NonlinearSolvers plugin

Welcome Guest! To enable all features please Login. New Registrations are disabled.

Notification

Error

14 Pages12 3 >»

NonlinearSolvers plugin - BDQRF, Bisection, Brent's, Broyden's, Newton-Raphson, Ridder's, Secant, Homotopy

Options

Previous Topic Next Topic

Davide Carpi		#1 Posted : 05 September 2012 05:08:15(UTC)
Rank: Advanced Member Groups: Registered, Advanced Member Joined: 13/01/2012(UTC) Posts: 2,710 Location: Italy Was thanked: 1378 time(s) in 902 post(s)		Hi all, This plugin contains some root-finding methods and optimization algorithms. Password (Extensions Manager): NonlinearSolvers Since the plugin may have big changes in future, I can't make a complete documentation but you can referrer to: - Martin's handbook - this album GoldenSectionSearch.sm (22kb) downloaded 175 time(s). GradientDescent.sm (17kb) downloaded 144 time(s). NCGM.sm (20kb) downloaded 120 time(s). LevenbergMarquardt.sm (46kb) downloaded 153 time(s). NewtonMethod.sm (19kb) downloaded 185 time(s). NelderMead.sm (34kb) downloaded 133 time(s). GaussNewton.sm (21kb) downloaded 153 time(s). [UNDER REVIEW/TO BE UPDATED] Plugin handles primitives listed below: Root finding methods BDQRF("1:function", "2:delimiter", "3:delimiter", "4:variable", "5:variable") - Bisected Direct Quadratic Regula Falsi root-finding method of function(s) "1:function", giving a couple of delimiters; calculation have "4:variable" result precision and no more than "5:variable" iterations. Returns a vector of solutions (if any) and the number of iterations if the optional argument "6:variable" is set and different from 0. Bisection("1:function", "2:delimiter", "3:delimiter", "4:variable", "5:variable") - Bisection root-finding method of function(s) "1:function", giving a couple of delimiters; calculation have "4:variable" result precision and no more than "5:variable" iterations. Returns a vector of solutions (if any) and the number of iterations if the optional argument "6:variable" is set and different from 0. Brent("1:function", "2:delimiter", "3:delimiter", "4:variable", "5:variable") - Brent's root-finding method of function(s) "1:function", giving a couple of delimiters; calculation have "4:variable" result precision and no more than "5:variable" iterations. Returns a vector of solutions (if any) and the number of iterations if the optional argument "6:variable" is set and different from 0. Broyden("1:function", "2:condition", "3:variable", "4:variable") - Broyden's root-finding method of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have "3:variable" result precision and no more than "4:variable" iterations. Returns a vector of solutions (if any) and the number of iterations if the optional argument "5:variable" is set and different from 0. HRE.B("1:function", "2:condition", "3:variable", "4:variable") - Homotopy root-estimation method of function(s) "1:function", giving an initial guess "2:condition" for each variable, using the Broyden algorithm; calculation have "3:variable" result precision using "4:variable" homotopy transformations. Returns a vector of solutions (if any) and the number of iterations if the optional argument "5:variable" is set and different from 0. HRE.NR("1:function", "2:condition", "3:variable", "4:variable") - Homotopy root-estimation method of function(s) "1:function", giving an initial guess "2:variable" for each variable, using the Newton-Raphson algorithm. Returns a vector of solutions (if any) and the number of iterations if the optional argument "5:variable" is set and different from 0. HRE.RK("1:function", "2:condition", "3:variable", "4:variable") - Homotopy root-estimation method of function(s) "1:function", giving an initial guess "2:variable" for each variable, using the Runge-Kutta 4th order algorithm; calculation have "3:variable" result precision using "4:variable" homotopy transformations. Returns a vector of solutions (if any) and the number of iterations if the optional argument "5:variable" is set and different from 0. Jacobian("1:function", "2:variable") - Multi-purpose derivatives of "1:function" evaluated in "2:variable"; returns differentiations/gradients/Jacobians. mapUnknowns("function") - Symbolical variables mapping of "1:function"; returns a vector of unassigned variables. NewtonRaphson("1:function", "2:condition", "3:variable", "4:variable") - Newton-Raphson root-finding method of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have "3:variable" result precision and no more than "4:variable" iterations. Returns a vector of solutions (if any) and the number of iterations if the optional argument "5:variable" is set and different from 0. Ridder("1:function", "2:delimiter", "3:delimiter", "4:variable", "5:variable") - Ridder's root-finding method of function(s) "1:function", giving a couple of delimiters; calculation have "4:variable" result precision and no more than "5:variable" iterations. Returns a vector of solutions (if any) and the number of iterations if the optional argument "6:variable" is set and different from 0. Secant("1:function", "2:variable", "3:variable", "4:variable", "5:variable") - Secant root-finding method of function(s) "1:function", giving a couple of points; calculation have "4:variable" result precision and no more than "5:variable" iterations. Returns a vector of solutions (if any) and the number of iterations if the optional argument "6:variable" is set and different from 0. BETA PLUGIN - REQUIRES customFunctions plugin - new functions NCGM(...) and NCGM.CD(...) - Nonlinear conjugate gradient method optimization algorithms; - new function Gradient.CD(...) - central differences based Gradient; - new function Jacobian.CD(...) - central differences based Jacobian; - new function Hessian.CD(...) - central differences based Hessian; - new functions GaussNewton.CD(...) and GaussNewton.CDGSS(...) - central differences based GaussNewton; - new function LevenbergMarquardt.CD(...) - central differences based LevenbergMarquardt; - new function NewtonRaphson.CD(...) - central differences based NewtonRaphson; - new functions NewtonMethod.CD(...) and NewtonMethod.CDGSS(...) - central differences based NewtonMethod; - increased performances on Gradient/Jacobian/Hessian-based functions; - fixed issues of Broyden(...) and HRE.B(...) about custom settings; - new function GaussNewton(...) - Gauss-Newton optimization algorithm; - new functions GoldenSectionSearch.min(...) and GoldenSectionSearch.max(...) - Golden Section Search minimization/maximization algorithms; - new functions GradientDescent(...) and GradientDescent.GSS(...) - Gradient Descent optimization algorithm (respectively with fixed step length and GoldenSectionSearch-based step length); - new function LevenbergMarquardt(...) - Levenberg-Marquardt optimization algorithm; - new functions NewtonMethod(...) and NewtonMethod.GSS(...) - Newton Method optimization algorithm (respectively with fixed step length and GoldenSectionSearch-based step length); - new function Diag(...) - improved SMath diag(); - new function Gradient(...) - 1st order derivatives; - new function Hessian(...) - 2nd order derivatives; - function Jacobian(...) revisited (now returns only a derivative or a mxn Jacobian); - solver Bisection(...) revisited (the number of iterations is no longer required, [url=http://en.smath.info/forum/yaf_postsm8005_Non-Linear-Solvers--root-finding-methods.aspx#post8005]as reported by adiaz[/url]); - All root-finding algorithms in k variable now accept multiple thresholds (a target precision value for each function); - Fixed "custom decimal symbol" issue of HRE functions.; UPDATES: - September 6, 2012: fixed some issues in Broyden(...); added Bisection(...); add a last optional parameter to show the number of iterations. - September 7, 2012: new solution strategy for Broyden(...). - September 8, 2012: added Secant(...); added Ridder(...); added Brent(...); fixed a common issue in the number of elements evaluation of the input functions. - September 10, 2012: added BDQRF(...); added NewtonRaphson(...). - September 14, 2012: added HRE(...) and HRE.B(...); fixed an issue of internal variable parser with differentiations and with number of equations. - September 22, 2012: added optional Convergence checking on bracket width (for bracketed algorithms only); fixed issues of Brent() with units of measurement. - October 01, 2012: solvers for systems of equations now accept multiple unknowns names; Broyden convergence criterion revisited; added HRE.RK(); all homotopy algorithms now works as Broyden() and NewtonRaphson(); HRE() renamed as HRE.NR(); plugin Jacobian(...) unlocked; fixed issues with Units in all HRE() solvers. LATEST BETA: June, 2013 PLEASE REPORT HERE ANY ISSUE Best regards, Davide requirements: .Net Framework 2.0 / AnyCPU / SMath Studio 0.95.4594 (30 July 2012) Edited by user 13 May 2016 12:55:27(UTC) \| Reason: EM password File Attachment(s): NonLinearSolvers Documentation.zip (63kb) downloaded 755 time(s). BETA_testing sm files.zip (32kb) downloaded 379 time(s). Davide Carpi attached the following image(s):
		If you like my plugins consider to support SMath Studio buying a plan; to offer me a coffee: paypal.me/dcprojects

4 users thanked Davide Carpi for this useful post.		on 05/09/2012(UTC), on 02/10/2012(UTC), on 02/10/2012(UTC), on 03/12/2016(UTC)
User Profile View All Posts by User View Thanks


	Wanna join the discussion?! Login to your SMath Studio Forum forum account. New Registrations are disabled.

omorr		#2 Posted : 05 September 2012 10:42:17(UTC)
Rank: Administration Groups: Registered, Advanced Member Joined: 23/06/2009(UTC) Posts: 1,740 Was thanked: 318 time(s) in 268 post(s)		w3b5urf3r you are my hero rinks: Many things like this one would make me very happy ancing: Regards, Radovan P.S. Do not take me wrong please, I am very happy that you've made this plugin but I think that my "home made" function does not deserve to be the reference to this rather welcome and appreciated plugin. I hope that your updates would base this plugin to some more trustworthy source. Edited by user 05 September 2012 11:55:38(UTC) \| Reason: Not specified
		When Sisyphus climbed to the top of a hill, they said: "Wrong boulder!"
		WWW

User Profile View All Posts by User View Thanks

omorr		#3 Posted : 05 September 2012 12:36:37(UTC)
Rank: Administration Groups: Registered, Advanced Member Joined: 23/06/2009(UTC) Posts: 1,740 Was thanked: 318 time(s) in 268 post(s)		Hello w3b5urf3r Rather surprised and excited with this sys() thing regarding Broyden() As I do not know how is this working yet, this is a minor observation at a first glance. It seems that the vector indices play main role here. Broyden(sys(el(x,1)-2el(x,2)+5,el(x,1)+3el(x,2)-1,2,1),sys(1,2,2,1),eps,maxiter)=mat(-2.6,1.2,2,1) Broyden(sys(el(a,1)-el(2b,2)+5,el(c,1)+3el(d,2)-1,2,1),sys(1,2,2,1),eps,maxiter)=mat(-2.6,1.2,2,1) Broyden(sys(el(a,1)-el(2b,2)+el(e,1),el(c,1)+3el(d,2)+el(f,1),2,1),sys(1,2,2,1),eps,maxiter)=mat(0,0,2,1) This might be a confusion because vectors a,b,c,d,e,f are not defined and there is still a result returned. You managed to avoid mentioning vector of unknowns like in the roots(), and I think that vector indices are crucial things here to distinguish between unknowns, not sure. Am I right? If that is the case, I thing that this should be taken care of in the case of different vectors elements with the same indices in order what to refer to as vector of unknowns. Best wishes, Radovan
		When Sisyphus climbed to the top of a hill, they said: "Wrong boulder!"
		WWW

User Profile View All Posts by User View Thanks

Davide Carpi		#4 Posted : 05 September 2012 16:39:55(UTC)
Rank: Advanced Member Groups: Registered, Advanced Member Joined: 13/01/2012(UTC) Posts: 2,710 Location: Italy Was thanked: 1378 time(s) in 902 post(s)		Originally Posted by: omorr w3b5urf3r you are my hero rinks: Many things like this one would make me very happy ancing: Regards, Radovan P.S. Do not take me wrong please, I am very happy that you've made this plugin but I think that my "home made" function does not deserve to be the reference to this rather welcome and appreciated plugin. I hope that your updates would base this plugin to some more trustworthy source. you're right, but I did not know where to start and that function was a good starting point. Currently, the plugin follows almost exactly that function, but if anyone has a more efficient version of the algorithm could certainly be implemented. Originally Posted by: omorr Hello w3b5urf3r Rather surprised and excited with this sys() thing regarding Broyden() Yes, I have lost a bit of time on this, I wanted the function to accept both individual functions or systems defined in vectors or in the "multiple values" item. Originally Posted by: omorr As I do not know how is this working yet, this is a minor observation at a first glance. It seems that the vector indices play main role here. Broyden(sys(el(x,1)-2el(x,2)+5,el(x,1)+3el(x,2)-1,2,1),sys(1,2,2,1),eps,maxiter)=mat(-2.6,1.2,2,1) Broyden(sys(el(a,1)-el(2b,2)+5,el(c,1)+3el(d,2)-1,2,1),sys(1,2,2,1),eps,maxiter)=mat(-2.6,1.2,2,1) Broyden(sys(el(a,1)-el(2b,2)+el(e,1),el(c,1)+3el(d,2)+el(f,1),2,1),sys(1,2,2,1),eps,maxiter)=mat(0,0,2,1) This might be a confusion because vectors a,b,c,d,e,f are not defined and there is still a result returned. You managed to avoid mentioning vector of unknowns like in the roots(), and I think that vector indices are crucial things here to distinguish between unknowns, not sure. Am I right? If that is the case, I thing that this should be taken care of in the case of different vectors elements with the same indices in order what to refer to as vector of unknowns. Best wishes, Radovan You're right, my parser check if there are undefined variables but it doesn't distinguish between them... Actually the assumption is that there is "one variable" (x,X,K,or something you want) or "a system of variables" (x[1],x[2],x[3],...), so actually a[1] and b[1] are both the same thing (the first element of the starting values vector) I think I can easily add a control that returns an error on the number of vars... If you want to use "multiple variables" (one varibale -> one vector element) I think we can do something, but with some limitations regarding the names (f.e. "i" and "e" are both constants). regards, w3b5urf3r Edited by user 05 September 2012 16:59:48(UTC) \| Reason: Not specified
		If you like my plugins consider to support SMath Studio buying a plan; to offer me a coffee: paypal.me/dcprojects

1 user thanked Davide Carpi for this useful post.		on 07/09/2012(UTC)
User Profile View All Posts by User View Thanks

omorr		#5 Posted : 05 September 2012 17:28:52(UTC)
Rank: Administration Groups: Registered, Advanced Member Joined: 23/06/2009(UTC) Posts: 1,740 Was thanked: 318 time(s) in 268 post(s)		Hello w3b5urf3r, Whatever you do regarding this plugin will be very welcome AFAIC I have just to mention in the case you based your plugin on my SMath function, that I made it from a simple code found somewhere on the Net (even do not remember where from). If you are interested to spare some more of your time, you could try to find yourself some better algorithm and make a plugin from it . Regards, Radovan
		When Sisyphus climbed to the top of a hill, they said: "Wrong boulder!"
		WWW

User Profile View All Posts by User View Thanks

omorr		#6 Posted : 05 September 2012 21:38:49(UTC)
Rank: Administration Groups: Registered, Advanced Member Joined: 23/06/2009(UTC) Posts: 1,740 Was thanked: 318 time(s) in 268 post(s)		Hello w3b5urf3r, Here is a bit of testing the Broyden plugin. It is a clasical "driving crasy" situation with multiple solutions. It was mentioned by kilele in the link to the document http://en.smath.info/forum/yaf_postsm7678_solve---and-roots-----again.aspx#post7678 Your plugin failed (if I did not do something wrong) but do not worry about it - it is a common situation. The problem is why "Can not calculate" error returned. I do not know. My function returned another solution than few Newton-Raphson iterations or roots(). I also used another software that uses some kind of broyden algorithm and here is the result - the same as roots() returned Code: `>function f(x):=[(x[1]+3)(x[2]^3-7)+18,sin(x[2]exp(x[1])-1)] >x0:=[-0.5,1.4] [ -0.5 1.4 ] >f(x0) [ 7.36 -0.150285529841 ] >res:=broyden("f",x0) [ 0 1 ] >f(res) [ 0 0 ]` Try, for instance to change the guess values (vector x0) from [-0.5,1.4] to [1,4]. Here is the picture and the sm file Regards, Radovan Edited by user 05 September 2012 21:41:29(UTC) \| Reason: Not specified File Attachment(s): Broyden_testings-1.sm (54kb) downloaded 120 time(s). omorr attached the following image(s):
		When Sisyphus climbed to the top of a hill, they said: "Wrong boulder!"
		WWW

User Profile View All Posts by User View Thanks

kilele		#7 Posted : 06 September 2012 02:10:18(UTC)
Rank: Advanced Member Groups: Registered Joined: 30/03/2011(UTC) Posts: 393 Was thanked: 133 time(s) in 114 post(s)		maybe a good approach would be combine homotopy + broyden ? or obtaining good approximations of roots with a generalized bisection method and then refine with broyden or other method, as explained at the conclusions of this document: ( see the link "pdf download" ) A Rapid Generalized Method of Bisection for Solving Systems of Non-linear Equations Feel free to explore that strategy, as for me I'll take it easy with a first plugin for a one dimension bisection Edited by user 06 September 2012 02:17:01(UTC) \| Reason: Not specified

1 user thanked kilele for this useful post.		on 07/09/2012(UTC)
User Profile View All Posts by User View Thanks

omorr		#8 Posted : 06 September 2012 10:38:03(UTC)
Rank: Administration Groups: Registered, Advanced Member Joined: 23/06/2009(UTC) Posts: 1,740 Was thanked: 318 time(s) in 268 post(s)		Hello kilele, I hope you would not mind if I repeat some of my comments I've already posted here on the Forum. All of you who are trying to make any SMath plugin have all my respect and appreciation. I really hope that you will enjoy this and the SMath users will benefited from that, no doubt. On the other hand, this will very likely take quite a long time until most of the basic numerical functions and procedures SMath needs would be realized, regarding that you are starting from scratch. In order not to "inventing the will" there must be some more pragmatical way to "fill up" the SMath with some already made, free available, mature and well tested numerical code (using them like black boxes and make plugins from them). Actually, I was told that this is not likely to be possible in SMath and I regret for that very much. I think this will, unfortunately, slow down the SMath progress and restrict the SMath user community. Many of the SMath users are (actual/former) Mathcad users as well, and I think that most of them would like that SMath had some Mathcad functionality comparing to even Mathcad 6 (originated from 1996). Regarding, Radovan
		When Sisyphus climbed to the top of a hill, they said: "Wrong boulder!"
		WWW
1 user thanked omorr for this useful post.		on 07/09/2012(UTC)
User Profile View All Posts by User View Thanks

kilele		#9 Posted : 06 September 2012 13:09:47(UTC)
Rank: Advanced Member Groups: Registered Joined: 30/03/2011(UTC) Posts: 393 Was thanked: 133 time(s) in 114 post(s)		Originally Posted by: w3b5urf3r_reloaded Currently, the plugin follows almost exactly that function, but if anyone has a more efficient version of the algorithm could certainly be implemented. I've just read that this implementation is better for large problems (see pag 133 of this pdf) and this is its matlab code @Radovan As for making use of third part libraries on SMath, I don't know if that is possible aside from license issues

1 user thanked kilele for this useful post.		on 07/09/2012(UTC)
User Profile View All Posts by User View Thanks

omorr		#10 Posted : 06 September 2012 14:36:24(UTC)
Rank: Administration Groups: Registered, Advanced Member Joined: 23/06/2009(UTC) Posts: 1,740 Was thanked: 318 time(s) in 268 post(s)		Hello, Originally Posted by: kilele Originally Posted by: w3b5urf3r_reloaded Currently, the plugin follows almost exactly that function, but if anyone has a more efficient version of the algorithm could certainly be implemented. I've just read that this implementation is better for large problems (see pag 133 of this pdf) and this is its matlab code Thank you for this link . I do not know if w3b5urf3r has enough time to devote to the Broyden method explained there (or any other one) This might be an example of how to make a plugin - as far as I understood this process. Ordinary user who understands Matlab could try to make the SMath function following this code. It might be more or less time consuming. A plugin developer could also use this Matlab code directly or the already made SMath function (do not know which one could make less trouble) and make a plugin by using some software tools. I have no idea how difficult might that be. On the other hand (have a vague idea about this) if there would be a plugin mechanism which will just include some kind of compiled Matlab (or C,C++,C#,F95) code where there should be defined input arguments output arguments and using a "black box" of this compiled function. This is working in many other software with the goal of reusing already made code. Otherwise, it would be a disaster to write everything from the beginning. I thought that the idea of "plugin" will follow this concept but as I was told this is not working in SMath this way. How is this actually working, I do not know. Originally Posted by: kilele @Radovan As for making use of third part libraries on SMath, I don't know if that is possible aside from license issues I was thinking about the freely available libraries, open source software etc. I do not see then any license problems (am I right?) except the ones I was talking about. Regards, Radovan Edited by user 06 September 2012 14:44:14(UTC) \| Reason: Not specified
		When Sisyphus climbed to the top of a hill, they said: "Wrong boulder!"
		WWW

User Profile View All Posts by User View Thanks

Davide Carpi		#11 Posted : 06 September 2012 16:09:21(UTC)
Rank: Advanced Member Groups: Registered, Advanced Member Joined: 13/01/2012(UTC) Posts: 2,710 Location: Italy Was thanked: 1378 time(s) in 902 post(s)		Plugin updated, many issues fixed and bisection (not generalized) implemented... an optional argument at the end of the function arguments, different from 0, can show you the number of iterations... Originally Posted by: omorr Hello w3b5urf3r, Here is a bit of testing the Broyden plugin. It is a clasical "driving crasy" situation with multiple solutions. It was mentioned by kilele in the link to the document http://en.smath.info/forum/yaf_postsm7678_solve---and-roots-----again.aspx#post7678 Your plugin failed (if I did not do something wrong) but do not worry about it - it is a common situation. The problem is why "Can not calculate" error returned. I do not know. My function returned another solution than few Newton-Raphson iterations or roots(). I also used another software that uses some kind of broyden algorithm and here is the result - the same as roots() returned Code: `>function f(x):=[(x[1]+3)(x[2]^3-7)+18,sin(x[2]exp(x[1])-1)] >x0:=[-0.5,1.4] [ -0.5 1.4 ] >f(x0) [ 7.36 -0.150285529841 ] >res:=broyden("f",x0) [ 0 1 ] >f(res) [ 0 0 ]` Try, for instance to change the guess values (vector x0) from [-0.5,1.4] to [1,4]. Here is the picture and the sm file Regards, Radovan The function as in the .sm file doesn't work because the first approximated inverse jacobian ( B ) is an Identity matrix... i've seen that is a common issue (f.e. root finding methods)... in SMath this could be fixed using the Jacob() function on the user input solution (see the attachment). Unfortunately the function Jacob() (as well as other functions such as error() function) are not in the 4 standard libraries; I will try to see if importing the library on which it was made by Andrey can be implemented. Originally Posted by: kilele Originally Posted by: w3b5urf3r_reloaded Currently, the plugin follows almost exactly that function, but if anyone has a more efficient version of the algorithm could certainly be implemented. I've just read that this implementation is better for large problems (see pag 133 of this pdf) and this is its matlab code @Radovan As for making use of third part libraries on SMath, I don't know if that is possible aside from license issues Thank you, is very useful; i've implemented this script in a Smath sheet and it's more readable, unfortunately the issue related to the first Jacob approximation still remains regards, w3b5urf3r Edited by user 06 September 2012 16:48:47(UTC) \| Reason: Not specified* File Attachment(s): Broyden_testings-2.sm (48kb) downloaded 111 time(s). Davide Carpi attached the following image(s):
		If you like my plugins consider to support SMath Studio buying a plan; to offer me a coffee: paypal.me/dcprojects

1 user thanked Davide Carpi for this useful post.		on 06/09/2012(UTC)
User Profile View All Posts by User View Thanks

omorr		#12 Posted : 06 September 2012 18:53:05(UTC)
Rank: Administration Groups: Registered, Advanced Member Joined: 23/06/2009(UTC) Posts: 1,740 Was thanked: 318 time(s) in 268 post(s)		Hello w3b5urf3r, Just keep up this way I would suggest you to strictly avoid using Jacob() inside Broyden - it will get new troubles. I really do not know what to use instead as a first Jacobian approximation. If someone have any idea, please help. When you have the time, put some examples using Bisection() as well in the next update. If I understood you well, you are trying to use Broyden with units (Dimensional analysis check failed...). Am I right? My suggestion is to skip this as well at the moment. Best wishes, Radovan Edited by user 06 September 2012 18:54:57(UTC) \| Reason: Not specified
		When Sisyphus climbed to the top of a hill, they said: "Wrong boulder!"
		WWW

User Profile View All Posts by User View Thanks

kilele		#13 Posted : 06 September 2012 21:59:50(UTC)
Rank: Advanced Member Groups: Registered Joined: 30/03/2011(UTC) Posts: 393 Was thanked: 133 time(s) in 114 post(s)		wow, have you used bisection as an initialization of broyden ? also i've searched information about the broyden method over time and it seems the most advanced/recent version is a modification of Johnson's by Baran : http://arxiv.org/abs/0805.4446 As for the Jacob() function, I thought that Broyden didn't use Jacob directly but an approximation.. EDIT: Never mind, the above paper refers to a gpl program based on other libraries. There you have the historial of Broyden method, http://www.unedf.org/con.../Day2/PackForest_JJM.pdf it seems to me that the "compact" version of 1994 corresponds to the matlab code that I linked above. Edited by user 06 September 2012 22:17:09(UTC) \| Reason: Not specified

2 users thanked kilele for this useful post.		on 07/09/2012(UTC), on 07/09/2012(UTC)
User Profile View All Posts by User View Thanks

Davide Carpi		#14 Posted : 07 September 2012 02:51:21(UTC)
Rank: Advanced Member Groups: Registered, Advanced Member Joined: 13/01/2012(UTC) Posts: 2,710 Location: Italy Was thanked: 1378 time(s) in 902 post(s)		Plugin updated. Broyden now use this solution strategy 1) check for results with the "bad" Broyden method - if solutions works -> output the results - if solutions are not closest to zero -> 2 2) check for results with the "good" Broyden method - if solutions works -> output the results - if solutions are not closest to zero -> output a can not solve error the algorithm is similar to that shown in the attachment (replace the B update definition to see the different behavior). Added a SMath file with examples for the Bisection() function. Originally Posted by: kilele wow, have you used bisection as an initialization of broyden ? also i've searched information about the broyden method over time and it seems the most advanced/recent version is a modification of Johnson's by Baran : http://arxiv.org/abs/0805.4446 As for the Jacob() function, I thought that Broyden didn't use Jacob directly but an approximation.. EDIT: Never mind, the above paper refers to a gpl program based on other libraries. There you have the historial of Broyden method, http://www.unedf.org/con.../Day2/PackForest_JJM.pdf it seems to me that the "compact" version of 1994 corresponds to the matlab code that I linked above. Very interesting articles, thank you regards, w3b5urfer Edited by user 07 September 2012 02:59:48(UTC) \| Reason: Not specified File Attachment(s): Broyden_alpha.sm (76kb) downloaded 97 time(s).
		If you like my plugins consider to support SMath Studio buying a plan; to offer me a coffee: paypal.me/dcprojects

1 user thanked Davide Carpi for this useful post.		on 07/09/2012(UTC)
User Profile View All Posts by User View Thanks

kilele		#15 Posted : 07 September 2012 03:01:45(UTC)
Rank: Advanced Member Groups: Registered Joined: 30/03/2011(UTC) Posts: 393 Was thanked: 133 time(s) in 114 post(s)		Another matlab code to reduce memory requirements on this quite recent pdf pag.211 Appendix B Thanks for your work!! Edit: Again since Broyden is not globally convergent, bisection might be interesting as an initial approaching to the roots Edited by user 07 September 2012 03:16:27(UTC) \| Reason: Not specified

1 user thanked kilele for this useful post.		on 07/09/2012(UTC)
User Profile View All Posts by User View Thanks

kilele		#16 Posted : 07 September 2012 13:22:44(UTC)
Rank: Advanced Member Groups: Registered Joined: 30/03/2011(UTC) Posts: 393 Was thanked: 133 time(s) in 114 post(s)		Originally Posted by: omorr I was thinking about the freely available libraries, open source software etc. I do not see then any license problems (am I right?) except the ones I was talking about. since SMath is not a commercial software i guess we can be not too strict about licenses anyway some licenses like gpl don't allow to publish opensource plugins for closed programs (unlike lgpl) as for distributing compiled matlab scripts, I think you are right! see this link don't know how this black boxes could be used in SMAth though, however the approach of making plugins out of matlab, fortran, pseudo-code from scientific papers.. could be more convenient due to compatibility and dll size

1 user thanked kilele for this useful post.		on 07/09/2012(UTC)
User Profile View All Posts by User View Thanks

omorr		#17 Posted : 07 September 2012 16:21:25(UTC)
Rank: Administration Groups: Registered, Advanced Member Joined: 23/06/2009(UTC) Posts: 1,740 Was thanked: 318 time(s) in 268 post(s)		Hello, This is one of my working problems I was already mentioned Primer 65a and struggled in SMath with. I reported there the problems of solve() and roots() solutions. I used it again for testing and attached it to this post. It seems the problem is a bit numerically "tricky" for solving in SMath. The original file is not working in the recent SMath version, neither solve() nor roots() (error message about T as undefined variable - not quite sure why). Here I attached the revised file - just removed eval() I was talking about in the previous post. Fortunately, solve() will now get the more accepted result , roots() will fail, Broyden() will give the answer if the guess value is quite close to the solution, Bisection() will fail as well. I hope I did not make any serious mistake here. Regarding this problem, I am satisfied that at least one of the possible tool in SMath can give the result. Regards, Radovan Edited by user 07 September 2012 16:29:03(UTC) \| Reason: Not specified File Attachment(s): Primer65aa.sm (42kb) downloaded 89 time(s). omorr attached the following image(s):
		When Sisyphus climbed to the top of a hill, they said: "Wrong boulder!"
		WWW

User Profile View All Posts by User View Thanks

kilele		#18 Posted : 07 September 2012 19:18:39(UTC)
Rank: Advanced Member Groups: Registered Joined: 30/03/2011(UTC) Posts: 393 Was thanked: 133 time(s) in 114 post(s)		According to what I've read, there seems not to be robust methods in multidimensions: Without insight into the nature of the problem, root finding is more or less blind search, this is why I suggested a multidimensional bisection method for a initial guess with just a few iterations. With some insight into the nature of the root, Newton’s method using derivative information, and Broyden’s method using only function information seem good candidates. Some information about methods followed by Octave: fsolve in Octave implements the multidimensional Newton method fzero in Octave uses Brent’s method for one dimension (bisection+secant) All these info is nearly copy-pasted of this doc I think also that there are some interesting advice on this pdf on page 20:Final Considerations, about how to rephrase your function so that all these algorithms work better. As a final suggestion (sorry for so many links to documents) it could be a good idea to make plugins for several methods: Brent (one dimension); Newton, Broyden and Homotopy methods (multidimension); and It could be even better combine some of these methods in a row or according to the type of function entered by the user (I assume that's how Smath Solve() works) Edited by user 07 September 2012 20:30:37(UTC) \| Reason: Not specified

1 user thanked kilele for this useful post.		on 07/09/2012(UTC)
User Profile View All Posts by User View Thanks

Davide Carpi		#19 Posted : 07 September 2012 20:08:33(UTC)
Rank: Advanced Member Groups: Registered, Advanced Member Joined: 13/01/2012(UTC) Posts: 2,710 Location: Italy Was thanked: 1378 time(s) in 902 post(s)		Originally Posted by: omorr Hello, This is one of my working problems I was already mentioned Primer 65a and struggled in SMath with. I reported there the problems of solve() and roots() solutions. I used it again for testing and attached it to this post. It seems the problem is a bit numerically "tricky" for solving in SMath. The original file is not working in the recent SMath version, neither solve() nor roots() (error message about T as undefined variable - not quite sure why). Here I attached the revised file - just removed eval() I was talking about in the previous post. Fortunately, solve() will now get the more accepted result , roots() will fail, Broyden() will give the answer if the guess value is quite close to the solution, Bisection() will fail as well. I hope I did not make any serious mistake here. Regarding this problem, I am satisfied that at least one of the possible tool in SMath can give the result. Regards, Radovan I omorr, i'll check this issue ASAP, especially because in this case the script seems to work while the plugin don't work... about eval(), you cannot use it where there are undefined variables because the function "force" the numeric evaluation. best regards, w3b5urf3r Edited by user 18 September 2012 01:29:23(UTC) \| Reason: Not specified Davide Carpi attached the following image(s):
		If you like my plugins consider to support SMath Studio buying a plan; to offer me a coffee: paypal.me/dcprojects

1 user thanked Davide Carpi for this useful post.		on 07/09/2012(UTC)
User Profile View All Posts by User View Thanks

omorr		#20 Posted : 07 September 2012 22:05:00(UTC)
Rank: Administration Groups: Registered, Advanced Member Joined: 23/06/2009(UTC) Posts: 1,740 Was thanked: 318 time(s) in 268 post(s)		Originally Posted by: kilele As a final suggestion (sorry for so many links to documents) it could be a good idea to make plugins for several methods: Brent (one dimension); Newton, Broyden and Homotopy methods (multidimension); and It could be even better combine some of these methods in a row or according to the type of function entered by the user (I assume that's how Smath Solve() works) I agree with you completely I also agree about the mentioned observation on the 20-page of your reference. This is up to the user. A simple advice is to rearrange the function f(x)= 0 by avoiding division of terms when denominator can be close to zero. @w3b5urf3r Based on the picture in your previous post (many methods in a plugin), did I say that you are my hero? Regards, Radovan Edited by user 07 September 2012 22:15:32(UTC) \| Reason: Not specified
		When Sisyphus climbed to the top of a hill, they said: "Wrong boulder!"
		WWW
1 user thanked omorr for this useful post.		on 08/09/2012(UTC)
User Profile View All Posts by User View Thanks

Users browsing this topic

14 Pages12 3 >»

Forum Jump

You cannot post new topics in this forum.
You cannot reply to topics in this forum.
You cannot delete your posts in this forum.
You cannot edit your posts in this forum.
You cannot create polls in this forum.
You cannot vote in polls in this forum.