.
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.GEVP": {"fullname": "pyerrors.correlators.Corr.GEVP", "modulename": "pyerrors.correlators", "qualname": "Corr.GEVP", "type": "function", "doc": "Solve the general eigenvalue problem on the current correlator
\n\nParameters \n\n\nt0 (int):\nThe time t0 for G(t)v= lambda G(t_0)vts (int):\nfixed time G(t_s)v= lambda G(t_0)v if return_list=False\nIf return_list=True and sorting=Eigenvector it gives a reference point for the sorting method.state (int):\nThe state one is interested in, ordered by energy. The lowest state is zero.sorted_list (string):\nif this argument is set, a list of vectors (len=self.T) is returned. If it is left as None, only one vector is returned.\n\"Eigenvalue\" - The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice.\n\"Eigenvector\" - Use the method described in arXiv:2004.10472 [hep-lat] to find the set of v(t) belonging to the state.\n The reference state is identified by its eigenvalue at t=ts \n", "signature": "(self, t0, ts=None, state=0, sorted_list='Eigenvalue')", "funcdef": "def"}, "pyerrors.correlators.Corr.Eigenvalue": {"fullname": "pyerrors.correlators.Corr.Eigenvalue", "modulename": "pyerrors.correlators", "qualname": "Corr.Eigenvalue", "type": "function", "doc": "Determines the eigenvalue of the GEVP by solving and projecting the correlator
\n\nParameters \n\n\nt0 (int):\nThe time t0 for G(t)v= lambda G(t_0)vts (int):\nfixed time G(t_s)v= lambda G(t_0)v if return_list=False\nIf return_list=True and sorting=Eigenvector it gives a reference point for the sorting method.state (int):\nThe state one is interested in ordered by energy. The lowest state is zero.sorted_list (string):\nif this argument is set, a list of vectors (len=self.T) is returned. If it is left as None, only one vector is returned.\n\"Eigenvalue\" - The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice.\n\"Eigenvector\" - Use the method described in arXiv:2004.10472 [hep-lat] to find the set of v(t) belonging to the state.\n The reference state is identified by its eigenvalue at t=ts \n", "signature": "(self, t0, ts=None, state=0, sorted_list=None)", "funcdef": "def"}, "pyerrors.correlators.Corr.Hankel": {"fullname": "pyerrors.correlators.Corr.Hankel", "modulename": "pyerrors.correlators", "qualname": "Corr.Hankel", "type": "function", "doc": "Constructs an NxN Hankel matrix
\n\nC(t) c(t+1) ... c(t+n-1)\nC(t+1) c(t+2) ... c(t+n)\n.................\nC(t+(n-1)) c(t+n) ... c(t+2(n-1))
\n\nParameters \n\n\nN (int):\nDimension of the Hankel matrixperiodic (bool, optional):\ndetermines whether the matrix is extended periodically \n", "signature": "(self, N, periodic=False)", "funcdef": "def"}, "pyerrors.correlators.Corr.roll": {"fullname": "pyerrors.correlators.Corr.roll", "modulename": "pyerrors.correlators", "qualname": "Corr.roll", "type": "function", "doc": "Periodically shift the correlator by dt timeslices
\n\nParameters \n\n\ndt (int):\nnumber of timeslices \n", "signature": "(self, dt)", "funcdef": "def"}, "pyerrors.correlators.Corr.reverse": {"fullname": "pyerrors.correlators.Corr.reverse", "modulename": "pyerrors.correlators", "qualname": "Corr.reverse", "type": "function", "doc": "Reverse the time ordering of the Corr
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.thin": {"fullname": "pyerrors.correlators.Corr.thin", "modulename": "pyerrors.correlators", "qualname": "Corr.thin", "type": "function", "doc": "Thin out a correlator to suppress correlations
\n\nParameters \n\n\nspacing (int):\nKeep only every 'spacing'th entry of the correlatoroffset (int):\nOffset the equal spacing \n", "signature": "(self, spacing=2, offset=0)", "funcdef": "def"}, "pyerrors.correlators.Corr.correlate": {"fullname": "pyerrors.correlators.Corr.correlate", "modulename": "pyerrors.correlators", "qualname": "Corr.correlate", "type": "function", "doc": "Correlate the correlator with another correlator or Obs
\n\nParameters \n\n\npartner (Obs or Corr):\npartner to correlate the correlator with.\nCan either be an Obs which is correlated with all entries of the\ncorrelator or a Corr of same length. \n", "signature": "(self, partner)", "funcdef": "def"}, "pyerrors.correlators.Corr.reweight": {"fullname": "pyerrors.correlators.Corr.reweight", "modulename": "pyerrors.correlators", "qualname": "Corr.reweight", "type": "function", "doc": "Reweight the correlator.
\n\nParameters \n\n\nweight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. \n", "signature": "(self, weight, **kwargs)", "funcdef": "def"}, "pyerrors.correlators.Corr.T_symmetry": {"fullname": "pyerrors.correlators.Corr.T_symmetry", "modulename": "pyerrors.correlators", "qualname": "Corr.T_symmetry", "type": "function", "doc": "Return the time symmetry average of the correlator and its partner
\n\nParameters \n\n\npartner (Corr):\nTime symmetry partner of the Corrpartity (int):\nParity quantum number of the correlator, can be +1 or -1 \n", "signature": "(self, partner, parity=1)", "funcdef": "def"}, "pyerrors.correlators.Corr.deriv": {"fullname": "pyerrors.correlators.Corr.deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.deriv", "type": "function", "doc": "Return the first derivative of the correlator with respect to x0.
\n\nParameters \n\n\nvariant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, forward, backward, improved, default: symmetric \n", "signature": "(self, variant='symmetric')", "funcdef": "def"}, "pyerrors.correlators.Corr.second_deriv": {"fullname": "pyerrors.correlators.Corr.second_deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.second_deriv", "type": "function", "doc": "Return the second derivative of the correlator with respect to x0.
\n\nParameters \n\n\nvariant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, improved, default: symmetric \n", "signature": "(self, variant='symmetric')", "funcdef": "def"}, "pyerrors.correlators.Corr.m_eff": {"fullname": "pyerrors.correlators.Corr.m_eff", "modulename": "pyerrors.correlators", "qualname": "Corr.m_eff", "type": "function", "doc": "Returns the effective mass of the correlator as correlator object
\n\nParameters \n\n\nvariant (str):\nlog : uses the standard effective mass log(C(t) / C(t+1))\ncosh, 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.\nsinh : 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.\nSee, e.g., arXiv:1205.5380\narccosh : Uses the explicit form of the symmetrized correlator (not recommended)guess (float):\nguess for the root finder, only relevant for the root variant \n", "signature": "(self, variant='log', guess=1.0)", "funcdef": "def"}, "pyerrors.correlators.Corr.fit": {"fullname": "pyerrors.correlators.Corr.fit", "modulename": "pyerrors.correlators", "qualname": "Corr.fit", "type": "function", "doc": "Fits function to the data
\n\nParameters \n\n\nfunction (obj):\nfunction to fit to the data. See fits.least_squares for details.fitrange (list):\nTwo element list containing the timeslices on which the fit is supposed to start and stop.\nCaution: This range is inclusive as opposed to standard python indexing.\nfitrange=[4, 6] corresponds to the three entries 4, 5 and 6.\nIf not specified, self.prange or all timeslices are used.silent (bool):\nDecides whether output is printed to the standard output. \n", "signature": "(self, function, fitrange=None, silent=False, **kwargs)", "funcdef": "def"}, "pyerrors.correlators.Corr.plateau": {"fullname": "pyerrors.correlators.Corr.plateau", "modulename": "pyerrors.correlators", "qualname": "Corr.plateau", "type": "function", "doc": "Extract a plateau value from a Corr object
\n\nParameters \n\n\nplateau_range (list):\nlist with two entries, indicating the first and the last timeslice\nof the plateau region.method (str):\nmethod to extract the plateau.\n 'fit' fits a constant to the plateau region\n 'avg', 'average' or 'mean' just average over the given timeslices.auto_gamma (bool):\napply gamma_method with default parameters to the Corr. Defaults to None \n", "signature": "(self, plateau_range=None, method='fit', auto_gamma=False)", "funcdef": "def"}, "pyerrors.correlators.Corr.set_prange": {"fullname": "pyerrors.correlators.Corr.set_prange", "modulename": "pyerrors.correlators", "qualname": "Corr.set_prange", "type": "function", "doc": "Sets the attribute prange of the Corr object.
\n", "signature": "(self, prange)", "funcdef": "def"}, "pyerrors.correlators.Corr.show": {"fullname": "pyerrors.correlators.Corr.show", "modulename": "pyerrors.correlators", "qualname": "Corr.show", "type": "function", "doc": "Plots the correlator using the tag of the correlator as label if available.
\n\nParameters \n\n\nx_range (list):\nlist of two values, determining the range of the x-axis e.g. [4, 8]comp (Corr or list of Corr):\nCorrelator or list of correlators which are plotted for comparison.\nThe tags of these correlators are used as labels if available.logscale (bool):\nSets y-axis to logscaleplateau (Obs):\nPlateau value to be visualized in the figurefit_res (Fit_result):\nFit_result object to be visualizedylabel (str):\nLabel for the y-axissave (str):\npath to file in which the figure should be savedauto_gamma (bool):\nApply the gamma method with standard parameters to all correlators and plateau values before plotting.hide_sigma (float):\nHides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.references (list):\nList of floating point values that are displayed as horizontal lines for reference. \n", "signature": "(\n self,\n x_range=None,\n comp=None,\n y_range=None,\n logscale=False,\n plateau=None,\n fit_res=None,\n ylabel=None,\n save=None,\n auto_gamma=False,\n hide_sigma=None,\n references=None\n)", "funcdef": "def"}, "pyerrors.correlators.Corr.spaghetti_plot": {"fullname": "pyerrors.correlators.Corr.spaghetti_plot", "modulename": "pyerrors.correlators", "qualname": "Corr.spaghetti_plot", "type": "function", "doc": "Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
\n\nParameters \n\n\nlogscale (bool):\nDetermines whether the scale of the y-axis is logarithmic or standard. \n", "signature": "(self, logscale=True)", "funcdef": "def"}, "pyerrors.correlators.Corr.dump": {"fullname": "pyerrors.correlators.Corr.dump", "modulename": "pyerrors.correlators", "qualname": "Corr.dump", "type": "function", "doc": "Dumps the Corr into a file of chosen type
\n\nParameters \n\n\nfilename (str):\nName of the file to be saved.datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"path (str):\nspecifies a custom path for the file (default '.') \n", "signature": "(self, filename, datatype='json.gz', **kwargs)", "funcdef": "def"}, "pyerrors.correlators.Corr.print": {"fullname": "pyerrors.correlators.Corr.print", "modulename": "pyerrors.correlators", "qualname": "Corr.print", "type": "function", "doc": "
\n", "signature": "(self, range=[0, None])", "funcdef": "def"}, "pyerrors.correlators.Corr.sqrt": {"fullname": "pyerrors.correlators.Corr.sqrt", "modulename": "pyerrors.correlators", "qualname": "Corr.sqrt", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.log": {"fullname": "pyerrors.correlators.Corr.log", "modulename": "pyerrors.correlators", "qualname": "Corr.log", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.exp": {"fullname": "pyerrors.correlators.Corr.exp", "modulename": "pyerrors.correlators", "qualname": "Corr.exp", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.sin": {"fullname": "pyerrors.correlators.Corr.sin", "modulename": "pyerrors.correlators", "qualname": "Corr.sin", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.cos": {"fullname": "pyerrors.correlators.Corr.cos", "modulename": "pyerrors.correlators", "qualname": "Corr.cos", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.tan": {"fullname": "pyerrors.correlators.Corr.tan", "modulename": "pyerrors.correlators", "qualname": "Corr.tan", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.sinh": {"fullname": "pyerrors.correlators.Corr.sinh", "modulename": "pyerrors.correlators", "qualname": "Corr.sinh", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.cosh": {"fullname": "pyerrors.correlators.Corr.cosh", "modulename": "pyerrors.correlators", "qualname": "Corr.cosh", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.tanh": {"fullname": "pyerrors.correlators.Corr.tanh", "modulename": "pyerrors.correlators", "qualname": "Corr.tanh", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsin": {"fullname": "pyerrors.correlators.Corr.arcsin", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsin", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arccos": {"fullname": "pyerrors.correlators.Corr.arccos", "modulename": "pyerrors.correlators", "qualname": "Corr.arccos", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arctan": {"fullname": "pyerrors.correlators.Corr.arctan", "modulename": "pyerrors.correlators", "qualname": "Corr.arctan", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsinh": {"fullname": "pyerrors.correlators.Corr.arcsinh", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsinh", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arccosh": {"fullname": "pyerrors.correlators.Corr.arccosh", "modulename": "pyerrors.correlators", "qualname": "Corr.arccosh", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arctanh": {"fullname": "pyerrors.correlators.Corr.arctanh", "modulename": "pyerrors.correlators", "qualname": "Corr.arctanh", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.real": {"fullname": "pyerrors.correlators.Corr.real", "modulename": "pyerrors.correlators", "qualname": "Corr.real", "type": "variable", "doc": "
\n"}, "pyerrors.correlators.Corr.imag": {"fullname": "pyerrors.correlators.Corr.imag", "modulename": "pyerrors.correlators", "qualname": "Corr.imag", "type": "variable", "doc": "
\n"}, "pyerrors.correlators.Corr.prune": {"fullname": "pyerrors.correlators.Corr.prune", "modulename": "pyerrors.correlators", "qualname": "Corr.prune", "type": "function", "doc": "Project large correlation matrix to lowest states
\n\nThis method can be used to reduce the size of an (N x N) correlation matrix\nto (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise\nis still small.
\n\nParameters \n\n\nNtrunc (int):\nRank of the target matrix.tproj (int):\nTime where the eigenvectors are evaluated, corresponds to ts in the GEVP method.\nThe default value is 3.t0proj (int):\nTime where the correlation matrix is inverted. Choosing t0proj=1 is strongly\ndiscouraged for O(a) improved theories, since the correctness of the procedure\ncannot be granted in this case. The default value is 2.basematrix (Corr):\nCorrelation matrix that is used to determine the eigenvectors of the\nlowest states based on a GEVP. basematrix is taken to be the Corr itself if\nis is not specified. \n\nNotes \n\nWe have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving\nthe GEVP $$C(t) v_n(t, t_0) = \\lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \\equiv t_\\mathrm{proj}$\nand $t_0 \\equiv t_{0, \\mathrm{proj}}$. The target matrix is projected onto the subspace of the\nresulting eigenvectors $v_n, n=1,\\dots,N_\\mathrm{trunc}$ via\n$$G^\\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large\ncorrelation matrix and to remove some noise that is added by irrelevant operators.\nThis may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated\nbound $t_0 \\leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.
\n", "signature": "(self, Ntrunc, tproj=3, t0proj=2, basematrix=None)", "funcdef": "def"}, "pyerrors.covobs": {"fullname": "pyerrors.covobs", "modulename": "pyerrors.covobs", "type": "module", "doc": "
\n"}, "pyerrors.covobs.Covobs": {"fullname": "pyerrors.covobs.Covobs", "modulename": "pyerrors.covobs", "qualname": "Covobs", "type": "class", "doc": "
\n"}, "pyerrors.covobs.Covobs.__init__": {"fullname": "pyerrors.covobs.Covobs.__init__", "modulename": "pyerrors.covobs", "qualname": "Covobs.__init__", "type": "function", "doc": "Initialize Covobs object.
\n\nParameters \n\n\nmean (float):\nMean value of the new Obscov (list or array):\n2d Covariance matrix or 1d diagonal entriesname (str):\nidentifier for the covariance matrixpos (int):\nPosition of the variance belonging to mean in cov.\nIs taken to be 1 if cov is 0-dimensionalgrad (list or array):\nGradient of the Covobs wrt. the means belonging to cov. \n", "signature": "(self, mean, cov, name, pos=None, grad=None)", "funcdef": "def"}, "pyerrors.covobs.Covobs.errsq": {"fullname": "pyerrors.covobs.Covobs.errsq", "modulename": "pyerrors.covobs", "qualname": "Covobs.errsq", "type": "function", "doc": "Return the variance (= square of the error) of the Covobs
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.covobs.Covobs.cov": {"fullname": "pyerrors.covobs.Covobs.cov", "modulename": "pyerrors.covobs", "qualname": "Covobs.cov", "type": "variable", "doc": "
\n"}, "pyerrors.covobs.Covobs.grad": {"fullname": "pyerrors.covobs.Covobs.grad", "modulename": "pyerrors.covobs", "qualname": "Covobs.grad", "type": "variable", "doc": "
\n"}, "pyerrors.dirac": {"fullname": "pyerrors.dirac", "modulename": "pyerrors.dirac", "type": "module", "doc": "
\n"}, "pyerrors.dirac.epsilon_tensor": {"fullname": "pyerrors.dirac.epsilon_tensor", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor", "type": "function", "doc": "Rank-3 epsilon tensor
\n\nBased on https://codegolf.stackexchange.com/a/160375
\n", "signature": "(i, j, k)", "funcdef": "def"}, "pyerrors.dirac.epsilon_tensor_rank4": {"fullname": "pyerrors.dirac.epsilon_tensor_rank4", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor_rank4", "type": "function", "doc": "Rank-4 epsilon tensor
\n\nExtension of https://codegolf.stackexchange.com/a/160375
\n", "signature": "(i, j, k, o)", "funcdef": "def"}, "pyerrors.dirac.Grid_gamma": {"fullname": "pyerrors.dirac.Grid_gamma", "modulename": "pyerrors.dirac", "qualname": "Grid_gamma", "type": "function", "doc": "Returns gamma matrix in Grid labeling.
\n", "signature": "(gamma_tag)", "funcdef": "def"}, "pyerrors.fits": {"fullname": "pyerrors.fits", "modulename": "pyerrors.fits", "type": "module", "doc": "
\n"}, "pyerrors.fits.Fit_result": {"fullname": "pyerrors.fits.Fit_result", "modulename": "pyerrors.fits", "qualname": "Fit_result", "type": "class", "doc": "Represents fit results.
\n\nAttributes \n\n\nfit_parameters (list):\nresults for the individual fit parameters,\nalso accessible via indices. \n", "bases": "collections.abc.Sequence"}, "pyerrors.fits.Fit_result.__init__": {"fullname": "pyerrors.fits.Fit_result.__init__", "modulename": "pyerrors.fits", "qualname": "Fit_result.__init__", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.fits.Fit_result.gamma_method": {"fullname": "pyerrors.fits.Fit_result.gamma_method", "modulename": "pyerrors.fits", "qualname": "Fit_result.gamma_method", "type": "function", "doc": "Apply the gamma method to all fit parameters
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.fits.least_squares": {"fullname": "pyerrors.fits.least_squares", "modulename": "pyerrors.fits", "qualname": "least_squares", "type": "function", "doc": "Performs a non-linear fit to y = func(x).
\n\nParameters \n\n\nx (list):\nlist of floats.y (list):\nlist of Obs.func (object):\nfit function, has to be of the form
\n\nimport autograd.numpy as anp \n\ndef func ( a , x ): \n return a [ 0 ] + a [ 1 ] * x + a [ 2 ] * anp . sinh ( x ) \nFor multiple x values func can be of the form
\n\ndef func ( a , x ): \n ( x1 , x2 ) = x \n return a [ 0 ] * x1 ** 2 + a [ 1 ] * x2 \nIt is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
priors (list, optional):\npriors has to be a list with an entry for every parameter in the fit. The entries can either be\nObs (e.g. results from a previous fit) or strings containing a value and an error formatted like\n0.548(23), 500(40) or 0.5(0.4)silent (bool, optional):\nIf true all output to the console is omitted (default False).initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for\nnon-linear fits with many parameters.method (str, optional):\ncan be used to choose an alternative method for the minimization of chisquare.\nThe possible methods are the ones which can be used for scipy.optimize.minimize and\nmigrad of iminuit. If no method is specified, Levenberg-Marquard is used.\nReliable alternatives are migrad, Powell and Nelder-Mead.correlated_fit (bool):\nIf True, use the full inverse covariance matrix in the definition of the chisquare cost function.\nFor details about how the covariance matrix is estimated see pyerrors.obs.covariance.\nIn practice the correlation matrix is Cholesky decomposed and inverted (instead of the covariance matrix).\nThis procedure should be numerically more stable as the correlation matrix is typically better conditioned (Jacobi preconditioning).\nAt the moment this option only works for prior==None and when no method is given.expected_chisquare (bool):\nIf True estimates the expected chisquare which is\ncorrected by effects caused by correlated input data (default False).resplot (bool):\nIf True, a plot which displays fit, data and residuals is generated (default False).qqplot (bool):\nIf True, a quantile-quantile plot of the fit result is generated (default False). \n", "signature": "(x, y, func, priors=None, silent=False, **kwargs)", "funcdef": "def"}, "pyerrors.fits.total_least_squares": {"fullname": "pyerrors.fits.total_least_squares", "modulename": "pyerrors.fits", "qualname": "total_least_squares", "type": "function", "doc": "Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.
\n\nParameters \n\n\nx (list):\nlist of Obs, or a tuple of lists of Obsy (list):\nlist of Obs. The dvalues of the Obs are used as x- and yerror for the fit.func (object):\nfunc has to be of the form
\n\nimport autograd.numpy as anp \n\ndef func ( a , x ): \n return a [ 0 ] + a [ 1 ] * x + a [ 2 ] * anp . sinh ( x ) \nFor multiple x values func can be of the form
\n\ndef func ( a , x ): \n ( x1 , x2 ) = x \n return a [ 0 ] * x1 ** 2 + a [ 1 ] * x2 \nIt is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
silent (bool, optional):\nIf true all output to the console is omitted (default False).initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for non-linear\nfits with many parameters.expected_chisquare (bool):\nIf true prints the expected chisquare which is\ncorrected by effects caused by correlated input data.\nThis can take a while as the full correlation matrix\nhas to be calculated (default False). \n\nNotes \n\nBased on the orthogonal distance regression module of scipy
\n", "signature": "(x, y, func, silent=False, **kwargs)", "funcdef": "def"}, "pyerrors.fits.fit_lin": {"fullname": "pyerrors.fits.fit_lin", "modulename": "pyerrors.fits", "qualname": "fit_lin", "type": "function", "doc": "Performs a linear fit to y = n + m * x and returns two Obs n, m.
\n\nParameters \n\n\nx (list):\nCan either be a list of floats in which case no xerror is assumed, or\na list of Obs, where the dvalues of the Obs are used as xerror for the fit.y (list):\nList of Obs, the dvalues of the Obs are used as yerror for the fit. \n", "signature": "(x, y, **kwargs)", "funcdef": "def"}, "pyerrors.fits.qqplot": {"fullname": "pyerrors.fits.qqplot", "modulename": "pyerrors.fits", "qualname": "qqplot", "type": "function", "doc": "Generates a quantile-quantile plot of the fit result which can be used to\ncheck if the residuals of the fit are gaussian distributed.
\n", "signature": "(x, o_y, func, p)", "funcdef": "def"}, "pyerrors.fits.residual_plot": {"fullname": "pyerrors.fits.residual_plot", "modulename": "pyerrors.fits", "qualname": "residual_plot", "type": "function", "doc": "Generates a plot which compares the fit to the data and displays the corresponding residuals
\n", "signature": "(x, y, func, fit_res)", "funcdef": "def"}, "pyerrors.fits.error_band": {"fullname": "pyerrors.fits.error_band", "modulename": "pyerrors.fits", "qualname": "error_band", "type": "function", "doc": "Returns the error band for an array of sample values x, for given fit function func with optimized parameters beta.
\n", "signature": "(x, func, beta)", "funcdef": "def"}, "pyerrors.fits.ks_test": {"fullname": "pyerrors.fits.ks_test", "modulename": "pyerrors.fits", "qualname": "ks_test", "type": "function", "doc": "Performs a Kolmogorov\u2013Smirnov test for the p-values of all fit object.
\n\nParameters \n\n\nobjects (list):\nList of fit results to include in the analysis (optional). \n", "signature": "(objects=None)", "funcdef": "def"}, "pyerrors.input": {"fullname": "pyerrors.input", "modulename": "pyerrors.input", "type": "module", "doc": "pyerrors includes an input submodule in which input routines and parsers for the output of various numerical programs are contained.
\n\nJackknife samples \n\nFor comparison with other analysis workflows pyerrors can also generate jackknife samples from an Obs object or import jackknife samples into an Obs object.\nSee pyerrors.obs.Obs.export_jackknife and pyerrors.obs.import_jackknife for details.
\n"}, "pyerrors.input.bdio": {"fullname": "pyerrors.input.bdio", "modulename": "pyerrors.input.bdio", "type": "module", "doc": "
\n"}, "pyerrors.input.bdio.read_ADerrors": {"fullname": "pyerrors.input.bdio.read_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "read_ADerrors", "type": "function", "doc": "Extract generic MCMC data from a bdio file
\n\nread_ADerrors requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
\n\nall: bdio.o $(LIBDIR)\n gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
\n\nParameters \n\n\nfile_path -- path to the bdio file bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so) \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs)", "funcdef": "def"}, "pyerrors.input.bdio.write_ADerrors": {"fullname": "pyerrors.input.bdio.write_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "write_ADerrors", "type": "function", "doc": "Write Obs to a bdio file according to ADerrors conventions
\n\nread_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
\n\nall: bdio.o $(LIBDIR)\n gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
\n\nParameters \n\n\nfile_path -- path to the bdio file bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so) \n", "signature": "(obs_list, file_path, bdio_path='./libbdio.so', **kwargs)", "funcdef": "def"}, "pyerrors.input.bdio.read_mesons": {"fullname": "pyerrors.input.bdio.read_mesons", "modulename": "pyerrors.input.bdio", "qualname": "read_mesons", "type": "function", "doc": "Extract mesons data from a bdio file and return it as a dictionary
\n\nThe dictionary can be accessed with a tuple consisting of (type, source_position, kappa1, kappa2)
\n\nread_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
\n\nall: bdio.o $(LIBDIR)\n gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
\n\nParameters \n\n\nfile_path (str):\npath to the bdio filebdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)start (int):\nThe first configuration to be read (default 1)stop (int):\nThe last configuration to be read (default None)step (int):\nFixed step size between two measurements (default 1)alternative_ensemble_name (str):\nManually overwrite ensemble name \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs)", "funcdef": "def"}, "pyerrors.input.bdio.read_dSdm": {"fullname": "pyerrors.input.bdio.read_dSdm", "modulename": "pyerrors.input.bdio", "qualname": "read_dSdm", "type": "function", "doc": "Extract dSdm data from a bdio file and return it as a dictionary
\n\nThe dictionary can be accessed with a tuple consisting of (type, kappa)
\n\nread_dSdm requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
\n\nall: bdio.o $(LIBDIR)\n gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
\n\nParameters \n\n\nfile_path (str):\npath to the bdio filebdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)start (int):\nThe first configuration to be read (default 1)stop (int):\nThe last configuration to be read (default None)step (int):\nFixed step size between two measurements (default 1)alternative_ensemble_name (str):\nManually overwrite ensemble name \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs)", "funcdef": "def"}, "pyerrors.input.dobs": {"fullname": "pyerrors.input.dobs", "modulename": "pyerrors.input.dobs", "type": "module", "doc": "
\n"}, "pyerrors.input.dobs.create_pobs_string": {"fullname": "pyerrors.input.dobs.create_pobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_pobs_string", "type": "function", "doc": "Export a list of Obs or structures containing Obs to an xml string\naccording to the Zeuthen pobs format.
\n\nTags are not written or recovered automatically. The separator | is removed from the replica names.
\n\nParameters \n\n\nobsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.name (str):\nThe name of the observable.spec (str):\nOptional string that describes the contents of the file.origin (str):\nSpecify where the data has its origin.symbol (list):\nA list of symbols that describe the observables to be written. May be empty.enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used. \n", "signature": "(obsl, name, spec='', origin='', symbol=[], enstag=None)", "funcdef": "def"}, "pyerrors.input.dobs.write_pobs": {"fullname": "pyerrors.input.dobs.write_pobs", "modulename": "pyerrors.input.dobs", "qualname": "write_pobs", "type": "function", "doc": "Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen pobs format.
\n\nTags are not written or recovered automatically. The separator | is removed from the replica names.
\n\nParameters \n\n\nobsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.fname (str):\nFilename of the output file.name (str):\nThe name of the observable.spec (str):\nOptional string that describes the contents of the file.origin (str):\nSpecify where the data has its origin.symbol (list):\nA list of symbols that describe the observables to be written. May be empty.enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.gz (bool):\nIf True, the output is a gzipped xml. If False, the output is an xml file. \n", "signature": "(\n obsl,\n fname,\n name,\n spec='',\n origin='',\n symbol=[],\n enstag=None,\n gz=True\n)", "funcdef": "def"}, "pyerrors.input.dobs.read_pobs": {"fullname": "pyerrors.input.dobs.read_pobs", "modulename": "pyerrors.input.dobs", "qualname": "read_pobs", "type": "function", "doc": "Import a list of Obs from an xml.gz file in the Zeuthen pobs format.
\n\nTags are not written or recovered automatically.
\n\nParameters \n\n\nfname (str):\nFilename of the input file.full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.separatior_insertion (str or int):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nNone (default): Replica names remain unchanged. \n", "signature": "(fname, full_output=False, gz=True, separator_insertion=None)", "funcdef": "def"}, "pyerrors.input.dobs.import_dobs_string": {"fullname": "pyerrors.input.dobs.import_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "import_dobs_string", "type": "function", "doc": "Import a list of Obs from a string in the Zeuthen dobs format.
\n\nTags are not written or recovered automatically.
\n\nParameters \n\n\ncontent (str):\nXML string containing the datanoemtpy (bool):\nIf True, ensembles with no contribution to the Obs are not included.\nIf False, ensembles are included as written in the file, possibly with vanishing entries.full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted. \n", "signature": "(content, noempty=False, full_output=False, separator_insertion=True)", "funcdef": "def"}, "pyerrors.input.dobs.read_dobs": {"fullname": "pyerrors.input.dobs.read_dobs", "modulename": "pyerrors.input.dobs", "qualname": "read_dobs", "type": "function", "doc": "Import a list of Obs from an xml.gz file in the Zeuthen dobs format.
\n\nTags are not written or recovered automatically.
\n\nParameters \n\n\nfname (str):\nFilename of the input file.noemtpy (bool):\nIf True, ensembles with no contribution to the Obs are not included.\nIf False, ensembles are included as written in the file.full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.gz (bool):\nIf True, assumes that data is gzipped. If False, assumes XML file.separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted. \n", "signature": "(\n fname,\n noempty=False,\n full_output=False,\n gz=True,\n separator_insertion=True\n)", "funcdef": "def"}, "pyerrors.input.dobs.create_dobs_string": {"fullname": "pyerrors.input.dobs.create_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_dobs_string", "type": "function", "doc": "Generate the string for the export of a list of Obs or structures containing Obs\nto a .xml.gz file according to the Zeuthen dobs format.
\n\nTags are not written or recovered automatically. The separator |is removed from the replica names.
\n\nParameters \n\n\nobsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.name (str):\nThe name of the observable.spec (str):\nOptional string that describes the contents of the file.origin (str):\nSpecify where the data has its origin.symbol (list):\nA list of symbols that describe the observables to be written. May be empty.who (str):\nProvide the name of the person that exports the data.enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used. \n", "signature": "(\n obsl,\n name,\n spec='dobs v1.0',\n origin='',\n symbol=[],\n who=None,\n enstags={}\n)", "funcdef": "def"}, "pyerrors.input.dobs.write_dobs": {"fullname": "pyerrors.input.dobs.write_dobs", "modulename": "pyerrors.input.dobs", "qualname": "write_dobs", "type": "function", "doc": "Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen dobs format.
\n\nTags are not written or recovered automatically. The separator | is removed from the replica names.
\n\nParameters \n\n\nobsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.fname (str):\nFilename of the output file.name (str):\nThe name of the observable.spec (str):\nOptional string that describes the contents of the file.origin (str):\nSpecify where the data has its origin.symbol (list):\nA list of symbols that describe the observables to be written. May be empty.who (str):\nProvide the name of the person that exports the data.enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.gz (bool):\nIf True, the output is a gzipped XML. If False, the output is a XML file. \n", "signature": "(\n obsl,\n fname,\n name,\n spec='dobs v1.0',\n origin='',\n symbol=[],\n who=None,\n enstags={},\n gz=True\n)", "funcdef": "def"}, "pyerrors.input.hadrons": {"fullname": "pyerrors.input.hadrons", "modulename": "pyerrors.input.hadrons", "type": "module", "doc": "
\n"}, "pyerrors.input.hadrons.read_meson_hd5": {"fullname": "pyerrors.input.hadrons.read_meson_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_meson_hd5", "type": "function", "doc": "Read hadrons meson hdf5 file and extract the meson labeled 'meson'
\n\nParameters \n\n\npath (str):\npath to the files to readfilestem (str):\nnamestem of the files to readens_id (str):\nname of the ensemble, required for internal bookkeepingmeson (str):\nlabel of the meson to be extracted, standard value meson_0 which\ncorresponds to the pseudoscalar pseudoscalar two-point function.idl (range):\nIf specified only configurations in the given range are read in. \n", "signature": "(path, filestem, ens_id, meson='meson_0', idl=None)", "funcdef": "def"}, "pyerrors.input.hadrons.read_DistillationContraction_hd5": {"fullname": "pyerrors.input.hadrons.read_DistillationContraction_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_DistillationContraction_hd5", "type": "function", "doc": "Read hadrons DistillationContraction hdf5 files in given directory structure
\n\nParameters \n\n\npath (str):\npath to the directories to readens_id (str):\nname of the ensemble, required for internal bookkeepingdiagrams (list):\nList of strings of the diagrams to extract, e.g. [\"direct\", \"box\", \"cross\"].idl (range):\nIf specified only configurations in the given range are read in. \n", "signature": "(path, ens_id, diagrams=['direct'], idl=None)", "funcdef": "def"}, "pyerrors.input.hadrons.Npr_matrix": {"fullname": "pyerrors.input.hadrons.Npr_matrix", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix", "type": "class", "doc": "ndarray(shape, dtype=float, buffer=None, offset=0,\n strides=None, order=None)
\n\nAn array object represents a multidimensional, homogeneous array\nof fixed-size items. An associated data-type object describes the\nformat of each element in the array (its byte-order, how many bytes it\noccupies in memory, whether it is an integer, a floating point number,\nor something else, etc.)
\n\nArrays should be constructed using array, zeros or empty (refer\nto the See Also section below). The parameters given here refer to\na low-level method (ndarray(...)) for instantiating an array.
\n\nFor more information, refer to the numpy module and examine the\nmethods and attributes of an array.
\n\nParameters \n\n\n(for the __new__ method; see Notes below) shape (tuple of ints):\nShape of created array.dtype (data-type, optional):\nAny object that can be interpreted as a numpy data type.buffer (object exposing buffer interface, optional):\nUsed to fill the array with data.offset (int, optional):\nOffset of array data in buffer.strides (tuple of ints, optional):\nStrides of data in memory.order ({'C', 'F'}, optional):\nRow-major (C-style) or column-major (Fortran-style) order. \n\nAttributes \n\n\nT (ndarray):\nTranspose of the array.data (buffer):\nThe array's elements, in memory.dtype (dtype object):\nDescribes the format of the elements in the array.flags (dict):\nDictionary containing information related to memory use, e.g.,\n'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc.flat (numpy.flatiter object):\nFlattened version of the array as an iterator. The iterator\nallows assignments, e.g., x.flat = 3 (See ndarray.flat for\nassignment examples; TODO).imag (ndarray):\nImaginary part of the array.real (ndarray):\nReal part of the array.size (int):\nNumber of elements in the array.itemsize (int):\nThe memory use of each array element in bytes.nbytes (int):\nThe total number of bytes required to store the array data,\ni.e., itemsize * size.ndim (int):\nThe array's number of dimensions.shape (tuple of ints):\nShape of the array.strides (tuple of ints):\nThe step-size required to move from one element to the next in\nmemory. For example, a contiguous (3, 4) array of type\nint16 in C-order has strides (8, 2). This implies that\nto move from element to element in memory requires jumps of 2 bytes.\nTo move from row-to-row, one needs to jump 8 bytes at a time\n(2 * 4).ctypes (ctypes object):\nClass containing properties of the array needed for interaction\nwith ctypes.base (ndarray):\nIf the array is a view into another array, that array is its base\n(unless that array is also a view). The base array is where the\narray data is actually stored. \n\nSee Also \n\narray: Construct an array. zeros: Create an array, each element of which is zero. empty: Create an array, but leave its allocated memory unchanged (i.e.,\nit contains \"garbage\"). dtype: Create a data-type. numpy.typing.NDArray: An ndarray alias :term:generic <generic type>\nw.r.t. its dtype.type <numpy.dtype.type>.
\n\nNotes \n\nThere are two modes of creating an array using __new__:
\n\n\nIf buffer is None, then only shape, dtype, and order\nare used. \nIf buffer is an object exposing the buffer interface, then\nall keywords are interpreted. \n \n\nNo __init__ method is needed because the array is fully initialized\nafter the __new__ method.
\n\nExamples \n\nThese examples illustrate the low-level ndarray constructor. Refer\nto the See Also section above for easier ways of constructing an\nndarray.
\n\nFirst mode, buffer is None:
\n\n>>> np . ndarray ( shape = ( 2 , 2 ), dtype = float , order = 'F' ) \narray([[0.0e+000, 0.0e+000], # random \n [ nan, 2.5e-323]]) \nSecond mode:
\n\n>>> np . ndarray (( 2 ,), buffer = np . array ([ 1 , 2 , 3 ]), \n... offset = np . int_ () . itemsize , \n... dtype = int ) # offset = 1*itemsize, i.e. skip first element \narray([2, 3]) \n
\n", "signature": "()", "funcdef": "def"}, "pyerrors.input.hadrons.Npr_matrix.g5H": {"fullname": "pyerrors.input.hadrons.Npr_matrix.g5H", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.g5H", "type": "variable", "doc": "Gamma_5 hermitean conjugate
\n\nUses the fact that the propagator is gamma5 hermitean, so just the\nin and out momenta of the propagator are exchanged.
\n"}, "pyerrors.input.hadrons.read_ExternalLeg_hd5": {"fullname": "pyerrors.input.hadrons.read_ExternalLeg_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_ExternalLeg_hd5", "type": "function", "doc": "Read hadrons ExternalLeg hdf5 file and output an array of CObs
\n\nParameters \n\n\npath (str):\npath to the files to readfilestem (str):\nnamestem of the files to readens_id (str):\nname of the ensemble, required for internal bookkeepingidl (range):\nIf specified only configurations in the given range are read in. \n", "signature": "(path, filestem, ens_id, idl=None)", "funcdef": "def"}, "pyerrors.input.hadrons.read_Bilinear_hd5": {"fullname": "pyerrors.input.hadrons.read_Bilinear_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Bilinear_hd5", "type": "function", "doc": "Read hadrons Bilinear hdf5 file and output an array of CObs
\n\nParameters \n\n\npath (str):\npath to the files to readfilestem (str):\nnamestem of the files to readens_id (str):\nname of the ensemble, required for internal bookkeepingidl (range):\nIf specified only configurations in the given range are read in. \n", "signature": "(path, filestem, ens_id, idl=None)", "funcdef": "def"}, "pyerrors.input.hadrons.read_Fourquark_hd5": {"fullname": "pyerrors.input.hadrons.read_Fourquark_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Fourquark_hd5", "type": "function", "doc": "Read hadrons FourquarkFullyConnected hdf5 file and output an array of CObs
\n\nParameters \n\n\npath (str):\npath to the files to readfilestem (str):\nnamestem of the files to readens_id (str):\nname of the ensemble, required for internal bookkeepingidl (range):\nIf specified only configurations in the given range are read in.vertices (list):\nVertex functions to be extracted. \n", "signature": "(path, filestem, ens_id, idl=None, vertices=['VA', 'AV'])", "funcdef": "def"}, "pyerrors.input.json": {"fullname": "pyerrors.input.json", "modulename": "pyerrors.input.json", "type": "module", "doc": "
\n"}, "pyerrors.input.json.create_json_string": {"fullname": "pyerrors.input.json.create_json_string", "modulename": "pyerrors.input.json", "qualname": "create_json_string", "type": "function", "doc": "Generate the string for the export of a list of Obs or structures containing Obs\nto a .json(.gz) file
\n\nParameters \n\n\nol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.description (str):\nOptional string that describes the contents of the json file.indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space. \n", "signature": "(ol, description='', indent=1)", "funcdef": "def"}, "pyerrors.input.json.dump_to_json": {"fullname": "pyerrors.input.json.dump_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_to_json", "type": "function", "doc": "Export a list of Obs or structures containing Obs to a .json(.gz) file
\n\nParameters \n\n\nol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.fname (str):\nFilename of the output file.description (str):\nOptional string that describes the contents of the json file.indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file. \n", "signature": "(ol, fname, description='', indent=1, gz=True)", "funcdef": "def"}, "pyerrors.input.json.import_json_string": {"fullname": "pyerrors.input.json.import_json_string", "modulename": "pyerrors.input.json", "qualname": "import_json_string", "type": "function", "doc": "Reconstruct a list of Obs or structures containing Obs from a json string.
\n\nThe following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
\n\nParameters \n\n\njson_string (str):\njson string containing the data.verbose (bool):\nPrint additional information that was written to the file.full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned. \n", "signature": "(json_string, verbose=True, full_output=False)", "funcdef": "def"}, "pyerrors.input.json.load_json": {"fullname": "pyerrors.input.json.load_json", "modulename": "pyerrors.input.json", "qualname": "load_json", "type": "function", "doc": "Import a list of Obs or structures containing Obs from a .json(.gz) file.
\n\nThe following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
\n\nParameters \n\n\nfname (str):\nFilename of the input file.verbose (bool):\nPrint additional information that was written to the file.gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned. \n", "signature": "(fname, verbose=True, gz=True, full_output=False)", "funcdef": "def"}, "pyerrors.input.json.dump_dict_to_json": {"fullname": "pyerrors.input.json.dump_dict_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_dict_to_json", "type": "function", "doc": "Export a dict of Obs or structures containing Obs to a .json(.gz) file
\n\nParameters \n\n\nod (dict):\nDict of JSON valid structures and objects that will be exported.\nAt the moment, these objects can be either of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.fname (str):\nFilename of the output file.description (str):\nOptional string that describes the contents of the json file.indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.reps (str):\nSpecify the structure of the placeholder in exported dict to be reps[0-9]+.gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file. \n", "signature": "(od, fname, description='', indent=1, reps='DICTOBS', gz=True)", "funcdef": "def"}, "pyerrors.input.json.load_json_dict": {"fullname": "pyerrors.input.json.load_json_dict", "modulename": "pyerrors.input.json", "qualname": "load_json_dict", "type": "function", "doc": "Import a dict of Obs or structures containing Obs from a .json(.gz) file.
\n\nThe following structures are supported: Obs, list, numpy.ndarray, Corr
\n\nParameters \n\n\nfname (str):\nFilename of the input file.verbose (bool):\nPrint additional information that was written to the file.gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.reps (str):\nSpecify the structure of the placeholder in imported dict to be reps[0-9]+. \n", "signature": "(fname, verbose=True, gz=True, full_output=False, reps='DICTOBS')", "funcdef": "def"}, "pyerrors.input.misc": {"fullname": "pyerrors.input.misc", "modulename": "pyerrors.input.misc", "type": "module", "doc": "
\n"}, "pyerrors.input.misc.read_pbp": {"fullname": "pyerrors.input.misc.read_pbp", "modulename": "pyerrors.input.misc", "qualname": "read_pbp", "type": "function", "doc": "Read pbp format from given folder structure. Returns a list of length nrw
\n\nParameters \n\n\nr_start (list):\nlist which contains the first config to be read for each replicumr_stop (list):\nlist which contains the last config to be read for each replicum \n", "signature": "(path, prefix, **kwargs)", "funcdef": "def"}, "pyerrors.input.openQCD": {"fullname": "pyerrors.input.openQCD", "modulename": "pyerrors.input.openQCD", "type": "module", "doc": "
\n"}, "pyerrors.input.openQCD.read_rwms": {"fullname": "pyerrors.input.openQCD.read_rwms", "modulename": "pyerrors.input.openQCD", "qualname": "read_rwms", "type": "function", "doc": "Read rwms format from given folder structure. Returns a list of length nrw
\n\nParameters \n\n\npath (str):\npath that contains the data filesprefix (str):\nall files in path that start with prefix are considered as input files.\nMay be used together postfix to consider only special file endings.\nPrefix is ignored, if the keyword 'files' is used.version (str):\nversion of openQCD, default 2.0names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!r_start (list):\nlist which contains the first config to be read for each replicumr_stop (list):\nlist which contains the last config to be read for each replicumr_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.postfix (str):\npostfix of the file to read, e.g. '.ms1' for openQCD-filesfiles (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.print_err (bool):\nPrint additional information that is useful for debugging. \n", "signature": "(path, prefix, version='2.0', names=None, **kwargs)", "funcdef": "def"}, "pyerrors.input.openQCD.extract_t0": {"fullname": "pyerrors.input.openQCD.extract_t0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_t0", "type": "function", "doc": "Extract t0 from given .ms.dat files. Returns t0 as Obs.
\n\nIt is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t^2 - 0.3\nis fitted with a linear function\nfrom which the exact root is extracted.
\n\nIt is assumed that one measurement is performed for each config.\nIf this is not the case, the resulting idl, as well as the handling\nof r_start, r_stop and r_step is wrong and the user has to correct\nthis in the resulting observable.
\n\nParameters \n\n\npath (str):\nPath to .ms.dat filesprefix (str):\nEnsemble prefixdtr_read (int):\nDetermines how many trajectories should be skipped\nwhen reading the ms.dat files.\nCorresponds to dtr_cnfg / dtr_ms in the openQCD input file.xmin (int):\nFirst timeslice where the boundary\neffects have sufficiently decayed.spatial_extent (int):\nspatial extent of the lattice, required for normalization.fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)r_start (list):\nlist which contains the first config to be read for each replicum.r_stop (list):\nlist which contains the last config to be read for each replicum.r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.plaquette (bool):\nIf true extract the plaquette estimate of t0 instead.names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.assume_thermalization (bool):\nIf True: If the first record divided by the distance between two measurements is larger than\n1, it is assumed that this is due to thermalization and the first measurement belongs\nto the first config (default).\nIf False: The config numbers are assumed to be traj_number // difference \n", "signature": "(path, prefix, dtr_read, xmin, spatial_extent, fit_range=5, **kwargs)", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop": {"fullname": "pyerrors.input.openQCD.read_qtop", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop", "type": "function", "doc": "Read the topologial charge based on openQCD gradient flow measurements.
\n\nParameters \n\n\npath (str):\npath of the measurement filesprefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files. c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.steps (int):\n(optional) Distance between two configurations in units of trajectories /\ncycles. Assumed to be the distance between two measurements * dtr_cnfg if not givenversion (str):\nEither openQCD or sfqcd, depending on the data.L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the headerr_start (list):\nlist which contains the first config to be read for each replicum.r_stop (list):\nlist which contains the last config to be read for each replicum.files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needednames (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.integer_charge (bool):\nIf True, the charge is rounded towards the nearest integer on each config. \n", "signature": "(path, prefix, c, dtr_cnfg=1, version='openQCD', **kwargs)", "funcdef": "def"}, "pyerrors.input.openQCD.qtop_projection": {"fullname": "pyerrors.input.openQCD.qtop_projection", "modulename": "pyerrors.input.openQCD", "qualname": "qtop_projection", "type": "function", "doc": "Returns the projection to the topological charge sector defined by target.
\n\nParameters \n\n\npath (Obs):\nTopological charge.target (int):\nSpecifies the topological sector to be reweighted to (default 0) \n", "signature": "(qtop, target=0)", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop_sector": {"fullname": "pyerrors.input.openQCD.read_qtop_sector", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop_sector", "type": "function", "doc": "Constructs reweighting factors to a specified topological sector.
\n\nParameters \n\n\npath (str):\npath of the measurement filesprefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / Ltarget (int):\nSpecifies the topological sector to be reweighted to (default 0)dtr_cnfg (int):\n(optional) parameter that specifies the number of trajectories\nbetween two configs.\nif it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.steps (int):\n(optional) Distance between two configurations in units of trajectories /\ncycles. Assumed to be the distance between two measurements * dtr_cnfg if not givenversion (str):\nversion string of the openQCD (sfqcd) version used to create\nthe ensemble. Default is 2.0. May also be set to sfqcd.L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the headerr_start (list):\noffset of the first ensemble, making it easier to match\nlater on with other Obsr_stop (list):\nlast configurations that need to be read (per replicum)files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needednames (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate lengthZeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used. \n", "signature": "(path, prefix, c, target=0, **kwargs)", "funcdef": "def"}, "pyerrors.input.sfcf": {"fullname": "pyerrors.input.sfcf", "modulename": "pyerrors.input.sfcf", "type": "module", "doc": "
\n"}, "pyerrors.input.sfcf.read_sfcf": {"fullname": "pyerrors.input.sfcf.read_sfcf", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf", "type": "function", "doc": "Read sfcf c format from given folder structure.
\n\nParameters \n\n\nquarks (str):\nLabel of the quarks used in the sfcf input file. e.g. \"quark quark\"\nfor version 0.0 this does NOT need to be given with the typical \" - \"\nthat is present in the output file,\nthis is done automatically for this versionnoffset (int):\nOffset of the source (only relevant when wavefunctions are used)wf (int):\nID of wave functionwf2 (int):\nID of the second wavefunction\n(only relevant for boundary-to-boundary correlation functions)im (bool):\nif True, read imaginary instead of real part\nof the correlation function.corr_type (str):\nchange between bi (boundary - inner) (default) bib (boundary - inner - boundary) and bb (boundary - boundary)\ncorrelator typesnames (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate lengthens_name (str):\nreplaces the name of the ensembleversion (str):\nversion of SFCF, with which the measurement was done.\nif the compact output option (-c) was specified,\nappend a \"c\" to the version (e.g. \"1.0c\")\nif the append output option (-a) was specified,\nappend an \"a\" to the versioncfg_separator (str):\nString that separates the ensemble identifier from the configuration number (default 'n').replica (list):\nlist of replica to be read, default is allfiles (list):\nlist of files to be read per replica, default is all.\nfor non-compact output format, hand the folders to be read here.check_configs: : list of list of supposed configs, eg. [range(1,1000)]\nfor one replicum with 1000 configs \n", "signature": "(\n path,\n prefix,\n name,\n quarks='.*',\n corr_type='bi',\n noffset=0,\n wf=0,\n wf2=0,\n version='1.0c',\n cfg_separator='n',\n **kwargs\n)", "funcdef": "def"}, "pyerrors.input.utils": {"fullname": "pyerrors.input.utils", "modulename": "pyerrors.input.utils", "type": "module", "doc": "Utilities for the input
\n"}, "pyerrors.input.utils.check_idl": {"fullname": "pyerrors.input.utils.check_idl", "modulename": "pyerrors.input.utils", "qualname": "check_idl", "type": "function", "doc": "Checks if list of configurations is contained in an idl
\n\nParameters \n\n\nidl (range or list):\nidl of the current replicumche (list):\nlist of configurations to be checked against \n", "signature": "(idl, che)", "funcdef": "def"}, "pyerrors.linalg": {"fullname": "pyerrors.linalg", "modulename": "pyerrors.linalg", "type": "module", "doc": "
\n"}, "pyerrors.linalg.matmul": {"fullname": "pyerrors.linalg.matmul", "modulename": "pyerrors.linalg", "qualname": "matmul", "type": "function", "doc": "Matrix multiply all operands.
\n\nParameters \n\n\noperands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.This implementation is faster compared to standard multiplication via the @ operator. \n", "signature": "(*operands)", "funcdef": "def"}, "pyerrors.linalg.jack_matmul": {"fullname": "pyerrors.linalg.jack_matmul", "modulename": "pyerrors.linalg", "qualname": "jack_matmul", "type": "function", "doc": "Matrix multiply both operands making use of the jackknife approximation.
\n\nParameters \n\n\noperands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.For large matrices this is considerably faster compared to matmul. \n", "signature": "(*operands)", "funcdef": "def"}, "pyerrors.linalg.einsum": {"fullname": "pyerrors.linalg.einsum", "modulename": "pyerrors.linalg", "qualname": "einsum", "type": "function", "doc": "Wrapper for numpy.einsum
\n\nParameters \n\n\nsubscripts (str):\nSubscripts for summation (see numpy documentation for details)operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued. \n", "signature": "(subscripts, *operands)", "funcdef": "def"}, "pyerrors.linalg.inv": {"fullname": "pyerrors.linalg.inv", "modulename": "pyerrors.linalg", "qualname": "inv", "type": "function", "doc": "Inverse of Obs or CObs valued matrices.
\n", "signature": "(x)", "funcdef": "def"}, "pyerrors.linalg.cholesky": {"fullname": "pyerrors.linalg.cholesky", "modulename": "pyerrors.linalg", "qualname": "cholesky", "type": "function", "doc": "Cholesky decomposition of Obs valued matrices.
\n", "signature": "(x)", "funcdef": "def"}, "pyerrors.linalg.det": {"fullname": "pyerrors.linalg.det", "modulename": "pyerrors.linalg", "qualname": "det", "type": "function", "doc": "Determinant of Obs valued matrices.
\n", "signature": "(x)", "funcdef": "def"}, "pyerrors.linalg.eigh": {"fullname": "pyerrors.linalg.eigh", "modulename": "pyerrors.linalg", "qualname": "eigh", "type": "function", "doc": "Computes the eigenvalues and eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh.
\n", "signature": "(obs, **kwargs)", "funcdef": "def"}, "pyerrors.linalg.eig": {"fullname": "pyerrors.linalg.eig", "modulename": "pyerrors.linalg", "qualname": "eig", "type": "function", "doc": "Computes the eigenvalues of a given matrix of Obs according to np.linalg.eig.
\n", "signature": "(obs, **kwargs)", "funcdef": "def"}, "pyerrors.linalg.pinv": {"fullname": "pyerrors.linalg.pinv", "modulename": "pyerrors.linalg", "qualname": "pinv", "type": "function", "doc": "Computes the Moore-Penrose pseudoinverse of a matrix of Obs.
\n", "signature": "(obs, **kwargs)", "funcdef": "def"}, "pyerrors.linalg.svd": {"fullname": "pyerrors.linalg.svd", "modulename": "pyerrors.linalg", "qualname": "svd", "type": "function", "doc": "Computes the singular value decomposition of a matrix of Obs.
\n", "signature": "(obs, **kwargs)", "funcdef": "def"}, "pyerrors.misc": {"fullname": "pyerrors.misc", "modulename": "pyerrors.misc", "type": "module", "doc": "
\n"}, "pyerrors.misc.dump_object": {"fullname": "pyerrors.misc.dump_object", "modulename": "pyerrors.misc", "qualname": "dump_object", "type": "function", "doc": "Dump object into pickle file.
\n\nParameters \n\n\nobj (object):\nobject to be saved in the pickle filename (str):\nname of the filepath (str):\nspecifies a custom path for the file (default '.') \n", "signature": "(obj, name, **kwargs)", "funcdef": "def"}, "pyerrors.misc.load_object": {"fullname": "pyerrors.misc.load_object", "modulename": "pyerrors.misc", "qualname": "load_object", "type": "function", "doc": "Load object from pickle file.
\n\nParameters \n\n\npath (str):\npath to the file \n", "signature": "(path)", "funcdef": "def"}, "pyerrors.misc.pseudo_Obs": {"fullname": "pyerrors.misc.pseudo_Obs", "modulename": "pyerrors.misc", "qualname": "pseudo_Obs", "type": "function", "doc": "Generate an Obs object with given value, dvalue and name for test purposes
\n\nParameters \n\n\nvalue (float):\ncentral value of the Obs to be generated.dvalue (float):\nerror of the Obs to be generated.name (str):\nname of the ensemble for which the Obs is to be generated.samples (int):\nnumber of samples for the Obs (default 1000). \n", "signature": "(value, dvalue, name, samples=1000)", "funcdef": "def"}, "pyerrors.misc.gen_correlated_data": {"fullname": "pyerrors.misc.gen_correlated_data", "modulename": "pyerrors.misc", "qualname": "gen_correlated_data", "type": "function", "doc": "Generate observables with given covariance and autocorrelation times.
\n\nParameters \n\n\nmeans (list):\nlist containing the mean value of each observable.cov (numpy.ndarray):\ncovariance matrix for the data to be generated.name (str):\nensemble name for the data to be geneated.tau (float or list):\ncan either be a real number or a list with an entry for\nevery dataset.samples (int):\nnumber of samples to be generated for each observable. \n", "signature": "(means, cov, name, tau=0.5, samples=1000)", "funcdef": "def"}, "pyerrors.mpm": {"fullname": "pyerrors.mpm", "modulename": "pyerrors.mpm", "type": "module", "doc": "
\n"}, "pyerrors.mpm.matrix_pencil_method": {"fullname": "pyerrors.mpm.matrix_pencil_method", "modulename": "pyerrors.mpm", "qualname": "matrix_pencil_method", "type": "function", "doc": "Matrix pencil method to extract k energy levels from data
\n\nImplementation of the matrix pencil method based on\neq. (2.17) of Y. Hua, T. K. Sarkar, IEEE Trans. Acoust. 38, 814-824 (1990)
\n\nParameters \n\n\ndata (list):\ncan be a list of Obs for the analysis of a single correlator, or a list of lists\nof Obs if several correlators are to analyzed at once.k (int):\nNumber of states to extract (default 1).p (int):\nmatrix pencil parameter which filters noise. The optimal value is expected between\nlen(data)/3 and 2*len(data)/3. The computation is more expensive the closer p is\nto len(data)/2 but could possibly suppress more noise (default len(data)//2). \n", "signature": "(corrs, k=1, p=None, **kwargs)", "funcdef": "def"}, "pyerrors.obs": {"fullname": "pyerrors.obs", "modulename": "pyerrors.obs", "type": "module", "doc": "
\n"}, "pyerrors.obs.Obs": {"fullname": "pyerrors.obs.Obs", "modulename": "pyerrors.obs", "qualname": "Obs", "type": "class", "doc": "Class for a general observable.
\n\nInstances of Obs are the basic objects of a pyerrors error analysis.\nThey are initialized with a list which contains arrays of samples for\ndifferent ensembles/replica and another list of same length which contains\nthe names of the ensembles/replica. Mathematical operations can be\nperformed on instances. The result is another instance of Obs. The error of\nan instance can be computed with the gamma_method. Also contains additional\nmethods for output and visualization of the error calculation.
\n\nAttributes \n\n\nS_global (float):\nStandard value for S (default 2.0)S_dict (dict):\nDictionary for S values. If an entry for a given ensemble\nexists this overwrites the standard value for that ensemble.tau_exp_global (float):\nStandard value for tau_exp (default 0.0)tau_exp_dict (dict):\nDictionary for tau_exp values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.N_sigma_global (float):\nStandard value for N_sigma (default 1.0)N_sigma_dict (dict):\nDictionary for N_sigma values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble. \n"}, "pyerrors.obs.Obs.__init__": {"fullname": "pyerrors.obs.Obs.__init__", "modulename": "pyerrors.obs", "qualname": "Obs.__init__", "type": "function", "doc": "Initialize Obs object.
\n\nParameters \n\n\nsamples (list):\nlist of numpy arrays containing the Monte Carlo samplesnames (list):\nlist of strings labeling the individual samplesidl (list, optional):\nlist of ranges or lists on which the samples are defined \n", "signature": "(self, samples, names, idl=None, **kwargs)", "funcdef": "def"}, "pyerrors.obs.Obs.S_global": {"fullname": "pyerrors.obs.Obs.S_global", "modulename": "pyerrors.obs", "qualname": "Obs.S_global", "type": "variable", "doc": "
\n", "default_value": " = 2.0"}, "pyerrors.obs.Obs.S_dict": {"fullname": "pyerrors.obs.Obs.S_dict", "modulename": "pyerrors.obs", "qualname": "Obs.S_dict", "type": "variable", "doc": "
\n", "default_value": " = {}"}, "pyerrors.obs.Obs.tau_exp_global": {"fullname": "pyerrors.obs.Obs.tau_exp_global", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_global", "type": "variable", "doc": "
\n", "default_value": " = 0.0"}, "pyerrors.obs.Obs.tau_exp_dict": {"fullname": "pyerrors.obs.Obs.tau_exp_dict", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_dict", "type": "variable", "doc": "
\n", "default_value": " = {}"}, "pyerrors.obs.Obs.N_sigma_global": {"fullname": "pyerrors.obs.Obs.N_sigma_global", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_global", "type": "variable", "doc": "
\n", "default_value": " = 1.0"}, "pyerrors.obs.Obs.N_sigma_dict": {"fullname": "pyerrors.obs.Obs.N_sigma_dict", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_dict", "type": "variable", "doc": "
\n", "default_value": " = {}"}, "pyerrors.obs.Obs.filter_eps": {"fullname": "pyerrors.obs.Obs.filter_eps", "modulename": "pyerrors.obs", "qualname": "Obs.filter_eps", "type": "variable", "doc": "
\n", "default_value": " = 1e-10"}, "pyerrors.obs.Obs.names": {"fullname": "pyerrors.obs.Obs.names", "modulename": "pyerrors.obs", "qualname": "Obs.names", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.shape": {"fullname": "pyerrors.obs.Obs.shape", "modulename": "pyerrors.obs", "qualname": "Obs.shape", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.r_values": {"fullname": "pyerrors.obs.Obs.r_values", "modulename": "pyerrors.obs", "qualname": "Obs.r_values", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.deltas": {"fullname": "pyerrors.obs.Obs.deltas", "modulename": "pyerrors.obs", "qualname": "Obs.deltas", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.N": {"fullname": "pyerrors.obs.Obs.N", "modulename": "pyerrors.obs", "qualname": "Obs.N", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.is_merged": {"fullname": "pyerrors.obs.Obs.is_merged", "modulename": "pyerrors.obs", "qualname": "Obs.is_merged", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.idl": {"fullname": "pyerrors.obs.Obs.idl", "modulename": "pyerrors.obs", "qualname": "Obs.idl", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.ddvalue": {"fullname": "pyerrors.obs.Obs.ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.ddvalue", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.reweighted": {"fullname": "pyerrors.obs.Obs.reweighted", "modulename": "pyerrors.obs", "qualname": "Obs.reweighted", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.tag": {"fullname": "pyerrors.obs.Obs.tag", "modulename": "pyerrors.obs", "qualname": "Obs.tag", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.value": {"fullname": "pyerrors.obs.Obs.value", "modulename": "pyerrors.obs", "qualname": "Obs.value", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.dvalue": {"fullname": "pyerrors.obs.Obs.dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.dvalue", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_names": {"fullname": "pyerrors.obs.Obs.e_names", "modulename": "pyerrors.obs", "qualname": "Obs.e_names", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.cov_names": {"fullname": "pyerrors.obs.Obs.cov_names", "modulename": "pyerrors.obs", "qualname": "Obs.cov_names", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.mc_names": {"fullname": "pyerrors.obs.Obs.mc_names", "modulename": "pyerrors.obs", "qualname": "Obs.mc_names", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_content": {"fullname": "pyerrors.obs.Obs.e_content", "modulename": "pyerrors.obs", "qualname": "Obs.e_content", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.covobs": {"fullname": "pyerrors.obs.Obs.covobs", "modulename": "pyerrors.obs", "qualname": "Obs.covobs", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.gamma_method": {"fullname": "pyerrors.obs.Obs.gamma_method", "modulename": "pyerrors.obs", "qualname": "Obs.gamma_method", "type": "function", "doc": "Estimate the error and related properties of the Obs.
\n\nParameters \n\n\nS (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.tau_exp (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).N_sigma (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).fft (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True) \n", "signature": "(self, **kwargs)", "funcdef": "def"}, "pyerrors.obs.Obs.details": {"fullname": "pyerrors.obs.Obs.details", "modulename": "pyerrors.obs", "qualname": "Obs.details", "type": "function", "doc": "Output detailed properties of the Obs.
\n\nParameters \n\n\nens_content (bool):\nprint details about the ensembles and replica if true. \n", "signature": "(self, ens_content=True)", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero_within_error": {"fullname": "pyerrors.obs.Obs.is_zero_within_error", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero_within_error", "type": "function", "doc": "Checks whether the observable is zero within 'sigma' standard errors.
\n\nParameters \n\n\nsigma (int):\nNumber of standard errors used for the check.Works only properly when the gamma method was run. \n", "signature": "(self, sigma=1)", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero": {"fullname": "pyerrors.obs.Obs.is_zero", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero", "type": "function", "doc": "Checks whether the observable is zero within a given tolerance.
\n\nParameters \n\n\natol (float):\nAbsolute tolerance (for details see numpy documentation). \n", "signature": "(self, atol=1e-10)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_tauint": {"fullname": "pyerrors.obs.Obs.plot_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.plot_tauint", "type": "function", "doc": "Plot integrated autocorrelation time for each ensemble.
\n\nParameters \n\n\nsave (str):\nsaves the figure to a file named 'save' if. \n", "signature": "(self, save=None)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rho": {"fullname": "pyerrors.obs.Obs.plot_rho", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rho", "type": "function", "doc": "Plot normalized autocorrelation function time for each ensemble.
\n\nParameters \n\n\nsave (str):\nsaves the figure to a file named 'save' if. \n", "signature": "(self, save=None)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rep_dist": {"fullname": "pyerrors.obs.Obs.plot_rep_dist", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rep_dist", "type": "function", "doc": "Plot replica distribution for each ensemble with more than one replicum.
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_history": {"fullname": "pyerrors.obs.Obs.plot_history", "modulename": "pyerrors.obs", "qualname": "Obs.plot_history", "type": "function", "doc": "Plot derived Monte Carlo history for each ensemble
\n\nParameters \n\n\nexpand (bool):\nshow expanded history for irregular Monte Carlo chains (default: True). \n", "signature": "(self, expand=True)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_piechart": {"fullname": "pyerrors.obs.Obs.plot_piechart", "modulename": "pyerrors.obs", "qualname": "Obs.plot_piechart", "type": "function", "doc": "Plot piechart which shows the fractional contribution of each\nensemble to the error and returns a dictionary containing the fractions.
\n\nParameters \n\n\nsave (str):\nsaves the figure to a file named 'save' if. \n", "signature": "(self, save=None)", "funcdef": "def"}, "pyerrors.obs.Obs.dump": {"fullname": "pyerrors.obs.Obs.dump", "modulename": "pyerrors.obs", "qualname": "Obs.dump", "type": "function", "doc": "Dump the Obs to a file 'name' of chosen format.
\n\nParameters \n\n\nfilename (str):\nname of the file to be saved.datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"description (str):\nDescription for output file, only relevant for json.gz format.path (str):\nspecifies a custom path for the file (default '.') \n", "signature": "(self, filename, datatype='json.gz', description='', **kwargs)", "funcdef": "def"}, "pyerrors.obs.Obs.export_jackknife": {"fullname": "pyerrors.obs.Obs.export_jackknife", "modulename": "pyerrors.obs", "qualname": "Obs.export_jackknife", "type": "function", "doc": "Export jackknife samples from the Obs
\n\nReturns \n\n\nnumpy.ndarray : Returns a numpy array of length N + 1 where N is the number of samples\nfor the given ensemble and replicum. The zeroth entry of the array contains\nthe mean value of the Obs, entries 1 to N contain the N jackknife samples\nderived from the Obs. The current implementation only works for observables\ndefined on exactly one ensemble and replicum. The derived jackknife samples\nshould agree with samples from a full jackknife analysis up to O(1/N). \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.sqrt": {"fullname": "pyerrors.obs.Obs.sqrt", "modulename": "pyerrors.obs", "qualname": "Obs.sqrt", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.log": {"fullname": "pyerrors.obs.Obs.log", "modulename": "pyerrors.obs", "qualname": "Obs.log", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.exp": {"fullname": "pyerrors.obs.Obs.exp", "modulename": "pyerrors.obs", "qualname": "Obs.exp", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.sin": {"fullname": "pyerrors.obs.Obs.sin", "modulename": "pyerrors.obs", "qualname": "Obs.sin", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.cos": {"fullname": "pyerrors.obs.Obs.cos", "modulename": "pyerrors.obs", "qualname": "Obs.cos", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.tan": {"fullname": "pyerrors.obs.Obs.tan", "modulename": "pyerrors.obs", "qualname": "Obs.tan", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arcsin": {"fullname": "pyerrors.obs.Obs.arcsin", "modulename": "pyerrors.obs", "qualname": "Obs.arcsin", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arccos": {"fullname": "pyerrors.obs.Obs.arccos", "modulename": "pyerrors.obs", "qualname": "Obs.arccos", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arctan": {"fullname": "pyerrors.obs.Obs.arctan", "modulename": "pyerrors.obs", "qualname": "Obs.arctan", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.sinh": {"fullname": "pyerrors.obs.Obs.sinh", "modulename": "pyerrors.obs", "qualname": "Obs.sinh", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.cosh": {"fullname": "pyerrors.obs.Obs.cosh", "modulename": "pyerrors.obs", "qualname": "Obs.cosh", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.tanh": {"fullname": "pyerrors.obs.Obs.tanh", "modulename": "pyerrors.obs", "qualname": "Obs.tanh", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arcsinh": {"fullname": "pyerrors.obs.Obs.arcsinh", "modulename": "pyerrors.obs", "qualname": "Obs.arcsinh", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arccosh": {"fullname": "pyerrors.obs.Obs.arccosh", "modulename": "pyerrors.obs", "qualname": "Obs.arccosh", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arctanh": {"fullname": "pyerrors.obs.Obs.arctanh", "modulename": "pyerrors.obs", "qualname": "Obs.arctanh", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.N_sigma": {"fullname": "pyerrors.obs.Obs.N_sigma", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.S": {"fullname": "pyerrors.obs.Obs.S", "modulename": "pyerrors.obs", "qualname": "Obs.S", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_ddvalue": {"fullname": "pyerrors.obs.Obs.e_ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_ddvalue", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_drho": {"fullname": "pyerrors.obs.Obs.e_drho", "modulename": "pyerrors.obs", "qualname": "Obs.e_drho", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_dtauint": {"fullname": "pyerrors.obs.Obs.e_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_dtauint", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_dvalue": {"fullname": "pyerrors.obs.Obs.e_dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_dvalue", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_n_dtauint": {"fullname": "pyerrors.obs.Obs.e_n_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_dtauint", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_n_tauint": {"fullname": "pyerrors.obs.Obs.e_n_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_tauint", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_rho": {"fullname": "pyerrors.obs.Obs.e_rho", "modulename": "pyerrors.obs", "qualname": "Obs.e_rho", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_tauint": {"fullname": "pyerrors.obs.Obs.e_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_tauint", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_windowsize": {"fullname": "pyerrors.obs.Obs.e_windowsize", "modulename": "pyerrors.obs", "qualname": "Obs.e_windowsize", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.tau_exp": {"fullname": "pyerrors.obs.Obs.tau_exp", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp", "type": "variable", "doc": "
\n"}, "pyerrors.obs.CObs": {"fullname": "pyerrors.obs.CObs", "modulename": "pyerrors.obs", "qualname": "CObs", "type": "class", "doc": "Class for a complex valued observable.
\n"}, "pyerrors.obs.CObs.__init__": {"fullname": "pyerrors.obs.CObs.__init__", "modulename": "pyerrors.obs", "qualname": "CObs.__init__", "type": "function", "doc": "
\n", "signature": "(self, real, imag=0.0)", "funcdef": "def"}, "pyerrors.obs.CObs.tag": {"fullname": "pyerrors.obs.CObs.tag", "modulename": "pyerrors.obs", "qualname": "CObs.tag", "type": "variable", "doc": "
\n"}, "pyerrors.obs.CObs.real": {"fullname": "pyerrors.obs.CObs.real", "modulename": "pyerrors.obs", "qualname": "CObs.real", "type": "variable", "doc": "
\n"}, "pyerrors.obs.CObs.imag": {"fullname": "pyerrors.obs.CObs.imag", "modulename": "pyerrors.obs", "qualname": "CObs.imag", "type": "variable", "doc": "
\n"}, "pyerrors.obs.CObs.gamma_method": {"fullname": "pyerrors.obs.CObs.gamma_method", "modulename": "pyerrors.obs", "qualname": "CObs.gamma_method", "type": "function", "doc": "Executes the gamma_method for the real and the imaginary part.
\n", "signature": "(self, **kwargs)", "funcdef": "def"}, "pyerrors.obs.CObs.is_zero": {"fullname": "pyerrors.obs.CObs.is_zero", "modulename": "pyerrors.obs", "qualname": "CObs.is_zero", "type": "function", "doc": "Checks whether both real and imaginary part are zero within machine precision.
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.CObs.conjugate": {"fullname": "pyerrors.obs.CObs.conjugate", "modulename": "pyerrors.obs", "qualname": "CObs.conjugate", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.derived_observable": {"fullname": "pyerrors.obs.derived_observable", "modulename": "pyerrors.obs", "qualname": "derived_observable", "type": "function", "doc": "Construct a derived Obs according to func(data, **kwargs) using automatic differentiation.
\n\nParameters \n\n\nfunc (object):\narbitrary function of the form func(data, **kwargs). For the\nautomatic differentiation to work, all numpy functions have to have\nthe autograd wrapper (use 'import autograd.numpy as anp').data (list):\nlist of Obs, e.g. [obs1, obs2, obs3].num_grad (bool):\nif True, numerical derivatives are used instead of autograd\n(default False). To control the numerical differentiation the\nkwargs of numdifftools.step_generators.MaxStepGenerator\ncan be used.man_grad (list):\nmanually supply a list or an array which contains the jacobian\nof func. Use cautiously, supplying the wrong derivative will\nnot be intercepted. \n\nNotes \n\nFor simple mathematical operations it can be practical to use anonymous\nfunctions. For the ratio of two observables one can e.g. use
\n\nnew_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2])
\n", "signature": "(func, data, array_mode=False, **kwargs)", "funcdef": "def"}, "pyerrors.obs.reweight": {"fullname": "pyerrors.obs.reweight", "modulename": "pyerrors.obs", "qualname": "reweight", "type": "function", "doc": "Reweight a list of observables.
\n\nParameters \n\n\nweight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.obs (list):\nlist of Obs, e.g. [obs1, obs2, obs3].all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. \n", "signature": "(weight, obs, **kwargs)", "funcdef": "def"}, "pyerrors.obs.correlate": {"fullname": "pyerrors.obs.correlate", "modulename": "pyerrors.obs", "qualname": "correlate", "type": "function", "doc": "Correlate two observables.
\n\nParameters \n\n\nobs_a (Obs):\nFirst observableobs_b (Obs):\nSecond observable \n\nNotes \n\nKeep in mind to only correlate primary observables which have not been reweighted\nyet. The reweighting has to be applied after correlating the observables.\nCurrently only works if ensembles are identical (this is not strictly necessary).
\n", "signature": "(obs_a, obs_b)", "funcdef": "def"}, "pyerrors.obs.covariance": {"fullname": "pyerrors.obs.covariance", "modulename": "pyerrors.obs", "qualname": "covariance", "type": "function", "doc": "Calculates the error covariance matrix of a set of observables.
\n\nThe gamma method has to be applied first to all observables.
\n\nParameters \n\n\nobs (list or numpy.ndarray):\nList or one dimensional array of Obsvisualize (bool):\nIf True plots the corresponding normalized correlation matrix (default False).correlation (bool):\nIf True the correlation matrix instead of the error covariance matrix is returned (default False).smooth (None or int):\nIf smooth is an integer 'E' between 2 and the dimension of the matrix minus 1 the eigenvalue\nsmoothing procedure of hep-lat/9412087 is applied to the correlation matrix which leaves the\nlargest E eigenvalues essentially unchanged and smoothes the smaller eigenvalues to avoid extremely\nsmall ones. \n\nNotes \n\nThe error covariance is defined such that it agrees with the squared standard error for two identical observables\n$$\\operatorname{cov}(a,a)=\\sum_{s=1}^N\\delta_a^s\\delta_a^s/N^2=\\Gamma_{aa}(0)/N=\\operatorname{var}(a)/N=\\sigma_a^2$$\nin the absence of autocorrelation.\nThe error covariance is estimated by calculating the correlation matrix assuming no autocorrelation and then rescaling the correlation matrix by the full errors including the previous gamma method estimate for the autocorrelation of the observables. The covariance at windowsize 0 is guaranteed to be positive semi-definite\n$$\\sum_{i,j}v_i\\Gamma_{ij}(0)v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i,j}v_i\\delta_i^s\\delta_j^s v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i}|v_i\\delta_i^s|^2\\geq 0\\,,$$ for every $v\\in\\mathbb{R}^M$, while such an identity does not hold for larger windows/lags.\nFor observables defined on a single ensemble our approximation is equivalent to assuming that the integrated autocorrelation time of an off-diagonal element is equal to the geometric mean of the integrated autocorrelation times of the corresponding diagonal elements.\n$$\\tau_{\\mathrm{int}, ij}=\\sqrt{\\tau_{\\mathrm{int}, i}\\times \\tau_{\\mathrm{int}, j}}$$\nThis construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors).
\n", "signature": "(obs, visualize=False, correlation=False, smooth=None, **kwargs)", "funcdef": "def"}, "pyerrors.obs.import_jackknife": {"fullname": "pyerrors.obs.import_jackknife", "modulename": "pyerrors.obs", "qualname": "import_jackknife", "type": "function", "doc": "Imports jackknife samples and returns an Obs
\n\nParameters \n\n\njacks (numpy.ndarray):\nnumpy array containing the mean value as zeroth entry and\nthe N jackknife samples as first to Nth entry.name (str):\nname of the ensemble the samples are defined on. \n", "signature": "(jacks, name, idl=None)", "funcdef": "def"}, "pyerrors.obs.merge_obs": {"fullname": "pyerrors.obs.merge_obs", "modulename": "pyerrors.obs", "qualname": "merge_obs", "type": "function", "doc": "Combine all observables in list_of_obs into one new observable
\n\nParameters \n\n\nlist_of_obs (list):\nlist of the Obs object to be combined \n\nNotes \n\nIt is not possible to combine obs which are based on the same replicum
\n", "signature": "(list_of_obs)", "funcdef": "def"}, "pyerrors.obs.cov_Obs": {"fullname": "pyerrors.obs.cov_Obs", "modulename": "pyerrors.obs", "qualname": "cov_Obs", "type": "function", "doc": "Create an Obs based on mean(s) and a covariance matrix
\n\nParameters \n\n\nmean (list of floats or float):\nN mean value(s) of the new Obscov (list or array):\n2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariancename (str):\nidentifier for the covariance matrixgrad (list or array):\nGradient of the Covobs wrt. the means belonging to cov. \n", "signature": "(means, cov, name, grad=None)", "funcdef": "def"}, "pyerrors.roots": {"fullname": "pyerrors.roots", "modulename": "pyerrors.roots", "type": "module", "doc": "
\n"}, "pyerrors.roots.find_root": {"fullname": "pyerrors.roots.find_root", "modulename": "pyerrors.roots", "qualname": "find_root", "type": "function", "doc": "Finds the root of the function func(x, d) where d is an Obs.
\n\nParameters \n\n\nd (Obs):\nObs passed to the function.func (object):\nFunction to be minimized. Any numpy functions have to use the autograd.numpy wrapper.\nExample:\npython\nimport autograd.numpy as anp\ndef root_func(x, d):\n return anp.exp(-x ** 2) - d\nguess (float):\nInitial guess for the minimization. \n\nReturns \n\n\nObs : Obs valued root of the function. \n", "signature": "(d, func, guess=1.0, **kwargs)", "funcdef": "def"}, "pyerrors.version": {"fullname": "pyerrors.version", "modulename": "pyerrors.version", "type": "module", "doc": "
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\n\n\nautomatic differentiation for exact liner error propagation as suggested in arXiv:1809.01289 (partly based on the autograd package). \ntreatment of slow modes in the simulation as suggested in arXiv:1009.5228 . \ncoherent error propagation for data from different Markov chains. \nnon-linear fits with x- and y-errors and exact linear error propagation based on automatic differentiation as introduced in arXiv:1809.01289 . \nreal and complex matrix operations and their error propagation based on automatic differentiation (Matrix inverse, Cholesky decomposition, calculation of eigenvalues and eigenvectors, singular value decomposition...). \n \n\nThere exist similar publicly available implementations of gamma method error analysis suites in Fortran , Julia and Python .
\n\nBasic example \n\nimport numpy as np \nimport pyerrors as pe \n\nmy_obs = pe . Obs ([ samples ], [ 'ensemble_name' ]) # Initialize an Obs object \nmy_new_obs = 2 * np . log ( my_obs ) / my_obs ** 2 # Construct derived Obs object \nmy_new_obs . gamma_method () # Estimate the statistical error \nprint ( my_new_obs ) # Print the result to stdout \n> 0.31498 ( 72 ) \nThe Obs class \n\npyerrors introduces a new datatype, Obs, which simplifies error propagation and estimation for auto- and cross-correlated data.\nAn Obs object can be initialized with two arguments, the first is a list containing the samples for an observable from a Monte Carlo chain.\nThe samples can either be provided as python list or as numpy array.\nThe second argument is a list containing the names of the respective Monte Carlo chains as strings. These strings uniquely identify a Monte Carlo chain/ensemble.
\n\nimport pyerrors as pe \n\nmy_obs = pe . Obs ([ samples ], [ 'ensemble_name' ]) \nError propagation \n\nWhen performing mathematical operations on Obs objects the correct error propagation is intrinsically taken care of using a first order Taylor expansion\n$$\\delta_f^i=\\sum_\\alpha \\bar{f}_\\alpha \\delta_\\alpha^i\\,,\\quad \\delta_\\alpha^i=a_\\alpha^i-\\bar{a}_\\alpha\\,,$$\nas introduced in arXiv:hep-lat/0306017 .\nThe required derivatives $\\bar{f}_\\alpha$ are evaluated up to machine precision via automatic differentiation as suggested in arXiv:1809.01289 .
\n\nThe Obs class is designed such that mathematical numpy functions can be used on Obs just as for regular floats.
\n\nimport numpy as np \nimport pyerrors as pe \n\nmy_obs1 = pe . Obs ([ samples1 ], [ 'ensemble_name' ]) \nmy_obs2 = pe . Obs ([ samples2 ], [ 'ensemble_name' ]) \n\nmy_sum = my_obs1 + my_obs2 \n\nmy_m_eff = np . log ( my_obs1 / my_obs2 ) \n\niamzero = my_m_eff - my_m_eff \n# Check that value and fluctuations are zero within machine precision \nprint ( iamzero == 0.0 ) \n> True \nError estimation \n\nThe error estimation within pyerrors is based on the gamma method introduced in arXiv:hep-lat/0306017 .\nAfter having arrived at the derived quantity of interest the gamma_method can be called as detailed in the following example.
\n\nmy_sum . gamma_method () \nprint ( my_sum ) \n> 1.70 ( 57 ) \nmy_sum . details () \n> Result 1.70000000e+00 +/- 5.72046658e-01 +/- 7.56746598e-02 ( 33.650 % ) \n> t_int 2.71422900e+00 +/- 6.40320983e-01 S = 2.00 \n> 1000 samples in 1 ensemble : \n> \u00b7 Ensemble 'ensemble_name' : 1000 configurations ( from 1 to 1000 ) \nWe use the following definition of the integrated autocorrelation time established in Madras & Sokal 1988 \n$$\\tau_\\mathrm{int}=\\frac{1}{2}+\\sum_{t=1}^{W}\\rho(t)\\geq \\frac{1}{2}\\,.$$\nThe window $W$ is determined via the automatic windowing procedure described in arXiv:hep-lat/0306017 .\nThe standard value for the parameter $S$ of this automatic windowing procedure is $S=2$. Other values for $S$ can be passed to the gamma_method as parameter.
\n\nmy_sum . gamma_method ( S = 3.0 ) \nmy_sum . details () \n> Result 1.70000000e+00 +/- 6.30675201e-01 +/- 1.04585650e-01 ( 37.099 % ) \n> t_int 3.29909703e+00 +/- 9.77310102e-01 S = 3.00 \n> 1000 samples in 1 ensemble : \n> \u00b7 Ensemble 'ensemble_name' : 1000 configurations ( from 1 to 1000 ) \nThe integrated autocorrelation time $\\tau_\\mathrm{int}$ and the autocorrelation function $\\rho(W)$ can be monitored via the methods pyerrors.obs.Obs.plot_tauint and pyerrors.obs.Obs.plot_tauint.
\n\nIf the parameter $S$ is set to zero it is assumed that the dataset does not exhibit any autocorrelation and the windowsize is chosen to be zero.\nIn this case the error estimate is identical to the sample standard error.
\n\nExponential tails \n\nSlow modes in the Monte Carlo history can be accounted for by attaching an exponential tail to the autocorrelation function $\\rho$ as suggested in arXiv:1009.5228 . The longest autocorrelation time in the history, $\\tau_\\mathrm{exp}$, can be passed to the gamma_method as parameter. In this case the automatic windowing procedure is vacated and the parameter $S$ does not affect the error estimate.
\n\nmy_sum . gamma_method ( tau_exp = 7.2 ) \nmy_sum . details () \n> Result 1.70000000e+00 +/- 6.28097762e-01 +/- 5.79077524e-02 ( 36.947 % ) \n> t_int 3.27218667e+00 +/- 7.99583654e-01 tau_exp = 7.20 , N_sigma = 1 \n> 1000 samples in 1 ensemble : \n> \u00b7 Ensemble 'ensemble_name' : 1000 configurations ( from 1 to 1000 ) \nFor the full API see pyerrors.obs.Obs.gamma_method.
\n\nMultiple ensembles/replica \n\nError propagation for multiple ensembles (Markov chains with different simulation parameters) is handled automatically. Ensembles are uniquely identified by their name.
\n\nobs1 = pe . Obs ([ samples1 ], [ 'ensemble1' ]) \nobs2 = pe . Obs ([ samples2 ], [ 'ensemble2' ]) \n\nmy_sum = obs1 + obs2 \nmy_sum . details () \n> Result 2.00697958e+00 \n> 1500 samples in 2 ensembles : \n> \u00b7 Ensemble 'ensemble1' : 1000 configurations ( from 1 to 1000 ) \n> \u00b7 Ensemble 'ensemble2' : 500 configurations ( from 1 to 500 ) \npyerrors identifies multiple replica (independent Markov chains with identical simulation parameters) by the vertical bar | in the name of the data set.
\n\nobs1 = pe . Obs ([ samples1 ], [ 'ensemble1|r01' ]) \nobs2 = pe . Obs ([ samples2 ], [ 'ensemble1|r02' ]) \n\n> my_sum = obs1 + obs2 \n> my_sum . details () \n> Result 2.00697958e+00 \n> 1500 samples in 1 ensemble : \n> \u00b7 Ensemble 'ensemble1' \n> \u00b7 Replicum 'r01' : 1000 configurations ( from 1 to 1000 ) \n> \u00b7 Replicum 'r02' : 500 configurations ( from 1 to 500 ) \nError estimation for multiple ensembles \n\nIn order to keep track of different error analysis parameters for different ensembles one can make use of global dictionaries as detailed in the following example.
\n\npe . Obs . S_dict [ 'ensemble1' ] = 2.5 \npe . Obs . tau_exp_dict [ 'ensemble2' ] = 8.0 \npe . Obs . tau_exp_dict [ 'ensemble3' ] = 2.0 \nIn case the gamma_method is called without any parameters it will use the values specified in the dictionaries for the respective ensembles.\nPassing arguments to the gamma_method still dominates over the dictionaries.
\n\nIrregular Monte Carlo chains \n\nObs objects defined on irregular Monte Carlo chains can be initialized with the parameter idl.
\n\n# Observable defined on configurations 20 to 519 \nobs1 = pe . Obs ([ samples1 ], [ 'ensemble1' ], idl = [ range ( 20 , 520 )]) \nobs1 . details () \n> Result 9.98319881e-01 \n> 500 samples in 1 ensemble : \n> \u00b7 Ensemble 'ensemble1' : 500 configurations ( from 20 to 519 ) \n\n# Observable defined on every second configuration between 5 and 1003 \nobs2 = pe . Obs ([ samples2 ], [ 'ensemble1' ], idl = [ range ( 5 , 1005 , 2 )]) \nobs2 . details () \n> Result 9.99100712e-01 \n> 500 samples in 1 ensemble : \n> \u00b7 Ensemble 'ensemble1' : 500 configurations ( from 5 to 1003 in steps of 2 ) \n\n# Observable defined on configurations 2, 9, 28, 29 and 501 \nobs3 = pe . Obs ([ samples3 ], [ 'ensemble1' ], idl = [[ 2 , 9 , 28 , 29 , 501 ]]) \nobs3 . details () \n> Result 1.01718064e+00 \n> 5 samples in 1 ensemble : \n> \u00b7 Ensemble 'ensemble1' : 5 configurations ( irregular range ) \nObs objects defined on regular and irregular histories of the same ensemble can be combined with each other and the correct error propagation and estimation is automatically taken care of.
\n\nWarning: Irregular Monte Carlo chains can result in odd patterns in the autocorrelation functions.\nMake sure to check the autocorrelation time with e.g. pyerrors.obs.Obs.plot_rho or pyerrors.obs.Obs.plot_tauint.
\n\nFor the full API see pyerrors.obs.Obs.
\n\nCorrelators \n\nWhen one is not interested in single observables but correlation functions, pyerrors offers the Corr class which simplifies the corresponding error propagation and provides the user with a set of standard methods. In order to initialize a Corr objects one needs to arrange the data as a list of Obs
\n\nmy_corr = pe . Corr ([ obs_0 , obs_1 , obs_2 , obs_3 ]) \nprint ( my_corr ) \n> x0 / a Corr ( x0 / a ) \n> ------------------ \n> 0 0.7957 ( 80 ) \n> 1 0.5156 ( 51 ) \n> 2 0.3227 ( 33 ) \n> 3 0.2041 ( 21 ) \nIn case the correlation functions are not defined on the outermost timeslices, for example because of fixed boundary conditions, a padding can be introduced.
\n\nmy_corr = pe . Corr ([ obs_0 , obs_1 , obs_2 , obs_3 ], padding = [ 1 , 1 ]) \nprint ( my_corr ) \n> x0 / a Corr ( x0 / a ) \n> ------------------ \n> 0 \n> 1 0.7957 ( 80 ) \n> 2 0.5156 ( 51 ) \n> 3 0.3227 ( 33 ) \n> 4 0.2041 ( 21 ) \n> 5 \nThe individual entries of a correlator can be accessed via slicing
\n\nprint ( my_corr [ 3 ]) \n> 0.3227 ( 33 ) \nError propagation with the Corr class works very similar to Obs objects. Mathematical operations are overloaded and Corr objects can be computed together with other Corr objects, Obs objects or real numbers and integers.
\n\nmy_new_corr = 0.3 * my_corr [ 2 ] * my_corr * my_corr + 12 / my_corr \npyerrors provides the user with a set of regularly used methods for the manipulation of correlator objects:
\n\n\nCorr.gamma_method applies the gamma method to all entries of the correlator.Corr.m_eff to construct effective masses. Various variants for periodic and fixed temporal boundary conditions are available.Corr.deriv returns the first derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.Corr.second_deriv returns the second derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.Corr.symmetric symmetrizes parity even correlations functions, assuming periodic boundary conditions.Corr.anti_symmetric anti-symmetrizes parity odd correlations functions, assuming periodic boundary conditions.Corr.T_symmetry averages a correlator with its time symmetry partner, assuming fixed boundary conditions.Corr.plateau extracts a plateau value from the correlator in a given range.Corr.roll periodically shifts the correlator.Corr.reverse reverses the time ordering of the correlator.Corr.correlate constructs a disconnected correlation function from the correlator and another Corr or Obs object.Corr.reweight reweights the correlator. \n\npyerrors can also handle matrices of correlation functions and extract energy states from these matrices via a generalized eigenvalue problem (see pyerrors.correlators.Corr.GEVP).
\n\nFor the full API see pyerrors.correlators.Corr.
\n\nComplex valued observables \n\npyerrors can handle complex valued observables via the class pyerrors.obs.CObs.\nCObs are initialized with a real and an imaginary part which both can be Obs valued.
\n\nmy_real_part = pe . Obs ([ samples1 ], [ 'ensemble1' ]) \nmy_imag_part = pe . Obs ([ samples2 ], [ 'ensemble1' ]) \n\nmy_cobs = pe . CObs ( my_real_part , my_imag_part ) \nmy_cobs . gamma_method () \nprint ( my_cobs ) \n> ( 0.9959 ( 91 ) + 0.659 ( 28 ) j ) \nElementary mathematical operations are overloaded and samples are properly propagated as for the Obs class.
\n\nmy_derived_cobs = ( my_cobs + my_cobs . conjugate ()) / np . abs ( my_cobs ) \nmy_derived_cobs . gamma_method () \nprint ( my_derived_cobs ) \n> ( 1.668 ( 23 ) + 0.0 j ) \nThe Covobs class \n\nIn many projects, auxiliary data that is not based on Monte Carlo chains enters. Examples are experimentally determined mesons masses which are used to set the scale or renormalization constants. These numbers come with an error that has to be propagated through the analysis. The Covobs class allows to define such quantities in pyerrors. Furthermore, external input might consist of correlated quantities. An example are the parameters of an interpolation formula, which are defined via mean values and a covariance matrix between all parameters. The contribution of the interpolation formula to the error of a derived quantity therefore might depend on the complete covariance matrix.
\n\nThis concept is built into the definition of Covobs. In pyerrors, external input is defined by $M$ mean values, a $M\\times M$ covariance matrix, where $M=1$ is permissible, and a name that uniquely identifies the covariance matrix. Below, we define the pion mass, based on its mean value and error, 134.9768(5). Note, that the square of the error enters cov_Obs, since the second argument of this function is the covariance matrix of the Covobs.
\n\nimport pyerrors.obs as pe \n\nmpi = pe . cov_Obs ( 134.9768 , 0.0005 ** 2 , 'pi^0 mass' ) \nmpi . gamma_method () \nmpi . details () \n> Result 1.34976800e+02 +/- 5.00000000e-04 +/- 0.00000000e+00 ( 0.000 % ) \n> pi ^ 0 mass 5.00000000e-04 \n> 0 samples in 1 ensemble : \n> \u00b7 Covobs 'pi^0 mass' \nThe resulting object mpi is an Obs that contains a Covobs. In the following, it may be handled as any other Obs. The contribution of the covariance matrix to the error of an Obs is determined from the $M \\times M$ covariance matrix $\\Sigma$ and the gradient of the Obs with respect to the external quantities, which is the $1\\times M$ Jacobian matrix $J$, via\n$$s = \\sqrt{J^T \\Sigma J}\\,,$$\nwhere the Jacobian is computed for each derived quantity via automatic differentiation.
\n\nCorrelated auxiliary data is defined similarly to above, e.g., via
\n\nRAP = pe . cov_Obs ([ 16.7457 , - 19.0475 ], [[ 3.49591 , - 6.07560 ], [ - 6.07560 , 10.5834 ]], 'R_AP, 1906.03445, (5.3a)' ) \nprint ( RAP ) \n> [ Obs [ 16.7 ( 1.9 )], Obs [ - 19.0 ( 3.3 )]] \nwhere RAP now is a list of two Obs that contains the two correlated parameters.
\n\nSince the gradient of a derived observable with respect to an external covariance matrix is propagated through the entire analysis, the Covobs class allows to quote the derivative of a result with respect to the external quantities. If these derivatives are published together with the result, small shifts in the definition of external quantities, e.g., the definition of the physical point, can be performed a posteriori based on the published information. This may help to compare results of different groups. The gradient of an Obs o with respect to a covariance matrix with the identifying string k may be accessed via
\n\n\n\nError propagation in iterative algorithms \n\npyerrors supports exact linear error propagation for iterative algorithms like various variants of non-linear least sqaures fits or root finding. The derivatives required for the error propagation are calculated as described in arXiv:1809.01289 .
\n\nLeast squares fits \n\nStandard non-linear least square fits with errors on the dependent but not the independent variables can be performed with pyerrors.fits.least_squares. As default solver the Levenberg-Marquardt algorithm implemented in scipy is used.
\n\nFit functions have to be of the following form
\n\nimport autograd.numpy as anp \n\ndef func ( a , x ): \n return a [ 1 ] * anp . exp ( - a [ 0 ] * x ) \nIt is important that numerical functions refer to autograd.numpy instead of numpy for the automatic differentiation in iterative algorithms to work properly.
\n\nFits can then be performed via
\n\nfit_result = pe . fits . least_squares ( x , y , func ) \nprint ( " \\n " , fit_result ) \n> Fit with 2 parameters \n> Method : Levenberg - Marquardt \n> ` ftol ` termination condition is satisfied . \n> chisquare / d . o . f . : 0.9593035785160936 \n\n> Goodness of fit : \n> \u03c7 \u00b2 / d . o . f . = 0.959304 \n> p - value = 0.5673 \n> Fit parameters : \n> 0 0.0548 ( 28 ) \n> 1 1.933 ( 64 ) \nwhere x is a list or numpy.array of floats and y is a list or numpy.array of Obs.
\n\nData stored in Corr objects can be fitted directly using the Corr.fit method.
\n\nmy_corr = pe . Corr ( y ) \nfit_result = my_corr . fit ( func , fitrange = [ 12 , 25 ]) \nthis can simplify working with absolute fit ranges and takes care of gaps in the data automatically.
\n\nFor fit functions with multiple independent variables the fit function can be of the form
\n\ndef func ( a , x ): \n ( x1 , x2 ) = x \n return a [ 0 ] * x1 ** 2 + a [ 1 ] * x2 \npyerrors also supports correlated fits which can be triggered via the parameter correlated_fit=True.\nDetails about how the required covariance matrix is estimated can be found in pyerrors.obs.covariance.
\n\nDirect visualizations of the performed fits can be triggered via resplot=True or qqplot=True. For all available options see pyerrors.fits.least_squares.
\n\nTotal least squares fits \n\npyerrors can also fit data with errors on both the dependent and independent variables using the total least squares method also referred to orthogonal distance regression as implemented in scipy , see pyerrors.fits.least_squares. The syntax is identical to the standard least squares case, the only diffrence being that x also has to be a list or numpy.array of Obs.
\n\nFor the full API see pyerrors.fits for fits and pyerrors.roots for finding roots of functions.
\n\nMatrix operations \n\npyerrors provides wrappers for Obs- and CObs-valued matrix operations based on numpy.linalg. The supported functions include:
\n\n\ninv for the matrix inverse.cholseky for the Cholesky decomposition.det for the matrix determinant.eigh for eigenvalues and eigenvectors of hermitean matrices.eig for eigenvalues of general matrices.pinv for the Moore-Penrose pseudoinverse.svd for the singular-value-decomposition. \n\nFor the full API see pyerrors.linalg.
\n\nExport data \n\nThe preferred exported file format within pyerrors is json.gz. Files written to this format are valid JSON files that have been compressed using gzip. The structure of the content is inspired by the dobs format of the ALPHA collaboration. The aim of the format is to facilitate the storage of data in a self-contained way such that, even years after the creation of the file, it is possible to extract all necessary information:
\n\n\nWhat observables are stored? Possibly: How exactly are they defined. \nHow does each single ensemble or external quantity contribute to the error of the observable? \nWho did write the file when and on which machine? \n \n\nThis can be achieved by storing all information in one single file. The export routines of pyerrors are written such that as much information as possible is written automatically as described in the following example
\n\nmy_obs = pe . Obs ([ samples ], [ "test_ensemble" ]) \nmy_obs . tag = "My observable" \n\npe . input . json . dump_to_json ( my_obs , "test_output_file" , description = "This file contains a test observable" ) \n# For a single observable one can equivalently use the class method dump \nmy_obs . dump ( "test_output_file" , description = "This file contains a test observable" ) \n\ncheck = pe . input . json . load_json ( "test_output_file" ) \n\nprint ( my_obs == check ) \n> True \nThe format also allows to directly write out the content of Corr objects or lists and arrays of Obs objects by passing the desired data to pyerrors.input.json.dump_to_json.
\n\n\n\nThe first entries of the file provide optional auxiliary information:
\n\n\nprogram is a string that indicates which program was used to write the file.version is a string that specifies the version of the format.who is a string that specifies the user name of the creator of the file.date is a string and contains the creation date of the file.host is a string and contains the hostname of the machine where the file has been written.description contains information on the content of the file. This field is not filled automatically in pyerrors. The user is advised to provide as detailed information as possible in this field. Examples are: Input files of measurements or simulations, LaTeX formulae or references to publications to specify how the observables have been computed, details on the analysis strategy, ... This field may be any valid JSON type. Strings, arrays or objects (equivalent to dicts in python) are well suited to provide information. \n\nThe only necessary entry of the file is the field\n-obsdata, an array that contains the actual data.
\n\nEach entry of the array belongs to a single structure of observables. Currently, these structures can be either of Obs, list, numpy.ndarray, Corr. All Obs inside a structure (with dimension > 0) have to be defined on the same set of configurations. Different structures, that are represented by entries of the array obsdata, are treated independently. Each entry of the array obsdata has the following required entries:
\n\n\ntype is a string that specifies the type of the structure. This allows to parse the content to the correct form after reading the file. It is always possible to interpret the content as list of Obs.value is an array that contains the mean values of the Obs inside the structure.\nThe following entries are optional:layout is a string that specifies the layout of multi-dimensional structures. Examples are \"2, 2\" for a 2x2 dimensional matrix or \"64, 4, 4\" for a Corr with $T=64$ and 4x4 matrices on each time slices. \"1\" denotes a single Obs. Multi-dimensional structures are stored in row-major format (see below).tag is any JSON type. It contains additional information concerning the structure. The tag of an Obs in pyerrors is written here.reweighted is a Bool that may be used to specify, whether the Obs in the structure have been reweighted.data is an array that contains the data from MC chains. We will define it below.cdata is an array that contains the data from external quantities with an error (Covobs in pyerrors). We will define it below. \n\nThe array data contains the data from MC chains. Each entry of the array corresponds to one ensemble and contains:
\n\n\nid, a string that contains the name of the ensemblereplica, an array that contains an entry per replica of the ensemble. \n\nEach entry of replica contains\nname, a string that contains the name of the replica\ndeltas, an array that contains the actual data.
\n\nEach entry in deltas corresponds to one configuration of the replica and has $1+N$ many entries. The first entry is an integer that specifies the configuration number that, together with ensemble and replica name, may be used to uniquely identify the configuration on which the data has been obtained. The following N entries specify the deltas, i.e., the deviation of the observable from the mean value on this configuration, of each Obs inside the structure. Multi-dimensional structures are stored in a row-major format. For primary observables, such as correlation functions, $value + delta_i$ matches the primary data obtained on the configuration.
\n\nThe array cdata contains information about the contribution of auxiliary observables, represented by Covobs in pyerrors, to the total error of the observables. Each entry of the array belongs to one auxiliary covariance matrix and contains:
\n\n\nid, a string that identifies the covariance matrixlayout, a string that defines the dimensions of the $M\\times M$ covariance matrix (has to be \"M, M\" or \"1\").cov, an array that contains the $M\\times M$ many entries of the covariance matrix, stored in row-major format.grad, an array that contains N entries, one for each Obs inside the structure. Each entry itself is an array, that contains the M gradients of the Nth observable with respect to the quantity that corresponds to the Mth diagonal entry of the covariance matrix. \n\nA JSON schema that may be used to verify the correctness of a file with respect to the format definition is stored in ./examples/json_schema.json. The schema is a self-descriptive format definition and contains an exemplary file.
\n\nJulia I/O routines for the json.gz format, compatible with ADerrors.jl , can be found here .
\n\nCiting \n\nIf you use pyerrors for research that leads to a publication please consider citing:
\n\n\nUlli Wolff, Monte Carlo errors with less errors . Comput.Phys.Commun. 156 (2004) 143-153, Comput.Phys.Commun. 176 (2007) 383 (erratum). \nStefan Schaefer, Rainer Sommer, Francesco Virotta, Critical slowing down and error analysis in lattice QCD simulations . Nucl.Phys.B 845 (2011) 93-119. \nAlberto Ramos, Automatic differentiation for error analysis of Monte Carlo data . Comput.Phys.Commun. 238 (2019) 19-35. \n \n"}, "pyerrors.correlators": {"fullname": "pyerrors.correlators", "modulename": "pyerrors.correlators", "type": "module", "doc": "
\n"}, "pyerrors.correlators.Corr": {"fullname": "pyerrors.correlators.Corr", "modulename": "pyerrors.correlators", "qualname": "Corr", "type": "class", "doc": "The class for a correlator (time dependent sequence of pe.Obs).
\n\nEverything, this class does, can be achieved using lists or arrays of Obs.\nBut it is simply more convenient to have a dedicated object for correlators.\nOne often wants to add or multiply correlators of the same length at every timeslice and it is inconvenient\nto iterate over all timeslices for every operation. This is especially true, when dealing with matrices.
\n\nThe correlator can have two types of content: An Obs at every timeslice OR a GEVP\nmatrix at every timeslice. Other dependency (eg. spatial) are not supported.
\n"}, "pyerrors.correlators.Corr.__init__": {"fullname": "pyerrors.correlators.Corr.__init__", "modulename": "pyerrors.correlators", "qualname": "Corr.__init__", "type": "function", "doc": "Initialize a Corr object.
\n\nParameters \n\n\ndata_input (list or array):\nlist of Obs or list of arrays of Obs or array of Corrspadding (list, optional):\nList with two entries where the first labels the padding\nat the front of the correlator and the second the padding\nat the back.prange (list, optional):\nList containing the first and last timeslice of the plateau\nregion indentified for this correlator. \n", "signature": "(self, data_input, padding=[0, 0], prange=None)", "funcdef": "def"}, "pyerrors.correlators.Corr.reweighted": {"fullname": "pyerrors.correlators.Corr.reweighted", "modulename": "pyerrors.correlators", "qualname": "Corr.reweighted", "type": "variable", "doc": "
\n"}, "pyerrors.correlators.Corr.gamma_method": {"fullname": "pyerrors.correlators.Corr.gamma_method", "modulename": "pyerrors.correlators", "qualname": "Corr.gamma_method", "type": "function", "doc": "Apply the gamma method to the content of the Corr.
\n", "signature": "(self, **kwargs)", "funcdef": "def"}, "pyerrors.correlators.Corr.projected": {"fullname": "pyerrors.correlators.Corr.projected", "modulename": "pyerrors.correlators", "qualname": "Corr.projected", "type": "function", "doc": "We need to project the Correlator with a Vector to get a single value at each timeslice.
\n\nThe method can use one or two vectors.\nIf two are specified it returns v1@G@v2 (the order might be very important.)\nBy default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to
\n", "signature": "(self, vector_l=None, vector_r=None, normalize=False)", "funcdef": "def"}, "pyerrors.correlators.Corr.item": {"fullname": "pyerrors.correlators.Corr.item", "modulename": "pyerrors.correlators", "qualname": "Corr.item", "type": "function", "doc": "Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice.
\n\nParameters \n\n\ni (int):\nFirst index to be picked.j (int):\nSecond index to be picked. \n", "signature": "(self, i, j)", "funcdef": "def"}, "pyerrors.correlators.Corr.plottable": {"fullname": "pyerrors.correlators.Corr.plottable", "modulename": "pyerrors.correlators", "qualname": "Corr.plottable", "type": "function", "doc": "Outputs the correlator in a plotable format.
\n\nOutputs three lists containing the timeslice index, the value on each\ntimeslice and the error on each timeslice.
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.symmetric": {"fullname": "pyerrors.correlators.Corr.symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.symmetric", "type": "function", "doc": "Symmetrize the correlator around x0=0.
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.anti_symmetric": {"fullname": "pyerrors.correlators.Corr.anti_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.anti_symmetric", "type": "function", "doc": "Anti-symmetrize the correlator around x0=0.
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.matrix_symmetric", "type": "function", "doc": "Symmetrizes the correlator matrices on every timeslice.
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.GEVP": {"fullname": "pyerrors.correlators.Corr.GEVP", "modulename": "pyerrors.correlators", "qualname": "Corr.GEVP", "type": "function", "doc": "Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors.
\n\nThe eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the\nlargest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing
\n\nC . GEVP ( t0 = 2 )[ 0 ] # Ground state vector(s) \nC . GEVP ( t0 = 2 )[: 3 ] # Vectors for the lowest three states \nParameters \n\n\nt0 (int):\nThe 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):\nfixed time $G(t_s)v_i=\\lambda_i G(t_0)v_i$ if sort=None.\nIf sort=\"Eigenvector\" it gives a reference point for the sorting method.sort (string):\nIf 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.\n\n\"Eigenvalue\": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice. \n\"Eigenvector\": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state.\nThe reference state is identified by its eigenvalue at $t=t_s$. \n \n\nOther Parameters \n\n\nstate (int):\nReturns only the vector(s) for a specified state. The lowest state is zero. \n", "signature": "(self, t0, ts=None, sort='Eigenvalue', **kwargs)", "funcdef": "def"}, "pyerrors.correlators.Corr.Eigenvalue": {"fullname": "pyerrors.correlators.Corr.Eigenvalue", "modulename": "pyerrors.correlators", "qualname": "Corr.Eigenvalue", "type": "function", "doc": "Determines the eigenvalue of the GEVP by solving and projecting the correlator
\n\nParameters \n\n\nstate (int):\nThe state one is interested in ordered by energy. The lowest state is zero.All other parameters are identical to the ones of Corr.GEVP. \n", "signature": "(self, t0, ts=None, state=0, sort='Eigenvalue')", "funcdef": "def"}, "pyerrors.correlators.Corr.Hankel": {"fullname": "pyerrors.correlators.Corr.Hankel", "modulename": "pyerrors.correlators", "qualname": "Corr.Hankel", "type": "function", "doc": "Constructs an NxN Hankel matrix
\n\nC(t) c(t+1) ... c(t+n-1)\nC(t+1) c(t+2) ... c(t+n)\n.................\nC(t+(n-1)) c(t+n) ... c(t+2(n-1))
\n\nParameters \n\n\nN (int):\nDimension of the Hankel matrixperiodic (bool, optional):\ndetermines whether the matrix is extended periodically \n", "signature": "(self, N, periodic=False)", "funcdef": "def"}, "pyerrors.correlators.Corr.roll": {"fullname": "pyerrors.correlators.Corr.roll", "modulename": "pyerrors.correlators", "qualname": "Corr.roll", "type": "function", "doc": "Periodically shift the correlator by dt timeslices
\n\nParameters \n\n\ndt (int):\nnumber of timeslices \n", "signature": "(self, dt)", "funcdef": "def"}, "pyerrors.correlators.Corr.reverse": {"fullname": "pyerrors.correlators.Corr.reverse", "modulename": "pyerrors.correlators", "qualname": "Corr.reverse", "type": "function", "doc": "Reverse the time ordering of the Corr
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.thin": {"fullname": "pyerrors.correlators.Corr.thin", "modulename": "pyerrors.correlators", "qualname": "Corr.thin", "type": "function", "doc": "Thin out a correlator to suppress correlations
\n\nParameters \n\n\nspacing (int):\nKeep only every 'spacing'th entry of the correlatoroffset (int):\nOffset the equal spacing \n", "signature": "(self, spacing=2, offset=0)", "funcdef": "def"}, "pyerrors.correlators.Corr.correlate": {"fullname": "pyerrors.correlators.Corr.correlate", "modulename": "pyerrors.correlators", "qualname": "Corr.correlate", "type": "function", "doc": "Correlate the correlator with another correlator or Obs
\n\nParameters \n\n\npartner (Obs or Corr):\npartner to correlate the correlator with.\nCan either be an Obs which is correlated with all entries of the\ncorrelator or a Corr of same length. \n", "signature": "(self, partner)", "funcdef": "def"}, "pyerrors.correlators.Corr.reweight": {"fullname": "pyerrors.correlators.Corr.reweight", "modulename": "pyerrors.correlators", "qualname": "Corr.reweight", "type": "function", "doc": "Reweight the correlator.
\n\nParameters \n\n\nweight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. \n", "signature": "(self, weight, **kwargs)", "funcdef": "def"}, "pyerrors.correlators.Corr.T_symmetry": {"fullname": "pyerrors.correlators.Corr.T_symmetry", "modulename": "pyerrors.correlators", "qualname": "Corr.T_symmetry", "type": "function", "doc": "Return the time symmetry average of the correlator and its partner
\n\nParameters \n\n\npartner (Corr):\nTime symmetry partner of the Corrpartity (int):\nParity quantum number of the correlator, can be +1 or -1 \n", "signature": "(self, partner, parity=1)", "funcdef": "def"}, "pyerrors.correlators.Corr.deriv": {"fullname": "pyerrors.correlators.Corr.deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.deriv", "type": "function", "doc": "Return the first derivative of the correlator with respect to x0.
\n\nParameters \n\n\nvariant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, forward, backward, improved, default: symmetric \n", "signature": "(self, variant='symmetric')", "funcdef": "def"}, "pyerrors.correlators.Corr.second_deriv": {"fullname": "pyerrors.correlators.Corr.second_deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.second_deriv", "type": "function", "doc": "Return the second derivative of the correlator with respect to x0.
\n\nParameters \n\n\nvariant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, improved, default: symmetric \n", "signature": "(self, variant='symmetric')", "funcdef": "def"}, "pyerrors.correlators.Corr.m_eff": {"fullname": "pyerrors.correlators.Corr.m_eff", "modulename": "pyerrors.correlators", "qualname": "Corr.m_eff", "type": "function", "doc": "Returns the effective mass of the correlator as correlator object
\n\nParameters \n\n\nvariant (str):\nlog : uses the standard effective mass log(C(t) / C(t+1))\ncosh, 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.\nsinh : 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.\nSee, e.g., arXiv:1205.5380\narccosh : Uses the explicit form of the symmetrized correlator (not recommended)guess (float):\nguess for the root finder, only relevant for the root variant \n", "signature": "(self, variant='log', guess=1.0)", "funcdef": "def"}, "pyerrors.correlators.Corr.fit": {"fullname": "pyerrors.correlators.Corr.fit", "modulename": "pyerrors.correlators", "qualname": "Corr.fit", "type": "function", "doc": "Fits function to the data
\n\nParameters \n\n\nfunction (obj):\nfunction to fit to the data. See fits.least_squares for details.fitrange (list):\nTwo element list containing the timeslices on which the fit is supposed to start and stop.\nCaution: This range is inclusive as opposed to standard python indexing.\nfitrange=[4, 6] corresponds to the three entries 4, 5 and 6.\nIf not specified, self.prange or all timeslices are used.silent (bool):\nDecides whether output is printed to the standard output. \n", "signature": "(self, function, fitrange=None, silent=False, **kwargs)", "funcdef": "def"}, "pyerrors.correlators.Corr.plateau": {"fullname": "pyerrors.correlators.Corr.plateau", "modulename": "pyerrors.correlators", "qualname": "Corr.plateau", "type": "function", "doc": "Extract a plateau value from a Corr object
\n\nParameters \n\n\nplateau_range (list):\nlist with two entries, indicating the first and the last timeslice\nof the plateau region.method (str):\nmethod to extract the plateau.\n 'fit' fits a constant to the plateau region\n 'avg', 'average' or 'mean' just average over the given timeslices.auto_gamma (bool):\napply gamma_method with default parameters to the Corr. Defaults to None \n", "signature": "(self, plateau_range=None, method='fit', auto_gamma=False)", "funcdef": "def"}, "pyerrors.correlators.Corr.set_prange": {"fullname": "pyerrors.correlators.Corr.set_prange", "modulename": "pyerrors.correlators", "qualname": "Corr.set_prange", "type": "function", "doc": "Sets the attribute prange of the Corr object.
\n", "signature": "(self, prange)", "funcdef": "def"}, "pyerrors.correlators.Corr.show": {"fullname": "pyerrors.correlators.Corr.show", "modulename": "pyerrors.correlators", "qualname": "Corr.show", "type": "function", "doc": "Plots the correlator using the tag of the correlator as label if available.
\n\nParameters \n\n\nx_range (list):\nlist of two values, determining the range of the x-axis e.g. [4, 8]comp (Corr or list of Corr):\nCorrelator or list of correlators which are plotted for comparison.\nThe tags of these correlators are used as labels if available.logscale (bool):\nSets y-axis to logscaleplateau (Obs):\nPlateau value to be visualized in the figurefit_res (Fit_result):\nFit_result object to be visualizedylabel (str):\nLabel for the y-axissave (str):\npath to file in which the figure should be savedauto_gamma (bool):\nApply the gamma method with standard parameters to all correlators and plateau values before plotting.hide_sigma (float):\nHides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.references (list):\nList of floating point values that are displayed as horizontal lines for reference. \n", "signature": "(\n self,\n x_range=None,\n comp=None,\n y_range=None,\n logscale=False,\n plateau=None,\n fit_res=None,\n ylabel=None,\n save=None,\n auto_gamma=False,\n hide_sigma=None,\n references=None\n)", "funcdef": "def"}, "pyerrors.correlators.Corr.spaghetti_plot": {"fullname": "pyerrors.correlators.Corr.spaghetti_plot", "modulename": "pyerrors.correlators", "qualname": "Corr.spaghetti_plot", "type": "function", "doc": "Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
\n\nParameters \n\n\nlogscale (bool):\nDetermines whether the scale of the y-axis is logarithmic or standard. \n", "signature": "(self, logscale=True)", "funcdef": "def"}, "pyerrors.correlators.Corr.dump": {"fullname": "pyerrors.correlators.Corr.dump", "modulename": "pyerrors.correlators", "qualname": "Corr.dump", "type": "function", "doc": "Dumps the Corr into a file of chosen type
\n\nParameters \n\n\nfilename (str):\nName of the file to be saved.datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"path (str):\nspecifies a custom path for the file (default '.') \n", "signature": "(self, filename, datatype='json.gz', **kwargs)", "funcdef": "def"}, "pyerrors.correlators.Corr.print": {"fullname": "pyerrors.correlators.Corr.print", "modulename": "pyerrors.correlators", "qualname": "Corr.print", "type": "function", "doc": "
\n", "signature": "(self, range=[0, None])", "funcdef": "def"}, "pyerrors.correlators.Corr.sqrt": {"fullname": "pyerrors.correlators.Corr.sqrt", "modulename": "pyerrors.correlators", "qualname": "Corr.sqrt", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.log": {"fullname": "pyerrors.correlators.Corr.log", "modulename": "pyerrors.correlators", "qualname": "Corr.log", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.exp": {"fullname": "pyerrors.correlators.Corr.exp", "modulename": "pyerrors.correlators", "qualname": "Corr.exp", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.sin": {"fullname": "pyerrors.correlators.Corr.sin", "modulename": "pyerrors.correlators", "qualname": "Corr.sin", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.cos": {"fullname": "pyerrors.correlators.Corr.cos", "modulename": "pyerrors.correlators", "qualname": "Corr.cos", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.tan": {"fullname": "pyerrors.correlators.Corr.tan", "modulename": "pyerrors.correlators", "qualname": "Corr.tan", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.sinh": {"fullname": "pyerrors.correlators.Corr.sinh", "modulename": "pyerrors.correlators", "qualname": "Corr.sinh", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.cosh": {"fullname": "pyerrors.correlators.Corr.cosh", "modulename": "pyerrors.correlators", "qualname": "Corr.cosh", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.tanh": {"fullname": "pyerrors.correlators.Corr.tanh", "modulename": "pyerrors.correlators", "qualname": "Corr.tanh", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsin": {"fullname": "pyerrors.correlators.Corr.arcsin", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsin", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arccos": {"fullname": "pyerrors.correlators.Corr.arccos", "modulename": "pyerrors.correlators", "qualname": "Corr.arccos", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arctan": {"fullname": "pyerrors.correlators.Corr.arctan", "modulename": "pyerrors.correlators", "qualname": "Corr.arctan", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsinh": {"fullname": "pyerrors.correlators.Corr.arcsinh", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsinh", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arccosh": {"fullname": "pyerrors.correlators.Corr.arccosh", "modulename": "pyerrors.correlators", "qualname": "Corr.arccosh", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arctanh": {"fullname": "pyerrors.correlators.Corr.arctanh", "modulename": "pyerrors.correlators", "qualname": "Corr.arctanh", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.real": {"fullname": "pyerrors.correlators.Corr.real", "modulename": "pyerrors.correlators", "qualname": "Corr.real", "type": "variable", "doc": "
\n"}, "pyerrors.correlators.Corr.imag": {"fullname": "pyerrors.correlators.Corr.imag", "modulename": "pyerrors.correlators", "qualname": "Corr.imag", "type": "variable", "doc": "
\n"}, "pyerrors.correlators.Corr.prune": {"fullname": "pyerrors.correlators.Corr.prune", "modulename": "pyerrors.correlators", "qualname": "Corr.prune", "type": "function", "doc": "Project large correlation matrix to lowest states
\n\nThis method can be used to reduce the size of an (N x N) correlation matrix\nto (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise\nis still small.
\n\nParameters \n\n\nNtrunc (int):\nRank of the target matrix.tproj (int):\nTime where the eigenvectors are evaluated, corresponds to ts in the GEVP method.\nThe default value is 3.t0proj (int):\nTime where the correlation matrix is inverted. Choosing t0proj=1 is strongly\ndiscouraged for O(a) improved theories, since the correctness of the procedure\ncannot be granted in this case. The default value is 2.basematrix (Corr):\nCorrelation matrix that is used to determine the eigenvectors of the\nlowest states based on a GEVP. basematrix is taken to be the Corr itself if\nis is not specified. \n\nNotes \n\nWe have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving\nthe GEVP $$C(t) v_n(t, t_0) = \\lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \\equiv t_\\mathrm{proj}$\nand $t_0 \\equiv t_{0, \\mathrm{proj}}$. The target matrix is projected onto the subspace of the\nresulting eigenvectors $v_n, n=1,\\dots,N_\\mathrm{trunc}$ via\n$$G^\\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large\ncorrelation matrix and to remove some noise that is added by irrelevant operators.\nThis may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated\nbound $t_0 \\leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.
\n", "signature": "(self, Ntrunc, tproj=3, t0proj=2, basematrix=None)", "funcdef": "def"}, "pyerrors.covobs": {"fullname": "pyerrors.covobs", "modulename": "pyerrors.covobs", "type": "module", "doc": "
\n"}, "pyerrors.covobs.Covobs": {"fullname": "pyerrors.covobs.Covobs", "modulename": "pyerrors.covobs", "qualname": "Covobs", "type": "class", "doc": "
\n"}, "pyerrors.covobs.Covobs.__init__": {"fullname": "pyerrors.covobs.Covobs.__init__", "modulename": "pyerrors.covobs", "qualname": "Covobs.__init__", "type": "function", "doc": "Initialize Covobs object.
\n\nParameters \n\n\nmean (float):\nMean value of the new Obscov (list or array):\n2d Covariance matrix or 1d diagonal entriesname (str):\nidentifier for the covariance matrixpos (int):\nPosition of the variance belonging to mean in cov.\nIs taken to be 1 if cov is 0-dimensionalgrad (list or array):\nGradient of the Covobs wrt. the means belonging to cov. \n", "signature": "(self, mean, cov, name, pos=None, grad=None)", "funcdef": "def"}, "pyerrors.covobs.Covobs.errsq": {"fullname": "pyerrors.covobs.Covobs.errsq", "modulename": "pyerrors.covobs", "qualname": "Covobs.errsq", "type": "function", "doc": "Return the variance (= square of the error) of the Covobs
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.covobs.Covobs.cov": {"fullname": "pyerrors.covobs.Covobs.cov", "modulename": "pyerrors.covobs", "qualname": "Covobs.cov", "type": "variable", "doc": "
\n"}, "pyerrors.covobs.Covobs.grad": {"fullname": "pyerrors.covobs.Covobs.grad", "modulename": "pyerrors.covobs", "qualname": "Covobs.grad", "type": "variable", "doc": "
\n"}, "pyerrors.dirac": {"fullname": "pyerrors.dirac", "modulename": "pyerrors.dirac", "type": "module", "doc": "
\n"}, "pyerrors.dirac.epsilon_tensor": {"fullname": "pyerrors.dirac.epsilon_tensor", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor", "type": "function", "doc": "Rank-3 epsilon tensor
\n\nBased on https://codegolf.stackexchange.com/a/160375
\n", "signature": "(i, j, k)", "funcdef": "def"}, "pyerrors.dirac.epsilon_tensor_rank4": {"fullname": "pyerrors.dirac.epsilon_tensor_rank4", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor_rank4", "type": "function", "doc": "Rank-4 epsilon tensor
\n\nExtension of https://codegolf.stackexchange.com/a/160375
\n", "signature": "(i, j, k, o)", "funcdef": "def"}, "pyerrors.dirac.Grid_gamma": {"fullname": "pyerrors.dirac.Grid_gamma", "modulename": "pyerrors.dirac", "qualname": "Grid_gamma", "type": "function", "doc": "Returns gamma matrix in Grid labeling.
\n", "signature": "(gamma_tag)", "funcdef": "def"}, "pyerrors.fits": {"fullname": "pyerrors.fits", "modulename": "pyerrors.fits", "type": "module", "doc": "
\n"}, "pyerrors.fits.Fit_result": {"fullname": "pyerrors.fits.Fit_result", "modulename": "pyerrors.fits", "qualname": "Fit_result", "type": "class", "doc": "Represents fit results.
\n\nAttributes \n\n\nfit_parameters (list):\nresults for the individual fit parameters,\nalso accessible via indices. \n", "bases": "collections.abc.Sequence"}, "pyerrors.fits.Fit_result.__init__": {"fullname": "pyerrors.fits.Fit_result.__init__", "modulename": "pyerrors.fits", "qualname": "Fit_result.__init__", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.fits.Fit_result.gamma_method": {"fullname": "pyerrors.fits.Fit_result.gamma_method", "modulename": "pyerrors.fits", "qualname": "Fit_result.gamma_method", "type": "function", "doc": "Apply the gamma method to all fit parameters
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.fits.least_squares": {"fullname": "pyerrors.fits.least_squares", "modulename": "pyerrors.fits", "qualname": "least_squares", "type": "function", "doc": "Performs a non-linear fit to y = func(x).
\n\nParameters \n\n\nx (list):\nlist of floats.y (list):\nlist of Obs.func (object):\nfit function, has to be of the form
\n\nimport autograd.numpy as anp \n\ndef func ( a , x ): \n return a [ 0 ] + a [ 1 ] * x + a [ 2 ] * anp . sinh ( x ) \nFor multiple x values func can be of the form
\n\ndef func ( a , x ): \n ( x1 , x2 ) = x \n return a [ 0 ] * x1 ** 2 + a [ 1 ] * x2 \nIt is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
priors (list, optional):\npriors has to be a list with an entry for every parameter in the fit. The entries can either be\nObs (e.g. results from a previous fit) or strings containing a value and an error formatted like\n0.548(23), 500(40) or 0.5(0.4)silent (bool, optional):\nIf true all output to the console is omitted (default False).initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for\nnon-linear fits with many parameters.method (str, optional):\ncan be used to choose an alternative method for the minimization of chisquare.\nThe possible methods are the ones which can be used for scipy.optimize.minimize and\nmigrad of iminuit. If no method is specified, Levenberg-Marquard is used.\nReliable alternatives are migrad, Powell and Nelder-Mead.correlated_fit (bool):\nIf True, use the full inverse covariance matrix in the definition of the chisquare cost function.\nFor details about how the covariance matrix is estimated see pyerrors.obs.covariance.\nIn practice the correlation matrix is Cholesky decomposed and inverted (instead of the covariance matrix).\nThis procedure should be numerically more stable as the correlation matrix is typically better conditioned (Jacobi preconditioning).\nAt the moment this option only works for prior==None and when no method is given.expected_chisquare (bool):\nIf True estimates the expected chisquare which is\ncorrected by effects caused by correlated input data (default False).resplot (bool):\nIf True, a plot which displays fit, data and residuals is generated (default False).qqplot (bool):\nIf True, a quantile-quantile plot of the fit result is generated (default False). \n", "signature": "(x, y, func, priors=None, silent=False, **kwargs)", "funcdef": "def"}, "pyerrors.fits.total_least_squares": {"fullname": "pyerrors.fits.total_least_squares", "modulename": "pyerrors.fits", "qualname": "total_least_squares", "type": "function", "doc": "Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.
\n\nParameters \n\n\nx (list):\nlist of Obs, or a tuple of lists of Obsy (list):\nlist of Obs. The dvalues of the Obs are used as x- and yerror for the fit.func (object):\nfunc has to be of the form
\n\nimport autograd.numpy as anp \n\ndef func ( a , x ): \n return a [ 0 ] + a [ 1 ] * x + a [ 2 ] * anp . sinh ( x ) \nFor multiple x values func can be of the form
\n\ndef func ( a , x ): \n ( x1 , x2 ) = x \n return a [ 0 ] * x1 ** 2 + a [ 1 ] * x2 \nIt is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
silent (bool, optional):\nIf true all output to the console is omitted (default False).initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for non-linear\nfits with many parameters.expected_chisquare (bool):\nIf true prints the expected chisquare which is\ncorrected by effects caused by correlated input data.\nThis can take a while as the full correlation matrix\nhas to be calculated (default False). \n\nNotes \n\nBased on the orthogonal distance regression module of scipy
\n", "signature": "(x, y, func, silent=False, **kwargs)", "funcdef": "def"}, "pyerrors.fits.fit_lin": {"fullname": "pyerrors.fits.fit_lin", "modulename": "pyerrors.fits", "qualname": "fit_lin", "type": "function", "doc": "Performs a linear fit to y = n + m * x and returns two Obs n, m.
\n\nParameters \n\n\nx (list):\nCan either be a list of floats in which case no xerror is assumed, or\na list of Obs, where the dvalues of the Obs are used as xerror for the fit.y (list):\nList of Obs, the dvalues of the Obs are used as yerror for the fit. \n", "signature": "(x, y, **kwargs)", "funcdef": "def"}, "pyerrors.fits.qqplot": {"fullname": "pyerrors.fits.qqplot", "modulename": "pyerrors.fits", "qualname": "qqplot", "type": "function", "doc": "Generates a quantile-quantile plot of the fit result which can be used to\ncheck if the residuals of the fit are gaussian distributed.
\n", "signature": "(x, o_y, func, p)", "funcdef": "def"}, "pyerrors.fits.residual_plot": {"fullname": "pyerrors.fits.residual_plot", "modulename": "pyerrors.fits", "qualname": "residual_plot", "type": "function", "doc": "Generates a plot which compares the fit to the data and displays the corresponding residuals
\n", "signature": "(x, y, func, fit_res)", "funcdef": "def"}, "pyerrors.fits.error_band": {"fullname": "pyerrors.fits.error_band", "modulename": "pyerrors.fits", "qualname": "error_band", "type": "function", "doc": "Returns the error band for an array of sample values x, for given fit function func with optimized parameters beta.
\n", "signature": "(x, func, beta)", "funcdef": "def"}, "pyerrors.fits.ks_test": {"fullname": "pyerrors.fits.ks_test", "modulename": "pyerrors.fits", "qualname": "ks_test", "type": "function", "doc": "Performs a Kolmogorov\u2013Smirnov test for the p-values of all fit object.
\n\nParameters \n\n\nobjects (list):\nList of fit results to include in the analysis (optional). \n", "signature": "(objects=None)", "funcdef": "def"}, "pyerrors.input": {"fullname": "pyerrors.input", "modulename": "pyerrors.input", "type": "module", "doc": "pyerrors includes an input submodule in which input routines and parsers for the output of various numerical programs are contained.
\n\nJackknife samples \n\nFor comparison with other analysis workflows pyerrors can also generate jackknife samples from an Obs object or import jackknife samples into an Obs object.\nSee pyerrors.obs.Obs.export_jackknife and pyerrors.obs.import_jackknife for details.
\n"}, "pyerrors.input.bdio": {"fullname": "pyerrors.input.bdio", "modulename": "pyerrors.input.bdio", "type": "module", "doc": "
\n"}, "pyerrors.input.bdio.read_ADerrors": {"fullname": "pyerrors.input.bdio.read_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "read_ADerrors", "type": "function", "doc": "Extract generic MCMC data from a bdio file
\n\nread_ADerrors requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
\n\nall: bdio.o $(LIBDIR)\n gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
\n\nParameters \n\n\nfile_path -- path to the bdio file bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so) \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs)", "funcdef": "def"}, "pyerrors.input.bdio.write_ADerrors": {"fullname": "pyerrors.input.bdio.write_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "write_ADerrors", "type": "function", "doc": "Write Obs to a bdio file according to ADerrors conventions
\n\nread_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
\n\nall: bdio.o $(LIBDIR)\n gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
\n\nParameters \n\n\nfile_path -- path to the bdio file bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so) \n", "signature": "(obs_list, file_path, bdio_path='./libbdio.so', **kwargs)", "funcdef": "def"}, "pyerrors.input.bdio.read_mesons": {"fullname": "pyerrors.input.bdio.read_mesons", "modulename": "pyerrors.input.bdio", "qualname": "read_mesons", "type": "function", "doc": "Extract mesons data from a bdio file and return it as a dictionary
\n\nThe dictionary can be accessed with a tuple consisting of (type, source_position, kappa1, kappa2)
\n\nread_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
\n\nall: bdio.o $(LIBDIR)\n gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
\n\nParameters \n\n\nfile_path (str):\npath to the bdio filebdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)start (int):\nThe first configuration to be read (default 1)stop (int):\nThe last configuration to be read (default None)step (int):\nFixed step size between two measurements (default 1)alternative_ensemble_name (str):\nManually overwrite ensemble name \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs)", "funcdef": "def"}, "pyerrors.input.bdio.read_dSdm": {"fullname": "pyerrors.input.bdio.read_dSdm", "modulename": "pyerrors.input.bdio", "qualname": "read_dSdm", "type": "function", "doc": "Extract dSdm data from a bdio file and return it as a dictionary
\n\nThe dictionary can be accessed with a tuple consisting of (type, kappa)
\n\nread_dSdm requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
\n\nall: bdio.o $(LIBDIR)\n gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
\n\nParameters \n\n\nfile_path (str):\npath to the bdio filebdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)start (int):\nThe first configuration to be read (default 1)stop (int):\nThe last configuration to be read (default None)step (int):\nFixed step size between two measurements (default 1)alternative_ensemble_name (str):\nManually overwrite ensemble name \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs)", "funcdef": "def"}, "pyerrors.input.dobs": {"fullname": "pyerrors.input.dobs", "modulename": "pyerrors.input.dobs", "type": "module", "doc": "
\n"}, "pyerrors.input.dobs.create_pobs_string": {"fullname": "pyerrors.input.dobs.create_pobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_pobs_string", "type": "function", "doc": "Export a list of Obs or structures containing Obs to an xml string\naccording to the Zeuthen pobs format.
\n\nTags are not written or recovered automatically. The separator | is removed from the replica names.
\n\nParameters \n\n\nobsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.name (str):\nThe name of the observable.spec (str):\nOptional string that describes the contents of the file.origin (str):\nSpecify where the data has its origin.symbol (list):\nA list of symbols that describe the observables to be written. May be empty.enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used. \n", "signature": "(obsl, name, spec='', origin='', symbol=[], enstag=None)", "funcdef": "def"}, "pyerrors.input.dobs.write_pobs": {"fullname": "pyerrors.input.dobs.write_pobs", "modulename": "pyerrors.input.dobs", "qualname": "write_pobs", "type": "function", "doc": "Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen pobs format.
\n\nTags are not written or recovered automatically. The separator | is removed from the replica names.
\n\nParameters \n\n\nobsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.fname (str):\nFilename of the output file.name (str):\nThe name of the observable.spec (str):\nOptional string that describes the contents of the file.origin (str):\nSpecify where the data has its origin.symbol (list):\nA list of symbols that describe the observables to be written. May be empty.enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.gz (bool):\nIf True, the output is a gzipped xml. If False, the output is an xml file. \n", "signature": "(\n obsl,\n fname,\n name,\n spec='',\n origin='',\n symbol=[],\n enstag=None,\n gz=True\n)", "funcdef": "def"}, "pyerrors.input.dobs.read_pobs": {"fullname": "pyerrors.input.dobs.read_pobs", "modulename": "pyerrors.input.dobs", "qualname": "read_pobs", "type": "function", "doc": "Import a list of Obs from an xml.gz file in the Zeuthen pobs format.
\n\nTags are not written or recovered automatically.
\n\nParameters \n\n\nfname (str):\nFilename of the input file.full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.separatior_insertion (str or int):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nNone (default): Replica names remain unchanged. \n", "signature": "(fname, full_output=False, gz=True, separator_insertion=None)", "funcdef": "def"}, "pyerrors.input.dobs.import_dobs_string": {"fullname": "pyerrors.input.dobs.import_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "import_dobs_string", "type": "function", "doc": "Import a list of Obs from a string in the Zeuthen dobs format.
\n\nTags are not written or recovered automatically.
\n\nParameters \n\n\ncontent (str):\nXML string containing the datanoemtpy (bool):\nIf True, ensembles with no contribution to the Obs are not included.\nIf False, ensembles are included as written in the file, possibly with vanishing entries.full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted. \n", "signature": "(content, noempty=False, full_output=False, separator_insertion=True)", "funcdef": "def"}, "pyerrors.input.dobs.read_dobs": {"fullname": "pyerrors.input.dobs.read_dobs", "modulename": "pyerrors.input.dobs", "qualname": "read_dobs", "type": "function", "doc": "Import a list of Obs from an xml.gz file in the Zeuthen dobs format.
\n\nTags are not written or recovered automatically.
\n\nParameters \n\n\nfname (str):\nFilename of the input file.noemtpy (bool):\nIf True, ensembles with no contribution to the Obs are not included.\nIf False, ensembles are included as written in the file.full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.gz (bool):\nIf True, assumes that data is gzipped. If False, assumes XML file.separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted. \n", "signature": "(\n fname,\n noempty=False,\n full_output=False,\n gz=True,\n separator_insertion=True\n)", "funcdef": "def"}, "pyerrors.input.dobs.create_dobs_string": {"fullname": "pyerrors.input.dobs.create_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_dobs_string", "type": "function", "doc": "Generate the string for the export of a list of Obs or structures containing Obs\nto a .xml.gz file according to the Zeuthen dobs format.
\n\nTags are not written or recovered automatically. The separator |is removed from the replica names.
\n\nParameters \n\n\nobsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.name (str):\nThe name of the observable.spec (str):\nOptional string that describes the contents of the file.origin (str):\nSpecify where the data has its origin.symbol (list):\nA list of symbols that describe the observables to be written. May be empty.who (str):\nProvide the name of the person that exports the data.enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used. \n", "signature": "(\n obsl,\n name,\n spec='dobs v1.0',\n origin='',\n symbol=[],\n who=None,\n enstags={}\n)", "funcdef": "def"}, "pyerrors.input.dobs.write_dobs": {"fullname": "pyerrors.input.dobs.write_dobs", "modulename": "pyerrors.input.dobs", "qualname": "write_dobs", "type": "function", "doc": "Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen dobs format.
\n\nTags are not written or recovered automatically. The separator | is removed from the replica names.
\n\nParameters \n\n\nobsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.fname (str):\nFilename of the output file.name (str):\nThe name of the observable.spec (str):\nOptional string that describes the contents of the file.origin (str):\nSpecify where the data has its origin.symbol (list):\nA list of symbols that describe the observables to be written. May be empty.who (str):\nProvide the name of the person that exports the data.enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.gz (bool):\nIf True, the output is a gzipped XML. If False, the output is a XML file. \n", "signature": "(\n obsl,\n fname,\n name,\n spec='dobs v1.0',\n origin='',\n symbol=[],\n who=None,\n enstags={},\n gz=True\n)", "funcdef": "def"}, "pyerrors.input.hadrons": {"fullname": "pyerrors.input.hadrons", "modulename": "pyerrors.input.hadrons", "type": "module", "doc": "
\n"}, "pyerrors.input.hadrons.read_meson_hd5": {"fullname": "pyerrors.input.hadrons.read_meson_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_meson_hd5", "type": "function", "doc": "Read hadrons meson hdf5 file and extract the meson labeled 'meson'
\n\nParameters \n\n\npath (str):\npath to the files to readfilestem (str):\nnamestem of the files to readens_id (str):\nname of the ensemble, required for internal bookkeepingmeson (str):\nlabel of the meson to be extracted, standard value meson_0 which\ncorresponds to the pseudoscalar pseudoscalar two-point function.idl (range):\nIf specified only configurations in the given range are read in. \n", "signature": "(path, filestem, ens_id, meson='meson_0', idl=None)", "funcdef": "def"}, "pyerrors.input.hadrons.read_DistillationContraction_hd5": {"fullname": "pyerrors.input.hadrons.read_DistillationContraction_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_DistillationContraction_hd5", "type": "function", "doc": "Read hadrons DistillationContraction hdf5 files in given directory structure
\n\nParameters \n\n\npath (str):\npath to the directories to readens_id (str):\nname of the ensemble, required for internal bookkeepingdiagrams (list):\nList of strings of the diagrams to extract, e.g. [\"direct\", \"box\", \"cross\"].idl (range):\nIf specified only configurations in the given range are read in. \n", "signature": "(path, ens_id, diagrams=['direct'], idl=None)", "funcdef": "def"}, "pyerrors.input.hadrons.Npr_matrix": {"fullname": "pyerrors.input.hadrons.Npr_matrix", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix", "type": "class", "doc": "ndarray(shape, dtype=float, buffer=None, offset=0,\n strides=None, order=None)
\n\nAn array object represents a multidimensional, homogeneous array\nof fixed-size items. An associated data-type object describes the\nformat of each element in the array (its byte-order, how many bytes it\noccupies in memory, whether it is an integer, a floating point number,\nor something else, etc.)
\n\nArrays should be constructed using array, zeros or empty (refer\nto the See Also section below). The parameters given here refer to\na low-level method (ndarray(...)) for instantiating an array.
\n\nFor more information, refer to the numpy module and examine the\nmethods and attributes of an array.
\n\nParameters \n\n\n(for the __new__ method; see Notes below) shape (tuple of ints):\nShape of created array.dtype (data-type, optional):\nAny object that can be interpreted as a numpy data type.buffer (object exposing buffer interface, optional):\nUsed to fill the array with data.offset (int, optional):\nOffset of array data in buffer.strides (tuple of ints, optional):\nStrides of data in memory.order ({'C', 'F'}, optional):\nRow-major (C-style) or column-major (Fortran-style) order. \n\nAttributes \n\n\nT (ndarray):\nTranspose of the array.data (buffer):\nThe array's elements, in memory.dtype (dtype object):\nDescribes the format of the elements in the array.flags (dict):\nDictionary containing information related to memory use, e.g.,\n'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc.flat (numpy.flatiter object):\nFlattened version of the array as an iterator. The iterator\nallows assignments, e.g., x.flat = 3 (See ndarray.flat for\nassignment examples; TODO).imag (ndarray):\nImaginary part of the array.real (ndarray):\nReal part of the array.size (int):\nNumber of elements in the array.itemsize (int):\nThe memory use of each array element in bytes.nbytes (int):\nThe total number of bytes required to store the array data,\ni.e., itemsize * size.ndim (int):\nThe array's number of dimensions.shape (tuple of ints):\nShape of the array.strides (tuple of ints):\nThe step-size required to move from one element to the next in\nmemory. For example, a contiguous (3, 4) array of type\nint16 in C-order has strides (8, 2). This implies that\nto move from element to element in memory requires jumps of 2 bytes.\nTo move from row-to-row, one needs to jump 8 bytes at a time\n(2 * 4).ctypes (ctypes object):\nClass containing properties of the array needed for interaction\nwith ctypes.base (ndarray):\nIf the array is a view into another array, that array is its base\n(unless that array is also a view). The base array is where the\narray data is actually stored. \n\nSee Also \n\narray: Construct an array. zeros: Create an array, each element of which is zero. empty: Create an array, but leave its allocated memory unchanged (i.e.,\nit contains \"garbage\"). dtype: Create a data-type. numpy.typing.NDArray: An ndarray alias :term:generic <generic type>\nw.r.t. its dtype.type <numpy.dtype.type>.
\n\nNotes \n\nThere are two modes of creating an array using __new__:
\n\n\nIf buffer is None, then only shape, dtype, and order\nare used. \nIf buffer is an object exposing the buffer interface, then\nall keywords are interpreted. \n \n\nNo __init__ method is needed because the array is fully initialized\nafter the __new__ method.
\n\nExamples \n\nThese examples illustrate the low-level ndarray constructor. Refer\nto the See Also section above for easier ways of constructing an\nndarray.
\n\nFirst mode, buffer is None:
\n\n>>> np . ndarray ( shape = ( 2 , 2 ), dtype = float , order = 'F' ) \narray([[0.0e+000, 0.0e+000], # random \n [ nan, 2.5e-323]]) \nSecond mode:
\n\n>>> np . ndarray (( 2 ,), buffer = np . array ([ 1 , 2 , 3 ]), \n... offset = np . int_ () . itemsize , \n... dtype = int ) # offset = 1*itemsize, i.e. skip first element \narray([2, 3]) \n
\n", "signature": "()", "funcdef": "def"}, "pyerrors.input.hadrons.Npr_matrix.g5H": {"fullname": "pyerrors.input.hadrons.Npr_matrix.g5H", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.g5H", "type": "variable", "doc": "Gamma_5 hermitean conjugate
\n\nUses the fact that the propagator is gamma5 hermitean, so just the\nin and out momenta of the propagator are exchanged.
\n"}, "pyerrors.input.hadrons.read_ExternalLeg_hd5": {"fullname": "pyerrors.input.hadrons.read_ExternalLeg_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_ExternalLeg_hd5", "type": "function", "doc": "Read hadrons ExternalLeg hdf5 file and output an array of CObs
\n\nParameters \n\n\npath (str):\npath to the files to readfilestem (str):\nnamestem of the files to readens_id (str):\nname of the ensemble, required for internal bookkeepingidl (range):\nIf specified only configurations in the given range are read in. \n", "signature": "(path, filestem, ens_id, idl=None)", "funcdef": "def"}, "pyerrors.input.hadrons.read_Bilinear_hd5": {"fullname": "pyerrors.input.hadrons.read_Bilinear_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Bilinear_hd5", "type": "function", "doc": "Read hadrons Bilinear hdf5 file and output an array of CObs
\n\nParameters \n\n\npath (str):\npath to the files to readfilestem (str):\nnamestem of the files to readens_id (str):\nname of the ensemble, required for internal bookkeepingidl (range):\nIf specified only configurations in the given range are read in. \n", "signature": "(path, filestem, ens_id, idl=None)", "funcdef": "def"}, "pyerrors.input.hadrons.read_Fourquark_hd5": {"fullname": "pyerrors.input.hadrons.read_Fourquark_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Fourquark_hd5", "type": "function", "doc": "Read hadrons FourquarkFullyConnected hdf5 file and output an array of CObs
\n\nParameters \n\n\npath (str):\npath to the files to readfilestem (str):\nnamestem of the files to readens_id (str):\nname of the ensemble, required for internal bookkeepingidl (range):\nIf specified only configurations in the given range are read in.vertices (list):\nVertex functions to be extracted. \n", "signature": "(path, filestem, ens_id, idl=None, vertices=['VA', 'AV'])", "funcdef": "def"}, "pyerrors.input.json": {"fullname": "pyerrors.input.json", "modulename": "pyerrors.input.json", "type": "module", "doc": "
\n"}, "pyerrors.input.json.create_json_string": {"fullname": "pyerrors.input.json.create_json_string", "modulename": "pyerrors.input.json", "qualname": "create_json_string", "type": "function", "doc": "Generate the string for the export of a list of Obs or structures containing Obs\nto a .json(.gz) file
\n\nParameters \n\n\nol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.description (str):\nOptional string that describes the contents of the json file.indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space. \n", "signature": "(ol, description='', indent=1)", "funcdef": "def"}, "pyerrors.input.json.dump_to_json": {"fullname": "pyerrors.input.json.dump_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_to_json", "type": "function", "doc": "Export a list of Obs or structures containing Obs to a .json(.gz) file
\n\nParameters \n\n\nol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.fname (str):\nFilename of the output file.description (str):\nOptional string that describes the contents of the json file.indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file. \n", "signature": "(ol, fname, description='', indent=1, gz=True)", "funcdef": "def"}, "pyerrors.input.json.import_json_string": {"fullname": "pyerrors.input.json.import_json_string", "modulename": "pyerrors.input.json", "qualname": "import_json_string", "type": "function", "doc": "Reconstruct a list of Obs or structures containing Obs from a json string.
\n\nThe following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
\n\nParameters \n\n\njson_string (str):\njson string containing the data.verbose (bool):\nPrint additional information that was written to the file.full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned. \n", "signature": "(json_string, verbose=True, full_output=False)", "funcdef": "def"}, "pyerrors.input.json.load_json": {"fullname": "pyerrors.input.json.load_json", "modulename": "pyerrors.input.json", "qualname": "load_json", "type": "function", "doc": "Import a list of Obs or structures containing Obs from a .json(.gz) file.
\n\nThe following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
\n\nParameters \n\n\nfname (str):\nFilename of the input file.verbose (bool):\nPrint additional information that was written to the file.gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned. \n", "signature": "(fname, verbose=True, gz=True, full_output=False)", "funcdef": "def"}, "pyerrors.input.json.dump_dict_to_json": {"fullname": "pyerrors.input.json.dump_dict_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_dict_to_json", "type": "function", "doc": "Export a dict of Obs or structures containing Obs to a .json(.gz) file
\n\nParameters \n\n\nod (dict):\nDict of JSON valid structures and objects that will be exported.\nAt the moment, these objects can be either of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.fname (str):\nFilename of the output file.description (str):\nOptional string that describes the contents of the json file.indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.reps (str):\nSpecify the structure of the placeholder in exported dict to be reps[0-9]+.gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file. \n", "signature": "(od, fname, description='', indent=1, reps='DICTOBS', gz=True)", "funcdef": "def"}, "pyerrors.input.json.load_json_dict": {"fullname": "pyerrors.input.json.load_json_dict", "modulename": "pyerrors.input.json", "qualname": "load_json_dict", "type": "function", "doc": "Import a dict of Obs or structures containing Obs from a .json(.gz) file.
\n\nThe following structures are supported: Obs, list, numpy.ndarray, Corr
\n\nParameters \n\n\nfname (str):\nFilename of the input file.verbose (bool):\nPrint additional information that was written to the file.gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.reps (str):\nSpecify the structure of the placeholder in imported dict to be reps[0-9]+. \n", "signature": "(fname, verbose=True, gz=True, full_output=False, reps='DICTOBS')", "funcdef": "def"}, "pyerrors.input.misc": {"fullname": "pyerrors.input.misc", "modulename": "pyerrors.input.misc", "type": "module", "doc": "
\n"}, "pyerrors.input.misc.read_pbp": {"fullname": "pyerrors.input.misc.read_pbp", "modulename": "pyerrors.input.misc", "qualname": "read_pbp", "type": "function", "doc": "Read pbp format from given folder structure. Returns a list of length nrw
\n\nParameters \n\n\nr_start (list):\nlist which contains the first config to be read for each replicumr_stop (list):\nlist which contains the last config to be read for each replicum \n", "signature": "(path, prefix, **kwargs)", "funcdef": "def"}, "pyerrors.input.openQCD": {"fullname": "pyerrors.input.openQCD", "modulename": "pyerrors.input.openQCD", "type": "module", "doc": "
\n"}, "pyerrors.input.openQCD.read_rwms": {"fullname": "pyerrors.input.openQCD.read_rwms", "modulename": "pyerrors.input.openQCD", "qualname": "read_rwms", "type": "function", "doc": "Read rwms format from given folder structure. Returns a list of length nrw
\n\nParameters \n\n\npath (str):\npath that contains the data filesprefix (str):\nall files in path that start with prefix are considered as input files.\nMay be used together postfix to consider only special file endings.\nPrefix is ignored, if the keyword 'files' is used.version (str):\nversion of openQCD, default 2.0names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!r_start (list):\nlist which contains the first config to be read for each replicumr_stop (list):\nlist which contains the last config to be read for each replicumr_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.postfix (str):\npostfix of the file to read, e.g. '.ms1' for openQCD-filesfiles (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.print_err (bool):\nPrint additional information that is useful for debugging. \n", "signature": "(path, prefix, version='2.0', names=None, **kwargs)", "funcdef": "def"}, "pyerrors.input.openQCD.extract_t0": {"fullname": "pyerrors.input.openQCD.extract_t0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_t0", "type": "function", "doc": "Extract t0 from given .ms.dat files. Returns t0 as Obs.
\n\nIt is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t^2 - 0.3\nis fitted with a linear function\nfrom which the exact root is extracted.
\n\nIt is assumed that one measurement is performed for each config.\nIf this is not the case, the resulting idl, as well as the handling\nof r_start, r_stop and r_step is wrong and the user has to correct\nthis in the resulting observable.
\n\nParameters \n\n\npath (str):\nPath to .ms.dat filesprefix (str):\nEnsemble prefixdtr_read (int):\nDetermines how many trajectories should be skipped\nwhen reading the ms.dat files.\nCorresponds to dtr_cnfg / dtr_ms in the openQCD input file.xmin (int):\nFirst timeslice where the boundary\neffects have sufficiently decayed.spatial_extent (int):\nspatial extent of the lattice, required for normalization.fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)r_start (list):\nlist which contains the first config to be read for each replicum.r_stop (list):\nlist which contains the last config to be read for each replicum.r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.plaquette (bool):\nIf true extract the plaquette estimate of t0 instead.names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.assume_thermalization (bool):\nIf True: If the first record divided by the distance between two measurements is larger than\n1, it is assumed that this is due to thermalization and the first measurement belongs\nto the first config (default).\nIf False: The config numbers are assumed to be traj_number // difference \n", "signature": "(path, prefix, dtr_read, xmin, spatial_extent, fit_range=5, **kwargs)", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop": {"fullname": "pyerrors.input.openQCD.read_qtop", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop", "type": "function", "doc": "Read the topologial charge based on openQCD gradient flow measurements.
\n\nParameters \n\n\npath (str):\npath of the measurement filesprefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files. c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.steps (int):\n(optional) Distance between two configurations in units of trajectories /\ncycles. Assumed to be the distance between two measurements * dtr_cnfg if not givenversion (str):\nEither openQCD or sfqcd, depending on the data.L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the headerr_start (list):\nlist which contains the first config to be read for each replicum.r_stop (list):\nlist which contains the last config to be read for each replicum.files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needednames (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.integer_charge (bool):\nIf True, the charge is rounded towards the nearest integer on each config. \n", "signature": "(path, prefix, c, dtr_cnfg=1, version='openQCD', **kwargs)", "funcdef": "def"}, "pyerrors.input.openQCD.qtop_projection": {"fullname": "pyerrors.input.openQCD.qtop_projection", "modulename": "pyerrors.input.openQCD", "qualname": "qtop_projection", "type": "function", "doc": "Returns the projection to the topological charge sector defined by target.
\n\nParameters \n\n\npath (Obs):\nTopological charge.target (int):\nSpecifies the topological sector to be reweighted to (default 0) \n", "signature": "(qtop, target=0)", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop_sector": {"fullname": "pyerrors.input.openQCD.read_qtop_sector", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop_sector", "type": "function", "doc": "Constructs reweighting factors to a specified topological sector.
\n\nParameters \n\n\npath (str):\npath of the measurement filesprefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / Ltarget (int):\nSpecifies the topological sector to be reweighted to (default 0)dtr_cnfg (int):\n(optional) parameter that specifies the number of trajectories\nbetween two configs.\nif it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.steps (int):\n(optional) Distance between two configurations in units of trajectories /\ncycles. Assumed to be the distance between two measurements * dtr_cnfg if not givenversion (str):\nversion string of the openQCD (sfqcd) version used to create\nthe ensemble. Default is 2.0. May also be set to sfqcd.L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the headerr_start (list):\noffset of the first ensemble, making it easier to match\nlater on with other Obsr_stop (list):\nlast configurations that need to be read (per replicum)files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needednames (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate lengthZeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used. \n", "signature": "(path, prefix, c, target=0, **kwargs)", "funcdef": "def"}, "pyerrors.input.sfcf": {"fullname": "pyerrors.input.sfcf", "modulename": "pyerrors.input.sfcf", "type": "module", "doc": "
\n"}, "pyerrors.input.sfcf.read_sfcf": {"fullname": "pyerrors.input.sfcf.read_sfcf", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf", "type": "function", "doc": "Read sfcf c format from given folder structure.
\n\nParameters \n\n\nquarks (str):\nLabel of the quarks used in the sfcf input file. e.g. \"quark quark\"\nfor version 0.0 this does NOT need to be given with the typical \" - \"\nthat is present in the output file,\nthis is done automatically for this versionnoffset (int):\nOffset of the source (only relevant when wavefunctions are used)wf (int):\nID of wave functionwf2 (int):\nID of the second wavefunction\n(only relevant for boundary-to-boundary correlation functions)im (bool):\nif True, read imaginary instead of real part\nof the correlation function.corr_type (str):\nchange between bi (boundary - inner) (default) bib (boundary - inner - boundary) and bb (boundary - boundary)\ncorrelator typesnames (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate lengthens_name (str):\nreplaces the name of the ensembleversion (str):\nversion of SFCF, with which the measurement was done.\nif the compact output option (-c) was specified,\nappend a \"c\" to the version (e.g. \"1.0c\")\nif the append output option (-a) was specified,\nappend an \"a\" to the versioncfg_separator (str):\nString that separates the ensemble identifier from the configuration number (default 'n').replica (list):\nlist of replica to be read, default is allfiles (list):\nlist of files to be read per replica, default is all.\nfor non-compact output format, hand the folders to be read here.check_configs: : list of list of supposed configs, eg. [range(1,1000)]\nfor one replicum with 1000 configs \n", "signature": "(\n path,\n prefix,\n name,\n quarks='.*',\n corr_type='bi',\n noffset=0,\n wf=0,\n wf2=0,\n version='1.0c',\n cfg_separator='n',\n **kwargs\n)", "funcdef": "def"}, "pyerrors.input.utils": {"fullname": "pyerrors.input.utils", "modulename": "pyerrors.input.utils", "type": "module", "doc": "Utilities for the input
\n"}, "pyerrors.input.utils.check_idl": {"fullname": "pyerrors.input.utils.check_idl", "modulename": "pyerrors.input.utils", "qualname": "check_idl", "type": "function", "doc": "Checks if list of configurations is contained in an idl
\n\nParameters \n\n\nidl (range or list):\nidl of the current replicumche (list):\nlist of configurations to be checked against \n", "signature": "(idl, che)", "funcdef": "def"}, "pyerrors.linalg": {"fullname": "pyerrors.linalg", "modulename": "pyerrors.linalg", "type": "module", "doc": "
\n"}, "pyerrors.linalg.matmul": {"fullname": "pyerrors.linalg.matmul", "modulename": "pyerrors.linalg", "qualname": "matmul", "type": "function", "doc": "Matrix multiply all operands.
\n\nParameters \n\n\noperands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.This implementation is faster compared to standard multiplication via the @ operator. \n", "signature": "(*operands)", "funcdef": "def"}, "pyerrors.linalg.jack_matmul": {"fullname": "pyerrors.linalg.jack_matmul", "modulename": "pyerrors.linalg", "qualname": "jack_matmul", "type": "function", "doc": "Matrix multiply both operands making use of the jackknife approximation.
\n\nParameters \n\n\noperands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.For large matrices this is considerably faster compared to matmul. \n", "signature": "(*operands)", "funcdef": "def"}, "pyerrors.linalg.einsum": {"fullname": "pyerrors.linalg.einsum", "modulename": "pyerrors.linalg", "qualname": "einsum", "type": "function", "doc": "Wrapper for numpy.einsum
\n\nParameters \n\n\nsubscripts (str):\nSubscripts for summation (see numpy documentation for details)operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued. \n", "signature": "(subscripts, *operands)", "funcdef": "def"}, "pyerrors.linalg.inv": {"fullname": "pyerrors.linalg.inv", "modulename": "pyerrors.linalg", "qualname": "inv", "type": "function", "doc": "Inverse of Obs or CObs valued matrices.
\n", "signature": "(x)", "funcdef": "def"}, "pyerrors.linalg.cholesky": {"fullname": "pyerrors.linalg.cholesky", "modulename": "pyerrors.linalg", "qualname": "cholesky", "type": "function", "doc": "Cholesky decomposition of Obs valued matrices.
\n", "signature": "(x)", "funcdef": "def"}, "pyerrors.linalg.det": {"fullname": "pyerrors.linalg.det", "modulename": "pyerrors.linalg", "qualname": "det", "type": "function", "doc": "Determinant of Obs valued matrices.
\n", "signature": "(x)", "funcdef": "def"}, "pyerrors.linalg.eigh": {"fullname": "pyerrors.linalg.eigh", "modulename": "pyerrors.linalg", "qualname": "eigh", "type": "function", "doc": "Computes the eigenvalues and eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh.
\n", "signature": "(obs, **kwargs)", "funcdef": "def"}, "pyerrors.linalg.eig": {"fullname": "pyerrors.linalg.eig", "modulename": "pyerrors.linalg", "qualname": "eig", "type": "function", "doc": "Computes the eigenvalues of a given matrix of Obs according to np.linalg.eig.
\n", "signature": "(obs, **kwargs)", "funcdef": "def"}, "pyerrors.linalg.pinv": {"fullname": "pyerrors.linalg.pinv", "modulename": "pyerrors.linalg", "qualname": "pinv", "type": "function", "doc": "Computes the Moore-Penrose pseudoinverse of a matrix of Obs.
\n", "signature": "(obs, **kwargs)", "funcdef": "def"}, "pyerrors.linalg.svd": {"fullname": "pyerrors.linalg.svd", "modulename": "pyerrors.linalg", "qualname": "svd", "type": "function", "doc": "Computes the singular value decomposition of a matrix of Obs.
\n", "signature": "(obs, **kwargs)", "funcdef": "def"}, "pyerrors.misc": {"fullname": "pyerrors.misc", "modulename": "pyerrors.misc", "type": "module", "doc": "
\n"}, "pyerrors.misc.dump_object": {"fullname": "pyerrors.misc.dump_object", "modulename": "pyerrors.misc", "qualname": "dump_object", "type": "function", "doc": "Dump object into pickle file.
\n\nParameters \n\n\nobj (object):\nobject to be saved in the pickle filename (str):\nname of the filepath (str):\nspecifies a custom path for the file (default '.') \n", "signature": "(obj, name, **kwargs)", "funcdef": "def"}, "pyerrors.misc.load_object": {"fullname": "pyerrors.misc.load_object", "modulename": "pyerrors.misc", "qualname": "load_object", "type": "function", "doc": "Load object from pickle file.
\n\nParameters \n\n\npath (str):\npath to the file \n", "signature": "(path)", "funcdef": "def"}, "pyerrors.misc.pseudo_Obs": {"fullname": "pyerrors.misc.pseudo_Obs", "modulename": "pyerrors.misc", "qualname": "pseudo_Obs", "type": "function", "doc": "Generate an Obs object with given value, dvalue and name for test purposes
\n\nParameters \n\n\nvalue (float):\ncentral value of the Obs to be generated.dvalue (float):\nerror of the Obs to be generated.name (str):\nname of the ensemble for which the Obs is to be generated.samples (int):\nnumber of samples for the Obs (default 1000). \n", "signature": "(value, dvalue, name, samples=1000)", "funcdef": "def"}, "pyerrors.misc.gen_correlated_data": {"fullname": "pyerrors.misc.gen_correlated_data", "modulename": "pyerrors.misc", "qualname": "gen_correlated_data", "type": "function", "doc": "Generate observables with given covariance and autocorrelation times.
\n\nParameters \n\n\nmeans (list):\nlist containing the mean value of each observable.cov (numpy.ndarray):\ncovariance matrix for the data to be generated.name (str):\nensemble name for the data to be geneated.tau (float or list):\ncan either be a real number or a list with an entry for\nevery dataset.samples (int):\nnumber of samples to be generated for each observable. \n", "signature": "(means, cov, name, tau=0.5, samples=1000)", "funcdef": "def"}, "pyerrors.mpm": {"fullname": "pyerrors.mpm", "modulename": "pyerrors.mpm", "type": "module", "doc": "
\n"}, "pyerrors.mpm.matrix_pencil_method": {"fullname": "pyerrors.mpm.matrix_pencil_method", "modulename": "pyerrors.mpm", "qualname": "matrix_pencil_method", "type": "function", "doc": "Matrix pencil method to extract k energy levels from data
\n\nImplementation of the matrix pencil method based on\neq. (2.17) of Y. Hua, T. K. Sarkar, IEEE Trans. Acoust. 38, 814-824 (1990)
\n\nParameters \n\n\ndata (list):\ncan be a list of Obs for the analysis of a single correlator, or a list of lists\nof Obs if several correlators are to analyzed at once.k (int):\nNumber of states to extract (default 1).p (int):\nmatrix pencil parameter which filters noise. The optimal value is expected between\nlen(data)/3 and 2*len(data)/3. The computation is more expensive the closer p is\nto len(data)/2 but could possibly suppress more noise (default len(data)//2). \n", "signature": "(corrs, k=1, p=None, **kwargs)", "funcdef": "def"}, "pyerrors.obs": {"fullname": "pyerrors.obs", "modulename": "pyerrors.obs", "type": "module", "doc": "
\n"}, "pyerrors.obs.Obs": {"fullname": "pyerrors.obs.Obs", "modulename": "pyerrors.obs", "qualname": "Obs", "type": "class", "doc": "Class for a general observable.
\n\nInstances of Obs are the basic objects of a pyerrors error analysis.\nThey are initialized with a list which contains arrays of samples for\ndifferent ensembles/replica and another list of same length which contains\nthe names of the ensembles/replica. Mathematical operations can be\nperformed on instances. The result is another instance of Obs. The error of\nan instance can be computed with the gamma_method. Also contains additional\nmethods for output and visualization of the error calculation.
\n\nAttributes \n\n\nS_global (float):\nStandard value for S (default 2.0)S_dict (dict):\nDictionary for S values. If an entry for a given ensemble\nexists this overwrites the standard value for that ensemble.tau_exp_global (float):\nStandard value for tau_exp (default 0.0)tau_exp_dict (dict):\nDictionary for tau_exp values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.N_sigma_global (float):\nStandard value for N_sigma (default 1.0)N_sigma_dict (dict):\nDictionary for N_sigma values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble. \n"}, "pyerrors.obs.Obs.__init__": {"fullname": "pyerrors.obs.Obs.__init__", "modulename": "pyerrors.obs", "qualname": "Obs.__init__", "type": "function", "doc": "Initialize Obs object.
\n\nParameters \n\n\nsamples (list):\nlist of numpy arrays containing the Monte Carlo samplesnames (list):\nlist of strings labeling the individual samplesidl (list, optional):\nlist of ranges or lists on which the samples are defined \n", "signature": "(self, samples, names, idl=None, **kwargs)", "funcdef": "def"}, "pyerrors.obs.Obs.S_global": {"fullname": "pyerrors.obs.Obs.S_global", "modulename": "pyerrors.obs", "qualname": "Obs.S_global", "type": "variable", "doc": "
\n", "default_value": " = 2.0"}, "pyerrors.obs.Obs.S_dict": {"fullname": "pyerrors.obs.Obs.S_dict", "modulename": "pyerrors.obs", "qualname": "Obs.S_dict", "type": "variable", "doc": "
\n", "default_value": " = {}"}, "pyerrors.obs.Obs.tau_exp_global": {"fullname": "pyerrors.obs.Obs.tau_exp_global", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_global", "type": "variable", "doc": "
\n", "default_value": " = 0.0"}, "pyerrors.obs.Obs.tau_exp_dict": {"fullname": "pyerrors.obs.Obs.tau_exp_dict", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_dict", "type": "variable", "doc": "
\n", "default_value": " = {}"}, "pyerrors.obs.Obs.N_sigma_global": {"fullname": "pyerrors.obs.Obs.N_sigma_global", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_global", "type": "variable", "doc": "
\n", "default_value": " = 1.0"}, "pyerrors.obs.Obs.N_sigma_dict": {"fullname": "pyerrors.obs.Obs.N_sigma_dict", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_dict", "type": "variable", "doc": "
\n", "default_value": " = {}"}, "pyerrors.obs.Obs.filter_eps": {"fullname": "pyerrors.obs.Obs.filter_eps", "modulename": "pyerrors.obs", "qualname": "Obs.filter_eps", "type": "variable", "doc": "
\n", "default_value": " = 1e-10"}, "pyerrors.obs.Obs.names": {"fullname": "pyerrors.obs.Obs.names", "modulename": "pyerrors.obs", "qualname": "Obs.names", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.shape": {"fullname": "pyerrors.obs.Obs.shape", "modulename": "pyerrors.obs", "qualname": "Obs.shape", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.r_values": {"fullname": "pyerrors.obs.Obs.r_values", "modulename": "pyerrors.obs", "qualname": "Obs.r_values", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.deltas": {"fullname": "pyerrors.obs.Obs.deltas", "modulename": "pyerrors.obs", "qualname": "Obs.deltas", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.N": {"fullname": "pyerrors.obs.Obs.N", "modulename": "pyerrors.obs", "qualname": "Obs.N", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.is_merged": {"fullname": "pyerrors.obs.Obs.is_merged", "modulename": "pyerrors.obs", "qualname": "Obs.is_merged", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.idl": {"fullname": "pyerrors.obs.Obs.idl", "modulename": "pyerrors.obs", "qualname": "Obs.idl", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.ddvalue": {"fullname": "pyerrors.obs.Obs.ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.ddvalue", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.reweighted": {"fullname": "pyerrors.obs.Obs.reweighted", "modulename": "pyerrors.obs", "qualname": "Obs.reweighted", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.tag": {"fullname": "pyerrors.obs.Obs.tag", "modulename": "pyerrors.obs", "qualname": "Obs.tag", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.value": {"fullname": "pyerrors.obs.Obs.value", "modulename": "pyerrors.obs", "qualname": "Obs.value", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.dvalue": {"fullname": "pyerrors.obs.Obs.dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.dvalue", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_names": {"fullname": "pyerrors.obs.Obs.e_names", "modulename": "pyerrors.obs", "qualname": "Obs.e_names", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.cov_names": {"fullname": "pyerrors.obs.Obs.cov_names", "modulename": "pyerrors.obs", "qualname": "Obs.cov_names", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.mc_names": {"fullname": "pyerrors.obs.Obs.mc_names", "modulename": "pyerrors.obs", "qualname": "Obs.mc_names", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_content": {"fullname": "pyerrors.obs.Obs.e_content", "modulename": "pyerrors.obs", "qualname": "Obs.e_content", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.covobs": {"fullname": "pyerrors.obs.Obs.covobs", "modulename": "pyerrors.obs", "qualname": "Obs.covobs", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.gamma_method": {"fullname": "pyerrors.obs.Obs.gamma_method", "modulename": "pyerrors.obs", "qualname": "Obs.gamma_method", "type": "function", "doc": "Estimate the error and related properties of the Obs.
\n\nParameters \n\n\nS (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.tau_exp (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).N_sigma (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).fft (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True) \n", "signature": "(self, **kwargs)", "funcdef": "def"}, "pyerrors.obs.Obs.details": {"fullname": "pyerrors.obs.Obs.details", "modulename": "pyerrors.obs", "qualname": "Obs.details", "type": "function", "doc": "Output detailed properties of the Obs.
\n\nParameters \n\n\nens_content (bool):\nprint details about the ensembles and replica if true. \n", "signature": "(self, ens_content=True)", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero_within_error": {"fullname": "pyerrors.obs.Obs.is_zero_within_error", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero_within_error", "type": "function", "doc": "Checks whether the observable is zero within 'sigma' standard errors.
\n\nParameters \n\n\nsigma (int):\nNumber of standard errors used for the check.Works only properly when the gamma method was run. \n", "signature": "(self, sigma=1)", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero": {"fullname": "pyerrors.obs.Obs.is_zero", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero", "type": "function", "doc": "Checks whether the observable is zero within a given tolerance.
\n\nParameters \n\n\natol (float):\nAbsolute tolerance (for details see numpy documentation). \n", "signature": "(self, atol=1e-10)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_tauint": {"fullname": "pyerrors.obs.Obs.plot_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.plot_tauint", "type": "function", "doc": "Plot integrated autocorrelation time for each ensemble.
\n\nParameters \n\n\nsave (str):\nsaves the figure to a file named 'save' if. \n", "signature": "(self, save=None)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rho": {"fullname": "pyerrors.obs.Obs.plot_rho", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rho", "type": "function", "doc": "Plot normalized autocorrelation function time for each ensemble.
\n\nParameters \n\n\nsave (str):\nsaves the figure to a file named 'save' if. \n", "signature": "(self, save=None)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rep_dist": {"fullname": "pyerrors.obs.Obs.plot_rep_dist", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rep_dist", "type": "function", "doc": "Plot replica distribution for each ensemble with more than one replicum.
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_history": {"fullname": "pyerrors.obs.Obs.plot_history", "modulename": "pyerrors.obs", "qualname": "Obs.plot_history", "type": "function", "doc": "Plot derived Monte Carlo history for each ensemble
\n\nParameters \n\n\nexpand (bool):\nshow expanded history for irregular Monte Carlo chains (default: True). \n", "signature": "(self, expand=True)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_piechart": {"fullname": "pyerrors.obs.Obs.plot_piechart", "modulename": "pyerrors.obs", "qualname": "Obs.plot_piechart", "type": "function", "doc": "Plot piechart which shows the fractional contribution of each\nensemble to the error and returns a dictionary containing the fractions.
\n\nParameters \n\n\nsave (str):\nsaves the figure to a file named 'save' if. \n", "signature": "(self, save=None)", "funcdef": "def"}, "pyerrors.obs.Obs.dump": {"fullname": "pyerrors.obs.Obs.dump", "modulename": "pyerrors.obs", "qualname": "Obs.dump", "type": "function", "doc": "Dump the Obs to a file 'name' of chosen format.
\n\nParameters \n\n\nfilename (str):\nname of the file to be saved.datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"description (str):\nDescription for output file, only relevant for json.gz format.path (str):\nspecifies a custom path for the file (default '.') \n", "signature": "(self, filename, datatype='json.gz', description='', **kwargs)", "funcdef": "def"}, "pyerrors.obs.Obs.export_jackknife": {"fullname": "pyerrors.obs.Obs.export_jackknife", "modulename": "pyerrors.obs", "qualname": "Obs.export_jackknife", "type": "function", "doc": "Export jackknife samples from the Obs
\n\nReturns \n\n\nnumpy.ndarray : Returns a numpy array of length N + 1 where N is the number of samples\nfor the given ensemble and replicum. The zeroth entry of the array contains\nthe mean value of the Obs, entries 1 to N contain the N jackknife samples\nderived from the Obs. The current implementation only works for observables\ndefined on exactly one ensemble and replicum. The derived jackknife samples\nshould agree with samples from a full jackknife analysis up to O(1/N). \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.sqrt": {"fullname": "pyerrors.obs.Obs.sqrt", "modulename": "pyerrors.obs", "qualname": "Obs.sqrt", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.log": {"fullname": "pyerrors.obs.Obs.log", "modulename": "pyerrors.obs", "qualname": "Obs.log", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.exp": {"fullname": "pyerrors.obs.Obs.exp", "modulename": "pyerrors.obs", "qualname": "Obs.exp", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.sin": {"fullname": "pyerrors.obs.Obs.sin", "modulename": "pyerrors.obs", "qualname": "Obs.sin", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.cos": {"fullname": "pyerrors.obs.Obs.cos", "modulename": "pyerrors.obs", "qualname": "Obs.cos", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.tan": {"fullname": "pyerrors.obs.Obs.tan", "modulename": "pyerrors.obs", "qualname": "Obs.tan", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arcsin": {"fullname": "pyerrors.obs.Obs.arcsin", "modulename": "pyerrors.obs", "qualname": "Obs.arcsin", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arccos": {"fullname": "pyerrors.obs.Obs.arccos", "modulename": "pyerrors.obs", "qualname": "Obs.arccos", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arctan": {"fullname": "pyerrors.obs.Obs.arctan", "modulename": "pyerrors.obs", "qualname": "Obs.arctan", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.sinh": {"fullname": "pyerrors.obs.Obs.sinh", "modulename": "pyerrors.obs", "qualname": "Obs.sinh", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.cosh": {"fullname": "pyerrors.obs.Obs.cosh", "modulename": "pyerrors.obs", "qualname": "Obs.cosh", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.tanh": {"fullname": "pyerrors.obs.Obs.tanh", "modulename": "pyerrors.obs", "qualname": "Obs.tanh", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arcsinh": {"fullname": "pyerrors.obs.Obs.arcsinh", "modulename": "pyerrors.obs", "qualname": "Obs.arcsinh", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arccosh": {"fullname": "pyerrors.obs.Obs.arccosh", "modulename": "pyerrors.obs", "qualname": "Obs.arccosh", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arctanh": {"fullname": "pyerrors.obs.Obs.arctanh", "modulename": "pyerrors.obs", "qualname": "Obs.arctanh", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.N_sigma": {"fullname": "pyerrors.obs.Obs.N_sigma", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.S": {"fullname": "pyerrors.obs.Obs.S", "modulename": "pyerrors.obs", "qualname": "Obs.S", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_ddvalue": {"fullname": "pyerrors.obs.Obs.e_ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_ddvalue", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_drho": {"fullname": "pyerrors.obs.Obs.e_drho", "modulename": "pyerrors.obs", "qualname": "Obs.e_drho", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_dtauint": {"fullname": "pyerrors.obs.Obs.e_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_dtauint", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_dvalue": {"fullname": "pyerrors.obs.Obs.e_dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_dvalue", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_n_dtauint": {"fullname": "pyerrors.obs.Obs.e_n_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_dtauint", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_n_tauint": {"fullname": "pyerrors.obs.Obs.e_n_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_tauint", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_rho": {"fullname": "pyerrors.obs.Obs.e_rho", "modulename": "pyerrors.obs", "qualname": "Obs.e_rho", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_tauint": {"fullname": "pyerrors.obs.Obs.e_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_tauint", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_windowsize": {"fullname": "pyerrors.obs.Obs.e_windowsize", "modulename": "pyerrors.obs", "qualname": "Obs.e_windowsize", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.tau_exp": {"fullname": "pyerrors.obs.Obs.tau_exp", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp", "type": "variable", "doc": "
\n"}, "pyerrors.obs.CObs": {"fullname": "pyerrors.obs.CObs", "modulename": "pyerrors.obs", "qualname": "CObs", "type": "class", "doc": "Class for a complex valued observable.
\n"}, "pyerrors.obs.CObs.__init__": {"fullname": "pyerrors.obs.CObs.__init__", "modulename": "pyerrors.obs", "qualname": "CObs.__init__", "type": "function", "doc": "
\n", "signature": "(self, real, imag=0.0)", "funcdef": "def"}, "pyerrors.obs.CObs.tag": {"fullname": "pyerrors.obs.CObs.tag", "modulename": "pyerrors.obs", "qualname": "CObs.tag", "type": "variable", "doc": "
\n"}, "pyerrors.obs.CObs.real": {"fullname": "pyerrors.obs.CObs.real", "modulename": "pyerrors.obs", "qualname": "CObs.real", "type": "variable", "doc": "
\n"}, "pyerrors.obs.CObs.imag": {"fullname": "pyerrors.obs.CObs.imag", "modulename": "pyerrors.obs", "qualname": "CObs.imag", "type": "variable", "doc": "
\n"}, "pyerrors.obs.CObs.gamma_method": {"fullname": "pyerrors.obs.CObs.gamma_method", "modulename": "pyerrors.obs", "qualname": "CObs.gamma_method", "type": "function", "doc": "Executes the gamma_method for the real and the imaginary part.
\n", "signature": "(self, **kwargs)", "funcdef": "def"}, "pyerrors.obs.CObs.is_zero": {"fullname": "pyerrors.obs.CObs.is_zero", "modulename": "pyerrors.obs", "qualname": "CObs.is_zero", "type": "function", "doc": "Checks whether both real and imaginary part are zero within machine precision.
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.CObs.conjugate": {"fullname": "pyerrors.obs.CObs.conjugate", "modulename": "pyerrors.obs", "qualname": "CObs.conjugate", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.derived_observable": {"fullname": "pyerrors.obs.derived_observable", "modulename": "pyerrors.obs", "qualname": "derived_observable", "type": "function", "doc": "Construct a derived Obs according to func(data, **kwargs) using automatic differentiation.
\n\nParameters \n\n\nfunc (object):\narbitrary function of the form func(data, **kwargs). For the\nautomatic differentiation to work, all numpy functions have to have\nthe autograd wrapper (use 'import autograd.numpy as anp').data (list):\nlist of Obs, e.g. [obs1, obs2, obs3].num_grad (bool):\nif True, numerical derivatives are used instead of autograd\n(default False). To control the numerical differentiation the\nkwargs of numdifftools.step_generators.MaxStepGenerator\ncan be used.man_grad (list):\nmanually supply a list or an array which contains the jacobian\nof func. Use cautiously, supplying the wrong derivative will\nnot be intercepted. \n\nNotes \n\nFor simple mathematical operations it can be practical to use anonymous\nfunctions. For the ratio of two observables one can e.g. use
\n\nnew_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2])
\n", "signature": "(func, data, array_mode=False, **kwargs)", "funcdef": "def"}, "pyerrors.obs.reweight": {"fullname": "pyerrors.obs.reweight", "modulename": "pyerrors.obs", "qualname": "reweight", "type": "function", "doc": "Reweight a list of observables.
\n\nParameters \n\n\nweight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.obs (list):\nlist of Obs, e.g. [obs1, obs2, obs3].all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. \n", "signature": "(weight, obs, **kwargs)", "funcdef": "def"}, "pyerrors.obs.correlate": {"fullname": "pyerrors.obs.correlate", "modulename": "pyerrors.obs", "qualname": "correlate", "type": "function", "doc": "Correlate two observables.
\n\nParameters \n\n\nobs_a (Obs):\nFirst observableobs_b (Obs):\nSecond observable \n\nNotes \n\nKeep in mind to only correlate primary observables which have not been reweighted\nyet. The reweighting has to be applied after correlating the observables.\nCurrently only works if ensembles are identical (this is not strictly necessary).
\n", "signature": "(obs_a, obs_b)", "funcdef": "def"}, "pyerrors.obs.covariance": {"fullname": "pyerrors.obs.covariance", "modulename": "pyerrors.obs", "qualname": "covariance", "type": "function", "doc": "Calculates the error covariance matrix of a set of observables.
\n\nThe gamma method has to be applied first to all observables.
\n\nParameters \n\n\nobs (list or numpy.ndarray):\nList or one dimensional array of Obsvisualize (bool):\nIf True plots the corresponding normalized correlation matrix (default False).correlation (bool):\nIf True the correlation matrix instead of the error covariance matrix is returned (default False).smooth (None or int):\nIf smooth is an integer 'E' between 2 and the dimension of the matrix minus 1 the eigenvalue\nsmoothing procedure of hep-lat/9412087 is applied to the correlation matrix which leaves the\nlargest E eigenvalues essentially unchanged and smoothes the smaller eigenvalues to avoid extremely\nsmall ones. \n\nNotes \n\nThe error covariance is defined such that it agrees with the squared standard error for two identical observables\n$$\\operatorname{cov}(a,a)=\\sum_{s=1}^N\\delta_a^s\\delta_a^s/N^2=\\Gamma_{aa}(0)/N=\\operatorname{var}(a)/N=\\sigma_a^2$$\nin the absence of autocorrelation.\nThe error covariance is estimated by calculating the correlation matrix assuming no autocorrelation and then rescaling the correlation matrix by the full errors including the previous gamma method estimate for the autocorrelation of the observables. The covariance at windowsize 0 is guaranteed to be positive semi-definite\n$$\\sum_{i,j}v_i\\Gamma_{ij}(0)v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i,j}v_i\\delta_i^s\\delta_j^s v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i}|v_i\\delta_i^s|^2\\geq 0\\,,$$ for every $v\\in\\mathbb{R}^M$, while such an identity does not hold for larger windows/lags.\nFor observables defined on a single ensemble our approximation is equivalent to assuming that the integrated autocorrelation time of an off-diagonal element is equal to the geometric mean of the integrated autocorrelation times of the corresponding diagonal elements.\n$$\\tau_{\\mathrm{int}, ij}=\\sqrt{\\tau_{\\mathrm{int}, i}\\times \\tau_{\\mathrm{int}, j}}$$\nThis construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors).
\n", "signature": "(obs, visualize=False, correlation=False, smooth=None, **kwargs)", "funcdef": "def"}, "pyerrors.obs.import_jackknife": {"fullname": "pyerrors.obs.import_jackknife", "modulename": "pyerrors.obs", "qualname": "import_jackknife", "type": "function", "doc": "Imports jackknife samples and returns an Obs
\n\nParameters \n\n\njacks (numpy.ndarray):\nnumpy array containing the mean value as zeroth entry and\nthe N jackknife samples as first to Nth entry.name (str):\nname of the ensemble the samples are defined on. \n", "signature": "(jacks, name, idl=None)", "funcdef": "def"}, "pyerrors.obs.merge_obs": {"fullname": "pyerrors.obs.merge_obs", "modulename": "pyerrors.obs", "qualname": "merge_obs", "type": "function", "doc": "Combine all observables in list_of_obs into one new observable
\n\nParameters \n\n\nlist_of_obs (list):\nlist of the Obs object to be combined \n\nNotes \n\nIt is not possible to combine obs which are based on the same replicum
\n", "signature": "(list_of_obs)", "funcdef": "def"}, "pyerrors.obs.cov_Obs": {"fullname": "pyerrors.obs.cov_Obs", "modulename": "pyerrors.obs", "qualname": "cov_Obs", "type": "function", "doc": "Create an Obs based on mean(s) and a covariance matrix
\n\nParameters \n\n\nmean (list of floats or float):\nN mean value(s) of the new Obscov (list or array):\n2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariancename (str):\nidentifier for the covariance matrixgrad (list or array):\nGradient of the Covobs wrt. the means belonging to cov. \n", "signature": "(means, cov, name, grad=None)", "funcdef": "def"}, "pyerrors.roots": {"fullname": "pyerrors.roots", "modulename": "pyerrors.roots", "type": "module", "doc": "
\n"}, "pyerrors.roots.find_root": {"fullname": "pyerrors.roots.find_root", "modulename": "pyerrors.roots", "qualname": "find_root", "type": "function", "doc": "Finds the root of the function func(x, d) where d is an Obs.
\n\nParameters \n\n\nd (Obs):\nObs passed to the function.func (object):\nFunction to be minimized. Any numpy functions have to use the autograd.numpy wrapper.\nExample:\npython\nimport autograd.numpy as anp\ndef root_func(x, d):\n return anp.exp(-x ** 2) - d\nguess (float):\nInitial guess for the minimization. \n\nReturns \n\n\nObs : Obs valued root of the function. \n", "signature": "(d, func, guess=1.0, **kwargs)", "funcdef": "def"}, "pyerrors.version": {"fullname": "pyerrors.version", "modulename": "pyerrors.version", "type": "module", "doc": "
\n"}}, "docInfo": {"pyerrors": {"qualname": 0, "fullname": 1, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 7902}, "pyerrors.correlators": {"qualname": 0, "fullname": 2, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 3}, "pyerrors.correlators.Corr": {"qualname": 1, "fullname": 3, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 108}, "pyerrors.correlators.Corr.__init__": {"qualname": 3, "fullname": 5, "annotation": 0, "default_value": 0, "signature": 10, "bases": 0, "doc": 94}, "pyerrors.correlators.Corr.reweighted": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 3}, "pyerrors.correlators.Corr.gamma_method": {"qualname": 3, "fullname": 5, "annotation": 0, "default_value": 0, "signature": 4, "bases": 0, "doc": 13}, "pyerrors.correlators.Corr.projected": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 11, "bases": 0, "doc": 64}, "pyerrors.correlators.Corr.item": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 5, "bases": 0, "doc": 53}, "pyerrors.correlators.Corr.plottable": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 3, "bases": 0, "doc": 31}, "pyerrors.correlators.Corr.symmetric": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 3, "bases": 0, "doc": 9}, "pyerrors.correlators.Corr.anti_symmetric": {"qualname": 3, "fullname": 5, "annotation": 0, "default_value": 0, "signature": 3, "bases": 0, "doc": 10}, "pyerrors.correlators.Corr.matrix_symmetric": {"qualname": 3, "fullname": 5, "annotation": 0, "default_value": 0, "signature": 3, "bases": 0, "doc": 10}, "pyerrors.correlators.Corr.GEVP": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 9, "bases": 0, "doc": 324}, "pyerrors.correlators.Corr.Eigenvalue": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 10, "bases": 0, "doc": 59}, "pyerrors.correlators.Corr.Hankel": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 6, "bases": 0, "doc": 67}, "pyerrors.correlators.Corr.roll": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 4, "bases": 0, "doc": 26}, "pyerrors.correlators.Corr.reverse": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 3, "bases": 0, "doc": 9}, "pyerrors.correlators.Corr.thin": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 7, "bases": 0, "doc": 43}, "pyerrors.correlators.Corr.correlate": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 4, "bases": 0, "doc": 53}, "pyerrors.correlators.Corr.reweight": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 5, "bases": 0, "doc": 79}, "pyerrors.correlators.Corr.T_symmetry": {"qualname": 3, "fullname": 5, "annotation": 0, "default_value": 0, "signature": 6, "bases": 0, "doc": 51}, "pyerrors.correlators.Corr.deriv": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 5, "bases": 0, "doc": 46}, "pyerrors.correlators.Corr.second_deriv": {"qualname": 3, "fullname": 5, "annotation": 0, "default_value": 0, "signature": 5, "bases": 0, "doc": 44}, "pyerrors.correlators.Corr.m_eff": {"qualname": 3, "fullname": 5, "annotation": 0, "default_value": 0, "signature": 8, "bases": 0, "doc": 135}, "pyerrors.correlators.Corr.fit": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 9, "bases": 0, "doc": 110}, "pyerrors.correlators.Corr.plateau": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 11, "bases": 0, "doc": 92}, "pyerrors.correlators.Corr.set_prange": {"qualname": 3, "fullname": 5, "annotation": 0, "default_value": 0, "signature": 4, "bases": 0, "doc": 11}, "pyerrors.correlators.Corr.show": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 30, "bases": 0, "doc": 222}, "pyerrors.correlators.Corr.spaghetti_plot": {"qualname": 3, "fullname": 5, "annotation": 0, "default_value": 0, "signature": 5, "bases": 0, "doc": 42}, "pyerrors.correlators.Corr.dump": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 8, "bases": 0, "doc": 69}, "pyerrors.correlators.Corr.print": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 6, "bases": 0, "doc": 3}, "pyerrors.correlators.Corr.sqrt": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 3, "bases": 0, "doc": 3}, "pyerrors.correlators.Corr.log": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 3, "bases": 0, "doc": 3}, "pyerrors.correlators.Corr.exp": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 3, "bases": 0, "doc": 3}, "pyerrors.correlators.Corr.sin": {"qualname": 2, "fullname": 4, 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