fslove using Jacobian

[Tatsuro MATSUOKA]

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






--------------------------------------
2010 FIFA World Cup News [Yahoo!Sports/sportsnavi]
http://pr.mail.yahoo.co.jp/southafrica2010/