Re: fslove using Jacobian

[Thomas Shores]

The documentation is a bit vague on this point, but the syntax of fsolve 
has changed.  Try this

# fslovetest.m
1;
function [y,J] = f(x)
  y = zeros(size(x));
  y(1) = -2*x(1)^2 + 3*x(1)*x(2)   + 4*sin(x(2)) - 6;
  y(2) =  3*x(1)^2 - 2*x(1)*x(2)^2 + 3*cos(x(1)) + 4;
  if (nargout == 2)
    J(1,1) =  3*x(2) - 4*x(1);
    J(1,2) =  4*cos(x(2)) + 3*x(1);
    J(2,1) = -2*x(2)^2 - 3*sin(x(1)) + 6*x(1);
    J(2,2) = -4*x(1)*x(2);
  end
endfunction
[x, fval, info] = fsolve (@f, [1; 2],optimset("Jacobian","on"))
# end of fslovetest.m

Resulting output:

octave:1> fsolvetest
x =

   0.57983
   2.54621

fval =

   6.1872e-08
  -3.2708e-07

info =  1


On 06/14/2010 03:17 AM, Tatsuro MATSUOKA wrote:
> Hello
>
> I am now revising my documentations for my lecture concerning the octave.
>
> > From octave 3.2, fslove are improved extensively.
>
> In the octave manual (3.2.4)
>
> An example, fsolve using Jacobian, is written as,
>
>
> function y = f (x)
>         y(1) = -2*x(1)^2 + 3*x(1)*x(2)   + 4*sin(x(2)) - 6;
>         y(2) =  3*x(1)^2 - 2*x(1)*x(2)^2 + 3*cos(x(1)) + 4;
> endfunction
>
> function J = jacobian(x)
>         J(1,1) =  3*x(2) - 4*x(1);
>         J(1,2) =  4*cos(x(2)) + 3*x(1);
>         J(2,1) = -2*x(2)^2 - 3*sin(x(1)) + 6*x(1);
>         J(2,2) = -4*x(1)*x(2);
> endfunction
>
> [x, fval, info] = fsolve (address@hidden, @jacobian}, [1; 2]);
> *********************************************
>
> So I made a script,
>
> # fslovetest.m
>
> 1;
> function y = f (x)
>         y(1) = -2*x(1)^2 + 3*x(1)*x(2)   + 4*sin(x(2)) - 6;
>         y(2) =  3*x(1)^2 - 2*x(1)*x(2)^2 + 3*cos(x(1)) + 4;
> endfunction
>
> function J = jacobian(x)
>         J(1,1) =  3*x(2) - 4*x(1);
>         J(1,2) =  4*cos(x(2)) + 3*x(1);
>         J(2,1) = -2*x(2)^2 - 3*sin(x(1)) + 6*x(1);
>         J(2,2) = -4*x(1)*x(2);
> endfunction
>
> [x, fval, info] = fsolve (address@hidden, @jacobian}, [1; 2])
>
> # end of fslovetest.m
>
> For, octave 3.0, it works as written in manual.
>
> octave.exe:3>  fslovetest
> x =
>
>     0.57983
>     2.54621
>
> fval =
>
>    -5.7184e-010
>    5.5461e-010
>
> For octave 3.2,
>
> octave-3.2.4.exe:3>  fslovetest
> error: xnorm: wrong type argument `cell'
> error: called from:
> error:   
> C:\Programs\Octave\3.2.4_gcc-4.4.0\share\octave\3.2.4\m\optimization\fsolve.m 
> at line 180,
> column 6
> error:   D:\usr\Lecture\ .....\work\fslovetest.m at line 14, column 18
>
> In the same manual (and in help fsolve), example of the use-defined function,
> ****
> function [fvec, fjac] = user_func (x, optimvalues, state)
>   :
>
> ******
>
> The example of the manual is obviously obsolete.
> Unfortunately I have never seen the manual generated in octave-3.3.51+ because 
> of the latex problem. I
> do not know the latest manual.
>
> I have tried
>
> # fslovetest2.m
> 1;
> function y = f (x)
>         y(1) = -2*x(1)^2 + 3*x(1)*x(2)   + 4*sin(x(2)) - 6;
>         y(2) =  3*x(1)^2 - 2*x(1)*x(2)^2 + 3*cos(x(1)) + 4;
> endfunction
>
> function J = jacobian(x)
>         J(1,1) =  3*x(2) - 4*x(1);
>         J(1,2) =  4*cos(x(2)) + 3*x(1);
>         J(2,1) = -2*x(2)^2 - 3*sin(x(1)) + 6*x(1);
>         J(2,2) = -4*x(1)*x(2);
> endfunction
>
> function f = fcn(x)
>         f=[(f(x)).', jacobian(x)];
> endfunction
>
>
> [x, fval, info]=fsolve (@fcn, [1; 2],optimset("Jacobian","on"))
> # end of fslovetest2.m
>
> error: element number 2 undefined in return list
> error: called from:
> error:   
> C:\Programs\Octave\3.2.4_gcc-4.4.0\share\octave\3.2.4\m\optimization\fsolve.m 
> at line 204,
> column 21
> error:   D:\usr\Lecture\ ..........\work\fslovetest2.m at li
> ne 19, column 1
>
>
> How should I correct the fsolve script using Jacobian on octave 3.2 or later in 
> the example for the
> octave 3.0?
>
> Regards
>
> Tatsuro
>
>
>
>
>
>
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