There is a file called normxcorr2_general on MathWorks here that the author claims always gives correct answers while Matlab's built-in normxcorr2 gives incorrect answers when the two input matrices are close in size. After doing some testing, it is clear that the two functions do give significantly different outputs when the inputs are the same size.
Is normxcorr2_general actually more accurate? I don't have much experience in Matlab and I'm having trouble figuring that out from reading through the function script.
Edit: To clarify, if I understand it correctly then these functions are both implementing equation number (2) in this paper about computing normalized cross-correlations.
I'm trying to implement an algorithm which has been described in a paper. It deals with accelerometer data which has to be filtered and differentiated. My input is a vector (1 column, multiple rows).
As described here
The vector has to differentiated using a Gaussian CWT with the MatLab function cwt. Scale has to be 'scale10' and wavelet 'gaus1'.
When I try to implement the instructions in MatLab, I type the following:
dudx=cwt(vector,'scale10','gaus1');
This is the error I get:
Undefined function 'sqrt' for input arguments of type 'char'.
Error in cwt (line 278)
coefs(ind,:) = -sqrt(a)*wkeep1(diff(wconv1(ySIG,f)),lenSIG);
As it should actually work with the input, I've really no idea what I could change. I also went through the mathworks pages from cwt and wavefun but without any solution.
I've never before used a CWT, therefore I thought that I may misunderstood something and applied the instructions wrong. Can anyone help me out on this?
You're not using the function right. The second parameter is a vector of scales where each number is the desired scale you want. scale10 doesn't mean anything. Do you want the 10th scale?
Do this:
dudx=cwt(vector,10,'gaus1');
Please read the documentation here: http://www.mathworks.com/help/wavelet/ref/cwt.html
The Matlab function interpn does n-grid interpolation. According to the documentation page:
In a future release, interpn will not accept mixed combinations of row and column vectors for the sample and query grids.
This page provides a bit more information but is still kind of cryptic.
My question is this: Why is this modification being implemented? In particular, are there any pitfalls to using interpn?
I am writing a program in fortran that is supposed to produce similar results to a Matlab program that uses interpn as a crucial component. I'm wondering if the Matlab program might have a problem that is related to this modification.
No, I don't think this indicates that there is any sort of problem with using interpn, or any of the other MATLAB interpolation functions.
Over the last few releases MathWorks has been introducing some new/better functionality for interpolation (for example the griddedInterpolant, scatteredInterpolant and delaunayTriangulation classes). This has been going on in small steps since R2009a, when they replaced the underlying QHULL libraries for computational geometry with CGAL.
It seems likely to me that interpn has for a long time supported an unusual form of input arguments (i.e. mixed row and column vectors to define the sample grid) that is probably a bit confusing for people, hardly ever used, and a bit of a pain for MathWorks to support. So as they move forward with the newer functionality, they're just taking the opportunity to simplify some of the syntaxes supported: it doesn't mean that there is any problem with interpn.
Matlab's command for defining a vector time series model is vgxset, the formalism for which can be accessed by the command "doc vgxset". It says that the model parameter Q is "[a]n n-by-n symmetric innovations covariance matrix". No description of what it is for. I assumed that it was the covariance of the noise sources that show up in the equations for each times series in the archetypal representation of a vector time series, e.g., http://faculty.chicagobooth.edu/john.cochrane/research/papers/time_series_book.pdf.
I could be off about something (I often am), but this doesn't seem to match results from actually issuing the command to estimate a model's parameters. You can access the code that illustrates such estimation via the command "doc vgxvarx":
load Data_VARMA22
[EstSpec, EstStdErrors] = vgxvarx(vgxar(Spec), Y, [], Y0);
The object EstSpec contains the model, and the Q matrix is:
0.0518 0.0071
0.0071 0.0286
I would have expected that a covariance matrix as ones on the diagonal. Obviously, I misunderstand and/or mis-guessed at the purpose of Q. However, if you actually pull up the code for vgxset ("edit vgxset"), the comments explicitly describe Q as an "[i]nnovations covariance matrix".
I have 3 questions:
(1) What exactly is Q?
(2)Is there a Matlab reference document that I've failed to locate for fundamental parameters like this?
(3)If it isn't the covariance matrix for the noise sources, how does one actually supply actual noise source covariances to the model?
Please note that this question is specifically about Matlab's command for setting up the model, and as such, does not belong in the more concept-oriented Cross Validated Stack Exchange forum. I have posted this to:
(1) vgxset command: Q parameter for resulting model object?
(2) http://groups.google.com/forum/#!topic/comp.soft-sys.matlab/tg59h1wkRCw
I will try to iterate to an answer, but being so many branches of discussion, i prefer to access directly onto this format. Whatever mean, this is a constructive process, as the purpose of this forum is...
Some previous "clarifications":
The Output Covariance from EstSpec.Q after and before running the command vgxvarx are quite similar. Thus the command is outputting what he is shiningly expecting from itself.
As an Output Covariance -or whatever other meaning for the Q parameter- is almost never to be a "mask" of the parameters to use, -i.e. an identity or a sparse zero-one matrix input parameter-. If you can assign it as a diagonal multiplied by some scalar univariate scalar is a different history. This is a covariance, plainly, just as in other MATLAB commands.
Hence:
(2) Is there a Matlab reference document that I've failed to locate for fundamental parameters like this?
No, Matlab ussualy don't give further explanations for "non popular" commands. Yes, this is, under some measure, "not popular", so i would not be impressed if the answer for this question is no.
Of course, the doctoral method is to check the provided references, on this case, those provided under doc vartovec. Which i dunno the hell where to find without order the books seeking the proper library or seeking the overall internet on five minutes...
Thus the obscure method is always better... check the code for the function by doing edit vgxvarx. Check the commented Section % Step 7 - Solve for parameters (Line 515, Matlab R2014b). There are calculations for a Q matrix through a function mvregress. At this point, both of us know, this is the core function.
This mvregress function (Line 62, Matlab R2014b) receives an input parameter called Covar0, which is described as a *D-by-D matrix to be used as the initial estimate for SIGMA*.
This antecedent leads to the answer for (1).
(1) What exactly is Q?
The MATLAB code has dozens of switch -both as options and auto-triggered- so i am actually not sure of which algorithm are you interested on, or based on your data, which ones are actually "triggered" :). Please read the previous answer, and place a Debug Point on the mvregress function:
Covar=Covar+CovAdj; %Line 433, Matlab R2014b
and/or at:
Covar = (Covar + Resid'*Resid) / Count; % Line 439, Matlab R2014b
Having that, the exact meaning of Q, and as indicated by the mvregress help, would be an "Initial Matrix for the Estimate of the Output Covariance Matrix". The average is simply given by averaging the Counts...
But, for the provided data, making:
Spec.Q=[1 0.1;0.1 1];
and then running vgxvarx, the parameter Covar never got initialized!.
Which for the presented unfortunate case, leads to a simply "Unused Parameter".
(3) If it isn't the covariance matrix for the noise sources, how does one actually supply actual noise source covariances to the model?
I've lost tons of manhours trying to gather the correct information from pre-built Matlab commands. Thus, my suggestion here, is to stick onto the concepts of system identification, and I would put my faith under one of the following alternatives:
Keep believing, and dig a bit and debug inside the mvregress function, and check if some of the EstMethods -i.e. cwls ecm mvn under Line 195- leads to a proper filling of the Covar0 parameter,
Stick to the vgxvarx command, but let the Q parameter go, and diagonalize | normalize the data properly, in order to let the algorithm identify the data as a Identically Distributed Gaussian Noise,
Send vgxvarx to the hell, and use arx. I am not sure about the current stability of vgxvarx, but i am quite sure arx should be more "stable" on this regard...
Good Luck,
hypfco.
EDIT
A huge and comprehensive comment, i have nothing much to add.
Indeed, it is quite probable the vgxvarx was run on the Matlab data sample. Hence the results lay explained,
I tried to use the Q parameter on the vgxvarx, with no success by now. If any working code is found, it would be interesting to include it,
The implementation of the noise transformation over the data should be really simple, of the form:
Y1=(Y-Y0)*L
with L the left triangular cholesky for the inverse calculated covariance of Y, and Y0 the mean,
I think the MA part is as critical as the AR part. Unless you have very good reasons, you usually cannot say you explained your data in a gaussian way.
From your very last comment, I really suggest you to move onto a better, more established command for doing AR, MA, ARMA and such flavours. I am pretty sure they handle the MV case...
Again, Matlab don't impress me on that behaviour...
Cheers...
hypfco
I need to construct an interpolating function from a 2D array of data. The reason I need something that returns an actual function is, that I need to be able to evaluate the function as part of an expression that I need to numerically integrate.
For that reason, "interp2" doesn't cut it: it does not return a function.
I could use "TriScatteredInterp", but that's heavy-weight: my grid is equally spaced (and big); so I don't need the delaunay triangularisation.
Are there any alternatives?
(Apologies for the 'late' answer, but I have some suggestions that might help others if the existing answer doesn't help them)
It's not clear from your question how accurate the resulting function needs to be (or how big, 'big' is), but one approach that you could adopt is to regress the data points that you have using a least-squares or Kalman filter-based method. You'd need to do this with a number of candidate function forms and then choose the one that is 'best', for example by using an measure such as MAE or MSE.
Of course this requires some idea of what the form underlying function could be, but your question isn't clear as to whether you have this kind of information.
Another approach that could work (and requires no knowledge of what the underlying function might be) is the use of the fuzzy transform (F-transform) to generate line segments that provide local approximations to the surface.
The method for this would be:
Define a 2D universe that includes the x and y domains of your input data
Create a 2D fuzzy partition of this universe - chosing partition sizes that give the accuracy you require
Apply the discrete F-transform using your input data to generate fuzzy data points in a 3D fuzzy space
Pass the inverse F-transform as a function handle (along with the fuzzy data points) to your integration function
If you're not familiar with the F-transform then I posted a blog a while ago about how the F-transform can be used as a universal approximator in a 1D case: http://iainism-blogism.blogspot.co.uk/2012/01/fuzzy-wuzzy-was.html
To see the mathematics behind the method and extend it to a multidimensional case then the University of Ostravia has published a PhD thesis that explains its application to various engineering problems and also provides an example of how it is constructed for the case of a 2D universe: http://irafm.osu.cz/f/PhD_theses/Stepnicka.pdf
If you want a function handle, why not define f=#(xi,yi)interp2(X,Y,Z,xi,yi) ?
It might be a little slow, but I think it should work.
If I understand you correctly, you want to perform a surface/line integral of 2-D data. There are ways to do it but maybe not the way you want it. I had the exact same problem and it's annoying! The only way I solved it was using the Surface Fitting Tool (sftool) to create a surface then integrating it.
After you create your fit using the tool (it has a GUI as well), it will generate an sftool object which you can then integrate in (2-D) using quad2d
I also tried your method of using interp2 and got the results (which were similar to the sfobject) but I had no idea how to do a numerical integration (line/surface) with the data. Creating thesfobject and then integrating it was much faster.
It was the first time I do something like this so I confirmed it using a numerically evaluated line integral. According to Stoke's theorem, the surface integral and the line integral should be the same and it did turn out to be the same.
I asked this question in the mathematics stackexchange, wanted to do a line integral of 2-d data, ended up doing a surface integral and then confirming the answer using a line integral!