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Revising Levenberg Marquardt Method
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on 21/12/2019(UTC), on 27/12/2019(UTC)
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Solution using the Maxima package lsquares via the interface functions of the Maxima plugin fit1.sm (30kb) downloaded 42 time(s). |
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2 users thanked mkraska for this useful post.
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on 21/12/2019(UTC), on 21/12/2019(UTC)
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Thanks: Carlos, Martin. SS 6179 does not complain but still pedaling in 10 min ??? 1. in Mathcad [8 Pro ... 11] type ERR= after Minerr ERR is undocumented = SSD [discovered by Paul W.] 2. alternate to corr, SSD sometimes meaningless [Viod ratio, Verhulst]. 3. Often, the best fit is Conjugate Gradient. Jean Genfit VoidRatio.sm (66kb) downloaded 28 time(s). Genfit Verhulst.sm (57kb) downloaded 23 time(s). Genfit Weibull.sm (55kb) downloaded 26 time(s).
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Thanks, Martin Hello Jean: I tried to run the algorithm of Levenberg Marquardt, in the version of SS6179, but it inevitably fails, giving an incorrect solution. It seems that the error could be in some operation where a single value vector is produced. Could you take a look to see if you can doctorate ?. I post again the version of the algorithm in SS7251 with some minor changes. Algorithm_Levenberg_M_with_DF_SS6179.sm (514kb) downloaded 26 time(s). Algorithm_Levenberg_M_with_DF_SS7251_R1.sm (210kb) downloaded 22 time(s).Best Regards Carlos
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Originally Posted by: CBG It seems that the error could be in some operation where a single value vector is produced. Could you take a look to see if you can doctorate ?. Helo Carlos, I deleted all previous postings of no more interest. I found no way to iterate LM ? Otherwise, easy to initialize from the al_nleqsolve as suggested in the last part of the attached. In Mathcad, LM was found hyper robust to initialize, but most of the times, better fit are concluded from CG. The Weibull example is one of the easiest to fit. Very many aren't so easy to fit from model(s), more reflexive. Some model functions can't be fitted at all, unless from trial/error. A great piece of work, to get familiarized in fitting session. Thanks Carlos ... Jean Genfit Weibull [LM_Iteretive CG] Copy.sm (437kb) downloaded 20 time(s).
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Originally Posted by: Jean Giraud I found no way to iterate LM ? Otherwise, easy to initialize from the al_nleqsolve as suggested in the last part of the attached. ... then like this: refit from observing the bar deviation. Genfit Weibull [LM,al_nleqsolve Companion].sm (103kb) downloaded 16 time(s).
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Hello Jean
Thank you very much.
The question is: Why does the SS7251 version directly obtain the solution, changing the values correctly of the β variable, while the SS6179 version does not, and they have to be manually entered as new values of the vector of the assumed initial solution. ?
The algorithm is the same for the 2 versions of SmathStudio, so what is the difference if the programming and decision definitions are supposed to work the same?
Best Regards
Carlos
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Originally Posted by: CBG Thank you very much.
The question is: Why does the SS7251 version directly obtain the solution, changing the values correctly of the β variable, while the SS6179 version does not, and they have to be manually entered as new values of the vector of the assumed initial solution. ?
The algorithm is the same for the 2 versions of SmathStudio, so what is the difference if the programming and decision definitions are supposed to work the same? A most interesting observation ! SS 6179 may have to do with the conditional statement. SS 6179 is "zero" tolerance. So, it may just navigate then end. It could be SS 7251 conditional is coded more tolerant Mathcad style and reaches convergence ? Watson, are you there ? Cheers Carlos ... later on.
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Originally Posted by: CBG Hello Jean
Thank you very much.
The question is: Why does the SS7251 version directly obtain the solution, changing the values correctly of the β variable, while the SS6179 version does not, and they have to be manually entered as new values of the vector of the assumed initial solution. ?
The algorithm is the same for the 2 versions of SmathStudio, so what is the difference if the programming and decision definitions are supposed to work the same?
Best Regards
Carlos Hola Carlos. Just check the code from the SS6179 version, in the while not(stop) loop, the line with A:=J^T*f is wrong, it must to be A:=J^T*J. Best regards. Alvaro.
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Originally Posted by: Razonar Hola Carlos. Just check the code from the SS6179 version, in the while not(stop) loop, the line with A:=J^T*f is wrong, it must to be A:=J^T*J. Thanks Alvaro ... doctored ! Weibull LM [0.1,1] 1 min Weibull CG [0.1,1] 2.3 sec ... ½ max residual deviation Carlos, your very original LM [Pharmacokinetics] works faster. an it be compacted algo style ... tried not to avail ? Hola ! Avaro, Carlos ... Jean Genfit Weibull [LM_Iteretive CG].sm (438kb) downloaded 21 time(s). Genfit [Algo Minimize(L-M)].sm (117kb) downloaded 21 time(s).
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Originally Posted by: Razonar
Hola Carlos. Just check the code from the SS6179 version, in the while not(stop) loop, the line with A:=J^T*f is wrong, it must to be A:=J^T*J.
Best regards. Alvaro.
Hola Alvaro. Muchas gracias por tu corrección. Cuando copie y pegue directamente el codigo de SS7251 a SS6179 daba el error de "Ecuacion demasiado larga para visualizarla" con un tiempo de ejecusion de mas de 7 minutos, por lo que opté por copiar manualmente el codigo, pensando que las declaraciones eran interpretados erroneamente, y fue cuando copie mal la formula. Hello Alvaro. Thank you very much for your correction. When copying and pasting directly the code from SS7251 to SS6179 it gave the error of "Equation too long to display" with an execution time of more than 7 minutes, So I chose to manually copy the code, thinking that the statements were misinterpreted, and It was when I copied the formula badly. Muchas gracias tambien a Jean por su apoyo y sus comentarios tan acertados. Best Regards Carlos
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Originally Posted by: CBG Muchas gracias tambien a Jean por su apoyo y sus comentarios tan acertados. I Understand Carlos ... Now, for your bed time reading, these two fits level Mathcad GenfitMatrix. By far, they beat former NBS-125. Rational fractions have exceptional fitting/interpolation virtues. Thanks and credit to Jeff who helped me so much ... About same timing as MCD 11 Jean ... enjoy. Genfit 0000000 Rational Auto-init ITER Copy.sm (150kb) downloaded 19 time(s).
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Originally Posted by: mkraska Solution using the Maxima package lsquares via the interface functions of the Maxima plugin fit1.sm (30kb) downloaded 42 time(s).my god.. i didn't know this was a thing! i'm really glad a friend led me to this forum. hey can you check out this website? solidpapers.com was where I had one of my geometry homework done and I got a passing grade! can you see if it also works for you? i'm planning to order another paper from them again. tell me what you think!!!
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Fitting data set is a long discours, much longer in techniques/methods. The Mathcad/Mathsoft LM is the quick/robust ... bingo/done. Not the best in very many instances. Attach your data set in this Forum. Make sure they are raw data from collection, i.e: not freaked by unknown. Cheers ... are we going to see you again ?
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Hello Jean I know you understand perfectly, and that has been the intention.
The second Levenberg Marquardt algorithm has been passed as a function in the versions of SS7251 and SS6179, the examples published by Jean in "Genfit linfit HyperRobust [Ge Crystal] .sm" and 2 other previous examples have also been solved.
Unfortunately, version SS6179, for unknown reasons does not solve the first example, and results in the same starting solution vector, the other examples are solved without problem.
LM2A_as_a_Function_SS7251.sm (151kb) downloaded 18 time(s).
LM2A_as_a_Function_SS6179.sm (145kb) downloaded 19 time(s).
Best Regards
Carlos
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Unfortunately, version SS6179, for unknown reasons does not solve the first example, and results in the same starting solution vector, the other examples are solved without problem.Hola ! Carlos. You don't specify if the SS 7251 solves that example. Please, don't drop dead at reading. This example attached, Mathcad [L-M, CG, QN] does not even return the exact coefficients. I tortured myself on that. On the other hand as well, many model functions can't be fitted from being too much reflexive within themselves. For those non willing fit, al_nleqsolve will generally succeeds. Mathcad failed as well the ITER Cadarache Cu resistivity. Was done otherwise via sub methods. At least for ITER, Mathcad returned: "Too complicated to solve" u:=(0≤x)*(x≤10) useful constrain the Quick plot. Thanks for your immense dedication. Jean Genfit [Algo Minimize(al_nleqsolve Pharmacokinetics) ... AUTOMATED] Copy.sm (105kb) downloaded 14 time(s).
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Hola Jean! Levenberg Marquardt's second algorithm in SS7251 does solve the example. All data with a tolerance of 10 ^ -16 can be used, or 4 selected data with a tolerance of 10 ^ -8 can be used, in both cases, the starting vector is [0.5 1 1 1]. LM2A_as_a_Function_SS7251_R1.pdf (799kb) downloaded 17 time(s). LM2A_as_a_Function_SS7251_R1.sm (206kb) downloaded 20 time(s).The idea was to run the LM algorithm as a function for SS7251 and SS6179, for which use your examples. Jean, I tell you that I take the results you show in your exercises as the exact or correct ones Thank you Best Regards Carlos
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Originally Posted by: CBG Jean, I tell you that I take the results you show in your exercises as the exact or correct ones They are all correct, good fit from model. There are many more techniques to best fit by region(s) The last example SS 6179 spits the fit very fast vs other solvable previous examples ... supports tol 0.00000001. Comfort yourself: model fit needs no more than 6 decimals or less ... from zillions done. Thanks Carlos for your doctoring expertise. Jean Genfit 000000000000 L-M AUTOMATED Carlos 20200115 [Exampless].sm (212kb) downloaded 21 time(s).
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