Initial comments on Example 2.1.2

[jkmacc-LANL]

The Example 2.1.2 directory contains a .mat data file, and a Jupyter notebook that follows the Example 2.1.1 matlab script. Jupyter was chosen because it supports narrative code + output far better than commented Python code, and is widely available and easy to install. It also fully renders in GitHub repositories, making them useful to view on their own without installing/running Jupyter.

@brianborchers I'm seeking any feedback on the minor differences in outputs (compared to Octave). I notice small (third decimal place-ish) differences in values. For example, in cell 17, for the singular vectors of the covariance matrix. In this cell, the singular vectors have small differences in value and are of opposite sign.

[brianborchers]

I'm not going to have time to look at this until I get back from a funeral later this week. However, I think I can explain some things:

On Fri, Jun 29, 2018 at 9:01 PM, jkmacc-LANL ***@***.***> wrote: The Example 2.1.2 directory <https://github.com/jkmacc-LANL/peip-python/blob/master/Examples/chap2/ex_2_1_2> contains a .mat data file, and a Jupyter notebook that follows the Example 2.1.1 matlab script. Jupyter was chosen because it supports narrative code + output far better than commented Python code, and is widely available and easy to install. It also fully renders in GitHub repositories, making them useful to view on their own without installing/running Jupyter.

So you're recommending the Anaconda distribution too? Or, is there some other way to get Python and friends working with a Jupyter notebook?

@brianborchers <https://github.com/brianborchers> I'm seeking any feedback on the minor differences in outputs (compared to Octave). I notice small (third decimal place-ish) differences in values. For example, in cell 17, for the singular vectors of the covariance matrix. In this cell, the singular vectors have small differences in value and are of opposite sign.

Sign changes in the singular vectors should not be a problem. If you think about the formula, you can see that flipping the sign of $U_{i}$ and the sign of $V_{i}$ cancels out in the sum(sigma(i)*U(:,i)*V(:,i)') to give you the same answer. There's no way to ensure that two different SVD computations will find singular vectors with the same signs. Except possibly for some places where we plotted singular vectors in the book, nothing that we do in calculations should break if the signs of the singular vectors change in a way that is consistent with the SVD. Also note that when there are repeated singular values (or multiple singular values that are effectively 0) there can be infinitely many SVD's! Any set of orthogonal vectors that spans the appropriate space will work. For example, if you take A=I, then the singular values are all 1's. You can let U be any orthogonal matrix, let Sigma=I, and let V=U, and you'll have an SVD of the identity matrix. What gets computed by the svd function in Octave or MATLAB in these cases is really pretty arbitrary as long as it is a correct SVD.

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[jkmacc-LANL]

Thanks for having a look. To the best of my knowledge, Jupyter will install just fine with pip. I personally use and recommend Anaconda/Miniconda, but others should be fine.