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

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annona 2012-9-16

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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

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Star Strider 2012-9-16

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 2012-9-17

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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 =
0000
0000
feval =
0e-07 *
0227
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?

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Answer 1

Star Strider 2012-9-17

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编辑：Star Strider 2012-9-17

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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?

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annona 2012-9-18

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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 2012-9-18

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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.

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Answer 2

Walter Roberson 2012-9-16

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

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annona 2012-9-16

编辑：annona 2012-9-16

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 2012-9-17

在 MATLAB Online 中打开

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 2012-9-17

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.

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

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