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.
Related
I have two complex datasets for which I intend to find a suitable function to fit them. The first dataset is presented as follows:
As you can see, although complicated, it seems that this dataset is a combination of rectangle functions. These data describe the relation of 'Amplitude' of complex numbers with time. The second picture looks like this:
And this relation actually describes the 'Phase' of the above complex numbers with time, it seems that they are also combinations of rectangle functions. At first, I want to use combinations of Fourier cosine and sine series to fit the amplitude and phase using
lsqcurvefit
in MATLAB, but it seems that the provided parameters fail to converge to the correct values. (I have tried a number of options, like adjusting FiniteDifferenceStepSize, FiniteDifferenceType, StepTolerance and so on). Despite many failures, I saw someone said we could use Normal cumulative distribution function (CDF) to fit a step function, and I thought that it might be possible if we use the combinations of parameterized CDF and
y = erfc(x)
to achieve successful fitting. So, could anyone provide any solutions or ways to fit the above two relations? Giving some valuable ideas will also be very helpful to me.
PS: For now I don't care any hidden physics inside these data, and all I want to do is to find a mathematical way to fit the above two relations in MATLAB.
Thanks!
I was wondering if there exists a technical way to choose initial parameters to these kind of problems (as they can take virtually any form). My question arises from the fact that my solution depends a little on initial parameters (as usual). My fit consists of 10 parameters and approximately 5120 data points (x,y,z) and has non linear constraints. I have been doing this by brute force, that is, trying parameters randomly and trying to observe a pattern but it led me nowhere.
I also have tried using MATLAB's Genetic Algorithm (to find a global optimum) but with no success as it seems my function has a ton of local minima.
For the purpose of my problem, I need justfy in some manner the reasons behind choosing initial parameters.
Without any insight on the model and likely values of the parameters, the search space is too large for anything feasible. Think that just trying ten values for every parameter corresponds to ten billion combinations.
There is no magical black box.
You can try Bayesian Optimization to find a global optimum for expensive black box functions. Matlab describes it's implementation [bayesopt][2] as
Select optimal machine learning hyperparameters using Bayesian optimization
but you can use it to optimize any function. Bayesian Optimization works by updating a prior belief over a distribution of functions with the observed data.
To speed up the optimization I would recommend adding your existing data via the InitialX and InitialObjective input arguments.
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 want to optimize a multi-variable function with the patternsearch function in MATLAB. The function requires a lower and upper boundary and looks within the boundaries in a continuous domain.
I however have a discrete set of values in an excel file and would like the algorithm to search within this discrete domain instead of in the continuous domain.
Is this possible with patternsearch?
Maybe I don't understand correctly your question but if you have a (discret and finite) set of values, why don't you compute the function's value at these points and return the minium?
In short, no. That is not what patternsearch is intended for. Optimization techniques for discrete and continuous search spaces are quite expectedly different.
If you're looking for an approximate answer however, it is possible to use spline, polyfit, etc. to arrive at an approximate continuous function for your data and then apply patternsearch on it.
If you provide greater detail about your problem, I or someone else may be able to suggest a more suitable way of working with your data.
The best optimization tool for this is the Genetic Algorithm. This optimization tool comes with Matlab's global optimization toolbox and allows for optimization of both continuous and discrete variables at the same time.
In the genetic algorithm variables that are integers have to be declared as such. Non-declared variables are continuous by default.
Check the Global Optimization Toolbox guide for information on how it works: http://it.mathworks.com/help/pdf_doc/gads/gads_tb.pdf.
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