As far as I understand R's nonlinear equation solver nleqslv(x, fn) finds only one solution of the nonlinear equation.
However (as Bhas commented) searchZeros function (the same package) can find my solutions depending on the starting points.
Question: are there some function in R which can help choosing the set of initial points for searchZeros ,which will help me to find all the solutions ?
I am interested in the case of function with several variables.
I undestand that solution to be found pretty much depends on the initial approximation. So the brute force way is to check some reasonable grid of intial approximations. However there might be some more intelligent way to get all the solutions ?
Related
I am trying to solve a numerical equation in R but would want a method which perform similar to vpasolve in Matlab. I have a non linear equation (involving lot of log functions) which when solve in R with uniroot gives me complete different answer compared to what vpasolve gives in matlab.
First, a word of caution: it's often much more productive to learn that there's a better way to do something than the way you are used to doing.
edit
I went back to MATLAB and realized that the "vpa" collection is using extended precision. Is that absolutely necessary for your purposes? If not, then my suggestions below may suffice.
If you do require extended precision, then perhaps Rmpfr::unirootR function will suffice. I would like to point out that, since all these solvers are generating an approximate solution (as opposed to analytic), the use of extended precision operations seems a bit pointless.
Next, you need to determine whether MATLAB::vpasolve or uniroot is getting you the correct answer. Or maybe you simply are converging to a root that's not the one you want, in which case you need to read up on setting limits on the starting conditions or the search region.
Finally, in addition to uniroot, I recommend you learn to use the R packages BBsolve , nleqslv, rootsolve, and ktsolve (disclaimer: I am the owner and maintainer of ktsolve). These packages are pretty flexible and may lead you to better solutions to your original problem.
Sorry, maybe I am blind, but I couldn't find anything specific for a rather common problem:
I want to implement
solve(A,b)
with
A
being a large square matrix in the sense that command above uses all my memory and issues an error (b is a vector with corresponding length). The matrix I have is not sparse in the sense that there would be large blocks of zero etc.
There must be some function out there which implements a stepwise iterative scheme such that a solution can be found even with limited memory available.
I found several posts on sparse matrix and, of course, the Matrix package, but could not identify a function which does what I need. I have also seen this post but
biglm
produces a complete linear model fit. All I need is a simple solve. I will have to repeat that step several times, so it would be great to keep it as slim as possible.
I already worry about the "duplication of an old issue" and "look here" comments, but I would be really grateful for some help.
Can anyone give me a good explanation for what the parameter "algorithm" does in the nls function in R?
Also, how does the formula work? I know it uses a tilda, but I can't really find a down-to-earth explanation of it.
Also, how important are the start values? Do I need to try multiple start values, or can I still have a guarantee that nls will find the correct parameters regardless of the start values I use?
In brief:
nls() is going to vary parameters to try to minimize the square error between your model and your data. There's several good methods it can try to find the minimum. Reading the details about "method" in ?optim will provide some good info and references.
In general, for nonlinear models, your results can be sensitive to initial guess. You should try several different guesses to make sure that the outputs are close. If your results are very sensitive to your guess, you can try re-parameterizing, using a different algorithm, or rethinking your model.
As for the formula, I'd echo the previous answer. Work through the examples in the bottom of ?nls and then try to ask a more specific question.
I would like to know if there is a package in R handling non linear integer optimization.
"Basically", I would like to solve the following problem:
max f(x) s.t x in (0,10) and x is integer.
I know that some branching algorithms are able to handle the linear version of this problem, but here my function f() might be more complicated. (I can't even make sure it would be quadratic of the form f(x)=xQx).
I guess there is always the brute force solution to test all the possibilities as long as they are bounded, but I was wondering if there wasn't anything smarter.
I have a few options for you, but none of them is the silver bullet, although it looks like your silver bullet is in the works under the rino project: http://r-forge.r-project.org/projects/rino/.
Since your function is complicated, you may want to use a genetic algorithm (i.e., gradient-based optimizers may not be reliable). genoud in the rgenoud library may do the trick (link text). If you set data.type.int=TRUE it should do the trick. I have not used this library, but have some experience with GAs in matlab and the time to convergence is sensitive to the settings, so you'll be well served to read the man page a few times through.
Or, if your function in strictly concave (unlikely, since you say it may be complicated) you can solve with a gradient solver (e.g., optim) then check the neighborhood around the optimum (can't be more than 2^n points to check).
Sorry, I can't be of more help.
If it is hardly nonlinear there is no better method than brute force (you will never know if the minimum is local or if some flat-looking fragment doesn't have any narrow and deep valleys), except of course symbolic computation (which probably won't work because the function is too complicated) or soft computing, I mean things like genetic algorithms, Monte-Carlo, swarms, etc. (here you don't have a guarantee that it will find the very global minimum and because you have integer x it can be slower than brute force).
http://cran.r-project.org/web/views/Optimization.html lists the packages Rdonlp2 and Rsolnp which may be suitable.
Discrete filled function method is one of the recent methods that can find global solution of nonlinear integer programming with about 100 constraints and variables.
I'm building a custom regression tree and want to use m-estimate for pruning.
Does anyone know how to calculate that.
http://www.ailab.si/blaz/predavanja/UISP/slides/uisp07-RegTrees.ppt might help (slide 12, how should Em look like?)
There are a lot of m-estimates. They all boil down to recasting your estimation problem as a minimization problem. If you use squared error as the function you're minimizing, you just get sample mean. If you use absolute value of the error, you get the sample median. The idea is to use a function that is a compromise between these two so that you get some of the efficiency of the mean and some of the robustness of the median.
Once you've picked your function, finding an m-estimate is just an optimization problem. So your question really boils down to one of finding optimization software. If your optimization problem is convex (and you can pick your m-estimator so that the problem is convex) then there's a lot of high quality software out there.