Thank you w3bsurf3r the quick response

I am very grateful to you and that my examples can finaly be solved in SMath . There will be more examples to come, of course.

Could you please check this out once more. Actually, HRE crashes for the same example. It might be due to my computer WinXP(32). I will check this out tommorow on Win7(64) as well.

Regards,
Radovan

Thank you w3b5urf3r,

I put this on the Bugs forum including the Hang report. Hope that this will make any help to Andrey.

Regards,
Radovan

EDIT: Unfortunately, it crashes on Win7(64) and in Ubuntu for me as well. In Ubuntu "Stack overflow" error appeared.

Edited by user 15 September 2012 13:24:22(UTC)  | Reason: Not specified

Hello w3b5urf3r

This is working now just great . Thank you very much
Find attached the pictures both from the WinXP(32) and Win7(64)

Regards,
Radovan

Edited by user 16 September 2012 09:09:28(UTC)  | Reason: Not specified

Great,

it seems that the number of nested iterations was excessive to handle, I just placed some eval here and there...




A first check show me that Broyden returns a wrong result, but I don't know why; comparing them with the snippet in the reference sheets (using γ:1) the script works fine... I'll check it a little more

EDIT: the snippet is wrong, use Newton instead of Broyden, so the results are a little bit differents but are both wrong (so I think that HRE.B() can't be used in this example...)


regards,

w3b5urfer

Edited by user 18 September 2012 01:27:44(UTC)  | Reason: Not specified

Hi omorr,

most likely both will be revisited...

actually HRE/HRE.B are based on the simplest algorithm that I've found, and seems that it's quite onerous (Broyden and Newton are both much more faster), so I think that Homotopy function (at the time, at least) should be used only for testing purposes or when both Broyden and Newton fails; consequently I've limited the CPU usage using this convergence criterion: f(x)<10^-2 with no more than 100 sub-iterations for each Homotopy iteration (no more than 1100=100x11 iterations for HRE and 2200=100x2x11 iterations for HRE.B).

BTW note that in both case the convergence criterion is met (see the attachment).


regards,

w3b5urf3r

Edited by user 16 September 2012 18:45:16(UTC)  | Reason: Not specified

PLUGIN UPDATED

- added optional Convergence checking on bracket width (for bracketed algorithms only: BDQRF(),Bisection(),Brent(),Ridder());

- fixed issues of Brent() with units of measurement.


regards,

w3b5urf3r


EDIT: added plugin sources

Edited by user 26 September 2012 11:10:45(UTC)  | Reason: added plugin sources

FOR TESTING PURPOSES ONLY

Hi all,

a (big) little update in the attached plugin:

- New feature: solvers for systems of equations now accept multiple unknowns names (see the example below)

- Broyden convergence criterion revisited

- Plugin Jacobian(...) unlocked


NOTES:
- known starting values must be placed with reference to the alphabetical order of the unknowns (a,A,b,B,c,C,...,z,Z,α,Α,β,Β,γ,Γ,...). If you are unsure about the order, call the function mapUnknowns(1) (see the example below);
- Jacobian() generates derivatives, gradients or Jacobians depending on the type of arguments.

PLEASE REPORT ANY ISSUE

regards,

w3b5urf3r

Hi w3b5urf3r and Radovan,


I'm delighted seeing your interesting work.
I tried to apply the plugin to one of my problems - one equation - here attached.
It is obvious that the ability of various algorithms is enough dependent on the initial guess.
I'm interested if you have some suggestions concerning the initial unknown guess strategy for this case, seeing the parameters variation ranges.


Thanks and congratulations again for your work,


Ioan,

Thanks for your effort!
Please w3b5rf3r, take a look at this pseudocode for homotopy with test functions and iteration results (pdf page 227)
http://www.iit.upcomilla...umenes/450608814dabe.pdf
This method uses Runge-Kutta 4th order on every iteration, the followed algorithm is explained above the pseudocode section. The same strategy of runge-kutta 4 is explained more clearly on this paper pdf page 8
http://personales.upv.es...grado/prac_no_lineal.pdf

Edited by user 05 October 2012 15:25:01(UTC)  | Reason: Not specified

Sorry Uni, I don't understand your pdfs
Homotopy methods seem to be appropriate to guess an initial zero on large systems since the usual methods need a good initial approximation to converge.
That's what I grasped from the above document: Homotopy is based on deform your equation f(1) into another one f(0) easier (known) to resolve. Then you have to get to f(1) from f(0) through a path like a segment (or another curve if it doesn't make sense this road to get to the solution)
f(t)=(1-t)f(0)+tf(1), where t is a number between 0 and 1.
Now he assumes X(t) as the solution for f(t), so f(t)(x(t))=0, then he derivates this expression resulting an ode system to resolve x(t), since x(0) is known he says to resolve the initial value problem with RK4 (good balance between cost and precision) or the ode23() matlab function.

Edited by user 28 September 2012 22:28:44(UTC)  | Reason: Not specified