error using fsolve 'Index exceeds matrix dimensions.' and ' Failure in initial user-supplied objective function evaluation. FSOLVE cannot continue.'

hello all.

I am trying to solve a system of nonlinear equations in a symbolic form using matlabFunction and fsolve but I have an error. Here is the code

eqns=vpa([ eqn_17 ; eqn_18]); %eqn_17 has 5 equations,eqn_18 has 5 equations

t=symvar(eqns); %10 symbolic variables used in eqns

F1=matlabFunction(eqns,'vars',{t}); %return function handle of the 10 eqns

x0=ones(10,1);

[soln,fval,exitflag]=fsolve(F1,x0)

at the last line I have the following error

Index exceeds matrix dimensions.

Error in F:\MATLAB_setup\toolbox\symbolic\symbolic\symengine.p

Error in fsolve (line 241) fuser = feval(funfcn{3},x,varargin{:});

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

I do not understand that. Any help would be appreciated.

Thanks

[Star Strider]

I suggest doing simplify on your eqns variable. It might make subsequent calculations easier.

Look carefully at your t and F1 variables to be sure they make sense. I suspect F1 is not what you believe it to be.

Note that matlabFunction considers subscripted variables in the equations given to it as input arguments to be functions. So instead of treating x as a vector and its elements as discrete variables, it assumes x(1) is a function x() with an argument of 1.

I suggest you experiment with vectorize on your eqns variable, then create your own anonymous function or functions out of them. The behavior of matlabFunction can be different from what you expect.

[annona]

As a simple example I used the following equations to solve:

syms p q
F=[sin(p)*sin(q);q^2+p^2-1]
 t=[p;q]
F1=matlabFunction(F,'vars',{t})

which results in

@(in1)[sin(in1(1,:)).*sin(in1(2,:));in1(1,:).^2+in1(2,:).^2-1.0]

Then I did

x0=rand(2,1)
  [soln,feval]=fsolve(F1,x0)

which gives me the results without any problem

soln =

      0.0000
      1.0000

feval =

     1.0e-07 *

      0.0227
      0.1076

with the same procedure I tried on my complex case but it did not work?? why is that? what is the difference between the two example?

Answer 1

[Star Strider]

The problem I see is that in F1 you define your in1 vector as [1 x 10], then you give it your initial x0 as a [10 x 1] vector, so it threw the error you posted.

You can eliminate the column-vector requirement by changing in1(:,1) ... in1(:,10) to in1(1) ... in1(10), unless you have a specific reason for requiring in1 to be a column vector. With the single subscripts, F1 will be happy with either row or column vectors for in1.

When I run this code:

          F1 = @(in1)[in1(:,1).*-5.592228285836476e11+in1(:,6).*3.34246646076234e10+in1(:,1).*in1(:,6).*4.665753353923766e11+5.338430977835152e10;in1(:,2).*-5.595115494912028e11+in1(:,7).*3.34246646076234e10+in1(:,2).*in1(:,7).*4.665753353923766e11+5.338429087540035e10;in1(:,3).*-5.598175072243341e11+in1(:,8).*3.34246646076234e10+in1(:,3).*in1(:,8).*4.665753353923766e11+5.338427320731596e10;in1(:,4).*-5.601417301942708e11+in1(:,9).*3.34246646076234e10+in1(:,4).*in1(:,9).*4.665753353923766e11+5.338425666965504e10;in1(:,5).*-5.604853082262216e11+in1(:,10).*3.34246646076234e10+in1(:,5).*in1(:,10).*4.665753353923766e11+5.338424116873857e10;in1(:,1).*1.0e12-in1(:,6).*6.791397396184978e10-in1(:,1).*in1(:,6).*9.331506707847532e11+3.232237330148703e7;in1(:,2).*1.0e12-in1(:,7).*6.793060676517363e10-in1(:,2).*in1(:,7).*9.331506707847532e11+4.063877496341306e7;in1(:,3).*1.0e12-in1(:,8).*6.794632422932858e10-in1(:,3).*in1(:,8).*9.331506707847532e11+4.849750704088881e7;in1(:,4).*1.0e12-in1(:,9).*6.795466436527876e10-in1(:,4).*in1(:,9).*9.331506707847532e11+5.266757501597958e7;in1(:,5).*1.0e12-in1(:,10).*6.795074806819398e10-in1(:,5).*in1(:,10).*9.331506707847532e11+5.070942647358813e7];

          x0 = ones(1,10);          % <— NOTE: this is [1 x 10], *NOT* [10 x 1]

          [soln,fval,exitflag]=fsolve(F1,x0)

I get:

soln =

    Columns 1 through 5

     892.7806e-003   888.3838e-003   883.7788e-003   878.9839e-003   874.0104e-003

    Columns 6 through 10

     990.8993e-003   990.5208e-003   990.1217e-003   989.7065e-003   989.2783e-003

fval =

      15.2588e-006
     -38.1470e-006
     -15.2588e-006
       7.6294e-006
     -15.2588e-006
     -26.6433e-006
     156.2238e-006
    -126.8163e-006
     110.4400e-006
      77.3892e-006

exitflag =

       2.0000e+000

A second minimum appears at:

soln =

    Columns 1 through 5

     -73.5049e-003   -73.5340e-003   -73.5614e-003   -73.5757e-003   -73.5685e-003

    Columns 6 through 10

     108.4937e+000   106.8749e+000   105.3948e+000   104.6480e+000   105.0634e+000

fval =

    -534.0576e-006
     -38.1470e-006
      45.7764e-006
    -236.5112e-006
    -198.3643e-006
     705.7786e-006
      -1.4307e-003
      -1.1034e-003
    -621.9819e-006
     -44.6811e-006

exitflag =

       2.0000e+000

Is this what you want or what you were expecting?

[annona]

ohhhhhhhh ... Star Strider you are my hero. You answered me in another question and you did it again ... I cannot thank you enough.

The first result is what I expect but the second is not. When I tried this I did not get a second minimum like you. Only the first answer appeared (which is fine with me). But I want to know the reason why it did not appear just for knowledge.

Another question please for you to confirm. The order of soln is the same as I entered in t variable in the third line. right?

    eqns=simplify(vpa([ eqn_17 ; eqn_18]));
    t=symvar(eqns);
    F1=matlabFunction(eqns,'vars',{t});
    x0=ones(1,2*(2*M+1));
    [soln,fval,exitflag]=fsolve(F1,x0)

Thanks again

[Star Strider]

Thank you! It is always my pleasure to help!

To get the other minima, start at a different initial guess. (I usually search for several, because there are usually more than one. That explains the 100000 multiplier, since I added zeros to see if there were more minima.) I simply used:

x0 = -ones(1,10)*100000;

to get the second minimum, adding the ‘-’ to my first guess to get the second.

According to the documentation for matlabFunction, the order should be the same as {t}.

Again, my pleasure.

Answer 2

[Walter Roberson]

Your F1 will take 10 different variables, but you are trying to pass in a single variable that is a scalar of length 10.

[annona]

you mean by a scalar of length 10 x0? how can I solve it?

[Walter Roberson]

Sorry I should have said a vector of length 10 rather than a scalar of length 10.

[soln,fval,exitflag]=fsolve(@(x) F1(x(1),x(2),x(3),x(4),x(5),x(6),x(7),x(8),x(9),x(10)), x0)

[annona]

It still produces the following error

Error using

symengine>@(in1)[in1(:,1).*-5.922282858364763e10-in1(:,6).*(in1(:,1).*6.68493292152468e10-6.68493292152468e10).*5.0e-1+in1(:,1).*(in1(:,6).*5.0e11-5.0e11)+5.338430977835152e10;in1(:,2).*-5.95115494912028e10-in1(:,7).*(in1(:,2).*6.68493292152468e10-6.68493292152468e10).*5.0e-1+in1(:,2).*(in1(:,7).*5.0e11-5.0e11)+5.338429087540035e10;in1(:,3).*-5.981750722433409e10-in1(:,8).*(in1(:,3).*6.68493292152468e10-6.68493292152468e10).*5.0e-1+in1(:,3).*(in1(:,8).*5.0e11-5.0e11)+5.338427320731596e10;in1(:,4).*-6.014173019427077e10-in1(:,9).*(in1(:,4).*6.68493292152468e10-6.68493292152468e10).*5.0e-1+in1(:,4).*(in1(:,9).*5.0e11-5.0e11)+5.338425666965504e10;in1(:,5).*-6.048530822622155e10-in1(:,10).*(in1(:,5).*6.68493292152468e10-6.68493292152468e10).*5.0e-1+in1(:,5).*(in1(:,10).*5.0e11-5.0e11)+5.338424116873857e10;in1(:,6).*-1.064644746602974e9+in1(:,6).*(in1(:,1).*6.68493292152468e10-6.68493292152468e10)-in1(:,1).*(in1(:,6).*5.0e11-5.0e11).*2.0+3.232237330148703e7;in1(:,7).*-1.081277549926826e9+in1(:,7).*(in1(:,2).*6.68493292152468e10-6.68493292152468e10)-in1(:,2).*(in1(:,7).*5.0e11-5.0e11).*2.0+4.063877496341306e7;in1(:,8).*-1.096995014081778e9+in1(:,8).*(in1(:,3).*6.68493292152468e10-6.68493292152468e10)-in1(:,3).*(in1(:,8).*5.0e11-5.0e11).*2.0+4.849750704088881e7;in1(:,9).*-1.105335150031959e9+in1(:,9).*(in1(:,4).*6.68493292152468e10-6.68493292152468e10)-in1(:,4).*(in1(:,9).*5.0e11-5.0e11).*2.0+5.266757501597958e7;in1(:,10).*-1.101418852947176e9+in1(:,10).*(in1(:,5).*6.68493292152468e10-6.68493292152468e10)-in1(:,5).*(in1(:,10).*5.0e11-5.0e11).*2.0+5.070942647358813e7]

Too many input arguments.

Error in try_GS_ES_prob>@(x)F1(x(1),x(2),x(3),x(4),x(5),x(6),x(7),x(8),x(9),x(10)) (line 46) [soln,fval,exitflag]=fsolve(@(x) F1(x(1),x(2),x(3),x(4),x(5),x(6),x(7),x(8),x(9),x(10)), x0)

Error in fsolve (line 241) fuser = feval(funfcn{3},x,varargin{:});

Error in try_GS_ES_prob (line 46) [soln,fval,exitflag]=fsolve(@(x) F1(x(1),x(2),x(3),x(4),x(5),x(6),x(7),x(8),x(9),x(10)), x0)

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

[Walter Roberson]

Hmmm, okay instead of what I showed, try using your original code but setting x0 = ones(1,10) as it appears your symbolic function expects a row vector.

[annona]

still giving the same error !!

As a simple example I used the following equations to solve:

syms p q
F=[sin(p)*sin(q);q^2+p^2-1]
 t=[p;q]
F1=matlabFunction(F,'vars',{t})

which results in

@(in1)[sin(in1(1,:)).*sin(in1(2,:));in1(1,:).^2+in1(2,:).^2-1.0]

Then I did

x0=rand(2,1)
  [soln,feval]=fsolve(F1,x0)

which gives me the results without any problem

soln =
      0.0000
      1.0000
feval =
     1.0e-07 *
      0.0227
      0.1076

with the same procedure I tried on my complex case but it did not work?? why is that? what is the difference between the two example? If you have any suggestion I will be grateful

[Walter Roberson]

Which of the two errors? Index out of range or two many input arguments?

To confirm, you are now testing with

x0=ones(1,10);
[soln,fval,exitflag]=fsolve(F1,x0)

[annona]

Error using symengine>@(in1)[in1(:,1).*-5.592228285836476e11+in1(:,6).*3.34246646076234e10+in1(:,1).*in1(:,6).*4.665753353923766e11+5.338430977835152e10;in1(:,2).*-5.595115494912028e11+in1(:,7).*3.34246646076234e10+in1(:,2).*in1(:,7).*4.665753353923766e11+5.338429087540035e10;in1(:,3).*-5.598175072243341e11+in1(:,8).*3.34246646076234e10+in1(:,3).*in1(:,8).*4.665753353923766e11+5.338427320731596e10;in1(:,4).*-5.601417301942708e11+in1(:,9).*3.34246646076234e10+in1(:,4).*in1(:,9).*4.665753353923766e11+5.338425666965504e10;in1(:,5).*-5.604853082262216e11+in1(:,10).*3.34246646076234e10+in1(:,5).*in1(:,10).*4.665753353923766e11+5.338424116873857e10;in1(:,1).*1.0e12-in1(:,6).*6.791397396184978e10-in1(:,1).*in1(:,6).*9.331506707847532e11+3.232237330148703e7;in1(:,2).*1.0e12-in1(:,7).*6.793060676517363e10-in1(:,2).*in1(:,7).*9.331506707847532e11+4.063877496341306e7;in1(:,3).*1.0e12-in1(:,8).*6.794632422932858e10-in1(:,3).*in1(:,8).*9.331506707847532e11+4.849750704088881e7;in1(:,4).*1.0e12-in1(:,9).*6.795466436527876e10-in1(:,4).*in1(:,9).*9.331506707847532e11+5.266757501597958e7;in1(:,5).*1.0e12-in1(:,10).*6.795074806819398e10-in1(:,5).*in1(:,10).*9.331506707847532e11+5.070942647358813e7]

Too many input arguments.

Error in try_GS_ES_prob/@(x)F1(x(1),x(2),x(3),x(4),x(5),x(6),x(7),x(8),x(9),x(10))

Error in fsolve (line 241) fuser = feval(funfcn{3},x,varargin{:});

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