📄 multilinear5sym.m
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function vec5 =multilinear5sym(q1,q2,q3,q4,q5,nphase,n)
%----------------------------------------------------
% This file computes T^(n)*q1*q2*q3*q4*q5, where T^(n) is 5th derivative
% of map f^(n) .
%----------------------------------------------------
global cds T1global T2global T3global T4global T5global
if n==1
T5=T5global(:,:,:,:,:,:,1);
vec5=tensor5op(T5,q1,q2,q3,q4,q5,nphase);
else
if (q1==q2 & q1 ==q3)
if (q1==q4 & q1==q5)
Vj1=multilinear1sym(q1,n-1);
Vh1=multilinear2sym(q1,q1,nphase,n-1);
VT=multilinear3sym(q1,q1,q1,nphase,n-1);
VT4=multilinear4sym(q1,q1,q1,q1,nphase,n-1);
T5=T5global(:,:,:,:,:,:,n);
V1=tensor5op(T5,Vj1,Vj1,Vj1,Vj1,Vj1,nphase);
T4=T4global(:,:,:,:,:,n);
V2=tensor4op(T4,Vh1,Vj1,Vj1,Vj1,nphase);
T3=T3global(:,:,:,:,n);
V3=tensor3op(T3,Vh1,Vh1,Vj1,nphase);
V4=tensor3op(T3,VT,Vj1,Vj1,nphase);
T2=T2global(:,:,:,n);
V5=tensor2op(T2,VT4,Vj1,nphase);
V6=tensor2op(T2,VT,Vh1,nphase);
T1=T1global(:,:,n);
VT7=multilinear5sym(q1,q1,q1,q1,q1,nphase,n-1);
V7=T1*VT7;
vec5=V1+10.0*V2+15.0*V3+10.0*V4+5.0*V5+10.0*V6+V7;
else % q1==q2==q3 noteq q4 and q5
Vj1=multilinear1sym(q1,n);
Vj4=multilinear1sym(q4,n-1);
Vj5=multilinear1sym(q5,n-1);
Vh11=multilinear2sym(q1,q1,nphase,n-1);
Vh14=multilinear2sym(q1,q4,nphase,n-1);
Vh15=multilinear2sym(q1,q5,nphase,n-1);
Vh45=multilinear2sym(q4,q5,nphase,n-1);
VT114=multilinear3sym(q1,q1,q4,nphase,n-1);
VT115=multilinear3sym(q1,q1,q5,nphase,n-1);
VT111=multilinear3sym(q1,q1,q1,nphase,n-1);
VT145=multilinear3sym(q1,q4,q5,nphase,n-1);
VT1114=multilinear4sym(q1,q1,q1,q4,nphase,n-1);
VT1145=multilinear4sym(q1,q1,q4,q5,nphase,n-1);
VT1115=multilinear4sym(q1,q1,q1,q5,nphase,n-1);
T5=T5global(:,:,:,:,:,:,n);
V1=tensor5op(T5,Vj1,Vj1,Vj1,Vj4,Vj5,nphase);
T4=T4global(:,:,:,:,:,n);
V2=tensor4op(T4,Vh11,Vj1,Vj4,Vj5,nphase);
V3=tensor4op(T4,Vh14,Vj1,Vj1,Vj5,nphase);
V4=tensor4op(T4,Vh15,Vj1,Vj1,Vj4,nphase);
V5=tensor4op(T4,Vh45,Vj1,Vj1,Vj1,nphase);
T3=T3global(:,:,:,:,n);
V6=tensor3op(T3,Vh11,Vh14,Vj5,nphase);
V7=tensor3op(T3,Vh11,Vh15,Vj4,nphase);
V8=tensor3op(T3,Vh14,Vh15,Vj1,nphase);
V9=tensor3op(T3,Vh14,Vh15,Vj1,nphase);
V10=tensor3op(T3,Vh11,Vh45,Vj1,nphase);
V11=tensor3op(T3,VT114,Vj1,Vj5,nphase);
V12=tensor3op(T3,VT115,Vj1,Vj4,nphase);
V13=tensor3op(T3,VT145,Vj1,Vj1,nphase);
VE1=tensor3op(T3,VT111,Vj4,Vj5,nphase);
T2=T2global(:,:,:,n);
V14=tensor2op(T2,VT1114,Vj5,nphase);
V15=tensor2op(T2,VT114,Vh15,nphase);
V16=tensor2op(T2,VT115,Vh14,nphase);
V17=tensor2op(T2,VT111,Vh45,nphase);
V18=tensor2op(T2,VT145,Vh11,nphase);
V19=tensor2op(T2,VT1115,Vj4,nphase);
V20=tensor2op(T2,VT1145,Vj1,nphase);
T1=T1global(:,:,n);
VT21=multilinear5sym(q1,q1,q1,q4,q5,nphase,n-1);
V21=T1*VT21;
vec51=V1+V5+V14+V17+V19+V21;
vec52=3.0*(V2+V3+V4+V6+V7+V8+V9+V10+V11+V12+V13+V15+V16+V18+V20);
vec5=vec51+vec52+VE1;
end
else
Vj1=multilinear1sym(q1,n-1);
Vj2=multilinear1sym(q2,n-1);
Vj3=multilinear1sym(q3,n-1);
Vj4=multilinear1sym(q4,n-1);
Vj5=multilinear1sym(q5,n-1);
Vh12=multilinear2sym(q1,q2,nphase,n-1);
Vh13=multilinear2sym(q1,q3,nphase,n-1);
Vh14=multilinear2sym(q1,q4,nphase,n-1);
Vh15=multilinear2sym(q1,q5,nphase,n-1);
Vh23=multilinear2sym(q2,q3,nphase,n-1);
Vh24=multilinear2sym(q2,q4,nphase,n-1);
Vh25=multilinear2sym(q2,q5,nphase,n-1);
Vh34=multilinear2sym(q3,q4,nphase,n-1);
Vh35=multilinear2sym(q3,q5,nphase,n-1);
Vh45=multilinear2sym(q4,q5,nphase,n-1);
VT123=multilinear3sym(q1,q1,q3,nphase,n-1);
VT135=multilinear3sym(q1,q3,q5,nphase,n-1);
VT134=multilinear3sym(q1,q3,q4,nphase,n-1);
VT124=multilinear3sym(q1,q2,q4,nphase,n-1);
VT145=multilinear3sym(q1,q4,q5,nphase,n-1);
VT125=multilinear3sym(q1,q2,q5,nphase,n-1);
VT234=multilinear3sym(q2,q3,q4,nphase,n-1);
VT235=multilinear3sym(q2,q3,q5,nphase,n-1);
VT345=multilinear3sym(q3,q4,q5,nphase,n-1);
VT245=multilinear3sym(q2,q4,q5,nphase,n-1);
VT1234=multilinear4sym(q1,q2,q3,q4,nphase,n-1);
VT1235=multilinear4sym(q1,q2,q3,q5,nphase,n-1);
VT1345=multilinear4sym(q1,q3,q4,q5,nphase,n-1);
VT1245=multilinear4sym(q1,q2,q4,q5,nphase,n-1);
VT2345=multilinear4sym(q2,q3,q4,q5,nphase,n-1);
T5=T5global(:,:,:,:,:,:,n);
V1=tensor5op(T5,Vj1,Vj2,Vj3,Vj4,Vj5,nphase);
T4=T4global(:,:,:,:,:,n);
V2=tensor4op(T4,Vh12,Vj3,Vj4,Vj5,nphase);
V3=tensor4op(T4,Vh13,Vj2,Vj4,Vj5,nphase);
V4=tensor4op(T4,Vh14,Vj2,Vj3,Vj5,nphase);
V5=tensor4op(T4,Vh15,Vj2,Vj3,Vj4,nphase);
V6=tensor4op(T4,Vh23,Vj1,Vj4,Vj5,nphase);
V7=tensor4op(T4,Vh24,Vj1,Vj3,Vj5,nphase);
V8=tensor4op(T4,Vh25,Vj1,Vj3,Vj4,nphase);
V9=tensor4op(T4,Vh35,Vj1,Vj2,Vj4,nphase);
V10=tensor4op(T4,Vh45,Vj1,Vj2,Vj3,nphase);
V11=tensor4op(T4,Vh34,Vj1,Vj2,Vj5,nphase);
T3=T3global(:,:,:,:,n);
V12=tensor3op(T3,Vh23,Vh14,Vj5,nphase);
V13=tensor3op(T3,Vh23,Vh15,Vj4,nphase);
V14=tensor3op(T3,Vh13,Vh24,Vj5,nphase);
V15=tensor3op(T3,Vh24,Vh15,Vj4,nphase);
V16=tensor3op(T3,Vh13,Vh25,Vj4,nphase);
V17=tensor3op(T3,Vh14,Vh25,Vj3,nphase);
V18=tensor3op(T3,Vh12,Vh34,Vj5,nphase);
V19=tensor3op(T3,Vh34,Vh15,Vj2,nphase);
V20=tensor3op(T3,Vh34,Vh25,Vj1,nphase);
V21=tensor3op(T3,Vh12,Vh35,Vj4,nphase);
V22=tensor3op(T3,Vh14,Vh35,Vj2,nphase);
V23=tensor3op(T3,Vh24,Vh35,Vj1,nphase);
V24=tensor3op(T3,Vh12,Vh45,Vj2,nphase);
V25=tensor3op(T3,Vh13,Vh45,Vj2,nphase);
V26=tensor3op(T3,Vh23,Vh45,Vj1,nphase);%
V27=tensor3op(T3,VT124,Vj3,Vj5,nphase);
V28=tensor3op(T3,VT125,Vj3,Vj4,nphase);
V29=tensor3op(T3,VT134,Vj2,Vj5,nphase);
V30=tensor3op(T3,VT234,Vj1,Vj5,nphase);
V31=tensor3op(T3,VT135,Vj2,Vj4,nphase);
V32=tensor3op(T3,VT235,Vj1,Vj4,nphase);
V33=tensor3op(T3,VT145,Vj2,Vj3,nphase);
V34=tensor3op(T3,VT245,Vj1,Vj3,nphase);
V35=tensor3op(T3,VT345,Vj1,Vj2,nphase);
T2=T2global(:,:,:,n);
V36=tensor2op(T2,VT1234,Vj5,nphase);
V37=tensor2op(T2,VT234,Vh15,nphase);
V38=tensor2op(T2,VT125,Vh34,nphase);
V39=tensor2op(T2,VT134,Vh25,nphase);
V40=tensor2op(T2,VT124,Vh35,nphase);
V41=tensor2op(T2,VT123,Vh45,nphase);
V42=tensor2op(T2,VT145,Vh23,nphase);
V43=tensor2op(T2,VT245,Vh13,nphase);
V44=tensor2op(T2,VT135,Vh24,nphase);
V45=tensor2op(T2,VT235,Vh14,nphase);
V46=tensor2op(T2,VT345,Vh12,nphase);
V47=tensor2op(T2,VT1235,Vj4,nphase);
V48=tensor2op(T2,VT1245,Vj3,nphase);
V49=tensor2op(T2,VT1345,Vj2,nphase);
V50=tensor2op(T2,VT2345,Vj1,nphase);
VE1=tensor3op(T3,VT123,Vj4,Vj5,nphase);
T1=T1global(:,:,n);
VT51=multilinear5sym(q1,q2,q3,q4,q5,nphase,n-1);
V51=T1*VT51;
vec51=V1+V2+V3+V4+V5+V6+V7+V8+V9+V10+V11+V12+V13+V14+V15+V16+V17+V18;
vec52=V19+V20+V21+V22+V23+V24+V25+V26+V27+V28+V29+V30+V31+V32+V33+V34+V35+V36;
vec53=V37+V38+V39+V40+V41+V42+V43+V44+V45+V46+V47+V48+V49+V50+V51;
vec5=vec51+vec52+vec53+VE1;
end
end
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