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!
Related
Assume that I have an array of counts (ideally returned by histcounts). Is there an official Matlab way to plot such a histogram with all the standard normalization options available?
It seems that the best suggestion I have is to get the counts from histcounts and then plot them with bar. Something like:
edges = linspace(0,bound,nbins);
hist_c = histcounts(X,nbins);
bar(edges(1:nbins-1),hist_c);
unfortunately as far as I know it seems that using bar is really not recommended according to this link. Probably because as its obvious from the code, it seems that it moves a lot of implementation details into user code (like produces edges array manually when only needing nbins or having to know if to use 1:nbins-1 vs 2:nbins).
Furthermore, which I believe is the worst, is that it leave the user to have to implement the normalization options on its own. One may point out that histcounts can do the normalization options for you, however, it can only do them given the data matrix X. If one had an extremely large matrix X, then one would be in trouble because producing the histogram counts of X could be done on the fly (as done in this question) but the other normalization options could not be easily be done on the fly. One practice the user could try to implement each normalization option as described by the equations in the documentation but it seems extremely inefficient to have users implement this by hand. Is there a way to get access to the code that actually performs this normalization?
In reality what my question is going for is, is there an official matlab way to produce histogram having only the histogram counts? In particular hiding all the implementation details of producing the counts, normalization, binning, edges, etc?
The ideal code in my mind should look like this to the user:
histogram_counts = get_hist_count(X)
plot_histogram(histogram_counts,'Normalization',normalization)
and produces the desired histogram plot.
Related question:
https://www.mathworks.com/matlabcentral/answers/332178-how-does-one-plot-a-histogram-from-the-histogram-counts
https://www.mathworks.com/matlabcentral/answers/275278-what-is-the-recommended-practice-for-plotting-the-outputs-of-histcounts
https://www.mathworks.com/matlabcentral/answers/91944-how-can-i-combine-the-options-histc-and-stack-in-a-bar-plot-in-matlab-7-4-r2007a#answer_101295
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 working with image processing in MATLAB. I have two different images whose histogram plots are as shown below.
Image 1:
and
Image 2:
I have multiple images like those and the only distinguishing(separating) features is that some have single peak and others have two peaks.
In other words some can be thresholded (to generate good results) while others cannot. Is there any way I can separate the two images? Are there any functions that do so in MATLAB or any reference code that will help?
The function used is imhist()
If you mean "distinguish" by "separate", then yes: The property you describe is called bimodality, i.e. you have 2 peaks that can be seperated by one threshold. So your question is actually "how do I test for an underlying bimodal distribution?"
One option to do this programmatically is Binning. This is not the most robust method but the easiest. It might work, it might not.
Kernel Smoothing is probably the more robust solution. You basically shift and scale a certain function (e.g. Gaussian) to fit the data. This can be done with histfit in matlab.
There's more solutions for this problem which you can research for yourself since you now know the terms needed. Be aware though that your problem is not a trivial one if you want to do it properly.
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
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.