fsolve function not solving nonlinear equations, I had observed "Invalid datatype. Options argument must be created with OPTIMOPTIONS"; could you assist me, pse

DESCRIPTIO OF TASK

function [FN, Q, y] = mag2(Q0, y0)

ee=0.04; vs=0.00000131; D=[0.220, 0.097, 0.110, 0.220, 0.247, 0.0247, 0.353]; L=[900,400,400,800,500,900,400];

FUN = @(Q,y)[Q(1)-Q(2)-0.03; Q(2)+Q(6)-Q(3)-0.04; Q(3)+Q(4)-0.035; Q(5)-Q(4)-0.01; Q(7)-Q(6)-Q(5)-0.015; ...

1/(y(1)).^0.5+4*log(ee./(3.7*D(1,1))+2.54*3.14*D(1,1)*vs./(4*Q(1)*(y(1)).^0.5)); 1/(y(2)).^0.5+4*log(ee./(3.7*D(1,2))+2.54*3.14*D(1,2)*vs./(4*Q(2)*(y(2)).^0.5));...

1/(y(3)).^0.5+4*log(ee./(3.7*D(1,3))+2.54*3.14*D(1,3)*vs./(4*Q(3)*(y(3)).^0.5)); 1/(y(4)).^0.5+4*log(ee./(3.7*D(1,4))+2.54*3.14*D(1,4)*vs./(4*Q(4)*(y(4)).^0.5));...

1/(y(5)).^0.5+4*log(ee./(3.7*D(1,5))+2.54*3.14*D(1,5)*vs./(4*Q(5)*(y(5)).^0.5)); 1/(y(6)).^0.5+4*log(ee./(3.7*D(1,6))+2.54*3.14*D(1,6)*vs./(4*Q(6)*(y(6)).^0.5));...

1/(y(7)).^0.5+4*log(ee./(3.7*D(1,7))+2.54*3.14*D(1,7)*vs./(4*Q(7)*(y(7)).^0.5));...

Q(1)*abs(y(1)*8*L(1,1)*Q(1)./(9.81*3.14.^2*D(1,1).^5))+Q(2)*abs(y(2)*8*L(1,2)*Q(2)./(9.81*3.14.^2*D(1,2).^5)) ...

-Q(6)*abs(y(6)*8*L(1,6)*Q(6)./(9.81*3.14.^2*D(1,6).^5))+Q(7)*abs(y(7)*8*L(1,7)*Q(7)./(9.81*3.14.^2*D(1,7).^5)); ...

Q(3)*abs(y(3)*8*L(1,3)*Q(3)./(9.81*3.14.^2*D(1,3).^5))-Q(4)*abs(y(4)*8*L(1,4)*Q(4)./(9.81*3.14.^2*D(1,4).^5))...

+Q(6)*abs(y(6)*8*L(1,6)*Q(6)./(9.81*3.14.^2*D(1,6).^5))-Q(5)*abs(y(5)*8*L(1,5)*Q(5)./(9.81*3.14.^2*D(1,5).^5))];

options = optimoptions('fsolve','Display','iter');

[Q,y]=fsolve(FUN,Q0,y0,options);

end

Q0=[-0.15, 0.15]; y0=[0.00001, 0.1]; mag2(Q0, y0)

THE OUTPUT, I GOT

Error using fsolve

Invalid datatype. Options argument must be created with OPTIMOPTIONS.

Error in mag2 (line 15)

[Q,y]=fsolve(FUN,Q0,y0,options);

[Eng.]

Hi Star

any option, pse; seems fsolve cant solve!!!

[Torsten]

You have 14 unknowns (Q(1)-Q(7), y(1)-y(7)), but only 12 equations. Is this intentionally ?

[Star Strider]

@Eng. —

First, I do not know what ‘fsolve can’t solve’ means. What code are you using? Did you make the changes that I suggested (or something similar)?

Second, note @Torsten’s Comment. If there are fewer equations than parameters, the estimated parameters will not be unique.

Answer 1

[Star Strider]

One problem is that fsolve wants the initial parameter estimates as a single vector, and the third argument is the ‘options’ structure. I initially combined ‘Q0’ and‘y0’ into a single vector to successfully solve the ‘options’ problem. However, then the indexing of ‘Q’ became an issue. Note that ‘Q0’ and‘y0’ only have two elements, however your code addresses at least six elements in each.

You probably need to do sometning like this:

Q0 = rand(1,6)

y0 = rand(1,6);

Qy = [Q0; y0];

[Q,y]=fsolve(FUN,Qy,options);

so that ‘Q1’ becomes ‘Qy(1,1)’ , ‘Q(2)’ becomes ‘Qy(1,2)’ , ‘y(1)’ becomes ‘Qy(2,1)’ and so for the rest. I leave that to you. If there are no other problems in your code, that should work.

Q0=[-0.15, 0.15]; y0=[0.00001, 0.1]; mag2(Q0, y0)

Index exceeds the number of array elements. Index must not exceed 4.

Error in solution>@(Q,y)[Q(1)-Q(2)-0.03;Q(2)+Q(6)-Q(3)-0.04;Q(3)+Q(4)-0.035;Q(5)-Q(4)-0.01;Q(7)-Q(6)-Q(5)-0.015;1/(y(1)).^0.5+4*log(ee./(3.7*D(1,1))+2.54*3.14*D(1,1)*vs./(4*Q(1)*(y(1)).^0.5));1/(y(2)).^0.5+4*log(ee./(3.7*D(1,2))+2.54*3.14*D(1,2)*vs./(4*Q(2)*(y(2)).^0.5));1/(y(3)).^0.5+4*log(ee./(3.7*D(1,3))+2.54*3.14*D(1,3)*vs./(4*Q(3)*(y(3)).^0.5));1/(y(4)).^0.5+4*log(ee./(3.7*D(1,4))+2.54*3.14*D(1,4)*vs./(4*Q(4)*(y(4)).^0.5));1/(y(5)).^0.5+4*log(ee./(3.7*D(1,5))+2.54*3.14*D(1,5)*vs./(4*Q(5)*(y(5)).^0.5));1/(y(6)).^0.5+4*log(ee./(3.7*D(1,6))+2.54*3.14*D(1,6)*vs./(4*Q(6)*(y(6)).^0.5));1/(y(7)).^0.5+4*log(ee./(3.7*D(1,7))+2.54*3.14*D(1,7)*vs./(4*Q(7)*(y(7)).^0.5));Q(1)*abs(y(1)*8*L(1,1)*Q(1)./(9.81*3.14.^2*D(1,1).^5))+Q(2)*abs(y(2)*8*L(1,2)*Q(2)./(9.81*3.14.^2*D(1,2).^5)),-Q(6)*abs(y(6)*8*L(1,6)*Q(6)./(9.81*3.14.^2*D(1,6).^5))+Q(7)*abs(y(7)*8*L(1,7)*Q(7)./(9.81*3.14.^2*D(1,7).^5));Q(3)*abs(y(3)*8*L(1,3)*Q(3)./(9.81*3.14.^2*D(1,3).^5))-Q(4)*abs(y(4)*8*L(1,4)*Q(4)./(9.81*3.14.^2*D(1,4).^5)),+Q(6)*abs(y(6)*8*L(1,6)*Q(6)./(9.81*3.14.^2*D(1,6).^5))-Q(5)*abs(y(5)*8*L(1,5)*Q(5)./(9.81*3.14.^2*D(1,5).^5))] (line 5)
FUN = @(Q,y)[Q(1)-Q(2)-0.03; Q(2)+Q(6)-Q(3)-0.04; Q(3)+Q(4)-0.035; Q(5)-Q(4)-0.01; Q(7)-Q(6)-Q(5)-0.015; ...

Error in fsolve (line 270)
fuser = feval(funfcn{3},x,varargin{:});

Error in solution>mag2 (line 16)
[Q,y]=fsolve(FUN,[Q0,y0],options);

Caused by:
Failure in initial objective function evaluation. FSOLVE cannot continue.

function [FN, Q, y] = mag2(Q0, y0)
    ee=0.04;     vs=0.00000131;             D=[0.220,  0.097,  0.110, 0.220,  0.247,  0.0247, 0.353];     L=[900,400,400,800,500,900,400]; 
   FUN = @(Qy)[Q(1)-Q(2)-0.03;...
               Q(2)+Q(6)-Q(3)-0.04;...      
               Q(3)+Q(4)-0.035;...      
               Q(5)-Q(4)-0.01; Q(7)-Q(6)-Q(5)-0.015; ...
               1/(y(1)).^0.5+4*log(ee./(3.7*D(1,1))+2.54*3.14*D(1,1)*vs./...
               (4*Q(1)*(y(1)).^0.5));...
               1/(y(2)).^0.5+4*log(ee./(3.7*D(1,2))+2.54*3.14*D(1,2)*vs./...
               (4*Q(2)*(y(2)).^0.5));...
               1/(y(3)).^0.5+4*log(ee./(3.7*D(1,3))+2.54*3.14*D(1,3)*vs....
               /(4*Q(3)*(y(3)).^0.5));...    
               1/(y(4)).^0.5+4*log(ee./(3.7*D(1,4))+2.54*3.14*D(1,4)*vs./ ...
               (4*Q(4)*(y(4)).^0.5));...
               1/(y(5)).^0.5+4*log(ee./(3.7*D(1,5))+2.54*3.14*D(1,5)*vs./...
               (4*Q(5)*(y(5)).^0.5));...
               1/(y(6)).^0.5+4*log(ee./(3.7*D(1,6))+2.54*3.14*D(1,6)*vs./ ...
               (4*Q(6)*(y(6)).^0.5));...
               1/(y(7)).^0.5+4*log(ee./(3.7*D(1,7))+2.54*3.14*D(1,7)*vs./...
               (4*Q(7)*(y(7)).^0.5));...
               Q(1)*abs(y(1)*8*L(1,1)*Q(1)./(9.81*3.14.^2*D(1,1).^5))+...
               Q(2)*abs(y(2)*8*L(1,2)*Q(2)./(9.81*3.14.^2*D(1,2).^5))-...
               Q(6)*abs(y(6)*8*L(1,6)*Q(6)./(9.81*3.14.^2*D(1,6).^5))+...
               Q(7)*abs(y(7)*8*L(1,7)*Q(7)./(9.81*3.14.^2*D(1,7).^5)); ...    
               Q(3)*abs(y(3)*8*L(1,3)*Q(3)./(9.81*3.14.^2*D(1,3).^5))-...
               Q(4)*abs(y(4)*8*L(1,4)*Q(4)./(9.81*3.14.^2*D(1,4).^5))+...
               Q(6)*abs(y(6)*8*L(1,6)*Q(6)./(9.81*3.14.^2*D(1,6).^5))-...
               Q(5)*abs(y(5)*8*L(1,5)*Q(5)./(9.81*3.14.^2*D(1,5).^5))];  
   options = optimoptions('fsolve','Display','iter');
   % [Q,y]=fsolve(FUN,Q0,y0,options);
   Q0 = rand(1,6)
   y0 = rand(1,6);
   Qy = [Q0; y0];
   [Q,y]=fsolve(FUN,Qy,options);
end

.

[Eng.]

Hi Torsten

First of all appreciated the way you have advice me, but unfortunately dont known how to go and combine Q-y; furthermore, I have 14 eqns and 14 unknown (5 linear eqns, and 7 and 2 nonlinera eqns). Would you assist the remaining task, pse.

Thanks

[Eng.]

Moreover, y>0

[Torsten]

And where are equations (13)-(14) ? Your function FUN returns a 12x1 vector.

[Star Strider]

@Eng. —

I demonstrated a way to combine ‘Q’ and ‘y’ and how to refer to them in the equations in my original Answer.

[Eng.]

Well, thanks alot, Star S; I have successfully coded Qy in singly termed variable in 14 eqns, and absolotely answered within appropriate Trust Region Simulation model.

Thanks

[Alex Sha]

refer to the results below:

q1: 0.0469485401123028
q2: 0.0169485400700552
q6: 0.000149927973562496
q3: -0.0229015319578391
q4: 0.0579015318964189
q5: 0.0679015321342485
q7: 0.0830514600277715
y1: 0.00689798266403546
y2: 0.012995928970676
y3: 0.0116007205080187
y4: 0.00689539239643874
y5: 0.00639537063426373
y6: 0.0922685733214674
y7: 0.00515822449799586

[Star Strider]

@Eng. — As always, my pleasure!

I am happy that it works for you!

For our interest, would it be possible fo you to post the working code?