Compute RDTs (#821)

* fix matlab bug in avemu

* avoid import twice numpy + bugfix

* add rdt module to pyat

* add quadrupole rdts

* docstring + blacked

* 2nd order tuneshift

* 2nd order geometric

* blacked

* remove atlinopt from matlab avedata

* reformat formulas

* reformat formulas

* parallelized calculation

* black

* fix phase

* fix h00310

* initialize periodicfactor with dtype=complex

* compute tune for nperiods

* compute periodicfactor outside loop

* improve comments and help

* fix sign and add refs

* switch to import numpy as np

* perdiodicity in docstring

* correct coupling rdts

* sign of coupling rdt

* Remove dataclass and separate second order

* improve docs

* remove np.complex

* docstring

* restore matlab avemu

* add tests + bugfix

* fix docstring

Author: swhite2401

atmat/atphysics/atavedata.m

@@ -26,7 +26,11 @@
 needed=refs | [false;long]; %lr
 initial=[long(needed(1:end-1));false]; %needed
 final=[false;initial(1:end-1)]; %needed
-[lind,nu,xsi]=atlinopt(ring,dpp,needed,varargin{:}); %needed
+setoption('WarningDp6D',false)
+[ringdata, lind]=atlinopt6(ring,needed,'dp',dpp,'get_chrom',varargin{:}); %needed
+setoption('WarningDp6D',true)
+nu = ringdata.tune;
+xsi = ringdata.chromaticity;
 
 lindata=lind(refs(needed)); %refpts
 avebeta=cat(1,lindata.beta); %refpts
@@ -41,7 +45,7 @@
 
 beta0=avebeta(lg,:); %long
 alpha0=cat(1,lin0.alpha); %long
-mu0=avemu(lg,:);
+mu0=avemu(lg,:); %long
 disp0=avedisp(lg,:); %long
 
 mu1=cat(1,lin1.mu); %long

pyat/at/physics/__init__.py

@@ -18,4 +18,5 @@
 from .nonlinear import *
 from .fastring import *
 from .frequency_maps import fmap_parallel_track
+from .rdt import *
 from .magnet_tools import *

pyat/at/physics/linear.py

@@ -102,11 +102,10 @@
 
 
 _IDX_DTYPE = [("idx", np.uint32)]
-
-
 warnings.filterwarnings("always", category=AtWarning, module=__name__)
 
 
+
 def _twiss22(t12, alpha0, beta0):
     """Propagate Twiss parameters"""
     bbb = t12[:, 0, 1]
@@ -1372,7 +1371,7 @@ def displong(disp0, ir, k2, lg):
     longi_refpts = np.append(longelem, [False])
     longf_refpts = np.roll(longi_refpts, 1)
     all_refs = boolrefs | longf_refpts
-    _, bd, d_all = linopt4(ring, refpts=all_refs, dp=dp, get_chrom=True, **kwargs)
+    _, bd, d_all = get_optics(ring, refpts=all_refs, dp=dp, get_chrom=True, **kwargs)
     lindata = d_all[boolrefs[all_refs]]  # Optics at entrance of selected elements
 
     avebeta = lindata.beta.copy()