Asked by nasrin
on 25 Jul 2012

to solve this equation "f = a+b θs + c θv cos(φ)" : unknowns are : f, a, b & c i am working on space image and can calculate θs, θv & φ for all pixel of image so i can write a lot of equation. and there are 2 constraint :

How do I solve this system of equations?

Answer by Sargondjani
on 25 Jul 2012

i think fmincon (constrained optimization) will work best... if you try to minimize some error use as the objective: objective=error^2.

if you dont have the optimization toolbox you can try fminsearchcon from the file exchange (but this only works properly for a couple of variables at most)

note that fmincon can only find one local solution and it requires a continuous function + continuous derivate. if not continuous, then you should try genetic algorithm

nasrin
on 25 Jul 2012

Sargondjani
on 31 Jul 2012

fminsearchcon does exist in the 'file exchange', ie. you have to download it.

MJTHDSN
on 12 Apr 2018

Dear Matlabers,

I have a similar question but a little bit confusing. Let`s assume we have 6 equations as below:

EQ1:a{{(L^2)*(Z^2)+(L^2)*(M^2)-2*L*(Z^2)+(Z^2)}}=(L^2)*(T^2)-2*L*(T^2)+ (T^2)-(2*L*T*B)+(T*B)+(B^2)

EQ2: b{{(L^2)*(Z^2)+(L^2)*(M^2)-2*L*(Z^2)+(Z^2)}}=(L^2)*(T^2)+(2*L*T*B)+(B^2)

EQ3: c{{(L^2)*(Z^2)+(L^2)*(M^2)-2*L*(Z^2)+(Z^2)}}=(T^2)+(2*T*B)+(B^2)

EQ4:d{{(L^2)*(Z^2)+(L^2)*(M^2)-2*L*(Z^2)+(Z^2)}}=(L^2)*(T^2)-2*L*(T^2)+ (T^2)-(2*L*T*B)-(T*B)+(B^2)

EQ5: e{{(L^2)*(Z^2)+(L^2)*(M^2)-2*L*(Z^2)+(Z^2)}}=(L^2)*(T^2)-(2*L*T*B)+(B^2)

EQ6: f{{(L^2)*(Z^2)+(L^2)*(M^2)-2*L*(Z^2)+(Z^2)}}=(T^2)-(2*T*B)+(B^2)

in the equations above a,b,c,d,e and f are the numerical known values (0.543 for example). So we have 6 equations with 5 unknowns as L, Z, M, T and B.

Can you please give me cues how to solve the equations to find these unknowns using MATLAB.

Best Regards,

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## 4 Comments

## Greg Heath (view profile)

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## Greg Heath (view profile)

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## Jan (view profile)

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## nasrin (view profile)

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