CODEWITHSUNDEEP
matlab
Achraf Ahmed Belkhiria
Achraf Ahmed Belkhiria

Reputation: 80

Solving non linear equations in Matlab

consider the following equations :

eqn1 =


    sin(t6)*(cos(t4)*sin(t1) + sin(t4)*(cos(t1)*sin(t2)*sin(t3) - cos(t1)*cos(t2)*cos(t3))) + cos(t6)*(cos(t5)*(sin(t1)*sin(t4) - cos(t4)*(cos(t1)*sin(t2)*sin(t3) - cos(t1)*cos(t2)*cos(t3))) - sin(t5)*(cos(t1)*cos(t2)*sin(t3) + cos(t1)*cos(t3)*sin(t2))) == 1


eqn2 =


    cos(t6)*(cos(t4)*sin(t1) + sin(t4)*(cos(t1)*sin(t2)*sin(t3) - cos(t1)*cos(t2)*cos(t3))) - sin(t6)*(cos(t5)*(sin(t1)*sin(t4) - cos(t4)*(cos(t1)*sin(t2)*sin(t3) - cos(t1)*cos(t2)*cos(t3))) - sin(t5)*(cos(t1)*cos(t2)*sin(t3) + cos(t1)*cos(t3)*sin(t2))) == 0


eqn3 =


    - sin(t5)*(sin(t1)*sin(t4) - cos(t4)*(cos(t1)*sin(t2)*sin(t3) - cos(t1)*cos(t2)*cos(t3))) - cos(t5)*(cos(t1)*cos(t2)*sin(t3) + cos(t1)*cos(t3)*sin(t2)) == 0


eqn4 =


    cos(t1)/100 + (19*cos(t1)*cos(t2))/100 - (21*cos(t1)*sin(t2)*sin(t3))/1000 + (21*cos(t1)*cos(t2)*cos(t3))/1000 - (219*cos(t1)*cos(t2)*sin(t3))/1000 - (219*cos(t1)*cos(t3)*sin(t2))/1000 == 619/1000


eqn5 =


    - sin(t6)*(cos(t1)*cos(t4) - sin(t4)*(sin(t1)*sin(t2)*sin(t3) - cos(t2)*cos(t3)*sin(t1))) - cos(t6)*(cos(t5)*(cos(t1)*sin(t4) + cos(t4)*(sin(t1)*sin(t2)*sin(t3) - cos(t2)*cos(t3)*sin(t1))) + sin(t5)*(cos(t2)*sin(t1)*sin(t3) + cos(t3)*sin(t1)*sin(t2))) == 0


eqn6 =


    sin(t6)*(cos(t5)*(cos(t1)*sin(t4) + cos(t4)*(sin(t1)*sin(t2)*sin(t3) - cos(t2)*cos(t3)*sin(t1))) + sin(t5)*(cos(t2)*sin(t1)*sin(t3) + cos(t3)*sin(t1)*sin(t2))) - cos(t6)*(cos(t1)*cos(t4) - sin(t4)*(sin(t1)*sin(t2)*sin(t3) - cos(t2)*cos(t3)*sin(t1))) == 1


eqn7 =


    sin(t5)*(cos(t1)*sin(t4) + cos(t4)*(sin(t1)*sin(t2)*sin(t3) - cos(t2)*cos(t3)*sin(t1))) - cos(t5)*(cos(t2)*sin(t1)*sin(t3) + cos(t3)*sin(t1)*sin(t2)) == 0


eqn8 =


    sin(t1)/100 + (19*cos(t2)*sin(t1))/100 - (219*cos(t2)*sin(t1)*sin(t3))/1000 - (219*cos(t3)*sin(t1)*sin(t2))/1000 - (21*sin(t1)*sin(t2)*sin(t3))/1000 + (21*cos(t2)*cos(t3)*sin(t1))/1000 == 0


eqn9 =


    sin(t4)*sin(t6)*(cos(t2)*sin(t3) + cos(t3)*sin(t2)) - cos(t6)*(sin(t5)*(cos(t2)*cos(t3) - sin(t2)*sin(t3)) + cos(t4)*cos(t5)*(cos(t2)*sin(t3) + cos(t3)*sin(t2))) == 0


eqn10 =


    sin(t6)*(sin(t5)*(cos(t2)*cos(t3) - sin(t2)*sin(t3)) + cos(t4)*cos(t5)*(cos(t2)*sin(t3) + cos(t3)*sin(t2))) + cos(t6)*sin(t4)*(cos(t2)*sin(t3) + cos(t3)*sin(t2)) == 0


eqn11 =


    cos(t4)*sin(t5)*(cos(t2)*sin(t3) + cos(t3)*sin(t2)) - cos(t5)*(cos(t2)*cos(t3) - sin(t2)*sin(t3)) == 1


eqn12 =


    (219*sin(t2)*sin(t3))/1000 - (219*cos(t2)*cos(t3))/1000 - (21*cos(t2)*sin(t3))/1000 - (21*cos(t3)*sin(t2))/1000 - (19*sin(t2))/100 == 261/1000

is there a function that can solve these equations ?

Upvotes: 0

Views: 51

Answers (1)

Jörg
Jörg

Reputation: 71

fminsearch should do the trick.

https://de.mathworks.com/help/matlab/ref/fminsearch.html

Notice that solving non-linear equations may lead to local optima instead of global optima if the problem isn't convex. You can't really be sure to be globally optimal in many practical cases.

You would need to reformulate this to make it a minimization problem though.

f(x)=1 for example could be written as minimize abs(f(x)-1)

Upvotes: 2

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