How does MATLAB 2016b eig function compute all eigenvalues and eigenvectors?

Dear all,

I know the source code of certain built-in functions like 'eig' is confidential and property of Mathworks. However, I could not find in the documentation a clear explanation of which methods are used by 'eig' to compute ALL eigenvalues AND eigenvectors of a (let's say dense) symmetric matrix. Does 'eig' rely on some LAPACK (and/or ARPACK?) routines (as it did in R2011b, for example)? Which ones?

[Walter Roberson]

https://www.mathworks.com/company/newsletters/articles/this-is-a-supplement-to-the-cleves-corner-article-matlab-incorporates-lapack.html

https://www.mathworks.com/company/newsletters/articles/matlab-incorporates-lapack.html

Answer 1

[Jan]

As long as the source code is confidential and a reverse engineering is forbidden by the license agreement, all we know is what you find in the documentation.

You could provide a LAPACK library compiled by your own including debugging information, but I'm afraid this is a kind of reverse engineering already.

You can call the LAPACK routines through Mex functions directly, see e.g. https://www.mathworks.com/matlabcentral/fileexchange/16777-lapack an some other FileExchange submissions. Then you might find out what happens internally by comparing the results. But this is sophisticated guessing only. Therefore I suggest to solve the problem from another direction: Why do you want to know this? The solution might be to solve the actual problem without knowing, how Matlab does it.

[Douglas Gonçalves]

Thanks Jan for your answer.

Let me try to be clearer.

You can call the LAPACK routines through Mex functions directly, see e.g. https://www.mathworks.com/matlabcentral/fileexchange/16777-lapack an some other FileExchange submissions. Then you might find out what happens internally by comparing the results. But this is sophisticated guessing only.

That's what I meant when I said that R2011b relies on some LAPACK routines. But as you said, it's just a sophisticated guess.

Therefore I suggest to solve the problem from another direction: Why do you want to know this? The solution might be to solve the actual problem without knowing, how Matlab does it.

Well, let us suppose you are teaching numerical linear algebra and, a clever student asks: "What is the method implemented in the 'eig' routine? I could not find it in MATLAB documentation."

Thus, I would be very glad if someone can provide me a more specific reference about which methods(shifted QR, divide-and-conquer, MRRR, etc) are used by 'eig'.

[Steven Lord]

You tell them it uses LAPACK and point them to the documents Walter linked in his comment. If you want to learn the exact routines used by the built-in source code (which we do not distribute) the first step in that process is here.

[Jan]

@Steven Lord: This is cut out from the background slideshow:

I'm interested in the device the women in front is running Matlab on. Without a monitor and a desktop machine, I expect to get less troubles with incompatibile graphic drivers and OS versions.

[Jan]

@Douglas: Matlab selects a suiting method based on smart but automatic assumptions about the nature of the matrix. If the properties of the matrix are known already, calling the best LAPACK or sparse function can be much more efficient. I've seen many scientists without a deep knowledge of numerics, who used an inadequate method - with the argument: "I've taken the routine from a well known and stable library!" Matlab's eig() prevents such mistakes. But your students can learn, when to apply which method intentionally.

[Steven Lord]

@Jan: that's a conference room -- note the orange "whiteboard" to the left. The monitor is on the wall she's facing, just outside the limits of the picture.

And if you're interested in running MATLAB on a device without a monitor to do number crunching, start a cluster of workers using Parallel Computing Toolbox. Alternately, if you have the correct type of license take a look at MATLAB Online.