I have 3 sets of data: xdata, ydata and error_ydata.
I need to fit this data according to a equation like this:
y_fit = c1*sin((2*pi*x_data)/c2 - c3) + c4
where c are constants, and the parameters to find.
I've tried several matlab functions like fittype or lsqcurvefit but they require very close initial estimates for the 4 constants to work. The point was to find these constants whichever are the initial estimates you give.
Any idea?
Thank you in advance.
My best regards
Sorry, but the fact is, nonlinear estimation requires at least decent starting values. If you can't bother to supply them, then expect at least some of the time random crapola for results.
Do those tools require VERY close estimates? Hardly so IMHO, but the definition of "very" is a highly subjective one. Perhaps you need to learn more about optimization and the tools that you will use. Once you do, you will start to know how to make them work better. A workman who lacks understanding of their tools should expect to get hurt on a frequent basis.
You might do some reading. Here is one place to start.
There ARE some tools out there that allow a reduction of the problem using a partitioned least squares approach. fminspleas is one. (You can also find pleas in the optimization toips and tricks file.). But in order to use that tool, you will need to learn something about its estimation methodology, understanding how it splits the parameters into two classes. Again, understand your tools.
Related
I have been looking for a Matlab function that can do a nonlinear total least square fit, basically fit a custom function to data which has errors in all dimensions. The easiest case being x and y data-points with different given standard deviations in x and y, for every single point. This is a very common scenario in all natural sciences and just because most people only know how to do a least square fit with errors in y does not mean it wouldn't be extremely useful. I know the problem is far more complicated than a simple y-error, this is probably why most (not even physicists like myself) learned how to properly do this with multidimensional errors.
I would expect that a software like matlab could do it but unless I'm bad at reading the otherwise mostly useful help pages I think even a 'full' Matlab license doesn't provide such fitting functionality. Other tools like Origin, Igor, Scipy use the freely available fortran package "ODRPACK95", for instance. There are few contributions about total least square or deming fits on the file exchange, but they're for linear fits only, which is of little use to me.
I'd be happy for any hint that can help me out
kind regards
First I should point out that I haven't practiced MATLAB much since I graduated last year (also as a Physicist). That being said, I remember using
lsqcurvefit()
in MATLAB to perform non-linear curve fits. Now, this may, or may not work depending on what you mean by custom function? I'm assuming you want to fit some known expression similar to one of these,
y = A*sin(x)+B
y = A*e^(B*x) + C
It is extremely difficult to perform a fit without knowning the form, e.g. as above. Ultimately, all mathematical functions can be approximated by polynomials for small enough intervals. This is something you might want to consider, as MATLAB does have lots of tools for doing polynomial regression.
In the end, I would acutally reccomend you to write your own fit-function. There are tons of examples for this online. The idea is to know the true solution's form as above, and guess on the parameters, A,B,C.... Create an error- (or cost-) function, which produces an quantitative error (deviation) between your data and the guessed solution. The problem is then reduced to minimizing the error, for which MATLAB has lots of built-in functionality.
I am currently running a multiple linear regression using MATLAB's LinearModel.fit function, and I am bit confused in regards to how to properly add interaction terms to the model by hand. As I am aware, LinearModel.fit does not standardize variables on its own, so I have been doing so manually.
So far, the way I have done it has been to
Standardize the observations for each variables
Multiply corresponding standardized values from specific variables to create the interaction terms and then add these new variables to the set of regression data
Run the regression
Is this the correct way to go about doing this? Should I standardize the interaction term variables also after calculating the 'raw' terms? Any help would be greatly appreciated!
Whether or not to standardize interaction terms probably depends on what you intend to do with the model. Standardization typically does not affect model performance as much as it allows for more straightforward model interpretation as your learned coefficients will be on similar scales. I suspect whether to do this or not is largely a matter of opinion. Here is a relevant stats.stackexchange post that may help.
My intuition would be the same as how you have described your process so far.
I have a curve which looks roughly / qualitative like the curves displayed in those 3 images.
The only thing I know is that the first part of the curve is hardware-specific supposed to be a linear curve and the second part is some sort of logarithmic part (might be a combination of two logarithmic curves), i.e. linlog camera. But I couldn't tell the mathematic structure of the equation, e.g. wether it looks like a*log(b)+c or a*(log(c+b))^2 etc. Is there a way to best fit/find out a good regression for this type of curve and is there a certain way to do this specifically in MATLAB? :-) I've got the student version, i.e. all toolboxes etc.
fminsearch is a very general way to find best-fit parameters once you have decided on a parametric equation. And the optimization toolbox has a range of more-sophisticated ways.
Comparing the merits of one parametric equation against another, however, is a deep topic. The main thing to be aware of is that you can always tweak the equation, adding another term or parameter or whatever, and get a better fit in terms of lower sum-squared-error or whatever other goodness-of-fit metric you decide is appropriate. That doesn't mean it's a good thing to keep adding parameters: your solution might be becoming overly complex. In the end the most reliable way to compare how well two different parametric models are doing is to cross-validate: optimize the parameters on a subset of the data, and evaluate only on data that the optimization procedure has not yet seen.
You can try the "function finder" on my curve fitting web site zunzun.com and see what it comes up with - it is free. If you have any trouble please email me directly and I'll do my best to help.
James Phillips
zunzun#zunzun.com
Are there any faster and more efficient solvers other than fmincon? I'm using fmincon for a specific problem and I run out of memory for modest sized vector variable. I don't have any supercomputers or cloud computing options at my disposal, either. I know that any alternate solution will still run out of memory but I'm just trying to see where the problem is.
P.S. I don't want a solution that would change the way I'm approaching the actual problem. I know convex optimization is the way to go and I have already done enough work to get up until here.
P.P.S I saw the other question regarding the open source alternatives. That's not what I'm looking for. I'm looking for more efficient ones, if someone faced the same problem adn shifted to a better solver.
Hmmm...
Without further information, I'd guess that fmincon runs out of memory because it needs the Hessian (which, given that your decision variable is 10^4, will be 10^4 x numel(f(x1,x2,x3,....)) large).
It also takes a lot of time to determine the values of the Hessian, because fmincon normally uses finite differences for that if you don't specify derivatives explicitly.
There's a couple of things you can do to speed things up here.
If you know beforehand that there will be a lot of zeros in your Hessian, you can pass sparsity patterns of the Hessian matrix via HessPattern. This saves a lot of memory and computation time.
If it is fairly easy to come up with explicit formulae for the Hessian of your objective function, create a function that computes the Hessian and pass it on to fmincon via the HessFcn option in optimset.
The same holds for the gradients. The GradConstr (for your non-linear constraint functions) and/or GradObj (for your objective function) apply here.
There's probably a few options I forgot here, that could also help you. Just go through all the options in the optimization toolbox' optimset and see if they could help you.
If all this doesn't help, you'll really have to switch optimizers. Given that fmincon is the pride and joy of MATLAB's optimization toolbox, there really isn't anything much better readily available, and you'll have to search elsewhere.
TOMLAB is a very good commercial solution for MATLAB. If you don't mind going to C or C++...There's SNOPT (which is what TOMLAB/SNOPT is based on). And there's a bunch of things you could try in the GSL (although I haven't seen anything quite as advanced as SNOPT in there...).
I don't know on what version of MATLAB you have, but I know for a fact that in R2009b (and possibly also later), fmincon has a few real weaknesses for certain types of problems. I know this very well, because I once lost a very prestigious competition (the GTOC) because of it. Our approach turned out to be exactly the same as that of the winners, except that they had access to SNOPT which made their few-million variable optimization problem converge in a couple of iterations, whereas fmincon could not be brought to converge at all, whatever we tried (and trust me, WE TRIED). To this day I still don't know exactly why this happens, but I verified it myself when I had access to SNOPT. Once, when I have an infinite amount of time, I'll find this out and report this to the MathWorks. But until then...I lost a bit of trust in fmincon :)
I have some data for which I have a set of numerically determined model curves. Now I would like to find the one with least square deviation, I only need to vary one parameter, which is the amplitude of these model curves.
I used fitting with analytic functions, but I did not find a way to handle such a problem.
Is there any solution?
Thanks a lot!
One of the optimize functions should do the trick. You can also read the section on optimization in the manual. Without any specifics on the data or the model you wish to match, it's hard to recommend anything more specific. For example, if your cost function has many maxima and minima or is not differentiable, you'll have to choose some of the more expensive routines.