EquivalentGradientsFromAlignments6D

[kn,    1) estimated normal quad gradients from sext offsets, quad
           errors in quadrupoles and sextupoles.
 ks,    2) estimated skew quad gradients from sext offsets, quad
           errors in quadrupoles, quadrupole rotation.
 ind    3) indexes of locations at wich kn and ks are found
 ]=EquivalentGradientsFromAlignments6D(
 r,     1) AT lattice structure with errors
 inCOD
 )

 the function finds the closed orbit at sextupoles and converts it to
 equivalent quadrupole and skew quadrupole gradients for the computation
 of skew and normal quadrupole RDT 
 quadrupole rotations are also converted in skew quadrupole gradients.
 
 it returns the complete list of normal (kn) and skew (ks) quadrupole
 gradients at the given indexes (ind) ( not integrated, PolynomB)
 
 
see also:

0001 function [kn,ks,ind]=EquivalentGradientsFromAlignments6D(r,inCOD)
0002 %[kn,    1) estimated normal quad gradients from sext offsets, quad
0003 %           errors in quadrupoles and sextupoles.
0004 % ks,    2) estimated skew quad gradients from sext offsets, quad
0005 %           errors in quadrupoles, quadrupole rotation.
0006 % ind    3) indexes of locations at wich kn and ks are found
0007 % ]=EquivalentGradientsFromAlignments6D(
0008 % r,     1) AT lattice structure with errors
0009 % inCOD
0010 % )
0011 %
0012 % the function finds the closed orbit at sextupoles and converts it to
0013 % equivalent quadrupole and skew quadrupole gradients for the computation
0014 % of skew and normal quadrupole RDT
0015 % quadrupole rotations are also converted in skew quadrupole gradients.
0016 %
0017 % it returns the complete list of normal (kn) and skew (ks) quadrupole
0018 % gradients at the given indexes (ind) ( not integrated, PolynomB)
0019 %
0020 %
0021 %see also:
0022 
0023 % quadrupole and skew quadrupole errors are introduced via COD in
0024 % sextupoles
0025 indsext=find(atgetcells(r,'Class','Sextupole'))';
0026 
0027 b3=atgetfieldvalues(r,indsext,'PolynomB',{1,3});
0028 
0029 oin=findorbit6(r,indsext,inCOD);% orbit at entrance of sextupole DO NOT USE HERE findorbit6Err!
0030 oout=findorbit6(r,indsext+1,inCOD); % orbit at exit of sextupole
0031 
0032 xmisal=cellfun(@(a)getT1(a,1),r(indsext));
0033 ymisal=cellfun(@(a)getT1(a,3),r(indsext));
0034 
0035 Dx=(oout(1,:)+oin(1,:))/2; % orbit average in sextupole
0036 Dy=(oout(3,:)+oin(3,:))/2; % orbit average in sextupole
0037 
0038 % quarupole errors in sextupoles
0039 kn_sext_err=cellfun(@(a)a.PolynomB(2),r(indsext));
0040 ks_sext_err=cellfun(@(a)a.PolynomA(2),r(indsext));
0041 
0042 kn_sext=-2.*b3.*(-Dx+xmisal')'+kn_sext_err;
0043 ks_sext=-2.*b3.*(-Dy+ymisal')'+ks_sext_err;
0044 
0045 % quadrupole rotations
0046 indquad=find(atgetcells(r,'Class','Quadrupole'))';
0047 
0048 kn2=atgetfieldvalues(r,indquad,'PolynomB',{1,2});
0049 ks2=atgetfieldvalues(r,indquad,'PolynomA',{1,2});
0050 srot=cellfun(@(a)getR1(a),r(indquad));
0051 
0052 kn_quad=(1-srot).*kn2;
0053 ks_quad=-srot.*kn2+ks2;
0054 
0055 % all elements with PolynomB, not sextupoles or quadrupoles
0056 indPolB=find(atgetcells(r,'PolynomB') & ...
0057     ~atgetcells(r,'Class','Quadrupole') & ...
0058     ~atgetcells(r,'Class','Sextupole' ))';
0059 
0060 NpolB=cellfun(@(a)length(a.PolynomB),r(indPolB));
0061 NpolA=cellfun(@(a)length(a.PolynomA),r(indPolB));
0062 
0063 indPolB=indPolB(NpolB>=2 & NpolA>=2 & ~ismember(indPolB,[indquad indsext])');
0064 
0065 kn_all=cellfun(@(a)a.PolynomB(2),r(indPolB));%-kn0_all;
0066 ks_all=cellfun(@(a)a.PolynomA(2),r(indPolB));%-ks0_all;
0067 
0068 [ind,ord]=sort([indsext,indquad,indPolB]);
0069 
0070 kn=[kn_sext;kn_quad;kn_all];
0071 ks=[ks_sext;ks_quad;ks_all];
0072 
0073 % integrated strengths
0074 %L=cellfun(@(a)a.Length,r(ind));
0075 
0076 kn=kn(ord);%.*L;
0077 ks=ks(ord);%.*L;
0078 
0079 
0080 return
0081 
0082 
0083 function t1=getT1(a,ind)
0084 t1=0;
0085 if isfield(a,'T1')
0086     t1=-a.T1(ind);
0087 end
0088 return
0089 
0090 
0091 function r1=getR1(a)
0092 r1=0;
0093 if isfield(a,'R1')
0094     r1=asin(a.R1(1,3));
0095 end
0096 return