Newton-Rapson method problem
Show older comments
Dear MATLAB professionnals, I have one problem, and I would appreciate any help: I'm trying to apply the Newton Rapson method to a function Fx(q1,q2,q3,q4,q5) : using the initial guess: q1=1.4149; q2=-2.2620; q3=-0.1296; q4=2.5791; q5=1.9264;
q4=q4-pi/2;
but unexpectably, my method diverge... I really don't understand why.. because seems like i'm doing everything right. Please, can you see a little my code. Thank you.
p.s.
the initial guess and input parameters are surely correct.
Code:
lx =0.040970753763384423762339281438472 ly =0.07266173178751561545496429062041 lz =0.99651476159146734623561769694788 mx =0.10065200218161578227249464134729 my =0.99197864781133593403694703738438 mz =-0.076469188195151485687439674165944 nx =-0.99407774937018489325168957293499 ny =0.10343420623774618460899432648148 nz =0.033328564131616292276483193290915 px =0.037841706328807789283530382817844 py =0.58006500641103753146410326735349 pz =2.0389844182682974604858827660792
q1=1.4149;
q2=-2.2620;
q3=-0.1296;
q4=2.5791;
q5=1.9264;
q4=q4-pi/2;
for i=1:5
Fx = [...
nz*sin(q2) - nx*(cos(q1)*cos(q2) - (4967757600021511*sin(q1)*sin(q2))/81129638414606681695789005144064) - ny*((4967757600021511*cos(q1)*sin(q2))/81129638414606681695789005144064 + cos(q2)*sin(q1)) - sin(q3)/4 - (3^(1/2)*sin(q5)*(cos(q3)*cos(q4) - (4967757600021511*sin(q3)*sin(q4))/81129638414606681695789005144064))/2 + (3^(1/2)*cos(q3)*sin(q4))/4 + (4967757600021511*3^(1/2)*cos(q4)*sin(q3))/324518553658426726783156020576256 - (3^(1/2)*cos(q5)*((cos(q3)*sin(q4))/2 + (620969700002689*cos(q4)*sin(q3))/20282409603651670423947251286016 + (3^(1/2)*sin(q3))/2))/2;...
cos(q3)/4 + nx*(cos(q1)*sin(q2) + (4967757600021511*cos(q2)*sin(q1))/81129638414606681695789005144064) - ny*((4967757600021511*cos(q1)*cos(q2))/81129638414606681695789005144064 - sin(q1)*sin(q2)) + nz*cos(q2) - (3^(1/2)*sin(q5)*((4967757600021511*cos(q3)*sin(q4))/81129638414606681695789005144064 + cos(q4)*sin(q3)))/2 - (4967757600021511*3^(1/2)*cos(q3)*cos(q4))/324518553658426726783156020576256 + (3^(1/2)*cos(q5)*((620969700002689*cos(q3)*cos(q4))/20282409603651670423947251286016 - (sin(q3)*sin(q4))/2 + (3^(1/2)*cos(q3))/2))/2 + (3^(1/2)*sin(q3)*sin(q4))/4;...
(3^(1/2)*cos(q4))/4 - (4967757600021511*nz)/81129638414606681695789005144064 - ny*cos(q1) + nx*sin(q1) - (3^(1/2)*cos(q5)*(cos(q4)/2 - 8604408562923685/162259276829213363391578010288128))/2 + (3^(1/2)*sin(q4)*sin(q5))/2 + 620969700002689/40564819207303340847894502572032;...
(9*cos(q2))/20 - px*(cos(q1)*cos(q2) - (4967757600021511*sin(q1)*sin(q2))/81129638414606681695789005144064) - py*((4967757600021511*cos(q1)*sin(q2))/81129638414606681695789005144064 + cos(q2)*sin(q1)) - sin(q3)*((171*cos(q5))/4000 + (3557011297428607*3^(1/2))/144115188075855872 - (3557011297428607*3^(1/2)*cos(q5))/144115188075855872 + 5657/4000) + (4967757600021511*sin(q3)*((10671033892285821*cos(q4))/144115188075855872 + (3557011297428607*cos(q4)*cos(q5))/144115188075855872 - (3557011297428607*sin(q4)*sin(q5))/72057594037927936 + (57*3^(1/2)*cos(q4))/4000 - (57*3^(1/2)*cos(q4)*cos(q5))/4000 + (57*3^(1/2)*sin(q4)*sin(q5))/2000))/81129638414606681695789005144064 + pz*sin(q2) + cos(q3)*((10671033892285821*sin(q4))/144115188075855872 + (3557011297428607*cos(q4)*sin(q5))/72057594037927936 + (3557011297428607*cos(q5)*sin(q4))/144115188075855872 + (57*3^(1/2)*sin(q4))/4000 - (57*3^(1/2)*cos(q4)*sin(q5))/2000 - (57*3^(1/2)*cos(q5)*sin(q4))/4000 + 27/100) + 19/20;...
cos(q3)*((171*cos(q5))/4000 + (3557011297428607*3^(1/2))/144115188075855872 - (3557011297428607*3^(1/2)*cos(q5))/144115188075855872 + 5657/4000) - (9*sin(q2))/20 + px*(cos(q1)*sin(q2) + (4967757600021511*cos(q2)*sin(q1))/81129638414606681695789005144064) - py*((4967757600021511*cos(q1)*cos(q2))/81129638414606681695789005144064 - sin(q1)*sin(q2)) - (4967757600021511*cos(q3)*((10671033892285821*cos(q4))/144115188075855872 + (3557011297428607*cos(q4)*cos(q5))/144115188075855872 - (3557011297428607*sin(q4)*sin(q5))/72057594037927936 + (57*3^(1/2)*cos(q4))/4000 - (57*3^(1/2)*cos(q4)*cos(q5))/4000 + (57*3^(1/2)*sin(q4)*sin(q5))/2000))/81129638414606681695789005144064 + pz*cos(q2) + sin(q3)*((10671033892285821*sin(q4))/144115188075855872 + (3557011297428607*cos(q4)*sin(q5))/72057594037927936 + (3557011297428607*cos(q5)*sin(q4))/144115188075855872 + (57*3^(1/2)*sin(q4))/4000 - (57*3^(1/2)*cos(q4)*sin(q5))/2000 - (57*3^(1/2)*cos(q5)*sin(q4))/4000 + 27/100)]
JacFx =[...
[ nx*((4967757600021511*cos(q1)*sin(q2))/81129638414606681695789005144064 + cos(q2)*sin(q1)) - ny*(cos(q1)*cos(q2) - (4967757600021511*sin(q1)*sin(q2))/81129638414606681695789005144064), nx*(cos(q1)*sin(q2) + (4967757600021511*cos(q2)*sin(q1))/81129638414606681695789005144064) - ny*((4967757600021511*cos(q1)*cos(q2))/81129638414606681695789005144064 - sin(q1)*sin(q2)) + nz*cos(q2), (8604408562923685*cos(q3)*cos(q4))/324518553658426726783156020576256 - cos(q3)/4 + (3^(1/2)*sin(q5)*((4967757600021511*cos(q3)*sin(q4))/81129638414606681695789005144064 + cos(q4)*sin(q3)))/2 - (3^(1/2)*cos(q5)*((620969700002689*cos(q3)*cos(q4))/20282409603651670423947251286016 - (sin(q3)*sin(q4))/2 + (3^(1/2)*cos(q3))/2))/2 - (3^(1/2)*sin(q3)*sin(q4))/4, (3^(1/2)*sin(q5)*(cos(q3)*sin(q4) + (4967757600021511*cos(q4)*sin(q3))/81129638414606681695789005144064))/2 - (8604408562923685*sin(q3)*sin(q4))/324518553658426726783156020576256 + (3^(1/2)*cos(q3)*cos(q4))/4 - (3^(1/2)*cos(q5)*((cos(q3)*cos(q4))/2 - (620969700002689*sin(q3)*sin(q4))/20282409603651670423947251286016))/2, (3^(1/2)*sin(q5)*((cos(q3)*sin(q4))/2 + (620969700002689*cos(q4)*sin(q3))/20282409603651670423947251286016 + (3^(1/2)*sin(q3))/2))/2 - (3^(1/2)*cos(q5)*(cos(q3)*cos(q4) - (4967757600021511*sin(q3)*sin(q4))/81129638414606681695789005144064))/2];...
[ nx*((4967757600021511*cos(q1)*cos(q2))/81129638414606681695789005144064 - sin(q1)*sin(q2)) + ny*(cos(q1)*sin(q2) + (4967757600021511*cos(q2)*sin(q1))/81129638414606681695789005144064), nx*(cos(q1)*cos(q2) - (4967757600021511*sin(q1)*sin(q2))/81129638414606681695789005144064) + ny*((4967757600021511*cos(q1)*sin(q2))/81129638414606681695789005144064 + cos(q2)*sin(q1)) - nz*sin(q2), (8604408562923685*cos(q4)*sin(q3))/324518553658426726783156020576256 - sin(q3)/4 - (3^(1/2)*sin(q5)*(cos(q3)*cos(q4) - (4967757600021511*sin(q3)*sin(q4))/81129638414606681695789005144064))/2 + (3^(1/2)*cos(q3)*sin(q4))/4 - (3^(1/2)*cos(q5)*((cos(q3)*sin(q4))/2 + (620969700002689*cos(q4)*sin(q3))/20282409603651670423947251286016 + (3^(1/2)*sin(q3))/2))/2, (8604408562923685*cos(q3)*sin(q4))/324518553658426726783156020576256 - (3^(1/2)*sin(q5)*((4967757600021511*cos(q3)*cos(q4))/81129638414606681695789005144064 - sin(q3)*sin(q4)))/2 + (3^(1/2)*cos(q4)*sin(q3))/4 - (3^(1/2)*cos(q5)*((620969700002689*cos(q3)*sin(q4))/20282409603651670423947251286016 + (cos(q4)*sin(q3))/2))/2, - (3^(1/2)*cos(q5)*((4967757600021511*cos(q3)*sin(q4))/81129638414606681695789005144064 + cos(q4)*sin(q3)))/2 - (3^(1/2)*sin(q5)*((620969700002689*cos(q3)*cos(q4))/20282409603651670423947251286016 - (sin(q3)*sin(q4))/2 + (3^(1/2)*cos(q3))/2))/2];...
[ nx*cos(q1) + ny*sin(q1), 0, 0, (3^(1/2)*cos(q4)*sin(q5))/2 - (3^(1/2)*sin(q4))/4 + (3^(1/2)*cos(q5)*sin(q4))/4, (3^(1/2)*sin(q5)*(cos(q4)/2 - 8604408562923685/162259276829213363391578010288128))/2 + (3^(1/2)*cos(q5)*sin(q4))/2];...
[ px*((4967757600021511*cos(q1)*sin(q2))/81129638414606681695789005144064 + cos(q2)*sin(q1)) - py*(cos(q1)*cos(q2) - (4967757600021511*sin(q1)*sin(q2))/81129638414606681695789005144064), px*(cos(q1)*sin(q2) + (4967757600021511*cos(q2)*sin(q1))/81129638414606681695789005144064) - (9*sin(q2))/20 - py*((4967757600021511*cos(q1)*cos(q2))/81129638414606681695789005144064 - sin(q1)*sin(q2)) + pz*cos(q2), (4967757600021511*cos(q3)*((2667758473071455*cos(q4))/36028797018963968 + (3557011297428607*cos(q4)*cos(q5))/144115188075855872 - (3557011297428607*sin(q4)*sin(q5))/72057594037927936 + (57*3^(1/2)*cos(q4))/4000 - (57*3^(1/2)*cos(q4)*cos(q5))/4000 + (57*3^(1/2)*sin(q4)*sin(q5))/2000))/81129638414606681695789005144064 - cos(q3)*((33*cos(q5))/9007199254740992000 + 1457/1000) - sin(q3)*((2667758473071455*sin(q4))/36028797018963968 + (3557011297428607*cos(q4)*sin(q5))/72057594037927936 + (3557011297428607*cos(q5)*sin(q4))/144115188075855872 + (57*3^(1/2)*sin(q4))/4000 - (57*3^(1/2)*cos(q4)*sin(q5))/2000 - (57*3^(1/2)*cos(q5)*sin(q4))/4000 + 27/100), cos(q3)*((2667758473071455*cos(q4))/36028797018963968 + (3557011297428607*cos(q4)*cos(q5))/144115188075855872 - (3557011297428607*sin(q4)*sin(q5))/72057594037927936 + (57*3^(1/2)*cos(q4))/4000 - (57*3^(1/2)*cos(q4)*cos(q5))/4000 + (57*3^(1/2)*sin(q4)*sin(q5))/2000) - (4967757600021511*sin(q3)*((2667758473071455*sin(q4))/36028797018963968 + (3557011297428607*cos(q4)*sin(q5))/72057594037927936 + (3557011297428607*cos(q5)*sin(q4))/144115188075855872 + (57*3^(1/2)*sin(q4))/4000 - (57*3^(1/2)*cos(q4)*sin(q5))/2000 - (57*3^(1/2)*cos(q5)*sin(q4))/4000))/81129638414606681695789005144064, (33*sin(q3)*sin(q5))/9007199254740992000 + cos(q3)*((3557011297428607*cos(q4)*cos(q5))/72057594037927936 - (3557011297428607*sin(q4)*sin(q5))/144115188075855872 - (57*3^(1/2)*cos(q4)*cos(q5))/2000 + (57*3^(1/2)*sin(q4)*sin(q5))/4000) - (4967757600021511*sin(q3)*((3557011297428607*cos(q4)*sin(q5))/144115188075855872 + (3557011297428607*cos(q5)*sin(q4))/72057594037927936 - (57*3^(1/2)*cos(q4)*sin(q5))/4000 - (57*3^(1/2)*cos(q5)*sin(q4))/2000))/81129638414606681695789005144064];...
[ px*((4967757600021511*cos(q1)*cos(q2))/81129638414606681695789005144064 - sin(q1)*sin(q2)) + py*(cos(q1)*sin(q2) + (4967757600021511*cos(q2)*sin(q1))/81129638414606681695789005144064), px*(cos(q1)*cos(q2) - (4967757600021511*sin(q1)*sin(q2))/81129638414606681695789005144064) - (9*cos(q2))/20 + py*((4967757600021511*cos(q1)*sin(q2))/81129638414606681695789005144064 + cos(q2)*sin(q1)) - pz*sin(q2), (4967757600021511*sin(q3)*((2667758473071455*cos(q4))/36028797018963968 + (3557011297428607*cos(q4)*cos(q5))/144115188075855872 - (3557011297428607*sin(q4)*sin(q5))/72057594037927936 + (57*3^(1/2)*cos(q4))/4000 - (57*3^(1/2)*cos(q4)*cos(q5))/4000 + (57*3^(1/2)*sin(q4)*sin(q5))/2000))/81129638414606681695789005144064 - sin(q3)*((33*cos(q5))/9007199254740992000 + 1457/1000) + cos(q3)*((2667758473071455*sin(q4))/36028797018963968 + (3557011297428607*cos(q4)*sin(q5))/72057594037927936 + (3557011297428607*cos(q5)*sin(q4))/144115188075855872 + (57*3^(1/2)*sin(q4))/4000 - (57*3^(1/2)*cos(q4)*sin(q5))/2000 - (57*3^(1/2)*cos(q5)*sin(q4))/4000 + 27/100), sin(q3)*((2667758473071455*cos(q4))/36028797018963968 + (3557011297428607*cos(q4)*cos(q5))/144115188075855872 - (3557011297428607*sin(q4)*sin(q5))/72057594037927936 + (57*3^(1/2)*cos(q4))/4000 - (57*3^(1/2)*cos(q4)*cos(q5))/4000 + (57*3^(1/2)*sin(q4)*sin(q5))/2000) + (4967757600021511*cos(q3)*((2667758473071455*sin(q4))/36028797018963968 + (3557011297428607*cos(q4)*sin(q5))/72057594037927936 + (3557011297428607*cos(q5)*sin(q4))/144115188075855872 + (57*3^(1/2)*sin(q4))/4000 - (57*3^(1/2)*cos(q4)*sin(q5))/2000 - (57*3^(1/2)*cos(q5)*sin(q4))/4000))/81129638414606681695789005144064, (4967757600021511*cos(q3)*((3557011297428607*cos(q4)*sin(q5))/144115188075855872 + (3557011297428607*cos(q5)*sin(q4))/72057594037927936 - (57*3^(1/2)*cos(q4)*sin(q5))/4000 - (57*3^(1/2)*cos(q5)*sin(q4))/2000))/81129638414606681695789005144064 - (33*cos(q3)*sin(q5))/9007199254740992000 + sin(q3)*((3557011297428607*cos(q4)*cos(q5))/72057594037927936 - (3557011297428607*sin(q4)*sin(q5))/144115188075855872 - (57*3^(1/2)*cos(q4)*cos(q5))/2000 + (57*3^(1/2)*sin(q4)*sin(q5))/4000)]]
DeltX=JacFx\(-Fx)
q1=q1+DeltX(1);
q2=q1+DeltX(2);
q3=q3+DeltX(3);
q4=q4+DeltX(4);
q5=q5+DeltX(5);
end
Answers (0)
Categories
Find more on Problem-Based Optimization Setup in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!
